Finite Group Databasebeta

← #14914487

Subgroups — #14914487

Order 2816.

2826 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2#13071632C212yesmaximal, complemented
3#13071621C212yesmaximal, complemented
4#13071595C214yesmaximal, complemented
5#13071558C212yesmaximal, complemented
6#13071520C212yesmaximal, complemented
7#13071511C211yesmaximal, characteristic, complemented
8#13071503C211yesmaximal, characteristic, complemented
9#13071453C211yesmaximal, characteristic, complemented
10#13071444C211yesmaximal, characteristic, complemented
11#13071402C214yesmaximal, complemented
12#13071250C212yesmaximal, complemented
13#13071144C212yesmaximal, complemented
14#13071122C212yesmaximal, complemented
15#13070974C212yesmaximal, complemented
16C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
17C2×C11×#380C211yesmaximal, characteristic, complemented
18C24×C4×C11C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C22×C11×C4⋊C4C2212yes—
21C22×C11×C22⋊C4C2212yes—
22C2×#67006C2212yes—
23C22×C22⋊Dic11C2212yes—
24#10623322C4116yescomplemented
25C2×#66983C2211yescharacteristic
26C2×#66983C2211yescharacteristic
27C2×#66982C2212yes—
28C2×C4×C22⋊D11C2214yes—
29C2×C4×C22⋊D11C2212yes—
30C2×C4×C22⋊D11C2212yes—
31C2×#66979C2211yescharacteristic
32C2×#66977C2211yescharacteristic
33C2×#66977C2211yescharacteristic
34C22×C4×Dic11C2212yes—
35C2×#66946C2212yescomplemented
36C2×#66940C2212yescomplemented
37C2×(C22⋊D11)⋊C4C2214yes—
38C11×#380C2212yes—
39C11×#380C2212yes—
40C11×#380C2211yescharacteristic
41C11×#380C2211yescharacteristic
42C11×#380C2212yes—
43C2×C11×#95C2212yes—
44#10622826C2214yes—
45#10622823C2214yes—
46C4×C22⋊Dic11C2212yes—
47C4×C22⋊Dic11C2214yes—
48C4×C22⋊Dic11C2212yes—
49C4×C22⋊Dic11C2211yescharacteristic
50C4×C22⋊Dic11C2211yescharacteristic
51C4×C22⋊Dic11C2211yescharacteristic
52C4×C22⋊Dic11C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622603C2214yescomplemented
56#10622602C2214yescomplemented
57#10622601C2212yescomplemented
58#10622591C2214yescomplemented
59C4⋊C4×Dic11C2212yescomplemented
60C4⋊C4×Dic11C2212yescomplemented
61#10622587C2212yescomplemented
62#10622586C2212yescomplemented
63#10622586C2212yescomplemented
64#10622585C2214yescomplemented
65#10622571C2214yes—
66#10622570C2214yes—
67#10622569C2214yes—
68#10622559C2214yes—
69#10622558C2214yes—
70#10622557C2214yes—
71C22⋊C4×Dic11C2214yes—
72#10622282C2214yescomplemented
73#10622280C2212yescomplemented
74#10622279C2214yescomplemented
75#10622279C2212yescomplemented
76#10622277C2212yescomplemented
77D11×#95C2212yescomplemented
78#10622265C2214yescomplemented
79#10622264C2212yescomplemented
80#10622263C2212yescomplemented
81#10622262C2214yescomplemented
82#10622262C2212yescomplemented
83#10622261C2212yescomplemented
84C25×C11C2311yescharacteristic
85C23×C4×C11—44no—
86C23×C4×C11C2×C418yescomplemented
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2314yes—
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C22×C22⋊D11C2312yes—
