Finite Group Databasebeta

← #14769834

Subgroups — #14769834

Order 2816.

1202 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623059C211yesmaximal, characteristic
2C2×#10622449C211yesmaximal, characteristic, complemented
3C2×#10622447C211yesmaximal, characteristic, complemented
4#13069555C211yesmaximal, characteristic, complemented
5#13069551C211yesmaximal, characteristic, complemented
6#13068910C211yesmaximal, characteristic, complemented
7#13068905C211yesmaximal, characteristic, complemented
8#13068905C211yesmaximal, characteristic, complemented
9#13068905C211yesmaximal, characteristic, complemented
10#13068686C211yesmaximal, characteristic, complemented
11#13068683C211yesmaximal, characteristic, complemented
12#13068382C211yesmaximal, characteristic, complemented
13#13068311C211yesmaximal, characteristic, complemented
14D11×#336C211yesmaximal, characteristic, complemented
15C11×#1798C211yesmaximal, characteristic, complemented
16C2×C11×#117C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23#10623059—24no—
24#10623059—24no—
25C2×#66951C411yescharacteristic
26C2×#66949C411yescharacteristic
27C2×#66947C411yescharacteristic
28C2×#66942C411yescharacteristic
29C2×#66938C411yescharacteristic
30C2×#66937C411yescharacteristic
31C2×#66936C411yescharacteristic
32C2×#66932C411yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C2×#66925C2211yescharacteristic
35C2×C42×D11C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic
46C2×(C2×D11)⋊C8C2211yescharacteristic
47C2×#66867C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622449—24no—
50#10622447—24no—
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11C2×C411yescharacteristic
65C22×C22⋊D11C2×C411yescharacteristic
66C22×D44C2×C411yescharacteristic
67C22×C4×D11C2×C411yescharacteristic
68C22×C4×D11C2×C411yescharacteristic
69C22×C4×D11C2311yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×Dic22C2×C411yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×#117—22no—
77C11×#117—22no—
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C11×C4⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4C2×C411yescharacteristic
81C2×C11×C22⋊C4C2×C411yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11C2×C411yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86C4×C22⋊D11—22no—
87C4×C22⋊D11—22no—
88C4×C22⋊D11—22no—
89C4×C22⋊D11—22no—
90C2×(C2×D11)⋊C4C2×C411yescharacteristic
91C2×(C2×D11)⋊C4C2×C411yescharacteristic
92C2×(C2×D11)⋊C4C2×C411yescharacteristic
93C2×(C2×D11)⋊C4C2×C411yescharacteristic
94C2×(C2×D11)⋊C4C2×C411yescharacteristic
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96C2×C4⋊Dic11C2×C411yescharacteristic
97C2×C4⋊Dic11C2×C411yescharacteristic
98C2×Dic11⋊C4C2×C411yescharacteristic
99C2×Dic11⋊C4C2×C411yescharacteristic
100C2×Dic11⋊C4C2×C411yescharacteristic
101C2×Dic11⋊C4C2×C411yescharacteristic
102C2×Dic11⋊C4C2×C411yescharacteristic
103C2×Dic11⋊C4C2×C411yescharacteristic
104C2×C4×Dic11C2×C411yescharacteristic
105C2×C4×Dic11C2×C411yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C2×#4313—22no—
