Finite Group Databasebeta

← #14913912

Subgroups — #14913912

Order 2816.

2542 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4339C211yesmaximal, characteristic
2#13071574C212yesmaximal, complemented
3#13071568C212yesmaximal, complemented
4#13071566C212yesmaximal, complemented
5#13071560C212yesmaximal, complemented
6#13071548C212yesmaximal, complemented
7#13071546C212yesmaximal, complemented
8#13071542C212yesmaximal, complemented
9#13071538C212yesmaximal, complemented
10#13071223C212yesmaximal, complemented
11#13071221C212yesmaximal, complemented
12#13071205C212yesmaximal
13#13071023C211yesmaximal, characteristic, complemented
14#13071021C211yesmaximal, characteristic, complemented
15#13071021C211yesmaximal, characteristic, complemented
16#13071021C211yesmaximal, characteristic, complemented
17D11×#384C211yesmaximal, characteristic, complemented
18#13070970C212yesmaximal, complemented
19C11×#2285C211yesmaximal, characteristic, complemented
20C22×#4339C2211yescharacteristic
21C2×C11×#117C2212yes—
22C22×C42×C11C2211yescharacteristic
23C2×C4×C22⋊D11C2211yescharacteristic
24C2×C4×C22⋊D11C2211yescharacteristic
25C2×C4×C22⋊D11C2211yescharacteristic
26C2×C4×C22⋊D11C2211yescharacteristic
27C2×#66979C2212yes—
28C2×#66979C2211yescharacteristic
29C2×#66945C2212yes—
30C2×#66945C2212yes—
31C2×#66945C2212yes—
32C2×C4⋊C4×D11C2212yes—
33C2×C4⋊C4×D11C2212yes—
34C2×C4⋊C4×D11C2212yes—
35C4×#4339C4116yescomplemented
36C2×C4×D44C2211yescharacteristic
37C2×C4×D44C2211yescharacteristic
38C2×#66925C2211yescharacteristic
39C2×#66925C2211yescharacteristic
40C2×C42×D11C2211yescharacteristic
41C2×C42×D11C2211yescharacteristic
42C2×C4×Dic22C2211yescharacteristic
43C2×C4×Dic22C2211yescharacteristic
44C11×#384C2211yescharacteristic
45C11×#384C2211yescharacteristic
46C11×#382C2212yes—
47C11×#380C2212yes—
48C11×#380C2212yes—
49C4×C11×C4⋊C4C2212yes—
50C4×C11×C4⋊C4C2212yes—
51#10622825C2212yes—
52#10622825C2212yes—
53#10622600C2212yes—
54#10622600C2212yes—
55#10622600C2212yes—
56#10622600C2212yes—
57#10622600C2212yes—
58#10622600C2212yes—
59#10622590C2212yes—
60#10622590C2212yes—
61#10622590C2212yes—
62#10622589C2212yes—
63#10622589C2212yes—
64#10622589C2212yes—
65C4⋊C4×Dic11C2212yes—
66C4⋊C4×Dic11C2212yes—
67C4⋊C4×Dic11C2212yes—
68C4⋊C4×Dic11C2212yes—
69C4⋊C4×Dic11C2212yes—
70C4⋊C4×Dic11C2212yes—
71#10622570C2214yes—
72#10622569C2214yes—
73#10622558C2214yes—
74#10622557C2214yes—
75#10622553C2214yes—
76C4×(C2×D11)⋊C4C2214yes—
77#10622549C2212yes—
78#10622548C2211yescharacteristic
79#10622548C2211yescharacteristic
80C4×C4⋊Dic11C2212yes—
81C4×C4⋊Dic11C2212yes—
82#10622546C2214yes—
83C4×Dic11⋊C4C2214yes—
84#10622282C2214yes—
85#10622279C2214yes—
86#10622278C2214yes—
87#10622267C2214yes—
88#10622266C2214yes—
