Finite Group Databasebeta

← C2×#13071954 #14922079

Subgroups — C2×#13071954 #14922079

Order 2816.

5998 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4341C211yesmaximal, characteristic, complemented
2C22×#66931C211yesmaximal, characteristic, complemented
3C22×#66992C211yesmaximal, characteristic, complemented
4C22×D4×Dic11C211yesmaximal, characteristic, complemented
5#13071954C2116yesmaximal, direct product factor
6C2×#10622574C211yesmaximal, characteristic, complemented
7C2×#10622835C211yesmaximal, characteristic, complemented
8C2×#10622836C211yesmaximal, characteristic, complemented
9C2×#10622259C211yesmaximal, characteristic, complemented
10C2×#10622570C211yesmaximal, characteristic, complemented
11C2×#10622833C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622563C211yesmaximal, characteristic, complemented
14C2×#10622281C211yesmaximal, characteristic, complemented
15C2×#10622555C211yesmaximal, characteristic, complemented
16C2×C11×#392C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C24×Dic11C2211yescharacteristic
25C24×Dic11C2211yescharacteristic
26C22×#4341—28no—
27C22×#4341—28no—
28C22×#4341—28no—
29C22×#4341C2218yescomplemented
30C23×C4×D11C2211yescharacteristic
31C23×Dic22C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C22×C22⋊Dic11C2211yescharacteristic
38C22×C22⋊Dic11C2211yescharacteristic
39C22×C22⋊Dic11C2211yescharacteristic
40C22×C22⋊Dic11C2211yescharacteristic
41C2×#66992—28no—
42C2×#66992C2218yescomplemented
43C2×D4×Dic11—28no—
44C2×D4×Dic11C2218yescomplemented
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×(C2×D11)⋊C4C2211yescharacteristic
47C22×(C2×D11)⋊C4C2211yescharacteristic
48C22×C4⋊Dic11C2211yescharacteristic
49C22×C4⋊Dic11C2211yescharacteristic
50C22×Dic11⋊C4C2211yescharacteristic
51C22×Dic11⋊C4C2211yescharacteristic
52C22×Dic11⋊C4C2211yescharacteristic
53C22×C4×Dic11C2211yescharacteristic
54C2×#66931—28no—
55C2×#66931C2218yescomplemented
56C11×#392C2218yescomplemented
57C2×C11×#95C2211yescharacteristic
58#10622836C2218yescomplemented
59#10622835C2218yescomplemented
60#10622833C2218yescomplemented
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64C2×C11⋊#95C2211yescharacteristic
65C2×C11⋊#95C2211yescharacteristic
66#10622574C2218yescomplemented
67#10622570C2218yescomplemented
68#10622569C2218yescomplemented
69#10622563C2218yescomplemented
70#10622555C2218yescomplemented
71#10622281C2218yescomplemented
72#10622259C2218yescomplemented
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C25×C11C2311yescharacteristic
76C24×D11C2311yescharacteristic
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—24no—
82C22×D4×C11—24no—
83C22×D4×C11—24no—
84C22×D4×C11—24no—
85C22×D4×C11—42no—
86C22×D4×C11C2314yes—
87C22×D4×C11C2314yes—
88C22×D4×C11C2314yes—
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C22×C22⋊D11—24no—
94C22×C22⋊D11—24no—
95C22×C22⋊D11—24no—
96C22×C22⋊D11—24no—
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11—42no—