95C22×C22⋊D11C2312yes—
96C22×C22⋊D11C2312yes—
97C23×Dic11C2312yes—
98C23×Dic11C2312yes—
99C2×#4339—44no—
100C2×#4339C2×C418yescomplemented
101C22×D44C2311yescharacteristic
102C22×C4×D11C2314yes—
103C22×C4×D11C2312yes—
104C22×Dic22C2311yescharacteristic
105C2×C11×C4⋊C4—44no—
106C2×C11×C4⋊C4C2312yes—
107C2×C11×C4⋊C4C2312yes—
108C2×C11×C4⋊C4C2314yes—
109C2×C11×C22⋊C4—44no—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113#67006C2×C4116yescomplemented
114C2×C22⋊Dic11—28no—
115C2×C22⋊Dic11C2312yes—
116C2×C22⋊Dic11C2312yes—
117C2×C22⋊Dic11C2312yes—
118C2×C22⋊Dic11C2312yes—
119C2×C22⋊Dic11C2312yes—
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2312yes—
122#66983C2×C418yescomplemented
123#66983C2×C418yescomplemented
124#66982C2×C4116yescomplemented
125C4×C22⋊D11—216no—
126C4×C22⋊D11C2×C4116yescomplemented
127C4×C22⋊D11C2×C4116yescomplemented
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2312yes—
133#66979C2×C418yescomplemented
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136#66977C2×C418yescomplemented
137#66977C2×C418yescomplemented
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2312yes—
142C2×Dic11⋊C4C2312yes—
143C2×C4×Dic11—44no—
144C2×C4×Dic11C2312yes—
145C2×C4×Dic11C2314yes—
146C2×C4×Dic11C2312yes—
147C2×C4×Dic11C2314yes—
148C2×C4×Dic11C2314yes—
149C2×C4×Dic11C2312yes—
150C2×C4×Dic11C2312yes—
151C2×C4×Dic11C2312yes—
152#66946—44no—
153#66940—44no—
154(C22⋊D11)⋊C4—48no—
155C11×#95C2312yes—
156C11×#95C2312yes—
157C11×#95C2314yes—
158C11⋊#95C2311yescharacteristic
159C11⋊#95C2314yes—
160C11⋊#95C2311yescharacteristic
161C11⋊#95C2314yes—
162C11⋊#95C2311yescharacteristic
163C11⋊#95C2314yes—
164C11⋊#95C2311yescharacteristic
165C11⋊#95C2314yes—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2312yes—
169C11⋊#95C2312yes—
170#34233—111nomaximal, Sylow
171C24×C11—24no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—42no—
175C24×C11C22×C414yes—
176C24×C11C2411yescharacteristic
177C24×C11C2411yescharacteristic
178C24×C11C2411yescharacteristic
179C23×D11C2412yes—
180C22×C4×C11—24no—
181C22×C4×C11—24no—
182C22×C4×C11—24no—
183C22×C4×C11—28no—
184C22×C4×C11—416no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11—44no—
189C22×C4×C11—44no—
190C22×C4×C11C22×C414yes—
191C22×C4×C11C22×C414yes—
192C22×C4×C11C22×C414yes—
193C22×C4×C11C22×C414yes—
194C22×C4×C11C22×C414yes—
195C22×C4×C11C22×C414yes—
196C22×C4×C11C2414yes—
197C22×C4×C11C2414yes—
198C22×C4×C11C2411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C22×C4×C11C2411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—28no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—44no—
206C2×C22⋊D11C22×C418yes—
207C2×C22⋊D11C22×C418yes—
208C2×C22⋊D11C22×C418yes—
209C22×Dic11—24no—
210C22×Dic11—24no—
211C22×Dic11—24no—
212C22×Dic11—24no—
213C22×Dic11—42no—
214C22×Dic11—42no—
215C22×Dic11C2412yes—
216C22×Dic11C2412yes—
217C22×Dic11C2412yes—
218C22×Dic11C2412yes—
219C22×Dic11C2412yes—
220C22×Dic11C2412yes—
221C22×Dic11C2412yes—
