Finite Group Databasebeta

← #14769851

Subgroups — #14769851

Order 2816.

1424 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4343C211yesmaximal, characteristic
2C2×#10622319C211yesmaximal, characteristic, complemented
3C2×#10622449C211yesmaximal, characteristic, complemented
4#13069557C211yesmaximal, characteristic, complemented
5#13068912C211yesmaximal, characteristic, complemented
6#13068912C211yesmaximal, characteristic, complemented
7#13068907C211yesmaximal, characteristic, complemented
8#13068907C211yesmaximal, characteristic, complemented
9#13068683C211yesmaximal, characteristic, complemented
10#13068683C211yesmaximal, characteristic, complemented
11#13068593C211yesmaximal, characteristic, complemented
12#13068379C211yesmaximal, characteristic, complemented
13#13068308C211yesmaximal, characteristic, complemented
14D11×#336C211yesmaximal, characteristic, complemented
15C11×#1985C211yesmaximal, characteristic, complemented
16C22×#4343C411yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C411yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23C4×#4343—24no—
24C4×#4343—24no—
25C2×#66946C411yescharacteristic
26C2×#66946C411yescharacteristic
27C2×#66946C411yescharacteristic
28C2×#66945C411yescharacteristic
29C2×#66945C411yescharacteristic
30C2×#66945C411yescharacteristic
31C2×C4×D44C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C2×C42×D11C2211yescharacteristic
35C2×C42×D11C2211yescharacteristic
36C2×C42×D11C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#97C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×(C2×D11)⋊C8C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic
46C2×(C2×D11)⋊C8C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49#10622449—24no—
50#10622319—24no—
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11C2×C411yescharacteristic
64C2×#4343—24no—
65C2×#4343—24no—
66C2×#4343—24no—
67C22×D44C2×C411yescharacteristic
68C22×D44C2×C411yescharacteristic
69C22×D44C2×C411yescharacteristic
70C22×C4×D11C2×C411yescharacteristic
71C22×C4×D11C2×C411yescharacteristic
72C22×C4×D11C2×C411yescharacteristic
73C22×C4×D11C2×C411yescharacteristic
74C22×C4×D11C2×C411yescharacteristic
75C22×C4×D11C2×C411yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C22×C4×D11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C4×Q8×C11—22no—
84C4×Q8×C11—22no—
85C2×C11×C4⋊C4C2×C411yescharacteristic
86C2×C11×C4⋊C4C2×C411yescharacteristic
87C2×C11×C4⋊C4C2×C411yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91Q8×Dic11—24no—
92C2×(C2×D11)⋊C4C2×C411yescharacteristic
93C2×(C2×D11)⋊C4C2×C411yescharacteristic
94C2×(C2×D11)⋊C4C2×C411yescharacteristic
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×C4⋊Dic11C2×C411yescharacteristic
99C2×C4⋊Dic11C2×C411yescharacteristic
100C2×C4⋊Dic11C2×C411yescharacteristic
101C2×C4×Dic11C2×C411yescharacteristic
102C2×C4×Dic11C2×C411yescharacteristic
103C2×C4×Dic11C2×C411yescharacteristic
104C2×C4×Dic11C2×C411yescharacteristic
105C2×C4×Dic11C2×C411yescharacteristic
106C2×C4×Dic11C2×C411yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C2×#4313—22no—
113C2×#4313—22no—
114C2×#4313—22no—
115C2×#4313—22no—
116C2×#4313—41no—
117C2×#4313—41no—
118C2×C8×D11—22no—
119C2×C8×D11—22no—
120C2×C8×D11—22no—
121C2×C8×D11—22no—
122C2×C8×D11—41no—
123C2×C8×D11—41no—
124#66946—24no—
125#66946—24no—
