Finite Group Databasebeta

← C2×#13071315 #14912547

Subgroups — C2×#13071315 #14912547

Order 2816.

4150 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66948C211yesmaximal, characteristic
2C22×C4×D44C211yesmaximal, characteristic, complemented
3C22×#66946C211yesmaximal, characteristic, complemented
4#13071315C2116yesmaximal, direct product factor
5C2×#10622553C211yesmaximal, characteristic, complemented
6C2×#10622282C211yesmaximal, characteristic, complemented
7C2×#10622594C211yesmaximal, characteristic, complemented
8C2×#10622278C211yesmaximal, characteristic, complemented
9C2×#10622278C211yesmaximal, characteristic, complemented
10C2×#10622278C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622281C211yesmaximal, characteristic, complemented
13C2×#10622602C211yesmaximal, characteristic, complemented
14C2×#10622280C211yesmaximal, characteristic, complemented
15C2×D11×#95C211yesmaximal, characteristic, complemented
16C2×C11×#387C211yesmaximal, characteristic, complemented
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×#66948C4116yescomplemented
43C2×#66948C2218yes—
44C2×#66946—28no—
45C2×#66946C2218yescomplemented
46C2×C4×D44—28no—
47C2×C4×D44C2218yescomplemented
48C11×#387C2218yescomplemented
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51C2×C11×#95C2211yescharacteristic
52C2×C11×#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59#10622602C2218yescomplemented
60#10622594C2218yescomplemented
61#10622553C2218yescomplemented
62#10622282C2218yescomplemented
63#10622281C2218yescomplemented
64#10622280C2218yescomplemented
65#10622278C2218yescomplemented
66#10622278C2218yescomplemented
67#10622278C2218yescomplemented
68#10622278C2218yescomplemented
69D11×#95C2218yescomplemented
70C24×D11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C22×D44—24no—
86C22×D44—24no—
87C22×D44—24no—
88C22×D44—24no—
89C22×D44—42no—
90C22×D44—42no—
91C22×D44C2×C418yescomplemented
92C22×D44C2×C418yescomplemented
93C22×D44C2×C418yescomplemented
94C22×D44C2314yes—
95C22×D44C2314yes—
96C22×D44C2314yes—
97C22×C4×D11—24no—
98C22×C4×D11—24no—
99C22×C4×D11—24no—
100C22×C4×D11—42no—
101C22×C4×D11—42no—
102C22×C4×D11—42no—
103C22×C4×D11—42no—
104C22×C4×D11—42no—
105C22×C4×D11—42no—
106C22×C4×D11—42no—
107C22×C4×D11—42no—
108C22×C4×D11—42no—
109C22×C4×D11—42no—
110C22×C4×D11C2×C418yescomplemented
111C22×C4×D11D418yescomplemented
112C22×C4×D11C2314yes—
113C22×C4×D11C2314yes—
114C22×C4×D11C2314yes—
115C22×C4×D11C2314yes—
116C22×C4×D11C2314yes—
117C2×C11×C4⋊C4—24no—
118C2×C11×C4⋊C4C2×C418yescomplemented
119C2×C11×C4⋊C4C2314yes—
120C2×C11×C4⋊C4C2314yes—
121C2×C42×C11—24no—
122C2×C42×C11C2314yes—
123C2×(C2×D11)⋊C4—24no—
124C2×(C2×D11)⋊C4—24no—
125C2×(C2×D11)⋊C4—24no—
126C2×(C2×D11)⋊C4—24no—
127C2×(C2×D11)⋊C4—42no—
128C2×(C2×D11)⋊C4—42no—
129C2×(C2×D11)⋊C4—42no—
130C2×(C2×D11)⋊C4—42no—
131C2×(C2×D11)⋊C4C2×C418yescomplemented
132C2×(C2×D11)⋊C4C2×C418yescomplemented
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×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×C4⋊Dic11—24no—
144C2×C4⋊Dic11C2314yes—
145C2×Dic11⋊C4—42no—
146C2×Dic11⋊C4—42no—
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149C2×C4×Dic11—24no—
150C2×C4×Dic11C2314yes—
151#66948C2×C4164yescomplemented
152#66946—232no—
153C4×D44—232no—
154C11×#95C2314yes—
155C11×#95C2314yes—
156C11×#95C2314yes—