222#4339—416no—
223C2×D44—24no—
224C2×D44C22×C414yes—
225C2×C4×D11—28no—
226C2×C4×D11—44no—
227C2×C4×D11—44no—
228C2×C4×D11—44no—
229C2×C4×D11C22×C418yes—
230C2×Dic22—24no—
231C2×Dic22C22×C414yes—
232C11×C4⋊C4—24no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—44no—
235C11×C22⋊C4—28no—
236C11×C22⋊C4—42no—
237C11×C22⋊C4—42no—
238C22⋊Dic11—24no—
239C22⋊Dic11—24no—
240C22⋊Dic11—24no—
241C22⋊Dic11C22×C418yes—
242C22⋊Dic11C22×C418yes—
243C22⋊Dic11C22×C418yes—
244C22⋊Dic11#4118yescomplemented
245(C2×D11)⋊C4—28no—
246(C2×D11)⋊C4—44no—
247(C2×D11)⋊C4—44no—
248(C2×D11)⋊C4C22×C418yes—
249(C2×D11)⋊C4C22×C418yes—
250C4⋊Dic11C22×C414yes—
251C4⋊Dic11C22×C414yes—
252Dic11⋊C4—28no—
253Dic11⋊C4—44no—
254Dic11⋊C4—44no—
255Dic11⋊C4C22×C418yes—
256Dic11⋊C4C22×C418yes—
257C4×Dic11—28no—
258C4×Dic11—24no—
259C4×Dic11—24no—
260C4×Dic11—44no—
261C4×Dic11—44no—
262C4×Dic11—42no—
263C4×Dic11—42no—
264C4×Dic11C22×C418yes—
265C2×#525—111no—
266#2361—112no—
267#2360—112no—
268#2358—114no—
269#2353—112no—
270#2349—112no—
271#2347—111no—
272#2346—111no—
273#2341—111no—
274#2339—111no—
275#2335—114no—
276#2318—112no—
277C4×C22⋊Q8—112no—
278C4×#121—112no—
279C2×#380D1111yescharacteristic, complemented
280#2275—112no—
281C2×C4×C22⋊C4—111no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—28no—
288C23×C11—28no—
289C23×C11—22no—
290C23×C11—21no—
291C23×C11—22no—
292C23×C11—21no—
293C23×C11—44no—
294C23×C11—48no—
295C23×C11—48no—
296C23×C11C23×C412yes—
297C23×C11C23×C412yes—
298C23×C11C23×C412yes—
299C23×C11C2×#4114yes—
300C23×C11H(5,𝔽2)12yes—
301C23×C112−1+412yes—
302C23×C11C2511yescharacteristic
303C22×D11—24no—
304C22×D11—22no—
305C22×D11—24no—
306C22×D11—22no—
307C22×D11C23×C414yes—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—28no—
312C2×C4×C11—28no—
313C2×C4×C11—28no—
314C2×C4×C11—24no—
315C2×C4×C11—24no—
316C2×C4×C11—24no—
317C2×C4×C11—24no—
318C2×C4×C11—24no—
319C2×C4×C11—24no—
320C2×C4×C11—44no—
321C2×C4×C11—44no—
322C2×C4×C11—44no—
323C2×C4×C11—88no—
324C2×C4×C11C23×C412yes—
325C2×C4×C11C23×C412yes—
326C2×C4×C11C23×C412yes—
327C2×C4×C11C23×C412yes—
328C2×C4×C11H(5,𝔽2)14yes—
329C22⋊D11—216no—
330C22⋊D11—216no—
331C22⋊D11—48no—
332C2×Dic11—24no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—24no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—48no—
347C2×Dic11—48no—
348C2×Dic11C23×C414yes—
349C2×Dic11C23×C414yes—
350C2×Dic11C23×C414yes—
351C2×Dic11C2×#4114yes—
352C2×Dic11C2×#4114yes—
353D44—28no—
354C4×D11—48no—
355C4×D11—88no—
356Dic22—28no—
357C22×#41—111no—
358C24×C4C2×D1111yescharacteristic
359#525—1116no—
360C2×#123—112no—
361C2×C22⋊Q8—111no—
362C2×C22⋊Q8—111no—
363C2×#121—111no—
364C2×#121—111no—
365C2×#120—112no—
366C2×C4×Q8—112no—
367C2×C4×D4—112no—
368C2×C4×D4—112no—
369C2×C4×D4—114no—
370C2×C4×D4—112no—
371C2×C4×D4—114no—
372C2×#117—111no—
373C22×C4⋊C4C2×D1112yes—
374C22×C22⋊C4—112no—
375C22×C22⋊C4C2×D1112yes—
376C22×C42—112no—
377#391—112no—
378#390—112no—
379#390—114no—
