Finite Group Databasebeta

← #14914767

Subgroups — #14914767

Order 2816.

2426 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623054C211yesmaximal, characteristic
2#13071550C214yesmaximal, complemented
3#13071539C214yesmaximal, complemented
4#13071505C212yesmaximal, complemented
5#13071497C212yesmaximal, complemented
6#13071489C212yesmaximal, complemented
7#13071481C212yesmaximal, complemented
8#13071268C212yesmaximal, complemented
9#13071260C212yesmaximal, complemented
10#13071232C211yesmaximal, characteristic, complemented
11#13071204C211yesmaximal, characteristic
12#13071106C211yesmaximal, characteristic
13#13071093C212yesmaximal, complemented
14#13071080C212yesmaximal, complemented
15C2×#10622541C211yesmaximal, characteristic, complemented
16#13070972C211yesmaximal, characteristic, complemented
17C4×C11×#117C211yesmaximal, characteristic, complemented
18C22×#4339C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26#10623054C4116yescomplemented
27C2×#66945C2212yes—
28C2×C4⋊C4×D11C2212yes—
29C2×(C22⋊D11)⋊C4C2214yes—
30C2×C4×D44C2212yes—
31C2×#66925C2214yes—
32C2×C4×Dic22C2212yes—
33C4×C11×C4⋊C4C2211yescharacteristic
34C4×C11×C4⋊C4C2211yescharacteristic
35C4×C11×C4⋊C4C2211yescharacteristic
36C4×C11×C4⋊C4C2211yescharacteristic
37C4×C11×C22⋊C4C2212yes—
38C4×C11×C22⋊C4C2212yes—
39C11×#376C2212yes—
40C43×C11C2212yes—
41#10622826C2212yes—
42#10622826C2212yes—
43C2×C11⋊#95C2212yes—
44#10622600C2212yes—
45#10622600C2212yes—
46C4⋊C4×Dic11C2212yes—
47C4⋊C4×Dic11C2212yes—
48#10622586C2212yes—
49#10622586C2212yes—
50#10622571C2214yes—
51#10622555C2214yes—
52C22⋊C4×Dic11C2214yes—
53#10622553C2214yes—
54#10622553C2214yes—
55#10622552C2211yescharacteristic
56#10622552C2211yescharacteristic
57#10622552C2212yes—
58C4×(C2×D11)⋊C4C2212yes—
59C4×(C2×D11)⋊C4C2212yes—
60C4×(C2×D11)⋊C4C2214yes—
61C4×C4⋊Dic11C2212yes—
62C4×C4⋊Dic11C2212yes—
63#10622546C2214yes—
64#10622546C2214yes—
65#10622545C2214yes—
66C4×Dic11⋊C4C2214yes—
67#10622542C2211yescharacteristic
68#10622542C2211yescharacteristic
69#10622542C2212yes—
70#10622541C2212yes—
71#10622541C2212yes—
72#10622541C2212yes—
73#10622541C2212yes—
74#10622541C2212yes—
75#10622541C2212yes—
76#10622282C2214yes—
77#10622282C2214yes—
78#10622280C2214yes—
79#10622277C2214yes—
80#10622265C2214yes—
81#10622265C2214yes—
82#10622264C2214yes—
83#10622263C2214yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11C2312yes—
88C23×Dic11C2312yes—
89C23×Dic11C2312yes—
90C2×#4339—24no—
91C2×#4339—24no—
92C2×#4339C2×C418yes—
93C22×D44C2311yescharacteristic
94C22×C4×D11C2312yes—
95C22×C4×D11C2314yes—
96C22×Dic22C2311yescharacteristic
97C11×#117—24no—
98C11×#117C2×C418yes—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C22⋊C4C2312yes—
104C2×C11×C22⋊C4C2312yes—
105C2×C42×C11—24no—
106C2×C42×C11C2312yes—
107C2×C42×C11C2311yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2312yes—
110C2×C42×C11C2311yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2312yes—
113C2×C42×C11C2312yes—
114C2×C42×C11C2312yes—
115C2×C42×C11C2312yes—
116C2×C22⋊Dic11C2312yes—
117C2×(C2×D11)⋊C4C2312yes—
118C2×(C2×D11)⋊C4C2312yes—
119C2×(C2×D11)⋊C4C2314yes—
120C2×(C2×D11)⋊C4C2312yes—
