Finite Group Databasebeta

← C2×#13131335 #16807540

Subgroups — C2×#13131335 #16807540

Order 3328.

2982 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131335C2116yesmaximal, direct product factor
2C2×#11719151C211yesmaximal, characteristic
3C2×#11719083C211yesmaximal, characteristic, complemented
4C2×#11719071C211yesmaximal, characteristic, complemented
5C2×#11719071C211yesmaximal, characteristic, complemented
6C2×#11719071C211yesmaximal, characteristic, complemented
7C2×#11719071C211yesmaximal, characteristic, complemented
8C2×#11719082C211yesmaximal, characteristic, complemented
9C2×#11719082C211yesmaximal, characteristic, complemented
10C2×#11719150C211yesmaximal, characteristic
11C2×#11719070C211yesmaximal, characteristic, complemented
12C2×#11719136C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×#261C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×#261C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊#261C211yesmaximal, characteristic, complemented
16C2×D13×#123C211yesmaximal, characteristic
17C24×#261C2211yescharacteristic
18C22×D4×D13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C22×C22⋊#261C2211yescharacteristic
21C22×C22⋊#261C2211yescharacteristic
22C22×C22⋊#261C2211yescharacteristic
23C22×C22⋊#261C2211yescharacteristic
24C22×C22⋊#261C2211yescharacteristic
25C22×C22⋊#261C2211yescharacteristic
26C22×C22⋊#261C2211yescharacteristic
27C22×C4⋊#261C2211yescharacteristic
28C22×C4⋊#261C2211yescharacteristic
29C22×C4⋊#261C2211yescharacteristic
30C22×C4⋊#261C2211yescharacteristic
31C22×C4⋊#261C2211yescharacteristic
32C22×C4×#261C2211yescharacteristic
33C22×C4×#261C2211yescharacteristic
34C22×C4×#261C2211yescharacteristic
35C22×C4×#261C2211yescharacteristic
36C22×C4×#261C2211yescharacteristic
37C2×C13×#123C411yescharacteristic, complemented
38C2×#88189C411yescharacteristic, complemented
39C2×#88183C411yescharacteristic, complemented
40D13×#123C418yescomplemented
41D13×#123C2218yes—
42C2×#88148C411yescharacteristic, complemented
43C2×#88148C411yescharacteristic, complemented
44C2×C4⋊C4×D13C2211yescharacteristic
45C2×C4⋊C4×D13C2211yescharacteristic
46C2×#88140C411yescharacteristic, complemented
47C2×#88137C411yescharacteristic, complemented
48C2×#88137C411yescharacteristic, complemented
49C2×C22⋊C4×D13C2211yescharacteristic
50C2×C22⋊C4×D13C2211yescharacteristic
51C2×C22⋊C4×D13C2211yescharacteristic
52#11719151C2218yes—
53#11719150C2218yes—
54#11719136C2218yescomplemented
55C4×C22⋊#261C2218yescomplemented
56C2×(C2×#261)⋊C4C2211yescharacteristic
57C2×(C2×#261)⋊C4C2211yescharacteristic
58C2×(C2×#261)⋊C4C2211yescharacteristic
59C2×(C2×#261)⋊C4C2211yescharacteristic
60C2×(C2×#261)⋊C4C2211yescharacteristic
61C2×(C2×#261)⋊C4C2211yescharacteristic
62C2×(C2×#261)⋊C4C2211yescharacteristic
63C2×(C2×#261)⋊C4C2211yescharacteristic
64C2×(C2×#261)⋊C4C2211yescharacteristic
65C2×(C2×#261)⋊C4C2211yescharacteristic
66#11719083C2218yescomplemented
67#11719082C2218yescomplemented
68#11719082C2218yescomplemented
69C4⋊C4×#261C2218yescomplemented
70#11719071C2218yescomplemented
71#11719071C2218yescomplemented
72#11719071C2218yescomplemented
73#11719071C2218yescomplemented
74#11719070C2218yescomplemented
75C22⋊C4×#261C2218yescomplemented
76C24×D13C2311yescharacteristic
77C24×D13C2311yescharacteristic
78C23×#261—24no—
79C23×#261—42no—
80C23×#261—42no—
