Finite Group Databasebeta

← C2×#13072585 #14921636

Subgroups — C2×#13072585 #14921636

Order 2816.

3786 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic, complemented
2C22×#66936C211yesmaximal, characteristic, complemented
3C22×#66949C211yesmaximal, characteristic, complemented
4C22×C4×D44C211yesmaximal, characteristic, complemented
5#13072585C2116yesmaximal, direct product factor
6C2×#10622561C211yesmaximal, characteristic, complemented
7C2×#10622269C211yesmaximal, characteristic, complemented
8C2×#10622285C211yesmaximal, characteristic, complemented
9C2×#10622573C211yesmaximal, characteristic
10C2×#10622570C211yesmaximal, characteristic, complemented
11C2×#10622283C211yesmaximal, characteristic, complemented
12C2×#10622282C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, characteristic, complemented
15C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×Dic22C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×#66949—28no—
47C2×#66949C2218yescomplemented
48C2×#66938—28no—
49C2×#66938C2218yescomplemented
50C2×#66936—28no—
51C2×#66936C2218yescomplemented
52C2×C4×D44—28no—
53C2×C4×D44C2218yescomplemented
54C11×#388C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622602C2218yescomplemented
62#10622573C2218yes—
63#10622570C2218yescomplemented
64#10622569C2218yescomplemented
65#10622561C2218yescomplemented
66C4×Dic11⋊C4C2218yescomplemented
67#10622285C2218yescomplemented
68#10622283C2218yescomplemented
69#10622282C2218yescomplemented
70#10622269C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—24no—
81C22×C22⋊D11—24no—
82C22×C22⋊D11—24no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11—42no—
85C22×C22⋊D11—42no—
86C22×C22⋊D11C2314yes—
87C22×C22⋊D11C2314yes—
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C22×D44—24no—
95C22×D44—24no—
96C22×D44—24no—
97C22×D44C2314yes—
98C22×C4×D11—24no—
99C22×C4×D11—24no—
100C22×C4×D11—24no—
101C22×C4×D11—24no—
102C22×C4×D11—42no—
103C22×C4×D11—42no—
104C22×C4×D11C2314yes—
105C22×C4×D11C2314yes—
106C22×Dic22—24no—
107C22×Dic22—24no—
108C22×Dic22—42no—
109C22×Dic22C2314yes—
110C2×C11×C4⋊C4—24no—
111C2×C11×C4⋊C4C2314yes—
112C2×C11×C22⋊C4—24no—
113C2×C11×C22⋊C4—24no—
114C2×C11×C22⋊C4—24no—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C42×C11—24no—
119C2×C42×C11C2314yes—
120C2×C22⋊Dic11—24no—
121C2×C22⋊Dic11—24no—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×(C2×D11)⋊C4—24no—
125C2×(C2×D11)⋊C4—24no—
126C2×(C2×D11)⋊C4—24no—
127C2×(C2×D11)⋊C4—24no—
128C2×(C2×D11)⋊C4—24no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4D418yescomplemented
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×C4⋊Dic11—24no—
141C2×C4⋊Dic11—24no—
142C2×C4⋊Dic11C2314yes—
143C2×C4⋊Dic11C2314yes—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4—24no—
146C2×Dic11⋊C4—42no—
147C2×Dic11⋊C4D418yescomplemented
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×C4×Dic11—24no—
153C2×C4×Dic11—24no—
154C2×C4×Dic11C2314yes—
155C2×C4×Dic11C2314yes—
156#66949—232no—
157#66938—232no—
158#66936—232no—
159C4×D44—232no—
160C11×#95C2314yes—
