Finite Group Databasebeta

← C2×#13072814 #14922203

Subgroups — C2×#13072814 #14922203

Order 2816.

3070 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×#66931C211yesmaximal, characteristic, complemented
2C22×#66979C211yesmaximal, characteristic, complemented
3#13072814C2116yesmaximal, direct product factor
4C2×#10622272C211yesmaximal, characteristic, complemented
5C2×#10622566C211yesmaximal, characteristic, complemented
6C2×#10622835C211yesmaximal, characteristic
7C2×#10622560C211yesmaximal, characteristic, complemented
8C2×#10622259C211yesmaximal, characteristic, complemented
9C2×#10622558C211yesmaximal, characteristic, complemented
10C2×#10622557C211yesmaximal, characteristic, complemented
11C2×#10622267C211yesmaximal, characteristic, complemented
12C2×#10622265C211yesmaximal, characteristic, complemented
13C2×#10622833C211yesmaximal, characteristic
14C2×#10622823C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C2×#66979—28no—
32C2×#66979C2218yescomplemented
33C22×C4⋊Dic11C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×#66931—28no—
43C2×#66931C2218yescomplemented
44C11×#386C2218yes—
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47#10622835C2218yes—
48#10622833C2218yes—
49#10622823C2218yescomplemented
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60#10622566C2218yescomplemented
61#10622560C2218yescomplemented
62#10622558C2218yescomplemented
63#10622557C2218yescomplemented
64C22⋊C4×Dic11C2218yescomplemented
65#10622272C2218yescomplemented
66#10622267C2218yescomplemented
67#10622265C2218yescomplemented
68#10622259C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C22×D4×C11—24no—
72C22×D4×C11—24no—
73C22×D4×C11—42no—
74C22×D4×C11C2314yes—
75C23×C4×C11—24no—
76C23×C4×C11—24no—
77C23×C4×C11—24no—
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2314yes—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×Dic11—24no—
85C23×Dic11—24no—
86C23×Dic11—42no—
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2314yes—
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C22×Dic22—24no—
97C22×Dic22—24no—
98C22×Dic22—42no—
99C22×Dic22C2314yes—
100C2×C11×C22⋊C4—24no—
101C2×C11×C22⋊C4—24no—
102C2×C11×C22⋊C4—42no—
103C2×C11×C22⋊C4C2314yes—
104C2×C11×C22⋊C4C2314yes—
105C2×C11×C22⋊C4C2314yes—
106C2×C22⋊Dic11—24no—
107C2×C22⋊Dic11—24no—
108C2×C22⋊Dic11—24no—
109C2×C22⋊Dic11—24no—
110C2×C22⋊Dic11—24no—
111C2×C22⋊Dic11—24no—
112C2×C22⋊Dic11—24no—
113C2×C22⋊Dic11C2314yes—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2314yes—
116C2×C22⋊Dic11C2314yes—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120#66979—232no—
121C2×C4⋊Dic11—24no—
122C2×C4⋊Dic11D418yescomplemented
123C2×C4⋊Dic11C2314yes—
124C2×C4⋊Dic11C2314yes—
125C2×Dic11⋊C4—24no—
126C2×Dic11⋊C4—24no—
127C2×Dic11⋊C4—24no—
128C2×Dic11⋊C4—42no—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×Dic11⋊C4C2314yes—
132C2×Dic11⋊C4C2314yes—
133C2×C4×Dic11—24no—
134C2×C4×Dic11—24no—
135C2×C4×Dic11—42no—
136C2×C4×Dic11C2314yes—
137C2×C4×Dic11C2314yes—
138C2×C4×Dic11C2314yes—
139#66931—232no—
140C11×#95C2314yes—
141C11×#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C2×#2477—111nomaximal, Sylow
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11—22no—
158C24×C11—22no—
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11#4114yes—
166C24×C11#4114yes—
167C24×C11C2412yes—
168C24×C11C2412yes—
169C24×C11C2411yescharacteristic
170C2×D4×C11—28no—
171C2×D4×C11—28no—
172C2×D4×C11—44no—
173C2×D4×C11—416no—
174C22×C4×C11—232no—