101C22×C22⋊D11D418yescomplemented
102C22×C22⋊D11C2314yes—
103C22×C22⋊D11C2314yes—
104C22×C22⋊D11C2314yes—
105C23×Dic11—24no—
106C23×Dic11—24no—
107C23×Dic11—24no—
108C23×Dic11—24no—
109C23×Dic11—24no—
110C23×Dic11—24no—
111C23×Dic11—24no—
112C23×Dic11—24no—
113C23×Dic11D418yescomplemented
114C23×Dic11C2314yes—
115C23×Dic11C2311yescharacteristic
116C23×Dic11C2311yescharacteristic
117C23×Dic11C2311yescharacteristic
118C23×Dic11C2311yescharacteristic
119C23×Dic11C2314yes—
120C23×Dic11C2311yescharacteristic
121C23×Dic11C2311yescharacteristic
122C23×Dic11C2314yes—
123C23×Dic11C2311yescharacteristic
124C2×#4341—2128no—
125C2×#4341—232no—
126C2×#4341—232no—
127C2×#4341—232no—
128C22×C4×D11—24no—
129C22×C4×D11—24no—
130C22×C4×D11—24no—
131C22×C4×D11C2314yes—
132C22×Dic22—24no—
133C22×Dic22—24no—
134C22×Dic22D418yescomplemented
135C22×Dic22C2314yes—
136C2×C11×C22⋊C4—24no—
137C2×C11×C22⋊C4—24no—
138C2×C11×C22⋊C4—42no—
139C2×C11×C22⋊C4C2314yes—
140C2×C11×C22⋊C4C2314yes—
141C2×C11×C22⋊C4C2314yes—
142C2×C22⋊Dic11—24no—
143C2×C22⋊Dic11—24no—
144C2×C22⋊Dic11—24no—
145C2×C22⋊Dic11—24no—
146C2×C22⋊Dic11—42no—
147C2×C22⋊Dic11—42no—
148C2×C22⋊Dic11C2314yes—
149C2×C22⋊Dic11C2314yes—
150C2×C22⋊Dic11C2314yes—
151C2×C22⋊Dic11C2314yes—
152C2×C22⋊Dic11C2314yes—
153C2×C22⋊Dic11C2314yes—
154#66992—232no—
155D4×Dic11—232no—
156C2×(C2×D11)⋊C4—24no—
157C2×(C2×D11)⋊C4—24no—
158C2×(C2×D11)⋊C4—42no—
159C2×(C2×D11)⋊C4C2314yes—
160C2×(C2×D11)⋊C4C2314yes—
161C2×(C2×D11)⋊C4C2314yes—
162C2×C4⋊Dic11—24no—
163C2×C4⋊Dic11—24no—
164C2×C4⋊Dic11C2314yes—
165C2×C4⋊Dic11C2314yes—
166C2×Dic11⋊C4—24no—
167C2×Dic11⋊C4—24no—
168C2×Dic11⋊C4—24no—
169C2×Dic11⋊C4C2314yes—
170C2×Dic11⋊C4C2314yes—
171C2×Dic11⋊C4C2314yes—
172C2×C4×Dic11—24no—
173C2×C4×Dic11C2314yes—
174#66931—232no—
175C11×#95C2314yes—
176C11⋊#95C2314yes—
177C11⋊#95C2314yes—
178C11⋊#95C2314yes—
179C11⋊#95C2314yes—
180C11⋊#95C2314yes—
181C2×#2407—111nomaximal, Sylow
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11—22no—
187C24×C11—22no—
188C24×C11—22no—
189C24×C11—22no—
190C24×C11—22no—
191C24×C11—22no—
192C24×C11—22no—
193C24×C11—22no—
194C24×C11—22no—
195C24×C11—22no—
196C24×C11—22no—
197C24×C11—22no—
198C24×C11—22no—
199C24×C11—22no—
200C24×C11C2×D414yes—
201C24×C11C2×D414yes—
202C24×C11#4114yescomplemented
203C24×C11C2412yes—
204C24×C11C2412yes—
205C24×C11C2412yes—
206C24×C11C2411yescharacteristic
207C23×D11—22no—
208C23×D11—22no—
209C23×D11—22no—
210C23×D11—22no—
211C23×D11—22no—
212C23×D11—22no—
213C23×D11C2×D414yes—
214C23×D11C2412yes—
215C2×D4×C11—232no—
216C2×D4×C11—232no—
217C2×D4×C11—28no—
218C2×D4×C11—28no—
219C2×D4×C11—28no—
220C2×D4×C11—28no—
221C2×D4×C11—28no—
222C2×D4×C11—28no—
223C2×D4×C11—28no—
224C2×D4×C11—28no—
225C2×D4×C11—44no—
226C2×D4×C11—416no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11C2×D414yes—
238C22×C4×C11#4114yescomplemented
239C22×C4×C11C2412yes—
240C22×C4×C11C2412yes—