380#389—114no—
381#389—112no—
382#389—112no—
383#388—114no—
384#388—114no—
385#388—114no—
386#388—114no—
387#387—114no—
388#387—114no—
389#386—114no—
390#386—114no—
391#386—114no—
392#385—114no—
393#385—114no—
394#385—114no—
395#383—112no—
396#382—112no—
397#381—112no—
398#380—112no—
399#380C2×D1112yes—
400#380C2×D1111yescharacteristic
401#380C2×D1111yescharacteristic
402#380C2×D1112yes—
403#380C2×D1112yes—
404C4×C4⋊C4—112no—
405C4×C4⋊C4—112no—
406C4×C4⋊C4—114no—
407C4×C4⋊C4—112no—
408C4×C22⋊C4—111no—
409C4×C22⋊C4—112no—
410C4×C22⋊C4—111no—
411C4×C22⋊C4—111no—
412C4×C22⋊C4—114no—
413C4×C22⋊C4—112no—
414C4×C22⋊C4—111no—
415C4×C22⋊C4—114no—
416C4×C22⋊C4—114no—
417C4×C22⋊C4—112no—
418#376—112no—
419C2×#95—111no—
420C2×#95—111no—
421C2×#95—112no—
422C2×#95C2×D1112yes—
423C22×C11—22no—
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—24no—
428C22×C11—24no—
429C22×C11—24no—
430C22×C11—24no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—416no—
435C22×C11—42no—
436C22×C11—42no—
437C22×C11C4×#4114yes—
438C22×C11#52014yes—
439C22×C11C24×C411yescharacteristic
440C22×C11C22×#4112yes—
441C22×C11C2×H(5,𝔽2)12yes—
442C22×C11C2×H(5,𝔽2)11yescharacteristic
443C22×C11C2×2−1+411yescharacteristic
444C2×D11—24no—
445C2×D11—24no—
446C2×D11—24no—
447C2×D11—44no—
448C2×D11—44no—
449C4×C11—22no—
450C4×C11—22no—
451C4×C11—22no—
452C4×C11—44no—
453C4×C11—44no—
454C4×C11#51814yes—
455Dic11—24no—
456Dic11—24no—
457Dic11—24no—
458Dic11—24no—
459Dic11—24no—
460Dic11—42no—
461Dic11—42no—
462C25C22×D1111yescharacteristic
463C2×#41—118no—
464C2×#41—444no—
465C22×Q8—111no—
466C22×D4—112no—
467C22×D4—112no—
468C22×D4—112no—
469C22×D4—111no—
470C23×C4—44no—
471C23×C4—112no—
472C23×C4—112no—
473C23×C4—112no—
474C23×C4—114no—
475C23×C4C4×D1118yescomplemented
476C23×C4C22×D1111yescharacteristic
477C23×C4C22×D1111yescharacteristic
478C23×C4C22×D1111yescharacteristic
479C23×C4C22×D1114yes—
480C23×C4C22×D1111yescharacteristic
481C23×C4C22×D1111yescharacteristic
482C23×C4C22×D1111yescharacteristic
483#123—1116no—
484C22⋊Q8—118no—
485C22⋊Q8—118no—
486#121—118no—
487#121—118no—
488#120—1116no—
489C4×Q8—444no—
490C4×D4—1116no—
491C4×D4—1116no—
492C4×D4—2216no—
493C4×D4—444no—
494C4×D4—448no—
495#117—118no—
496C2×C4⋊C4—44no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—112no—
500C2×C4⋊C4—112no—
501C2×C4⋊C4—114no—
502C2×C4⋊C4—114no—
503C2×C4⋊C4—114no—
504C2×C4⋊C4C22×D1112yes—
505C2×C4⋊C4C22×D1112yes—
506C2×C4⋊C4C22×D1114yes—
507C2×C22⋊C4—44no—
508C2×C22⋊C4—112no—
509C2×C22⋊C4—112no—
510C2×C22⋊C4—112no—
511C2×C22⋊C4—112no—
512C2×C22⋊C4—112no—
513C2×C22⋊C4—112no—
514C2×C22⋊C4—112no—
515C2×C22⋊C4—112no—
516C2×C22⋊C4—112no—
517C2×C22⋊C4—114no—
518C2×C22⋊C4—114no—
519C2×C22⋊C4—114no—
520C2×C22⋊C4—228no—
521C2×C22⋊C4C22×D1114yes—
522C2×C22⋊C4C22×D1112yes—
523C2×C22⋊C4C22×D1112yes—
524C2×C42—112no—
525C2×C42—114no—
526C2×C42—112no—
527C2×C42—112no—
528C2×C42—114no—
529C2×C42—114no—
530C2×C42—112no—
531C2×C42—112no—
532C2×C42—444no—
