Finite Group Databasebeta

← C2×#13072731 #14922350

Subgroups — C2×#13072731 #14922350

Order 2816.

3330 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×#66982C211yesmaximal, characteristic, complemented
2C22×#66930C211yesmaximal, characteristic, complemented
3#13072731C2116yesmaximal, direct product factor
4C2×#10622562C211yesmaximal, characteristic, complemented
5C2×#10622288C211yesmaximal, characteristic, complemented
6C2×#10622561C211yesmaximal, characteristic, complemented
7C2×#10622836C211yesmaximal, characteristic
8C2×#10622570C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622283C211yesmaximal, characteristic, complemented
11C2×#10622265C211yesmaximal, characteristic, complemented
12C2×#10622265C211yesmaximal, characteristic, complemented
13C2×#10622833C211yesmaximal, characteristic, complemented
14C2×#10622571C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C2×#66982—28no—
31C2×#66982C2218yescomplemented
32C22×(C2×D11)⋊C4C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×#66930—28no—
47C2×#66930C2218yescomplemented
48C11×#386C2218yescomplemented
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51#10622836C2218yes—
52#10622833C2218yescomplemented
53C4×C22⋊Dic11C2218yescomplemented
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60#10622571C2218yescomplemented
61#10622570C2218yescomplemented
62#10622570C2218yescomplemented
63#10622562C2218yescomplemented
64#10622561C2218yescomplemented
65#10622288C2218yescomplemented
66#10622283C2218yescomplemented
67#10622265C2218yescomplemented
68#10622265C2218yescomplemented
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—24no—
78C23×C4×C11—42no—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2314yes—
84C23×C4×C11C2311yescharacteristic
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×Dic11—24no—
94C23×Dic11—24no—
95C23×Dic11—24no—
96C23×Dic11C2314yes—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C2×C11×C22⋊C4—24no—
105C2×C11×C22⋊C4—42no—
106C2×C11×C22⋊C4—42no—
107C2×C11×C22⋊C4C2314yes—
108C2×C11×C22⋊C4C2314yes—
109C2×C11×C22⋊C4C2314yes—
110C2×C22⋊Dic11—24no—
111C2×C22⋊Dic11—24no—
112C2×C22⋊Dic11—24no—
113C2×C22⋊Dic11—24no—
114C2×C22⋊Dic11—42no—
115C2×C22⋊Dic11C2314yes—
116C2×C22⋊Dic11C2314yes—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120#66982—232no—
121C2×(C2×D11)⋊C4—24no—
122C2×(C2×D11)⋊C4—24no—
123C2×(C2×D11)⋊C4—24no—
124C2×(C2×D11)⋊C4—42no—
125C2×(C2×D11)⋊C4—42no—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×C4⋊Dic11—42no—
132C2×C4⋊Dic11C2314yes—
133C2×Dic11⋊C4—24no—
134C2×Dic11⋊C4—24no—
135C2×Dic11⋊C4—24no—
136C2×Dic11⋊C4—42no—
137C2×Dic11⋊C4D418yescomplemented
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×C4×Dic11—24no—
144C2×C4×Dic11—24no—
145C2×C4×Dic11—42no—
146C2×C4×Dic11C2314yes—
147C2×C4×Dic11C2314yes—
148C2×C4×Dic11C2314yes—
149#66930—232no—
150C11×#95C2314yes—
151C11×#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2471—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#4114yes—
172C24×C11#4114yes—
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—22no—
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—28no—
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—22no—
202C22×C4×C11—22no—
203C22×C4×C11—28no—
204C22×C4×C11—44no—
205C22×C4×C11—416no—
206C22×C4×C11C2×D414yes—
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—232no—
221C22×Dic11—28no—
222C22×Dic11—28no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—28no—
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×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11C2×D414yes—
242C22×Dic11C2×D414yes—
243C22×Dic11#4114yes—
244C22×Dic11#4114yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C11×C22⋊C4—28no—
253C11×C22⋊C4—44no—
254C11×C22⋊C4—44no—
255C22⋊Dic11—28no—
256C22⋊Dic11—28no—
257C22⋊Dic11—28no—
258C22⋊Dic11—28no—
259C22⋊Dic11—44no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—44no—
264(C2×D11)⋊C4—44no—
265C4⋊Dic11—44no—
266Dic11⋊C4—28no—
267Dic11⋊C4—28no—
268Dic11⋊C4—28no—
269Dic11⋊C4—44no—
270Dic11⋊C4C2×D4116yescomplemented
271C4×Dic11—28no—
272C4×Dic11—28no—
273C4×Dic11—44no—
274C22×#123—111no—
275C22×#117—111no—
276#2471—1116no—
277C2×#399—111no—
278C2×#397—111no—
279C2×#396—111no—
280C2×#392—111no—
281C2×#390—111no—
282C2×#390—111no—
283C2×#388—111no—
284C2×#387—111no—
285C2×#387—111no—
286C2×#386—111no—
287C2×#386—111no—
288C2×#386D1111yescharacteristic, complemented
