Finite Group Databasebeta

← C2×#13071377 #14912636

Subgroups — C2×#13071377 #14912636

Order 2816.

3414 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66991C211yesmaximal, characteristic
2#13071377C2116yesmaximal, direct product factor
3C2×#10622570C211yesmaximal, characteristic, complemented
4C2×#10622570C211yesmaximal, characteristic, complemented
5C2×#10622558C211yesmaximal, characteristic, complemented
6C2×#10622557C211yesmaximal, characteristic, complemented
7C2×#10622266C211yesmaximal, characteristic, complemented
8C2×#10622267C211yesmaximal, characteristic, complemented
9C2×#10622833C211yesmaximal, characteristic, complemented
10C2×#10622826C211yesmaximal, characteristic, complemented
11C2×#10622571C211yesmaximal, characteristic, complemented
12C2×#10622277C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C2×#66991C4116yescomplemented
32C2×#66991C2218yes—
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C11×#386C2218yescomplemented
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47#10622833C2218yescomplemented
48#10622826C2218yescomplemented
49C4×C22⋊Dic11C2218yescomplemented
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58#10622571C2218yescomplemented
59#10622570C2218yescomplemented
60#10622570C2218yescomplemented
61#10622558C2218yescomplemented
62#10622557C2218yescomplemented
63C22⋊C4×Dic11C2218yescomplemented
64#10622279C2218yescomplemented
65#10622277C2218yescomplemented
66#10622267C2218yescomplemented
67#10622266C2218yescomplemented
68C25×C11C2311yescharacteristic
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C22×D4×C11—42no—
72C22×D4×C11—42no—
73C22×D4×C11C2×C418yes—
74C22×D4×C11C2314yes—
75C23×C4×C11—24no—
76C23×C4×C11—42no—
77C23×C4×C11—42no—
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2314yes—
84C22×C22⋊D11—42no—
85C22×C22⋊D11—42no—
86C22×C22⋊D11—42no—
87C22×C22⋊D11—42no—
88C22×C22⋊D11C2×C418yescomplemented
89C22×C22⋊D11C2×C418yescomplemented
90C22×C22⋊D11C2314yes—
91C22×C22⋊D11C2314yes—
92C23×Dic11—24no—
93C23×Dic11—42no—
94C23×Dic11—42no—
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2314yes—
103C22×C4×D11—42no—
104C22×C4×D11—42no—
105C22×C4×D11C2×C418yescomplemented
106C22×C4×D11C2314yes—
107C2×C11×C22⋊C4—24no—
108C2×C11×C22⋊C4—42no—
109C2×C11×C22⋊C4—42no—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2314yes—
112C2×C11×C22⋊C4C2314yes—
113C2×C22⋊Dic11—24no—
114C2×C22⋊Dic11—42no—
115C2×C22⋊Dic11—42no—
116C2×C22⋊Dic11C2×C418yescomplemented
117C2×C22⋊Dic11C2×C418yescomplemented
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123#66991C2×C4164yescomplemented
124C2×(C2×D11)⋊C4—24no—
125C2×(C2×D11)⋊C4—24no—
126C2×(C2×D11)⋊C4—42no—
127C2×(C2×D11)⋊C4—42no—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×C4⋊Dic11C2×C418yescomplemented
133C2×C4⋊Dic11C2314yes—
134C2×Dic11⋊C4—42no—
135C2×Dic11⋊C4—42no—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2314yes—
138C2×C4×Dic11—42no—
139C2×C4×Dic11—42no—
140C2×C4×Dic11—42no—
141C2×C4×Dic11—42no—
142C2×C4×Dic11C2314yes—
143C2×C4×Dic11C2314yes—
144C2×C4×Dic11C2314yes—
145C2×C4×Dic11C2314yes—
146C11×#95C2314yes—
147C11×#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C2×#2333—111nomaximal, Sylow
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—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11C22×C414yes—
170C24×C11C22×C414yes—
171C24×C11C2412yes—
172C24×C11C2412yes—
173C24×C11C2411yescharacteristic
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11C22×C414yes—
181C23×D11C2412yes—
182C2×D4×C11—416no—
183C2×D4×C11—44no—
184C2×D4×C11—44no—
185C2×D4×C11C22×C4116yes—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—28no—
200C22×C4×C11—44no—
201C22×C4×C11—44no—
202C22×C4×C11—416no—
203C22×C4×C11C22×C414yes—
204C22×C4×C11#4114yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C2×C22⋊D11—416no—
211C2×C22⋊D11—416no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11—44no—
