Finite Group Databasebeta

← #14914748

Subgroups — #14914748

Order 2816.

2442 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×#10623035C211yesmaximal, characteristic
2#13071585C212yesmaximal, complemented
3#13071577C212yesmaximal, complemented
4#13071569C212yesmaximal, complemented
5#13071561C212yesmaximal, complemented
6#13071505C212yesmaximal, complemented
7#13071497C212yesmaximal, complemented
8#13071489C212yesmaximal, complemented
9#13071481C212yesmaximal, complemented
10#13071250C214yesmaximal, complemented
11#13071240C211yesmaximal, characteristic, complemented
12#13071209C211yesmaximal, characteristic
13#13071106C211yesmaximal, characteristic
14#13071099C211yesmaximal, characteristic, complemented
15#13071059C214yesmaximal, complemented
16#13070973C211yesmaximal, characteristic, complemented
17C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
18C22×#4339C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×C42×C11C2212yes—
23C2×C4×C22⋊D11C2214yes—
24C2×#66979C2211yescharacteristic
25C2×#66979C2211yescharacteristic
26C2×#66979C2211yescharacteristic
27#10623035C4116yescomplemented
28C2×#66946C2212yes—
29C2×#66945C2212yes—
30C2×C4⋊C4×D11C2212yes—
31C2×#66940C2212yes—
32C2×#66925C2214yes—
33C4×C11×C4⋊C4C2212yes—
34C4×C11×C4⋊C4C2212yes—
35C4×C11×C4⋊C4C2212yes—
36C4×C11×C4⋊C4C2212yes—
37C2×C11×#95C2212yes—
38#10622826C2212yes—
39#10622826C2212yes—
40#10622826C2214yes—
41#10622823C2214yes—
42#10622823C2212yes—
43#10622823C2212yes—
44C4×C22⋊Dic11C2214yes—
45#10622601C2212yes—
46#10622600C2212yes—
47#10622600C2212yes—
48#10622590C2212yes—
49#10622589C2212yes—
50C4⋊C4×Dic11C2212yes—
51C4⋊C4×Dic11C2212yes—
52C4⋊C4×Dic11C2212yes—
53C4⋊C4×Dic11C2212yes—
54#10622587C2212yes—
55#10622586C2212yes—
56#10622586C2212yes—
57#10622553C2214yes—
58#10622553C2214yes—
59#10622552C2211yescharacteristic
60#10622552C2211yescharacteristic
61C4×(C2×D11)⋊C4C2212yes—
62C4×(C2×D11)⋊C4C2212yes—
63C4×(C2×D11)⋊C4C2214yes—
64#10622546C2214yes—
65#10622546C2214yes—
66#10622545C2214yes—
67C4×Dic11⋊C4C2214yes—
68C4×Dic11⋊C4C2212yes—
69C4×Dic11⋊C4C2212yes—
70#10622542C2211yescharacteristic
71#10622542C2211yescharacteristic
72#10622541C2211yescharacteristic
73#10622541C2211yescharacteristic
74#10622541C2211yescharacteristic
75#10622541C2211yescharacteristic
76#10622282C2214yes—
77#10622282C2214yes—
78#10622280C2214yes—
79#10622277C2214yes—
80#10622265C2214yes—
81#10622265C2214yes—
82#10622264C2214yes—
83#10622263C2214yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2312yes—
87C23×C4×C11C2312yes—
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11C2312yes—
90C2×#4339—24no—
91C2×#4339—24no—
92C2×#4339C2×C418yes—
93C22×D44C2311yescharacteristic
94C22×C4×D11C2312yes—
95C22×C4×D11C2314yes—
96C22×Dic22C2311yescharacteristic
97C2×C11×C4⋊C4—24no—
98C2×C11×C4⋊C4C2×C418yes—
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C4⋊C4C2312yes—
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C4⋊C4C2312yes—
103C2×C42×C11—24no—
104C2×C42×C11—44no—
105C2×C42×C11C2314yes—
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2314yes—
111C2×C22⋊Dic11C2312yes—
112C2×C22⋊Dic11C2312yes—
113C2×C22⋊Dic11C2312yes—
114C4×C22⋊D11C2×C4132yes—
115C2×(C2×D11)⋊C4C2312yes—
116C2×(C2×D11)⋊C4C2312yes—
117C2×(C2×D11)⋊C4C2314yes—
118C2×(C2×D11)⋊C4C2312yes—
119C2×(C2×D11)⋊C4C2312yes—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122#66979—24no—
123#66979—24no—
124#66979C2×C418yes—
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×Dic11⋊C4C2312yes—
