Finite Group Databasebeta

← C2×#13073714 #14923889

Subgroups — C2×#13073714 #14923889

Order 2816.

3330 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66989C211yesmaximal, characteristic, complemented
2C22×#66936C211yesmaximal, characteristic, complemented
3#13073714C2116yesmaximal, direct product factor
4C2×#10622565C211yesmaximal, characteristic, complemented
5C2×#10622565C211yesmaximal, characteristic, complemented
6C2×#10622286C211yesmaximal, characteristic, complemented
7C2×#10622836C211yesmaximal, characteristic
8C2×#10622259C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622564C211yesmaximal, characteristic, complemented
11C2×#10622268C211yesmaximal, characteristic, complemented
12C2×#10622826C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, 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
21C23×C4×D11C2211yescharacteristic
22C23×Dic22C2211yescharacteristic
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
31C22×C22⋊Dic11C2211yescharacteristic
32C2×#66989—28no—
33C2×#66989C2218yescomplemented
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×#66936—28no—
45C2×#66936C2218yescomplemented
46C11×#386C2218yescomplemented
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49#10622836C2218yes—
50#10622826C2218yescomplemented
51C4×C22⋊Dic11C2218yescomplemented
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#10622570C2218yescomplemented
61#10622569C2218yescomplemented
62#10622565C2218yescomplemented
63#10622565C2218yescomplemented
64#10622564C2218yescomplemented
65#10622286C2218yescomplemented
66#10622279C2218yescomplemented
67#10622268C2218yescomplemented
68#10622259C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C22×D4×C11—24no—
73C22×D4×C11—24no—
74C22×D4×C11—42no—
75C22×D4×C11C2314yes—
76C23×C4×C11—24no—
77C23×C4×C11—42no—
78C23×C4×C11—42no—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2314yes—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—42no—
90C22×C22⋊D11—42no—
91C22×C22⋊D11C2314yes—
92C22×C22⋊D11C2314yes—
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C22×C4×D11—24no—
101C22×C4×D11—24no—
102C22×C4×D11—42no—
103C22×C4×D11C2314yes—
104C22×Dic22—24no—
105C22×Dic22—24no—
106C22×Dic22—42no—
107C22×Dic22C2314yes—
108C2×C11×C22⋊C4—24no—
109C2×C11×C22⋊C4—24no—
110C2×C11×C22⋊C4—42no—
111C2×C11×C22⋊C4C2314yes—
112C2×C11×C22⋊C4C2314yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C22⋊Dic11—24no—
115C2×C22⋊Dic11—24no—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—24no—
118C2×C22⋊Dic11—42no—
119C2×C22⋊Dic11D418yescomplemented
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126#66989—232no—
127C2×(C2×D11)⋊C4—24no—
128C2×(C2×D11)⋊C4—24no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—42no—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×C4⋊Dic11—24no—
136C2×C4⋊Dic11C2314yes—
137C2×Dic11⋊C4—24no—
138C2×Dic11⋊C4—24no—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×C4×Dic11—24no—
142C2×C4×Dic11—42no—
143C2×C4×Dic11—42no—
144C2×C4×Dic11C2314yes—
145C2×C4×Dic11C2314yes—
146C2×C4×Dic11C2314yes—
147#66936—232no—
148C11×#95C2314yes—
149C11×#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2557—111nomaximal, Sylow
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×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11C2×D414yes—
173C24×C11C2412yes—
174C24×C11C2412yes—
175C24×C11C2411yescharacteristic
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—22no—
182C23×D11#4114yes—
183C23×D11C2412yes—
184C2×D4×C11—28no—
185C2×D4×C11—28no—
186C2×D4×C11—44no—
187C2×D4×C11—416no—
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—22no—
200C22×C4×C11—22no—
201C22×C4×C11—28no—
202C22×C4×C11—44no—
203C22×C4×C11—44no—
204C22×C4×C11—416no—
205C22×C4×C11#4114yes—
