Finite Group Databasebeta

← C2×#13129157 #16770058

Subgroups — C2×#13129157 #16770058

Order 3328.

8122 conjugacy classes of subgroups.

The subgroup lattice has 1444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129157C2132yesmaximal, direct product factor
2C2×#11719326C212yesmaximal, complemented
3C2×#11719300C212yesmaximal, complemented
4C2×#11719321C211yesmaximal, characteristic, complemented
5C2×#11719263C211yesmaximal, characteristic, complemented
6C2×#11719246C211yesmaximal, characteristic, complemented
7C2×#11719292C212yesmaximal, complemented
8C2×#11719423C211yesmaximal, characteristic, complemented
9C2×#11719316C211yesmaximal, characteristic, complemented
10C2×#11719511C212yesmaximal, complemented
11C2×#11719511C211yesmaximal, characteristic, complemented
12C2×#11719511C211yesmaximal, characteristic, complemented
13C2×#11719266C211yesmaximal, characteristic, complemented
14C2×#11719424C211yesmaximal, characteristic, complemented
15C2×#11719320C212yesmaximal, complemented
16C2×#11719298C212yesmaximal, complemented
17C2×#11719313C211yesmaximal, characteristic, complemented
18C2×#11719510C211yesmaximal, characteristic, complemented
19C2×#11719297C212yesmaximal, complemented
20C2×#11719509C212yesmaximal, complemented
21C2×#11719311C211yesmaximal, characteristic, complemented
22C2×#11719252C211yesmaximal, characteristic, complemented
23C22×#88192C211yesmaximal, characteristic, complemented
24C2×D42×C13C211yesmaximal, characteristic, complemented
25C23×D4×C13C2211yescharacteristic
26C23×D4×C13C2212yes—
27C23×D4×C13C2211yescharacteristic, complemented
28C23×C22⋊D13C2212yescomplemented
29C22×#6129C2212yescomplemented
30C22×#6129C2211yescharacteristic, complemented
31C22×#6129C2211yescharacteristic, complemented
32C22×#6127C2211yescharacteristic, complemented
33C23×C4×D13C2211yescharacteristic, complemented
34D42×C13C22116yescomplemented
35C2×C13×#127C2211yescharacteristic, complemented
36C2×C13×#121C2211yescharacteristic
37C2×C13×#121C2212yescomplemented
38C2×C13×#121C2211yescharacteristic, complemented
39C2×C13×#120C2212yes—
40C2×C13×#120C2212yescomplemented
41C2×C4×D4×C13C2211yescharacteristic
42C2×C4×D4×C13C2211yescharacteristic, complemented
43C2×#88207C2212yescomplemented
44C2×#88207C2212yescomplemented
45C2×#88207C2212yescomplemented
46C2×#88207C2212yescomplemented
47C22×C22⋊Dic13C2212yescomplemented
48C22×C22⋊Dic13C2212yescomplemented
49C22×C22⋊Dic13C2212yescomplemented
50#11719511C22132yescomplemented
51#11719511C22116yescomplemented
52#11719511C22116yescomplemented
53#11719510C22116yescomplemented
54#11719509C22132yescomplemented
55C2×#88194C2212yescomplemented
56C2×#88194C2212yescomplemented
57C2×#88193C2211yescharacteristic
58C2×#88193C2212yescomplemented
59C2×#88193C2212yescomplemented
60C2×#88193C2212yescomplemented
61C2×#88193C2212yescomplemented
62C2×#88193C2212yescomplemented
63C2×#88193C2212yescomplemented
64C2×#88193C2212yescomplemented
65C2×#88193C2212yescomplemented
66C2×#88192C2211yescharacteristic
67C2×#88192C2211yescharacteristic
68C2×#88192C2212yescomplemented
69C2×#88192C2211yescharacteristic, complemented
70C2×#88192C2211yescharacteristic, complemented
71C2×#88192C2211yescharacteristic, complemented
72C2×#88192C2212yescomplemented
73C2×#88192C2211yescharacteristic, complemented
74C2×#88192C2211yescharacteristic, complemented
75C2×#88192C2212yescomplemented
76C2×#88192C22116yescomplemented
77C2×#88191C2211yescharacteristic
78C2×#88191C2212yescomplemented
79C2×#88190C2212yescomplemented
80C2×#88190C2211yescharacteristic, complemented
81C2×#88190C2212yescomplemented
82C2×#88189C2212yes—
83C2×#88189C2212yescomplemented
84C2×#88189C2212yescomplemented
85C2×#88189C2212yescomplemented
86C2×#88189C2212yescomplemented
87C2×#88189C2212yescomplemented
88C2×D4×Dic13C2211yescharacteristic, complemented
89C2×D4×Dic13C2211yescharacteristic, complemented
90C2×D4×Dic13C2212yescomplemented
91C2×D4×Dic13C2212yescomplemented
92C2×#88183C2212yescomplemented
93C2×#88183C2212yescomplemented
94C2×C4×C22⋊D13C2211yescharacteristic, complemented
95C2×C4×C22⋊D13C2211yescharacteristic, complemented
96C2×C4×C22⋊D13C2212yescomplemented
97C2×#88180C2211yescharacteristic, complemented
98C22×C4⋊Dic13C2211yescharacteristic, complemented
99C2×#88178C2212yescomplemented
100C2×#88178C2211yescharacteristic, complemented
101C2×#88178C2211yescharacteristic, complemented
102#11719424C22116yescomplemented
103#11719423C22116yescomplemented
104#11719326C22132yescomplemented
105#11719321C22116yescomplemented
106#11719320C22132yescomplemented
107#11719316C22116yescomplemented
108#11719313C22116yescomplemented
109#11719311C22116yescomplemented
110#11719300C22132yescomplemented
111#11719298C22132yescomplemented
112#11719297C22132yescomplemented
113#11719292C22132yescomplemented
114#11719266C22116yescomplemented
115#11719263C22116yescomplemented
116#11719252C22116yescomplemented
117#11719246C22116yescomplemented
118C2×#88151C2211yescharacteristic, complemented
119C2×#88150C2211yescharacteristic, complemented