157C11×#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C2×#2325—111nomaximal, Sylow
165C24×C11C2411yescharacteristic
166C23×D11—22no—
167C23×D11—22no—
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—22no—
182C23×D11C22×C414yes—
183C23×D11C22×C414yes—
184C23×D11C22×C414yes—
185C23×D11C2×D414yes—
186C23×D11#4114yes—
187C23×D11C2412yes—
188C23×D11C2412yes—
189C23×D11C2412yes—
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—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11C22×C414yes—
208C22×C4×C11C22×C414yes—
209C22×C4×C11C22×C414yes—
210C22×C4×C11C2×D414yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
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×Dic11C22×C414yes—
232C22×Dic11C2×D414yes—
233C22×Dic11C2412yes—
234C22×Dic11C2412yes—
235C22×Dic11C2412yes—
236C22×Dic11C2412yes—
237C22×Dic11C2412yes—
238C2×D44—232no—
239C2×D44—232no—
240C2×D44—28no—
241C2×D44—28no—
242C2×D44—28no—
243C2×D44—28no—
244C2×D44—416no—
245C2×D44—44no—
246C2×D44—44no—
247C2×D44C22×C4116yescomplemented
248C2×D44C22×C4116yescomplemented
249C2×D44C22×C4116yescomplemented
250C2×C4×D11—28no—
251C2×C4×D11—28no—
252C2×C4×D11—28no—
253C2×C4×D11—416no—
254C2×C4×D11—416no—
255C2×C4×D11—44no—
256C2×C4×D11—44no—
257C2×C4×D11—44no—
258C2×C4×D11—44no—
259C2×C4×D11—44no—
260C2×C4×D11—44no—
261C2×C4×D11—44no—
262C2×C4×D11—44no—
263C2×C4×D11—44no—
264C2×C4×D11—44no—
265C2×C4×D11—416no—
266C2×C4×D11—416no—
267C2×C4×D11—416no—
268C2×C4×D11C22×C4116yescomplemented
269C2×C4×D11C2×D4116yescomplemented
270C11×C4⋊C4—28no—
271C11×C4⋊C4C22×C4116yescomplemented
272C42×C11—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—44no—
278(C2×D11)⋊C4—44no—
279(C2×D11)⋊C4—44no—
280(C2×D11)⋊C4—44no—
281(C2×D11)⋊C4C22×C4116yescomplemented
282(C2×D11)⋊C4C22×C4116yescomplemented
283C4⋊Dic11—28no—
284Dic11⋊C4—44no—
285Dic11⋊C4—44no—
286C4×Dic11—28no—
287C22×#121—111no—
288C22×C4×D4—111no—
289C22×C4×D4—111no—
290#2325—1116no—
291C2×#388—111no—
292C2×#388—111no—
293C2×#387—111no—
294C2×#387D1111yescharacteristic, complemented
295C2×#386—111no—
296C2×#386—111no—
297C2×#386—111no—
298C2×#386—111no—
299C2×#385—111no—
300C2×#385—111no—
301C2×#380—111no—
302C22×#95—111no—
303C23×C11C23×C412yes—
304C23×C11C22×D412yes—
305C23×C11C2×#4112yes—
306C23×C11H(5,𝔽2)12yes—
307C23×C11H(5,𝔽2)12yes—
308C23×C11H(5,𝔽2)12yes—
309C23×C112−1+412yes—
310C23×C11C2511yescharacteristic
311C22×D11—28no—
312C22×D11—28no—
313C22×D11—28no—
314C22×D11—28no—
315C22×D11—28no—
316C22×D11—28no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—28no—
322C22×D11—28no—
323C22×D11—28no—
324C22×D11—28no—
325C22×D11—28no—
326C22×D11—28no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
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—44no—
340C22×D11—44no—
341C22×D11—44no—
342C22×D11—44no—
343C22×D11—44no—
344C22×D11—44no—
345C22×D11—44no—
346C22×D11—44no—
347C22×D11C4×D4116yes—
348C22×D11C23×C414yes—
349C22×D11C23×C414yes—
350C22×D11C23×C414yes—
351C22×D11C22×D414yes—
352C22×D11C2×#4114yes—
353C2×C4×C11—28no—
354C2×C4×C11—28no—
355C2×C4×C11—28no—
356C2×C4×C11—28no—
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—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—44no—
375C2×C4×C11—44no—
376C2×C4×C11—44no—
377C2×C4×C11C23×C414yes—
378C2×C4×C11C23×C414yes—
379C2×C4×C11C23×C414yes—
380C2×C4×C11C22×D414yes—
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—44no—