81C23×#261C2311yescharacteristic
82C23×#261C2311yescharacteristic
83C23×#261C2311yescharacteristic
84C23×#261C2311yescharacteristic
85C23×#261C2311yescharacteristic
86C23×#261C2311yescharacteristic
87C23×#261C2311yescharacteristic
88C23×#261C2311yescharacteristic
89C23×#261C2314yes—
90C22×D4×C13C2×C411yescharacteristic
91C23×C4×C13C2×C411yescharacteristic, complemented
92C22×C22⋊D13C2×C411yescharacteristic
93C22×C22⋊D13C2×C411yescharacteristic
94C23×Dic13C2×C411yescharacteristic, complemented
95C2×D4×D13—42no—
96C2×D4×D13—42no—
97C2×D4×D13C2×C414yes—
98C2×D4×D13C2314yes—
99C22×D52C2×C411yescharacteristic
100C22×C4×D13—42no—
101C22×C4×D13—42no—
102C22×C4×D13C2×C414yescomplemented
103C22×C4×D13C2×C411yescharacteristic, complemented
104C22×C4×D13C2×C411yescharacteristic, complemented
105C22×C4×D13C2311yescharacteristic
106C22×C4×D13C2311yescharacteristic
107C22×C4×D13C2311yescharacteristic
108C22×C4×D13C2311yescharacteristic
109C22×C4×D13C2311yescharacteristic
110C22×C4×D13C2314yes—
111C2×C22⋊#261—24no—
112C2×C22⋊#261—24no—
113C2×C22⋊#261—24no—
114C2×C22⋊#261—42no—
115C2×C22⋊#261—42no—
116C2×C22⋊#261—42no—
117C2×C22⋊#261—42no—
118C2×C22⋊#261C2314yes—
119C2×C22⋊#261C2314yes—
120C2×C22⋊#261C2314yes—
121C2×C22⋊#261C2314yes—
122C2×C22⋊#261C2314yes—
123C2×C22⋊#261C2314yes—
124C2×C22⋊#261C2314yes—
125C2×C4⋊#261—24no—
126C2×C4⋊#261—42no—
127C2×C4⋊#261—42no—
128C2×C4⋊#261—42no—
129C2×C4⋊#261—42no—
130C2×C4⋊#261C2314yes—
131C2×C4⋊#261C2314yes—
132C2×C4⋊#261C2314yes—
133C2×C4⋊#261C2314yes—
134C2×C4⋊#261C2314yes—
135C2×C4×#261—24no—
136C2×C4×#261—42no—
137C2×C4×#261—42no—
138C2×C4×#261—42no—
139C2×C4×#261—42no—
140C2×C4×#261C2314yes—
141C2×C4×#261C2314yes—
142C2×C4×#261C2314yes—
143C2×C4×#261C2314yes—
144C2×C4×#261C2314yes—
145C13×#123C2×C418yescomplemented
146C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
147C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
148C2×C13×C22⋊C4C2×C411yescharacteristic
149C2×C13×C22⋊C4C2×C411yescharacteristic
150C2×C13×C22⋊C4C2×C411yescharacteristic, complemented
151C2×C22⋊Dic13C2×C411yescharacteristic
152C2×C22⋊Dic13C2×C411yescharacteristic
153C2×C22⋊Dic13C2×C411yescharacteristic, complemented
154#88189C2×C418yescomplemented
155#88183C2×C418yescomplemented
156C2×#6103C2×C411yescharacteristic
157C2×#6103C2×C411yescharacteristic
158C2×#6103C2×C411yescharacteristic
159C2×#6103C2×C411yescharacteristic
160C2×#6103C2×C411yescharacteristic, complemented
161C2×#6103C2×C411yescharacteristic, complemented
162C2×C4⋊Dic13C2×C411yescharacteristic, complemented
163C2×C4⋊Dic13C2×C411yescharacteristic, complemented
164C2×#6101C2×C411yescharacteristic, complemented
165C2×#6101C2×C411yescharacteristic, complemented
166C2×#6101C2×C411yescharacteristic, complemented
167C2×#6101C2×C411yescharacteristic, complemented
168#88148C2×C418yescomplemented
169#88148C2×C418yescomplemented
170C4⋊C4×D13C2×C414yescomplemented
171C4⋊C4×D13C2×C414yescomplemented
172C4⋊C4×D13C2314yes—
173C4⋊C4×D13C2314yes—
174#88140C2×C418yescomplemented
175#88137C2×C418yescomplemented
176#88137C2×C418yescomplemented
177C22⋊C4×D13C2×C414yes—
178C22⋊C4×D13C2×C414yes—
179C22⋊C4×D13C2×C414yescomplemented
180C22⋊C4×D13C2314yes—
181C22⋊C4×D13C2314yes—
182C22⋊C4×D13C2314yes—
183(C2×#261)⋊C4C2314yes—
184(C2×#261)⋊C4C2314yes—
185(C2×#261)⋊C4C2314yes—
186(C2×#261)⋊C4C2314yes—
187(C2×#261)⋊C4C2314yes—
188(C2×#261)⋊C4C2314yes—