132C2×Dic11⋊C4C2312yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2312yes—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2312yes—
137C2×Dic11⋊C4C2314yes—
138C2×C4×Dic11C2312yes—
139C2×C4×Dic11C2312yes—
140C2×C4×Dic11C2314yes—
141C2×C4×Dic11C2314yes—
142C2×C4×Dic11C2314yes—
143C2×C4×Dic11C2312yes—
144#66946C2×C4116yescomplemented
145#66945C2×C4116yescomplemented
146C4⋊C4×D11C2×C4116yescomplemented
147#66940C2×C4116yescomplemented
148#66925—48no—
149C11×#95C2314yes—
150C11×#95C2314yes—
151C11⋊#95C2312yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2312yes—
155C11⋊#95C2312yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2312yes—
160C11⋊#95C2314yes—
161C11⋊#95C2312yes—
162C11⋊#95C2312yes—
163C11⋊#95C2312yes—
164C11⋊#95C2312yes—
165#34252—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—24no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—41no—
177C22×C4×C11—41no—
178C22×C4×C11—42no—
179C22×C4×C11C22×C418yes—
180C22×C4×C11C22×C414yes—
181C22×C4×C11#4114yes—
182C22×C4×C11#4114yes—
183C22×C4×C11C2411yescharacteristic
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2414yes—
186C22×C4×C11C2414yes—
187C22×C4×C11C2411yescharacteristic
188C22×C4×C11C2411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C22×C4×C11C2411yescharacteristic
191C2×C22⋊D11—24no—
192C2×C22⋊D11—24no—
193C2×C22⋊D11C22×C418yes—
194C22×Dic11C2412yes—
195C22×Dic11C2412yes—
196C22×Dic11C2412yes—
197C22×Dic11C2412yes—
198C22×Dic11C2412yes—
199C22×Dic11C2412yes—
200C22×Dic11C2412yes—
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—24no—
215C11×C4⋊C4—24no—
216C11×C4⋊C4C22×C418yes—
217C11×C4⋊C4C22×C418yes—
218C42×C11—22no—
219C42×C11—22no—
220C42×C11—22no—
221C42×C11—22no—
222C42×C11—28no—
223C42×C11—44no—
224C22⋊Dic11—24no—
225C22⋊Dic11—24no—
226C22⋊Dic11C22×C418yes—
227(C2×D11)⋊C4—24no—
228(C2×D11)⋊C4—24no—
229(C2×D11)⋊C4—44no—
230(C2×D11)⋊C4—44no—
231(C2×D11)⋊C4—42no—
232(C2×D11)⋊C4—42no—
233(C2×D11)⋊C4C22×C4116yes—
234C4⋊Dic11—22no—
235C4⋊Dic11—22no—
236C4⋊Dic11—22no—
237C4⋊Dic11—22no—
238C4⋊Dic11C22×C414yes—
239C4⋊Dic11C22×C414yes—
240Dic11⋊C4—24no—
241Dic11⋊C4—24no—
242Dic11⋊C4—44no—
243Dic11⋊C4—42no—
244Dic11⋊C4—42no—
245Dic11⋊C4—44no—
246Dic11⋊C4C22×C4116yes—
247C4×Dic11—24no—
248C4×Dic11—24no—
249C4×Dic11—44no—
250C4×Dic11—44no—
251C4×Dic11C22×C4116yes—
252C4×Dic11C22×C418yes—
253C2×#520—111no—
254#2357—112no—
255#2356—112no—
256#2355—112no—
257#2354—112no—
258#2347—112no—
259#2346—112no—
260#2345—112no—
261#2344—112no—
262#2318—114no—
263#2317—111no—
264#2311—111no—
265#2297—111no—
266#2296—111no—
267#2290—114no—
268#2274—111no—
269C2×C4×C4⋊C4D1111yescharacteristic, 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—28no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—24no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—24no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—24no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—48no—
302C2×C4×C11—44no—
303C2×C4×C11—48no—
304C2×C4×C11#117116yescomplemented
305C2×C4×C11C23×C418yes—
306C2×C4×C11C23×C412yes—
307C2×C4×C11C23×C412yes—
308C2×C4×C11C2×#4112yes—
309C2×C4×C11C2×#4112yes—
310C2×C4×C11C2×#4112yes—
311C2×C4×C11C2×#4112yes—
312C2×C4×C11H(5,𝔽2)12yes—
313C2×C4×C112−1+412yes—
314C22⋊D11—216no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11C23×C414yes—
334C2×Dic11C23×C414yes—
335C2×Dic11C23×C414yes—
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—111no—
347C2×#117—111no—
348C2×#117—112no—