397C2×Dic11—44no—
398C2×Dic11—44no—
399C2×Dic11C23×C414yes—
400C2×Dic11C22×D414yes—
401D44—232no—
402D44—232no—
403D44—416no—
404C4×D11—416no—
405C4×D11—416no—
406C4×D11—416no—
407C4×D11—416no—
408C4×D11—416no—
409C23×D4—111no—
410C23×D4—111no—
411C23×D4—111no—
412C24×C4—111no—
413C24×C4—111no—
414C24×C4—111no—
415C24×C4—111no—
416C24×C4—111no—
417C2×#121—118no—
418C2×#121—1116no—
419C2×C4×D4—118no—
420C2×C4×D4—118no—
421C2×C4×D4—228no—
422C2×C4×D4—228no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C4⋊C4—111no—
426C22×C4⋊C4C2×D1111yescharacteristic
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×C42—111no—
439C22×C42C2×D1111yescharacteristic
440#388—118no—
441#388—118no—
442#387—118no—
443#387C2×D1118yescomplemented
444#386—118no—
445#386—118no—
446#386—118no—
447#386—118no—
448#385—118no—
449#385—118no—
450#380—118no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—118no—
458C2×#95C2×D1111yescharacteristic
459C2×#95C2×D1111yescharacteristic
460C2×#95C2×D1111yescharacteristic
461C2×#95C2×D1111yescharacteristic
462C22×C11C2×C4×D414yes—
463C22×C11#51814yes—
464C22×C11#52014yes—
465C22×C11#53414yes—
466C22×C11#53714yes—
467C22×C11#53814yes—
468C22×C11#53914yes—
469C22×C11C24×C411yescharacteristic
470C22×C11C23×D411yescharacteristic
471C22×C11C22×#4111yescharacteristic
472C22×C11C2×H(5,𝔽2)11yescharacteristic
473C22×C11C2×H(5,𝔽2)11yescharacteristic
474C22×C11C2×H(5,𝔽2)11yescharacteristic
475C22×C11C2×2−1+411yescharacteristic
476C2×D11—232no—
477C2×D11—24no—
478C2×D11—24no—
479C2×D11—24no—
480C2×D11—24no—
481C2×D11—24no—
482C2×D11—24no—
483C2×D11—24no—
484C2×D11—24no—
485C2×D11—24no—
486C2×D11—24no—
487C2×D11—24no—
488C2×D11—24no—
489C2×D11—416no—
490C2×D11—416no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11C2×C4×D418yes—
500C4×C11—24no—
501C4×C11—24no—
502C4×C11—24no—
503C4×C11—24no—
504C4×C11—42no—
505C4×C11—42no—
506C4×C11—42no—
507Dic11—24no—
508Dic11—24no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512C25—111no—
513C25—111no—
514C25—111no—
515C22×D4—118no—
516C22×D4—118no—
517C22×D4—118no—
518C22×D4—114no—
519C22×D4—114no—
520C22×D4—114no—
521C22×D4—224no—
522C22×D4—224no—
523C22×D4—224no—
524C22×D4—224no—
525C22×D4—442no—
526C22×D4—442no—
527C23×C4—111no—
528C23×C4—111no—
529C23×C4—118no—
530C23×C4—118no—
531C23×C4—114no—
532C23×C4—114no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—114no—
537C23×C4—114no—
538C23×C4—114no—
539C23×C4—224no—
540C23×C4—224no—
541C23×C4—224no—
542C23×C4—442no—
543C23×C4—442no—
544C23×C4—442no—
545C23×C4—442no—
546C23×C4—442no—
547C23×C4—442no—
548C23×C4—442no—
549C23×C4—442no—
550C23×C4—442no—
551C23×C4—442no—
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1111yescharacteristic
556C23×C4C22×D1111yescharacteristic
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1111yescharacteristic
559#121—1164no—
560C4×D4—2232no—
561C4×D4—2232no—
562C2×C4⋊C4—24no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—224no—
567C2×C4⋊C4—442no—
568C2×C4⋊C4—442no—
569C2×C4⋊C4C4×D1118yescomplemented
570C2×C4⋊C4C22×D1114yes—
571C2×C4⋊C4C22×D1114yes—
572C2×C22⋊C4—118no—
573C2×C22⋊C4—118no—
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—114no—
583C2×C22⋊C4—114no—
584C2×C22⋊C4—224no—
585C2×C22⋊C4—224no—
586C2×C22⋊C4—224no—
587C2×C22⋊C4—224no—
588C2×C22⋊C4—442no—
589C2×C22⋊C4—442no—