189(C2×#261)⋊C4C2314yes—
190(C2×#261)⋊C4C2314yes—
191(C2×#261)⋊C4C2314yes—
192(C2×#261)⋊C4C2314yes—
193C2×#2335—131nomaximal, Sylow
194C24×C13C22×C411yescharacteristic
195C24×C13C22×C411yescharacteristic
196C23×D13—22no—
197C23×D13—22no—
198C23×D13—22no—
199C23×D13—22no—
200C23×D13—22no—
201C23×D13—22no—
202C23×D13—22no—
203C23×D13—22no—
204C23×D13—22no—
205C23×D13—22no—
206C23×D13—22no—
207C23×D13—22no—
208C23×D13C22×C412yes—
209C23×D13C22×C412yes—
210C23×D13C22×C411yescharacteristic
211C23×D13C22×C411yescharacteristic
212C23×D13C2412yes—
213C23×D13C2412yes—
214C23×D13C2411yescharacteristic
215C22×#261—22no—
216C22×#261—22no—
217C22×#261—22no—
218C22×#261—22no—
219C22×#261—22no—
220C22×#261—22no—
221C22×#261—22no—
222C22×#261—22no—
223C22×#261—22no—
224C22×#261—22no—
225C22×#261—22no—
226C22×#261—22no—
227C22×#261—22no—
228C22×#261—22no—
229C22×#261—22no—
230C22×#261—22no—
231C22×#261—22no—
232C22×#261—22no—
233C22×#261—22no—
234C22×#261—22no—
235C22×#261—22no—
236C22×#261—22no—
237C22×#261—28no—
238C22×#261—44no—
239C22×#261—44no—
240C22×#261—416no—
241C22×#261#4114yes—
242C22×#261#4114yes—
243C22×#261C2412yes—
244C22×#261C2412yes—
245C22×#261C2412yes—
246C22×#261C2412yes—
247C22×#261C2412yes—
248C22×#261C2412yes—
249C22×#261C2412yes—
250C22×#261C2412yes—
251C2×D4×C13—42no—
252C2×D4×C13C22×C414yes—
253C22×C4×C13—42no—
254C22×C4×C13C22×C411yescharacteristic
255C22×C4×C13C22×C411yescharacteristic
256C22×C4×C13C22×C411yescharacteristic
257C22×C4×C13C22×C411yescharacteristic
258C22×C4×C13C22×C411yescharacteristic
259C22×C4×C13C22×C414yescomplemented
260C2×C22⋊D13—42no—
261C2×C22⋊D13—42no—
262C2×C22⋊D13C22×C414yes—
263C2×C22⋊D13C22×C414yes—
264C22×Dic13—42no—
265C22×Dic13C22×C411yescharacteristic
266C22×Dic13C22×C411yescharacteristic
267C22×Dic13C22×C411yescharacteristic
268C22×Dic13C22×C411yescharacteristic
269C22×Dic13C22×C411yescharacteristic
270C22×Dic13C22×C414yescomplemented
271D4×D13—48no—
272D4×D13—44no—
273D4×D13—44no—
274C2×D52—42no—
275C2×D52C22×C414yes—
276C2×C4×D13—22no—
277C2×C4×D13—22no—
278C2×C4×D13—22no—
279C2×C4×D13—22no—
280C2×C4×D13—22no—
281C2×C4×D13—22no—
282C2×C4×D13—22no—
283C2×C4×D13—22no—
284C2×C4×D13—22no—
285C2×C4×D13—22no—
286C2×C4×D13—48no—
287C2×C4×D13—44no—
288C2×C4×D13—44no—
289C2×C4×D13—42no—
290C2×C4×D13—42no—
291C2×C4×D13C22×C412yes—
292C2×C4×D13C22×C412yes—
293C2×C4×D13C22×C412yes—
294C2×C4×D13C22×C412yes—
295C2×C4×D13C22×C412yes—
296C2×C4×D13C22×C414yescomplemented
297C2×C4×D13C22×C414yescomplemented
298C2×C4×D13C2412yes—
299C2×C4×D13C2412yes—
300C2×C4×D13C2412yes—
301C2×C4×D13C2412yes—
302C2×C4×D13C2412yes—
303C22⋊#261—28no—
304C22⋊#261—28no—
305C22⋊#261—28no—
306C22⋊#261—44no—
307C22⋊#261—44no—
308C22⋊#261—44no—
309C22⋊#261—44no—
310C4⋊#261—28no—
311C4⋊#261—44no—
312C4⋊#261—44no—
313C4⋊#261—44no—
314C4⋊#261—44no—
315C4×#261—28no—
316C4×#261—44no—
317C4×#261—44no—
318C4×#261—44no—
319C4×#261—44no—
320C13×C4⋊C4C22×C414yescomplemented
321C13×C4⋊C4C22×C414yescomplemented
322C13×C22⋊C4C22×C414yes—
323C13×C22⋊C4C22×C414yes—
324C13×C22⋊C4C22×C414yescomplemented
325C22⋊Dic13C22×C414yes—
326C22⋊Dic13C22×C414yes—
327C22⋊Dic13C22×C414yescomplemented
328#6103C22×C414yes—
329#6103C22×C414yes—
330#6103C22×C414yes—
331#6103C22×C414yes—
332#6103C22×C414yescomplemented
333#6103C22×C414yescomplemented
334C4⋊Dic13C22×C414yescomplemented