126#66946—24no—
127#66945—24no—
128#66945—24no—
129#66945—24no—
130C4×D44—22no—
131C4×D44—22no—
132C4×D44—22no—
133C4×D44—22no—
134C4×D44D414yes—
135C4×D44D414yes—
136C42×D11—22no—
137C42×D11—22no—
138C42×D11—22no—
139C42×D11—22no—
140C42×D11—22no—
141C42×D11—22no—
142C11×C4⋊C8—22no—
143C11×#97—22no—
144(C2×D11)⋊C8—22no—
145(C2×D11)⋊C8—22no—
146(C2×D11)⋊C8—22no—
147(C2×D11)⋊C8—22no—
148(C2×D11)⋊C8—22no—
149(C2×D11)⋊C8—22no—
150(C2×D11)⋊C8—41no—
151(C2×D11)⋊C8—41no—
152C4⋊(C11⋊C8)—22no—
153#66867—22no—
154#22471—111nomaximal, Sylow
155C23×D11C22×C411yescharacteristic
156C23×D11C22×C411yescharacteristic
157C23×D11C22×C411yescharacteristic
158C2×Q8×C11—22no—
159C2×Q8×C11—22no—
160C2×Q8×C11—22no—
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C22×C411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C22×Dic11C22×C411yescharacteristic
169C22×Dic11C22×C411yescharacteristic
170C22×Dic11C22×C411yescharacteristic
171C22×Dic11C22×C411yescharacteristic
172C22×Dic11C22×C411yescharacteristic
173#4343—232no—
174C2×D44—22no—
175C2×D44—22no—
176C2×D44—22no—
177C2×D44—22no—
178C2×D44—22no—
179C2×D44—22no—
180C2×D44—22no—
181C2×D44C22⋊C414yes—
182C2×D44M1614yescomplemented
183C2×C4×D11—22no—
184C2×C4×D11—22no—
185C2×C4×D11—22no—
186C2×C4×D11—22no—
187C2×C4×D11—22no—
188C2×C4×D11—22no—
189C2×C4×D11—22no—
190C2×C4×D11—22no—
191C2×C4×D11—22no—
192C2×C4×D11—22no—
193C2×C4×D11—22no—
194C2×C4×D11—22no—
195C2×C4×D11—22no—
196C2×C4×D11—22no—
197C2×C4×D11—21no—
198C2×C4×D11—21no—
199C2×C4×D11—21no—
200C2×C4×D11—21no—
201C2×C4×D11—21no—
202C2×C4×D11—21no—
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C2×C4×D11—21no—
206C2×C4×D11—21no—
207C2×C4×D11—21no—
208C2×C4×D11—21no—
209C2×C4×D11—21no—
210C2×C4×D11—21no—
211C2×C4×D11—41no—
212C2×C4×D11—41no—
213C2×C4×D11—41no—
214C2×C4×D11M1614yescomplemented
215C2×C4×D11C2×D412yes—
216C2×C4×D11C2×D412yes—
217C2×C4×D11C2×D412yes—
218C2×C4×D11C2×D412yes—
219C2×C8×C11—21no—
220C2×C8×C11—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11#4112yescomplemented
231C11×C4⋊C4—22no—
232C11×C4⋊C4—22no—
233C11×C4⋊C4—22no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11—21no—
237C42×C11—21no—
238C42×C11C2×D412yes—
239C42×C11C2×D412yes—
240(C2×D11)⋊C4—22no—
241(C2×D11)⋊C4—22no—
242(C2×D11)⋊C4—22no—
243(C2×D11)⋊C4—22no—
244(C2×D11)⋊C4C22⋊C414yes—
245(C2×D11)⋊C4C22⋊C414yes—
246C4⋊Dic11—22no—
247C4⋊Dic11—22no—
248C4⋊Dic11C22⋊C414yes—
249C4×Dic11—22no—
250C4×Dic11—22no—
251C4×Dic11—22no—
252C4×Dic11—22no—
253C4×Dic11—22no—
254C4×Dic11—22no—
255C4×Dic11—21no—
256C4×Dic11—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8#4112yescomplemented
269#4313—44no—
270#4313—44no—
271C8×D11—44no—
272C8×D11—44no—
273C2×C4×#41—111no—
274C2×#435—111no—
275C2×#435—111no—
276#1985—111no—
277#1985D1111yescharacteristic, complemented
278#1870—111no—
279#1870—111no—
280#1869—111no—
281#1869—111no—
282#1817—111no—
283#1817—111no—
284#1797—111no—
285#1749—111no—
286#1728—111no—
287C2×#336—111no—
288C23×C11C23×C411yescharacteristic
289C22×D11—21no—
290C22×D11—21no—
291C22×D11—21no—
292C22×D11—21no—
293C22×D11—21no—
294C22×D11—21no—
295C22×D11—21no—
296C22×D11—21no—
297C22×D11—21no—
298C22×D11—21no—
299C22×D11—21no—
300C22×D11—21no—
301C22×D11—21no—
302C22×D11—21no—
303C22×D11—21no—
304C22×D11—21no—
305C22×D11C2×C22⋊C412yes—
