Finite Group Databasebeta

← C2×#13071248 #14912410

Subgroups — C2×#13071248 #14912410

Order 2816.

3262 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
1C22×#66946C211yesmaximal, characteristic
2#13071248C2116yesmaximal, direct product factor
3C2×#10622553C211yesmaximal, characteristic, complemented
4C2×#10622282C211yesmaximal, characteristic, complemented
5C2×#10622594C211yesmaximal, characteristic, complemented
6C2×#10622278C211yesmaximal, characteristic
7C2×#10622278C211yesmaximal, characteristic
8C2×#10622281C211yesmaximal, characteristic, complemented
9C2×#10622602C211yesmaximal, characteristic, complemented
10C2×#10622264C211yesmaximal, characteristic, complemented
11C2×#10622263C211yesmaximal, characteristic, complemented
12C2×#10622277C211yesmaximal, characteristic, complemented
13C2×#10622600C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
15C2×D11×#95C211yesmaximal, characteristic, complemented
16C2×C11×#387C211yesmaximal, characteristic, complemented
17C23×D44C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C2×#66946C4116yescomplemented
39C2×#66946C2218yes—
40C11×#387C2218yescomplemented
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622602C2218yescomplemented
56#10622600C2218yescomplemented
57#10622594C2218yescomplemented
58#10622553C2218yescomplemented
59C4×(C2×D11)⋊C4C2218yescomplemented
60#10622282C2218yescomplemented
61#10622281C2218yescomplemented
62#10622278C2218yes—
63#10622278C2218yes—
64#10622277C2218yescomplemented
65D11×#95C2218yescomplemented
66#10622264C2218yescomplemented
67#10622263C2218yescomplemented
68C24×D11C2311yescharacteristic
69C24×D11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C22×D44—24no—
84C22×D44—24no—
85C22×D44C2×C418yes—
86C22×D44C2314yes—
87C22×C4×D11—24no—
88C22×C4×D11—24no—
89C22×C4×D11—42no—
90C22×C4×D11—42no—
91C22×C4×D11—42no—
92C22×C4×D11—42no—
93C22×C4×D11—42no—
94C22×C4×D11—42no—
95C22×C4×D11—42no—
96C22×C4×D11—42no—
97C22×C4×D11C2×C418yes—
98C22×C4×D11C2×C418yescomplemented
99C22×C4×D11C2314yes—
100C22×C4×D11C2314yes—
101C22×C4×D11C2314yes—
102C22×C4×D11C2314yes—
103C2×C11×C4⋊C4—42no—
104C2×C11×C4⋊C4C2×C418yescomplemented
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2314yes—
107C2×C42×C11—42no—
108C2×C42×C11C2314yes—
109C2×(C2×D11)⋊C4—24no—
110C2×(C2×D11)⋊C4—24no—
111C2×(C2×D11)⋊C4—42no—
112C2×(C2×D11)⋊C4—42no—
113C2×(C2×D11)⋊C4—42no—
114C2×(C2×D11)⋊C4—42no—
115C2×(C2×D11)⋊C4C2×C418yes—
116C2×(C2×D11)⋊C4C2×C418yescomplemented
117C2×(C2×D11)⋊C4C2314yes—
118C2×(C2×D11)⋊C4C2314yes—
119C2×(C2×D11)⋊C4C2314yes—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×C4⋊Dic11—42no—
126C2×C4⋊Dic11C2314yes—
127C2×Dic11⋊C4—42no—
128C2×Dic11⋊C4—42no—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×C4×Dic11—42no—
132C2×C4×Dic11C2×C418yescomplemented
133C2×C4×Dic11C2314yes—
134C2×C4×Dic11C2314yes—
135#66946C2×C4164yescomplemented
136C11×#95C2314yes—
137C11×#95C2314yes—
138C11×#95C2314yes—
139C11×#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C2×#2318—111nomaximal, Sylow
