Finite Group Databasebeta

← #14913974

Subgroups — #14913974

Order 2816.

2414 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4341C211yesmaximal, characteristic
2#13071566C212yesmaximal, complemented
3#13071565C211yesmaximal, characteristic, complemented
4#13071560C212yesmaximal, complemented
5C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
6#13071528C211yesmaximal, characteristic, complemented
7#13071506C214yesmaximal, complemented
8#13071505C212yesmaximal, complemented
9#13071455C212yesmaximal
10#13071257C214yesmaximal, complemented
11#13071253C212yesmaximal, complemented
12#13071021C211yesmaximal, characteristic, complemented
13#13071019C212yesmaximal, complemented
14#13071012C211yesmaximal, characteristic, complemented
15#13071011C212yesmaximal, complemented
16#13070980C212yesmaximal, complemented
17C11×#2354C211yesmaximal, characteristic, complemented
18C22×#4341C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#117C2212yes—
21C2×D4×Dic11C2211yescharacteristic
22C2×C4×C22⋊D11C2212yes—
23C2×#66979C2212yes—
24C22×C4×Dic11C2212yes—
25C4×#4341C4116yescomplemented
26C2×#66945C2212yes—
27C2×#66945C2211yescharacteristic
28C2×#66940C2212yes—
29C2×#66940C2211yescharacteristic
30C2×(C22⋊D11)⋊C4C2212yes—
31C2×#66930C2212yes—
32C2×C42×D11C2211yescharacteristic
33C2×C4×Dic22C2212yes—
34C2×C4×Dic22C2211yescharacteristic
35C11×#390C2212yes—
36C11×#388C2214yes—
37C11×#384C2211yescharacteristic
38C11×#380C2212yes—
39C4×C11×C4⋊C4C2212yes—
40C4×C11×C4⋊C4C2211yescharacteristic
41#10622834C2212yes—
42#10622825C2212yes—
43#10622600C2212yes—
44#10622600C2212yes—
45#10622600C2211yescharacteristic
46#10622600C2211yescharacteristic
47#10622590C2211yescharacteristic
48#10622590C2212yes—
49#10622590C2211yescharacteristic
50#10622589C2212yes—
51#10622589C2212yes—
52C4⋊C4×Dic11C2212yes—
53C4⋊C4×Dic11C2212yes—
54C4⋊C4×Dic11C2212yes—
55C4⋊C4×Dic11C2212yes—
56C4⋊C4×Dic11C2212yes—
57#10622586C2212yes—
58#10622585C2214yes—
59#10622570C2214yes—
60#10622570C2214yes—
61#10622564C2214yes—
62#10622558C2214yes—
63#10622557C2214yes—
64#10622556C2214yes—
65#10622555C2214yes—
66#10622555C2214yes—
67C22⋊C4×Dic11C2214yes—
68#10622553C2214yes—
69C4×(C2×D11)⋊C4C2212yes—
70#10622548C2211yescharacteristic
71C4×C4⋊Dic11C2211yescharacteristic
72#10622545C2212yes—
73C4×Dic11⋊C4C2214yes—
74C4×Dic11⋊C4C2214yes—
75C4×Dic11⋊C4C2214yes—
76#10622541C2212yes—
77#10622282C2214yes—
78#10622277C2212yes—
79#10622264C2214yes—
80#10622264C2212yes—
81#10622262C2214yes—
82#10622261C2214yes—
83#10622260C2214yes—
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11C2312yes—
86C22×C22⋊D11C2312yes—
87C23×Dic11C2312yes—
88C23×Dic11C2312yes—
89C2×#4341—24no—
90C2×#4341—24no—
91C2×#4341C2×C418yes—
92C22×C4×D11C2311yescharacteristic
93C22×C4×D11C2311yescharacteristic
94C22×C4×D11C2311yescharacteristic
95C22×Dic22C2311yescharacteristic
96C4×D4×C11C2×C418yes—
97C11×#117—44no—
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C22⋊C4C2314yes—
105C2×C11×C22⋊C4C2314yes—
106C2×C11×C22⋊C4C2312yes—
107C2×C42×C11C2312yes—
108C2×C42×C11C2314yes—
109C2×C42×C11C2311yescharacteristic
110C2×C22⋊Dic11C2314yes—
111C2×C22⋊Dic11C2314yes—
112C2×C22⋊Dic11C2312yes—
113D4×Dic11C2×C418yes—
114C4×C22⋊D11C2×C4116yes—