175C22×C4×C11—22no—
176C22×C4×C11—28no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—28no—
181C22×C4×C11—28no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11C2×D414yes—
192C22×C4×C11#4114yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×Dic11—28no—
199C22×Dic11—28no—
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×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—44no—
222C22×Dic11—416no—
223C22×Dic11C2×D414yes—
224C22×Dic11C2×D414yes—
225C22×Dic11#4114yes—
226C22×Dic11C2412yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C2×Dic22—28no—
235C2×Dic22—28no—
236C2×Dic22—44no—
237C2×Dic22—416no—
238C11×C22⋊C4—28no—
239C11×C22⋊C4—28no—
240C11×C22⋊C4—44no—
241C22⋊Dic11—28no—
242C22⋊Dic11—28no—
243C22⋊Dic11—28no—
244C22⋊Dic11—28no—
245C22⋊Dic11—28no—
246C22⋊Dic11—28no—
247C22⋊Dic11—28no—
248C4⋊Dic11—28no—
249C4⋊Dic11C2×D4116yescomplemented
250Dic11⋊C4—28no—
251Dic11⋊C4—28no—
252Dic11⋊C4—28no—
253Dic11⋊C4—44no—
254C4×Dic11—28no—
255C4×Dic11—28no—
256C4×Dic11—44no—
257C22×C22⋊Q8—111no—
258C22×#117—111no—
259#2477—1116no—
260C2×#400—111no—
261C2×#397—111no—
262C2×#394—111no—
263C2×#393—111no—
264C2×#391—111no—
265C2×#388—111no—
266C2×#388—111no—
267C2×#387—111no—
268C2×#387—111no—
269C2×#386—111no—
270C2×#386D1111yescharacteristic
271C2×#385—111no—
272C2×C4×C22⋊C4—111no—
273C23×C11—28no—
274C23×C11—28no—
275C23×C11—28no—
276C23×C11—28no—
277C23×C11—28no—
278C23×C11—28no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—44no—
292C23×C11—44no—
293C23×C11—44no—
294C23×C11—44no—
295C23×C11—44no—
296C23×C11—44no—
297C23×C11—44no—
298C23×C11—44no—
299C23×C11C22×D412yes—
300C23×C11C2×#4114yes—
301C23×C11C2×#4112yes—
302C23×C11C2×#4114yes—
303C23×C11C2×#4112yes—
304C23×C11C2×#4112yes—
305C23×C11C2×#4112yes—
306C23×C11H(5,𝔽2)12yes—
307C23×C112−1+412yes—
308C23×C11C2511yescharacteristic
309D4×C11—416no—
310C2×C4×C11—232no—
311C2×C4×C11—28no—
312C2×C4×C11—28no—
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—44no—
327C2×C4×C11—44no—
328C2×C4×C11—44no—
329C2×C4×C11C22×D414yes—
330C2×C4×C11C2×#4114yes—
331C2×Dic11—28no—
332C2×Dic11—28no—
333C2×Dic11—28no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
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—22no—
355C2×Dic11—416no—
356C2×Dic11—44no—
357C2×Dic11—44no—
358C2×Dic11—44no—
359C2×Dic11—44no—
360C2×Dic11—44no—
361C2×Dic11C22×D414yes—
362C2×Dic11C22×D414yes—
363C2×Dic11C2×#4114yes—
364Dic22—416no—
365C23×Q8—111no—
366C23×D4C2×D1111yescharacteristic
367C24×C4—111no—
368C24×C4C2×D1111yescharacteristic
369C2×C22⋊Q8—118no—
370C2×C22⋊Q8—228no—
371C2×#117—118no—
372C2×#117—228no—
373C22×C4⋊C4—111no—
374C22×C4⋊C4—111no—
375C22×C4⋊C4—111no—
376C22×C4⋊C4—111no—
377C22×C4⋊C4—111no—
378C22×C4⋊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×C22⋊C4—111no—
386C22×C22⋊C4C2×D1111yescharacteristic
387C22×C22⋊C4C2×D1111yescharacteristic
388C22×C22⋊C4C2×D1111yescharacteristic
389C22×C42—111no—
390C22×C42—111no—
391C22×C42—111no—
392#400—118no—
393#397—118no—
394#394—118no—
395#393—118no—
396#391—118no—
397#388—118no—
398#388—118no—
399#387—118no—
400#387—118no—
401#386—118no—
402#386C2×D1118yes—
403#385—118no—
404C4×C22⋊C4—118no—
405C2×#95—111no—
406C2×#95—111no—
407C2×#95—111no—
408C2×#95—111no—
409C2×#95—111no—
410C2×#95—111no—
411C2×#95—111no—
412C2×#95—111no—
413C2×#95—111no—
414C2×#95—111no—
415C2×#95C2×D1111yescharacteristic
416C2×#95C2×D1111yescharacteristic
417C22×C11—24no—
418C22×C11—24no—
419C22×C11—24no—
420C22×C11—24no—
