Finite Group Databasebeta

← C2×#13073708 #14923879

Subgroups — C2×#13073708 #14923879

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×#66988C211yesmaximal, characteristic, complemented
3#13073708C2116yesmaximal, direct product factor
4C2×#10622565C211yesmaximal, characteristic, complemented
5C2×#10622566C211yesmaximal, characteristic, complemented
6C2×#10622560C211yesmaximal, characteristic, complemented
7C2×#10622259C211yesmaximal, characteristic, complemented
8C2×#10622834C211yesmaximal, characteristic, complemented
9C2×#10622557C211yesmaximal, characteristic, complemented
10C2×#10622267C211yesmaximal, characteristic, complemented
11C2×#10622833C211yesmaximal, characteristic, complemented
12C2×#10622833C211yesmaximal, characteristic, complemented
13C2×#10622833C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#392C211yesmaximal, characteristic
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
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
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C2×#66989—28no—
37C2×#66989C2218yescomplemented
38C2×#66988—28no—
39C2×#66988C2218yescomplemented
40C22×C4⋊Dic11C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C11×#392C2218yes—
47C2×C11×#95C2211yescharacteristic
48#10622834C2218yescomplemented
49#10622833C2218yescomplemented
50#10622833C2218yescomplemented
51#10622833C2218yescomplemented
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622566C2218yescomplemented
62#10622565C2218yescomplemented
63#10622560C2218yescomplemented
64#10622557C2218yescomplemented
65C22⋊C4×Dic11C2218yescomplemented
66C22⋊C4×Dic11C2218yescomplemented
67#10622267C2218yescomplemented
68#10622259C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C25×C11C2311yescharacteristic
72C22×D4×C11—24no—
73C22×D4×C11—24no—
74C22×D4×C11—24no—
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—24no—
78C22×D4×C11—42no—
79C22×D4×C11—42no—
80C22×D4×C11—42no—
81C22×D4×C11C2314yes—
82C22×D4×C11C2314yes—
83C22×D4×C11C2314yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×Dic11—24no—
89C23×Dic11—24no—
90C23×Dic11—24no—
91C23×Dic11—42no—
92C23×Dic11—42no—
93C23×Dic11—42no—
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2314yes—
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2314yes—
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—24no—
119C2×C22⋊Dic11—24no—
120C2×C22⋊Dic11—24no—
121C2×C22⋊Dic11—42no—
122C2×C22⋊Dic11—42no—
123C2×C22⋊Dic11D418yescomplemented
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134#66989—232no—
135#66988—232no—
136C2×C4⋊Dic11—24no—
137C2×C4⋊Dic11C2314yes—
138C2×Dic11⋊C4—24no—
139C2×Dic11⋊C4—24no—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×C4×Dic11—24no—
143C2×C4×Dic11—42no—
144C2×C4×Dic11—42no—
145C2×C4×Dic11C2314yes—
146C2×C4×Dic11C2314yes—
147C2×C4×Dic11C2314yes—
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×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11C2×D414yes—
179C24×C11#4114yes—
180C24×C11C2412yes—
181C24×C11C2412yes—
182C24×C11C2412yes—
183C24×C11C2411yescharacteristic
184C2×D4×C11—28no—
185C2×D4×C11—28no—
186C2×D4×C11—28no—
187C2×D4×C11—28no—
188C2×D4×C11—28no—
189C2×D4×C11—28no—
190C2×D4×C11—44no—
191C2×D4×C11—44no—
192C2×D4×C11—44no—
193C2×D4×C11—416no—
194C2×D4×C11—416no—
195C2×D4×C11—416no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11#4114yes—
207C22×C4×C11#4114yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×Dic11—28no—
213C22×Dic11—28no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—28no—
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—44no—
239C22×Dic11—416no—
240C22×Dic11—416no—
241C22×Dic11C2×D414yes—
242C22×Dic11C2×D414yes—
243C22×Dic11#4114yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
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—28no—
264C22⋊Dic11—28no—
265C22⋊Dic11—28no—
266C22⋊Dic11—44no—
267C22⋊Dic11—44no—
268C22⋊Dic11C2×D4116yescomplemented