590C2×C22⋊C4—442no—
591C2×C22⋊C4—442no—
592C2×C42—24no—
593C2×C42—114no—
594C2×C42—224no—
595C2×C42C22×D1114yes—
596#95—114no—
597#95—114no—
598#95—114no—
599#95—114no—
600#95—114no—
601#95—114no—
602#95C22×D1114yes—
603#95C22×D1114yes—
604#95C22×D1114yes—
605#95C22×D1114yes—
606C2×C11#232518yescomplemented
607C2×C11C22×C4×D411yescharacteristic
608C2×C11C2×#51811yescharacteristic
609C2×C11C2×#52011yescharacteristic
610C2×C11C2×#53411yescharacteristic
611C2×C11C2×#53711yescharacteristic
612C2×C11C2×#53811yescharacteristic
613C2×C11C2×#53911yescharacteristic
614D11—28no—
615D11—44no—
616D11—44no—
617C24—114no—
618C24—114no—
619C24—114no—
620C24—112no—
621C24—114no—
622C24—114no—
623C24—112no—
624C24—112no—
625C24—222no—
626C24—222no—
627C24—222no—
628C24—222no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24—222no—
638C24—222no—
639C24—222no—
640C24—222no—
641C24C23×D1111yescharacteristic
642C2×D4—1116no—
643C2×D4—1116no—
644C2×D4—1116no—
645C2×D4—228no—
646C2×D4—228no—
647C2×D4—2232no—
648C2×D4—2232no—
649C2×D4—228no—
650C2×D4—228no—
651C2×D4—4416no—
652C2×D4—444no—
653C2×D4—444no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
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—114no—
672C22×C4—114no—
673C22×C4—112no—
674C22×C4—112no—
675C22×C4—1116no—
676C22×C4—1116no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—228no—
681C22×C4—228no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—222no—
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—228no—
696C22×C4—4416no—
697C22×C4—4416no—
698C22×C4—444no—
699C22×C4—444no—
700C22×C4—444no—
701C22×C4—444no—
702C22×C4—444no—
703C22×C4—444no—
704C22×C4—444no—
705C22×C4—444no—
706C22×C4—444no—
707C22×C4—444no—
708C22×C4—4416no—
709C22×C4—4416no—
710C22×C4—4416no—
711C22×C4C2×C4×D1114yes—
712C22×C4C2×C4×D1114yes—
713C22×C4C2×C4×D1114yes—
714C22×C4D4×D1114yes—
715C22×C4C23×D1112yes—
716C22×C4C23×D1112yes—
717C22×C4C23×D1112yes—
718C22×C4C23×D1112yes—
719C22×C4C23×D1112yes—
720C22×C4C23×D1112yes—
721C22×C4C23×D1112yes—
722C4⋊C4—28no—
723C4⋊C4—228no—
724C4⋊C4—444no—
725C4⋊C4—444no—
726C4⋊C4C2×C4×D11116yescomplemented
727C22⋊C4—1116no—
728C22⋊C4—1116no—
729C22⋊C4—228no—
730C22⋊C4—228no—
731C22⋊C4—228no—
732C22⋊C4—228no—
733C22⋊C4—444no—
734C22⋊C4—444no—
735C22⋊C4—444no—
736C22⋊C4—444no—
737C42—28no—
738C42—228no—
739C11C2×#232511yescharacteristic, complemented, Sylow
740C23—1116no—
741C23—114no—
742C23—114no—
743C23—114no—
744C23—114no—
745C23—114no—
746C23—228no—
747C23—228no—
748C23—228no—
749C23—228no—
750C23—228no—
751C23—222no—
752C23—222no—
753C23—222no—
754C23—222no—
755C23—228no—
756C23—228no—
757C23—228no—
758C23—228no—
759C23—228no—
760C23—228no—
761C23—228no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—222no—
774C23—444no—
775C23—444no—
776C23—444no—
777C23—444no—
778C23—444no—
779C23—444no—
780C23—444no—
781C23—444no—
782C23C22×C4×D1112yes—
783C23C2×D4×D1112yes—
784C23#6704012yes—
785C23#41×D1112yes—
786C23#6704212yes—
787C23#6704212yes—
788C23#6704212yes—
789C23C24×D1111yescharacteristic
790D4—2232no—
791D4—2232no—
792D4—4416no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
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—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—114no—
818C2×C4—114no—
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—4416no—
835C2×C4—4416no—
836C2×C4—4416no—