120C2×#88148C2211yescharacteristic, complemented
121C2×#88146C2211yescharacteristic, complemented
122C2×C4⋊C4×D13C2211yescharacteristic, complemented
123C2×#88143C2212yescomplemented
124C2×#88142C2211yescharacteristic, complemented
125C2×#88139C2212yescomplemented
126C2×#88139C2212yescomplemented
127C2×#88138C2211yescharacteristic, complemented
128C2×#88138C2212yescomplemented
129C2×#88138C2212yescomplemented
130C2×#88137C2212yescomplemented
131C2×#88137C2212yescomplemented
132C2×#88137C2211yescharacteristic, complemented
133C2×#88136C2211yescharacteristic, complemented
134C2×#88135C2212yescomplemented
135C2×#88133C2212yescomplemented
136C2×#88133C2212yescomplemented
137C2×#88133C2212yescomplemented
138C2×#88132C2212yescomplemented
139C2×#88132C2212yescomplemented
140C2×#88132C2211yescharacteristic, complemented
141C2×#88131C2212yescomplemented
142C2×#88131C2212yescomplemented
143C2×C4×D52C2211yescharacteristic, complemented
144C2×#88126C2211yescharacteristic, complemented
145C2×#88124C2211yescharacteristic, complemented
146C2×C4×Dic26C2211yescharacteristic, complemented
147C25×C13C2312yes—
148C25×C13C2312yes—
149C24×D13C2311yescharacteristic
150C22×D4×C13—44no—
151C22×D4×C13—44no—
152C22×D4×C13—48no—
153C22×D4×C13C2312yes—
154C22×D4×C13C2311yescharacteristic
155C22×D4×C13C2311yescharacteristic
156C22×D4×C13C2311yescharacteristic
157C22×D4×C13C2311yescharacteristic
158C22×D4×C13C2312yes—
159C22×D4×C13C2312yes—
160C22×D4×C13C2312yes—
161C22×D4×C13C2312yes—
162C22×D4×C13C2312yes—
163C22×D4×C13C2318yes—
164C22×D4×C13C23116yes—
165C22×D4×C13C2318yescomplemented
166C23×C4×C13C2311yescharacteristic
167C23×C4×C13C2311yescharacteristic
168C23×C4×C13C2312yes—
169C22×C22⋊D13—48no—
170C22×C22⋊D13C2311yescharacteristic
171C22×C22⋊D13C2312yes—
172C22×C22⋊D13C2311yescharacteristic
173C22×C22⋊D13C2312yes—
174C22×C22⋊D13C2312yes—
175C22×C22⋊D13C2311yescharacteristic
176C22×C22⋊D13C2312yes—
177C22×C22⋊D13C2312yes—
178C22×C22⋊D13C2311yescharacteristic
179C22×C22⋊D13C2312yes—
180C22×C22⋊D13C2312yes—
181C22×C22⋊D13C2312yes—
182C22×C22⋊D13C2312yes—
183C22×C22⋊D13C23116yescomplemented
184C23×Dic13C2312yes—
185C23×Dic13C2312yes—
186C23×Dic13C2311yescharacteristic
187C23×Dic13C2312yes—
188C23×Dic13C2312yes—
189C23×Dic13C2312yes—
190C2×#6129—44no—
191C2×#6129—44no—
192C2×#6129—48no—
193C2×#6129C23116yescomplemented
194C2×#6129C2318yescomplemented
195C2×#6129C2318yescomplemented
196C2×#6127—44no—
197C2×#6127C2318yescomplemented
198C22×D52C2311yescharacteristic
199C22×D52C2311yescharacteristic
200C22×C4×D13—44no—
201C22×C4×D13C2311yescharacteristic
202C22×C4×D13C2311yescharacteristic
203C22×C4×D13C2311yescharacteristic
204C22×C4×D13C2311yescharacteristic
205C22×C4×D13C2311yescharacteristic
206C22×C4×D13C2312yes—
207C22×C4×D13C2318yescomplemented
208C22×Dic26C2311yescharacteristic
209C22×Dic26C2311yescharacteristic
210C22×Dic26C2312yes—
211C13×#127C2318yescomplemented
212C13×#121C2318yes—
213C13×#121C2318yescomplemented
214C13×#121C23116yescomplemented
215C13×#120C23116yes—
216C13×#120C23116yescomplemented
217C4×D4×C13C2318yes—
218C4×D4×C13C2318yescomplemented
219C2×C13×C4⋊C4C2311yescharacteristic
220C2×C13×C4⋊C4C2311yescharacteristic
221C2×C13×C22⋊C4C2311yescharacteristic
222C2×C13×C22⋊C4C2312yes—
223C2×C13×C22⋊C4C2312yes—
224C2×C13×C22⋊C4C2311yescharacteristic
225C2×C13×C22⋊C4C2312yes—
226C2×C42×C13C2311yescharacteristic
227#88207C23116yescomplemented
228#88207C23116yescomplemented
229#88207C23116yescomplemented
230#88207C23116yescomplemented
231C2×C22⋊Dic13C2312yes—
232C2×C22⋊Dic13C2312yes—
233C2×C22⋊Dic13C2311yescharacteristic
234C2×C22⋊Dic13C2312yes—
235C2×C22⋊Dic13C2312yes—
236C2×C22⋊Dic13C2312yes—
237C2×C22⋊Dic13C2312yes—
238C2×C22⋊Dic13C2312yes—
239C2×C22⋊Dic13C2312yes—
240C2×C22⋊Dic13C2312yes—
241C2×C22⋊Dic13C2312yes—
242C2×C22⋊Dic13C2311yescharacteristic
243C2×C22⋊Dic13C2312yes—
244C2×C22⋊Dic13C2312yes—
245C2×C22⋊Dic13C2312yes—
246C2×C22⋊Dic13C2312yes—
247C2×C22⋊Dic13C23116yescomplemented
248C2×C22⋊Dic13C23116yescomplemented
249C2×C22⋊Dic13C23116yescomplemented
250#88194C23116yescomplemented
251#88194C23116yescomplemented
252#88193C2318yes—
253#88193C23116yescomplemented
254#88193C23116yescomplemented
255#88193C23116yescomplemented
256#88193C23116yescomplemented
257#88193C23116yescomplemented
258#88193C23116yescomplemented
259#88193C23116yescomplemented
260#88193C23116yescomplemented
261#88192C2318yes—
262#88192C2318yes—
263#88192C2318yescomplemented
264#88192C2318yescomplemented
265#88192C23116yescomplemented
266#88192C23116yescomplemented
267#88192C2318yescomplemented
268#88192C2318yescomplemented
269#88192C2318yescomplemented
270#88192C23116yescomplemented
271#88191C2318yes—
272#88191C23116yescomplemented
273#88190C23116yescomplemented
274#88190C2318yescomplemented
275#88190C23116yescomplemented
276#88189C23116yes—
277#88189C23116yescomplemented
278#88189C23116yescomplemented
279#88189C23116yescomplemented
280#88189C23116yescomplemented
281#88189C23116yescomplemented
282D4×Dic13C2318yescomplemented
283D4×Dic13C2318yescomplemented