241C22×C4×C11C2412yes—
242C22×C4×C11C2412yes—
243C2×C22⋊D11—232no—
244C2×C22⋊D11—232no—
245C2×C22⋊D11—28no—
246C2×C22⋊D11—28no—
247C2×C22⋊D11—28no—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—28no—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—44no—
253C2×C22⋊D11—416no—
254C2×C22⋊D11C2×D4116yescomplemented
255C22×Dic11—232no—
256C22×Dic11—232no—
257C22×Dic11—28no—
258C22×Dic11—28no—
259C22×Dic11—28no—
260C22×Dic11—28no—
261C22×Dic11—28no—
262C22×Dic11—28no—
263C22×Dic11—28no—
264C22×Dic11—22no—
265C22×Dic11—22no—
266C22×Dic11—22no—
267C22×Dic11—22no—
268C22×Dic11—28no—
269C22×Dic11—22no—
270C22×Dic11—22no—
271C22×Dic11—22no—
272C22×Dic11—22no—
273C22×Dic11—22no—
274C22×Dic11—22no—
275C22×Dic11—22no—
276C22×Dic11—22no—
277C22×Dic11—22no—
278C22×Dic11—22no—
279C22×Dic11—22no—
280C22×Dic11—22no—
281C22×Dic11—416no—
282C22×Dic11C2×D414yes—
283C22×Dic11C2×D414yes—
284C22×Dic11C2×D414yes—
285C22×Dic11C2×D414yes—
286C22×Dic11C2×D414yes—
287C22×Dic11C2×D4116yescomplemented
288C22×Dic11C2412yes—
289C22×Dic11C2412yes—
290C22×Dic11C2412yes—
291C22×Dic11C2412yes—
292C22×Dic11C2412yes—
293C22×Dic11C2412yes—
294C22×Dic11C2412yes—
295#4341—2256no—
296C2×C4×D11—232no—
297C2×C4×D11—28no—
298C2×C4×D11—28no—
299C2×C4×D11—28no—
300C2×Dic22—232no—
301C2×Dic22—28no—
302C2×Dic22—28no—
303C2×Dic22C2×D4116yescomplemented
304C11×C22⋊C4—28no—
305C11×C22⋊C4—28no—
306C11×C22⋊C4—44no—
307C22⋊Dic11—28no—
308C22⋊Dic11—28no—
309C22⋊Dic11—28no—
310C22⋊Dic11—28no—
311C22⋊Dic11—44no—
312C22⋊Dic11—44no—
313(C2×D11)⋊C4—28no—
314(C2×D11)⋊C4—28no—
315(C2×D11)⋊C4—44no—
316C4⋊Dic11—28no—
317C4⋊Dic11—28no—
318Dic11⋊C4—28no—
319Dic11⋊C4—28no—
320Dic11⋊C4—28no—
321C4×Dic11—28no—
322C23×#41—111no—
323C22×C22⋊Q8—111no—
324C22×#121—111no—
325C22×C4×D4—111no—
326#2407—1116no—
327C2×#394—111no—
328C2×#394—111no—
329C2×#392—111no—
330C2×#392D1111yescharacteristic, complemented
331C2×#391—111no—
332C2×#390—111no—
333C2×#386—111no—
334C2×#386—111no—
335C2×#385—111no—
336C2×#385—111no—
337C2×#380—111no—
338C23×C11—28no—
339C23×C11—28no—
340C23×C11—28no—
341C23×C11—28no—
342C23×C11—28no—
343C23×C11—28no—
344C23×C11—28no—
345C23×C11—28no—
346C23×C11—28no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—44no—
366C23×C11—44no—
367C23×C11—44no—
368C23×C11—44no—
369C23×C11—44no—
370C23×C11—44no—
371C23×C11—44no—
372C23×C11—44no—
373C23×C11—44no—
374C23×C11—44no—
375C23×C11—44no—
376C23×C11—44no—
377C23×C11C22×D414yes—
378C23×C11C22×D414yes—
379C23×C11C22×D412yes—
380C23×C11C22×D412yes—
381C23×C11C22×D412yes—
382C23×C11C2×#4112yes—
383C23×C11C2×#4112yes—
384C23×C11C2×#4114yescomplemented
385C23×C11H(5,𝔽2)12yes—
386C23×C112−1+412yes—
387C23×C11C2511yescharacteristic
388C22×D11—28no—
389C22×D11—28no—
390C22×D11—28no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—44no—
398C22×D11—44no—
399C22×D11—44no—
400C22×D11—44no—
401C22×D11C22×D414yes—
402D4×C11—232no—
403D4×C11—232no—
404D4×C11—416no—
405C2×C4×C11—28no—