289C2×C4×C22⋊C4—111no—
290C23×C11—28no—
291C23×C11—28no—
292C23×C11—28no—
293C23×C11—28no—
294C23×C11—28no—
295C23×C11—28no—
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—22no—
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×C11C22×D412yes—
317C23×C11C2×#4114yes—
318C23×C11C2×#4112yes—
319C23×C11C2×#4114yes—
320C23×C11C2×#4112yes—
321C23×C11C2×#4112yes—
322C23×C11C2×#4112yes—
323C23×C11H(5,𝔽2)12yes—
324C23×C11H(5,𝔽2)12yes—
325C23×C11C2511yescharacteristic
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11—44no—
340D4×C11—416no—
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—22no—
356C2×C4×C11—416no—
357C2×C4×C11—44no—
358C2×C4×C11—44no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C2×C4×C11C22×D414yes—
362C22⋊D11—416no—
363C22⋊D11—416no—
364C2×Dic11—232no—
365C2×Dic11—28no—
366C2×Dic11—28no—
367C2×Dic11—28no—
368C2×Dic11—28no—
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×Dic11C22×D414yes—
390C2×Dic11C22×D414yes—
391C2×Dic11C2×#4114yes—
392C2×Dic11C2×#4114yes—
393C23×D4—111no—
394C23×D4—111no—
395C23×D4C2×D1111yescharacteristic
396C24×C4—111no—
397C24×C4C2×D1111yescharacteristic
398C2×#123—118no—
399C2×#123—228no—
400C2×#117—118no—
401C2×#117—228no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4—111no—
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#399—118no—
425#397—118no—
426#396—118no—
427#392—118no—
428#390—118no—
429#390—118no—
430#388—118no—
431#387—118no—
432#387—118no—
433#386—118no—
434#386—118no—
435#386C2×D1118yescomplemented
436C4×C22⋊C4—118no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95C2×D1111yescharacteristic
444C2×#95C2×D1111yescharacteristic
445C22×C11—24no—
446C22×C11—24no—
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11—24no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—416no—
460C22×C11—416no—
461C22×C11#52514yes—
462C22×C11#52914yes—
463C22×C11#54014yes—
464C22×C11#54614yes—
465C22×C11#55014yes—
466C22×C11#55114yes—
467C22×C11#55114yes—
468C22×C11C23×D411yescharacteristic
469C22×C11C22×#4111yescharacteristic
470C22×C11C22×#4111yescharacteristic
471C22×C11C22×#4111yescharacteristic
472C22×C11C22×#4111yescharacteristic
473C22×C11C2×H(5,𝔽2)11yescharacteristic
474C22×C11C2×H(5,𝔽2)11yescharacteristic
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—88no—
483C4×C11—24no—
484C4×C11—42no—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11—42no—
488Dic11—24no—
489Dic11—24no—
490Dic11—24no—
491Dic11—24no—
492Dic11—42no—
493Dic11—42no—
494Dic11—42no—
495C25—111no—
496C25C22×D1111yescharacteristic
497C25C22×D1111yescharacteristic
498C22×D4—24no—
499C22×D4—24no—
500C22×D4—42no—
501C22×D4—114no—
502C22×D4—114no—
503C22×D4—224no—
504C22×D4—224no—
505C22×D4—224no—
506C22×D4—224no—
507C22×D4—442no—
508C22×D4—442no—
509C22×D4C22×D1114yes—
510C23×C4—24no—
511C23×C4—24no—
512C23×C4—42no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—114no—
518C23×C4—111no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—224no—
522C23×C4—224no—
523C23×C4—224no—
524C23×C4C22×D1111yescharacteristic
525C23×C4C22×D1111yescharacteristic
526C23×C4C22×D1111yescharacteristic
527C23×C4C22×D1111yescharacteristic
528C23×C4C22×D1114yes—
529C23×C4C22×D1111yescharacteristic
530#123—2232no—
531#117—2232no—
532C2×C4⋊C4—118no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—114no—
539C2×C4⋊C4—224no—
540C2×C4⋊C4—224no—
541C2×C4⋊C4—224no—
542C2×C4⋊C4—442no—
543C2×C4⋊C4—442no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
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—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—224no—
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—442no—
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—224no—
575C2×C42—442no—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95—114no—
582#95C22×D1114yes—
583#95C22×D1114yes—
584C2×C11—44no—
585C2×C11—44no—
586C2×C11#247118yescomplemented
587C2×C11C2×#52511yescharacteristic
588C2×C11C2×#52911yescharacteristic
589C2×C11C2×#54011yescharacteristic
590C2×C11C2×#54611yescharacteristic
591C2×C11C2×#55011yescharacteristic
592C2×C11C2×#55111yescharacteristic
593C2×C11C2×#55111yescharacteristic
594D11—82no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—112no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24#433914yes—
616C24#434114yes—
617C24C23×D1112yes—
618C24C23×D1112yes—
619C24C23×D1111yescharacteristic