349C2×#117—114no—
350C22×C4⋊C4—112no—
351C22×C4⋊C4C2×D1111yescharacteristic
352C22×C4⋊C4C2×D1111yescharacteristic
353C22×C42C2×D1111yescharacteristic
354C22×C42C2×D1112yes—
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—111no—
364#389—111no—
365#389—111no—
366#389—111no—
367#388—114no—
368#388—114no—
369#388—114no—
370#388—114no—
371#387—114no—
372#387—114no—
373#387—114no—
374#387—114no—
375#386—114no—
376#386—112no—
377#386—112no—
378#385—114no—
379#385—112no—
380#385—112no—
381#384—112no—
382#383—114no—
383#382—112no—
384#382—114no—
385#381—114no—
386#380—112no—
387#380—112no—
388#380—114no—
389C4×C4⋊C4—112no—
390C4×C4⋊C4—112no—
391C4×C4⋊C4—112no—
392C4×C4⋊C4—112no—
393C4×C4⋊C4—114no—
394C4×C4⋊C4—112no—
395C4×C4⋊C4—112no—
396C4×C4⋊C4C2×D1112yes—
397C4×C4⋊C4C2×D1112yes—
398C4×C4⋊C4C2×D1112yes—
399C4×C4⋊C4C2×D1112yes—
400C4×C22⋊C4—114no—
401C4×C22⋊C4—112no—
402C4×C22⋊C4—112no—
403C4×C22⋊C4—114no—
404#376—114no—
405C2×#95C2×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—28no—
428C4×C11—22no—
429C4×C11—22no—
430C4×C11—41no—
431C4×C11—41no—
432C4×C11—44no—
433C4×C11C2×#11714yes—
434C4×C11C2×#11714yes—
435Dic11—24no—
436Dic11—24no—
437Dic11—24no—
438Dic11—42no—
439Dic11—42no—
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—114no—
450C23×C4C22×D1111yescharacteristic
451C23×C4C22×D1112yes—
452C23×C4C22×D1111yescharacteristic
453C23×C4C22×D1112yes—
454C23×C4C22×D1111yescharacteristic
455C4×Q8—1116no—
456C4×D4—1132no—
457C4×D4—1116no—
458#117—118no—
459#117—1116no—
460#117—224no—
461#117—224no—
462#117—448no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—114no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—1116no—
468C2×C4⋊C4—112no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—111no—
473C2×C4⋊C4—112no—
474C2×C4⋊C4—114no—
475C2×C4⋊C4—112no—
476C2×C4⋊C4—112no—
477C2×C4⋊C4—114no—
478C2×C4⋊C4C4×D1118yes—
479C2×C4⋊C4C22×D1112yes—
480C2×C4⋊C4C22×D1112yes—
481C2×C4⋊C4C22×D1112yes—
482C2×C4⋊C4C22×D1112yes—
483C2×C22⋊C4—112no—
484C2×C22⋊C4—114no—
485C2×C22⋊C4—112no—
486C2×C22⋊C4—112no—
487C2×C22⋊C4—112no—
488C2×C22⋊C4—112no—
489C2×C22⋊C4—114no—
490C2×C22⋊C4—114no—
491C2×C22⋊C4—112no—
492C2×C22⋊C4—112no—
493C2×C42—24no—
494C2×C42—44no—
495C2×C42—114no—
496C2×C42—112no—
497C2×C42—112no—
498C2×C42—112no—
499C2×C42—114no—
500C2×C42—114no—
501C2×C42C22×D1114yes—
502C2×C42C22×D1111yescharacteristic
503C2×C42C22×D1111yescharacteristic
504C2×C42C22×D1111yescharacteristic
505C2×C42C22×D1111yescharacteristic
506C2×C42C22×D1114yes—
507#95—112no—
508#95—112no—
509#95—114no—
510#95—114no—
511#95—112no—
512#95—114no—
513#95—114no—
514#95—112no—
515#95—114no—
516#95—112no—
517#95—112no—
518#95—114no—
519#95—112no—
520#95—112no—
521#95C22×D1114yes—
522#95C22×D1114yes—
523C2×C11—24no—
524C2×C11C22×#11711yescharacteristic
525C2×C11C4×H(5,𝔽2)11yescharacteristic
526C2×C11C4×2−1+411yescharacteristic
527C2×C11#349211yescharacteristic
528C2×C11#349311yescharacteristic
529C2×C11#350611yescharacteristic
530C2×C11#350711yescharacteristic
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—24no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—42no—
555C22×C4—112no—
556C22×C4—112no—
557C22×C4—112no—
558C22×C4—118no—
559C22×C4—1116no—
560C22×C4—112no—
561C22×C4—112no—
562C22×C4—112no—
563C22×C4—112no—
564C22×C4—224no—
565C22×C4—224no—
566C22×C4—444no—
567C22×C4—444no—
568C22×C4C2×C4×D1118yes—
569C22×C4C2×C4×D1114yes—
570C22×C4#433914yes—
571C22×C4#433914yes—
572C22×C4C23×D1111yescharacteristic
