Finite Group Databasebeta

← C2×#13074752 #14920501

Subgroups — C2×#13074752 #14920501

Order 2816.

3002 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66932C211yesmaximal, characteristic, complemented
2C22×#66938C211yesmaximal, characteristic, complemented
3#13074752C2116yesmaximal, direct product factor
4C2×#10622561C211yesmaximal, characteristic, complemented
5C2×#10622607C211yesmaximal, characteristic, complemented
6C2×#10622269C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622560C211yesmaximal, characteristic, complemented
10C2×#10622836C211yesmaximal, characteristic
11C2×#10622834C211yesmaximal, characteristic, complemented
12C2×#10622570C211yesmaximal, characteristic, complemented
13C2×#10622282C211yesmaximal, characteristic, complemented
14C2×#10622557C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×#66938—28no—
47C2×#66938C2218yescomplemented
48C2×#66932—28no—
49C2×#66932C2218yescomplemented
50C11×#394C2218yescomplemented
51C2×C11×#95C2211yescharacteristic
52#10622836C2218yes—
53#10622834C2218yescomplemented
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59#10622607C2218yescomplemented
60C4⋊C4×Dic11C2218yescomplemented
61#10622574C2218yescomplemented
62#10622574C2218yescomplemented
63#10622570C2218yescomplemented
64#10622561C2218yescomplemented
65#10622560C2218yescomplemented
66#10622557C2218yescomplemented
67#10622282C2218yescomplemented
68#10622269C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C22×D4×C11—24no—
73C22×D4×C11—42no—
74C22×D4×C11—42no—
75C22×D4×C11C2314yes—
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—24no—
82C22×C22⋊D11—24no—
83C22×C22⋊D11—42no—
84C22×C22⋊D11—42no—
85C22×C22⋊D11—42no—
86C22×C22⋊D11—42no—
87C22×C22⋊D11C2314yes—
88C22×C22⋊D11C2314yes—
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C22×Dic22—24no—
97C22×Dic22—42no—
98C22×Dic22—42no—
99C22×Dic22C2314yes—
100C2×C11×C4⋊C4—24no—
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C22⋊C4—24no—
103C2×C11×C22⋊C4—24no—
104C2×C11×C22⋊C4—42no—
105C2×C11×C22⋊C4—42no—
106C2×C11×C22⋊C4C2314yes—
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⋊Dic11—42no—
116C2×C22⋊Dic11C2314yes—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122C2×(C2×D11)⋊C4—24no—
123C2×(C2×D11)⋊C4—24no—
124C2×(C2×D11)⋊C4—24no—
125C2×(C2×D11)⋊C4—42no—
126C2×(C2×D11)⋊C4—42no—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×C4⋊Dic11—24no—
133C2×C4⋊Dic11—24no—
134C2×C4⋊Dic11—42no—
135C2×C4⋊Dic11C2314yes—
136C2×C4⋊Dic11C2314yes—
137C2×C4⋊Dic11C2314yes—
138C2×Dic11⋊C4—24no—
139C2×Dic11⋊C4—24no—
140C2×Dic11⋊C4—42no—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×C4×Dic11—42no—
145C2×C4×Dic11—42no—
146C2×C4×Dic11D418yescomplemented
147C2×C4×Dic11C2314yes—
148C2×C4×Dic11C2314yes—
149C2×C4×Dic11C2314yes—
150#66938—232no—
151#66932—232no—
152C11×#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2662—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×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—44no—
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×C11C2×D414yes—
202C22×C4×C11#4114yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C2×C22⋊D11—28no—
209C2×C22⋊D11—28no—
210C2×C22⋊D11—44no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11—416no—
215C2×C22⋊D11—416no—
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—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×Dic11C2×D414yes—