121C2×(C2×D11)⋊C4C2312yes—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2314yes—
124#66979—24no—
125C2×C4⋊Dic11—24no—
126C2×C4⋊Dic11C2×C418yes—
127C2×C4⋊Dic11C2312yes—
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2312yes—
131C2×C4⋊Dic11C2312yes—
132C2×C4⋊Dic11C2312yes—
133C2×Dic11⋊C4—44no—
134C2×Dic11⋊C4C2314yes—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×C4×Dic11C2312yes—
140C2×C4×Dic11C2314yes—
141C2×C4×Dic11C2314yes—
142C2×C4×Dic11C2314yes—
143#66945C2×C4116yescomplemented
144C4⋊C4×D11C2×C4116yescomplemented
145(C22⋊D11)⋊C4C2×C4132yes—
146C4×D44C2×C4116yescomplemented
147#66925—48no—
148C4×Dic22C2×C4116yescomplemented
149C11×#95C2312yes—
150C11×#95C2312yes—
151C11×#95C2312yes—
152C11×#95C2312yes—
153C11⋊#95C2312yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2312yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2312yes—
164C11⋊#95C2312yes—
165#34253—111nomaximal, Sylow
166C24×C11C2411yescharacteristic
167C23×D11C2412yes—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—41no—
173C22×C4×C11—41no—
174C22×C4×C11C22×C414yes—
175C22×C4×C11#4114yes—
176C22×C4×C11#4114yes—
177C22×C4×C11C2411yescharacteristic
178C22×C4×C11C2412yes—
179C22×C4×C11C2412yes—
180C22×C4×C11C2411yescharacteristic
181C22×C4×C11C2412yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2411yescharacteristic
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C2×C22⋊D11—24no—
188C2×C22⋊D11—24no—
189C2×C22⋊D11C22×C418yes—
190C22×Dic11—24no—
191C22×Dic11—42no—
192C22×Dic11—42no—
193C22×Dic11—42no—
194C22×Dic11—42no—
195C22×Dic11C22×C418yes—
196C22×Dic11C2412yes—
197C22×Dic11C2412yes—
198C22×Dic11C2414yes—
199C22×Dic11C2412yes—
200C22×Dic11C2414yes—
201#4339—232no—
202C2×D44—22no—
203C2×D44—22no—
204C2×D44C22×C414yes—
205C2×C4×D11—24no—
206C2×C4×D11—24no—
207C2×C4×D11—44no—
208C2×C4×D11—44no—
209C2×C4×D11C22×C418yes—
210C2×C4×D11C22×C4116yes—
211C2×Dic22—22no—
212C2×Dic22—22no—
213C2×Dic22C22×C414yes—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4C22×C414yes—
217C11×C4⋊C4C22×C414yes—
218C11×C22⋊C4—24no—
219C11×C22⋊C4C22×C418yes—
220C42×C11—22no—
221C42×C11—22no—
222C42×C11—22no—
223C42×C11—22no—
224C42×C11—24no—
225C42×C11—24no—
226C42×C11—24no—
227C42×C11—42no—
228C42×C11—42no—
229C42×C11C22×C418yes—
230C22⋊Dic11—24no—
231(C2×D11)⋊C4—24no—
232(C2×D11)⋊C4—24no—
233(C2×D11)⋊C4—44no—
234(C2×D11)⋊C4—44no—
235(C2×D11)⋊C4—42no—
236(C2×D11)⋊C4—42no—
237(C2×D11)⋊C4C22×C4116yes—
238C4⋊Dic11—24no—
239C4⋊Dic11—24no—
240C4⋊Dic11—22no—
241C4⋊Dic11—22no—
242C4⋊Dic11C22×C418yes—
243C4⋊Dic11C22×C418yes—
244Dic11⋊C4—28no—
245Dic11⋊C4—44no—
246Dic11⋊C4—44no—
247Dic11⋊C4—44no—
248Dic11⋊C4C22×C4116yes—
249C4×Dic11—24no—
250C4×Dic11—44no—
251C4×Dic11—44no—
252C4×Dic11C22×C4116yes—
253C2×#520—111no—
254#2353—114no—
255#2352—114no—
256#2347—112no—
257#2346—112no—
258#2345—112no—
259#2344—112no—
260#2320—112no—
261#2319—112no—
262#2316—111no—
263#2311—111no—
264#2297—111no—
265#2295—112no—
266#2293—112no—
267C2×#389—111no—
268#2274—111no—
269C4×#117D1111yescharacteristic, complemented
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11C23×C412yes—
275C23×C11C2×#4112yes—