89#10622265C2214yes—
90#10622262C2214yes—
91#10622259C2214yes—
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C22×C22⋊D11C2311yescharacteristic
96C22×C22⋊D11C2311yescharacteristic
97C2×#4339—24no—
98C2×#4339—24no—
99C2×#4339C2×C418yes—
100C22×D44C2311yescharacteristic
101C22×C4×D11C2311yescharacteristic
102C22×C4×D11C2311yescharacteristic
103C22×C4×D11C2311yescharacteristic
104C22×C4×D11C2311yescharacteristic
105C22×C4×D11C2311yescharacteristic
106C22×C4×D11C2314yes—
107C22×C4×D11C2311yescharacteristic
108C22×Dic22C2311yescharacteristic
109C11×#117—44no—
110C2×C11×C4⋊C4C2312yes—
111C2×C11×C4⋊C4C2312yes—
112C2×C11×C4⋊C4C2312yes—
113C2×C11×C4⋊C4C2312yes—
114C2×C11×C4⋊C4C2312yes—
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C42×C11C2×C418yescomplemented
118C2×C42×C11C2314yes—
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2311yescharacteristic
125C2×C22⋊Dic11C2311yescharacteristic
126C4×C22⋊D11C2×C418yes—
127C4×C22⋊D11C2×C418yes—
128C4×C22⋊D11C2×C418yescomplemented
129C4×C22⋊D11C2×C418yescomplemented
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2311yescharacteristic
134C2×(C2×D11)⋊C4C2311yescharacteristic
135C2×(C2×D11)⋊C4C2311yescharacteristic
136C2×(C2×D11)⋊C4C2311yescharacteristic
137#66979—44no—
138#66979C2×C418yescomplemented
139C2×C4⋊Dic11C2312yes—
140C2×C4⋊Dic11C2312yes—
141C2×C4⋊Dic11C2312yes—
142C2×C4⋊Dic11C2312yes—
143C2×C4⋊Dic11C2312yes—
144C2×C4⋊Dic11C2312yes—
145C2×C4⋊Dic11C2311yescharacteristic
146C2×C4⋊Dic11C2311yescharacteristic
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2311yescharacteristic
151C2×Dic11⋊C4C2311yescharacteristic
152C2×Dic11⋊C4C2311yescharacteristic
153C2×Dic11⋊C4C2311yescharacteristic
154C2×C4×Dic11C2314yes—
155C2×C4×Dic11C2314yes—
156C2×C4×Dic11C2314yes—
157C2×C4×Dic11C2314yes—
158C2×C4×Dic11C2311yescharacteristic
159C2×C4×Dic11C2311yescharacteristic
160C2×C4×Dic11C2311yescharacteristic
161C2×C4×Dic11C2311yescharacteristic
162C2×C4×Dic11C2311yescharacteristic
163C2×C4×Dic11C2311yescharacteristic
164#66945—28no—
165#66945—44no—
166#66945—44no—
167C4⋊C4×D11—28no—
168C4⋊C4×D11—44no—
169C4⋊C4×D11—44no—
170C4×D44C2×C418yes—
171C4×D44C2×C418yes—
172#66925C2×C418yes—
173#66925C2×C418yescomplemented
174C42×D11C2×C418yes—
175C42×D11C2×C418yescomplemented
176C4×Dic22C2×C418yescomplemented
177C4×Dic22C2×C418yescomplemented
178C11×#95C2314yes—
179C11×#95C2314yes—
180C11⋊#95C2314yes—
181C11⋊#95C2314yes—
182C11⋊#95C2314yes—
183C11⋊#95C2314yes—
184C11⋊#95C2314yes—
185C11⋊#95C2314yes—
186C11⋊#95C2314yes—
187C11⋊#95C2314yes—
188#34188—111nomaximal, Sylow
189C24×C11C2411yescharacteristic
190C23×D11C2411yescharacteristic
191C23×D11C2411yescharacteristic
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11C22×C414yes—