306C22×D11C2×C22⋊C412yes—
307C22×D11C2×M1612yes—
308C22×D11C2×M1612yes—
309C22×D11C2×M1612yes—
310Q8×C11—28no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11C2×C22⋊C412yes—
326C2×C4×C11C2×C22⋊C412yes—
327C2×C4×C11C2×M1612yes—
328C2×C4×C11C2×M1612yes—
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C2×#4111yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11H(5,𝔽2)11yescharacteristic
334C2×C4×C112−1+411yescharacteristic
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11C2×C22⋊C412yes—
347C2×Dic11C2×C22⋊C412yes—
348C2×Dic11C2×M1612yes—
349C2×Dic11#13112yes—
350D44—28no—
351D44—28no—
352D44—28no—
353C4×D11—28no—
354C4×D11—28no—
355C4×D11—28no—
356C4×D11—22no—
357C4×D11—22no—
358C4×D11—22no—
359C4×D11—22no—
360C4×D11—22no—
361C4×D11—22no—
362C4×D11—22no—
363C4×D11—22no—
364C4×D11—44no—
365C4×D11—44no—
366C4×D11—44no—
367C4×D11—41no—
368C4×D11—41no—
369C4×D11—41no—
370C4×D11—41no—
371C8×C11—22no—
372C8×C11—41no—
373C8×C11—41no—
374C8×C11—41no—
375C11⋊C8—22no—
376C11⋊C8—41no—
377C11⋊C8—41no—
378C11⋊C8—41no—
379C22×#41—111no—
380C22×M16—111no—
381C22×M16—111no—
382C23×C8—111no—
383C23×C8—111no—
384C4×#41—224no—
385C4×#41—224no—
386C2×C4×Q8—111no—
387C2×C4×Q8C2×D1111yescharacteristic
388C2×C4×D4—111no—
389C2×C4×D4—111no—
390C2×C4×D4—111no—
391C2×C4×D4—111no—
392C2×C4×D4—111no—
393C2×C4×D4—111no—
394C2×#117—111no—
395C2×#117—111no—
396C2×#117—111no—
397C22×C42—111no—
398C22×C42—111no—
399C22×C42—111no—
400#435—224no—
401#435—224no—
402C2×C4⋊C8—111no—
403C2×C4⋊C8C2×D1111yescharacteristic
404C2×C22⋊C8—111no—
405C2×C22⋊C8—111no—
406C2×C22⋊C8—111no—
407C2×C22⋊C8—111no—
408C2×C22⋊C8—111no—
409C2×C22⋊C8—111no—
410C2×C22⋊C8—111no—
411C2×C22⋊C8—111no—
412C2×#97—111no—
413C2×#97C2×D1111yescharacteristic
414#336—111no—
415#336—111no—
416#336—111no—
417#336—111no—
418#336—111no—
419#336—111no—
420#336—111no—
421#336—111no—
422#336C2×D1111yescharacteristic
423#336C2×D1111yescharacteristic
424#336C2×D1111yescharacteristic
425#336C2×D1111yescharacteristic
426C22×C11C22×C22⋊C411yescharacteristic
427C22×C11C4×#4111yescharacteristic
428C22×C11#52011yescharacteristic
429C22×C11C22×M1611yescharacteristic
430C22×C11C22×M1611yescharacteristic
431C22×C11C2×#13111yescharacteristic
432C22×C11#56811yescharacteristic
433C2×D11—22no—
434C2×D11—22no—
435C2×D11—22no—
436C2×D11—22no—
437C2×D11—22no—
438C2×D11—22no—
439C2×D11—22no—
440C2×D11—22no—
441C2×D11—22no—
442C2×D11—22no—
443C2×D11—22no—
444C2×D11—22no—
445C2×D11—41no—
446C2×D11—41no—
447C2×D11—41no—
448C2×D11—41no—
449C2×D11—41no—
450C2×D11—41no—
451C2×D11—41no—
452C2×D11—41no—
453C2×D11#40714yes—
454C4×C11—22no—
455C4×C11—22no—
456C4×C11—22no—
457C4×C11—22no—
458C4×C11—41no—
459C4×C11—41no—
460C4×C11#54611yescharacteristic
461C4×C11#54611yescharacteristic
462C4×C11#54711yescharacteristic
463C4×C11#54711yescharacteristic
464Dic11—22no—
465Dic11—22no—
466Dic11—22no—
467Dic11—22no—
468Dic11—41no—
469C2×#41—224no—
470C2×#41—224no—
471C2×#41—224no—
472C22×Q8C4×D1111yescharacteristic
473C22×D4—111no—
474C22×D4—111no—
475C22×D4—111no—
476C23×C4—111no—
477C23×C4—111no—
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—111no—
482C23×C4—111no—
483C23×C4—111no—
484C23×C4—111no—
485C2×M16—222no—
486C2×M16—222no—
487C2×M16—222no—
488C2×M16—222no—
489C2×M16—441no—
490C2×M16—441no—
491C22×C8—111no—
492C22×C8—111no—