206C22×C4×C11#4114yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C2×C22⋊D11—28no—
213C2×C22⋊D11—28no—
214C2×C22⋊D11—28no—
215C2×C22⋊D11—28no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—416no—
219C2×C22⋊D11—416no—
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—22no—
237C22×Dic11—22no—
238C22×Dic11C2×D414yes—
239C22×Dic11C2×D414yes—
240C22×Dic11#4114yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C2×C4×D11—28no—
249C2×C4×D11—28no—
250C2×C4×D11—44no—
251C2×C4×D11—416no—
252C2×Dic22—28no—
253C2×Dic22—28no—
254C2×Dic22—44no—
255C2×Dic22—416no—
256C11×C22⋊C4—28no—
257C11×C22⋊C4—28no—
258C11×C22⋊C4—44no—
259C22⋊Dic11—28no—
260C22⋊Dic11—28no—
261C22⋊Dic11—28no—
262C22⋊Dic11—28no—
263C22⋊Dic11—44no—
264C22⋊Dic11C2×D4116yescomplemented
265(C2×D11)⋊C4—28no—
266(C2×D11)⋊C4—28no—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—44no—
269C4⋊Dic11—28no—
270Dic11⋊C4—28no—
271Dic11⋊C4—28no—
272C4×Dic11—28no—
273C4×Dic11—44no—
274C4×Dic11—44no—
275C22×#124—111no—
276C22×#123—111no—
277#2557—1116no—
278C2×#397—111no—
279C2×#397—111no—
280C2×#393—111no—
281C2×#392—111no—
282C2×#391—111no—
283C2×#390—111no—
284C2×#388—111no—
285C2×#387—111no—
286C2×#386—111no—
287C2×#386—111no—
288C2×#386D1111yescharacteristic, complemented
289C2×C4×C22⋊C4—111no—
290C2×C4×C22⋊C4—111no—
291C23×C11—28no—
292C23×C11—28no—
293C23×C11—28no—
294C23×C11—22no—
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×C11—44no—
316C23×C11—44no—
317C23×C11—44no—
318C23×C11C22×D414yes—
319C23×C11C22×D412yes—
320C23×C11C2×#4112yes—
321C23×C11C2×#4112yes—
322C23×C11C2×#4112yes—
323C23×C11C2×#4112yes—
324C23×C11H(5,𝔽2)12yes—
325C23×C11H(5,𝔽2)12yes—
326C23×C11C2511yescharacteristic
327C22×D11—28no—
328C22×D11—28no—
329C22×D11—28no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11—44no—
340C22×D11C2×#4114yes—
341D4×C11—416no—
342C2×C4×C11—28no—
343C2×C4×C11—28no—
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—22no—
356C2×C4×C11—22no—
357C2×C4×C11—416no—
358C2×C4×C11—44no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C2×C4×C11C2×#4114yes—
362C2×C4×C11C2×#4114yes—
363C22⋊D11—416no—
364C22⋊D11—416no—
365C2×Dic11—28no—
366C2×Dic11—28no—
367C2×Dic11—28no—
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—22no—
385C2×Dic11—22no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11—44no—
389C2×Dic11—44no—
390C2×Dic11C22×D414yes—
391C2×Dic11C22×D414yes—
392C2×Dic11C2×#4114yes—
393C4×D11—416no—
394Dic22—416no—
395C23×Q8—111no—
396C23×D4—111no—
397C23×D4—111no—
398C23×D4C2×D1111yescharacteristic
399C24×C4—111no—
400C24×C4C2×D1111yescharacteristic
401C2×#124—118no—
402C2×#124—228no—
403C2×#123—118no—
404C2×#123—228no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407C22×C4⋊C4—111no—
408C22×C22⋊C4—111no—
409C22×C22⋊C4—111no—
410C22×C22⋊C4—111no—
411C22×C22⋊C4—111no—
412C22×C22⋊C4—111no—
413C22×C22⋊C4—111no—
414C22×C22⋊C4—111no—
415C22×C22⋊C4—111no—
416C22×C22⋊C4—111no—
417C22×C22⋊C4—111no—
418C22×C22⋊C4C2×D1111yescharacteristic
419C22×C22⋊C4C2×D1111yescharacteristic
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C42—111no—
422C22×C42—111no—
423C22×C42—111no—
424#397—118no—
425#397—118no—
426#393—118no—
427#392—118no—
428#391—118no—
429#390—118no—
430#388—118no—
431#387—118no—
432#386—118no—
433#386—118no—
434#386C2×D1118yescomplemented
435C4×C22⋊C4—118no—
436C4×C22⋊C4—118no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95—111no—
444C2×#95—111no—
445C2×#95C2×D1111yescharacteristic
446C2×#95C2×D1111yescharacteristic
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—416no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—88no—
463C22×C11#52914yes—
464C22×C11#53214yes—
465C22×C11#53814yes—
466C22×C11#54614yes—
467C22×C11#54614yes—
468C22×C11#55114yes—