199C22×C4×C11C22×C414yes—
200C22×C4×C11C22×C414yes—
201C22×C4×C11C2414yes—
202C22×C4×C11C2414yes—
203C22×C4×C11C2411yescharacteristic
204C22×C4×C11C2411yescharacteristic
205C22×C4×C11C2411yescharacteristic
206C22×C4×C11C2411yescharacteristic
207C22×C4×C11C2411yescharacteristic
208C22×C4×C11C2411yescharacteristic
209C2×C22⋊D11—22no—
210C2×C22⋊D11—22no—
211C2×C22⋊D11—22no—
212C2×C22⋊D11—22no—
213C2×C22⋊D11C22×C414yes—
214C2×C22⋊D11C22×C414yes—
215C22×Dic11C2414yes—
216C22×Dic11C2414yes—
217C22×Dic11C2411yescharacteristic
218C22×Dic11C2411yescharacteristic
219C22×Dic11C2411yescharacteristic
220C22×Dic11C2411yescharacteristic
221C22×Dic11C2411yescharacteristic
222C22×Dic11C2411yescharacteristic
223#4339—232no—
224C2×D44—22no—
225C2×D44—22no—
226C2×D44C22×C414yes—
227C2×C4×D11—28no—
228C2×C4×D11—22no—
229C2×C4×D11—22no—
230C2×C4×D11—22no—
231C2×C4×D11—22no—
232C2×C4×D11—22no—
233C2×C4×D11—22no—
234C2×C4×D11—22no—
235C2×C4×D11—22no—
236C2×C4×D11—22no—
237C2×C4×D11—22no—
238C2×C4×D11—44no—
239C2×C4×D11—44no—
240C2×C4×D11C22×C414yes—
241C2×C4×D11C22×C414yes—
242C2×C4×D11C22×C414yes—
243C2×C4×D11C22×C414yes—
244C2×C4×D11C22×C414yes—
245C2×C4×D11C22×C414yes—
246C2×C4×D11#4114yes—
247C2×C4×D11#4114yes—
248C2×Dic22—22no—
249C2×Dic22—22no—
250C2×Dic22C22×C414yes—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—24no—
255C11×C4⋊C4—24no—
256C11×C4⋊C4—24no—
257C11×C22⋊C4—44no—
258C42×C11—44no—
259C42×C11C22×C414yes—
260C42×C11C22×C414yes—
261C42×C11C22×C414yes—
262C42×C11C22×C414yes—
263C22⋊Dic11—44no—
264C22⋊Dic11C22×C414yes—
265C22⋊Dic11C22×C414yes—
266(C2×D11)⋊C4—28no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4C22×C414yes—
270(C2×D11)⋊C4C22×C414yes—
271(C2×D11)⋊C4C22×C414yes—
272(C2×D11)⋊C4C22×C414yes—
273C4⋊Dic11—24no—
274C4⋊Dic11—24no—
275C4⋊Dic11—24no—
276C4⋊Dic11—24no—
277C4⋊Dic11—24no—
278C4⋊Dic11—24no—
279C4⋊Dic11C22×C414yes—
280C4⋊Dic11C22×C414yes—
281Dic11⋊C4—28no—
282Dic11⋊C4—44no—
283Dic11⋊C4—44no—
284Dic11⋊C4C22×C414yes—
285Dic11⋊C4C22×C414yes—
286Dic11⋊C4C22×C414yes—
287Dic11⋊C4C22×C414yes—
288C4×Dic11—28no—
289C4×Dic11—44no—
290C4×Dic11—44no—
291C4×Dic11—44no—
292C4×Dic11C22×C414yes—
293C4×Dic11C22×C414yes—
294C4×Dic11C22×C414yes—
295C4×Dic11C22×C414yes—
296C4×Dic11C22×C414yes—
297C4×Dic11C22×C414yes—
298C2×C4×#41—111no—
299#2355—112no—
300#2355—112no—
301#2354—112no—
302#2354—112no—
303#2352—112no—
304#2352—112no—
305#2352—112no—
306#2352—112no—
307#2314—112no—
308#2314—112no—
309#2311—112no—
310#2285—111no—
311#2285—111no—
312#2285—111no—
313#2285—111no—
314#2285D1111yescharacteristic, complemented
315C2×#384—111no—
316#2274—112no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11C23×C412yes—
324C23×C11C2511yescharacteristic
325C22×D11—21no—
326C22×D11—21no—
327C22×D11—21no—