335C4⋊Dic13C22×C414yescomplemented
336#6101C22×C414yescomplemented
337#6101C22×C414yescomplemented
338#6101C22×C414yescomplemented
339#6101C22×C414yescomplemented
340C22×#123—131no—
341#2335—1316no—
342C2×#390—131no—
343C2×#389—131no—
344C2×#388—131no—
345C2×#388—131no—
346C2×#388—131no—
347C2×#388—131no—
348C2×#387—131no—
349C2×#387—131no—
350C2×#386—131no—
351C2×#385—131no—
352C2×#380—131no—
353C2×C4×C4⋊C4—131no—
354C2×C4×C22⋊C4—131no—
355C2×C4×C22⋊C4—131no—
356C23×C13—22no—
357C23×C13—22no—
358C23×C13—22no—
359C23×C13—22no—
360C23×C13—22no—
361C23×C13—22no—
362C23×C13C23×C412yes—
363C23×C13C23×C412yes—
364C23×C13C23×C411yescharacteristic
365C22×D13—22no—
366C22×D13—22no—
367C22×D13—22no—
368C22×D13—22no—
369C22×D13—22no—
370C22×D13—22no—
371C22×D13—24no—
372C22×D13—24no—
373C22×D13—24no—
374C22×D13—24no—
375C22×D13—24no—
376C22×D13—24no—
377C22×D13—22no—
378C22×D13—22no—
379C22×D13—22no—
380C22×D13—22no—
381C22×D13—22no—
382C22×D13—22no—
383C22×D13—22no—
384C22×D13—22no—
385C22×D13—22no—
386C22×D13—22no—
387C22×D13—22no—
388C22×D13—22no—
389C22×D13—44no—
390C22×D13—44no—
391C22×D13—44no—
392C22×D13—44no—
393C22×D13—44no—
394C22×D13—44no—
395C22×D13—44no—
396C22×D13—44no—
397C22×D13C23×C412yes—
398C22×D13C23×C412yes—
399C22×D13C23×C411yescharacteristic
400C22×D13C2×#4112yes—
401C22×D13C2×#4112yes—
402C22×D13H(5,𝔽2)12yes—
403C22×D13H(5,𝔽2)12yes—
404C22×D13H(5,𝔽2)12yes—
405C22×D132−1+412yes—
406C22×D13C2511yescharacteristic
407C2×#261—28no—
408C2×#261—28no—
409C2×#261—22no—
410C2×#261—22no—
411C2×#261—22no—
412C2×#261—22no—
413C2×#261—22no—
414C2×#261—22no—
415C2×#261—22no—
416C2×#261—22no—
417C2×#261—22no—
418C2×#261—22no—
419C2×#261—22no—
420C2×#261—22no—
421C2×#261—22no—
422C2×#261—22no—
423C2×#261—22no—
424C2×#261—22no—
425C2×#261—22no—
426C2×#261—22no—
427C2×#261—22no—
428C2×#261—22no—
429C2×#261—22no—
430C2×#261—22no—
431C2×#261—416no—
432C2×#261—44no—
433C2×#261—44no—
434C2×#261—44no—
435C2×#261—44no—
436C2×#261—44no—
437C2×#261—44no—
438C2×#261C2×#4114yes—
439C2×#261C2×#4114yes—
440D4×C13—44no—
441C2×C4×C13—22no—
442C2×C4×C13—22no—
443C2×C4×C13—22no—
444C2×C4×C13—22no—
445C2×C4×C13—22no—
446C2×C4×C13—44no—
447C2×C4×C13C23×C412yes—
448C2×C4×C13C23×C412yes—
449C2×C4×C13C23×C412yes—
450C2×C4×C13C23×C412yes—
451C2×C4×C13C23×C412yes—
452C22⋊D13—44no—
453C22⋊D13—44no—
454C2×Dic13—22no—
455C2×Dic13—22no—
456C2×Dic13—22no—
457C2×Dic13—22no—
458C2×Dic13—22no—
459C2×Dic13—44no—
460C2×Dic13C23×C412yes—
461C2×Dic13C23×C412yes—
462C2×Dic13C23×C412yes—
463C2×Dic13C23×C412yes—
464C2×Dic13C23×C412yes—
465D52—44no—
466C4×D13—24no—
467C4×D13—24no—
468C4×D13—24no—
469C4×D13—24no—
470C4×D13—24no—
471C4×D13—22no—
472C4×D13—22no—
473C4×D13—22no—
474C4×D13—22no—
475C4×D13—22no—
476C4×D13—22no—
477C4×D13—22no—
478C4×D13—22no—
479C4×D13—22no—
480C4×D13—22no—
481C4×D13—44no—
482C4×D13—44no—
483C23×D4—131no—
484C24×C4—131no—
485C24×C4—131no—
486C2×#123—131no—
487C2×#123—131no—
488C2×#123—138no—
489C2×#123—138no—
490C2×#123—131no—
491C2×#123—131no—
492C2×#123—131no—
493C2×#123—131no—
494C2×#123—131no—
495C2×#123#26111yescharacteristic, complemented
496C22×C4⋊C4—131no—
497C22×C4⋊C4—131no—
498C22×C4⋊C4—131no—
499C22×C4⋊C4—131no—
500C22×C4⋊C4—131no—
501C22×C4⋊C4—131no—
502C22×C4⋊C4—131no—
503C22×C22⋊C4—131no—
504C22×C22⋊C4—131no—
505C22×C22⋊C4—131no—
506C22×C22⋊C4—131no—
507C22×C22⋊C4—131no—