113C2×#4313—22no—
114C2×#4313—41no—
115C2×C8×D11—22no—
116C2×C8×D11—22no—
117C2×C8×D11—22no—
118C2×C8×D11—22no—
119C2×C8×D11—22no—
120C2×C8×D11—22no—
121C2×C8×D11—41no—
122C2×C8×D11—41no—
123C2×C8×D11—41no—
124#66951—24no—
125#66949—24no—
126#66947—24no—
127#66942—24no—
128#66938—24no—
129#66937—24no—
130#66936—24no—
131#66932—24no—
132C4×D44D414yes—
133C4×D44D414yes—
134#66925—22no—
135#66925—22no—
136C42×D11—22no—
137C42×D11—22no—
138C4×Dic22—22no—
139C4×Dic22—22no—
140C11×C4⋊C8—22no—
141C11×C4⋊C8—22no—
142C11×C22⋊C8—41no—
143C11×C22⋊C8—41no—
144C22⋊(C11⋊C8)—22no—
145C22⋊(C11⋊C8)—22no—
146(C2×D11)⋊C8—22no—
147(C2×D11)⋊C8—22no—
148(C2×D11)⋊C8—22no—
149(C2×D11)⋊C8—22no—
150#66867—22no—
151C4×C11⋊C8—22no—
152#22470—111nomaximal, Sylow
153C24×C11C22×C411yescharacteristic
154C23×D11C22×C411yescharacteristic
155C23×D11C22×C411yescharacteristic
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C22×C411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—22no—
169C2×C22⋊D11—22no—
170C2×C22⋊D11—22no—
171C2×C22⋊D11—22no—
172C2×C22⋊D11—22no—
173C2×C22⋊D11—41no—
174C22×Dic11C22×C411yescharacteristic
175C22×Dic11C22×C411yescharacteristic
176C22×Dic11C22×C411yescharacteristic
177C22×Dic11C22×C411yescharacteristic
178C22×Dic11C22×C411yescharacteristic
179C22×Dic11C22×C411yescharacteristic
180C2×D44—22no—
181C2×D44—22no—
182C2×D44C22⋊C414yes—
183C2×C4×D11—22no—
184C2×C4×D11—22no—
185C2×C4×D11—22no—
186C2×C4×D11—22no—
187C2×C4×D11—22no—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—21no—
192C2×C4×D11—21no—
193C2×C4×D11—21no—
194C2×C4×D11—21no—
195C2×C4×D11—21no—
196C2×C4×D11—41no—
197C2×C4×D11C2×D412yes—
198C2×C4×D11C2×D412yes—
199C2×C4×D11C2×D412yes—
200C2×C4×D11C2×D412yes—
201C2×Dic22—22no—
202C2×Dic22—22no—
203C2×Dic22—41no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11C2×D412yes—
223C42×C11C2×D412yes—
224C22⋊Dic11—22no—
225C22⋊Dic11—22no—
226(C2×D11)⋊C4—22no—
227(C2×D11)⋊C4—22no—
228(C2×D11)⋊C4—22no—
229(C2×D11)⋊C4—22no—
230(C2×D11)⋊C4C22⋊C414yes—
231(C2×D11)⋊C4C22⋊C414yes—
232C4⋊Dic11—22no—
233C4⋊Dic11C22⋊C414yes—
234Dic11⋊C4—22no—
235Dic11⋊C4—22no—
236Dic11⋊C4—22no—
237Dic11⋊C4—22no—
238Dic11⋊C4—22no—
239Dic11⋊C4—22no—
240C4×Dic11—22no—
241C4×Dic11—22no—
242C4×Dic11—21no—
243C4×Dic11—21no—
244C4×Dic11—21no—
245C4×Dic11—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8#4112yes—
257C2×C11⋊C8#4112yes—
258#4313—44no—
259C8×D11—44no—
260C8×D11—44no—
261C8×D11—44no—
262C2×#529—111no—
263C2×#435—111no—
264C2×C8×D4—111no—
265#1985—111no—
266#1984—111no—
267#1870—111no—
268#1869—111no—
269#1869—111no—
270#1869—111no—
271#1818—111no—
272#1817—111no—
273#1798D1111yescharacteristic, complemented
274#1750—111no—
275#1729—111no—
276C2×#336—111no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11C23×C411yescharacteristic
285C22×D11—21no—
286C22×D11—21no—
287C22×D11—21no—
288C22×D11—21no—
289C22×D11—21no—
290C22×D11—21no—
291C22×D11—21no—
292C22×D11—21no—
293C22×D11—21no—
294C22×D11—21no—
295C22×D11C2×C22⋊C412yes—
296C22×D11C2×C22⋊C412yes—
