Finite Group Databasebeta

← #16022492

Subgroups — #16022492

Order 3328.

3374 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719252C211yesmaximal, characteristic
2C2×C4×#6127C211yesmaximal, characteristic, complemented
3C2×D13×#117C211yesmaximal, characteristic, complemented
4#13117877C212yesmaximal, complemented
5#13117866C212yesmaximal, complemented
6#13117855C212yesmaximal, complemented
7#13117844C212yesmaximal, complemented
8#13117835C212yesmaximal, complemented
9#13117831C212yesmaximal, complemented
10#13117819C212yesmaximal, complemented
11#13117814C212yesmaximal, complemented
12#13117322C211yesmaximal, characteristic, complemented
13#13117316C211yesmaximal, characteristic, complemented
14#13117301C211yesmaximal, characteristic, complemented
15#13117295C211yesmaximal, characteristic, complemented
16#13117282C211yesmaximal, characteristic, complemented
17#13117282C211yesmaximal, characteristic, complemented
18#13117280C211yesmaximal, characteristic, complemented
19C42×C22⋊D13C211yesmaximal, characteristic, complemented
20C4×#88147C211yesmaximal, characteristic, complemented
21#13117175C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D13C211yesmaximal, characteristic, complemented
23C13×#2290C211yesmaximal, characteristic, complemented
24C22×#6127C2211yescharacteristic
25C23×C4×D13C2211yescharacteristic
26C2×C4×D4×C13C2211yescharacteristic
27C2×C13×#117C2211yescharacteristic
28C22×C42×C13C2211yescharacteristic, complemented
29C2×#88193C2211yescharacteristic
30C2×#88191C2211yescharacteristic
31C2×C4×C22⋊D13C2212yes—
32C2×C4×C22⋊D13C2212yes—
33C2×C4×C22⋊D13C2211yescharacteristic
34C2×C4×C22⋊D13C2211yescharacteristic
35C2×C4×C22⋊D13C2212yescomplemented
36C2×#88180C2211yescharacteristic
37C2×#88180C2211yescharacteristic, complemented
38#11719252C4116yescomplemented
39D13×#117—28no—
40C2×#88150C2211yescharacteristic
41C2×#88148C2211yescharacteristic
42C2×#88147C2212yes—
43C2×#88146C2212yes—
44C2×C4⋊C4×D13C2212yes—
45C2×#88138C2211yescharacteristic
46C2×#88137C2211yescharacteristic
47C2×#88136C2211yescharacteristic
48C2×C22⋊C4×D13C2212yes—
49C2×C22⋊C4×D13C2212yes—
50C2×#88132C2211yescharacteristic
51C2×#88131C2212yes—
52C4×#6127—28no—
53C2×C4×D52C2212yes—
54C2×C4×D52C2211yescharacteristic
55C2×#88126C2211yescharacteristic
56C2×#88126C2211yescharacteristic
57C2×#88126C2211yescharacteristic
58C2×#88126C2211yescharacteristic, complemented
59C2×C42×D13C2211yescharacteristic
60C2×C42×D13C2211yescharacteristic
61C2×C42×D13C2211yescharacteristic
62C2×C42×D13C2211yescharacteristic
63C2×C42×D13C2211yescharacteristic, complemented
64C2×C4×Dic26C2212yescomplemented
65C13×#388C2212yes—
66C13×#387C2212yescomplemented
67C13×#386C2212yes—
68C13×#385C2212yescomplemented
69C4×C13×C4⋊C4C2211yescharacteristic, complemented
70C4×C13×C22⋊C4C2211yescharacteristic
71C4×C13×C22⋊C4C2211yescharacteristic, complemented
72C13×#376C2211yescharacteristic, complemented
73#11718882C2212yes—
74C4×C22⋊Dic13C2211yescharacteristic
75C4×C22⋊Dic13C2211yescharacteristic, complemented
76C4×C22⋊Dic13C2212yescomplemented
77#11718651C2212yescomplemented
78#11718650C2212yes—
79#11718646C2212yescomplemented
80C4⋊C4×Dic13C2212yescomplemented
81#11718633C2212yescomplemented
82#11718633C2212yescomplemented
83#11718618C2212yes—
84#11718618C2212yescomplemented
85#11718617C2212yes—
86#11718617C2212yes—
87#11718617C2212yes—
88#11718612C2212yes—
89#11718612C2212yescomplemented
90#11718606C2212yes—
91#11718606C2212yes—
92#11718606C2212yescomplemented
93C22⋊C4×Dic13C2212yes—
94C4×#6103C2211yescharacteristic