573C22×C4C23×D1111yescharacteristic
574C22×C4C23×D1114yes—
575C22×C4C23×D1114yes—
576C22×C4C23×D1111yescharacteristic
577C22×C4C23×D1111yescharacteristic
578C22×C4C23×D1111yescharacteristic
579C22×C4C23×D1111yescharacteristic
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—114no—
583C4⋊C4—1116no—
584C4⋊C4—114no—
585C4⋊C4—222no—
586C4⋊C4—222no—
587C4⋊C4—222no—
588C4⋊C4—222no—
589C4⋊C4—224no—
590C4⋊C4—224no—
591C4⋊C4—444no—
592C4⋊C4—444no—
593C4⋊C4—442no—
594C4⋊C4—442no—
595C4⋊C4C2×C4×D1118yes—
596C4⋊C4C2×C4×D1118yes—
597C22⋊C4—118no—
598C22⋊C4—1116no—
599C22⋊C4—224no—
600C22⋊C4—224no—
601C22⋊C4—224no—
602C22⋊C4—224no—
603C22⋊C4—444no—
604C22⋊C4—442no—
605C22⋊C4—442no—
606C22⋊C4—444no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—28no—
612C42—44no—
613C42—1116no—
614C42—118no—
615C42—224no—
616C42—224no—
617C42—444no—
618C42—444no—
619C11#3425211yescharacteristic, 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—28no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—24no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—24no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—24no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—48no—
655C2×C4—48no—
656C2×C4—44no—
657C2×C4—114no—
658C2×C4—114no—
659C2×C4—114no—
660C2×C4—222no—
661C2×C4—222no—
662C2×C4—222no—
663C2×C4—222no—
664C2×C4—222no—
665C2×C4—222no—
666C2×C4—2216no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—222no—
672C2×C4—222no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—4416no—
680C2×C4#66925116yescomplemented
681C2×C4C22×C4×D1118yes—
682C2×C4C22×C4×D1112yes—
683C2×C4C22×C4×D1112yes—
684C2×C4C2×#433912yes—
685C2×C4C2×#433912yes—
686C2×C4C2×#433912yes—
687C2×C4C2×#433912yes—
688C2×C4#6703712yes—
689C2×C4#6704012yes—
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×#6703711yescharacteristic
708C22C2×#6704011yescharacteristic
709C22#1062345311yescharacteristic
710C22#1062345311yescharacteristic
711C4—22no—
712C4—22no—
713C4—28no—
714C4—44no—
715C4—41no—
716C4—41no—
717C4—224no—
718C4—224no—
719C4—224no—
720C4—442no—
721C4—442no—
722C4—442no—
723C4—442no—
724C4C2×#6692514yes—
725C4C2×#6692514yes—
726C2—24no—
727C2—444no—
728C2C22×#6692511yescharacteristic
729C2C4×#6703711yescharacteristic
730C2C4×#6704011yescharacteristic
731C2#1308232511yescharacteristic
732C2#1308233611yescharacteristic
733C2#1308246811yescharacteristic
734C2#1308248111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C4×C11×C4⋊C4C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#34252
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071585C2semidirect
3. #13071577C2semidirect
4. #13071569C2semidirect
5. #13071561C2semidirect
6. #13071505C2semidirect
7. #13071497C2semidirect
8. #13071489C2semidirect
9. #13071481C2semidirect
10. #13071250C2semidirect
11. #13071240C2semidirect
14. #13071099C2semidirect
15. #13071059C2semidirect
16. #13070973C2semidirect
17. C2×C4×C11×C4⋊C4C2semidirect
27. #10623035C4semidirect
144. #66946C2×C4semidirect
145. #66945C2×C4semidirect
146. C4⋊C4×D11C2×C4semidirect
147. #66940C2×C4semidirect
269. C2×C4×C4⋊C4D11semidirect
304. C2×C4×C11#117semidirect
619. C11#34252semidirect
680. C2×C4#66925semidirect

Maximal subgroups

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

subgroupindex
C2×#106230352
#130715852
#130715772
#130715692
#130715612
#130715052
#130714972
#130714892
#130714812
#130712502
#130712402
#130712092
#130711062
#130710992
#130710592
#130709732
C2×C4×C11×C4⋊C42
#3425211