235C22×Dic11C2×D414yes—
236C22×Dic11#4114yes—
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C2×Dic22—28no—
245C2×Dic22—44no—
246C2×Dic22—44no—
247C2×Dic22—416no—
248C11×C4⋊C4—28no—
249C11×C22⋊C4—28no—
250C11×C22⋊C4—28no—
251C11×C22⋊C4—44no—
252C11×C22⋊C4—44no—
253C22⋊Dic11—28no—
254C22⋊Dic11—28no—
255C22⋊Dic11—28no—
256C22⋊Dic11—28no—
257C22⋊Dic11—44no—
258C22⋊Dic11—44no—
259(C2×D11)⋊C4—28no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—44no—
263(C2×D11)⋊C4—44no—
264C4⋊Dic11—28no—
265C4⋊Dic11—28no—
266C4⋊Dic11—44no—
267Dic11⋊C4—28no—
268Dic11⋊C4—28no—
269Dic11⋊C4—44no—
270C4×Dic11—44no—
271C4×Dic11—44no—
272C4×Dic11C2×D4116yescomplemented
273C22×#126—111no—
274C22×#124—111no—
275#2662—1116no—
276C2×#396—111no—
277C2×#396—111no—
278C2×#395—111no—
279C2×#394—111no—
280C2×#394—111no—
281C2×#394D1111yescharacteristic, complemented
282C2×#393—111no—
283C2×#392—111no—
284C2×#390—111no—
285C2×#390—111no—
286C2×#388—111no—
287C2×#388—111no—
288C2×C4×C4⋊C4—111no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
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—44no—
304C23×C11—44no—
305C23×C11—44no—
306C23×C11—44no—
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×C11C22×D412yes—
318C23×C11C2×#4112yes—
319C23×C11C2×#4112yes—
320C23×C11H(5,𝔽2)12yes—
321C23×C11H(5,𝔽2)12yes—
322C23×C11H(5,𝔽2)12yes—
323C23×C112−1+412yes—
324C23×C11C2511yescharacteristic
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—44no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11—44no—
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—44no—
356C2×C4×C11—44no—
357C2×C4×C11—44no—
358C2×C4×C11C22×D414yes—
359C2×C4×C11C2×#4114yes—
360C22⋊D11—416no—
361C22⋊D11—416no—
362C2×Dic11—28no—
363C2×Dic11—28no—
364C2×Dic11—28no—
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—44no—
384C2×Dic11—44no—
385C2×Dic11—44no—
386C2×Dic11—44no—
387C2×Dic11C22×D414yes—
388C2×Dic11C22×D414yes—
389C2×Dic11C2×#4114yes—
390Dic22—416no—
391C23×Q8—111no—
392C23×D4—111no—
393C23×D4—111no—
394C23×D4C2×D1111yescharacteristic
395C2×#126—118no—
396C2×#126—228no—
397C2×#124—118no—
398C2×#124—228no—
399C22×C4⋊C4—111no—
400C22×C4⋊C4—111no—
401C22×C4⋊C4—111no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4—111no—
405C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
414C22×C22⋊C4—111no—
415C22×C22⋊C4—111no—
416C22×C22⋊C4—111no—
417C22×C22⋊C4C2×D1111yescharacteristic
418C22×C22⋊C4C2×D1111yescharacteristic
419C22×C22⋊C4C2×D1111yescharacteristic
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C42—111no—
422C22×C42—111no—
423C22×C42—111no—
424#396—118no—
425#396—118no—
426#395—118no—
427#394—118no—
428#394—118no—
429#394C2×D1118yescomplemented
430#393—118no—
431#392—118no—
432#390—118no—
433#390—118no—
434#388—118no—
435#388—118no—
436C4×C4⋊C4—118no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95C2×D1111yescharacteristic
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—88no—
458C22×C11—88no—
459C22×C11#53214yes—
460C22×C11#53514yes—
461C22×C11#53714yes—
462C22×C11#53814yes—
463C22×C11#53814yes—
464C22×C11#54214yes—
465C22×C11#54214yes—
466C22×C11C23×D411yescharacteristic
467C22×C11C22×#4111yescharacteristic
468C22×C11C22×#4111yescharacteristic
469C22×C11C2×H(5,𝔽2)11yescharacteristic
470C22×C11C2×H(5,𝔽2)11yescharacteristic
471C22×C11C2×H(5,𝔽2)11yescharacteristic
472C22×C11C2×2−1+411yescharacteristic