95C4×#6103C2212yes—
96C4×#6103C2211yescharacteristic
97C4×#6103C2211yescharacteristic, complemented
98C4×#6103C2211yescharacteristic, complemented
99C4×C4⋊Dic13C2211yescharacteristic, complemented
100#11718593C2211yescharacteristic, complemented
101C4×#6101C2211yescharacteristic, complemented
102C4×#6101C2211yescharacteristic, complemented
103C4×#6101C2212yescomplemented
104C42×Dic13C2211yescharacteristic, complemented
105C42×Dic13C2211yescharacteristic, complemented
106#11718331C2212yescomplemented
107#11718329C2212yes—
108#11718329C2212yes—
109#11718329C2212yes—
110#11718329C2212yescomplemented
111#11718327C2212yes—
112#11718327C2212yes—
113#11718327C2212yes—
114#11718327C2212yes—
115#11718327C2212yescomplemented
116#11718326C2212yes—
117#11718326C2212yes—
118D13×#95C2212yes—
119#11718316C2212yescomplemented
120#11718316C2212yescomplemented
121#11718314C2212yescomplemented
122#11718310C2212yescomplemented
123#11718310C2212yescomplemented
124#11718308C2212yescomplemented
125#11718307C2212yescomplemented
126C24×D13C2311yescharacteristic
127C22×D4×C13C2311yescharacteristic
128C23×C4×C13C2312yes—
129C23×C4×C13C2311yescharacteristic
130C23×C4×C13C2311yescharacteristic
131C22×C22⋊D13C2311yescharacteristic
132C22×C22⋊D13C2311yescharacteristic
133C22×C22⋊D13C2311yescharacteristic
134C22×C22⋊D13C2311yescharacteristic
135C23×Dic13C2311yescharacteristic
136C2×#6127—24no—
137C2×#6127—24no—
138C2×#6127C2×C418yescomplemented
139C22×D52C2311yescharacteristic
140C22×D52C2311yescharacteristic
141C22×C4×D13—24no—
142C22×C4×D13—24no—
143C22×C4×D13C2×C418yescomplemented
144C22×C4×D13C2312yes—
145C22×C4×D13C2312yes—
146C22×C4×D13C2312yes—
147C22×C4×D13C2312yes—
148C22×C4×D13C2312yes—
149C22×C4×D13C2311yescharacteristic
150C22×C4×D13C2311yescharacteristic
151C22×C4×D13C2311yescharacteristic
152C22×C4×D13C2311yescharacteristic
153C22×C4×D13C2311yescharacteristic
154C22×Dic26C2311yescharacteristic
155C4×D4×C13C2×C418yescomplemented
156C13×#117—24no—
157C2×C13×C4⋊C4C2312yes—
158C2×C13×C4⋊C4C2312yes—
159C2×C13×C4⋊C4C2311yescharacteristic
160C2×C13×C22⋊C4C2312yes—
161C2×C13×C22⋊C4C2312yes—
162C2×C13×C22⋊C4C2312yes—
163C2×C13×C22⋊C4C2311yescharacteristic
164C2×C13×C22⋊C4C2311yescharacteristic
165C2×C42×C13—24no—
166C2×C42×C13C2311yescharacteristic
167C2×C42×C13C2311yescharacteristic
168C2×C42×C13C2311yescharacteristic
169C2×C42×C13C2312yes—
170C2×C42×C13C2311yescharacteristic
171C2×C42×C13C2311yescharacteristic
172C2×C22⋊Dic13C2312yes—
173C2×C22⋊Dic13C2312yes—
174C2×C22⋊Dic13C2312yes—
175C2×C22⋊Dic13C2312yes—
176C2×C22⋊Dic13C2311yescharacteristic
177C2×C22⋊Dic13C2311yescharacteristic
178#88193C2×C418yescomplemented
179#88191C2×C418yescomplemented
180C4×C22⋊D13—28no—
181C4×C22⋊D13—28no—
182C4×C22⋊D13—28no—
183C4×C22⋊D13C2×C418yescomplemented
184C4×C22⋊D13C2×C418yescomplemented
185C2×#6103C2312yes—
186C2×#6103C2312yes—
187C2×#6103C2312yes—
188C2×#6103C2312yes—
189C2×#6103C2312yes—
190C2×#6103C2311yescharacteristic
191C2×#6103C2311yescharacteristic
192C2×#6103C2311yescharacteristic
193C2×#6103C2311yescharacteristic
194C2×#6103C2311yescharacteristic
195C2×#6103C2311yescharacteristic
196C2×#6103C2312yes—
197C2×#6103C2312yes—
198#88180—24no—
199#88180—24no—
200C2×C4⋊Dic13C2312yes—
201C2×C4⋊Dic13C2312yes—
202C2×C4⋊Dic13C2312yes—
203C2×C4⋊Dic13C2311yescharacteristic
204C2×#6101C2312yes—
205C2×#6101C2312yes—
206C2×#6101C2312yes—
207C2×#6101C2312yes—
208C2×#6101C2311yescharacteristic
209C2×#6101C2311yescharacteristic
210C2×#6101C2311yescharacteristic
211C2×#6101C2311yescharacteristic