115C2×(C2×D11)⋊C4C2314yes—
116C2×(C2×D11)⋊C4C2312yes—
117C2×(C2×D11)⋊C4C2312yes—
118C2×(C2×D11)⋊C4C2312yes—
119#66979—44no—
120C2×C4⋊Dic11C2312yes—
121C2×C4⋊Dic11C2312yes—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2312yes—
125C2×C4⋊Dic11C2311yescharacteristic
126C2×Dic11⋊C4C2314yes—
127C2×Dic11⋊C4C2314yes—
128C2×Dic11⋊C4C2314yes—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2312yes—
131C2×Dic11⋊C4C2312yes—
132C2×C4×Dic11C2×C4116yes—
133C2×C4×Dic11C2314yes—
134C2×C4×Dic11C2314yes—
135C2×C4×Dic11C2312yes—
136C2×C4×Dic11C2314yes—
137C2×C4×Dic11C2314yes—
138C2×C4×Dic11C2312yes—
139C2×C4×Dic11C2311yescharacteristic
140C2×C4×Dic11C2311yescharacteristic
141C2×C4×Dic11C2311yescharacteristic
142C2×C4×Dic11C2312yes—
143C2×C4×Dic11C2312yes—
144#66945—44no—
145#66945C2×C418yes—
146#66940—28no—
147#66940C2×C418yes—
148(C22⋊D11)⋊C4C2×C4116yes—
149#66930C2×C4116yes—
150C42×D11C2×C418yes—
151C4×Dic22—28no—
152C4×Dic22C2×C418yes—
153C11×#95C2312yes—
154C11×#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2312yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2312yes—
160C11⋊#95C2312yes—
161C11⋊#95C2312yes—
162C11⋊#95C2312yes—
163C11⋊#95C2312yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C11⋊#95C2312yes—
167#34193—111nomaximal, Sylow
168C24×C11C2412yes—
169C23×D11C2411yescharacteristic
170C2×D4×C11—22no—
171C2×D4×C11—22no—
172C2×D4×C11C22×C414yes—
173C22×C4×C11—24no—
174C22×C4×C11—24no—
175C22×C4×C11C22×C418yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2414yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2412yes—
180C22×C4×C11C2411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C22×C4×C11C2411yescharacteristic
183C2×C22⋊D11—24no—
184C2×C22⋊D11—24no—
185C2×C22⋊D11C22×C418yes—
186C22×Dic11—24no—
187C22×Dic11—24no—
188C22×Dic11—42no—
189C22×Dic11—42no—
190C22×Dic11C22×C418yes—
191C22×Dic11C22×C418yes—
192C22×Dic11C2412yes—
193C22×Dic11C2412yes—
194C22×Dic11C2414yes—
195C22×Dic11C2411yescharacteristic
196C22×Dic11C2411yescharacteristic
197C22×Dic11C2411yescharacteristic
198C22×Dic11C2412yes—
199C22×Dic11C2412yes—
200#4341—232no—
201C2×C4×D11—22no—
202C2×C4×D11—22no—
203C2×C4×D11—22no—
204C2×C4×D11—22no—
205C2×C4×D11—41no—
206C2×C4×D11—41no—
207C2×C4×D11C22×C414yes—
208C2×C4×D11C22×C414yes—
209C2×C4×D11C22×C414yes—
210C2×Dic22C22×C414yes—
211C2×Dic22#4114yes—
212C2×Dic22#4114yes—
213C11×C4⋊C4—24no—
214C11×C4⋊C4—24no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—42no—
218C11×C4⋊C4C22×C414yes—
219C11×C22⋊C4—44no—
220C11×C22⋊C4—44no—
221C11×C22⋊C4C22×C418yes—
222C42×C11—24no—
223C42×C11—44no—
224C42×C11C22×C414yes—
225C22⋊Dic11—44no—
226C22⋊Dic11—44no—
227C22⋊Dic11C22×C418yes—
228(C2×D11)⋊C4—44no—
229(C2×D11)⋊C4—42no—
230(C2×D11)⋊C4—42no—
231(C2×D11)⋊C4C22×C418yes—
232C4⋊Dic11—24no—
233C4⋊Dic11—24no—
234C4⋊Dic11—22no—
235C4⋊Dic11—22no—
236C4⋊Dic11—42no—
237C4⋊Dic11C22×C414yes—
238Dic11⋊C4—28no—
239Dic11⋊C4—28no—
240Dic11⋊C4—44no—
241Dic11⋊C4—44no—
242Dic11⋊C4C22×C418yes—
243Dic11⋊C4C22×C418yes—
244C4×Dic11—28no—
245C4×Dic11—28no—
246C4×Dic11—24no—
247C4×Dic11—44no—
248C4×Dic11—44no—
249C4×Dic11C22×C418yes—
250C4×Dic11C22×C414yes—
251C4×Dic11C22×C414yes—
252C4×Dic11C22×C414yes—
253C4×Dic11C22×C418yes—