297C22×D11#13112yes—
298C22×D11#13112yes—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11C2×C22⋊C412yes—
317C2×C4×C11C2×C22⋊C412yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×C4×C112−1+411yescharacteristic
324C22⋊D11—44no—
325C22⋊D11—44no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—21no—
334C2×Dic11—21no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11C2×C22⋊C412yes—
342C2×Dic11C2×C22⋊C412yes—
343C2×Dic11#13112yes—
344D44—28no—
345C4×D11—22no—
346C4×D11—22no—
347C4×D11—22no—
348C4×D11—22no—
349C4×D11—22no—
350C4×D11—22no—
351C4×D11—22no—
352C4×D11—22no—
353C4×D11—44no—
354C4×D11—44no—
355Dic22—44no—
356C8×C11—41no—
357C8×C11—41no—
358C8×C11—41no—
359C8×C11—41no—
360C11⋊C8—22no—
361C11⋊C8—22no—
362C11⋊C8—41no—
363C11⋊C8—41no—
364C22×M16—111no—
365C23×C8—111no—
366C23×C8—111no—
367C23×C8—111no—
368#529—224no—
369#529—224no—
370C2×#126—111no—
371C2×#126—111no—
372C2×#125—111no—
373C2×#124—111no—
374C2×#123—111no—
375C2×#123—111no—
376C2×C22⋊Q8—111no—
377C2×#121—111no—
378C2×C4×Q8—111no—
379C2×C4×D4—111no—
380C2×C4×D4—111no—
381C2×C4×D4—111no—
382C2×#117—111no—
383C2×#117C2×D1111yescharacteristic
384C22×C42—111no—
385#435—224no—
386C8×D4—224no—
387C2×C4⋊C8C2×D1111yescharacteristic
388C2×C4⋊C8C2×D1111yescharacteristic
389C2×C22⋊C8—111no—
390C2×C22⋊C8—111no—
391C2×C22⋊C8—111no—
392C2×C22⋊C8—111no—
393C2×C22⋊C8—111no—
394C2×C22⋊C8—111no—
395C2×C22⋊C8C2×D1111yescharacteristic
396C2×C22⋊C8C2×D1111yescharacteristic
397C2×#97—111no—
398C2×C4×C8—111no—
399#336—111no—
400#336—111no—
401#336—111no—
402#336—111no—
403#336—111no—
404#336—111no—
405#336—111no—
406#336—111no—
407#336—111no—
408#336—111no—
409#336C2×D1111yescharacteristic
410#336C2×D1111yescharacteristic
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11C22×C22⋊C411yescharacteristic
419C22×C11C4×#4111yescharacteristic
420C22×C11#52011yescharacteristic
421C22×C11C2×#13111yescharacteristic
422C22×C11C2×#13111yescharacteristic
423C22×C11C2×#13111yescharacteristic
424C22×C11#56811yescharacteristic
425C2×D11—22no—
426C2×D11—22no—
427C2×D11—22no—
428C2×D11—22no—
429C2×D11—22no—
430C2×D11—22no—
431C2×D11—22no—
432C2×D11—22no—
433C2×D11—22no—
434C2×D11—41no—
435C2×D11—41no—
436C2×D11—41no—
437C2×D11—41no—
438C2×D11#40814yes—
439C4×C11—22no—
440C4×C11—22no—
441C4×C11—41no—
442C4×C11—41no—
443C4×C11—41no—
444C4×C11#54611yescharacteristic
445C4×C11#54611yescharacteristic
446C4×C11#54711yescharacteristic
447C4×C11#54711yescharacteristic
448Dic11—22no—
449Dic11—22no—
450Dic11—22no—
451Dic11—41no—
452Dic11—41no—
453Dic11—41no—
454C22×Q8—111no—
455C22×D4—111no—
456C22×D4—111no—
457C22×D4—111no—
458C23×C4—111no—
459C23×C4—111no—
460C23×C4—111no—
461C23×C4—111no—
462C23×C4C22×D1111yescharacteristic
463C2×M16—222no—
464C2×M16—222no—
465C2×M16—441no—
466C22×C8—111no—
467C22×C8—111no—
468C22×C8—111no—
469C22×C8—111no—
470C22×C8—222no—
471C22×C8—222no—
472C22×C8—222no—
473C22×C8—222no—
474C22×C8—222no—
475C22×C8—222no—
476C22×C8—441no—
477C22×C8—441no—
478C22×C8—441no—