161C11×#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2461—111nomaximal, Sylow
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
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×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11C2×D414yes—
189C23×D11#4114yes—
190C23×D11C2412yes—
191C23×D11C2412yes—
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—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11C2×D414yes—
208C22×C4×C11C2×D414yes—
209C22×C4×C11#4114yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C2×C22⋊D11—28no—
217C2×C22⋊D11—28no—
218C2×C22⋊D11—28no—
219C2×C22⋊D11—28no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—416no—
223C2×C22⋊D11—416no—
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×Dic11C2×D414yes—
241C22×Dic11#4114yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C2×D44—232no—
249C2×D44—28no—
250C2×D44—28no—
251C2×D44—28no—
252C2×C4×D11—28no—
253C2×C4×D11—28no—
254C2×C4×D11—28no—
255C2×C4×D11—28no—
256C2×C4×D11—44no—
257C2×C4×D11—44no—
258C2×C4×D11—416no—
259C2×C4×D11—416no—
260C2×Dic22—28no—
261C2×Dic22—28no—
262C2×Dic22—44no—
263C2×Dic22—416no—
264C11×C4⋊C4—28no—
265C11×C22⋊C4—28no—
266C11×C22⋊C4—28no—
267C11×C22⋊C4—28no—
268C42×C11—28no—
269C22⋊Dic11—28no—
270C22⋊Dic11—28no—
271(C2×D11)⋊C4—28no—
272(C2×D11)⋊C4—28no—
273(C2×D11)⋊C4—28no—
274(C2×D11)⋊C4—28no—
275(C2×D11)⋊C4—28no—
276(C2×D11)⋊C4—28no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4C2×D4116yescomplemented
279C4⋊Dic11—28no—
280C4⋊Dic11—28no—
281Dic11⋊C4—28no—
282Dic11⋊C4—28no—
283Dic11⋊C4—44no—
284Dic11⋊C4C2×D4116yescomplemented
285C4×Dic11—28no—
286C4×Dic11—28no—
287C22×#124—111no—
288C22×#123—111no—
289C22×C22⋊Q8—111no—
290C22×C4×D4—111no—
291#2461—1116no—
292C2×#396—111no—
293C2×#395—111no—
294C2×#394—111no—
295C2×#392—111no—
296C2×#390—111no—
297C2×#388—111no—
298C2×#388—111no—
299C2×#388D1111yescharacteristic, complemented
300C2×#386—111no—
301C2×#385—111no—
302C2×C4×C4⋊C4—111no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
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×C11C22×D412yes—
319C23×C11C2×#4112yes—
320C23×C11C2×#4112yes—
321C23×C11C2×#4112yes—
322C23×C11H(5,𝔽2)12yes—
323C23×C112−1+412yes—
324C23×C11C2511yescharacteristic
325C22×D11—28no—
326C22×D11—28no—
327C22×D11—28no—
328C22×D11—28no—
329C22×D11—28no—
330C22×D11—28no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—44no—
344C22×D11—44no—
345C22×D11—44no—
346C22×D11—44no—
347C22×D11—44no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11C22×D414yes—
352C22×D11C2×#4114yes—
353C2×C4×C11—28no—
354C2×C4×C11—28no—
355C2×C4×C11—28no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—44no—
372C2×C4×C11—44no—
373C2×C4×C11—44no—
374C2×C4×C11C22×D414yes—
375C2×C4×C11C22×D414yes—
376C2×C4×C11C2×#4114yes—
377C22⋊D11—416no—
378C22⋊D11—416no—
379C2×Dic11—28no—
380C2×Dic11—28no—
381C2×Dic11—28no—
382C2×Dic11—28no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—44no—
398C2×Dic11—44no—
399C2×Dic11C22×D414yes—
400C2×Dic11C22×D414yes—
401C2×Dic11C22×D414yes—
402C2×Dic11C2×#4114yes—
403D44—232no—
404C4×D11—416no—