328C22×D11—21no—
329C22×D11—21no—
330C22×D11—21no—
331C22×D11—21no—
332C22×D11—21no—
333C22×D11—21no—
334C22×D11—21no—
335C22×D11C23×C412yes—
336C22×D11C23×C412yes—
337C22×D11C2×#4112yes—
338C22×D11C2×#4112yes—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—28no—
346C2×C4×C11—28no—
347C2×C4×C11—28no—
348C2×C4×C11—24no—
349C2×C4×C11—24no—
350C2×C4×C11—24no—
351C2×C4×C11—24no—
352C2×C4×C11—24no—
353C2×C4×C11—24no—
354C2×C4×C11C23×C412yes—
355C2×C4×C11C23×C412yes—
356C2×C4×C11C23×C412yes—
357C2×C4×C11C23×C412yes—
358C2×C4×C11C23×C412yes—
359C2×C4×C11C23×C412yes—
360C2×C4×C11C2×#4112yes—
361C2×C4×C11C2×#4112yes—
362C2×C4×C11H(5,𝔽2)12yes—
363C2×C4×C11H(5,𝔽2)12yes—
364C2×C4×C112−1+412yes—
365C2×C4×C112−1+412yes—
366C22⋊D11—28no—
367C22⋊D11—28no—
368C2×Dic11—21no—
369C2×Dic11—21no—
370C2×Dic11—21no—
371C2×Dic11—21no—
372C2×Dic11—21no—
373C2×Dic11—21no—
374C2×Dic11—21no—
375C2×Dic11—21no—
376C2×Dic11—21no—
377C2×Dic11—21no—
378C2×Dic11—24no—
379C2×Dic11—24no—
380C2×Dic11—24no—
381C2×Dic11—24no—
382C2×Dic11—24no—
383C2×Dic11—24no—
384C2×Dic11C23×C412yes—
385C2×Dic11C23×C412yes—
386C2×Dic11C23×C412yes—
387C2×Dic11C23×C412yes—
388C2×Dic11C23×C412yes—
389C2×Dic11C23×C412yes—
390C2×Dic11C2×#4112yes—
391C2×Dic11C2×#4112yes—
392D44—28no—
393C4×D11—28no—
394C4×D11—28no—
395C4×D11—28no—
396C4×D11—28no—
397C4×D11—28no—
398C4×D11—88no—
399C4×D11#117116yescomplemented
400Dic22—28no—
401C22×#41—111no—
402C4×#41—1116no—
403C2×C4×Q8—111no—
404C2×C4×Q8—111no—
405C2×C4×D4—111no—
406C2×C4×D4—111no—
407C2×C4×D4—111no—
408C2×C4×D4—111no—
409C2×C4×D4—111no—
410C2×C4×D4—111no—
411C2×#117—111no—
412C2×#117—112no—
413C2×#117—112no—
414C2×#117—112no—
415C2×#117—112no—
416C2×#117—111no—
417C2×#117—111no—
418C2×#117C2×D1112yes—
419C22×C4⋊C4—112no—
420C22×C4⋊C4—112no—
421C22×C4⋊C4—112no—
422C22×C42—111no—
423C22×C42—111no—
424C22×C42C2×D1111yescharacteristic
425#391—114no—
426#390—114no—
427#388—114no—
428#388—114no—
429#388—114no—
430#388—114no—
431#387—114no—
432#387—114no—
433#387—114no—
434#387—114no—
435#386—114no—
436#386—114no—
437#384—112no—
438#384—112no—
439#384—112no—
440#384—111no—
441#384—111no—
442#384C2×D1111yescharacteristic
443#384C2×D1111yescharacteristic
444#382—112no—
445#382—112no—
446#382—112no—
447#382—112no—
448#382C2×D1112yes—
449#380—112no—
450#380—112no—
451#380—112no—
452#380—112no—
453#380—112no—
454#380—112no—
455#380—112no—
456#380—112no—
457#380C2×D1112yes—
458#380C2×D1112yes—
459C4×C4⋊C4—112no—
460C4×C4⋊C4—112no—
461C4×C4⋊C4—112no—
462C4×C4⋊C4—112no—
463C4×C4⋊C4—112no—
464C4×C4⋊C4—112no—
465C4×C4⋊C4—112no—
466C4×C4⋊C4—112no—
467C4×C4⋊C4—114no—
468C4×C4⋊C4—114no—
469C4×C4⋊C4C2×D1112yes—
470C4×C4⋊C4C2×D1112yes—
471C4×C22⋊C4—114no—
472C4×C22⋊C4—114no—
473C22×C11—22no—