479C22×C8C22×D1111yescharacteristic
480C22×C8C22×D1111yescharacteristic
481C22×C8C22×D1111yescharacteristic
482C22×C8C22×D1111yescharacteristic
483#126—224no—
484#126—224no—
485#125—224no—
486#124—224no—
487#123—224no—
488#123—224no—
489C22⋊Q8—224no—
490#121—224no—
491C4×Q8—222no—
492C4×Q8—222no—
493C4×D4—114no—
494C4×D4—114no—
495C4×D4—222no—
496C4×D4—222no—
497C4×D4—222no—
498C4×D4—222no—
499#117—22no—
500#117—22no—
501#117—222no—
502#117—222no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4C4×D1111yescharacteristic
512C2×C4⋊C4C4×D1111yescharacteristic
513C2×C22⋊C4—111no—
514C2×C22⋊C4—111no—
515C2×C22⋊C4—111no—
516C2×C22⋊C4—111no—
517C2×C22⋊C4—111no—
518C2×C22⋊C4—111no—
519C2×C22⋊C4—111no—
520C2×C22⋊C4—111no—
521C2×C22⋊C4C4×D1111yescharacteristic
522C2×C22⋊C4C4×D1111yescharacteristic
523C2×C42—111no—
524C2×C42—111no—
525C2×C42—111no—
526C2×C42—111no—
527C2×C42—222no—
528C2×C42—222no—
529C2×C42C22×D1111yescharacteristic
530C2×C42C22×D1111yescharacteristic
531C4⋊C8—22no—
532C4⋊C8—22no—
533C22⋊C8—41no—
534C22⋊C8—41no—
535C22⋊C8—222no—
536C22⋊C8—222no—
537C22⋊C8—222no—
538C22⋊C8—222no—
539C22⋊C8—222no—
540C22⋊C8—222no—
541#97—222no—
542C4×C8—222no—
543C2×C11—81no—
544C2×C11#233911yescharacteristic
545C2×C11C2×#40811yescharacteristic
546C2×C11#288011yescharacteristic
547C2×C11#296611yescharacteristic
548C2×C11#296811yescharacteristic
549C2×C11#299211yescharacteristic
550C2×C11#299411yescharacteristic
551D11—24no—
552D11—42no—
553C24—111no—
554C24—111no—
555C24C2×C4×D1111yescharacteristic
556C2×Q8—222no—
557C2×Q8—222no—
558C2×Q8—441no—
559C2×D4—114no—
560C2×D4—222no—
561C2×D4—222no—
562C2×D4—222no—
563C2×D4—222no—
564C2×D4—222no—
565C2×D4—222no—
566C2×D4—222no—
567C2×D4—441no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—111no—
575C22×C4—111no—
576C22×C4—111no—
577C22×C4—112no—
578C22×C4—112no—
579C22×C4—112no—
580C22×C4—112no—
581C22×C4—111no—
582C22×C4—111no—
583C22×C4—111no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—441no—
598C22×C4C2×C4×D1111yescharacteristic
599C22×C4C2×C4×D1111yescharacteristic
600C22×C4C2×C4×D1111yescharacteristic
601C22×C4C2×C4×D1111yescharacteristic
602C22×C4C2×C4×D1111yescharacteristic
603C22×C4C23×D1111yescharacteristic
604M16—444no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—112no—
618C2×C8—112no—
619C2×C8—221no—
620C2×C8—221no—
621C2×C8—221no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—221no—
625C2×C8—221no—
626C2×C8—221no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—444no—
630C2×C8—444no—
631C2×C8—444no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—114no—
635C4⋊C4—222no—
636C4⋊C4—222no—
637C4⋊C4—222no—
638C4⋊C4—222no—
639C4⋊C4—222no—
640C4⋊C4—222no—
641C4⋊C4—222no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—114no—
645C22⋊C4—114no—
646C22⋊C4—222no—
647C22⋊C4—222no—
648C22⋊C4—222no—
649C22⋊C4—222no—
650C22⋊C4—222no—
651C22⋊C4—222no—
652C42—21no—
653C42—21no—
654C42—222no—
655C42—222no—
656C42—221no—
657C42—221no—
658C42—221no—
659C42—221no—
660C42D4×D1112yes—
661C42D4×D1112yes—