405C4×D11—416no—
406Dic22—416no—
407C23×Q8—111no—
408C23×D4—111no—
409C23×D4—111no—
410C23×D4—111no—
411C24×C4—111no—
412C24×C4—111no—
413C2×#124—118no—
414C2×#124—228no—
415C2×#123—118no—
416C2×#123—228no—
417C2×C22⋊Q8—118no—
418C2×C22⋊Q8—228no—
419C2×C4×D4—118no—
420C2×C4×D4—228no—
421C22×C4⋊C4—111no—
422C22×C4⋊C4—111no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C4⋊C4—111no—
426C22×C4⋊C4—111no—
427C22×C4⋊C4C2×D1111yescharacteristic
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4—111no—
431C22×C22⋊C4—111no—
432C22×C22⋊C4—111no—
433C22×C22⋊C4—111no—
434C22×C22⋊C4—111no—
435C22×C22⋊C4—111no—
436C22×C22⋊C4—111no—
437C22×C22⋊C4—111no—
438C22×C22⋊C4C2×D1111yescharacteristic
439C22×C22⋊C4C2×D1111yescharacteristic
440C22×C22⋊C4C2×D1111yescharacteristic
441C22×C42—111no—
442C22×C42—111no—
443C22×C42C2×D1111yescharacteristic
444#396—118no—
445#395—118no—
446#394—118no—
447#392—118no—
448#390—118no—
449#388—118no—
450#388—118no—
451#388C2×D1118yescomplemented
452#386—118no—
453#385—118no—
454C4×C4⋊C4—118no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95C2×D1111yescharacteristic
460C2×#95C2×D1111yescharacteristic
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—88no—
469C22×C11#52514yes—
470C22×C11#53214yes—
471C22×C11#54214yes—
472C22×C11D4214yes—
473C22×C11#54714yes—
474C22×C11#54814yes—
475C22×C11#55114yes—
476C22×C11C23×D411yescharacteristic
477C22×C11C23×D411yescharacteristic
478C22×C11C22×#4111yescharacteristic
479C22×C11C22×#4111yescharacteristic
480C22×C11C22×#4111yescharacteristic
481C22×C11C2×H(5,𝔽2)11yescharacteristic
482C22×C11C2×2−1+411yescharacteristic
483C2×D11—24no—
484C2×D11—24no—
485C2×D11—24no—
486C2×D11—24no—
487C2×D11—24no—
488C2×D11—24no—
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—416no—
498C2×D11—416no—
499C4×C11—24no—
500C4×C11—24no—
501C4×C11—24no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11—42no—
505Dic11—24no—
506Dic11—24no—
507Dic11—24no—
508Dic11—24no—
509Dic11—42no—
510Dic11—42no—
511C25—111no—
512C25—111no—
513C25C22×D1111yescharacteristic
514C22×Q8—114no—
515C22×Q8—224no—
516C22×Q8—224no—
517C22×Q8—442no—
518C22×D4—114no—
519C22×D4—114no—
520C22×D4—114no—
521C22×D4—224no—
522C22×D4—224no—
523C22×D4—224no—
524C22×D4—224no—
525C22×D4—224no—
526C22×D4—224no—
527C22×D4—224no—
528C22×D4—442no—
529C22×D4—442no—
530C23×C4—111no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—114no—
537C23×C4—114no—
538C23×C4—224no—
539C23×C4—224no—
540C23×C4—224no—
541C23×C4—224no—
542C23×C4—442no—
543C23×C4—442no—
544C23×C4C22×D1111yescharacteristic
545C23×C4C22×D1111yescharacteristic
546C23×C4C22×D1111yescharacteristic
547C23×C4C22×D1111yescharacteristic
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550#124—2232no—
551#123—2232no—
552C22⋊Q8—2232no—
553C4×D4—2232no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—118no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—114no—
558C2×C4⋊C4—114no—
559C2×C4⋊C4—114no—
560C2×C4⋊C4—114no—
561C2×C4⋊C4—114no—
562C2×C4⋊C4—224no—
563C2×C4⋊C4—224no—
564C2×C4⋊C4—224no—
565C2×C4⋊C4—224no—
566C2×C4⋊C4—442no—