474C22×C11—22no—
475C22×C11—22no—
476C22×C11—41no—
477C22×C11—41no—
478C22×C11—41no—
479C22×C11—41no—
480C22×C11C24×C411yescharacteristic
481C22×C11C22×#4111yescharacteristic
482C22×C11C22×#4111yescharacteristic
483C22×C11C2×H(5,𝔽2)11yescharacteristic
484C22×C11C2×H(5,𝔽2)11yescharacteristic
485C22×C11C2×2−1+411yescharacteristic
486C22×C11C2×2−1+411yescharacteristic
487C2×D11—22no—
488C2×D11—22no—
489C2×D11—22no—
490C2×D11—22no—
491C2×D11—22no—
492C2×D11—22no—
493C2×D11—22no—
494C2×D11—22no—
495C2×D11—22no—
496C2×D11—41no—
497C2×D11—41no—
498C2×D11—41no—
499C2×D11—41no—
500C2×D11C2×#11714yes—
501C4×C11—22no—
502C4×C11—22no—
503C4×C11—22no—
504C4×C11—44no—
505C4×C11—44no—
506C4×C11C2×#11714yes—
507C4×C11#52014yes—
508C4×C11#52014yes—
509Dic11—22no—
510Dic11—22no—
511Dic11—22no—
512Dic11—22no—
513Dic11—22no—
514Dic11—44no—
515Dic11—44no—
516Dic11C2×#11714yes—
517C2×#41—118no—
518C2×#41—224no—
519C2×#41—224no—
520C22×Q8—111no—
521C22×D4—111no—
522C22×D4—111no—
523C22×D4—111no—
524C23×C4—111no—
525C23×C4—111no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—111no—
529C23×C4—111no—
530C23×C4—114no—
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C4×Q8—118no—
535C4×Q8—118no—
536C4×D4—118no—
537C4×D4—118no—
538C4×D4—118no—
539C4×D4—118no—
540C4×D4—118no—
541C4×D4—118no—
542#117—44no—
543#117—118no—
544#117—118no—
545#117—118no—
546#117—228no—
547#117—444no—
548#117—444no—
549#117—444no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—111no—
553C2×C4⋊C4—111no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—112no—
557C2×C4⋊C4—112no—
558C2×C4⋊C4—112no—
559C2×C4⋊C4—114no—
560C2×C4⋊C4—112no—
561C2×C4⋊C4—112no—
562C2×C4⋊C4—112no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—228no—
566C2×C4⋊C4—444no—
567C2×C4⋊C4—444no—
568C2×C4⋊C4C22×D1112yes—
569C2×C4⋊C4C22×D1112yes—
570C2×C4⋊C4C22×D1112yes—
571C2×C4⋊C4C22×D1112yes—
572C2×C4⋊C4C22×D1112yes—
573C2×C4⋊C4C22×D1112yes—
574C2×C22⋊C4—111no—
575C2×C22⋊C4—111no—
576C2×C22⋊C4—111no—
577C2×C22⋊C4—111no—
578C2×C22⋊C4—111no—
579C2×C22⋊C4—111no—
580C2×C22⋊C4—114no—
581C2×C22⋊C4—114no—
582C2×C22⋊C4—114no—
583C2×C22⋊C4—114no—
584C2×C22⋊C4C22×D1114yes—
585C2×C42—111no—
586C2×C42—111no—
587C2×C42—111no—
588C2×C42—111no—
589C2×C42—111no—
590C2×C42—111no—
591C2×C42—118no—
592C2×C42—118no—
593C2×C42—114no—
594C2×C42—114no—
595C2×C42—114no—
596C2×C42—114no—
597C2×C42C4×D1118yescomplemented
598C2×C42C22×D1114yes—
599C2×C42C22×D1111yescharacteristic
600C2×C42C22×D1111yescharacteristic
601C2×C42C22×D1111yescharacteristic
602C2×C42C22×D1111yescharacteristic
603#95—114no—
604#95—114no—
605#95—114no—
606#95—114no—
607#95—114no—
608#95—114no—
609#95—114no—
610#95—114no—
611#95C22×D1114yes—
612#95C22×D1114yes—
613C2×C11—42no—
614C2×C11C22×#11711yescharacteristic