421C22×C11—24no—
422C22×C11—24no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—416no—
432C22×C11—416no—
433C22×C11#52514yes—
434C22×C11#52914yes—
435C22×C11#54214yes—
436C22×C11#54614yes—
437C22×C11#54814yes—
438C22×C11#55114yes—
439C22×C11#55214yes—
440C22×C11C23×D411yescharacteristic
441C22×C11C22×#4111yescharacteristic
442C22×C11C22×#4111yescharacteristic
443C22×C11C22×#4111yescharacteristic
444C22×C11C22×#4111yescharacteristic
445C22×C11C2×H(5,𝔽2)11yescharacteristic
446C22×C11C2×2−1+411yescharacteristic
447C4×C11—24no—
448C4×C11—24no—
449C4×C11—42no—
450C4×C11—42no—
451C4×C11—42no—
452Dic11—24no—
453Dic11—24no—
454Dic11—24no—
455Dic11—42no—
456Dic11—42no—
457Dic11—42no—
458Dic11—42no—
459Dic11—42no—
460C25C22×D1111yescharacteristic
461C25C22×D1111yescharacteristic
462C22×Q8—114no—
463C22×Q8—224no—
464C22×Q8—224no—
465C22×Q8—442no—
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—42no—
469C22×D4C22×D1114yes—
470C23×C4—24no—
471C23×C4—24no—
472C23×C4—24no—
473C23×C4—111no—
474C23×C4—111no—
475C23×C4—111no—
476C23×C4—111no—
477C23×C4—111no—
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—114no—
482C23×C4—224no—
483C23×C4—224no—
484C23×C4—442no—
485C23×C4C22×D1114yes—
486C23×C4C22×D1111yescharacteristic
487C23×C4C22×D1111yescharacteristic
488C23×C4C22×D1111yescharacteristic
489C23×C4C22×D1111yescharacteristic
490C23×C4C22×D1111yescharacteristic
491C22⋊Q8—2232no—
492#117—2232no—
493C2×C4⋊C4—118no—
494C2×C4⋊C4—114no—
495C2×C4⋊C4—114no—
496C2×C4⋊C4—114no—
497C2×C4⋊C4—114no—
498C2×C4⋊C4—114no—
499C2×C4⋊C4—114no—
500C2×C4⋊C4—224no—
501C2×C4⋊C4—224no—
502C2×C4⋊C4—224no—
503C2×C4⋊C4—224no—
504C2×C4⋊C4—442no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—42no—
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—224no—
518C2×C22⋊C4—224no—
519C2×C22⋊C4—224no—
520C2×C22⋊C4—224no—
521C2×C22⋊C4—224no—
522C2×C22⋊C4C22×D1114yes—
523C2×C22⋊C4C22×D1114yes—
524C2×C22⋊C4C22×D1114yes—
525C2×C42—114no—
526C2×C42—114no—
527C2×C42—114no—
528C2×C42—224no—
529C2×C42—224no—
530C2×C42—442no—
531#95—114no—
532#95—114no—
533#95—114no—
534#95—114no—
535#95—114no—
536#95—114no—
537#95—114no—
538#95—114no—
539#95—114no—
540#95—114no—
541#95C22×D1114yes—
542#95C22×D1114yes—
543C2×C11—44no—
544C2×C11—44no—
545C2×C11#247718yescomplemented
546C2×C11C2×#52511yescharacteristic
547C2×C11C2×#52911yescharacteristic
548C2×C11C2×#54211yescharacteristic
549C2×C11C2×#54611yescharacteristic
550C2×C11C2×#54811yescharacteristic
551C2×C11C2×#55111yescharacteristic
552C2×C11C2×#55211yescharacteristic
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24#433914yes—
566C24#434114yes—
567C24C23×D1112yes—
568C24C23×D1112yes—
569C24C23×D1111yescharacteristic
570C2×Q8—228no—
571C2×Q8—228no—
572C2×Q8—444no—
573C2×Q8—4416no—
574C2×D4—28no—
575C2×D4—28no—
576C2×D4—44no—
577C2×D4—416no—
578C22×C4—232no—
579C22×C4—22no—
580C22×C4—28no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—114no—
596C22×C4—114no—
597C22×C4—114no—
598C22×C4—112no—
599C22×C4—112no—
600C22×C4—112no—
601C22×C4—112no—
602C22×C4—112no—
603C22×C4—112no—
604C22×C4—112no—
605C22×C4—112no—
606C22×C4—228no—
607C22×C4—228no—
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—222no—
619C22×C4—222no—
620C22×C4—222no—
621C22×C4—222no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—222no—
629C22×C4—444no—
630C22×C4—4416no—
631C22×C4D4×D1114yes—
632C22×C4#434114yes—
633C22×C4C23×D1112yes—
634C22×C4C23×D1112yes—
635C22×C4C23×D1112yes—
636C22×C4C23×D1112yes—
637C22×C4C23×D1112yes—