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×#392D1111yescharacteristic
282C2×#391—111no—
283C2×#390—111no—
284C2×#388—111no—
285C2×#387—111no—
286C2×#386—111no—
287C2×#386—111no—
288C2×#386—111no—
289C2×C4×C22⋊C4—111no—
290C2×C4×C22⋊C4—111no—
291C23×C11—28no—
292C23×C11—28no—
293C23×C11—28no—
294C23×C11—28no—
295C23×C11—28no—
296C23×C11—28no—
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—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—44no—
317C23×C11—44no—
318C23×C11—44no—
319C23×C11—44no—
320C23×C11—44no—
321C23×C11—44no—
322C23×C11—44no—
323C23×C11—44no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11—44no—
331C23×C11C22×D414yes—
332C23×C11C22×D412yes—
333C23×C11C2×#4114yes—
334C23×C11C2×#4112yes—
335C23×C11C2×#4112yes—
336C23×C11C2×#4112yes—
337C23×C11C2×#4112yes—
338C23×C11H(5,𝔽2)12yes—
339C23×C11H(5,𝔽2)12yes—
340C23×C11C2511yescharacteristic
341D4×C11—416no—
342D4×C11—416no—
343D4×C11—416no—
344C2×C4×C11—28no—
345C2×C4×C11—28no—
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—44no—
357C2×C4×C11—44no—
358C2×C4×C11C2×#4114yes—
359C2×C4×C11C2×#4114yes—
360C2×Dic11—28no—
361C2×Dic11—28no—
362C2×Dic11—28no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
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—416no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11—44no—
389C2×Dic11—44no—
390C2×Dic11—44no—
391C2×Dic11C22×D414yes—
392C2×Dic11C22×D414yes—
393C2×Dic11C2×#4114yes—
394Dic22—416no—
395C23×Q8—111no—
396C23×D4C2×D1111yescharacteristic
397C23×D4C2×D1111yescharacteristic
398C23×D4C2×D1111yescharacteristic
399C24×C4—111no—
400C24×C4—111no—
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#392C2×D1118yes—
428#391—118no—
429#390—118no—
430#388—118no—
431#387—118no—
432#386—118no—
433#386—118no—
434#386—118no—
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×#95—111no—
446C2×#95C2×D1111yescharacteristic
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11—24no—
451C22×C11—24no—
452C22×C11—24no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—416no—
462C22×C11—416no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—88no—
471C22×C11#52914yes—
472C22×C11#53214yes—
473C22×C11#53814yes—
474C22×C11#54614yes—
475C22×C11#54614yes—
476C22×C11#55114yes—
477C22×C11#55914yes—
478C22×C11C23×D411yescharacteristic
479C22×C11C22×#4111yescharacteristic
480C22×C11C22×#4111yescharacteristic
481C22×C11C22×#4111yescharacteristic
482C22×C11C22×#4111yescharacteristic
483C22×C11C2×H(5,𝔽2)11yescharacteristic
484C22×C11C2×H(5,𝔽2)11yescharacteristic
485C4×C11—24no—
486C4×C11—24no—
487C4×C11—42no—
488C4×C11—42no—
489Dic11—24no—
490Dic11—24no—
491Dic11—24no—
492Dic11—42no—
493Dic11—42no—
494Dic11—42no—
495Dic11—42no—
496Dic11—42no—
497C25C22×D1111yescharacteristic
498C25C22×D1111yescharacteristic
499C25C22×D1111yescharacteristic
500C22×Q8—114no—
501C22×Q8—224no—
502C22×Q8—224no—
503C22×Q8—442no—
504C22×D4—24no—
505C22×D4—24no—
506C22×D4—24no—
507C22×D4—24no—
508C22×D4—24no—
509C22×D4—24no—
510C22×D4—42no—
511C22×D4—42no—
512C22×D4—42no—
513C22×D4C22×D1114yes—
514C22×D4C22×D1114yes—
515C22×D4C22×D1114yes—
516C23×C4—111no—
517C23×C4—111no—
518C23×C4—111no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—111no—
524C23×C4—114no—
525C23×C4—114no—
526C23×C4—224no—
527C23×C4—224no—
528C23×C4—224no—
529C23×C4—442no—
530C23×C4—442no—
531C23×C4—442no—
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C23×C4C22×D1111yescharacteristic
535C23×C4C22×D1111yescharacteristic
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#95—114no—
585#95C22×D1114yes—
586C2×C11—44no—
587C2×C11—44no—
588C2×C11—82no—
589C2×C11#255718yescomplemented
590C2×C11C2×#52911yescharacteristic
591C2×C11C2×#53211yescharacteristic
592C2×C11C2×#53811yescharacteristic
593C2×C11C2×#54611yescharacteristic
594C2×C11C2×#54611yescharacteristic
595C2×C11C2×#55111yescharacteristic
596C2×C11C2×#55911yescharacteristic