508C22×C22⋊C4—131no—
509C22×C22⋊C4—131no—
510C22×C22⋊C4—131no—
511C22×C22⋊C4—131no—
512C22×C22⋊C4—131no—
513C22×C42—131no—
514C22×C42—131no—
515C22×C42—131no—
516C22×C42—131no—
517C22×C42—131no—
518#390—138no—
519#389—138no—
520#388—138no—
521#388—138no—
522#388—138no—
523#388—138no—
524#387—138no—
525#387—138no—
526#386—138no—
527#385—138no—
528#380—138no—
529C4×C4⋊C4—138no—
530C4×C22⋊C4—138no—
531C4×C22⋊C4—138no—
532C2×#95—131no—
533C2×#95—131no—
534C2×#95—131no—
535C2×#95—131no—
536C2×#95—131no—
537C2×#95—131no—
538C2×#95—131no—
539C2×#95—131no—
540C2×#95—131no—
541C2×#95—131no—
542C22×C13—22no—
543C22×C13—22no—
544C22×C13—22no—
545C22×C13—22no—
546C22×C13—22no—
547C22×C13—22no—
548C22×C13—44no—
549C22×C13—44no—
550C22×C13C4×#4112yes—
551C22×C13#51812yes—
552C22×C13#52012yes—
553C22×C13C24×C411yescharacteristic
554C2×D13—22no—
555C2×D13—22no—
556C2×D13—22no—
557C2×D13—22no—
558C2×D13—22no—
559C2×D13—22no—
560C2×D13—44no—
561C2×D13—44no—
562C2×D13—48no—
563C2×D13—48no—
564C2×D13—42no—
565C2×D13—42no—
566C2×D13—42no—
567C2×D13—42no—
568C2×D13—42no—
569C2×D13—42no—
570C2×D13—42no—
571C2×D13—42no—
572C2×D13C4×#4112yes—
573C2×D13#51812yes—
574C2×D13#52012yes—
575C2×D13#53814yes—
576C2×D13#53914yes—
577C2×D13#54014yes—
578C2×D13#54214yes—
579C2×D13C22×#4111yescharacteristic
580C2×D13C22×#4111yescharacteristic
581C2×D13C2×H(5,𝔽2)11yescharacteristic
582C2×D13C2×H(5,𝔽2)11yescharacteristic
583C2×D13C2×H(5,𝔽2)11yescharacteristic
584C2×D13C2×2−1+411yescharacteristic
585#261—24no—
586#261—24no—
587#261—42no—
588#261—42no—
589#261—42no—
590#261—42no—
591#261—42no—
592#261—42no—
593C4×C13—22no—
594C4×C13—22no—
595C4×C13—22no—
596C4×C13—22no—
597C4×C13—22no—
598Dic13—22no—
599Dic13—22no—
600Dic13—22no—
601Dic13—22no—
602Dic13—22no—
603C25—131no—
604C25—131no—
605C22×D4—131no—
606C22×D4—131no—
607C22×D4—134no—
608C22×D4—134no—
609C22×D4—131no—
610C22×D4—522no—
611C22×D4—522no—
612C22×D4C2×#26111yescharacteristic
613C23×C4—131no—
614C23×C4—131no—
615C23×C4—131no—
616C23×C4—131no—
617C23×C4—131no—
618C23×C4—131no—
619C23×C4—131no—
620C23×C4—131no—
621C23×C4—131no—
622C23×C4—131no—
623C23×C4—134no—
624C23×C4—134no—
625C23×C4—131no—
626C23×C4—131no—
627C23×C4—131no—
628C23×C4—131no—
629C23×C4—131no—
630C23×C4—131no—
631C23×C4—134no—
632C23×C4—264no—
633C23×C4—522no—
634C23×C4—522no—
635C23×C4—522no—
636C23×C4—522no—
637C23×C4C2×#26111yescharacteristic, complemented
638#123—138no—
639#123—138no—
640#123—138no—
641#123—138no—
642#123—138no—
643#123—138no—
644#123—138no—
645#123C2×#26118yescomplemented
646C2×C4⋊C4—131no—
647C2×C4⋊C4—131no—
648C2×C4⋊C4—131no—
649C2×C4⋊C4—131no—
650C2×C4⋊C4—131no—
651C2×C4⋊C4—131no—
652C2×C4⋊C4—134no—
653C2×C4⋊C4—134no—
654C2×C4⋊C4—134no—
655C2×C4⋊C4—134no—
656C2×C4⋊C4—134no—
657C2×C4⋊C4—134no—
658C2×C4⋊C4—134no—
659C2×C4⋊C4—134no—
660C2×C4⋊C4—134no—
661C2×C4⋊C4—264no—
662C2×C4⋊C4—522no—
663C2×C4⋊C4—522no—
664C2×C4⋊C4—522no—
665C2×C4⋊C4—522no—
666C2×C4⋊C4C2×#26111yescharacteristic, complemented
667C2×C4⋊C4C2×#26111yescharacteristic, complemented
668C2×C22⋊C4—131no—
669C2×C22⋊C4—131no—
670C2×C22⋊C4—131no—
671C2×C22⋊C4—131no—
672C2×C22⋊C4—131no—
673C2×C22⋊C4—131no—
674C2×C22⋊C4—131no—
675C2×C22⋊C4—131no—
676C2×C22⋊C4—131no—
677C2×C22⋊C4—134no—
678C2×C22⋊C4—134no—
679C2×C22⋊C4—134no—
680C2×C22⋊C4—134no—
681C2×C22⋊C4—134no—
682C2×C22⋊C4—134no—
683C2×C22⋊C4—134no—