151C24×C11C2411yescharacteristic
152C23×D11—22no—
153C23×D11—22no—
154C23×D11—22no—
155C23×D11—22no—
156C23×D11—22no—
157C23×D11—22no—
158C23×D11—22no—
159C23×D11—22no—
160C23×D11—22no—
161C23×D11—22no—
162C23×D11C22×C414yes—
163C23×D11C22×C414yes—
164C23×D11#4114yes—
165C23×D11#4114yes—
166C23×D11C2412yes—
167C23×D11C2412yes—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11C22×C414yes—
187C22×C4×C11C22×C414yes—
188C22×C4×C11C22×C414yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11C22×C414yes—
213C22×Dic11C22×C414yes—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C22×Dic11C2412yes—
217C22×Dic11C2412yes—
218C22×Dic11C2412yes—
219C22×Dic11C2412yes—
220C2×D44—232no—
221C2×D44—28no—
222C2×D44—28no—
223C2×D44C22×C4116yes—
224C2×C4×D11—28no—
225C2×C4×D11—28no—
226C2×C4×D11—416no—
227C2×C4×D11—416no—
228C2×C4×D11—44no—
229C2×C4×D11—44no—
230C2×C4×D11—44no—
231C2×C4×D11—44no—
232C2×C4×D11—44no—
233C2×C4×D11—44no—
234C2×C4×D11—44no—
235C2×C4×D11—44no—
236C2×C4×D11—416no—
237C2×C4×D11—416no—
238C2×C4×D11C22×C4116yes—
239C2×C4×D11C22×C4116yescomplemented
240C11×C4⋊C4—44no—
241C11×C4⋊C4C22×C4116yescomplemented
242C42×C11—44no—
243(C2×D11)⋊C4—28no—
244(C2×D11)⋊C4—28no—
245(C2×D11)⋊C4—44no—
246(C2×D11)⋊C4—44no—
247(C2×D11)⋊C4—44no—
248(C2×D11)⋊C4—44no—
249(C2×D11)⋊C4C22×C4116yes—
250(C2×D11)⋊C4C22×C4116yescomplemented
251C4⋊Dic11—44no—
252Dic11⋊C4—44no—
253Dic11⋊C4—44no—
254C4×Dic11—44no—
255C4×Dic11C22×C4116yescomplemented
256C22×C4×D4—111no—
257#2318—1116no—
258C2×#388—111no—
259C2×#388—111no—
260C2×#387—111no—
261C2×#387D1111yescharacteristic, complemented
262C2×#386—111no—
263C2×#386—111no—
264C2×#385—111no—
265C2×#385—111no—
266C2×#383—111no—
267C2×#382—111no—
268C2×#381—111no—
269C2×#380—111no—
270C2×C4×C22⋊C4—111no—
271C22×#95—111no—
272C23×C11C23×C412yes—
273C23×C11C2×#4112yes—
274C23×C11C2×#4112yes—
275C23×C11H(5,𝔽2)12yes—
276C23×C11H(5,𝔽2)12yes—
277C23×C11H(5,𝔽2)12yes—
278C23×C112−1+412yes—
279C23×C11C2511yescharacteristic
280C22×D11—28no—
281C22×D11—28no—
282C22×D11—28no—
283C22×D11—28no—
284C22×D11—28no—
285C22×D11—28no—
286C22×D11—22no—
287C22×D11—22no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—28no—
291C22×D11—28no—
292C22×D11—28no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—44no—
300C22×D11—44no—
301C22×D11—44no—
302C22×D11—44no—
303C22×D11#117116yes—
304C22×D11C23×C414yes—
305C22×D11C23×C414yes—
306C22×D11C2×#4114yes—
307C22×D11C2×#4114yes—
308C2×C4×C11—28no—
309C2×C4×C11—28no—
310C2×C4×C11—28no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—44no—
330C2×C4×C11—44no—
331C2×C4×C11—44no—
332C2×C4×C11—44no—
333C2×C4×C11C23×C414yes—
334C2×C4×C11C23×C414yes—
335C2×C4×C11C23×C414yes—
336C2×Dic11—28no—
337C2×Dic11—28no—
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—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—44no—
355C2×Dic11—44no—
356C2×Dic11—44no—
357C2×Dic11—44no—
358C2×Dic11C23×C414yes—
359C2×Dic11C23×C414yes—
360D44—232no—
361C4×D11—416no—
362C4×D11—416no—