212C2×#6101C2312yes—
213C2×C4×Dic13C2312yes—
214C2×C4×Dic13C2312yes—
215C2×C4×Dic13C2311yescharacteristic
216C2×C4×Dic13C2311yescharacteristic
217C2×C4×Dic13C2312yes—
218C2×C4×Dic13C2312yes—
219C2×C4×Dic13C2312yes—
220C2×C4×Dic13C2311yescharacteristic
221C2×C4×Dic13C2312yes—
222C2×C4×Dic13C2312yes—
223C2×C4×Dic13C2312yes—
224C2×C4×Dic13C2312yes—
225C2×C4×Dic13C2311yescharacteristic
226C2×C4×Dic13C2311yescharacteristic
227#88150C2×C418yescomplemented
228#88148C2×C418yescomplemented
229#88147—28no—
230#88146—28no—
231C4⋊C4×D13—28no—
232#88138C2×C418yescomplemented
233#88137C2×C418yescomplemented
234#88136C2×C418yescomplemented
235C22⋊C4×D13—28no—
236C22⋊C4×D13—28no—
237#88132C2×C418yescomplemented
238#88131—28no—
239C4×D52—28no—
240C4×D52C2×C418yescomplemented
241#88126—24no—
242#88126—24no—
243#88126C2×C418yescomplemented
244#88126D418yescomplemented
245C42×D13—24no—
246C42×D13—24no—
247C42×D13—24no—
248C42×D13—24no—
249C42×D13—24no—
250C4×Dic26—28no—
251C13×#95C2312yes—
252C13×#95C2312yes—
253C13×#95C2312yes—
254C13×#95C2312yes—
255C13×#95C2312yes—
256#88071C2312yes—
257#88071C2312yes—
258#88071C2312yes—
259#88071C2312yes—
260#88071C2312yes—
261#88071C2312yes—
262#88071C2312yes—
263#88071C2312yes—
264#88071C2312yes—
265#88071C2312yes—
266#88071C2312yes—
267#34136—131nomaximal, Sylow
268C24×C13C2411yescharacteristic
269C24×C13C2411yescharacteristic
270C23×D13—22no—
271C23×D13—24no—
272C23×D13—22no—
273C23×D13—42no—
274C23×D13C22×C414yes—
275C23×D13C2411yescharacteristic
276C23×D13C2411yescharacteristic
277C23×D13C2411yescharacteristic
278C2×D4×C13—42no—
279C2×D4×C13C22×C414yes—
280C22×C4×C13—22no—
281C22×C4×C13—22no—
282C22×C4×C13—22no—
283C22×C4×C13—22no—
284C22×C4×C13—24no—
285C22×C4×C13—24no—
286C22×C4×C13—42no—
287C22×C4×C13C22×C414yes—
288C22×C4×C13C22×C414yes—
289C22×C4×C13C2412yes—
290C22×C4×C13C2412yes—
291C22×C4×C13C2411yescharacteristic
292C22×C4×C13C2411yescharacteristic
293C22×C4×C13C2411yescharacteristic
294C22×C4×C13C2411yescharacteristic
295C22×C4×C13C2412yes—
296C22×C4×C13C2412yes—
297C22×C4×C13C2411yescharacteristic
298C2×C22⋊D13—22no—
299C2×C22⋊D13—24no—
300C2×C22⋊D13—22no—
301C2×C22⋊D13—22no—
302C2×C22⋊D13—22no—
303C2×C22⋊D13—42no—
304C2×C22⋊D13C22×C414yes—
305C2×C22⋊D13C22×C414yes—
306C2×C22⋊D13C22×C414yes—
307C2×C22⋊D13C22×C414yes—
308C22×Dic13—22no—
309C22×Dic13—22no—
310C22×Dic13C22×C414yes—
311C22×Dic13C2412yes—
312C22×Dic13C2412yes—
313C22×Dic13C2411yescharacteristic
314C22×Dic13C2411yescharacteristic
315C22×Dic13C2411yescharacteristic
316C22×Dic13C2411yescharacteristic
317C22×Dic13C2412yes—
318C22×Dic13C2412yes—
319C22×Dic13C2411yescharacteristic
320#6127—232no—
321C2×D52—22no—
322C2×D52—24no—
323C2×D52—22no—
324C2×D52C22×C414yes—
325C2×D52C22×C414yes—
326C2×C4×D13—22no—
327C2×C4×D13—22no—
328C2×C4×D13—22no—
329C2×C4×D13—22no—
330C2×C4×D13—22no—
331C2×C4×D13—22no—
332C2×C4×D13—22no—
333C2×C4×D13—22no—
334C2×C4×D13—232no—
335C2×C4×D13—24no—
336C2×C4×D13—24no—
337C2×C4×D13—24no—
338C2×C4×D13—24no—
339C2×C4×D13—24no—
340C2×C4×D13—24no—
341C2×C4×D13—24no—
342C2×C4×D13—24no—
343C2×C4×D13—24no—
344C2×C4×D13—24no—
345C2×C4×D13—42no—
346C2×C4×D13—42no—
347C2×C4×D13—42no—
348C2×C4×D13—42no—
349C2×C4×D13—42no—
350C2×C4×D13C22×C414yes—
351C2×C4×D13C22×C414yes—
352C2×C4×D13C22×C414yes—
353C2×C4×D13C22×C414yes—
354C2×C4×D13C22×C414yes—
355C2×C4×D13C2×D414yes—
356C2×C4×D13#4114yes—
357C2×Dic26—22no—
358C2×Dic26—22no—
359C2×Dic26C22×C414yes—
360C13×C4⋊C4—24no—
361C13×C4⋊C4—24no—
362C13×C4⋊C4C22×C414yes—
363C13×C22⋊C4—24no—
364C13×C22⋊C4—24no—