284D4×Dic13C23116yescomplemented
285D4×Dic13C23116yescomplemented
286#88183C23116yescomplemented
287#88183C23116yescomplemented
288C4×C22⋊D13C2318yescomplemented
289C4×C22⋊D13C2318yescomplemented
290C4×C22⋊D13C23116yescomplemented
291C2×#6103C2311yescharacteristic
292C2×#6103C2311yescharacteristic
293C2×#6103C2311yescharacteristic
294C2×#6103C2311yescharacteristic
295C2×#6103C2312yes—
296C2×#6103C2311yescharacteristic
297C2×#6103C2311yescharacteristic
298C2×#6103C2312yes—
299#88180C2318yescomplemented
300C2×C4⋊Dic13C2311yescharacteristic
301C2×C4⋊Dic13C2311yescharacteristic
302C2×C4⋊Dic13C2311yescharacteristic
303C2×C4⋊Dic13C2311yescharacteristic
304C2×C4⋊Dic13C2312yes—
305C2×C4⋊Dic13C2312yes—
306C2×C4⋊Dic13C2318yescomplemented
307#88178C2318yescomplemented
308#88178C2318yescomplemented
309#88178C23116yescomplemented
310C2×#6101C2312yes—
311C2×#6101C2312yes—
312C2×#6101C2312yes—
313C2×#6101C2311yescharacteristic
314C2×#6101C2311yescharacteristic
315C2×#6101C2311yescharacteristic
316C2×#6101C2312yes—
317C2×#6101C2312yes—
318C2×#6101C2312yes—
319C2×#6101C2311yescharacteristic
320C2×#6101C2312yes—
321C2×C4×Dic13C2312yes—
322C2×C4×Dic13C2311yescharacteristic
323C2×C4×Dic13C2312yes—
324C2×C4×Dic13C2312yes—
325#88151C2318yescomplemented
326#88150C2318yescomplemented
327#88148C2318yescomplemented
328#88146C2318yescomplemented
329C4⋊C4×D13C2318yescomplemented
330#88143C23116yescomplemented
331#88142C2318yescomplemented
332#88139C23116yescomplemented
333#88139C23116yescomplemented
334#88138C2318yescomplemented
335#88138C23116yescomplemented
336#88138C23116yescomplemented
337#88137C2318yescomplemented
338#88137C23116yescomplemented
339#88137C23116yescomplemented
340#88136C2318yescomplemented
341#88135C23116yescomplemented
342#88133C23116yescomplemented
343#88133C23116yescomplemented
344#88133C23116yescomplemented
345#88132C2318yescomplemented
346#88132C23116yescomplemented
347#88132C23116yescomplemented
348#88131C23116yescomplemented
349#88131C23116yescomplemented
350C4×D52C2318yescomplemented
351#88126C2318yescomplemented
352#88124C2318yescomplemented
353C4×Dic26C2318yescomplemented
354C2×#3542—131nomaximal, Sylow
355C24×C13—28no—
356C24×C13—44no—
357C24×C13—44no—
358C24×C13—44no—
359C24×C13—44no—
360C24×C13—44no—
361C24×C13C2411yescharacteristic
362C24×C13C2412yes—
363C24×C13C2412yes—
364C24×C13C2412yes—
365C24×C13C2411yescharacteristic
366C24×C13C2418yes—
367C24×C13C2418yes—
368C23×D13—24no—
369C23×D13—42no—
370C23×D13—42no—
371C23×D13C2411yescharacteristic
372C23×D13C2411yescharacteristic
373C23×D13C2411yescharacteristic
374C23×D13C2414yes—
375C2×D4×C13—28no—
376C2×D4×C13—24no—
377C2×D4×C13—24no—
378C2×D4×C13—24no—
379C2×D4×C13—24no—
380C2×D4×C13—416no—
381C2×D4×C13—416no—
382C2×D4×C13—44no—
383C2×D4×C13—44no—
384C2×D4×C13—44no—
385C2×D4×C13—44no—
386C2×D4×C13—44no—
387C2×D4×C13—432no—
388C2×D4×C13C2418yes—
389C2×D4×C13C2414yes—
390C2×D4×C13C2414yes—
391C2×D4×C13C2414yes—
392C2×D4×C13C2414yes—
393C2×D4×C13C2418yes—
394C2×D4×C13C2418yes—
395C2×D4×C13C2418yes—
396C2×D4×C13C2418yes—
397C2×D4×C13C2418yes—
398C22×C4×C13—24no—
399C22×C4×C13—24no—
400C22×C4×C13—44no—
401C22×C4×C13C2411yescharacteristic
402C22×C4×C13C2411yescharacteristic
403C22×C4×C13C2412yes—
404C22×C4×C13C2411yescharacteristic
405C22×C4×C13C2411yescharacteristic
406C22×C4×C13C2414yes—
407C22×C4×C13C2414yes—
408C22×C4×C13C2418yes—
409C22×C4×C13C2411yescharacteristic
410C2×C22⋊D13—24no—
411C2×C22⋊D13—42no—
412C2×C22⋊D13—42no—
413C2×C22⋊D13—44no—
414C2×C22⋊D13—44no—
415C2×C22⋊D13—44no—
416C2×C22⋊D13—44no—
417C2×C22⋊D13—44no—
418C2×C22⋊D13—44no—
419C2×C22⋊D13—44no—
420C2×C22⋊D13—432no—
421C2×C22⋊D13—42no—
422C2×C22⋊D13—44no—
423C2×C22⋊D13—44no—
424C2×C22⋊D13C2414yes—
425C2×C22⋊D13C2418yes—
426C2×C22⋊D13C2414yes—
427C2×C22⋊D13C2418yes—
428C2×C22⋊D13C2418yes—
429C2×C22⋊D13C2414yes—
430C2×C22⋊D13C2418yes—
431C2×C22⋊D13C2418yes—
432C2×C22⋊D13C2414yes—
433C2×C22⋊D13C2418yes—
434C2×C22⋊D13C2418yes—
435C2×C22⋊D13C2418yes—
436C2×C22⋊D13C2418yes—
437C22×Dic13—28no—
438C22×Dic13—42no—
439C22×Dic13—44no—
440C22×Dic13—44no—
441C22×Dic13—44no—
442C22×Dic13—44no—
443C22×Dic13C2418yes—
444C22×Dic13C2412yes—
445C22×Dic13C2412yes—
446C22×Dic13C2411yescharacteristic
447C22×Dic13C2411yescharacteristic
448C22×Dic13C2412yes—
449C22×Dic13C2411yescharacteristic
450C22×Dic13C2412yes—
451C22×Dic13C2411yescharacteristic
452C22×Dic13C2411yescharacteristic
453C22×Dic13C2418yes—
454C22×Dic13C2414yes—
455C22×Dic13C2418yes—
456C22×Dic13C2418yes—
457C22×Dic13C2418yes—
458#6129—416no—
459#6129—416no—
460#6129—432no—
461#6127—416no—
462C2×D52—42no—
463C2×D52—42no—
464C2×D52C2414yes—
465C2×D52C2414yes—
466C2×C4×D13—24no—
467C2×C4×D13—24no—
468C2×C4×D13—24no—
469C2×C4×D13—416no—
470C2×C4×D13—42no—
471C2×C4×D13—42no—
472C2×C4×D13—44no—
473C2×C4×D13C2414yes—
474C2×C4×D13C2414yes—
475C2×C4×D13C2414yes—
476C2×C4×D13C2414yes—
477C2×C4×D13C2414yes—
478C2×C4×D13C2418yes—
479C2×Dic26—24no—
480C2×Dic26—42no—
481C2×Dic26—44no—
482C2×Dic26C2414yes—
483C2×Dic26C2414yes—