276C23×C11C2×#4112yes—
277C23×C11C2511yescharacteristic
278C22×D11—22no—
279C22×D11—22no—
280C22×D11—22no—
281C22×D11—22no—
282C22×D11—22no—
283C22×D11—22no—
284C22×D11C23×C414yes—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—22no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—21no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—44no—
306C2×C4×C11—44no—
307C2×C4×C11#117116yescomplemented
308C2×C4×C11C23×C414yes—
309C2×C4×C11C23×C414yes—
310C2×C4×C11C23×C412yes—
311C2×C4×C11C23×C412yes—
312C2×C4×C11C2×#4112yes—
313C2×C4×C11C2×#4112yes—
314C2×C4×C11C2×#4112yes—
315C2×C4×C11C2×#4112yes—
316C2×C4×C11H(5,𝔽2)12yes—
317C2×C4×C112−1+412yes—
318C22⋊D11—216no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—24no—
326C2×Dic11—22no—
327C2×Dic11—24no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—24no—
331C2×Dic11—22no—
332C2×Dic11—48no—
333C2×Dic11—84no—
334C2×Dic11C23×C414yes—
335C2×Dic11C23×C418yes—
336D44—28no—
337C4×D11—216no—
338C4×D11—416no—
339Dic22—28no—
340C22×#41—111no—
341#520—1116no—
342C2×C4×Q8—112no—
343C2×C4×D4—114no—
344C2×C4×D4—112no—
345C2×#117—111no—
346C2×#117—112no—
347C2×#117—114no—
348C2×#117C2×D1111yescharacteristic
349C2×#117C2×D1111yescharacteristic
350C22×C4⋊C4—111no—
351C22×C4⋊C4—112no—
352C22×C4⋊C4—111no—
353C22×C4⋊C4—112no—
354C22×C42C2×D1111yescharacteristic
355#391—112no—
356#391—111no—
357#391—111no—
358#390—112no—
359#390—111no—
360#390—111no—
361#389—112no—
362#389—112no—
363#389—112no—
364#389—112no—
365#389—112no—
366#389—112no—
367#389—112no—
368#389—112no—
369#388—114no—
370#388—114no—
371#388—114no—
372#388—114no—
373#387—114no—
374#387—114no—
375#387—114no—
376#387—114no—
377#386—112no—
378#386—112no—
379#386—114no—
380#383—114no—
381#382—114no—
382#381—114no—
383#380—112no—
384#380—112no—
385#380—114no—
386#380—114no—
387C4×C4⋊C4—112no—
388C4×C4⋊C4—112no—
389C4×C4⋊C4—112no—
390C4×C4⋊C4—112no—
391C4×C4⋊C4—114no—
392C4×C4⋊C4C2×D1111yescharacteristic
393C4×C4⋊C4C2×D1111yescharacteristic
394C4×C4⋊C4C2×D1111yescharacteristic
395C4×C4⋊C4C2×D1111yescharacteristic
396C4×C22⋊C4—114no—
397C4×C22⋊C4—112no—
398C4×C22⋊C4—112no—
399C4×C22⋊C4—114no—
400C4×C22⋊C4C2×D1112yes—
401C4×C22⋊C4C2×D1112yes—
402#376—114no—
403#376C2×D1112yes—
404C2×#95—112no—
405C43C2×D1112yes—
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11C2×#11714yes—
413C22×C11C24×C411yescharacteristic
414C22×C11C22×#4111yescharacteristic
415C22×C11C22×#4111yescharacteristic
416C22×C11C2×H(5,𝔽2)11yescharacteristic
417C22×C11C2×2−1+411yescharacteristic
418C22×C11#58511yescharacteristic
419C22×C11#58511yescharacteristic
420C2×D11—24no—
421C2×D11—24no—
422C2×D11—24no—
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—42no—
427C4×C11—24no—
428C4×C11—24no—
429C4×C11—22no—
430C4×C11—22no—
431C4×C11—41no—
432C4×C11—41no—
433C4×C11—42no—
434C4×C11—42no—
435C4×C11C2×#11714yes—
436C4×C11C2×#11714yes—
437Dic11—24no—
438Dic11—28no—
439Dic11—44no—
440Dic11—42no—
441Dic11—42no—
442C2×#41—118no—
443C2×#41—224no—
444C2×#41—224no—
445C22×Q8—111no—
446C22×D4—112no—
447C22×D4—111no—
448C23×C4—112no—
449C23×C4—112no—
450C23×C4—114no—
451C23×C4—112no—
452C23×C4C22×D1111yescharacteristic