215C2×C22⋊D11—44no—
216C2×C22⋊D11C22×C4116yescomplemented
217C2×C22⋊D11C22×C4116yescomplemented
218C22×Dic11—28no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—44no—
237C22×Dic11—44no—
238C22×Dic11—416no—
239C22×Dic11C22×C414yes—
240C22×Dic11C22×C414yes—
241C22×Dic11C22×C414yes—
242C22×Dic11#4114yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C2×C4×D11—416no—
251C2×C4×D11—44no—
252C2×C4×D11—44no—
253C2×C4×D11C22×C4116yescomplemented
254C11×C22⋊C4—28no—
255C11×C22⋊C4—44no—
256C11×C22⋊C4—44no—
257C22⋊Dic11—28no—
258C22⋊Dic11—44no—
259C22⋊Dic11—44no—
260C22⋊Dic11C22×C4116yescomplemented
261C22⋊Dic11C22×C4116yescomplemented
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—28no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266C4⋊Dic11C22×C4116yescomplemented
267Dic11⋊C4—44no—
268Dic11⋊C4—44no—
269C4×Dic11—44no—
270C4×Dic11—44no—
271C4×Dic11—44no—
272C4×Dic11—44no—
273C22×#121—111no—
274#2333—1116no—
275C2×#390—111no—
276C2×#390—111no—
277C2×#388—111no—
278C2×#388—111no—
279C2×#387—111no—
280C2×#387—111no—
281C2×#386—111no—
282C2×#386—111no—
283C2×#386—111no—
284C2×#386D1111yescharacteristic, complemented
285C2×#381—111no—
286C2×C4×C22⋊C4—111no—
287C2×C4×C22⋊C4—111no—
288C2×C4×C22⋊C4—111no—
289C23×C11—28no—
290C23×C11—28no—
291C23×C11—28no—
292C23×C11—28no—
293C23×C11—28no—
294C23×C11—28no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—44no—
308C23×C11—44no—
309C23×C11—44no—
310C23×C11—44no—
311C23×C11—44no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11C23×C414yes—
316C23×C11C23×C414yes—
317C23×C11C23×C412yes—
318C23×C11C2×#4112yes—
319C23×C11C2×#4112yes—
320C23×C11H(5,𝔽2)12yes—
321C23×C11H(5,𝔽2)12yes—
322C23×C11H(5,𝔽2)12yes—
323C23×C11H(5,𝔽2)12yes—
324C23×C11C2511yescharacteristic
325C22×D11—28no—
326C22×D11—28no—
327C22×D11—28no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11C23×C414yes—
339D4×C11—416no—
340C2×C4×C11—28no—
341C2×C4×C11—28no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—416no—
356C2×C4×C11—44no—
357C2×C4×C11—44no—
358C2×C4×C11—44no—
359C2×C4×C11C23×C414yes—
360C2×C4×C11C2×#4114yes—
361C22⋊D11—416no—
362C22⋊D11—416no—
363C2×Dic11—28no—
364C2×Dic11—28no—
365C2×Dic11—28no—
366C2×Dic11—28no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—416no—
385C2×Dic11—44no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11C23×C414yes—
389C2×Dic11C23×C414yes—
390C2×Dic11C23×C414yes—
391C2×Dic11C2×#4114yes—
392C4×D11—416no—
393C23×D4—111no—
394C23×D4—111no—
395C23×D4C2×D1111yescharacteristic
396C24×C4—111no—
397C24×C4—111no—
398C24×C4C2×D1111yescharacteristic
399C2×#121—118no—
400C2×#121—1116no—
401C22×C4⋊C4—111no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C22⋊C4—111no—
405C22×C22⋊C4—111no—
406C22×C22⋊C4—111no—
407C22×C22⋊C4—111no—
408C22×C22⋊C4—111no—
409C22×C22⋊C4—111no—
410C22×C22⋊C4—111no—
411C22×C22⋊C4—111no—
412C22×C22⋊C4—111no—
413C22×C22⋊C4C2×D1111yescharacteristic
414C22×C22⋊C4C2×D1111yescharacteristic
415C22×C22⋊C4C2×D1111yescharacteristic
416C22×C42—111no—
417C22×C42—111no—
418C22×C42—111no—
419C22×C42—111no—
420#390—118no—
421#390—118no—
422#388—118no—
423#388—118no—
424#387—118no—
425#387—118no—
426#386—118no—
427#386—118no—
428#386—118no—
429#386C2×D1118yescomplemented
430#381—118no—
431C4×C22⋊C4—118no—
432C4×C22⋊C4—118no—
433C4×C22⋊C4—118no—
434C2×#95—111no—
435C2×#95—111no—
436C2×#95—111no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95C2×D1111yescharacteristic
443C2×#95C2×D1111yescharacteristic
444C22×C11—24no—
445C22×C11—24no—
446C22×C11—24no—
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11—416no—
451C22×C11—416no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11C4×#4114yes—
461C22×C11#51814yes—
462C22×C11#51814yes—
463C22×C11#53814yes—
464C22×C11#53814yes—
465C22×C11#54014yes—
466C22×C11#54014yes—
467C22×C11C24×C411yescharacteristic
468C22×C11C22×#4111yescharacteristic
469C22×C11C22×#4111yescharacteristic