484C2×Dic26C2418yes—
485C13×C4⋊C4C2414yes—
486C13×C4⋊C4C2414yes—
487C13×C22⋊C4C2414yes—
488C13×C22⋊C4C2418yes—
489C13×C22⋊C4C2418yes—
490C13×C22⋊C4C2414yes—
491C13×C22⋊C4C2418yes—
492C42×C13C2414yes—
493C22⋊Dic13C2418yes—
494C22⋊Dic13C2418yes—
495C22⋊Dic13C2414yes—
496C22⋊Dic13C2418yes—
497C22⋊Dic13C2418yes—
498C22⋊Dic13C2418yes—
499C22⋊Dic13C2418yes—
500C22⋊Dic13C2418yes—
501C22⋊Dic13C2418yes—
502C22⋊Dic13C2418yes—
503C22⋊Dic13C2418yes—
504C22⋊Dic13C2414yes—
505C22⋊Dic13C2418yes—
506C22⋊Dic13C2418yes—
507C22⋊Dic13C2418yes—
508C22⋊Dic13C2418yes—
509#6103C2414yes—
510#6103C2414yes—
511#6103C2414yes—
512#6103C2414yes—
513#6103C2418yes—
514#6103C2414yes—
515#6103C2414yes—
516#6103C2418yes—
517C4⋊Dic13C2414yes—
518C4⋊Dic13C2414yes—
519C4⋊Dic13C2414yes—
520C4⋊Dic13C2414yes—
521C4⋊Dic13C2418yes—
522C4⋊Dic13C2418yes—
523#6101C2418yes—
524#6101C2418yes—
525#6101C2418yes—
526#6101C2414yes—
527#6101C2414yes—
528#6101C2414yes—
529#6101C2418yes—
530#6101C2418yes—
531#6101C2418yes—
532#6101C2414yes—
533#6101C2418yes—
534C4×Dic13C2418yes—
535C4×Dic13C2414yes—
536C4×Dic13C2418yes—
537C4×Dic13C2418yes—
538#3542—1332no—
539C2×#562—132no—
540C2×#560—132no—
541C2×#555—131no—
542C2×#553—131no—
543C2×#552—131no—
544C2×#551—132no—
545C2×#550—131no—
546C2×#547—131no—
547C2×#546—132no—
548C2×#546—131no—
549C2×#546—131no—
550C2×D42D1311yescharacteristic, complemented
551C2×#542—131no—
552C2×#540—131no—
553C2×#540—132no—
554C2×#538—132no—
555C2×#537—131no—
556C2×#535—131no—
557C2×#535—132no—
558C2×#534—132no—
559C2×#525—131no—
560C2×#525—131no—
561C22×#121—131no—
562C23×C13—22no—
563C23×C13—22no—
564C23×C13—24no—
565C23×C13—24no—
566C23×C13—24no—
567C23×C13—22no—
568C23×C13—24no—
569C23×C13—24no—
570C23×C13—22no—
571C23×C13—24no—
572C23×C13—24no—
573C23×C13—24no—
574C23×C13—22no—
575C23×C13—24no—
576C23×C13—216no—
577C23×C13—48no—
578C23×C13—48no—
579C23×C13—48no—
580C23×C13—48no—
581C23×C13—48no—
582C23×C13—816no—
583C23×C13—816no—
584C23×C13H(5,𝔽2)14yes—
585C23×C13C2512yes—
586C23×C13C2514yes—
587C23×C13C2514yes—
588C23×C13C2514yes—
589C23×C13C2512yes—
590C23×C13C2511yescharacteristic
591C22×D13—22no—
592C22×D13—22no—
593C22×D13—22no—
594C22×D13—22no—
595C22×D13—28no—
596C22×D13—22no—
597C22×D13—22no—
598C22×D13—22no—
599C22×D13—22no—
600C22×D13—22no—
601C22×D13—44no—
602C22×D13—44no—
603C22×D13—416no—
604C22×D13C2512yes—
605C22×D13C2512yes—
606C22×D13C2512yes—
607D4×C13—216no—
608D4×C13—28no—
609D4×C13—28no—
610D4×C13—28no—
611D4×C13—28no—
612D4×C13—48no—
613D4×C13—48no—
614D4×C13—48no—
615D4×C13—48no—
616D4×C13—48no—
617C2×C4×C13—24no—
618C2×C4×C13—22no—
619C2×C4×C13—22no—
620C2×C4×C13—22no—
621C2×C4×C13—22no—
622C2×C4×C13—28no—
623C2×C4×C13—28no—
624C2×C4×C13—48no—
625C2×C4×C13H(5,𝔽2)14yes—
626C2×C4×C13C2512yes—
627C2×C4×C13C2512yes—
628C2×C4×C13C2514yes—
629C2×C4×C13C2512yes—
630C2×C4×C13C2512yes—
631C2×C4×C13C2512yes—
632C22⋊D13—28no—
633C22⋊D13—44no—
634C22⋊D13—44no—
635C22⋊D13—48no—
636C22⋊D13—48no—
637C22⋊D13—48no—
638C22⋊D13—48no—
639C22⋊D13—48no—
640C22⋊D13—48no—
641C22⋊D13—48no—
642C22⋊D13—44no—
643C22⋊D13—48no—
644C22⋊D13—48no—
645C2×Dic13—24no—
646C2×Dic13—22no—
647C2×Dic13—22no—
648C2×Dic13—22no—
649C2×Dic13—24no—
650C2×Dic13—22no—
651C2×Dic13—24no—
652C2×Dic13—216no—
653C2×Dic13—22no—
654C2×Dic13—24no—
655C2×Dic13—44no—
656C2×Dic13—48no—
657C2×Dic13—48no—
658C2×Dic13—48no—
659C2×Dic13—48no—
660C2×Dic13C2514yes—
661C2×Dic13C2514yes—
662C2×Dic13C2512yes—
663C2×Dic13C2512yes—
664C2×Dic13C2514yes—
665C2×Dic13C2512yes—
666C2×Dic13C2514yes—
667C2×Dic13C2512yes—
668C2×Dic13C2512yes—
669D52—44no—
670D52—44no—
671C4×D13—28no—
672C4×D13—28no—
673C4×D13—28no—
674C4×D13—44no—
675C4×D13—44no—
676C4×D13—48no—
677Dic26—28no—
678Dic26—44no—
679Dic26—48no—
680C22×#41—131no—
681C22×#41—132no—
682C22×#41—131no—
683C22×#41—131no—
684C23×D4—132no—
685C23×D4C2×D1311yescharacteristic
686C23×D4C2×D1312yes—
687C23×D4C2×D1311yescharacteristic, complemented
688C24×C4—131no—
689#562—1332no—
690#560—1332no—
691#555—1316no—
692#553—1316no—
693#552—1316no—
694#551—1332no—
695#550—1316no—
696#547—1316no—
697#546—1332no—
698#546—1316no—
699#546—1316no—
700D42C2×D13116yescomplemented
701#542—1316no—
702#540—1316no—
703#540—1332no—
704#538—1332no—
705#537—1316no—
706#535—1316no—
707#535—1332no—
708#534—1332no—
709C2×C4⋊Q8—131no—
710C2×#127—132no—
711C2×#127—132no—
712C2×#127C2×D1311yescharacteristic, complemented
713C2×#126—132no—
714C2×#126—132no—
715C2×#126—132no—
716C2×#125—132no—
717C2×#125—131no—
718C2×#124—132no—
719C2×#124—132no—
720C2×#124—131no—
721C2×#124—132no—
722C2×#124—132no—
723#525—1316no—
724#525—1316no—
725C2×#123—132no—
726C2×#123—132no—
727C2×#123—132no—
728C2×#123—132no—
729C2×#123—132no—
730C2×#123—132no—
731C2×#123—132no—
732C2×#123—132no—
733C2×#123—131no—
734C2×#123—131no—
735C2×#123—132no—
736C2×#123—132no—
737C2×C22⋊Q8—131no—
738C2×C22⋊Q8—131no—
739C2×C22⋊Q8—132no—
740C2×C22⋊Q8—131no—
741C2×C22⋊Q8—131no—
742C2×C22⋊Q8—131no—
743C2×C22⋊Q8—132no—
744C2×C22⋊Q8—132no—
745C2×#121—131no—
746C2×#121—131no—
747C2×#121—131no—
748C2×#121—132no—