493C22×C8—111no—
494C22×C8—111no—
495C22×C8—222no—
496C22×C8—222no—
497C22×C8—222no—
498C22×C8—222no—
499C22×C8—441no—
500C22×C8—441no—
501C22×C8C22×D1111yescharacteristic
502C22×C8C22×D1111yescharacteristic
503C22×C8C22×D1111yescharacteristic
504C22×C8C22×D1111yescharacteristic
505C4×Q8—22no—
506C4×Q8—22no—
507C4×Q8—224no—
508C4×D4—114no—
509C4×D4—114no—
510C4×D4—222no—
511C4×D4—222no—
512C4×D4—222no—
513C4×D4—222no—
514C4×D4—224no—
515C4×D4—224no—
516C4×D4—224no—
517#117—224no—
518#117—224no—
519#117—224no—
520C2×C4⋊C4—111no—
521C2×C4⋊C4—111no—
522C2×C4⋊C4—111no—
523C2×C4⋊C4C4×D1111yescharacteristic
524C2×C4⋊C4C4×D1111yescharacteristic
525C2×C4⋊C4C4×D1111yescharacteristic
526C2×C22⋊C4—111no—
527C2×C22⋊C4—111no—
528C2×C22⋊C4—111no—
529C2×C22⋊C4—111no—
530C2×C22⋊C4—111no—
531C2×C22⋊C4—111no—
532C2×C42—111no—
533C2×C42—111no—
534C2×C42—111no—
535C2×C42—111no—
536C2×C42—111no—
537C2×C42—111no—
538C2×C42—111no—
539C2×C42—222no—
540C2×C42—222no—
541C2×C42—222no—
542C2×C42—222no—
543C2×C42—222no—
544C2×C42—222no—
545C2×C42C22×D1111yescharacteristic
546C2×C42C22×D1111yescharacteristic
547C2×C42C22×D1111yescharacteristic
548C4⋊C8—22no—
549C4⋊C8—222no—
550C22⋊C8—222no—
551C22⋊C8—222no—
552C22⋊C8—222no—
553C22⋊C8—222no—
554C22⋊C8—222no—
555C22⋊C8—222no—
556C22⋊C8—441no—
557C22⋊C8—441no—
558#97—22no—
559#97—222no—
560C2×C11#233911yescharacteristic
561C2×C11C2×#40711yescharacteristic
562C2×C11#288011yescharacteristic
563C2×C11#296511yescharacteristic
564C2×C11#297011yescharacteristic
565C2×C11#298911yescharacteristic
566C2×C11#299011yescharacteristic
567D11—24no—
568D11—42no—
569D11—42no—
570C24—111no—
571C24—111no—
572C24—111no—
573#41—2232no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×D4—114no—
578C2×D4—114no—
579C2×D4—222no—
580C2×D4—222no—
581C2×D4—222no—
582C2×D4—222no—
583C2×D4—222no—
584C2×D4—222no—
585C2×D4—222no—
586C22×C4—111no—
587C22×C4—111no—
588C22×C4—111no—
589C22×C4—111no—
590C22×C4—114no—
591C22×C4—112no—
592C22×C4—112no—
593C22×C4—112no—
594C22×C4—112no—
595C22×C4—111no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—222no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—221no—
624C22×C4—441no—
625C22×C4—441no—
626C22×C4—441no—
627C22×C4C2×C4×D1111yescharacteristic
628C22×C4C2×C4×D1111yescharacteristic
629C22×C4C2×C4×D1111yescharacteristic
630C22×C4C2×C4×D1111yescharacteristic
631C22×C4C2×C4×D1111yescharacteristic
632C22×C4C2×C4×D1111yescharacteristic
633C22×C4C23×D1111yescharacteristic
634M16—444no—
635M16—444no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—112no—
648C2×C8—221no—
649C2×C8—221no—
650C2×C8—221no—
651C2×C8—221no—
652C2×C8—221no—
653C2×C8—221no—
654C2×C8—221no—
655C2×C8—221no—
656C2×C8—221no—
657C2×C8—221no—
658C2×C8—221no—
659C2×C8—444no—
660C2×C8—444no—
661C2×C8#434312yescomplemented
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—114no—
666C4⋊C4—222no—
667C4⋊C4—222no—
668C22⋊C4—114no—
669C22⋊C4—114no—
670C22⋊C4—222no—
671C22⋊C4—222no—
672C22⋊C4—222no—
673C22⋊C4—222no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—222no—
679C42—222no—
680C42—222no—
681C42—222no—
682C42—222no—
683C42—222no—
684C42—221no—
685C42—221no—
686C42D4×D1112yes—
687C42D4×D1112yes—
688C11#2247111yescharacteristic, complemented, Sylow
689C23—112no—
690C23—112no—
691C23—112no—
692C23—112no—
693C23—112no—