254C4×Dic11C22×C418yes—
255C2×C4×#41—111no—
256#2354—112no—
257#2354—111no—
258#2354—112no—
259#2354D1111yescharacteristic, complemented
260Q8×C4⋊C4—111no—
261Q8×C4⋊C4—111no—
262#2347—114no—
263#2347—112no—
264#2341—112no—
265#2319—112no—
266#2319—114no—
267#2285—111no—
268#2285—112no—
269#2283—112no—
270#2283—111no—
271#2276—112no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11C23×C414yes—
279C23×C11C2511yescharacteristic
280C22×D11—21no—
281C22×D11—21no—
282C22×D11—21no—
283C22×D11—21no—
284C22×D11—21no—
285C22×D11—21no—
286C22×D11C23×C412yes—
287D4×C11—28no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—216no—
293C2×C4×C11—22no—
294C2×C4×C11—24no—
295C2×C4×C11—22no—
296C2×C4×C11—24no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—24no—
301C2×C4×C11—22no—
302C2×C4×C11C23×C414yes—
303C2×C4×C11C23×C412yes—
304C2×C4×C11C23×C412yes—
305C2×C4×C11C23×C412yes—
306C2×C4×C11C2×#4112yes—
307C2×C4×C11C2×#4112yes—
308C2×C4×C11H(5,𝔽2)12yes—
309C2×C4×C112−1+412yes—
310C22⋊D11—216no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—216no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—24no—
328C2×Dic11—22no—
329C2×Dic11—48no—
330C2×Dic11C23×C412yes—
331C2×Dic11C23×C412yes—
332C2×Dic11C23×C412yes—
333C2×Dic11C23×C414yes—
334C2×Dic11C23×C414yes—
335C2×Dic11C2×#4114yes—
336C2×Dic11C2×#4114yes—
337C4×D11—28no—
338C4×D11—28no—
339C4×D11—44no—
340Dic22#117116yescomplemented
341C22×#41—111no—
342C4×#41—1116no—
343C2×C4×Q8—111no—
344C2×C4×Q8—112no—
345C2×C4×Q8—111no—
346C2×C4×Q8—112no—
347C2×C4×D4—111no—
348C2×C4×D4—112no—
349C2×C4×D4—112no—
350C2×C4×D4C2×D1111yescharacteristic
351C2×#117—112no—
352C2×#117—111no—
353C2×#117—112no—
354C2×#117—112no—
355C2×#117C2×D1112yes—
356C22×C42—112no—
357C22×C42—111no—
358#390—112no—
359#390—114no—
360#390—114no—
361#390C2×D1112yes—
362#389—114no—
363#389—112no—
364#389—112no—
365#389—114no—
366#388—114no—
367#388—114no—
368#388—114no—
369#388—114no—
370#388—114no—
371#388C2×D1114yes—
372#384—112no—
373#384—112no—
374#384—111no—
375#384C2×D1111yescharacteristic
376#383—112no—
377#383—114no—
378#382—111no—
379#382—112no—
380#382—111no—
381#381—114no—
382#381—112no—
383#380—112no—
384#380—112no—
385#380—112no—
386#380—111no—
387#380—111no—
388#380—114no—
389#380—114no—
390#380C2×D1112yes—
391C4×C4⋊C4—112no—
392C4×C4⋊C4—112no—
393C4×C4⋊C4—112no—
394C4×C4⋊C4—112no—
395C4×C4⋊C4—112no—
396C4×C4⋊C4—114no—
397C4×C4⋊C4—114no—
398C4×C4⋊C4—114no—
399C4×C4⋊C4—111no—
400C4×C4⋊C4—114no—
401C4×C4⋊C4C2×D1112yes—
402C4×C4⋊C4C2×D1111yescharacteristic
403C4×C22⋊C4—114no—
404C4×C22⋊C4—112no—
405#376—112no—
406#376—114no—
407C22×C11—24no—
408C22×C11—24no—
409C22×C11—24no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—42no—
414C22×C11C24×C411yescharacteristic
415C22×C11C22×#4111yescharacteristic
416C22×C11C22×#4111yescharacteristic
417C22×C11C2×H(5,𝔽2)11yescharacteristic
418C22×C11C2×2−1+411yescharacteristic
419C22×C11#58511yescharacteristic
420C22×C11#58511yescharacteristic
421C2×D11—22no—
422C2×D11—22no—
423C2×D11—22no—
424C2×D11—41no—
425C2×D11—41no—
426C2×D11—41no—
427C2×D11—41no—
428C4×C11—24no—
429C4×C11—22no—
430C4×C11—44no—
431C4×C11—42no—
432C4×C11—42no—
433C4×C11C2×#11714yes—
434C4×C11#52014yes—