363C4×D11—416no—
364C4×D11—416no—
365C23×D4—111no—
366C24×C4—111no—
367C24×C4—111no—
368C24×C4—111no—
369C24×C4—111no—
370C2×C4×D4—118no—
371C2×C4×D4—1116no—
372C22×C4⋊C4—111no—
373C22×C4⋊C4—111no—
374C22×C4⋊C4—111no—
375C22×C4⋊C4C2×D1111yescharacteristic
376C22×C4⋊C4C2×D1111yescharacteristic
377C22×C22⋊C4—111no—
378C22×C22⋊C4—111no—
379C22×C22⋊C4—111no—
380C22×C22⋊C4—111no—
381C22×C22⋊C4—111no—
382C22×C22⋊C4—111no—
383C22×C22⋊C4—111no—
384C22×C22⋊C4—111no—
385C22×C42—111no—
386C22×C42—111no—
387C22×C42C2×D1111yescharacteristic
388#388—118no—
389#388—118no—
390#387—118no—
391#387C2×D1118yescomplemented
392#386—118no—
393#386—118no—
394#385—118no—
395#385—118no—
396#383—118no—
397#382—118no—
398#381—118no—
399#380—118no—
400C4×C22⋊C4—118no—
401C2×#95—111no—
402C2×#95—111no—
403C2×#95—111no—
404C2×#95—111no—
405C2×#95—111no—
406C2×#95—111no—
407C2×#95—111no—
408C2×#95—111no—
409C2×#95—111no—
410C2×#95—111no—
411C2×#95—118no—
412C2×#95C2×D1111yescharacteristic
413C2×#95C2×D1111yescharacteristic
414C2×#95C2×D1111yescharacteristic
415C2×#95C2×D1111yescharacteristic
416C22×C11C2×#11714yes—
417C22×C11#51814yes—
418C22×C11#52014yes—
419C22×C11#53814yes—
420C22×C11#53814yes—
421C22×C11#53914yes—
422C22×C11#53914yes—
423C22×C11C24×C411yescharacteristic
424C22×C11C22×#4111yescharacteristic
425C22×C11C22×#4111yescharacteristic
426C22×C11C2×H(5,𝔽2)11yescharacteristic
427C22×C11C2×H(5,𝔽2)11yescharacteristic
428C22×C11C2×H(5,𝔽2)11yescharacteristic
429C22×C11C2×2−1+411yescharacteristic
430C2×D11—232no—
431C2×D11—24no—
432C2×D11—24no—
433C2×D11—24no—
434C2×D11—24no—
435C2×D11—24no—
436C2×D11—24no—
437C2×D11—24no—
438C2×D11—24no—
439C2×D11—24no—
440C2×D11—416no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—42no—
444C2×D11—42no—
445C2×D11C2×#11718yes—
446C4×C11—24no—
447C4×C11—24no—
448C4×C11—24no—
449C4×C11—42no—
450C4×C11—42no—
451C4×C11—42no—
452C4×C11—42no—
453Dic11—24no—
454Dic11—24no—
455Dic11—42no—
456Dic11—42no—
457Dic11—42no—
458Dic11—42no—
459C25—111no—
460C25—111no—
461C22×D4—118no—
462C22×D4—114no—
463C22×D4—224no—
464C22×D4—224no—
465C23×C4—111no—
466C23×C4—111no—
467C23×C4—118no—
468C23×C4—118no—
469C23×C4—114no—
470C23×C4—114no—
471C23×C4—111no—
472C23×C4—111no—
473C23×C4—111no—
474C23×C4—111no—
475C23×C4—114no—
476C23×C4—114no—
477C23×C4—224no—
478C23×C4—224no—
479C23×C4—442no—
480C23×C4—442no—
481C23×C4—442no—
482C23×C4—442no—
483C23×C4—442no—
484C23×C4—442no—
485C23×C4—442no—
486C23×C4—442no—
487C23×C4C22×D1111yescharacteristic
488C23×C4C22×D1111yescharacteristic
489C23×C4C22×D1111yescharacteristic
490C23×C4C22×D1111yescharacteristic
491C23×C4C22×D1111yescharacteristic
492C23×C4C22×D1111yescharacteristic
493C23×C4C22×D1111yescharacteristic
494C4×D4—1164no—
495C2×C4⋊C4—42no—
496C2×C4⋊C4—114no—
497C2×C4⋊C4—114no—
498C2×C4⋊C4—114no—
499C2×C4⋊C4—442no—
500C2×C4⋊C4—442no—
501C2×C4⋊C4—442no—
502C2×C4⋊C4C4×D1118yescomplemented
503C2×C4⋊C4C22×D1114yes—
504C2×C4⋊C4C22×D1114yes—
505C2×C22⋊C4—118no—
506C2×C22⋊C4—118no—
507C2×C22⋊C4—114no—