837C2×C4—4416no—
838C2×C4—4416no—
839C2×C4—444no—
840C2×C4—444no—
841C2×C4—444no—
842C2×C4C22×C4×D1114yes—
843C2×C4C22×C4×D1114yes—
844C2×C4C22×C4×D1114yes—
845C2×C4C2×D4×D1114yes—
846C22—118no—
847C22—224no—
848C22—224no—
849C22—224no—
850C22—224no—
851C22—224no—
852C22—2232no—
853C22—224no—
854C22—224no—
855C22—224no—
856C22—224no—
857C22—224no—
858C22—224no—
859C22—224no—
860C22—442no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—442no—
866C22—442no—
867C22—442no—
868C22—4416no—
869C22—4416no—
870C22#1062305214yes—
871C22C4×D4×D1114yes—
872C22#1062310514yes—
873C22#1062316014yes—
874C22#1062318414yes—
875C22#1062322314yes—
876C22#1062323514yes—
877C22C23×C4×D1111yescharacteristic
878C22C22×D4×D1111yescharacteristic
879C22C2×#6704011yescharacteristic
880C22C2×#41×D1111yescharacteristic
881C22C2×#6704211yescharacteristic
882C22C2×#6704211yescharacteristic
883C22C2×#6704211yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—42no—
889C4—42no—
890C4—42no—
891C4—224no—
892C4—224no—
893C4—442no—
894C4—442no—
895C4—442no—
896C2—228no—
897C2—444no—
898C2—444no—
899C2#1307131518yesdirect product factor
900C2C2×C4×D4×D1111yescharacteristic
901C2C2×#1062305211yescharacteristic
902C2C2×#1062310511yescharacteristic
903C2C2×#1062318411yescharacteristic
904C2C2×#1062316011yescharacteristic
905C2C2×#1062323511yescharacteristic
906C2C2×#1062322311yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#387C2
socleC24×C11C24
prime radicalC22×#66948C2
cosocleC23×C11C25
hypercenterC2×#387D11
hypocenterC11C2×#2325
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×C4×D44C2semidirect
3. C22×#66946C2semidirect
4. #13071315C2direct (N × H)
5. C2×#10622553C2semidirect
6. C2×#10622282C2semidirect
7. C2×#10622594C2semidirect
8. C2×#10622278C2semidirect
9. C2×#10622278C2semidirect
10. C2×#10622278C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622281C2semidirect
13. C2×#10622602C2semidirect
14. C2×#10622280C2semidirect
15. C2×D11×#95C2semidirect
16. C2×C11×#387C2semidirect
42. C2×#66948C4semidirect
45. C2×#66946C22semidirect
47. C2×C4×D44C22semidirect
48. C11×#387C22semidirect
59. #10622602C22semidirect
60. #10622594C22semidirect
61. #10622553C22semidirect
62. #10622282C22semidirect
63. #10622281C22semidirect
64. #10622280C22semidirect
65. #10622278C22semidirect
66. #10622278C22semidirect
67. #10622278C22semidirect
68. #10622278C22semidirect
69. D11×#95C22semidirect
91. C22×D44C2×C4semidirect
92. C22×D44C2×C4semidirect
93. C22×D44C2×C4semidirect
110. C22×C4×D11C2×C4semidirect
111. C22×C4×D11D4semidirect
118. C2×C11×C4⋊C4C2×C4semidirect
131. C2×(C2×D11)⋊C4C2×C4semidirect
132. C2×(C2×D11)⋊C4C2×C4semidirect
151. #66948C2×C4semidirect
247. C2×D44C22×C4semidirect
248. C2×D44C22×C4semidirect
249. C2×D44C22×C4semidirect
268. C2×C4×D11C22×C4semidirect
269. C2×C4×D11C2×D4semidirect
271. C11×C4⋊C4C22×C4semidirect
281. (C2×D11)⋊C4C22×C4semidirect
282. (C2×D11)⋊C4C22×C4semidirect
294. C2×#387D11semidirect
443. #387C2×D11semidirect
569. C2×C4⋊C4C4×D11semidirect
606. C2×C11#2325semidirect
726. C4⋊C4C2×C4×D11semidirect
739. C11C2×#2325semidirect
899. C2#13071315direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669482
C22×C4×D442
C22×#669462
#130713152
C2×#106225532
C2×#106222822
C2×#106225942
C2×#106222782
C2×#106222812
C2×#106226022
C2×#106222802
C2×D11×#952
C2×C11×#3872
C2×#232511