406C2×C4×C11—28no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—44no—
418C2×C4×C11—44no—
419C2×C4×C11C22×D414yes—
420C2×C4×C11C2×#4114yescomplemented
421C22⋊D11—232no—
422C22⋊D11—232no—
423C22⋊D11—416no—
424C2×Dic11—232no—
425C2×Dic11—28no—
426C2×Dic11—28no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—232no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—44no—
445C2×Dic11—44no—
446C2×Dic11—44no—
447C2×Dic11—44no—
448C2×Dic11—416no—
449C2×Dic11#120116yes—
450C2×Dic11C22×D414yes—
451C2×Dic11C22×D414yes—
452C2×Dic11C22×D414yes—
453C2×Dic11C22×D414yes—
454C2×Dic11C22×D414yes—
455C4×D11—232no—
456Dic22—232no—
457C22×#41—118no—
458C22×#41—228no—
459C22×#41—228no—
460C22×#41—228no—
461C23×Q8—111no—
462C23×D4—111no—
463C23×D4—111no—
464C23×D4—111no—
465C23×D4C2×D1111yescharacteristic
466C23×D4C2×D1111yescharacteristic
467C23×D4C2×D1111yescharacteristic
468C24×C4—111no—
469C24×C4—111no—
470C24×C4—111no—
471C24×C4—111no—
472C2×C22⋊Q8—118no—
473C2×C22⋊Q8—228no—
474C2×#121—118no—
475C2×#121—228no—
476C2×C4×D4—118no—
477C2×C4×D4—228no—
478C22×C4⋊C4—111no—
479C22×C4⋊C4—111no—
480C22×C4⋊C4—111no—
481C22×C4⋊C4—111no—
482C22×C4⋊C4—111no—
483C22×C22⋊C4—111no—
484C22×C22⋊C4—111no—
485C22×C22⋊C4—111no—
486C22×C22⋊C4—111no—
487C22×C22⋊C4—111no—
488C22×C22⋊C4—111no—
489C22×C22⋊C4—111no—
490C22×C22⋊C4—111no—
491C22×C22⋊C4—111no—
492C22×C22⋊C4C2×D1111yescharacteristic
493C22×C22⋊C4C2×D1111yescharacteristic
494C22×C22⋊C4C2×D1111yescharacteristic
495C22×C42—111no—
496#394—118no—
497#394—118no—
498#392—118no—
499#392C2×D1118yescomplemented
500#391—118no—
501#390—118no—
502#386—118no—
503#386—118no—
504#385—118no—
505#385—118no—
506#380—118no—
507C2×#95—111no—
508C2×#95—111no—
509C2×#95—111no—
510C2×#95—111no—
511C2×#95—111no—
512C2×#95C2×D1111yescharacteristic
513C22×C11—24no—
514C22×C11—24no—
515C22×C11—24no—
516C22×C11—24no—
517C22×C11—24no—
518C22×C11—24no—
519C22×C11—24no—
520C22×C11—24no—
521C22×C11—24no—
522C22×C11—416no—
523C22×C11—416no—
524C22×C11—416no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11—42no—
529C22×C11—42no—
530C22×C11—42no—
531C22×C11—42no—
532C22×C11—42no—
533C22×C11—42no—
534C22×C11—42no—
535C22×C11—42no—
536C22×C11—42no—
537C22×C11C2×#12014yes—
538C22×C11#52514yes—
539C22×C11#53714yes—
540C22×C11#54614yes—
541C22×C11#54714yes—
542C22×C11#54814yes—
543C22×C11#55014yes—
544C22×C11C23×D411yescharacteristic
545C22×C11C23×D411yescharacteristic
546C22×C11C23×D411yescharacteristic
547C22×C11C22×#4111yescharacteristic
548C22×C11C22×#4111yescharacteristic
549C22×C11C2×H(5,𝔽2)11yescharacteristic
550C22×C11C2×2−1+411yescharacteristic
551C2×D11—24no—
552C2×D11—24no—
553C2×D11—24no—
554C2×D11—416no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C4×C11—24no—
560C4×C11—24no—
561C4×C11—42no—
562C4×C11—42no—
563Dic11—24no—
564Dic11—24no—
565Dic11—42no—
566Dic11—42no—
567Dic11—42no—
568Dic11—42no—
569Dic11C2×#12018yes—
570C25—111no—
571C25C22×D1111yescharacteristic