365C13×C22⋊C4—42no—
366C13×C22⋊C4C22×C414yes—
367C13×C22⋊C4C22×C414yes—
368C42×C13—24no—
369C42×C13—22no—
370C42×C13—22no—
371C42×C13—22no—
372C42×C13C22×C414yes—
373C42×C13C2×D414yes—
374C22⋊Dic13—24no—
375C22⋊Dic13—24no—
376C22⋊Dic13—24no—
377C22⋊Dic13—24no—
378C22⋊Dic13C22×C414yes—
379C22⋊Dic13C22×C414yes—
380#6103—24no—
381#6103—24no—
382#6103—24no—
383#6103—24no—
384#6103—42no—
385#6103C22×C414yes—
386#6103C22×C414yes—
387#6103C22×C414yes—
388#6103C22×C414yes—
389#6103C22×C414yes—
390#6103C22×C414yes—
391#6103C2×D418yes—
392#6103#4118yescomplemented
393C4⋊Dic13—24no—
394C4⋊Dic13—24no—
395C4⋊Dic13—42no—
396C4⋊Dic13C22×C414yes—
397#6101—24no—
398#6101—24no—
399#6101—24no—
400#6101—42no—
401#6101C22×C414yes—
402#6101C22×C414yes—
403#6101C22×C414yes—
404#6101C22×C414yes—
405#6101C2×D418yes—
406C4×Dic13—22no—
407C4×Dic13—22no—
408C4×Dic13—24no—
409C4×Dic13—22no—
410C4×Dic13—24no—
411C4×Dic13—24no—
412C4×Dic13—24no—
413C4×Dic13—24no—
414C4×Dic13—24no—
415C4×Dic13—24no—
416C4×Dic13—42no—
417C4×Dic13—42no—
418C4×Dic13C22×C414yes—
419C4×Dic13C2×D414yes—
420C2×#525—131no—
421C2×C4×#41—131no—
422C22×#117—131no—
423#2363—132no—
424#2362—132no—
425#2361—132no—
426#2360—132no—
427#2359—132no—
428#2359—132no—
429#2358—132no—
430#2358—132no—
431#2297—131no—
432#2296—131no—
433#2293—131no—
434#2293—131no—
435#2290—131no—
436#2290—131no—
437#2290—131no—
438#2290D1311yescharacteristic, complemented
439C42×D4—131no—
440C42×D4—131no—
441C4×#117—131no—
442C2×C4×C22⋊C4—131no—
443C23×C13—21no—
444C23×C13—21no—
445C23×C13—22no—
446C23×C13—22no—
447C23×C13—21no—
448C23×C13—21no—
449C23×C13—22no—
450C23×C13—22no—
451C23×C13C23×C412yes—
452C23×C13C23×C412yes—
453C23×C13C2511yescharacteristic
454C22×D13—21no—
455C22×D13—21no—
456C22×D13—22no—
457C22×D13—22no—
458C22×D13—22no—
459C22×D13—21no—
460C22×D13—22no—
461C22×D13—21no—
462C22×D13—22no—
463C22×D13—28no—
464C22×D13—28no—
465C22×D13—44no—
466C22×D13—48no—
467C22×D13—48no—
468C22×D13C23×C412yes—
469C22×D13C23×C412yes—
470C22×D13C23×C412yes—
471C22×D13C22×D412yes—
472C22×D13C2×#4112yes—
473C22×D13C2×#4114yes—
474D4×C13—44no—
475C2×C4×C13—22no—
476C2×C4×C13—21no—
477C2×C4×C13—21no—
478C2×C4×C13—22no—
479C2×C4×C13—22no—
480C2×C4×C13—21no—
481C2×C4×C13—21no—
482C2×C4×C13—22no—
483C2×C4×C13—22no—
484C2×C4×C13—22no—
485C2×C4×C13—28no—
486C2×C4×C13—28no—
487C2×C4×C13—22no—
488C2×C4×C13—22no—
489C2×C4×C13—22no—
490C2×C4×C13—22no—
491C2×C4×C13—22no—
492C2×C4×C13—22no—
493C2×C4×C13—48no—
494C2×C4×C13C23×C412yes—
495C2×C4×C13C23×C412yes—
496C2×C4×C13C23×C412yes—
497C2×C4×C13C23×C412yes—
498C2×C4×C13C23×C412yes—
499C2×C4×C13C22×D414yes—
500C2×C4×C13C22×D412yes—
501C2×C4×C13C2×#4114yes—
502C2×C4×C13C2×#4112yes—
503C22⋊D13—28no—
504C22⋊D13—28no—
505C22⋊D13—28no—
506C22⋊D13—44no—
507C2×Dic13—21no—
508C2×Dic13—21no—
509C2×Dic13—22no—
510C2×Dic13—22no—
511C2×Dic13—22no—
512C2×Dic13—21no—
513C2×Dic13—21no—
514C2×Dic13—22no—
515C2×Dic13—22no—
516C2×Dic13—22no—
517C2×Dic13—28no—
518C2×Dic13—22no—
519C2×Dic13—22no—
520C2×Dic13—22no—
521C2×Dic13—22no—
522C2×Dic13—22no—
523C2×Dic13—22no—
524C2×Dic13C23×C412yes—
525C2×Dic13C23×C412yes—
526C2×Dic13C23×C412yes—
527C2×Dic13C23×C412yes—
528C2×Dic13C23×C412yes—
529C2×Dic13C22×D414yes—
530C2×Dic13C22×D412yes—
531C2×Dic13C2×#4114yes—
532C2×Dic13C2×#4112yes—
533D52—28no—
534D52—28no—
535C4×D13—28no—
536C4×D13—28no—
537C4×D13—28no—
538C4×D13—28no—
539C4×D13—48no—
540C4×D13—48no—
541C4×D13—48no—
542C4×D13—48no—
543C4×D13—48no—
544C4×D13C4×D4116yescomplemented
545Dic26—28no—
546C22×#41—131no—
547C24×C4—131no—