533#95—111no—
534#95—111no—
535#95—111no—
536#95—111no—
537#95—112no—
538#95—112no—
539#95—114no—
540#95—114no—
541#95—114no—
542#95—114no—
543#95—114no—
544#95—114no—
545#95C22×D1112yes—
546#95C22×D1112yes—
547#95C22×D1114yes—
548C2×C11—24no—
549C2×C11—24no—
550C2×C11—42no—
551C2×C11C2×C4×#4111yescharacteristic
552C2×C11C2×#51811yescharacteristic
553C2×C11C2×#52011yescharacteristic
554C2×C11#351912yes—
555C2×C11#352012yes—
556D11—44no—
557C24—22no—
558C24—22no—
559C24—24no—
560C24—42no—
561C24—112no—
562C24C2×C4×D1114yes—
563C24C23×D1111yescharacteristic
564C24C23×D1111yescharacteristic
565C24C23×D1111yescharacteristic
566#41—4416no—
567C2×Q8—114no—
568C2×Q8—224no—
569C2×D4—118no—
570C2×D4—118no—
571C2×D4—118no—
572C2×D4—114no—
573C2×D4—224no—
574C2×D4—224no—
575C2×D4—228no—
576C2×D4—224no—
577C2×D4—444no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—28no—
582C22×C4—416no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—112no—
589C22×C4—112no—
590C22×C4—112no—
591C22×C4—112no—
592C22×C4—112no—
593C22×C4—118no—
594C22×C4—112no—
595C22×C4—112no—
596C22×C4—228no—
597C22×C4—224no—
598C22×C4—224no—
599C22×C4—224no—
600C22×C4—224no—
601C22×C4—444no—
602C22×C4—444no—
603C22×C4—444no—
604C22×C4—442no—
605C22×C4—442no—
606C22×C4C2×C4×D1114yes—
607C22×C4C2×C4×D1114yes—
608C22×C4C2×C4×D1114yes—
609C22×C4C2×C4×D1114yes—
610C22×C4C2×C4×D1114yes—
611C22×C4C2×C4×D1114yes—
612C22×C4C23×D1114yes—
613C22×C4C23×D1114yes—
614C22×C4C23×D1111yescharacteristic
615C22×C4C23×D1111yescharacteristic
616C22×C4C23×D1111yescharacteristic
617C22×C4C23×D1111yescharacteristic
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—44no—
621C4⋊C4—114no—
622C4⋊C4—114no—
623C4⋊C4—118no—
624C4⋊C4—118no—
625C4⋊C4—228no—
626C4⋊C4—444no—
627C4⋊C4—444no—
628C22⋊C4—28no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—118no—
632C22⋊C4—118no—
633C22⋊C4—118no—
634C22⋊C4—118no—
635C22⋊C4—118no—
636C22⋊C4—118no—
637C22⋊C4—228no—
638C22⋊C4—224no—
639C22⋊C4—224no—
640C22⋊C4—224no—
641C22⋊C4—444no—
642C22⋊C4—444no—
643C42—118no—
644C42—228no—
645C42—224no—
646C42—224no—
647C42—442no—
648C42—442no—
649C42—444no—
650C42—444no—
651C11#3423311yescharacteristic, complemented, Sylow
652C23—22no—
653C23—22no—
654C23—21no—
655C23—21no—
656C23—22no—
657C23—28no—
658C23—28no—
659C23—21no—
660C23—22no—
661C23—21no—
662C23—22no—
663C23—44no—
664C23—48no—
665C23—48no—
666C23—114no—
667C23—222no—
668C23—224no—
669C23—222no—
670C23—224no—
671C23C22×C4×D1112yes—
672C23C22×C4×D1112yes—
673C23C22×C4×D1112yes—
674C23#6703712yes—
675C23#6704012yes—
676C23#41×D1114yes—
677C23C24×D1111yescharacteristic
678Q8—228no—
679D4—2216no—
680D4—2216no—
681D4—228no—
682D4—448no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—28no—
687C2×C4—28no—
688C2×C4—28no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—88no—
699C2×C4—114no—
700C2×C4—114no—
701C2×C4—114no—
702C2×C4—114no—