684C2×C22⋊C4—134no—
685C2×C22⋊C4—134no—
686C2×C22⋊C4—134no—
687C2×C22⋊C4—134no—
688C2×C22⋊C4—134no—
689C2×C22⋊C4—134no—
690C2×C22⋊C4—264no—
691C2×C22⋊C4—264no—
692C2×C22⋊C4—264no—
693C2×C22⋊C4—522no—
694C2×C22⋊C4—522no—
695C2×C22⋊C4—522no—
696C2×C22⋊C4—522no—
697C2×C22⋊C4C2×#26111yescharacteristic
698C2×C22⋊C4C2×#26111yescharacteristic
699C2×C22⋊C4C2×#26111yescharacteristic, complemented
700C2×C42—134no—
701C2×C42—134no—
702C2×C42—134no—
703C2×C42—134no—
704C2×C42—134no—
705C2×C42—264no—
706C2×C42—522no—
707C2×C42—522no—
708C2×C42—522no—
709C2×C42—522no—
710#95—134no—
711#95—134no—
712#95—134no—
713#95—134no—
714#95—134no—
715#95—134no—
716#95—134no—
717#95—134no—
718#95—134no—
719#95—134no—
720C2×C13—42no—
721C2×C13—42no—
722C2×C13#233514yescomplemented
723C2×C13C2×C4×#4111yescharacteristic
724C2×C13C2×#51811yescharacteristic
725C2×C13C2×#52011yescharacteristic
726D13—42no—
727D13—42no—
728D13#233514yescomplemented
729D13C2×#53811yescharacteristic
730D13C2×#53911yescharacteristic
731D13C2×#54011yescharacteristic
732D13C2×#54211yescharacteristic
733C24—131no—
734C24—132no—
735C24—132no—
736C24—132no—
737C24—132no—
738C24—131no—
739C24—131no—
740C24—262no—
741C24—262no—
742C24—262no—
743C24—262no—
744C24—262no—
745C24—262no—
746C24—262no—
747C24—262no—
748C24—262no—
749C24—262no—
750C24—262no—
751C24—262no—
752C24C22×#26111yescharacteristic
753C24C22×#26111yescharacteristic
754C2×D4—42no—
755C2×D4—134no—
756C2×D4—134no—
757C2×D4—134no—
758C2×D4—522no—
759C2×D4—524no—
760C2×D4—524no—
761C2×D4—528no—
762C2×D4—522no—
763C2×D4—522no—
764C2×D4C22×#26114yes—
765C22×C4—42no—
766C22×C4—132no—
767C22×C4—132no—
768C22×C4—134no—
769C22×C4—134no—
770C22×C4—131no—
771C22×C4—131no—
772C22×C4—131no—
773C22×C4—131no—
774C22×C4—131no—
775C22×C4—134no—
776C22×C4—132no—
777C22×C4—132no—
778C22×C4—132no—
779C22×C4—132no—
780C22×C4—132no—
781C22×C4—132no—
782C22×C4—132no—
783C22×C4—132no—
784C22×C4—132no—
785C22×C4—132no—
786C22×C4—134no—
787C22×C4—134no—
788C22×C4—132no—
789C22×C4—132no—
790C22×C4—132no—
791C22×C4—132no—
792C22×C4—132no—
793C22×C4—132no—
794C22×C4—262no—
795C22×C4—262no—
796C22×C4—262no—
797C22×C4—262no—
798C22×C4—262no—
799C22×C4—262no—
800C22×C4—262no—
801C22×C4—262no—
802C22×C4—262no—
803C22×C4—262no—
804C22×C4—268no—
805C22×C4—262no—
806C22×C4—262no—
807C22×C4—262no—
808C22×C4—262no—
809C22×C4—262no—
810C22×C4—262no—
811C22×C4—262no—
812C22×C4—262no—
813C22×C4—262no—
814C22×C4—262no—
815C22×C4—262no—
816C22×C4—262no—
817C22×C4—262no—
818C22×C4—262no—
819C22×C4—262no—
820C22×C4—262no—
821C22×C4—262no—
822C22×C4—262no—
823C22×C4—262no—
824C22×C4—262no—
825C22×C4—262no—
826C22×C4—262no—
827C22×C4—522no—
828C22×C4—522no—
829C22×C4—524no—
830C22×C4—524no—
831C22×C4—528no—
832C22×C4—522no—
833C22×C4—524no—
834C22×C4—524no—
835C22×C4—5216no—
836C22×C4C22×#26111yescharacteristic
837C22×C4C22×#26111yescharacteristic
838C22×C4C22×#26111yescharacteristic
839C22×C4C22×#26111yescharacteristic
840C22×C4C22×#26111yescharacteristic
841C22×C4C22×#26114yescomplemented
842C4⋊C4—134no—
843C4⋊C4—134no—
844C4⋊C4—134no—
845C4⋊C4—134no—
846C4⋊C4—134no—
847C4⋊C4—134no—
848C4⋊C4—268no—
849C4⋊C4—524no—
850C4⋊C4—524no—
851C4⋊C4—524no—
852C4⋊C4—524no—
853C4⋊C4C22×#26114yescomplemented
854C4⋊C4C22×#26114yescomplemented
855C22⋊C4—134no—
856C22⋊C4—134no—
857C22⋊C4—134no—
858C22⋊C4—134no—
859C22⋊C4—134no—