548#525—1316no—
549C2×#123—131no—
550C2×#123—131no—
551C2×C22⋊Q8—131no—
552C2×C22⋊Q8—131no—
553C2×#121—131no—
554C2×#121—131no—
555C2×#120—131no—
556C2×#120—131no—
557C4×#41—268no—
558C2×C4×Q8—132no—
559C2×C4×D4—131no—
560C2×C4×D4—131no—
561C2×C4×D4—132no—
562C2×C4×D4—132no—
563C2×C4×D4—132no—
564C2×C4×D4—132no—
565C2×C4×D4—131no—
566C2×C4×D4—132no—
567C2×C4×D4C2×D1311yescharacteristic
568C2×#117—131no—
569C2×#117—131no—
570C2×#117—132no—
571C2×#117—132no—
572C2×#117—131no—
573C2×#117—131no—
574C2×#117—131no—
575C2×#117—131no—
576C2×#117—268no—
577C2×#117C2×D1311yescharacteristic
578C22×C4⋊C4—132no—
579C22×C22⋊C4—132no—
580C22×C22⋊C4—132no—
581C22×C42—131no—
582C22×C42—131no—
583C22×C42—131no—
584C22×C42—131no—
585C22×C42—131no—
586C22×C42C2×D1311yescharacteristic, complemented
587#391—132no—
588#390—132no—
589#390—132no—
590#390—132no—
591#389—132no—
592#389—132no—
593#389—132no—
594#389—132no—
595#388—132no—
596#388—132no—
597#388—132no—
598#388—132no—
599#388—132no—
600#388—132no—
601#388—132no—
602#388C2×D1312yes—
603#387—132no—
604#387—132no—
605#387—132no—
606#387C2×D1312yescomplemented
607#386—132no—
608#386—132no—
609#386—132no—
610#386—132no—
611#386—132no—
612#386C2×D1312yes—
613#385—132no—
614#385—132no—
615#385—132no—
616#385—132no—
617#385—132no—
618#385C2×D1312yescomplemented
619C4×C4⋊C4—132no—
620C4×C4⋊C4—132no—
621C4×C4⋊C4—131no—
622C4×C4⋊C4—131no—
623C4×C4⋊C4—131no—
624C4×C4⋊C4—132no—
625C4×C4⋊C4—132no—
626C4×C4⋊C4C2×D1311yescharacteristic, complemented
627C4×C22⋊C4—132no—
628C4×C22⋊C4—131no—
629C4×C22⋊C4—131no—
630C4×C22⋊C4—132no—
631C4×C22⋊C4—132no—
632C4×C22⋊C4—131no—
633C4×C22⋊C4—131no—
634C4×C22⋊C4—131no—
635C4×C22⋊C4—131no—
636C4×C22⋊C4—132no—
637C4×C22⋊C4—132no—
638C4×C22⋊C4—132no—
639C4×C22⋊C4—132no—
640C4×C22⋊C4—132no—
641C4×C22⋊C4C2×D1311yescharacteristic
642C4×C22⋊C4C2×D1311yescharacteristic, complemented
643#376—131no—
644#376C2×D1311yescharacteristic, complemented
645C2×#95—132no—
646C43—131no—
647C43—131no—
648C22×C13—22no—
649C22×C13—22no—
650C22×C13—22no—
651C22×C13—22no—
652C22×C13—22no—
653C22×C13—22no—
654C22×C13—42no—
655C22×C13—42no—
656C22×C13—42no—
657C22×C13—42no—
658C22×C13C24×C411yescharacteristic
659C22×C13C23×D411yescharacteristic
660C22×C13C22×#4111yescharacteristic
661C22×C13C22×#4112yes—
662C22×C13#58512yes—
663C2×D13—22no—
664C2×D13—22no—
665C2×D13—22no—
666C2×D13—22no—
667C2×D13—24no—
668C2×D13—24no—
669C2×D13—24no—
670C2×D13—24no—
671C2×D13—22no—
672C2×D13—22no—
673C2×D13—22no—
674C2×D13—416no—
675C2×D13—42no—
676C2×D13—42no—
677C2×D13C2×C4×D414yes—
678C2×D13C4×#4114yescomplemented
679C4×C13—22no—
680C4×C13—22no—
681C4×C13—22no—
682C4×C13—22no—
683C4×C13—24no—
684C4×C13—24no—
685C4×C13—42no—
686C4×C13—42no—
687C4×C13C2×C4×D414yes—
688Dic13—22no—
689Dic13—22no—
690Dic13—22no—
691Dic13—22no—
692Dic13—24no—
693Dic13—24no—
694Dic13—42no—
695Dic13—42no—
696Dic13C2×C4×D414yes—
697C25—131no—
698C2×#41—138no—
699C2×#41—264no—
700C2×#41—264no—
701C22×Q8—131no—
702C22×D4—131no—
703C22×D4—131no—
704C22×D4—131no—
705C22×D4—131no—
706C22×D4—131no—
707C22×D4—131no—
708C22×D4C22×D1311yescharacteristic
709C23×C4—131no—
710C23×C4—131no—
711C23×C4—138no—
712C23×C4—131no—
713C23×C4—131no—
714C23×C4—131no—
715C23×C4—131no—
716C23×C4—132no—
717C23×C4—132no—
718C23×C4—132no—
719C23×C4—132no—
720C23×C4—132no—
721C23×C4—264no—
722C23×C4—264no—
723C23×C4C22×D1312yes—
724C23×C4C22×D1311yescharacteristic
725C23×C4C22×D1311yescharacteristic
726#123—138no—
727#123—138no—
728C22⋊Q8—138no—
729C22⋊Q8—138no—
730#121—138no—
731#121—138no—