749C2×#121—131no—
750C2×#121—132no—
751C2×#121—1316no—
752C2×#121—131no—
753C2×#121—131no—
754C2×#121—131no—
755C2×#121—132no—
756C2×#121—131no—
757C2×#121—132no—
758C2×#121—132no—
759C2×#121—132no—
760C2×#121—132no—
761C2×#121—132no—
762C2×#121—132no—
763C2×#121—132no—
764C2×#121—132no—
765C2×#121—131no—
766C2×#121—132no—
767C2×#121—132no—
768C2×#121C2×D1311yescharacteristic
769C2×#121C2×D1311yescharacteristic, complemented
770C2×#121C2×D1312yescomplemented
771C2×#120—132no—
772C2×#120—132no—
773C2×#120—132no—
774C2×#120—132no—
775C2×#120—131no—
776C2×#120—132no—
777C2×#120—131no—
778C2×#120C2×D1312yes—
779C2×#120C2×D1312yescomplemented
780C2×C4×Q8—131no—
781C2×C4×D4—132no—
782C2×C4×D4—132no—
783C2×C4×D4—131no—
784C2×C4×D4—131no—
785C2×C4×D4—131no—
786C2×C4×D4—131no—
787C2×C4×D4—132no—
788C2×C4×D4—132no—
789C2×C4×D4—131no—
790C2×C4×D4C2×D1311yescharacteristic
791C2×C4×D4C2×D1311yescharacteristic, complemented
792C2×#117—131no—
793C2×#117—131no—
794C2×#117—132no—
795C2×#117—132no—
796C2×#117—131no—
797C22×C4⋊C4—131no—
798C22×C4⋊C4—131no—
799C22×C22⋊C4—132no—
800C22×C22⋊C4—132no—
801C22×C22⋊C4—132no—
802C22×C13—22no—
803C22×C13—22no—
804C22×C13—28no—
805C22×C13—24no—
806C22×C13—24no—
807C22×C13—24no—
808C22×C13—22no—
809C22×C13—24no—
810C22×C13—24no—
811C22×C13—22no—
812C22×C13—24no—
813C22×C13—24no—
814C22×C13—24no—
815C22×C13—22no—
816C22×C13—24no—
817C22×C13—48no—
818C22×C13—48no—
819C22×C13—44no—
820C22×C13—48no—
821C22×C13—816no—
822C22×C13—816no—
823C22×C13C2×H(5,𝔽2)14yes—
824C22×C13C2×H(5,𝔽2)12yes—
825C22×C13C2×H(5,𝔽2)12yes—
826C22×C13#58512yes—
827C22×C13C2611yescharacteristic
828C2×D13—22no—
829C2×D13—22no—
830C2×D13—22no—
831C2×D13—22no—
832C2×D13—22no—
833C2×D13—22no—
834C2×D13—22no—
835C2×D13—22no—
836C2×D13—22no—
837C2×D13—416no—
838C2×D13—44no—
839C2×D13—44no—
840C2×D13—44no—
841C4×C13—24no—
842C4×C13—22no—
843C4×C13—22no—
844C4×C13—22no—
845C4×C13—22no—
846C4×C13C2×H(5,𝔽2)14yes—
847Dic13—24no—
848Dic13—22no—
849Dic13—22no—
850Dic13—22no—
851Dic13—24no—
852Dic13—22no—
853Dic13—24no—
854Dic13—22no—
855Dic13—24no—
856C25—131no—
857C25C22×D1312yes—
858C25C22×D1312yes—
859C2×#41—138no—
860C2×#41—1316no—
861C2×#41—138no—
862C2×#41—138no—
863C2×#41—524no—
864C2×#41—528no—
865C2×#41—524no—
866C2×#41—524no—
867C22×Q8—131no—
868C22×Q8—131no—
869C22×Q8—132no—
870C22×D4—44no—
871C22×D4—44no—
872C22×D4—48no—
873C22×D4—131no—
874C22×D4—131no—
875C22×D4—132no—
876C22×D4—132no—
877C22×D4—131no—
878C22×D4—131no—
879C22×D4—132no—
880C22×D4—132no—
881C22×D4—132no—
882C22×D4—132no—
883C22×D4—132no—
884C22×D4—132no—
885C22×D4—132no—
886C22×D4—1316no—
887C22×D4—131no—
888C22×D4—131no—
889C22×D4—528no—
890C22×D4C22×D1312yes—
891C22×D4C22×D1311yescharacteristic
892C22×D4C22×D1311yescharacteristic
893C22×D4C22×D1311yescharacteristic
894C22×D4C22×D1311yescharacteristic
895C22×D4C22×D1312yes—
896C22×D4C22×D1312yes—
897C22×D4C22×D1312yes—
898C22×D4C22×D1312yes—
899C22×D4C22×D1312yes—
900C22×D4C22×D1318yes—
901C22×D4C22×D13116yes—
902C22×D4C22×D1318yescomplemented
903C23×C4—132no—
904C23×C4—131no—
905C23×C4—132no—
906C23×C4—132no—
907C23×C4—132no—
908C23×C4—132no—
909C23×C4—131no—
910C23×C4—131no—
911C23×C4—131no—
912C23×C4—132no—
913C23×C4—131no—
914C23×C4—131no—
915C23×C4—138no—
916C23×C4—524no—
917C23×C4C22×D1311yescharacteristic
918C23×C4C22×D1311yescharacteristic
919C23×C4C22×D1312yes—
920C4⋊Q8—138no—
921#127—1316no—
922#127—1316no—
923#127C22×D1318yescomplemented
924#126—1316no—
925#126—1316no—
926#126—1316no—
927#125—1316no—
928#125—138no—
929#124—1316no—
930#124—1316no—
931#124—138no—
932#124—1316no—
933#124—1316no—
934#123—1316no—
935#123—1316no—
936#123—1316no—
937#123—1316no—
938#123—1316no—
939#123—1316no—
940#123—1316no—
941#123—1316no—
942#123—138no—
943#123—138no—
944#123—1316no—
945#123—1316no—
946C22⋊Q8—138no—
947C22⋊Q8—138no—
948C22⋊Q8—1316no—
949C22⋊Q8—138no—
950C22⋊Q8—138no—
951C22⋊Q8—138no—
952C22⋊Q8—1316no—
953C22⋊Q8—1316no—
954#121—138no—
955#121—138no—
956#121—1316no—
957#121—138no—
958#121—138no—
959#121—1316no—
960#121—138no—
961#121—138no—
962#121—1316no—
963#121—1316no—
964#121—1316no—
965#121—1316no—
966#121—1316no—
967#121—138no—
968#121—1316no—
969#121—138no—
970#121—1316no—
971#121—1316no—
972#121—1316no—
973#121—138no—
974#121—1316no—
975#121—1316no—
976#121C22×D1318yes—
977#121C22×D1318yescomplemented
978#121C22×D13116yescomplemented
979#120—1316no—
980#120—1316no—
981#120—1316no—
982#120—1316no—
983#120—138no—
984#120—1316no—
985#120—138no—
986#120C22×D13116yes—
987#120C22×D13116yescomplemented
988C4×Q8—138no—
989C4×D4—1316no—
990C4×D4—1316no—
991C4×D4—138no—
992C4×D4—138no—
993C4×D4—138no—
994C4×D4—138no—
995C4×D4—1316no—
996C4×D4—1316no—
997C4×D4—138no—
998C4×D4C22×D1318yes—
999C4×D4C22×D1318yescomplemented
1000#117—138no—
1001#117—138no—
1002#117—1316no—
1003#117—1316no—
1004#117—138no—
1005C2×C4⋊C4—131no—
1006C2×C4⋊C4—131no—
1007C2×C4⋊C4—132no—
1008C2×C4⋊C4—138no—
1009C2×C4⋊C4—132no—
1010C2×C4⋊C4—131no—
1011C2×C4⋊C4—131no—
1012C2×C4⋊C4—132no—
1013C2×C4⋊C4—132no—