662C11#2247011yescharacteristic, complemented, Sylow
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—112no—
671C23—112no—
672C23—112no—
673C23—112no—
674C23—221no—
675C23—221no—
676C23—221no—
677C23—221no—
678C23—221no—
679C23—221no—
680C23—221no—
681C23—221no—
682C23—221no—
683C23—221no—
684C23C22×C4×D1111yescharacteristic
685Q8—444no—
686D4—228no—
687D4—444no—
688D4—444no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—112no—
707C2×C4—112no—
708C2×C4—112no—
709C2×C4—221no—
710C2×C4—221no—
711C2×C4—221no—
712C2×C4—221no—
713C2×C4—221no—
714C2×C4—221no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—221no—
724C2×C4—221no—
725C2×C4—221no—
726C2×C4—221no—
727C2×C4—221no—
728C2×C4—221no—
729C2×C4—221no—
730C2×C4—221no—
731C2×C4—221no—
732C2×C4—444no—
733C2×C4—444no—
734C2×C4C22⋊C4×D1112yes—
735C2×C4C22⋊C4×D1112yes—
736C2×C4C2×D4×D1111yescharacteristic
737C2×C4C2×D4×D1111yescharacteristic
738C2×C4#6703711yescharacteristic
739C2×C4#6704011yescharacteristic
740C2×C4#41×D1111yescharacteristic
741C2×C4#41×D1111yescharacteristic
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—222no—
747C8—222no—
748C8—441no—
749C8—441no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—114no—
758C22—222no—
759C22—222no—
760C22—222no—
761C22—222no—
762C22—222no—
763C22—222no—
764C22—222no—
765C22—222no—
766C22—222no—
767C22—441no—
768C22—441no—
769C22—441no—
770C22—441no—
771C22C2×C22⋊C4×D1111yescharacteristic
772C22#1062303511yescharacteristic
773C22#1062305311yescharacteristic
774C22D11×#13111yescharacteristic
775C22D11×#13111yescharacteristic
776C22D11×#13111yescharacteristic
777C22#1062328111yescharacteristic
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—222no—
784C4—222no—
785C4—222no—
786C4—441no—
787C4—441no—
788C4—441no—
789C4#1062314311yescharacteristic
790C4#1062314311yescharacteristic
791C4#1062316211yescharacteristic
792C4#1062316211yescharacteristic
793C2—81no—
794C2—224no—
795C2—442no—
796C2#1307144411yescharacteristic
797C2D11×#40811yescharacteristic
798C2#1307706411yescharacteristic
799C2#1307758911yescharacteristic
800C2#1307760811yescharacteristic
801C2#1307775311yescharacteristic
802C2#1307777411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1798C2
prime radicalC2×#66937C4
cosocleC22×C4×C11C24
hypercenter#1798D11
hypocenterC11#22470
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. C2×#10622449C2semidirect
3. C2×#10622447C2semidirect
4. #13069555C2semidirect
5. #13069551C2semidirect
6. #13068910C2semidirect
7. #13068905C2semidirect
8. #13068905C2semidirect
9. #13068905C2semidirect
10. #13068686C2semidirect
11. #13068683C2semidirect
12. #13068382C2semidirect
13. #13068311C2semidirect
14. D11×#336C2semidirect
15. C11×#1798C2semidirect
273. #1798D11semidirect
662. C11#22470semidirect

Maximal subgroups

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

subgroupindex
C2×#106230592
C2×#106224492
C2×#106224472
#130695552
#130695512
#130689102
#130689052
#130686862
#130686832
#130683822
#130683112
D11×#3362
C11×#17982
#2247011