508C2×C22⋊C4—114no—
509C2×C22⋊C4—114no—
510C2×C22⋊C4—114no—
511C2×C22⋊C4—114no—
512C2×C22⋊C4—114no—
513C2×C22⋊C4—114no—
514C2×C22⋊C4—114no—
515C2×C22⋊C4—224no—
516C2×C22⋊C4—224no—
517C2×C22⋊C4—442no—
518C2×C22⋊C4—442no—
519C2×C22⋊C4—442no—
520C2×C22⋊C4—442no—
521C2×C42—42no—
522C2×C42—118no—
523C2×C42—114no—
524C2×C42—114no—
525C2×C42—442no—
526C2×C42C22×D1114yes—
527#95—114no—
528#95—114no—
529#95—114no—
530#95—114no—
531#95—114no—
532#95—114no—
533#95—114no—
534#95—114no—
535#95—114no—
536#95—114no—
537#95C22×D1114yes—
538#95C22×D1114yes—
539#95C22×D1114yes—
540#95C22×D1114yes—
541C2×C11#231818yescomplemented
542C2×C11C22×#11711yescharacteristic
543C2×C11C2×#51811yescharacteristic
544C2×C11C2×#52011yescharacteristic
545C2×C11C2×#53811yescharacteristic
546C2×C11C2×#53811yescharacteristic
547C2×C11C2×#53911yescharacteristic
548C2×C11C2×#53911yescharacteristic
549D11—28no—
550D11—44no—
551C24—114no—
552C24—114no—
553C24—114no—
554C24—112no—
555C24—114no—
556C24—112no—
557C24—222no—
558C24—222no—
559C24—222no—
560C24—222no—
561C24—222no—
562C24—222no—
563C24—222no—
564C24—222no—
565C24—222no—
566C24—222no—
567C24C23×D1111yescharacteristic
568C2×D4—1116no—
569C2×D4—2232no—
570C2×D4—228no—
571C2×D4—228no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—114no—
591C22×C4—114no—
592C22×C4—112no—
593C22×C4—112no—
594C22×C4—1116no—
595C22×C4—1116no—
596C22×C4—112no—
597C22×C4—112no—
598C22×C4—112no—
599C22×C4—112no—
600C22×C4—228no—
601C22×C4—228no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—4416no—
619C22×C4—4416no—
620C22×C4—444no—
621C22×C4—444no—
622C22×C4—444no—
623C22×C4—444no—
624C22×C4—444no—
625C22×C4—444no—
626C22×C4—444no—
627C22×C4—444no—
628C22×C4—4416no—
629C22×C4—4416no—
630C22×C4C2×C4×D1114yes—
631C22×C4C2×C4×D1114yes—
632C22×C4C2×C4×D1114yes—
633C22×C4C23×D1112yes—
634C22×C4C23×D1112yes—
635C22×C4C23×D1112yes—
636C22×C4C23×D1112yes—
637C22×C4C23×D1112yes—
638C22×C4C23×D1112yes—
639C22×C4C23×D1112yes—
640C4⋊C4—44no—
641C4⋊C4—444no—
642C4⋊C4—444no—
643C4⋊C4—444no—
644C4⋊C4C2×C4×D11116yescomplemented
645C22⋊C4—1116no—
646C22⋊C4—1116no—
647C22⋊C4—228no—
648C22⋊C4—228no—
649C22⋊C4—444no—
650C22⋊C4—444no—
651C22⋊C4—444no—
652C22⋊C4—444no—
653C42—44no—
654C42—1116no—
655C42—444no—
656C11C2×#231811yescharacteristic, complemented, Sylow
657C23—1116no—
658C23—114no—
659C23—114no—
660C23—114no—
661C23—114no—
662C23—228no—
663C23—228no—
664C23—228no—
665C23—228no—
666C23—228no—
667C23—222no—
668C23—222no—
669C23—222no—
670C23—222no—
671C23—228no—
672C23—228no—
673C23—228no—
674C23—228no—
675C23—222no—
676C23—222no—
677C23—222no—
678C23—222no—
679C23—222no—
680C23—222no—
681C23—444no—
682C23—444no—
683C23—444no—
684C23—444no—
685C23C22×C4×D1112yes—
686C23#6703712yes—
687C23#6704012yes—
688C23#41×D1112yes—
689C23#41×D1112yes—
690C23#6704212yes—
691C23#6704212yes—
692C23C24×D1111yescharacteristic
693D4—2232no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—114no—
720C2×C4—114no—
721C2×C4—228no—
722C2×C4—228no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—4416no—