470C22×C11C2×H(5,𝔽2)11yescharacteristic
471C22×C11C2×H(5,𝔽2)11yescharacteristic
472C22×C11C2×H(5,𝔽2)11yescharacteristic
473C22×C11C2×H(5,𝔽2)11yescharacteristic
474C2×D11—24no—
475C2×D11—24no—
476C2×D11—24no—
477C2×D11—416no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C4×C11—24no—
483C4×C11—24no—
484C4×C11—42no—
485C4×C11—42no—
486C4×C11—42no—
487Dic11—24no—
488Dic11—24no—
489Dic11—24no—
490Dic11—24no—
491Dic11—42no—
492Dic11—42no—
493Dic11—42no—
494C25—111no—
495C25C22×D1111yescharacteristic
496C25C22×D1111yescharacteristic
497C22×D4—42no—
498C22×D4—42no—
499C22×D4—118no—
500C22×D4—118no—
501C22×D4—114no—
502C22×D4—114no—
503C22×D4—442no—
504C22×D4—442no—
505C22×D4—442no—
506C22×D4—442no—
507C22×D4C4×D1118yes—
508C22×D4C22×D1114yes—
509C23×C4—24no—
510C23×C4—42no—
511C23×C4—42no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—118no—
517C23×C4—114no—
518C23×C4—111no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—114no—
522C23×C4—224no—
523C23×C4—442no—
524C23×C4—442no—
525C23×C4—442no—
526C23×C4—442no—
527C23×C4C22×D1111yescharacteristic
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530C23×C4C22×D1111yescharacteristic
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1114yes—
533#121—1164no—
534C2×C4⋊C4—118no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—442no—
539C2×C4⋊C4—442no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—118no—
544C2×C22⋊C4—118no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—114no—
547C2×C22⋊C4—114no—
548C2×C22⋊C4—114no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—224no—
555C2×C22⋊C4—224no—
556C2×C22⋊C4—224no—
557C2×C22⋊C4—442no—
558C2×C22⋊C4—442no—
559C2×C22⋊C4—442no—
560C2×C22⋊C4—442no—
561C2×C22⋊C4C22×D1114yes—
562C2×C22⋊C4C22×D1114yes—
563C2×C22⋊C4C22×D1114yes—
564C2×C42—114no—
565C2×C42—114no—
566C2×C42—114no—
567C2×C42—114no—
568C2×C42—442no—
569C2×C42—442no—
570C2×C42—442no—
571C2×C42—442no—
572#95—114no—
573#95—114no—
574#95—114no—
575#95—114no—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95C22×D1114yes—
581#95C22×D1114yes—
582C2×C11—44no—
583C2×C11—44no—
584C2×C11#233318yescomplemented
585C2×C11C2×C4×#4111yescharacteristic
586C2×C11C2×#51811yescharacteristic
587C2×C11C2×#51811yescharacteristic
588C2×C11C2×#53811yescharacteristic
589C2×C11C2×#53811yescharacteristic
590C2×C11C2×#54011yescharacteristic
591C2×C11C2×#54011yescharacteristic
592D11—44no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—114no—
606C24—112no—
607C24—222no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24C2×C4×D1114yes—
614C24C2×C4×D1114yes—
615C24C23×D1112yes—
616C24C23×D1112yes—
617C24C23×D1111yescharacteristic
618C2×D4—44no—
619C2×D4—44no—
620C2×D4—416no—
621C2×D4—1116no—
622C2×D4—1116no—
623C2×D4—4416no—
624C2×D4—4416no—
625C2×D4—444no—
626C2×D4—444no—
627C2×D4—444no—
628C2×D4—444no—
629C2×D4C2×C4×D11116yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—28no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—416no—
647C22×C4—114no—
648C22×C4—114no—
649C22×C4—114no—
650C22×C4—114no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—1116no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—228no—
660C22×C4—222no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—222no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—222no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—222no—
677C22×C4—4416no—
678C22×C4—444no—
679C22×C4—444no—
680C22×C4—444no—
681C22×C4—444no—
682C22×C4—4416no—
683C22×C4C2×C4×D1114yes—
684C22×C4#434114yes—
685C22×C4C23×D1112yes—
686C22×C4C23×D1112yes—
687C22×C4C23×D1112yes—
688C22×C4C23×D1112yes—
689C22×C4C23×D1112yes—
690C4⋊C4—1116no—
691C4⋊C4—444no—
692C4⋊C4—444no—
693C22⋊C4—28no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—1116no—
697C22⋊C4—1116no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C22⋊C4—228no—
701C22⋊C4—444no—
702C22⋊C4—444no—
703C22⋊C4—444no—
704C22⋊C4—444no—
705C42—444no—
706C42—444no—