732#120—138no—
733#120—138no—
734C4×Q8—268no—
735C4×D4—138no—
736C4×D4—138no—
737C4×D4—138no—
738C4×D4—268no—
739C4×D4—268no—
740C4×D4—268no—
741C4×D4—268no—
742C4×D4—268no—
743C4×D4C4×D1318yescomplemented
744#117—24no—
745#117—138no—
746#117—138no—
747#117—264no—
748#117—264no—
749#117—264no—
750#117—268no—
751#117—268no—
752#117—264no—
753C2×C4⋊C4—132no—
754C2×C4⋊C4—131no—
755C2×C4⋊C4—131no—
756C2×C4⋊C4—131no—
757C2×C4⋊C4—131no—
758C2×C4⋊C4—131no—
759C2×C4⋊C4—132no—
760C2×C4⋊C4—132no—
761C2×C4⋊C4—132no—
762C2×C4⋊C4—132no—
763C2×C4⋊C4—132no—
764C2×C4⋊C4—132no—
765C2×C4⋊C4—132no—
766C2×C4⋊C4—268no—
767C2×C4⋊C4C22×D1312yes—
768C2×C4⋊C4C22×D1312yes—
769C2×C4⋊C4C22×D1311yescharacteristic
770C2×C22⋊C4—131no—
771C2×C22⋊C4—131no—
772C2×C22⋊C4—132no—
773C2×C22⋊C4—132no—
774C2×C22⋊C4—131no—
775C2×C22⋊C4—131no—
776C2×C22⋊C4—131no—
777C2×C22⋊C4—131no—
778C2×C22⋊C4—131no—
779C2×C22⋊C4—131no—
780C2×C22⋊C4—132no—
781C2×C22⋊C4—132no—
782C2×C22⋊C4—132no—
783C2×C22⋊C4—132no—
784C2×C22⋊C4—132no—
785C2×C22⋊C4—132no—
786C2×C22⋊C4—132no—
787C2×C22⋊C4—132no—
788C2×C22⋊C4—132no—
789C2×C22⋊C4—268no—
790C2×C22⋊C4—268no—
791C2×C22⋊C4C22×D1312yes—
792C2×C22⋊C4C22×D1312yes—
793C2×C22⋊C4C22×D1312yes—
794C2×C22⋊C4C22×D1311yescharacteristic
795C2×C22⋊C4C22×D1311yescharacteristic
796C2×C42—24no—
797C2×C42—131no—
798C2×C42—131no—
799C2×C42—132no—
800C2×C42—132no—
801C2×C42—132no—
802C2×C42—132no—
803C2×C42—132no—
804C2×C42—132no—
805C2×C42—132no—
806C2×C42—131no—
807C2×C42—131no—
808C2×C42—131no—
809C2×C42—132no—
810C2×C42—132no—
811C2×C42—264no—
812C2×C42—264no—
813C2×C42—264no—
814C2×C42—264no—
815C2×C42—264no—
816C2×C42C22×D1312yes—
817C2×C42C22×D1311yescharacteristic
818C2×C42C22×D1311yescharacteristic
819C2×C42C22×D1311yescharacteristic
820C2×C42C22×D1311yescharacteristic
821C2×C42C22×D1311yescharacteristic
822#95—132no—
823#95—132no—
824#95—132no—
825#95—132no—
826#95—132no—
827#95—132no—
828#95—132no—
829#95—132no—
830#95—132no—
831#95—132no—
832#95—132no—
833#95C22×D1312yes—
834#95C22×D1312yes—
835#95C22×D1312yes—
836#95C22×D1312yes—
837#95C22×D1312yes—
838C2×C13—42no—
839C2×C13—42no—
840C2×C13C22×C4×D411yescharacteristic
841C2×C13C2×C4×#4111yescharacteristic
842C2×C13#342811yescharacteristic
843C2×C13D4×#4112yes—
844C2×C13#347512yes—
845D13—24no—
846D13—24no—
847D13—42no—
848C24—131no—
849C24—131no—
850C24—131no—
851C24—134no—
852C24—262no—
853C24—264no—
854C24—262no—
855C24—522no—
856C24C23×D1311yescharacteristic
857C24C23×D1311yescharacteristic
858#41—2632no—
859C2×Q8—134no—
860C2×Q8—262no—
861C2×Q8—262no—
862C2×D4—42no—
863C2×D4—134no—
864C2×D4—134no—
865C2×D4—134no—
866C2×D4—134no—
867C2×D4—134no—
868C2×D4—134no—
869C2×D4—262no—
870C2×D4—264no—
871C2×D4—262no—
872C2×D4—262no—
873C2×D4—262no—
874C2×D4—262no—
875C2×D4—264no—
876C2×D4—262no—
877C2×D4—522no—
878C2×D4C2×C4×D1314yes—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—42no—
886C22×C4—131no—
887C22×C4—134no—
888C22×C4—134no—
889C22×C4—134no—
890C22×C4—134no—
891C22×C4—132no—
892C22×C4—131no—
893C22×C4—131no—
894C22×C4—131no—
895C22×C4—131no—
896C22×C4—132no—
897C22×C4—134no—
898C22×C4—134no—
899C22×C4—134no—
900C22×C4—134no—
901C22×C4—132no—
902C22×C4—132no—
903C22×C4—262no—
904C22×C4—262no—
905C22×C4—2632no—
906C22×C4—264no—
907C22×C4—264no—
908C22×C4—264no—
909C22×C4—262no—
910C22×C4—262no—
911C22×C4—264no—
912C22×C4—264no—
913C22×C4—264no—
914C22×C4—264no—
915C22×C4—262no—
916C22×C4—262no—
917C22×C4—262no—
918C22×C4—262no—
919C22×C4—262no—
920C22×C4—262no—
921C22×C4—264no—
922C22×C4—264no—
923C22×C4—264no—