567C2×C4⋊C4C22×D1114yes—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—118no—
572C2×C22⋊C4—114no—
573C2×C22⋊C4—114no—
574C2×C22⋊C4—114no—
575C2×C22⋊C4—114no—
576C2×C22⋊C4—114no—
577C2×C22⋊C4—114no—
578C2×C22⋊C4—114no—
579C2×C22⋊C4—114no—
580C2×C22⋊C4—114no—
581C2×C22⋊C4—114no—
582C2×C22⋊C4—224no—
583C2×C22⋊C4—224no—
584C2×C22⋊C4—224no—
585C2×C22⋊C4—224no—
586C2×C22⋊C4—224no—
587C2×C22⋊C4—224no—
588C2×C22⋊C4—224no—
589C2×C22⋊C4—224no—
590C2×C22⋊C4—224no—
591C2×C22⋊C4C22×D1114yes—
592C2×C22⋊C4C22×D1114yes—
593C2×C22⋊C4C22×D1114yes—
594C2×C42—24no—
595C2×C42—114no—
596C2×C42—114no—
597C2×C42—224no—
598C2×C42—224no—
599C2×C42C22×D1114yes—
600#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95C22×D1114yes—
605#95C22×D1114yes—
606C2×C11—82no—
607C2×C11#246118yescomplemented
608C2×C11C2×#52511yescharacteristic
609C2×C11C2×#53211yescharacteristic
610C2×C11C2×#54211yescharacteristic
611C2×C11C2×D4211yescharacteristic
612C2×C11C2×#54711yescharacteristic
613C2×C11C2×#54811yescharacteristic
614C2×C11C2×#55111yescharacteristic
615D11—44no—
616D11—44no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—114no—
625C24—114no—
626C24—112no—
627C24—112no—
628C24—222no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24—222no—
638C24—222no—
639C24—222no—
640C24C23×D1112yes—
641C24C23×D1111yescharacteristic
642C2×Q8—228no—
643C2×Q8—228no—
644C2×Q8—444no—
645C2×Q8—4416no—
646C2×D4—228no—
647C2×D4—228no—
648C2×D4—2232no—
649C2×D4—228no—
650C2×D4—228no—
651C2×D4—228no—
652C2×D4—228no—
653C2×D4—228no—
654C2×D4—444no—
655C2×D4—444no—
656C2×D4—4416no—
657C2×D4—4416no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—114no—
674C22×C4—114no—
675C22×C4—114no—
676C22×C4—114no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—228no—
684C22×C4—228no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—222no—
698C22×C4—222no—
699C22×C4—228no—
700C22×C4—228no—
701C22×C4—444no—
702C22×C4—444no—
703C22×C4—4416no—
704C22×C4—4416no—
705C22×C4#433914yes—
706C22×C4D4×D1114yes—
707C22×C4D4×D1114yes—
708C22×C4C23×D1112yes—
709C22×C4C23×D1112yes—
710C22×C4C23×D1112yes—
711C22×C4C23×D1112yes—
712C22×C4C23×D1112yes—
713C22×C4C23×D1112yes—
714C4⋊C4—28no—
715C4⋊C4—1116no—
716C4⋊C4—228no—
717C4⋊C4—228no—
718C4⋊C4—228no—
719C4⋊C4—228no—
720C4⋊C4—444no—
721C22⋊C4—28no—
722C22⋊C4—28no—
723C22⋊C4—28no—
724C22⋊C4—1116no—
725C22⋊C4—228no—
726C22⋊C4—228no—
727C22⋊C4—228no—
728C22⋊C4—228no—
729C22⋊C4—228no—
730C22⋊C4—228no—
731C22⋊C4—228no—
732C22⋊C4—228no—
733C22⋊C4—228no—
734C42—28no—
735C42—228no—
736C42—228no—
737C11C2×#246111yescharacteristic, complemented, Sylow
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—114no—
753C23—114no—
754C23—228no—
755C23—228no—
756C23—228no—
757C23—228no—
758C23—228no—
759C23—222no—
760C23—222no—
761C23—222no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—222no—
771C23—228no—
772C23—444no—
773C23—444no—
774C23—444no—
775C23—444no—
776C23—444no—
777C23—444no—
778C23—444no—
779C23—444no—
780C23C2×#433912yes—
781C23C2×D4×D1112yes—
782C23C2×D4×D1112yes—
783C23#41×D1112yes—
784C23#41×D1112yes—