860C22⋊C4—134no—
861C22⋊C4—134no—
862C22⋊C4—134no—
863C22⋊C4—134no—
864C22⋊C4—268no—
865C22⋊C4—268no—
866C22⋊C4—268no—
867C22⋊C4—524no—
868C22⋊C4—524no—
869C22⋊C4—524no—
870C22⋊C4—524no—
871C22⋊C4C22×#26114yes—
872C22⋊C4C22×#26114yes—
873C22⋊C4C22×#26114yescomplemented
874C42—268no—
875C42—524no—
876C42—524no—
877C42—524no—
878C42—524no—
879C13C2×#233511yescharacteristic, complemented, Sylow
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—132no—
887C23—132no—
888C23—132no—
889C23—132no—
890C23—132no—
891C23—132no—
892C23—131no—
893C23—131no—
894C23—132no—
895C23—132no—
896C23—262no—
897C23—262no—
898C23—262no—
899C23—262no—
900C23—262no—
901C23—262no—
902C23—262no—
903C23—264no—
904C23—262no—
905C23—262no—
906C23—262no—
907C23—264no—
908C23—264no—
909C23—264no—
910C23—264no—
911C23—264no—
912C23—262no—
913C23—262no—
914C23—262no—
915C23—262no—
916C23—262no—
917C23—262no—
918C23—262no—
919C23—262no—
920C23—524no—
921C23—524no—
922C23—524no—
923C23—524no—
924C23—524no—
925C23—524no—
926C23—524no—
927C23—524no—
928C23C23×#26112yes—
929C23C23×#26112yes—
930C23C23×#26111yescharacteristic
931D4—44no—
932D4—524no—
933D4—524no—
934D4—524no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—44no—
941C2×C4—134no—
942C2×C4—134no—
943C2×C4—132no—
944C2×C4—132no—
945C2×C4—132no—
946C2×C4—132no—
947C2×C4—132no—
948C2×C4—262no—
949C2×C4—262no—
950C2×C4—262no—
951C2×C4—262no—
952C2×C4—262no—
953C2×C4—262no—
954C2×C4—262no—
955C2×C4—262no—
956C2×C4—262no—
957C2×C4—264no—
958C2×C4—264no—
959C2×C4—262no—
960C2×C4—264no—
961C2×C4—264no—
962C2×C4—264no—
963C2×C4—262no—
964C2×C4—262no—
965C2×C4—262no—
966C2×C4—268no—
967C2×C4—262no—
968C2×C4—268no—
969C2×C4—262no—
970C2×C4—262no—
971C2×C4—262no—
972C2×C4—262no—
973C2×C4—262no—
974C2×C4—262no—
975C2×C4—262no—
976C2×C4—262no—
977C2×C4—262no—
978C2×C4—262no—
979C2×C4—262no—
980C2×C4—262no—
981C2×C4—262no—
982C2×C4—262no—
983C2×C4—262no—
984C2×C4—262no—
985C2×C4—262no—
986C2×C4—262no—
987C2×C4—262no—
988C2×C4—262no—
989C2×C4—262no—
990C2×C4—262no—
991C2×C4—262no—
992C2×C4—524no—
993C2×C4—524no—
994C2×C4—524no—
995C2×C4—5216no—
996C2×C4—524no—
997C2×C4—524no—
998C2×C4—524no—
999C2×C4—524no—
1000C2×C4—524no—
1001C2×C4—524no—
1002C2×C4C23×#26112yes—
1003C2×C4C23×#26112yes—
1004C2×C4C23×#26112yes—
1005C2×C4C23×#26112yes—
1006C2×C4C23×#26112yes—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—22no—
1011C22—22no—
1012C22—22no—
1013C22—44no—
1014C22—44no—
1015C22—132no—
1016C22—131no—
1017C22—131no—
1018C22—132no—
1019C22—131no—
1020C22—131no—
1021C22—132no—
1022C22—131no—
1023C22—131no—
1024C22—134no—
1025C22—134no—
1026C22—134no—
1027C22—134no—
1028C22—262no—
1029C22—262no—
1030C22—262no—
1031C22—262no—
1032C22—262no—
1033C22—262no—
1034C22—522no—
1035C22—522no—
1036C22—522no—
1037C22—522no—
1038C22—522no—
1039C22—522no—
1040C22—522no—
1041C22—522no—
1042C22—528no—
1043C22—528no—
1044C22—524no—
1045C22—524no—
1046C22#1171962312yes—
1047C22#41×#26112yes—
1048C22#1171963112yes—
1049C22C24×#26111yescharacteristic
1050C4—22no—
1051C4—22no—
1052C4—22no—
1053C4—22no—
1054C4—22no—
1055C4—264no—
1056C4—264no—
1057C4—262no—
1058C4—262no—
1059C4—262no—
1060C4—262no—
1061C4—262no—
1062C4—522no—
1063C4—522no—
1064C4—522no—
1065C4—522no—
1066C4—522no—
1067C4—522no—
1068C2—42no—
1069C2—42no—
1070C2—131no—
1071C2—131no—
1072C2—131no—
1073C2—131no—
1074C2—134no—