469C22×C11#55914yes—
470C22×C11C23×D411yescharacteristic
471C22×C11C22×#4111yescharacteristic
472C22×C11C22×#4111yescharacteristic
473C22×C11C22×#4111yescharacteristic
474C22×C11C22×#4111yescharacteristic
475C22×C11C2×H(5,𝔽2)11yescharacteristic
476C22×C11C2×H(5,𝔽2)11yescharacteristic
477C2×D11—24no—
478C2×D11—24no—
479C2×D11—24no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—416no—
485C4×C11—24no—
486C4×C11—24no—
487C4×C11—42no—
488C4×C11—42no—
489C4×C11—42no—
490Dic11—24no—
491Dic11—24no—
492Dic11—24no—
493Dic11—42no—
494Dic11—42no—
495Dic11—42no—
496Dic11—42no—
497C25—111no—
498C25C22×D1111yescharacteristic
499C25C22×D1111yescharacteristic
500C22×Q8—114no—
501C22×Q8—224no—
502C22×Q8—224no—
503C22×Q8—442no—
504C22×D4—24no—
505C22×D4—24no—
506C22×D4—42no—
507C22×D4—114no—
508C22×D4—114no—
509C22×D4—224no—
510C22×D4—224no—
511C22×D4—224no—
512C22×D4—224no—
513C22×D4—442no—
514C22×D4—442no—
515C22×D4C22×D1114yes—
516C23×C4—24no—
517C23×C4—42no—
518C23×C4—42no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—111no—
524C23×C4—111no—
525C23×C4—111no—
526C23×C4—114no—
527C23×C4—224no—
528C23×C4—224no—
529C23×C4—442no—
530C23×C4C22×D1111yescharacteristic
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C23×C4C22×D1111yescharacteristic
535C23×C4C22×D1114yes—
536#124—2232no—
537#123—2232no—
538C2×C4⋊C4—114no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—224no—
542C2×C4⋊C4—224no—
543C2×C4⋊C4—224no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—118no—
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—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—114no—
558C2×C22⋊C4—224no—
559C2×C22⋊C4—224no—
560C2×C22⋊C4—224no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—442no—
566C2×C22⋊C4—442no—
567C2×C22⋊C4C22×D1114yes—
568C2×C22⋊C4C22×D1114yes—
569C2×C22⋊C4C22×D1114yes—
570C2×C42—114no—
571C2×C42—114no—
572C2×C42—114no—
573C2×C42—224no—
574C2×C42—442no—
575C2×C42—442no—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95—114no—
582#95—114no—
583#95—114no—
584#95C22×D1114yes—
585#95C22×D1114yes—
586C2×C11—44no—
587C2×C11—82no—
588C2×C11#255718yescomplemented
589C2×C11C2×#52911yescharacteristic
590C2×C11C2×#53211yescharacteristic
591C2×C11C2×#53811yescharacteristic
592C2×C11C2×#54611yescharacteristic
593C2×C11C2×#54611yescharacteristic
594C2×C11C2×#55111yescharacteristic
595C2×C11C2×#55911yescharacteristic
596D11—44no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—114no—
611C24—112no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24—222no—
617C24—222no—
618C24D4×D1114yes—
619C24C23×D1112yes—
620C24C23×D1112yes—
621C24C23×D1111yescharacteristic
622C2×Q8—228no—
623C2×Q8—228no—
624C2×Q8—444no—
625C2×Q8—4416no—
626C2×D4—28no—
627C2×D4—28no—
628C2×D4—44no—
629C2×D4—416no—
630C2×D4—228no—
631C2×D4—228no—
632C2×D4—228no—
633C2×D4—228no—
634C2×D4—444no—
635C2×D4—444no—
636C2×D4—4416no—
637C2×D4—4416no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—416no—
655C22×C4—114no—
656C22×C4—114no—
657C22×C4—114no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—112no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—112no—
665C22×C4—228no—
666C22×C4—228no—
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—222no—
678C22×C4—222no—
679C22×C4—222no—
680C22×C4—222no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—444no—
686C22×C4—4416no—
687C22×C4#433914yes—
688C22×C4#434114yes—
689C22×C4C23×D1112yes—
690C22×C4C23×D1112yes—
691C22×C4C23×D1112yes—
692C22×C4C23×D1112yes—
693C22×C4C23×D1112yes—
694C4⋊C4—228no—
695C4⋊C4—228no—
696C4⋊C4—228no—
697C22⋊C4—28no—
698C22⋊C4—28no—
699C22⋊C4—44no—
700C22⋊C4—1116no—
701C22⋊C4—228no—
702C22⋊C4—228no—
703C22⋊C4—228no—
704C22⋊C4—228no—
705C22⋊C4—228no—
706C22⋊C4—228no—