740C2×C4—4416no—
741C2×C4—4416no—
742C2×C4—4416no—
743C2×C4—444no—
744C2×C4—444no—
745C2×C4—444no—
746C2×C4—444no—
747C2×C4C22×C4×D1114yes—
748C2×C4C22×C4×D1114yes—
749C2×C4C22×C4×D1114yes—
750C22—118no—
751C22—224no—
752C22—224no—
753C22—224no—
754C22—224no—
755C22—2232no—
756C22—224no—
757C22—224no—
758C22—224no—
759C22—224no—
760C22—224no—
761C22—442no—
762C22—442no—
763C22—442no—
764C22—442no—
765C22—4416no—
766C22D11×#11714yes—
767C22#1062307614yes—
768C22#1062310514yes—
769C22#1062316914yes—
770C22#1062318814yes—
771C22#1062322314yes—
772C22#1062323514yes—
773C22C23×C4×D1111yescharacteristic
774C22C2×#6703711yescharacteristic
775C22C2×#6704011yescharacteristic
776C22C2×#41×D1111yescharacteristic
777C22C2×#41×D1111yescharacteristic
778C22C2×#6704211yescharacteristic
779C22C2×#6704211yescharacteristic
780C4—24no—
781C4—24no—
782C4—24no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—224no—
788C4—224no—
789C4—442no—
790C4—442no—
791C4—442no—
792C4—442no—
793C2—228no—
794C2—444no—
795C2#1307124818yesdirect product factor
796C2C2×D11×#11711yescharacteristic
797C2C2×#1062307611yescharacteristic
798C2C2×#1062310511yescharacteristic
799C2C2×#1062318811yescharacteristic
800C2C2×#1062323511yescharacteristic
801C2C2×#1062316911yescharacteristic
802C2C2×#1062322311yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#387C2
socleC24×C11C24
prime radicalC23×D44C22
cosocleC23×C11C25
hypercenterC2×#387D11
hypocenterC11C2×#2318
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #13071248C2direct (N × H)
3. C2×#10622553C2semidirect
4. C2×#10622282C2semidirect
5. C2×#10622594C2semidirect
8. C2×#10622281C2semidirect
9. C2×#10622602C2semidirect
10. C2×#10622264C2semidirect
11. C2×#10622263C2semidirect
12. C2×#10622277C2semidirect
13. C2×#10622600C2semidirect
14. C2×C4×(C2×D11)⋊C4C2semidirect
15. C2×D11×#95C2semidirect
16. C2×C11×#387C2semidirect
38. C2×#66946C4semidirect
40. C11×#387C22semidirect
55. #10622602C22semidirect
56. #10622600C22semidirect
57. #10622594C22semidirect
58. #10622553C22semidirect
59. C4×(C2×D11)⋊C4C22semidirect
60. #10622282C22semidirect
61. #10622281C22semidirect
64. #10622277C22semidirect
65. D11×#95C22semidirect
66. #10622264C22semidirect
67. #10622263C22semidirect
98. C22×C4×D11C2×C4semidirect
104. C2×C11×C4⋊C4C2×C4semidirect
116. C2×(C2×D11)⋊C4C2×C4semidirect
132. C2×C4×Dic11C2×C4semidirect
135. #66946C2×C4semidirect
239. C2×C4×D11C22×C4semidirect
241. C11×C4⋊C4C22×C4semidirect
250. (C2×D11)⋊C4C22×C4semidirect
255. C4×Dic11C22×C4semidirect
261. C2×#387D11semidirect
391. #387C2×D11semidirect
502. C2×C4⋊C4C4×D11semidirect
541. C2×C11#2318semidirect
644. C4⋊C4C2×C4×D11semidirect
656. C11C2×#2318semidirect
795. C2#13071248direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669462
#130712482
C2×#106225532
C2×#106222822
C2×#106225942
C2×#106222782
C2×#106222812
C2×#106226022
C2×#106222642
C2×#106222632
C2×#106222772
C2×#106226002
C2×C4×(C2×D11)⋊C42
C2×D11×#952
C2×C11×#3872
C2×#231811