924C22×C4—522no—
925C22×C4—522no—
926C22×C4—522no—
927C22×C4—522no—
928C22×C4—522no—
929C22×C4C2×C4×D1314yes—
930C22×C4C2×C4×D1314yes—
931C22×C4C23×D1312yes—
932C22×C4C23×D1312yes—
933C22×C4C23×D1311yescharacteristic
934C22×C4C23×D1311yescharacteristic
935C22×C4C23×D1311yescharacteristic
936C22×C4C23×D1311yescharacteristic
937C22×C4C23×D1312yes—
938C22×C4C23×D1312yes—
939C22×C4C23×D1311yescharacteristic
940C4⋊C4—24no—
941C4⋊C4—24no—
942C4⋊C4—134no—
943C4⋊C4—134no—
944C4⋊C4—134no—
945C4⋊C4—134no—
946C4⋊C4—134no—
947C4⋊C4—138no—
948C4⋊C4—264no—
949C4⋊C4—264no—
950C4⋊C4—264no—
951C4⋊C4—264no—
952C4⋊C4—264no—
953C4⋊C4—522no—
954C4⋊C4—522no—
955C4⋊C4C2×C4×D1314yes—
956C22⋊C4—24no—
957C22⋊C4—24no—
958C22⋊C4—42no—
959C22⋊C4—134no—
960C22⋊C4—134no—
961C22⋊C4—134no—
962C22⋊C4—134no—
963C22⋊C4—134no—
964C22⋊C4—134no—
965C22⋊C4—134no—
966C22⋊C4—134no—
967C22⋊C4—138no—
968C22⋊C4—138no—
969C22⋊C4—264no—
970C22⋊C4—264no—
971C22⋊C4—264no—
972C22⋊C4—264no—
973C22⋊C4—264no—
974C22⋊C4—264no—
975C22⋊C4—264no—
976C22⋊C4—264no—
977C22⋊C4—522no—
978C22⋊C4C2×C4×D1314yes—
979C22⋊C4C2×C4×D1314yes—
980C42—22no—
981C42—24no—
982C42—22no—
983C42—22no—
984C42—134no—
985C42—134no—
986C42—264no—
987C42—264no—
988C42—264no—
989C42—264no—
990C42—264no—
991C42—264no—
992C42—264no—
993C42—262no—
994C42—262no—
995C42—262no—
996C42—522no—
997C42—522no—
998C42C2×C4×D1314yes—
999C42D4×D1314yes—
1000C13#3413611yescharacteristic, complemented, Sylow
1001C23—21no—
1002C23—21no—
1003C23—22no—
1004C23—22no—
1005C23—21no—
1006C23—21no—
1007C23—22no—
1008C23—22no—
1009C23—132no—
1010C23—132no—
1011C23—132no—
1012C23—134no—
1013C23—132no—
1014C23—132no—
1015C23—268no—
1016C23—268no—
1017C23—261no—
1018C23—261no—
1019C23—262no—
1020C23—262no—
1021C23—262no—
1022C23—261no—
1023C23—262no—
1024C23—261no—
1025C23—262no—
1026C23—524no—
1027C23—528no—
1028C23—528no—
1029C23C22×C4×D1312yes—
1030C23C22×C4×D1312yes—
1031C23C24×D1311yescharacteristic
1032Q8—268no—
1033D4—44no—
1034D4—268no—
1035D4—268no—
1036D4—268no—
1037D4—268no—
1038D4—268no—
1039D4—524no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—28no—
1051C2×C4—28no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—48no—
1059C2×C4—132no—
1060C2×C4—132no—
1061C2×C4—132no—
1062C2×C4—1316no—
1063C2×C4—132no—
1064C2×C4—132no—
1065C2×C4—132no—
1066C2×C4—132no—
1067C2×C4—134no—
1068C2×C4—134no—
1069C2×C4—268no—
1070C2×C4—268no—
1071C2×C4—268no—
1072C2×C4—261no—
1073C2×C4—261no—
1074C2×C4—262no—
1075C2×C4—262no—
1076C2×C4—262no—
1077C2×C4—261no—
1078C2×C4—261no—
1079C2×C4—262no—
1080C2×C4—262no—
1081C2×C4—262no—
1082C2×C4—268no—
1083C2×C4—268no—
1084C2×C4—262no—
1085C2×C4—262no—
1086C2×C4—262no—
1087C2×C4—262no—
1088C2×C4—262no—
1089C2×C4—262no—
1090C2×C4—528no—
1091C2×C4—528no—
1092C2×C4—528no—
1093C2×C4—528no—
1094C2×C4—528no—
1095C2×C4C22×C4×D1312yes—
1096C2×C4C22×C4×D1312yes—
1097C2×C4C22×C4×D1312yes—
1098C2×C4C22×C4×D1312yes—
1099C2×C4C22×C4×D1312yes—
1100C2×C4C2×D4×D1314yes—
1101C2×C4C2×D4×D1312yes—
1102C2×C4#41×D1314yes—
1103C2×C4#41×D1312yes—
1104C22—22no—
1105C22—22no—
1106C22—22no—
1107C22—22no—
1108C22—22no—
1109C22—22no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—134no—
1115C22—134no—
1116C22—262no—
1117C22—262no—
1118C22—262no—
1119C22—262no—
1120C22—264no—
1121C22—264no—
1122C22—264no—
1123C22—264no—
1124C22—262no—
1125C22—262no—
1126C22—262no—
1127C22—5216no—
1128C22—522no—
1129C22—522no—
1130C22C23×C4×D1311yescharacteristic
1131C22C22×D4×D1311yescharacteristic
1132C22C2×#41×D1311yescharacteristic
1133C22C2×#41×D1312yes—
1134C22#1171964812yes—