615C2×C11C2×#52011yescharacteristic
616C2×C11C2×#52011yescharacteristic
617C2×C11#350811yescharacteristic
618C2×C11#350911yescharacteristic
619C2×C11#351111yescharacteristic
620C2×C11#351111yescharacteristic
621D11—24no—
622D11—42no—
623C24—111no—
624C24—111no—
625C24C23×D1111yescharacteristic
626#41—2232no—
627C2×Q8—114no—
628C2×Q8—222no—
629C2×Q8—222no—
630C2×D4—114no—
631C2×D4—114no—
632C2×D4—114no—
633C2×D4—222no—
634C2×D4—222no—
635C2×D4—222no—
636C2×D4—222no—
637C2×D4—222no—
638C2×D4—222no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—111no—
646C22×C4—114no—
647C22×C4—114no—
648C22×C4—114no—
649C22×C4—111no—
650C22×C4—111no—
651C22×C4—111no—
652C22×C4—111no—
653C22×C4—111no—
654C22×C4—114no—
655C22×C4—114no—
656C22×C4—114no—
657C22×C4—114no—
658C22×C4—114no—
659C22×C4—114no—
660C22×C4—114no—
661C22×C4—228no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—222no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—444no—
673C22×C4—444no—
674C22×C4C2×C4×D1114yes—
675C22×C4C2×C4×D1114yes—
676C22×C4C2×C4×D1114yes—
677C22×C4C23×D1114yes—
678C22×C4C23×D1114yes—
679C22×C4C23×D1111yescharacteristic
680C22×C4C23×D1111yescharacteristic
681C22×C4C23×D1111yescharacteristic
682C22×C4C23×D1111yescharacteristic
683C22×C4C23×D1111yescharacteristic
684C22×C4C23×D1111yescharacteristic
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—114no—
692C4⋊C4—114no—
693C4⋊C4—114no—
694C4⋊C4—114no—
695C4⋊C4—114no—
696C4⋊C4—114no—
697C4⋊C4—228no—
698C4⋊C4—224no—
699C4⋊C4—224no—
700C4⋊C4—224no—
701C4⋊C4—224no—
702C4⋊C4—224no—
703C4⋊C4—224no—
704C4⋊C4—444no—
705C4⋊C4—444no—
706C22⋊C4—44no—
707C22⋊C4—114no—
708C22⋊C4—114no—
709C22⋊C4—114no—
710C22⋊C4—114no—
711C22⋊C4—114no—
712C22⋊C4—114no—
713C22⋊C4—228no—
714C22⋊C4—444no—
715C22⋊C4—444no—
716C22⋊C4—444no—
717C42—44no—
718C42—114no—
719C42—114no—
720C42—114no—
721C42—114no—
722C42—114no—
723C42—114no—
724C42—228no—
725C42—444no—
726C42—444no—
727C42—444no—
728C42C2×C4×D1114yes—
729C42C2×C4×D1114yes—
730C42C2×C4×D1114yes—
731C42C2×C4×D1114yes—
732C11#3418811yescharacteristic, complemented, Sylow
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—112no—
740C23—112no—
741C23—112no—
742C23—112no—
743C23—221no—
744C23—221no—
745C23—221no—
746C23—221no—
747C23—221no—
748C23—221no—
749C23—221no—
750C23—221no—
751C23—221no—
752C23—221no—
753C23C22×C4×D1112yes—
754C23C24×D1111yescharacteristic
755Q8—228no—
756D4—228no—
757D4—228no—
758D4—228no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—112no—
775C2×C4—112no—
776C2×C4—112no—
777C2×C4—1116no—
778C2×C4—112no—
779C2×C4—112no—
780C2×C4—112no—
781C2×C4—112no—
782C2×C4—112no—
783C2×C4—221no—
784C2×C4—221no—
785C2×C4—221no—
786C2×C4—221no—
787C2×C4—221no—
788C2×C4—221no—
789C2×C4—221no—