435Dic11—22no—
436Dic11—22no—
437Dic11—22no—
438Dic11—24no—
439Dic11—42no—
440Dic11—44no—
441Dic11—42no—
442Dic11C2×#11718yes—
443C2×#41—118no—
444C2×#41—224no—
445C2×#41—224no—
446C22×Q8—111no—
447C22×D4—112no—
448C22×D4C22×D1111yescharacteristic
449C23×C4—112no—
450C23×C4—112no—
451C23×C4—111no—
452C23×C4—111no—
453C23×C4—111no—
454C23×C4C22×D1112yes—
455C4×Q8—118no—
456C4×Q8—118no—
457C4×Q8—228no—
458C4×Q8—228no—
459C4×D4—118no—
460C4×D4—1116no—
461C4×D4—1116no—
462C4×D4C4×D1118yes—
463#117—44no—
464#117—118no—
465#117—1116no—
466#117—444no—
467#117—444no—
468C2×C4⋊C4—112no—
469C2×C4⋊C4—112no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—112no—
473C2×C4⋊C4—114no—
474C2×C4⋊C4—114no—
475C2×C4⋊C4—112no—
476C2×C4⋊C4—111no—
477C2×C4⋊C4—114no—
478C2×C4⋊C4—114no—
479C2×C4⋊C4—112no—
480C2×C4⋊C4C22×D1112yes—
481C2×C4⋊C4C22×D1111yescharacteristic
482C2×C4⋊C4C22×D1112yes—
483C2×C4⋊C4C22×D1111yescharacteristic
484C2×C4⋊C4C22×D1112yes—
485C2×C4⋊C4C22×D1111yescharacteristic
486C2×C22⋊C4—112no—
487C2×C22⋊C4—112no—
488C2×C22⋊C4—114no—
489C2×C22⋊C4—114no—
490C2×C22⋊C4—114no—
491C2×C22⋊C4—112no—
492C2×C22⋊C4—112no—
493C2×C22⋊C4C22×D1114yes—
494C2×C22⋊C4C22×D1114yes—
495C2×C22⋊C4C22×D1112yes—
496C2×C42—1116no—
497C2×C42—111no—
498C2×C42—112no—
499C2×C42—112no—
500C2×C42—111no—
501C2×C42—112no—
502C2×C42—111no—
503C2×C42—118no—
504C2×C42—114no—
505C2×C42—114no—
506C2×C42—112no—
507C2×C42—114no—
508C2×C42—114no—
509C2×C42C22×D1112yes—
510C2×C42C22×D1114yes—
511C2×C42C22×D1111yescharacteristic
512#95—112no—
513#95—114no—
514#95—112no—
515#95—112no—
516#95—112no—
517#95—114no—
518#95—112no—
519#95—114no—
520#95—112no—
521#95—114no—
522#95—114no—
523#95—112no—
524#95C22×D1114yes—
525#95C22×D1112yes—
526C2×C11—44no—
527C2×C11C22×#11711yescharacteristic
528C2×C11C2×#52011yescharacteristic
529C2×C11#342811yescharacteristic
530C2×C11#351711yescharacteristic
531C2×C11#351711yescharacteristic
532C2×C11#351811yescharacteristic
533C2×C11#351811yescharacteristic
534D11—42no—
535C24—111no—
536C24C23×D1112yes—
537#41—2232no—
538C2×Q8—114no—
539C2×Q8—114no—
540C2×Q8—114no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—118no—
544C2×D4—224no—
545C2×D4—224no—
546C2×D4C2×C4×D1114yes—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—112no—
550C22×C4—118no—
551C22×C4—111no—
552C22×C4—111no—
553C22×C4—111no—
554C22×C4—112no—
555C22×C4—118no—
556C22×C4—114no—
557C22×C4—114no—
558C22×C4—114no—
559C22×C4—112no—
560C22×C4—112no—
561C22×C4—114no—
562C22×C4—224no—
563C22×C4—224no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—441no—
569C22×C4—441no—
570C22×C4—442no—
571C22×C4—442no—
572C22×C4C2×C4×D1118yes—
573C22×C4C23×D1112yes—
574C22×C4C23×D1114yes—
575C22×C4C23×D1112yes—
576C22×C4C23×D1112yes—
577C22×C4C23×D1111yescharacteristic
578C22×C4C23×D1111yescharacteristic
579C22×C4C23×D1111yescharacteristic
580C4⋊C4—22no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—22no—
584C4⋊C4—42no—
585C4⋊C4—118no—
586C4⋊C4—118no—
587C4⋊C4—114no—
588C4⋊C4—228no—
589C4⋊C4—228no—
590C4⋊C4—224no—
591C4⋊C4—222no—
592C4⋊C4—224no—
593C4⋊C4—222no—
594C4⋊C4—444no—
595C4⋊C4—444no—
596C4⋊C4—442no—
597C4⋊C4C2×C4×D1114yes—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—118no—