1014C2×C4⋊C4—131no—
1015C2×C4⋊C4—131no—
1016C2×C4⋊C4—132no—
1017C2×C4⋊C4—131no—
1018C2×C4⋊C4—132no—
1019C2×C4⋊C4—132no—
1020C2×C4⋊C4—132no—
1021C2×C4⋊C4—131no—
1022C2×C4⋊C4—132no—
1023C2×C4⋊C4—138no—
1024C2×C4⋊C4C22×D1311yescharacteristic
1025C2×C4⋊C4C22×D1311yescharacteristic
1026C2×C22⋊C4—131no—
1027C2×C22⋊C4—132no—
1028C2×C22⋊C4—131no—
1029C2×C22⋊C4—132no—
1030C2×C22⋊C4—132no—
1031C2×C22⋊C4—132no—
1032C2×C22⋊C4—132no—
1033C2×C22⋊C4—132no—
1034C2×C22⋊C4—132no—
1035C2×C22⋊C4—132no—
1036C2×C22⋊C4—132no—
1037C2×C22⋊C4—1316no—
1038C2×C22⋊C4—1316no—
1039C2×C22⋊C4—1316no—
1040C2×C22⋊C4—132no—
1041C2×C22⋊C4—132no—
1042C2×C22⋊C4—132no—
1043C2×C22⋊C4—132no—
1044C2×C22⋊C4—132no—
1045C2×C22⋊C4—131no—
1046C2×C22⋊C4—132no—
1047C2×C22⋊C4—131no—
1048C2×C22⋊C4—131no—
1049C2×C22⋊C4—131no—
1050C2×C22⋊C4—132no—
1051C2×C22⋊C4—131no—
1052C2×C22⋊C4—131no—
1053C2×C22⋊C4C22×D1311yescharacteristic
1054C2×C22⋊C4C22×D1312yes—
1055C2×C22⋊C4C22×D1312yes—
1056C2×C22⋊C4C22×D1311yescharacteristic
1057C2×C22⋊C4C22×D1312yes—
1058C2×C42—132no—
1059C2×C42—132no—
1060C2×C42—131no—
1061C2×C42—132no—
1062C2×C42C22×D1311yescharacteristic
1063C2×C13—24no—
1064C2×C13—44no—
1065C2×C13—44no—
1066C2×C13—42no—
1067C2×C13—44no—
1068C2×C13#354214yescomplemented
1069C2×C13C22×H(5,𝔽2)11yescharacteristic
1070C2×C13C22×H(5,𝔽2)11yescharacteristic
1071C2×C13C2×#58511yescharacteristic
1072D13—42no—
1073D13—42no—
1074D13—42no—
1075C24—28no—
1076C24—44no—
1077C24—44no—
1078C24—44no—
1079C24—44no—
1080C24—44no—
1081C24—131no—
1082C24—131no—
1083C24—131no—
1084C24—134no—
1085C24—264no—
1086C24—522no—
1087C24—522no—
1088C24C23×D1311yescharacteristic
1089C24C23×D1312yes—
1090C24C23×D1312yes—
1091C24C23×D1312yes—
1092C24C23×D1311yescharacteristic
1093C24C23×D1318yes—
1094C24C23×D1318yes—
1095#41—5216no—
1096#41—5232no—
1097#41—5216no—
1098#41—5216no—
1099C2×Q8—134no—
1100C2×Q8—134no—
1101C2×Q8—138no—
1102C2×Q8—264no—
1103C2×Q8—522no—
1104C2×Q8—524no—
1105C2×D4—24no—
1106C2×D4—28no—
1107C2×D4—24no—
1108C2×D4—24no—
1109C2×D4—24no—
1110C2×D4—416no—
1111C2×D4—416no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C2×D4—44no—
1115C2×D4—44no—
1116C2×D4—44no—
1117C2×D4—432no—
1118C2×D4—134no—
1119C2×D4—134no—
1120C2×D4—138no—
1121C2×D4—138no—
1122C2×D4—134no—
1123C2×D4—134no—
1124C2×D4—138no—
1125C2×D4—138no—
1126C2×D4—138no—
1127C2×D4—138no—
1128C2×D4—138no—
1129C2×D4—138no—
1130C2×D4—138no—
1131C2×D4—134no—
1132C2×D4—134no—
1133C2×D4—264no—
1134C2×D4—522no—
1135C2×D4—522no—
1136C2×D4—524no—
1137C2×D4—524no—
1138C2×D4—524no—
1139C2×D4—524no—
1140C2×D4—5232no—
1141C2×D4—522no—
1142C2×D4—522no—
1143C2×D4—524no—
1144C2×D4—524no—
1145C2×D4—524no—
1146C2×D4—522no—
1147C2×D4—524no—
1148C2×D4—524no—
1149C2×D4C23×D1318yes—
1150C2×D4C23×D1314yes—
1151C2×D4C23×D1314yes—
1152C2×D4C23×D1314yes—
1153C2×D4C23×D1314yes—
1154C2×D4C23×D1318yes—
1155C2×D4C23×D1318yes—
1156C2×D4C23×D1318yes—
1157C2×D4C23×D1318yes—
1158C2×D4C23×D1318yes—
1159C22×C4—24no—
1160C22×C4—24no—
1161C22×C4—44no—
1162C22×C4—138no—
1163C22×C4—132no—
1164C22×C4—131no—
1165C22×C4—132no—
1166C22×C4—131no—
1167C22×C4—131no—
1168C22×C4—132no—
1169C22×C4—131no—
1170C22×C4—131no—
1171C22×C4—132no—
1172C22×C4—134no—
1173C22×C4—138no—
1174C22×C4—138no—
1175C22×C4—138no—
1176C22×C4—138no—
1177C22×C4—134no—
1178C22×C4—134no—
1179C22×C4—134no—
1180C22×C4—138no—
1181C22×C4—134no—
1182C22×C4—134no—
1183C22×C4—268no—
1184C22×C4—264no—
1185C22×C4—264no—
1186C22×C4—264no—
1187C22×C4—5216no—
1188C22×C4—522no—
1189C22×C4—522no—
1190C22×C4—524no—
1191C22×C4—522no—
1192C22×C4—524no—
1193C22×C4—524no—
1194C22×C4—524no—
1195C22×C4—524no—
1196C22×C4C23×D1314yes—
1197C22×C4C23×D1314yes—
1198C22×C4C23×D1311yescharacteristic
1199C22×C4C23×D1311yescharacteristic
1200C22×C4C23×D1312yes—
1201C22×C4C23×D1311yescharacteristic
1202C22×C4C23×D1311yescharacteristic
1203C22×C4C23×D1318yes—
1204C22×C4C23×D1311yescharacteristic
1205C4⋊C4—134no—
1206C4⋊C4—134no—
1207C4⋊C4—138no—
1208C4⋊C4—138no—
1209C4⋊C4—134no—
1210C4⋊C4—134no—
1211C4⋊C4—138no—
1212C4⋊C4—138no—
1213C4⋊C4—134no—
1214C4⋊C4—134no—
1215C4⋊C4—138no—
1216C4⋊C4—134no—
1217C4⋊C4—138no—
1218C4⋊C4—138no—
1219C4⋊C4—138no—
1220C4⋊C4—134no—
1221C4⋊C4—138no—
1222C4⋊C4C23×D1314yes—
1223C4⋊C4C23×D1314yes—
1224C22⋊C4—134no—
1225C22⋊C4—138no—
1226C22⋊C4—134no—
1227C22⋊C4—138no—
1228C22⋊C4—138no—
1229C22⋊C4—138no—
1230C22⋊C4—138no—
1231C22⋊C4—138no—
1232C22⋊C4—138no—
1233C22⋊C4—138no—
1234C22⋊C4—138no—
1235C22⋊C4—138no—
1236C22⋊C4—138no—
1237C22⋊C4—138no—
1238C22⋊C4—138no—
1239C22⋊C4—138no—
1240C22⋊C4—134no—
1241C22⋊C4—138no—
1242C22⋊C4—134no—
1243C22⋊C4—134no—
1244C22⋊C4—134no—
1245C22⋊C4—138no—
1246C22⋊C4—134no—
1247C22⋊C4—134no—
1248C22⋊C4C23×D1314yes—
1249C22⋊C4C23×D1318yes—
1250C22⋊C4C23×D1318yes—
1251C22⋊C4C23×D1314yes—
1252C22⋊C4C23×D1318yes—
1253C42—138no—
1254C42—138no—
1255C42—134no—
1256C42—138no—
1257C42C23×D1314yes—
1258C13C2×#354211yescharacteristic, complemented, Sylow
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—24no—
1263C23—24no—
1264C23—24no—
1265C23—24no—
1266C23—22no—