694C23—221no—
695C23—221no—
696C23—221no—
697C23—221no—
698C23—221no—
699C23—221no—
700C23—221no—
701C23—221no—
702C23—221no—
703C23—221no—
704C23—221no—
705C23—221no—
706C23—221no—
707C23—221no—
708C23—221no—
709C23—221no—
710C23C22×C4×D1111yescharacteristic
711Q8—28no—
712D4—228no—
713D4—228no—
714D4—228no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—112no—
730C2×C4—112no—
731C2×C4—112no—
732C2×C4—112no—
733C2×C4—228no—
734C2×C4—228no—
735C2×C4—228no—
736C2×C4—221no—
737C2×C4—221no—
738C2×C4—221no—
739C2×C4—221no—
740C2×C4—221no—
741C2×C4—221no—
742C2×C4—221no—
743C2×C4—221no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—221no—
753C2×C4—221no—
754C2×C4—221no—
755C2×C4—444no—
756C2×C4—444no—
757C2×C4—444no—
758C2×C4—441no—
759C2×C4—441no—
760C2×C4—441no—
761C2×C4—441no—
762C2×C4C22⋊C4×D1112yes—
763C2×C4C22⋊C4×D1112yes—
764C2×C4M16×D1112yes—
765C2×C4M16×D1112yes—
766C2×C4C2×D4×D1111yescharacteristic
767C2×C4C2×D4×D1111yescharacteristic
768C2×C4C2×#434311yescharacteristic
769C2×C4#6704011yescharacteristic
770C2×C4#41×D1111yescharacteristic
771C2×C4#6704211yescharacteristic
772C8—22no—
773C8—41no—
774C8—41no—
775C8—41no—
776C8—222no—
777C8—441no—
778C8—441no—
779C8—441no—
780C22—114no—
781C22—222no—
782C22—222no—
783C22—222no—
784C22—222no—
785C22—222no—
786C22—222no—
787C22—222no—
788C22—222no—
789C22—222no—
790C22—222no—
791C22—222no—
792C22—222no—
793C22—441no—
794C22—441no—
795C22—441no—
796C22—441no—
797C22—441no—
798C22—441no—
799C22—441no—
800C22—441no—
801C22C2×C22⋊C4×D1111yescharacteristic
802C22C4×#434311yescharacteristic
803C22#1062310511yescharacteristic
804C22C2×M16×D1111yescharacteristic
805C22C2×M16×D1111yescharacteristic
806C22D11×#13111yescharacteristic
807C22#1062328111yescharacteristic
808C4—22no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—41no—
813C4—41no—
814C4—222no—
815C4—222no—
816C4—222no—
817C4—222no—
818C4—441no—
819C4#1062316111yescharacteristic
820C4#1062316211yescharacteristic
821C4#1062320711yescharacteristic
822C4#1062325711yescharacteristic
823C2—224no—
824C2—442no—
825C2—442no—
826C2#1307144511yescharacteristic
827C2D11×#40711yescharacteristic
828C2#1307706411yescharacteristic
829C2#1307758111yescharacteristic
830C2#1307762911yescharacteristic
831C2#1307773211yescharacteristic
832C2#1307774011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1985C2
prime radicalC22×#4343C4
cosocleC22×C4×C11C24
hypercenter#1985D11
hypocenterC11#22471
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1985

Complements

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

NH ≅ G/Ntype
2. C2×#10622319C2semidirect
3. C2×#10622449C2semidirect
4. #13069557C2semidirect
5. #13068912C2semidirect
6. #13068912C2semidirect
7. #13068907C2semidirect
8. #13068907C2semidirect
9. #13068683C2semidirect
10. #13068683C2semidirect
11. #13068593C2semidirect
12. #13068379C2semidirect
13. #13068308C2semidirect
14. D11×#336C2semidirect
15. C11×#1985C2semidirect
182. C2×D44M16semidirect
214. C2×C4×D11M16semidirect
230. C2×C8×C11#41semidirect
268. C2×C11⋊C8#41semidirect
277. #1985D11semidirect
661. C2×C8#4343semidirect
688. C11#22471semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43432
C2×#106223192
C2×#106224492
#130695572
#130689122
#130689072
#130686832
#130685932
#130683792
#130683082
D11×#3362
C11×#19852
#2247111