707C42—444no—
708C42—444no—
709C11C2×#233311yescharacteristic, complemented, Sylow
710C23—28no—
711C23—28no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—114no—
737C23—228no—
738C23—228no—
739C23—228no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—222no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23C22×C4×D1114yes—
751C23C22×C4×D1114yes—
752C23C22×C4×D1112yes—
753C23C2×#434112yes—
754C23#6703712yes—
755C23#6703712yes—
756C23#6703712yes—
757C23#41×D1112yes—
758C23#6704212yes—
759C23C24×D1111yescharacteristic
760D4—416no—
761D4—4416no—
762D4—4416no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—416no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—114no—
783C2×C4—114no—
784C2×C4—114no—
785C2×C4—114no—
786C2×C4—228no—
787C2×C4—228no—
788C2×C4—228no—
789C2×C4—228no—
790C2×C4—222no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—4416no—
808C2×C4—4416no—
809C2×C4—444no—
810C2×C4—444no—
811C2×C4—444no—
812C2×C4C22×C4×D1114yes—
813C2×C4C2×#434114yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—416no—
821C22—416no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—224no—
831C22—224no—
832C22—224no—
833C22—4416no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—442no—
838C22#1062301714yes—
839C22C4×#434114yes—
840C22#1062307614yes—
841C22#1062312414yes—
842C22#1062314614yes—
843C22#1062315014yes—
844C22#1062318814yes—
845C22C23×C4×D1111yescharacteristic
846C22C22×#434111yescharacteristic
847C22C2×#6703711yescharacteristic
848C22C2×#6703711yescharacteristic
849C22C2×#6703711yescharacteristic
850C22C2×#41×D1111yescharacteristic
851C22C2×#6704211yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—224no—
858C4—224no—
859C4—224no—
860C4—224no—
861C4—442no—
862C4—442no—
863C4—442no—
864C2—44no—
865C2—44no—
866C2—444no—
867C2#1307137718yesdirect product factor
868C2C2×C4×#434111yescharacteristic
869C2C2×#1062307611yescharacteristic
870C2C2×#1062301711yescharacteristic
871C2C2×#1062312411yescharacteristic
872C2C2×#1062318811yescharacteristic
873C2C2×#1062314611yescharacteristic
874C2C2×#1062315011yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC22×#66991C2
cosocleC23×C11C25
hypercenterC2×#386D11
hypocenterC11C2×#2333
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. #13071377C2direct (N × H)
3. C2×#10622570C2semidirect
4. C2×#10622570C2semidirect
5. C2×#10622558C2semidirect
6. C2×#10622557C2semidirect
7. C2×#10622266C2semidirect
8. C2×#10622267C2semidirect
9. C2×#10622833C2semidirect
10. C2×#10622826C2semidirect
11. C2×#10622571C2semidirect
12. C2×#10622277C2semidirect
13. C2×C22⋊C4×Dic11C2semidirect
14. C2×C4×C22⋊Dic11C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#386C2semidirect
31. C2×#66991C4semidirect
44. C11×#386C22semidirect
47. #10622833C22semidirect
48. #10622826C22semidirect
49. C4×C22⋊Dic11C22semidirect
58. #10622571C22semidirect
59. #10622570C22semidirect
60. #10622570C22semidirect
61. #10622558C22semidirect
62. #10622557C22semidirect
63. C22⋊C4×Dic11C22semidirect
64. #10622279C22semidirect
65. #10622277C22semidirect
66. #10622267C22semidirect
67. #10622266C22semidirect
88. C22×C22⋊D11C2×C4semidirect
89. C22×C22⋊D11C2×C4semidirect
105. C22×C4×D11C2×C4semidirect
116. C2×C22⋊Dic11C2×C4semidirect
117. C2×C22⋊Dic11C2×C4semidirect
123. #66991C2×C4semidirect
132. C2×C4⋊Dic11C2×C4semidirect
216. C2×C22⋊D11C22×C4semidirect
217. C2×C22⋊D11C22×C4semidirect
253. C2×C4×D11C22×C4semidirect
260. C22⋊Dic11C22×C4semidirect
261. C22⋊Dic11C22×C4semidirect
266. C4⋊Dic11C22×C4semidirect
284. C2×#386D11semidirect
429. #386C2×D11semidirect
584. C2×C11#2333semidirect
709. C11C2×#2333semidirect
867. C2#13071377direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669912
#130713772
C2×#106225702
C2×#106225582
C2×#106225572
C2×#106222662
C2×#106222672
C2×#106228332
C2×#106228262
C2×#106225712
C2×#106222772
C2×C22⋊C4×Dic112
C2×C4×C22⋊Dic112
C2×#106222792
C2×C11×#3862
C2×#233311