638C4⋊C4—1116no—
639C4⋊C4—228no—
640C4⋊C4—228no—
641C4⋊C4—228no—
642C4⋊C4—228no—
643C4⋊C4—444no—
644C22⋊C4—28no—
645C22⋊C4—28no—
646C22⋊C4—44no—
647C22⋊C4—228no—
648C22⋊C4—228no—
649C22⋊C4—228no—
650C22⋊C4—228no—
651C22⋊C4—228no—
652C22⋊C4—228no—
653C22⋊C4—228no—
654C42—228no—
655C42—228no—
656C42—444no—
657C11C2×#247711yescharacteristic, complemented, Sylow
658C23—28no—
659C23—28no—
660C23—28no—
661C23—28no—
662C23—28no—
663C23—28no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23C2×#433914yes—
685C23C2×#433912yes—
686C23C2×D4×D1112yes—
687C23C2×#434114yes—
688C23C2×#434112yes—
689C23C2×#434112yes—
690C23#6703712yes—
691C23#41×D1112yes—
692C23#6704312yes—
693C23C24×D1111yescharacteristic
694Q8—4416no—
695D4—416no—
696C2×C4—232no—
697C2×C4—28no—
698C2×C4—28no—
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—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—114no—
716C2×C4—114no—
717C2×C4—114no—
718C2×C4—228no—
719C2×C4—228no—
720C2×C4—228no—
721C2×C4—222no—
722C2×C4—222no—
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—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—4416no—
743C2×C4—444no—
744C2×C4—444no—
745C2×C4—444no—
746C2×C4—444no—
747C2×C4—444no—
748C2×C4C2×D4×D1114yes—
749C2×C4C2×#434114yes—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—416no—
761C22—416no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22#1062302614yes—
767C22#1062306914yes—
768C22#1062308314yes—
769C22#1062311714yes—
770C22#1062313414yes—
771C22#1062314314yes—
772C22#1062318114yes—
773C22C22×#433911yescharacteristic
774C22C22×D4×D1111yescharacteristic
775C22C22×#434111yescharacteristic
776C22C22×#434111yescharacteristic
777C22C2×#6703711yescharacteristic
778C22C2×#41×D1111yescharacteristic
779C22C2×#6704311yescharacteristic
780C4—24no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—224no—
786C4—224no—
787C4—224no—
788C4—442no—
789C4—442no—
790C4—442no—
791C4—442no—
792C4—442no—
793C2—44no—
794C2—44no—
795C2#1307281418yesdirect product factor
796C2C2×#1062311711yescharacteristic
797C2C2×#1062306911yescharacteristic
798C2C2×#1062313411yescharacteristic
799C2C2×#1062314311yescharacteristic
800C2C2×#1062308311yescharacteristic
801C2C2×#1062302611yescharacteristic
802C2C2×#1062318111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11C2×#2477
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#66931C2semidirect
2. C22×#66979C2semidirect
3. #13072814C2direct (N × H)
4. C2×#10622272C2semidirect
5. C2×#10622566C2semidirect
7. C2×#10622560C2semidirect
8. C2×#10622259C2semidirect
9. C2×#10622558C2semidirect
10. C2×#10622557C2semidirect
11. C2×#10622267C2semidirect
12. C2×#10622265C2semidirect
14. C2×#10622823C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
32. C2×#66979C22semidirect
43. C2×#66931C22semidirect
49. #10622823C22semidirect
60. #10622566C22semidirect
61. #10622560C22semidirect
62. #10622558C22semidirect
63. #10622557C22semidirect
64. C22⋊C4×Dic11C22semidirect
65. #10622272C22semidirect
66. #10622267C22semidirect
67. #10622265C22semidirect
68. #10622259C22semidirect
122. C2×C4⋊Dic11D4semidirect
249. C4⋊Dic11C2×D4semidirect
545. C2×C11#2477semidirect
657. C11C2×#2477semidirect
795. C2#13072814direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669312
C22×#669792
#130728142
C2×#106222722
C2×#106225662
C2×#106228352
C2×#106225602
C2×#106222592
C2×#106225582
C2×#106225572
C2×#106222672
C2×#106222652
C2×#106228332
C2×#106228232
C2×C22⋊C4×Dic112
C2×C11×#3862
C2×#247711