703C2×C4—114no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—224no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—224no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—448no—
719C2×C4—448no—
720C2×C4—448no—
721C2×C4—888no—
722C2×C4C22×C4×D1112yes—
723C2×C4C22×C4×D1112yes—
724C2×C4C22×C4×D1112yes—
725C2×C4C22×C4×D1112yes—
726C2×C4#6703714yes—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—416no—
739C22—42no—
740C22—42no—
741C22—224no—
742C22—224no—
743C22—224no—
744C22—444no—
745C22—444no—
746C22#1062303514yes—
747C22#1062305314yes—
748C22C23×C4×D1111yescharacteristic
749C22C2×#6703711yescharacteristic
750C22C2×#6703712yes—
751C22C2×#6704011yescharacteristic
752C22C2×#41×D1112yes—
753C4—22no—
754C4—22no—
755C4—22no—
756C4—44no—
757C4—44no—
758C4—224no—
759C4—224no—
760C4—224no—
761C4—224no—
762C4—224no—
763C4—442no—
764C4—442no—
765C4#1062301714yes—
766C2—24no—
767C2—24no—
768C2—42no—
769C2—444no—
770C2C2×#1062305311yescharacteristic
771C2C2×#1062301711yescharacteristic
772C2C2×#1062303511yescharacteristic
773C2#1308264212yes—
774C2#1308265912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#380C2
socle, cosocleC23×C11C25
prime radicalC2×#10623322C2
hypercenterC2×#380D11
hypocenterC11#34233
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. #13071632C2semidirect
3. #13071621C2semidirect
4. #13071595C2semidirect
5. #13071558C2semidirect
6. #13071520C2semidirect
7. #13071511C2semidirect
8. #13071503C2semidirect
9. #13071453C2semidirect
10. #13071444C2semidirect
11. #13071402C2semidirect
12. #13071250C2semidirect
13. #13071144C2semidirect
14. #13071122C2semidirect
15. #13070974C2semidirect
16. C2×C4×C22⋊Dic11C2semidirect
17. C2×C11×#380C2semidirect
24. #10623322C4semidirect
35. C2×#66946C22semidirect
36. C2×#66940C22semidirect
55. #10622603C22semidirect
56. #10622602C22semidirect
57. #10622601C22semidirect
58. #10622591C22semidirect
59. C4⋊C4×Dic11C22semidirect
60. C4⋊C4×Dic11C22semidirect
61. #10622587C22semidirect
62. #10622586C22semidirect
63. #10622586C22semidirect
64. #10622585C22semidirect
72. #10622282C22semidirect
73. #10622280C22semidirect
74. #10622279C22semidirect
75. #10622279C22semidirect
76. #10622277C22semidirect
77. D11×#95C22semidirect
78. #10622265C22semidirect
79. #10622264C22semidirect
80. #10622263C22semidirect
81. #10622262C22semidirect
82. #10622262C22semidirect
83. #10622261C22semidirect
86. C23×C4×C11C2×C4semidirect
100. C2×#4339C2×C4semidirect
113. #67006C2×C4semidirect
122. #66983C2×C4semidirect
123. #66983C2×C4semidirect
124. #66982C2×C4semidirect
126. C4×C22⋊D11C2×C4semidirect
127. C4×C22⋊D11C2×C4semidirect
133. #66979C2×C4semidirect
136. #66977C2×C4semidirect
137. #66977C2×C4semidirect
244. C22⋊Dic11#41semidirect
279. C2×#380D11semidirect
475. C23×C4C4×D11semidirect
651. C11#34233semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
#130716322
#130716212
#130715952
#130715582
#130715202
#130715112
#130715032
#130714532
#130714442
#130714022
#130712502
#130711442
#130711222
#130709742
C2×C4×C22⋊Dic112
C2×C11×#3802
#3423311