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—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24D4×D1114yes—
617C24#434114yes—
618C24C23×D1112yes—
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—28no—
629C2×D4—28no—
630C2×D4—28no—
631C2×D4—28no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—416no—
636C2×D4—416no—
637C2×D4—416no—
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—114no—
649C22×C4—114no—
650C22×C4—114no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—228no—
660C22×C4—228no—
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—228no—
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—444no—
684C22×C4—444no—
685C22×C4—444no—
686C22×C4—4416no—
687C22×C4—4416no—
688C22×C4#434114yes—
689C22×C4#434114yes—
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—28no—
718C23—28no—
719C23—28no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23C2×D4×D1114yes—
755C23C2×D4×D1112yes—
756C23C2×#434114yes—
757C23C2×#434112yes—
758C23C2×#434112yes—
759C23C2×#434112yes—
760C23#6703712yes—
761C23#6703712yes—
762C23#41×D1112yes—
763C23C24×D1111yescharacteristic
764Q8—4416no—
765D4—416no—
766D4—416no—
767D4—416no—
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—44no—
781C2×C4—44no—
782C2×C4—114no—
783C2×C4—114no—
784C2×C4—114no—
785C2×C4—228no—
786C2×C4—228no—
787C2×C4—228no—
788C2×C4—222no—
789C2×C4—222no—
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—222no—
808C2×C4—222no—
809C2×C4—4416no—
810C2×C4—4416no—
811C2×C4—444no—
812C2×C4—444no—
813C2×C4—444no—
814C2×C4—444no—
815C2×C4—444no—
816C2×C4C2×#434114yes—
817C2×C4C2×#434114yes—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—416no—
828C22—416no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—88no—
842C22#1062311814yes—
843C22#1062312214yes—
844C22#1062312214yes—
845C22#1062312714yes—
846C22#1062313114yes—
847C22#1062314414yes—
848C22#1062324414yes—
849C22C22×D4×D1111yescharacteristic
850C22C22×#434111yescharacteristic
851C22C22×#434111yescharacteristic
852C22C22×#434111yescharacteristic
853C22C2×#6703711yescharacteristic
854C22C2×#6703711yescharacteristic
855C22C2×#41×D1111yescharacteristic
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—224no—
861C4—224no—
862C4—224no—
863C4—442no—
864C4—442no—
865C4—442no—
866C4—442no—
867C4—442no—
868C2—44no—
869C2—44no—
870C2—82no—
871C2#1307370818yesdirect product factor
872C2C2×#1062313111yescharacteristic
873C2C2×#1062312711yescharacteristic
874C2C2×#1062314411yescharacteristic
875C2C2×#1062312211yescharacteristic
876C2C2×#1062312211yescharacteristic
877C2C2×#1062311811yescharacteristic
878C2C2×#1062324411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
Fitting, prime radicalC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2557
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66989C2semidirect
2. C22×#66988C2semidirect
3. #13073708C2direct (N × H)
4. C2×#10622565C2semidirect
5. C2×#10622566C2semidirect
6. C2×#10622560C2semidirect
7. C2×#10622259C2semidirect
8. C2×#10622834C2semidirect
9. C2×#10622557C2semidirect
10. C2×#10622267C2semidirect
11. C2×#10622833C2semidirect
12. C2×#10622833C2semidirect
13. C2×#10622833C2semidirect
14. C2×C22⋊C4×Dic11C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
37. C2×#66989C22semidirect
39. C2×#66988C22semidirect
48. #10622834C22semidirect
49. #10622833C22semidirect
50. #10622833C22semidirect
51. #10622833C22semidirect
61. #10622566C22semidirect
62. #10622565C22semidirect
63. #10622560C22semidirect
64. #10622557C22semidirect
65. C22⋊C4×Dic11C22semidirect
66. C22⋊C4×Dic11C22semidirect
67. #10622267C22semidirect
68. #10622259C22semidirect
123. C2×C22⋊Dic11D4semidirect
268. C22⋊Dic11C2×D4semidirect
589. C2×C11#2557semidirect
713. C11C2×#2557semidirect
871. C2#13073708direct (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×#669882
#130737082
C2×#106225652
C2×#106225662
C2×#106225602
C2×#106222592
C2×#106228342
C2×#106225572
C2×#106222672
C2×#106228332
C2×C22⋊C4×Dic112
C2×C11×#3922
C2×#255711