1135C4—22no—
1136C4—22no—
1137C4—22no—
1138C4—22no—
1139C4—24no—
1140C4—24no—
1141C4—42no—
1142C4—42no—
1143C4—134no—
1144C4—262no—
1145C4—262no—
1146C4—262no—
1147C4—262no—
1148C4—264no—
1149C4—264no—
1150C4—522no—
1151C4—522no—
1152C4C4×D4×D1314yes—
1153C2—42no—
1154C2—42no—
1155C2—264no—
1156C2—264no—
1157C2—522no—
1158C2C2×C4×D4×D1311yescharacteristic
1159C2C4×#41×D1311yescharacteristic
1160C2#1312803711yescharacteristic
1161C2#1312831912yes—
1162C2#1312839212yes—
subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC13×#2290C2
socle, cosocleC23×C13C25
prime radicalC2×#11719252C2
hypercenter#2290D13
hypocenterC13#34136
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6127C2semidirect
3. C2×D13×#117C2semidirect
4. #13117877C2semidirect
5. #13117866C2semidirect
6. #13117855C2semidirect
7. #13117844C2semidirect
8. #13117835C2semidirect
9. #13117831C2semidirect
10. #13117819C2semidirect
11. #13117814C2semidirect
12. #13117322C2semidirect
13. #13117316C2semidirect
14. #13117301C2semidirect
15. #13117295C2semidirect
16. #13117282C2semidirect
17. #13117282C2semidirect
18. #13117280C2semidirect
19. C42×C22⋊D13C2semidirect
20. C4×#88147C2semidirect
21. #13117175C2semidirect
22. C4×C22⋊C4×D13C2semidirect
23. C13×#2290C2semidirect
28. C22×C42×C13C22semidirect
35. C2×C4×C22⋊D13C22semidirect
37. C2×#88180C22semidirect
38. #11719252C4semidirect
58. C2×#88126C22semidirect
63. C2×C42×D13C22semidirect
64. C2×C4×Dic26C22semidirect
66. C13×#387C22semidirect
68. C13×#385C22semidirect
69. C4×C13×C4⋊C4C22semidirect
71. C4×C13×C22⋊C4C22semidirect
72. C13×#376C22semidirect
75. C4×C22⋊Dic13C22semidirect
76. C4×C22⋊Dic13C22semidirect
77. #11718651C22semidirect
79. #11718646C22semidirect
80. C4⋊C4×Dic13C22semidirect
81. #11718633C22semidirect
82. #11718633C22semidirect
84. #11718618C22semidirect
89. #11718612C22semidirect
92. #11718606C22semidirect
97. C4×#6103C22semidirect
98. C4×#6103C22semidirect
99. C4×C4⋊Dic13C22semidirect
100. #11718593C22semidirect
101. C4×#6101C22semidirect
102. C4×#6101C22semidirect
103. C4×#6101C22semidirect
104. C42×Dic13C22semidirect
105. C42×Dic13C22semidirect
106. #11718331C22semidirect
110. #11718329C22semidirect
115. #11718327C22semidirect
119. #11718316C22semidirect
120. #11718316C22semidirect
121. #11718314C22semidirect
122. #11718310C22semidirect
123. #11718310C22semidirect
124. #11718308C22semidirect
125. #11718307C22semidirect
138. C2×#6127C2×C4semidirect
143. C22×C4×D13C2×C4semidirect
155. C4×D4×C13C2×C4semidirect
178. #88193C2×C4semidirect
179. #88191C2×C4semidirect
183. C4×C22⋊D13C2×C4semidirect
184. C4×C22⋊D13C2×C4semidirect
227. #88150C2×C4semidirect
228. #88148C2×C4semidirect
232. #88138C2×C4semidirect
233. #88137C2×C4semidirect
234. #88136C2×C4semidirect
237. #88132C2×C4semidirect
240. C4×D52C2×C4semidirect
243. #88126C2×C4semidirect
244. #88126D4semidirect
392. #6103#41semidirect
438. #2290D13semidirect
544. C4×D13C4×D4semidirect
586. C22×C42C2×D13semidirect
606. #387C2×D13semidirect
618. #385C2×D13semidirect
626. C4×C4⋊C4C2×D13semidirect
642. C4×C22⋊C4C2×D13semidirect
644. #376C2×D13semidirect
678. C2×D13C4×#41semidirect
743. C4×D4C4×D13semidirect
1000. C13#34136semidirect

Maximal subgroups

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

subgroupindex
C2×#117192522
C2×C4×#61272
C2×D13×#1172
#131178772
#131178662
#131178552
#131178442
#131178352
#131178312
#131178192
#131178142
#131173222
#131173162
#131173012
#131172952
#131172822
#131172802
C42×C22⋊D132
C4×#881472
#131171752
C4×C22⋊C4×D132
C13×#22902
#3413613