572C25C22×D1111yescharacteristic
573C25C22×D1111yescharacteristic
574C2×#41—2232no—
575C2×#41—2232no—
576C2×#41—2232no—
577C2×#41—22128no—
578C22×Q8—118no—
579C22×Q8—114no—
580C22×Q8—224no—
581C22×Q8—224no—
582C22×D4—24no—
583C22×D4—24no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—24no—
588C22×D4—24no—
589C22×D4—24no—
590C22×D4—42no—
591C22×D4—118no—
592C22×D4—114no—
593C22×D4—114no—
594C22×D4—114no—
595C22×D4—224no—
596C22×D4—224no—
597C22×D4—224no—
598C22×D4—224no—
599C22×D4—224no—
600C22×D4—224no—
601C22×D4—224no—
602C22×D4—442no—
603C22×D4C22×D1114yes—
604C22×D4C22×D1114yes—
605C22×D4C22×D1114yes—
606C23×C4—111no—
607C23×C4—118no—
608C23×C4—114no—
609C23×C4—111no—
610C23×C4—111no—
611C23×C4—114no—
612C23×C4—114no—
613C23×C4—111no—
614C23×C4—111no—
615C23×C4—111no—
616C23×C4—111no—
617C23×C4—114no—
618C23×C4—224no—
619C23×C4—224no—
620C23×C4—224no—
621C23×C4—224no—
622C23×C4—224no—
623C23×C4—224no—
624C23×C4—224no—
625C23×C4—224no—
626C23×C4—224no—
627C23×C4—224no—
628C23×C4—224no—
629C23×C4C22×D1111yescharacteristic
630C23×C4C22×D1111yescharacteristic
631C23×C4C22×D1111yescharacteristic
632C23×C4C22×D1111yescharacteristic
633C22⋊Q8—2232no—
634#121—2232no—
635C4×D4—2232no—
636C2×C4⋊C4—114no—
637C2×C4⋊C4—114no—
638C2×C4⋊C4—114no—
639C2×C4⋊C4—114no—
640C2×C4⋊C4—114no—
641C2×C4⋊C4—224no—
642C2×C4⋊C4—224no—
643C2×C4⋊C4—224no—
644C2×C4⋊C4—224no—
645C2×C4⋊C4—224no—
646C2×C22⋊C4—24no—
647C2×C22⋊C4—24no—
648C2×C22⋊C4—42no—
649C2×C22⋊C4—114no—
650C2×C22⋊C4—114no—
651C2×C22⋊C4—114no—
652C2×C22⋊C4—114no—
653C2×C22⋊C4—114no—
654C2×C22⋊C4—114no—
655C2×C22⋊C4—114no—
656C2×C22⋊C4—114no—
657C2×C22⋊C4—114no—
658C2×C22⋊C4—224no—
659C2×C22⋊C4—224no—
660C2×C22⋊C4—224no—
661C2×C22⋊C4—224no—
662C2×C22⋊C4—224no—
663C2×C22⋊C4—224no—
664C2×C22⋊C4—442no—
665C2×C22⋊C4—442no—
666C2×C22⋊C4—442no—
667C2×C22⋊C4C22×D1114yes—
668C2×C22⋊C4C22×D1114yes—
669C2×C22⋊C4C22×D1114yes—
670C2×C42—114no—
671C2×C42—224no—
672#95—114no—
673#95—114no—
674#95—114no—
675#95—114no—
676#95—114no—
677#95C22×D1114yes—
678C2×C11—44no—
679C2×C11—44no—
680C2×C11—44no—
681C2×C11#240718yescomplemented
682C2×C11C22×#12011yescharacteristic
683C2×C11C2×#52511yescharacteristic
684C2×C11C2×#53711yescharacteristic
685C2×C11C2×#54611yescharacteristic
686C2×C11C2×#54711yescharacteristic
687C2×C11C2×#54811yescharacteristic
688C2×C11C2×#55011yescharacteristic
689D11—44no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—22no—
702C24—22no—
703C24—22no—
704C24—22no—
705C24—22no—
706C24—22no—
707C24—22no—
708C24—114no—
709C24—112no—
710C24—222no—
711C24—222no—
712C24—222no—
713C24—222no—
714C24—222no—
715C24—222no—
716C24D4×D1114yes—
717C24D4×D1114yes—
718C24#434114yescomplemented
719C24C23×D1112yes—
720C24C23×D1112yes—
721C24C23×D1112yes—
722C24C23×D1111yescharacteristic
723#41—22256no—
724C2×Q8—1116no—
725C2×Q8—2232no—
726C2×Q8—228no—
727C2×Q8—228no—
728C2×D4—232no—
729C2×D4—232no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—44no—