707C22⋊C4—228no—
708C22⋊C4—444no—
709C22⋊C4—444no—
710C42—228no—
711C42—444no—
712C42—444no—
713C11C2×#255711yescharacteristic, complemented, Sylow
714C23—28no—
715C23—28no—
716C23—28no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—114no—
742C23—228no—
743C23—228no—
744C23—222no—
745C23—222no—
746C23—222no—
747C23—228no—
748C23—222no—
749C23—222no—
750C23—222no—
751C23—444no—
752C23—444no—
753C23—444no—
754C23—444no—
755C23C2×#433912yes—
756C23C2×D4×D1114yes—
757C23C2×D4×D1112yes—
758C23C2×#434112yes—
759C23#6703712yes—
760C23#6703712yes—
761C23#41×D1112yes—
762C23#41×D1112yes—
763C23C24×D1111yescharacteristic
764Q8—4416no—
765D4—416no—
766D4—4416no—
767D4—4416no—
768C2×C4—28no—
769C2×C4—28no—
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—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—416no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—114no—
788C2×C4—114no—
789C2×C4—114no—
790C2×C4—228no—
791C2×C4—228no—
792C2×C4—222no—
793C2×C4—228no—
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—222no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—4416no—
812C2×C4—444no—
813C2×C4—444no—
814C2×C4—444no—
815C2×C4—444no—
816C2×C4C2×#433914yes—
817C2×C4C2×#434114yes—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—42no—
822C22—42no—
823C22—416no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—88no—
834C22—224no—
835C22—224no—
836C22—224no—
837C22—442no—
838C22—4416no—
839C22—442no—
840C22—442no—
841C22—442no—
842C22#1062302114yes—
843C22#1062308814yes—
844C22#1062309014yes—
845C22#1062312414yes—
846C22#1062312714yes—
847C22#1062314114yes—
848C22#1062319014yes—
849C22C22×#433911yescharacteristic
850C22C22×D4×D1111yescharacteristic
851C22C22×#434111yescharacteristic
852C22C2×#6703711yescharacteristic
853C22C2×#6703711yescharacteristic
854C22C2×#41×D1111yescharacteristic
855C22C2×#41×D1111yescharacteristic
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—224no—
862C4—224no—
863C4—224no—
864C4—442no—
865C4—442no—
866C4—442no—
867C4—442no—
868C2—44no—
869C2—82no—
870C2—444no—
871C2#1307371418yesdirect product factor
872C2C2×#1062308811yescharacteristic
873C2C2×#1062312711yescharacteristic
874C2C2×#1062312411yescharacteristic
875C2C2×#1062314111yescharacteristic
876C2C2×#1062302111yescharacteristic
877C2C2×#1062319011yescharacteristic
878C2C2×#1062309011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#386D11
hypocenterC11C2×#2557
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#66989C2semidirect
2. C22×#66936C2semidirect
3. #13073714C2direct (N × H)
4. C2×#10622565C2semidirect
5. C2×#10622565C2semidirect
6. C2×#10622286C2semidirect
8. C2×#10622259C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622564C2semidirect
11. C2×#10622268C2semidirect
12. C2×#10622826C2semidirect
13. C2×#10622569C2semidirect
14. C2×C4×C22⋊Dic11C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#386C2semidirect
33. C2×#66989C22semidirect
45. C2×#66936C22semidirect
46. C11×#386C22semidirect
50. #10622826C22semidirect
51. C4×C22⋊Dic11C22semidirect
60. #10622570C22semidirect
61. #10622569C22semidirect
62. #10622565C22semidirect
63. #10622565C22semidirect
64. #10622564C22semidirect
65. #10622286C22semidirect
66. #10622279C22semidirect
67. #10622268C22semidirect
68. #10622259C22semidirect
119. C2×C22⋊Dic11D4semidirect
264. C22⋊Dic11C2×D4semidirect
288. C2×#386D11semidirect
434. #386C2×D11semidirect
588. C2×C11#2557semidirect
713. C11C2×#2557semidirect
871. C2#13073714direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669892
C22×#669362
#130737142
C2×#106225652
C2×#106222862
C2×#106228362
C2×#106222592
C2×#106225702
C2×#106225642
C2×#106222682
C2×#106228262
C2×#106225692
C2×C4×C22⋊Dic112
C2×#106222792
C2×C11×#3862
C2×#255711