790C2×C4—221no—
791C2×C4—221no—
792C2×C4—221no—
793C2×C4—228no—
794C2×C4—228no—
795C2×C4—228no—
796C2×C4—228no—
797C2×C4—228no—
798C2×C4—224no—
799C2×C4—224no—
800C2×C4—224no—
801C2×C4—224no—
802C2×C4—224no—
803C2×C4—224no—
804C2×C4—888no—
805C2×C4C22×C4×D1112yes—
806C2×C4C22×C4×D1112yes—
807C2×C4C22×C4×D1112yes—
808C2×C4C22×C4×D1112yes—
809C2×C4C22×C4×D1112yes—
810C2×C4C22×C4×D1112yes—
811C2×C4#6703712yes—
812C2×C4#6704012yes—
813C2×C4#41×D1112yes—
814C2×C4#41×D1112yes—
815C2×C4#6704212yes—
816C2×C4#6704312yes—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—114no—
825C22—222no—
826C22—222no—
827C22—222no—
828C22—222no—
829C22—222no—
830C22—222no—
831C22—222no—
832C22—222no—
833C22—222no—
834C22—441no—
835C22—441no—
836C22—441no—
837C22—441no—
838C22C23×C4×D1111yescharacteristic
839C22C2×#6703711yescharacteristic
840C22C2×#6704011yescharacteristic
841C22C2×#41×D1111yescharacteristic
842C22C2×#41×D1111yescharacteristic
843C22C2×#6704211yescharacteristic
844C22C2×#6704311yescharacteristic
845C4—22no—
846C4—22no—
847C4—22no—
848C4—44no—
849C4—44no—
850C4—114no—
851C4—222no—
852C4—222no—
853C4—222no—
854C4—222no—
855C4—222no—
856C4—444no—
857C4—444no—
858C4#1062303514yes—
859C4D11×#11714yes—
860C4#1062305414yes—
861C2—42no—
862C2—224no—
863C2—442no—
864C2C2×D11×#11711yescharacteristic
865C2C2×#1062305411yescharacteristic
866C2C2×#1062303511yescharacteristic
867C2#1308248511yescharacteristic
868C2#1308249511yescharacteristic
869C2#1308251711yescharacteristic
870C2#1308252811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2285C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenter#2285D11
hypocenterC11#34188
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #13071574C2semidirect
3. #13071568C2semidirect
4. #13071566C2semidirect
5. #13071560C2semidirect
6. #13071548C2semidirect
7. #13071546C2semidirect
8. #13071542C2semidirect
9. #13071538C2semidirect
10. #13071223C2semidirect
11. #13071221C2semidirect
13. #13071023C2semidirect
14. #13071021C2semidirect
15. #13071021C2semidirect
16. #13071021C2semidirect
17. D11×#384C2semidirect
18. #13070970C2semidirect
19. C11×#2285C2semidirect
35. C4×#4339C4semidirect
117. C2×C42×C11C2×C4semidirect
128. C4×C22⋊D11C2×C4semidirect
129. C4×C22⋊D11C2×C4semidirect
138. #66979C2×C4semidirect
173. #66925C2×C4semidirect
175. C42×D11C2×C4semidirect
176. C4×Dic22C2×C4semidirect
177. C4×Dic22C2×C4semidirect
314. #2285D11semidirect
399. C4×D11#117semidirect
597. C2×C42C4×D11semidirect
732. C11#34188semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43392
#130715742
#130715682
#130715662
#130715602
#130715482
#130715462
#130715422
#130715382
#130712232
#130712212
#130712052
#130710232
#130710212
D11×#3842
#130709702
C11×#22852
#3418811