1075C2—522no—
1076C2—522no—
1077C2#1313133514yesdirect product factor
1078C2C2×#41×#26111yescharacteristic
1079C2C2×#1171962311yescharacteristic
1080C2C2×#1171963111yescharacteristic
subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C13×#123C4
socleC23×C13C23×C4
prime radicalC22×D4×D13C22
cosocleC22×D13C25
hypercenterC2×#123#261
hypocenterC13C2×#2335
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #13131335C2direct (N × H)
3. C2×#11719083C2semidirect
4. C2×#11719071C2semidirect
5. C2×#11719071C2semidirect
6. C2×#11719071C2semidirect
7. C2×#11719071C2semidirect
8. C2×#11719082C2semidirect
9. C2×#11719082C2semidirect
11. C2×#11719070C2semidirect
12. C2×#11719136C2semidirect
13. C2×C4⋊C4×#261C2semidirect
14. C2×C22⋊C4×#261C2semidirect
15. C2×C4×C22⋊#261C2semidirect
37. C2×C13×#123C4semidirect
38. C2×#88189C4semidirect
39. C2×#88183C4semidirect
40. D13×#123C4semidirect
42. C2×#88148C4semidirect
43. C2×#88148C4semidirect
46. C2×#88140C4semidirect
47. C2×#88137C4semidirect
48. C2×#88137C4semidirect
54. #11719136C22semidirect
55. C4×C22⋊#261C22semidirect
66. #11719083C22semidirect
67. #11719082C22semidirect
68. #11719082C22semidirect
69. C4⋊C4×#261C22semidirect
70. #11719071C22semidirect
71. #11719071C22semidirect
72. #11719071C22semidirect
73. #11719071C22semidirect
74. #11719070C22semidirect
75. C22⋊C4×#261C22semidirect
91. C23×C4×C13C2×C4semidirect
94. C23×Dic13C2×C4semidirect
102. C22×C4×D13C2×C4semidirect
103. C22×C4×D13C2×C4semidirect
104. C22×C4×D13C2×C4semidirect
145. C13×#123C2×C4semidirect
146. C2×C13×C4⋊C4C2×C4semidirect
147. C2×C13×C4⋊C4C2×C4semidirect
150. C2×C13×C22⋊C4C2×C4semidirect
153. C2×C22⋊Dic13C2×C4semidirect
154. #88189C2×C4semidirect
155. #88183C2×C4semidirect
160. C2×#6103C2×C4semidirect
161. C2×#6103C2×C4semidirect
162. C2×C4⋊Dic13C2×C4semidirect
163. C2×C4⋊Dic13C2×C4semidirect
164. C2×#6101C2×C4semidirect
165. C2×#6101C2×C4semidirect
166. C2×#6101C2×C4semidirect
167. C2×#6101C2×C4semidirect
168. #88148C2×C4semidirect
169. #88148C2×C4semidirect
170. C4⋊C4×D13C2×C4semidirect
171. C4⋊C4×D13C2×C4semidirect
174. #88140C2×C4semidirect
175. #88137C2×C4semidirect
176. #88137C2×C4semidirect
179. C22⋊C4×D13C2×C4semidirect
259. C22×C4×C13C22×C4semidirect
270. C22×Dic13C22×C4semidirect
296. C2×C4×D13C22×C4semidirect
297. C2×C4×D13C22×C4semidirect
320. C13×C4⋊C4C22×C4semidirect
321. C13×C4⋊C4C22×C4semidirect
324. C13×C22⋊C4C22×C4semidirect
327. C22⋊Dic13C22×C4semidirect
332. #6103C22×C4semidirect
333. #6103C22×C4semidirect
334. C4⋊Dic13C22×C4semidirect
335. C4⋊Dic13C22×C4semidirect
336. #6101C22×C4semidirect
337. #6101C22×C4semidirect
338. #6101C22×C4semidirect
339. #6101C22×C4semidirect
495. C2×#123#261semidirect
637. C23×C4C2×#261semidirect
645. #123C2×#261semidirect
666. C2×C4⋊C4C2×#261semidirect
667. C2×C4⋊C4C2×#261semidirect
699. C2×C22⋊C4C2×#261semidirect
722. C2×C13#2335semidirect
728. D13#2335semidirect
841. C22×C4C22×#261semidirect
853. C4⋊C4C22×#261semidirect
854. C4⋊C4C22×#261semidirect
873. C22⋊C4C22×#261semidirect
879. C13C2×#2335semidirect
1077. C2#13131335direct (N × H)

Maximal subgroups

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

subgroupindex
#131313352
C2×#117191512
C2×#117190832
C2×#117190712
C2×#117190822
C2×#117191502
C2×#117190702
C2×#117191362
C2×C4⋊C4×#2612
C2×C22⋊C4×#2612
C2×C4×C22⋊#2612
C2×D13×#1232
C2×#233513