453C23×C4C22×D1111yescharacteristic
454C23×C4C22×D1111yescharacteristic
455C4×Q8—1116no—
456C4×D4—1132no—
457C4×D4—1116no—
458#117—24no—
459#117—1116no—
460#117—224no—
461#117—448no—
462#117C4×D1118yes—
463C2×C4⋊C4—118no—
464C2×C4⋊C4—112no—
465C2×C4⋊C4—114no—
466C2×C4⋊C4—112no—
467C2×C4⋊C4—1116no—
468C2×C4⋊C4—114no—
469C2×C4⋊C4—112no—
470C2×C4⋊C4—112no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—111no—
473C2×C4⋊C4—114no—
474C2×C4⋊C4—114no—
475C2×C4⋊C4—114no—
476C2×C4⋊C4—224no—
477C2×C4⋊C4—444no—
478C2×C4⋊C4C22×D1111yescharacteristic
479C2×C4⋊C4C22×D1111yescharacteristic
480C2×C4⋊C4C22×D1111yescharacteristic
481C2×C4⋊C4C22×D1111yescharacteristic
482C2×C22⋊C4—114no—
483C2×C22⋊C4—112no—
484C2×C22⋊C4—112no—
485C2×C22⋊C4—112no—
486C2×C22⋊C4—114no—
487C2×C22⋊C4—112no—
488C2×C22⋊C4—114no—
489C2×C22⋊C4—112no—
490C2×C22⋊C4C22×D1112yes—
491C2×C22⋊C4C22×D1112yes—
492C2×C42—24no—
493C2×C42—114no—
494C2×C42—112no—
495C2×C42—114no—
496C2×C42—114no—
497C2×C42C22×D1112yes—
498C2×C42C22×D1112yes—
499C2×C42C22×D1111yescharacteristic
500C2×C42C22×D1112yes—
501C2×C42C22×D1111yescharacteristic
502C2×C42C22×D1111yescharacteristic
503C2×C42C22×D1111yescharacteristic
504C2×C42C22×D1112yes—
505C2×C42C22×D1112yes—
506C2×C42C22×D1112yes—
507#95—114no—
508#95—114no—
509#95—112no—
510#95—114no—
511#95—114no—
512#95—114no—
513#95—114no—
514#95—112no—
515#95—114no—
516#95—112no—
517#95—112no—
518#95—114no—
519#95C22×D1112yes—
520#95C22×D1112yes—
521#95C22×D1112yes—
522#95C22×D1112yes—
523C2×C11—24no—
524C2×C11C22×#11711yescharacteristic
525C2×C11C4×H(5,𝔽2)11yescharacteristic
526C2×C11C4×2−1+411yescharacteristic
527C2×C11#349411yescharacteristic
528C2×C11#349511yescharacteristic
529C2×C11#351111yescharacteristic
530C2×C11#351211yescharacteristic
531D11—44no—
532C24—112no—
533C24C23×D1111yescharacteristic
534#41—2232no—
535C2×Q8—114no—
536C2×Q8—222no—
537C2×Q8—222no—
538C2×D4—118no—
539C2×D4—114no—
540C2×D4—224no—
541C2×D4—224no—
542C2×D4—222no—
543C2×D4—222no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—112no—
551C22×C4—114no—
552C22×C4—118no—
553C22×C4—118no—
554C22×C4—1116no—
555C22×C4—112no—
556C22×C4—112no—
557C22×C4—114no—
558C22×C4—224no—
559C22×C4—224no—
560C22×C4—224no—
561C22×C4—444no—
562C22×C4—444no—
563C22×C4—442no—
564C22×C4—442no—
565C22×C4—442no—
566C22×C4—442no—
567C22×C4C2×C4×D1114yes—
568C22×C4#433914yes—
569C22×C4#433914yes—
570C22×C4C23×D1111yescharacteristic
571C22×C4C23×D1112yes—
572C22×C4C23×D1112yes—
573C22×C4C23×D1111yescharacteristic
574C22×C4C23×D1112yes—
575C22×C4C23×D1112yes—
576C22×C4C23×D1111yescharacteristic
577C22×C4C23×D1111yescharacteristic
578C22×C4C23×D1111yescharacteristic
579C22×C4C23×D1111yescharacteristic
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—118no—
583C4⋊C4—1116no—
584C4⋊C4—118no—
585C4⋊C4—224no—
586C4⋊C4—224no—
587C4⋊C4—222no—
588C4⋊C4—222no—
589C4⋊C4—228no—
590C4⋊C4—444no—
591C4⋊C4—444no—
592C4⋊C4—444no—
593C4⋊C4C2×C4×D1114yes—
594C4⋊C4C2×C4×D1114yes—
595C22⋊C4—24no—
596C22⋊C4—1116no—
597C22⋊C4—224no—
598C22⋊C4—224no—
599C22⋊C4—224no—
600C22⋊C4—444no—
601C22⋊C4—444no—
602C22⋊C4—442no—
603C22⋊C4—442no—