739C2×D4—416no—
740C2×D4—1116no—
741C2×D4—2232no—
742C2×D4—228no—
743C2×D4—228no—
744C2×D4—228no—
745C2×D4—228no—
746C2×D4—2232no—
747C2×D4—228no—
748C2×D4—228no—
749C2×D4—228no—
750C2×D4—444no—
751C2×D4—4416no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—114no—
763C22×C4—114no—
764C22×C4—114no—
765C22×C4—112no—
766C22×C4—114no—
767C22×C4—114no—
768C22×C4—1116no—
769C22×C4—112no—
770C22×C4—112no—
771C22×C4—112no—
772C22×C4—112no—
773C22×C4—112no—
774C22×C4—112no—
775C22×C4—228no—
776C22×C4—228no—
777C22×C4—2232no—
778C22×C4—2232no—
779C22×C4—228no—
780C22×C4—228no—
781C22×C4—228no—
782C22×C4—228no—
783C22×C4—228no—
784C22×C4—228no—
785C22×C4—228no—
786C22×C4—2232no—
787C22×C4—222no—
788C22×C4—222no—
789C22×C4—222no—
790C22×C4—222no—
791C22×C4—228no—
792C22×C4—228no—
793C22×C4—222no—
794C22×C4—222no—
795C22×C4—222no—
796C22×C4—222no—
797C22×C4—222no—
798C22×C4—222no—
799C22×C4—222no—
800C22×C4—222no—
801C22×C4—222no—
802C22×C4—222no—
803C22×C4—222no—
804C22×C4—222no—
805C22×C4—4416no—
806C22×C4D4×D1114yes—
807C22×C4#434114yescomplemented
808C22×C4C23×D1112yes—
809C22×C4C23×D1112yes—
810C22×C4C23×D1112yes—
811C22×C4C23×D1112yes—
812C4⋊C4—228no—
813C4⋊C4—228no—
814C4⋊C4—228no—
815C4⋊C4—228no—
816C4⋊C4—228no—
817C22⋊C4—28no—
818C22⋊C4—28no—
819C22⋊C4—44no—
820C22⋊C4—228no—
821C22⋊C4—228no—
822C22⋊C4—228no—
823C22⋊C4—228no—
824C22⋊C4—228no—
825C22⋊C4—228no—
826C22⋊C4—444no—
827C22⋊C4—444no—
828C22⋊C4—444no—
829C42—228no—
830C11C2×#240711yescharacteristic, complemented, Sylow
831C23—28no—
832C23—28no—
833C23—28no—
834C23—28no—
835C23—28no—
836C23—28no—
837C23—28no—
838C23—28no—
839C23—28no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—44no—
859C23—44no—
860C23—44no—
861C23—44no—
862C23—44no—
863C23—44no—
864C23—44no—
865C23—44no—
866C23—44no—
867C23—44no—
868C23—44no—
869C23—44no—
870C23—114no—
871C23—228no—
872C23—228no—
873C23—228no—
874C23—222no—
875C23—222no—
876C23—222no—
877C23—222no—
878C23—222no—
879C23—222no—
880C23—444no—
881C23—444no—
882C23—444no—
883C23—444no—
884C23C2×D4×D1114yes—
885C23C2×D4×D1114yes—
886C23C2×D4×D1112yes—
887C23C2×D4×D1112yes—
888C23C2×D4×D1112yes—
889C23C2×#434112yes—
890C23C2×#434112yes—
891C23C2×#434114yescomplemented
892C23#6703712yes—
893C23#6704312yes—
894C23C24×D1111yescharacteristic
895Q8—2232no—
896D4—232no—
897D4—232no—
898D4—416no—
899D4—2232no—
900D4—2232no—
901D4—4416no—
902C2×C4—28no—
903C2×C4—28no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—44no—
915C2×C4—44no—
916C2×C4—1116no—
917C2×C4—114no—
918C2×C4—114no—
919C2×C4—114no—
920C2×C4—114no—
921C2×C4—114no—
922C2×C4—2232no—
923C2×C4—2232no—
924C2×C4—2232no—
925C2×C4—228no—
926C2×C4—228no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—222no—
943C2×C4—4416no—
944C2×C4—444no—
945C2×C4—444no—
946C2×C4—444no—
947C2×C4—444no—
948C2×C4C2×D4×D1114yes—
949C2×C4C2×#434114yescomplemented
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—24no—