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—88no—
481C4×C11—24no—
482C4×C11—24no—
483C4×C11—42no—
484C4×C11—42no—
485C4×C11—42no—
486Dic11—24no—
487Dic11—24no—
488Dic11—24no—
489Dic11—42no—
490Dic11—42no—
491Dic11—42no—
492Dic11—42no—
493C25—111no—
494C25C22×D1111yescharacteristic
495C25C22×D1111yescharacteristic
496C22×Q8—114no—
497C22×Q8—224no—
498C22×Q8—442no—
499C22×Q8—442no—
500C22×D4—24no—
501C22×D4—42no—
502C22×D4—42no—
503C22×D4—114no—
504C22×D4—114no—
505C22×D4—224no—
506C22×D4—224no—
507C22×D4—442no—
508C22×D4—442no—
509C22×D4—442no—
510C22×D4—442no—
511C22×D4C22×D1114yes—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—111no—
518C23×C4—111no—
519C23×C4C22×D1111yescharacteristic
520C23×C4C22×D1111yescharacteristic
521C23×C4C22×D1111yescharacteristic
522C23×C4C22×D1111yescharacteristic
523C23×C4C22×D1111yescharacteristic
524#126—2232no—
525#124—2232no—
526C2×C4⋊C4—24no—
527C2×C4⋊C4—114no—
528C2×C4⋊C4—114no—
529C2×C4⋊C4—114no—
530C2×C4⋊C4—114no—
531C2×C4⋊C4—114no—
532C2×C4⋊C4—114no—
533C2×C4⋊C4—224no—
534C2×C4⋊C4—224no—
535C2×C4⋊C4—224no—
536C2×C4⋊C4—224no—
537C2×C4⋊C4—442no—
538C2×C4⋊C4—442no—
539C2×C4⋊C4C22×D1114yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—114no—
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—114no—
555C2×C22⋊C4—224no—
556C2×C22⋊C4—224no—
557C2×C22⋊C4—224no—
558C2×C22⋊C4—224no—
559C2×C22⋊C4—224no—
560C2×C22⋊C4—224no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—442no—
563C2×C22⋊C4—442no—
564C2×C22⋊C4—442no—
565C2×C22⋊C4—442no—
566C2×C22⋊C4C22×D1114yes—
567C2×C22⋊C4C22×D1114yes—
568C2×C22⋊C4C22×D1114yes—
569C2×C22⋊C4C22×D1114yes—
570C2×C42—118no—
571C2×C42—114no—
572C2×C42—114no—
573C2×C42—114no—
574C2×C42—442no—
575C2×C42—442no—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95C22×D1114yes—
582C2×C11—82no—
583C2×C11—82no—
584C2×C11#266218yescomplemented
585C2×C11C2×#53211yescharacteristic
586C2×C11C2×#53511yescharacteristic
587C2×C11C2×#53711yescharacteristic
588C2×C11C2×#53811yescharacteristic
589C2×C11C2×#53811yescharacteristic
590C2×C11C2×#54211yescharacteristic
591C2×C11C2×#54211yescharacteristic
592D11—82no—
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—22no—
606C24—22no—
607C24—112no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24C23×D1112yes—
616C24C23×D1112yes—
617C24C23×D1111yescharacteristic
618C2×Q8—228no—
619C2×Q8—444no—
620C2×Q8—444no—
621C2×Q8—4416no—
622C2×D4—28no—
623C2×D4—44no—
624C2×D4—44no—
625C2×D4—416no—
626C2×D4—228no—
627C2×D4—228no—
628C2×D4—444no—
629C2×D4—444no—
630C2×D4—444no—
631C2×D4—444no—
632C2×D4—4416no—
633C2×D4—4416no—
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—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—114no—
648C22×C4—114no—
649C22×C4—114no—
650C22×C4—112no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—222no—
658C22×C4—222no—
659C22×C4—222no—
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×C4D4×D1114yes—
676C22×C4#434114yes—
677C22×C4C23×D1112yes—
678C22×C4C23×D1112yes—
679C22×C4C23×D1112yes—
680C22×C4C23×D1112yes—
681C22×C4C23×D1112yes—
682C4⋊C4—28no—
683C4⋊C4—228no—
684C4⋊C4—228no—
685C4⋊C4—228no—
686C4⋊C4—228no—
687C4⋊C4—444no—
688C4⋊C4—444no—
689C22⋊C4—28no—
690C22⋊C4—28no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—228no—
694C22⋊C4—228no—
695C22⋊C4—228no—
696C22⋊C4—228no—
697C22⋊C4—228no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C22⋊C4—444no—