1267C23—24no—
1268C23—24no—
1269C23—24no—
1270C23—24no—
1271C23—22no—
1272C23—24no—
1273C23—216no—
1274C23—48no—
1275C23—48no—
1276C23—48no—
1277C23—48no—
1278C23—48no—
1279C23—816no—
1280C23—816no—
1281C23—132no—
1282C23—132no—
1283C23—132no—
1284C23—262no—
1285C23—262no—
1286C23—262no—
1287C23—262no—
1288C23—268no—
1289C23—262no—
1290C23—262no—
1291C23—262no—
1292C23—262no—
1293C23—262no—
1294C23—524no—
1295C23—524no—
1296C23—5216no—
1297C23#8825114yes—
1298C23C24×D1312yes—
1299C23C24×D1314yes—
1300C23C24×D1314yes—
1301C23C24×D1314yes—
1302C23C24×D1312yes—
1303C23C24×D1311yescharacteristic
1304Q8—268no—
1305Q8—524no—
1306Q8—528no—
1307D4—28no—
1308D4—216no—
1309D4—28no—
1310D4—28no—
1311D4—28no—
1312D4—48no—
1313D4—48no—
1314D4—48no—
1315D4—48no—
1316D4—48no—
1317D4—268no—
1318D4—524no—
1319D4—524no—
1320D4—524no—
1321D4—528no—
1322D4—528no—
1323D4—528no—
1324D4—528no—
1325D4—528no—
1326D4—528no—
1327D4—524no—
1328D4—524no—
1329D4—528no—
1330D4—528no—
1331D4—528no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—28no—
1338C2×C4—28no—
1339C2×C4—48no—
1340C2×C4—134no—
1341C2×C4—132no—
1342C2×C4—134no—
1343C2×C4—132no—
1344C2×C4—132no—
1345C2×C4—134no—
1346C2×C4—132no—
1347C2×C4—132no—
1348C2×C4—134no—
1349C2×C4—262no—
1350C2×C4—264no—
1351C2×C4—262no—
1352C2×C4—262no—
1353C2×C4—264no—
1354C2×C4—2616no—
1355C2×C4—262no—
1356C2×C4—264no—
1357C2×C4—262no—
1358C2×C4—264no—
1359C2×C4—268no—
1360C2×C4—268no—
1361C2×C4—268no—
1362C2×C4—524no—
1363C2×C4—524no—
1364C2×C4—528no—
1365C2×C4—528no—
1366C2×C4—524no—
1367C2×C4—528no—
1368C2×C4—528no—
1369C2×C4—528no—
1370C2×C4#8825114yes—
1371C2×C4C24×D1312yes—
1372C2×C4C24×D1312yes—
1373C2×C4C24×D1314yes—
1374C2×C4C24×D1312yes—
1375C2×C4C24×D1312yes—
1376C2×C4C24×D1312yes—
1377C22—22no—
1378C22—22no—
1379C22—28no—
1380C22—22no—
1381C22—24no—
1382C22—24no—
1383C22—24no—
1384C22—24no—
1385C22—22no—
1386C22—24no—
1387C22—24no—
1388C22—24no—
1389C22—24no—
1390C22—22no—
1391C22—24no—
1392C22—48no—
1393C22—48no—
1394C22—44no—
1395C22—48no—
1396C22—816no—
1397C22—816no—
1398C22—262no—
1399C22—262no—
1400C22—262no—
1401C22—262no—
1402C22—262no—
1403C22—262no—
1404C22—262no—
1405C22—262no—
1406C22—262no—
1407C22—5216no—
1408C22—524no—
1409C22—524no—
1410C22—524no—
1411C22C2×#8825114yes—
1412C22C2×#8825112yes—
1413C22C2×#8825112yes—
1414C22#1171965012yes—
1415C22C25×D1311yescharacteristic
1416C4—22no—
1417C4—22no—
1418C4—22no—
1419C4—24no—
1420C4—22no—
1421C4—262no—
1422C4—264no—
1423C4—262no—
1424C4—262no—
1425C4—264no—
1426C4—262no—
1427C4—264no—
1428C4—262no—
1429C4—264no—
1430C4C2×#8825114yes—
1431C2—24no—
1432C2—42no—
1433C2—44no—
1434C2—44no—
1435C2—44no—
1436C2—522no—
1437C2—522no—
1438C2—522no—
1439C2#1312915714yesdirect product factor
1440C2C22×#8825111yescharacteristic
1441C2C22×#8825111yescharacteristic
1442C2C2×#1171965011yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×D42×C13C2
socleC23×C13C25
hypercenterC2×D42D13
hypocenterC13C2×#3542
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×D42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13129157C2direct (N × H)
2. C2×#11719326C2semidirect
3. C2×#11719300C2semidirect
4. C2×#11719321C2semidirect
5. C2×#11719263C2semidirect
6. C2×#11719246C2semidirect
7. C2×#11719292C2semidirect
8. C2×#11719423C2semidirect
9. C2×#11719316C2semidirect
10. C2×#11719511C2semidirect
11. C2×#11719511C2semidirect
12. C2×#11719511C2semidirect
13. C2×#11719266C2semidirect
14. C2×#11719424C2semidirect
15. C2×#11719320C2semidirect
16. C2×#11719298C2semidirect
17. C2×#11719313C2semidirect
18. C2×#11719510C2semidirect
19. C2×#11719297C2semidirect
20. C2×#11719509C2semidirect
21. C2×#11719311C2semidirect
22. C2×#11719252C2semidirect
23. C22×#88192C2semidirect
24. C2×D42×C13C2semidirect
27. C23×D4×C13C22semidirect
28. C23×C22⋊D13C22semidirect
29. C22×#6129C22semidirect
30. C22×#6129C22semidirect
31. C22×#6129C22semidirect
32. C22×#6127C22semidirect
33. C23×C4×D13C22semidirect
34. D42×C13C22semidirect
35. C2×C13×#127C22semidirect
37. C2×C13×#121C22semidirect
38. C2×C13×#121C22semidirect
40. C2×C13×#120C22semidirect
42. C2×C4×D4×C13C22semidirect
43. C2×#88207C22semidirect
44. C2×#88207C22semidirect
45. C2×#88207C22semidirect
46. C2×#88207C22semidirect
47. C22×C22⋊Dic13C22semidirect
48. C22×C22⋊Dic13C22semidirect
49. C22×C22⋊Dic13C22semidirect
50. #11719511C22semidirect
51. #11719511C22semidirect
52. #11719511C22semidirect
53. #11719510C22semidirect
54. #11719509C22semidirect
55. C2×#88194C22semidirect
56. C2×#88194C22semidirect
58. C2×#88193C22semidirect
59. C2×#88193C22semidirect
60. C2×#88193C22semidirect
61. C2×#88193C22semidirect
62. C2×#88193C22semidirect
63. C2×#88193C22semidirect
64. C2×#88193C22semidirect
65. C2×#88193C22semidirect
68. C2×#88192C22semidirect
69. C2×#88192C22semidirect
70. C2×#88192C22semidirect
71. C2×#88192C22semidirect
72. C2×#88192C22semidirect
73. C2×#88192C22semidirect
74. C2×#88192C22semidirect
75. C2×#88192C22semidirect
76. C2×#88192C22semidirect
78. C2×#88191C22semidirect
79. C2×#88190C22semidirect