601C22⋊C4—118no—
602C22⋊C4—444no—
603C22⋊C4—442no—
604C22⋊C4—442no—
605C22⋊C4—444no—
606C22⋊C4—444no—
607C22⋊C4C2×C4×D1118yes—
608C42—24no—
609C42—44no—
610C42—114no—
611C42—118no—
612C42—114no—
613C42—118no—
614C42—118no—
615C42—114no—
616C42—228no—
617C42—228no—
618C42—224no—
619C42—444no—
620C42—444no—
621C42C2×C4×D1114yes—
622C11#3419311yescharacteristic, complemented, Sylow
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—112no—
630C23—221no—
631C23—221no—
632C23—221no—
633C23—221no—
634C23—221no—
635C23—221no—
636C23C22×C4×D1114yes—
637C23C24×D1111yescharacteristic
638Q8—1116no—
639D4—28no—
640D4—2216no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—216no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—114no—
656C2×C4—114no—
657C2×C4—114no—
658C2×C4—112no—
659C2×C4—112no—
660C2×C4—112no—
661C2×C4—114no—
662C2×C4—2216no—
663C2×C4—221no—
664C2×C4—221no—
665C2×C4—221no—
666C2×C4—221no—
667C2×C4—222no—
668C2×C4—221no—
669C2×C4—222no—
670C2×C4—221no—
671C2×C4—228no—
672C2×C4—228no—
673C2×C4—222no—
674C2×C4—224no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—224no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—224no—
682C2×C4—444no—
683C2×C4—448no—
684C2×C4C22×C4×D1114yes—
685C2×C4C22×C4×D1112yes—
686C2×C4C22×C4×D1112yes—
687C2×C4C22×C4×D1112yes—
688C2×C4#6703712yes—
689C2×C4#41×D1112yes—
690C2×C4#41×D1112yes—
691C2×C4#6704312yes—
692C22—24no—
693C22—24no—
694C22—24no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—222no—
700C22—222no—
701C22—222no—
702C22—441no—
703C22—441no—
704C22—441no—
705C22—441no—
706C22C23×C4×D1111yescharacteristic
707C22C2×#6703711yescharacteristic
708C22C2×#41×D1111yescharacteristic
709C22C2×#41×D1111yescharacteristic
710C22C2×#6704311yescharacteristic
711C22#1062345511yescharacteristic
712C22#1062345711yescharacteristic
713C4—24no—
714C4—22no—
715C4—42no—
716C4—44no—
717C4—42no—
718C4—118no—
719C4—222no—
720C4—222no—
721C4—222no—
722C4—224no—
723C4—442no—
724C4—442no—
725C4—444no—
726C4D11×#11714yes—
727C4#1062307714yes—
728C2—44no—
729C2—442no—
730C2C2×D11×#11711yescharacteristic
731C2C2×#1062307711yescharacteristic
732C2#1308181611yescharacteristic
733C2#1308261911yescharacteristic
734C2#1308262111yescharacteristic
735C2#1308263011yescharacteristic
736C2#1308263211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2354C2
socle, cosocleC23×C11C25
prime radicalC22×#4341C22
hypercenter#2354D11
hypocenterC11#34193
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #13071566C2semidirect
3. #13071565C2semidirect
4. #13071560C2semidirect
5. C4⋊C4×Dic22C2semidirect
6. #13071528C2semidirect
7. #13071506C2semidirect
8. #13071505C2semidirect
10. #13071257C2semidirect
11. #13071253C2semidirect
12. #13071021C2semidirect
13. #13071019C2semidirect
14. #13071012C2semidirect
15. #13071011C2semidirect
16. #13070980C2semidirect
17. C11×#2354C2semidirect
25. C4×#4341C4semidirect
259. #2354D11semidirect
340. Dic22#117semidirect
622. C11#34193semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43412
#130715662
#130715652
#130715602
C4⋊C4×Dic222
#130715282
#130715062
#130715052
#130714552
#130712572
#130712532
#130710212
#130710192
#130710122
#130710112
#130709802
C11×#23542
#3419311