957C22—24no—
958C22—24no—
959C22—42no—
960C22—42no—
961C22—416no—
962C22—416no—
963C22—416no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—224no—
975C22—224no—
976C22—224no—
977C22—442no—
978C22—4416no—
979C22—442no—
980C22—442no—
981C22—442no—
982C22#1062311714yes—
983C22D11×#12014yes—
984C22#1062312214yes—
985C22#1062312814yes—
986C22#1062312914yes—
987C22#1062314214yes—
988C22#1062324914yes—
989C22C22×D4×D1111yescharacteristic
990C22C22×D4×D1111yescharacteristic
991C22C22×D4×D1111yescharacteristic
992C22C22×#434111yescharacteristic
993C22C22×#434111yescharacteristic
994C22C2×#6703711yescharacteristic
995C22C2×#6704311yescharacteristic
996C4—24no—
997C4—24no—
998C4—42no—
999C4—42no—
1000C4—118no—
1001C4—224no—
1002C4—224no—
1003C4—442no—
1004C4—442no—
1005C4—442no—
1006C4—442no—
1007C2—44no—
1008C2—44no—
1009C2—44no—
1010C2—444no—
1011C2#1307195418yesdirect product factor
1012C2C2×D11×#12011yescharacteristic
1013C2C2×#1062311711yescharacteristic
1014C2C2×#1062312811yescharacteristic
1015C2C2×#1062312211yescharacteristic
1016C2C2×#1062314211yescharacteristic
1017C2C2×#1062312911yescharacteristic
1018C2C2×#1062324911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2407
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C23×#4341C2semidirect
2. C22×#66931C2semidirect
3. C22×#66992C2semidirect
4. C22×D4×Dic11C2semidirect
5. #13071954C2direct (N × H)
6. C2×#10622574C2semidirect
7. C2×#10622835C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622259C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622833C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622563C2semidirect
14. C2×#10622281C2semidirect
15. C2×#10622555C2semidirect
16. C2×C11×#392C2semidirect
29. C22×#4341C22semidirect
42. C2×#66992C22semidirect
44. C2×D4×Dic11C22semidirect
55. C2×#66931C22semidirect
56. C11×#392C22semidirect
58. #10622836C22semidirect
59. #10622835C22semidirect
60. #10622833C22semidirect
66. #10622574C22semidirect
67. #10622570C22semidirect
68. #10622569C22semidirect
69. #10622563C22semidirect
70. #10622555C22semidirect
71. #10622281C22semidirect
72. #10622259C22semidirect
101. C22×C22⋊D11D4semidirect
113. C23×Dic11D4semidirect
134. C22×Dic22D4semidirect
202. C24×C11#41semidirect
238. C22×C4×C11#41semidirect
254. C2×C22⋊D11C2×D4semidirect
287. C22×Dic11C2×D4semidirect
303. C2×Dic22C2×D4semidirect
330. C2×#392D11semidirect
384. C23×C11C2×#41semidirect
420. C2×C4×C11C2×#41semidirect
499. #392C2×D11semidirect
681. C2×C11#2407semidirect
718. C24#4341semidirect
807. C22×C4#4341semidirect
830. C11C2×#2407semidirect
891. C23C2×#4341semidirect
949. C2×C4C2×#4341semidirect
1011. C2#13071954direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43412
C22×#669312
C22×#669922
C22×D4×Dic112
#130719542
C2×#106225742
C2×#106228352
C2×#106228362
C2×#106222592
C2×#106225702
C2×#106228332
C2×#106225692
C2×#106225632
C2×#106222812
C2×#106225552
C2×C11×#3922
C2×#240711