80. C2×#88190C22semidirect
81. C2×#88190C22semidirect
83. C2×#88189C22semidirect
84. C2×#88189C22semidirect
85. C2×#88189C22semidirect
86. C2×#88189C22semidirect
87. C2×#88189C22semidirect
88. C2×D4×Dic13C22semidirect
89. C2×D4×Dic13C22semidirect
90. C2×D4×Dic13C22semidirect
91. C2×D4×Dic13C22semidirect
92. C2×#88183C22semidirect
93. C2×#88183C22semidirect
94. C2×C4×C22⋊D13C22semidirect
95. C2×C4×C22⋊D13C22semidirect
96. C2×C4×C22⋊D13C22semidirect
97. C2×#88180C22semidirect
98. C22×C4⋊Dic13C22semidirect
99. C2×#88178C22semidirect
100. C2×#88178C22semidirect
101. C2×#88178C22semidirect
102. #11719424C22semidirect
103. #11719423C22semidirect
104. #11719326C22semidirect
105. #11719321C22semidirect
106. #11719320C22semidirect
107. #11719316C22semidirect
108. #11719313C22semidirect
109. #11719311C22semidirect
110. #11719300C22semidirect
111. #11719298C22semidirect
112. #11719297C22semidirect
113. #11719292C22semidirect
114. #11719266C22semidirect
115. #11719263C22semidirect
116. #11719252C22semidirect
117. #11719246C22semidirect
118. C2×#88151C22semidirect
119. C2×#88150C22semidirect
120. C2×#88148C22semidirect
121. C2×#88146C22semidirect
122. C2×C4⋊C4×D13C22semidirect
123. C2×#88143C22semidirect
124. C2×#88142C22semidirect
125. C2×#88139C22semidirect
126. C2×#88139C22semidirect
127. C2×#88138C22semidirect
128. C2×#88138C22semidirect
129. C2×#88138C22semidirect
130. C2×#88137C22semidirect
131. C2×#88137C22semidirect
132. C2×#88137C22semidirect
133. C2×#88136C22semidirect
134. C2×#88135C22semidirect
135. C2×#88133C22semidirect
136. C2×#88133C22semidirect
137. C2×#88133C22semidirect
138. C2×#88132C22semidirect
139. C2×#88132C22semidirect
140. C2×#88132C22semidirect
141. C2×#88131C22semidirect
142. C2×#88131C22semidirect
143. C2×C4×D52C22semidirect
144. C2×#88126C22semidirect
145. C2×#88124C22semidirect
146. C2×C4×Dic26C22semidirect
165. C22×D4×C13C23semidirect
183. C22×C22⋊D13C23semidirect
193. C2×#6129C23semidirect
194. C2×#6129C23semidirect
195. C2×#6129C23semidirect
197. C2×#6127C23semidirect
207. C22×C4×D13C23semidirect
211. C13×#127C23semidirect
213. C13×#121C23semidirect
214. C13×#121C23semidirect
216. C13×#120C23semidirect
218. C4×D4×C13C23semidirect
227. #88207C23semidirect
228. #88207C23semidirect
229. #88207C23semidirect
230. #88207C23semidirect
247. C2×C22⋊Dic13C23semidirect
248. C2×C22⋊Dic13C23semidirect
249. C2×C22⋊Dic13C23semidirect
250. #88194C23semidirect
251. #88194C23semidirect
253. #88193C23semidirect
254. #88193C23semidirect
255. #88193C23semidirect
256. #88193C23semidirect
257. #88193C23semidirect
258. #88193C23semidirect
259. #88193C23semidirect
260. #88193C23semidirect
263. #88192C23semidirect
264. #88192C23semidirect
265. #88192C23semidirect
266. #88192C23semidirect
267. #88192C23semidirect
268. #88192C23semidirect
269. #88192C23semidirect
270. #88192C23semidirect
272. #88191C23semidirect
273. #88190C23semidirect
274. #88190C23semidirect
275. #88190C23semidirect
277. #88189C23semidirect
278. #88189C23semidirect
279. #88189C23semidirect
280. #88189C23semidirect
281. #88189C23semidirect
282. D4×Dic13C23semidirect
283. D4×Dic13C23semidirect
284. D4×Dic13C23semidirect
285. D4×Dic13C23semidirect
286. #88183C23semidirect
287. #88183C23semidirect
288. C4×C22⋊D13C23semidirect
289. C4×C22⋊D13C23semidirect
290. C4×C22⋊D13C23semidirect
299. #88180C23semidirect
306. C2×C4⋊Dic13C23semidirect
307. #88178C23semidirect
308. #88178C23semidirect
309. #88178C23semidirect
325. #88151C23semidirect
326. #88150C23semidirect
327. #88148C23semidirect
328. #88146C23semidirect
329. C4⋊C4×D13C23semidirect
330. #88143C23semidirect
331. #88142C23semidirect
332. #88139C23semidirect
333. #88139C23semidirect
334. #88138C23semidirect
335. #88138C23semidirect
336. #88138C23semidirect
337. #88137C23semidirect
338. #88137C23semidirect
339. #88137C23semidirect
340. #88136C23semidirect
341. #88135C23semidirect
342. #88133C23semidirect
343. #88133C23semidirect
344. #88133C23semidirect
345. #88132C23semidirect
346. #88132C23semidirect
347. #88132C23semidirect
348. #88131C23semidirect
349. #88131C23semidirect
350. C4×D52C23semidirect
351. #88126C23semidirect
352. #88124C23semidirect
353. C4×Dic26C23semidirect
550. C2×D42D13semidirect
687. C23×D4C2×D13semidirect
700. D42C2×D13semidirect
712. C2×#127C2×D13semidirect
769. C2×#121C2×D13semidirect
770. C2×#121C2×D13semidirect
779. C2×#120C2×D13semidirect
791. C2×C4×D4C2×D13semidirect
902. C22×D4C22×D13semidirect
923. #127C22×D13semidirect
977. #121C22×D13semidirect
978. #121C22×D13semidirect
987. #120C22×D13semidirect
999. C4×D4C22×D13semidirect
1068. C2×C13#3542semidirect
1258. C13C2×#3542semidirect
1439. C2#13129157direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131291572
C2×#117193262
C2×#117193002
C2×#117193212
C2×#117192632
C2×#117192462
C2×#117192922
C2×#117194232
C2×#117193162
C2×#117195112
C2×#117192662
C2×#117194242
C2×#117193202
C2×#117192982
C2×#117193132
C2×#117195102
C2×#117192972
C2×#117195092
C2×#117193112
C2×#117192522
C22×#881922
C2×D42×C132
C2×#354213