620C2×D4—28no—
621C2×D4—28no—
622C2×D4—44no—
623C2×D4—416no—
624C2×D4—228no—
625C2×D4—228no—
626C2×D4—228no—
627C2×D4—228no—
628C2×D4—444no—
629C2×D4—444no—
630C2×D4—4416no—
631C2×D4—4416no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—28no—
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—28no—
648C22×C4—44no—
649C22×C4—416no—
650C22×C4—114no—
651C22×C4—114no—
652C22×C4—114no—
653C22×C4—114no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—228no—
662C22×C4—228no—
663C22×C4—2232no—
664C22×C4—228no—
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—222no—
678C22×C4—222no—
679C22×C4—222no—
680C22×C4—222no—
681C22×C4—222no—
682C22×C4D4×D1114yes—
683C22×C4C23×D1112yes—
684C22×C4C23×D1112yes—
685C22×C4C23×D1112yes—
686C22×C4C23×D1112yes—
687C22×C4C23×D1112yes—
688C4⋊C4—1116no—
689C4⋊C4—228no—
690C4⋊C4—228no—
691C4⋊C4—228no—
692C4⋊C4—444no—
693C4⋊C4—444no—
694C22⋊C4—28no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—228no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C22⋊C4—228no—
701C22⋊C4—228no—
702C22⋊C4—228no—
703C22⋊C4—228no—
704C22⋊C4—444no—
705C22⋊C4—444no—
706C22⋊C4—444no—
707C42—228no—
708C42—228no—
709C42—444no—
710C11C2×#247111yescharacteristic, complemented, Sylow
711C23—28no—
712C23—28no—
713C23—28no—
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—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—444no—
745C23—444no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23C2×#433914yes—
752C23C2×#433912yes—
753C23C2×D4×D1112yes—
754C23C2×#434114yes—
755C23C2×#434112yes—
756C23#6703712yes—
757C23#6703712yes—
758C23#41×D1112yes—
759C23#41×D1112yes—
760C23C24×D1111yescharacteristic
761D4—416no—
762D4—4416no—
763D4—4416no—
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—22no—
779C2×C4—416no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—114no—
785C2×C4—114no—
786C2×C4—114no—
787C2×C4—114no—
788C2×C4—2232no—
789C2×C4—228no—
790C2×C4—228no—
791C2×C4—228no—
792C2×C4—228no—
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—222no—
810C2×C4—444no—
811C2×C4—444no—
812C2×C4—444no—
813C2×C4C2×D4×D1114yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—416no—
824C22—416no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—888no—
838C22#1062302614yes—
839C22#1062307814yes—
840C22#1062308714yes—
841C22#1062312214yes—
842C22#1062313014yes—
843C22#1062314614yes—
844C22#1062318014yes—
845C22C22×#433911yescharacteristic
846C22C22×D4×D1111yescharacteristic
847C22C22×#434111yescharacteristic
848C22C2×#6703711yescharacteristic
849C22C2×#6703711yescharacteristic
850C22C2×#41×D1111yescharacteristic
851C22C2×#41×D1111yescharacteristic
852C4—24no—
853C4—42no—
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—882no—
867C2#1307273118yesdirect product factor
868C2C2×#1062307811yescharacteristic
869C2C2×#1062318011yescharacteristic
870C2C2×#1062314611yescharacteristic
871C2C2×#1062312211yescharacteristic
872C2C2×#1062313011yescharacteristic
873C2C2×#1062302611yescharacteristic
874C2C2×#1062308711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#386D11
hypocenterC11C2×#2471
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#66982C2semidirect
2. C22×#66930C2semidirect
3. #13072731C2direct (N × H)
4. C2×#10622562C2semidirect
5. C2×#10622288C2semidirect
6. C2×#10622561C2semidirect
8. C2×#10622570C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622283C2semidirect
11. C2×#10622265C2semidirect
12. C2×#10622265C2semidirect
13. C2×#10622833C2semidirect
14. C2×#10622571C2semidirect
15. C2×C4×C22⋊Dic11C2semidirect
16. C2×C11×#386C2semidirect
31. C2×#66982C22semidirect
47. C2×#66930C22semidirect
48. C11×#386C22semidirect
52. #10622833C22semidirect
53. C4×C22⋊Dic11C22semidirect
60. #10622571C22semidirect
61. #10622570C22semidirect
62. #10622570C22semidirect
63. #10622562C22semidirect
64. #10622561C22semidirect
65. #10622288C22semidirect
66. #10622283C22semidirect
67. #10622265C22semidirect
68. #10622265C22semidirect
137. C2×Dic11⋊C4D4semidirect
270. Dic11⋊C4C2×D4semidirect
288. C2×#386D11semidirect
435. #386C2×D11semidirect
586. C2×C11#2471semidirect
710. C11C2×#2471semidirect
867. C2#13072731direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669822
C22×#669302
#130727312
C2×#106225622
C2×#106222882
C2×#106225612
C2×#106228362
C2×#106225702
C2×#106222832
C2×#106222652
C2×#106228332
C2×#106225712
C2×C4×C22⋊Dic112
C2×C11×#3862
C2×#247111