604C22⋊C4C2×C4×D1118yes—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—24no—
610C42—24no—
611C42—24no—
612C42—42no—
613C42—42no—
614C42—1116no—
615C42—224no—
616C42—444no—
617C42—444no—
618C42C2×C4×D1118yes—
619C11#3425311yescharacteristic, complemented, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—114no—
625C23—222no—
626C23—222no—
627C23—222no—
628C23—222no—
629C23—222no—
630C23—222no—
631C23C22×C4×D1112yes—
632C23C2×#433912yes—
633C23C2×#433912yes—
634C23C24×D1111yescharacteristic
635Q8—228no—
636D4—2216no—
637D4—228no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—114no—
661C2×C4—118no—
662C2×C4—222no—
663C2×C4—222no—
664C2×C4—224no—
665C2×C4—224no—
666C2×C4—2216no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—224no—
670C2×C4—222no—
671C2×C4—224no—
672C2×C4—222no—
673C2×C4—222no—
674C2×C4—224no—
675C2×C4—222no—
676C2×C4—4416no—
677C2×C4—448no—
678C2×C4—884no—
679C2×C4#66925116yescomplemented
680C2×C4C22×C4×D1114yes—
681C2×C4C22×C4×D1114yes—
682C2×C4C22×C4×D1112yes—
683C2×C4C22×C4×D1112yes—
684C2×C4C2×#433912yes—
685C2×C4C2×#433912yes—
686C2×C4C2×#433912yes—
687C2×C4C2×#433912yes—
688C2×C4#6704212yes—
689C2×C4#6704312yes—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—224no—
697C22—224no—
698C22—224no—
699C22—442no—
700C22—442no—
701C22—442no—
702C22—442no—
703C22C2×#6692514yes—
704C22C23×C4×D1111yescharacteristic
705C22C22×#433911yescharacteristic
706C22C22×#433911yescharacteristic
707C22C2×#6704211yescharacteristic
708C22C2×#6704311yescharacteristic
709C22#1062345311yescharacteristic
710C22#1062345311yescharacteristic
711C4—22no—
712C4—24no—
713C4—24no—
714C4—22no—
715C4—41no—
716C4—42no—
717C4—42no—
718C4—41no—
719C4—224no—
720C4—228no—
721C4—442no—
722C4—442no—
723C4—444no—
724C4C2×#6692514yes—
725C4C2×#6692514yes—
726C2—24no—
727C2—444no—
728C2C22×#6692511yescharacteristic
729C2C4×#6704211yescharacteristic
730C2C4×#6704311yescharacteristic
731C2#1308235111yescharacteristic
732C2#1308236811yescharacteristic
733C2#1308252711yescharacteristic
734C2#1308253811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC4×C11×#117C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenterC4×#117D11
hypocenterC11#34253
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
2. #13071550C2semidirect
3. #13071539C2semidirect
4. #13071505C2semidirect
5. #13071497C2semidirect
6. #13071489C2semidirect
7. #13071481C2semidirect
8. #13071268C2semidirect
9. #13071260C2semidirect
10. #13071232C2semidirect
13. #13071093C2semidirect
14. #13071080C2semidirect
15. C2×#10622541C2semidirect
16. #13070972C2semidirect
17. C4×C11×#117C2semidirect
26. #10623054C4semidirect
143. #66945C2×C4semidirect
144. C4⋊C4×D11C2×C4semidirect
146. C4×D44C2×C4semidirect
148. C4×Dic22C2×C4semidirect
269. C4×#117D11semidirect
307. C2×C4×C11#117semidirect
619. C11#34253semidirect
679. C2×C4#66925semidirect

Maximal subgroups

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

subgroupindex
C2×#106230542
#130715502
#130715392
#130715052
#130714972
#130714892
#130714812
#130712682
#130712602
#130712322
#130712042
#130711062
#130710932
#130710802
C2×#106225412
#130709722
C4×C11×#1172
#3425311