785C23#6704212yes—
786C23#6704312yes—
787C23C24×D1111yescharacteristic
788Q8—4416no—
789D4—2232no—
790D4—4416no—
791D4—4416no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—114no—
814C2×C4—114no—
815C2×C4—114no—
816C2×C4—114no—
817C2×C4—228no—
818C2×C4—228no—
819C2×C4—228no—
820C2×C4—228no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—4416no—
836C2×C4—4416no—
837C2×C4—444no—
838C2×C4—444no—
839C2×C4C2×#433914yes—
840C2×C4C2×D4×D1114yes—
841C2×C4C2×D4×D1114yes—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—88no—
850C22—224no—
851C22—224no—
852C22—224no—
853C22—224no—
854C22—224no—
855C22—224no—
856C22—442no—
857C22—442no—
858C22—442no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22—4416no—
863C22—4416no—
864C22—442no—
865C22—442no—
866C22#1062306514yes—
867C22#1062307814yes—
868C22#1062307914yes—
869C22#1062314014yes—
870C22#1062318614yes—
871C22#1062320814yes—
872C22#1062323614yes—
873C22C22×#433911yescharacteristic
874C22C22×D4×D1111yescharacteristic
875C22C22×D4×D1111yescharacteristic
876C22C2×#41×D1111yescharacteristic
877C22C2×#41×D1111yescharacteristic
878C22C2×#6704211yescharacteristic
879C22C2×#6704311yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—224no—
887C4—224no—
888C4—224no—
889C4—224no—
890C4—442no—
891C4—442no—
892C2—82no—
893C2—444no—
894C2—444no—
895C2#1307258518yesdirect product factor
896C2C2×#1062307811yescharacteristic
897C2C2×#1062307911yescharacteristic
898C2C2×#1062306511yescharacteristic
899C2C2×#1062314011yescharacteristic
900C2C2×#1062318611yescharacteristic
901C2C2×#1062320811yescharacteristic
902C2C2×#1062323611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×#388D11
hypocenterC11C2×#2461
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#66938C2semidirect
2. C22×#66936C2semidirect
3. C22×#66949C2semidirect
4. C22×C4×D44C2semidirect
5. #13072585C2direct (N × H)
6. C2×#10622561C2semidirect
7. C2×#10622269C2semidirect
8. C2×#10622285C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622283C2semidirect
12. C2×#10622282C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622602C2semidirect
15. C2×C4×Dic11⋊C4C2semidirect
16. C2×C11×#388C2semidirect
47. C2×#66949C22semidirect
49. C2×#66938C22semidirect
51. C2×#66936C22semidirect
53. C2×C4×D44C22semidirect
54. C11×#388C22semidirect
61. #10622602C22semidirect
63. #10622570C22semidirect
64. #10622569C22semidirect
65. #10622561C22semidirect
66. C4×Dic11⋊C4C22semidirect
67. #10622285C22semidirect
68. #10622283C22semidirect
69. #10622282C22semidirect
70. #10622269C22semidirect
131. C2×(C2×D11)⋊C4D4semidirect
147. C2×Dic11⋊C4D4semidirect
278. (C2×D11)⋊C4C2×D4semidirect
284. Dic11⋊C4C2×D4semidirect
299. C2×#388D11semidirect
451. #388C2×D11semidirect
607. C2×C11#2461semidirect
737. C11C2×#2461semidirect
895. C2#13072585direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669382
C22×#669362
C22×#669492
C22×C4×D442
#130725852
C2×#106225612
C2×#106222692
C2×#106222852
C2×#106225732
C2×#106225702
C2×#106222832
C2×#106222822
C2×#106225692
C2×#106226022
C2×C4×Dic11⋊C42
C2×C11×#3882
C2×#246111