701C22⋊C4—444no—
702C22⋊C4—444no—
703C22⋊C4—444no—
704C42—1116no—
705C42—444no—
706C42—444no—
707C11C2×#266211yescharacteristic, complemented, Sylow
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—444no—
744C23—444no—
745C23—444no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23C2×D4×D1112yes—
751C23C2×#434112yes—
752C23#6703712yes—
753C23#6703712yes—
754C23#41×D1112yes—
755C23#6704212yes—
756C23#6704312yes—
757C23C24×D1111yescharacteristic
758Q8—4416no—
759D4—416no—
760D4—4416no—
761D4—4416no—
762C2×C4—28no—
763C2×C4—28no—
764C2×C4—22no—
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—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—114no—
781C2×C4—114no—
782C2×C4—114no—
783C2×C4—228no—
784C2×C4—228no—
785C2×C4—228no—
786C2×C4—222no—
787C2×C4—222no—
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—444no—
805C2×C4—444no—
806C2×C4—444no—
807C2×C4—444no—
808C2×C4C2×D4×D1114yes—
809C2×C4C2×#434114yes—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—88no—
825C22—88no—
826C22—442no—
827C22—442no—
828C22—442no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—888no—
834C22#1062312414yes—
835C22#1062312714yes—
836C22#1062313814yes—
837C22#1062313914yes—
838C22#1062318814yes—
839C22#1062319314yes—
840C22#1062321314yes—
841C22C22×D4×D1111yescharacteristic
842C22C22×#434111yescharacteristic
843C22C2×#6703711yescharacteristic
844C22C2×#6703711yescharacteristic
845C22C2×#41×D1111yescharacteristic
846C22C2×#6704211yescharacteristic
847C22C2×#6704311yescharacteristic
848C4—24no—
849C4—24no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—224no—
854C4—224no—
855C4—224no—
856C4—442no—
857C4—442no—
858C4—442no—
859C4—442no—
860C2—82no—
861C2—82no—
862C2—882no—
863C2#1307475218yesdirect product factor
864C2C2×#1062312711yescharacteristic
865C2C2×#1062313811yescharacteristic
866C2C2×#1062313911yescharacteristic
867C2C2×#1062312411yescharacteristic
868C2C2×#1062318811yescharacteristic
869C2C2×#1062319311yescharacteristic
870C2C2×#1062321311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#394D11
hypocenterC11C2×#2662
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66932C2semidirect
2. C22×#66938C2semidirect
3. #13074752C2direct (N × H)
4. C2×#10622561C2semidirect
5. C2×#10622607C2semidirect
6. C2×#10622269C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622560C2semidirect
11. C2×#10622834C2semidirect
12. C2×#10622570C2semidirect
13. C2×#10622282C2semidirect
14. C2×#10622557C2semidirect
15. C2×C4⋊C4×Dic11C2semidirect
16. C2×C11×#394C2semidirect
47. C2×#66938C22semidirect
49. C2×#66932C22semidirect
50. C11×#394C22semidirect
53. #10622834C22semidirect
59. #10622607C22semidirect
60. C4⋊C4×Dic11C22semidirect
61. #10622574C22semidirect
62. #10622574C22semidirect
63. #10622570C22semidirect
64. #10622561C22semidirect
65. #10622560C22semidirect
66. #10622557C22semidirect
67. #10622282C22semidirect
68. #10622269C22semidirect
146. C2×C4×Dic11D4semidirect
272. C4×Dic11C2×D4semidirect
281. C2×#394D11semidirect
429. #394C2×D11semidirect
584. C2×C11#2662semidirect
707. C11C2×#2662semidirect
863. C2#13074752direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669322
C22×#669382
#130747522
C2×#106225612
C2×#106226072
C2×#106222692
C2×#106225742
C2×#106225602
C2×#106228362
C2×#106228342
C2×#106225702
C2×#106222822
C2×#106225572
C2×C4⋊C4×Dic112
C2×C11×#3942
C2×#266211