Finite Group Databasebeta

← C2×#13072586 #14921633

Subgroups — C2×#13072586 #14921633

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×#67000C211yesmaximal, characteristic, complemented
2C22×#66947C211yesmaximal, characteristic, complemented
3C22×#66999C211yesmaximal, characteristic, complemented
4C22×#66946C211yesmaximal, characteristic, complemented
5#13072586C2116yesmaximal, direct product factor
6C2×#10622607C211yesmaximal, characteristic, complemented
7C2×#10622285C211yesmaximal, characteristic, complemented
8C2×#10622284C211yesmaximal, characteristic
9C2×#10622601C211yesmaximal, characteristic, complemented
10C2×#10622283C211yesmaximal, characteristic, complemented
11C2×#10622603C211yesmaximal, characteristic, complemented
12C2×#10622282C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, characteristic, complemented
15C2×#10622262C211yesmaximal, characteristic, complemented
16C2×C11×#395C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C2×#67000—28no—
27C2×#67000C2218yescomplemented
28C2×#66999—28no—
29C2×#66999C2218yescomplemented
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×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×C4⋊Dic11C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×#66947—28no—
51C2×#66947C2218yescomplemented
52C2×#66946—28no—
53C2×#66946C2218yescomplemented
54C11×#395C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57C2×C11×#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622607C2218yescomplemented
62#10622603C2218yescomplemented
63#10622602C2218yescomplemented
64#10622601C2218yescomplemented
65#10622285C2218yescomplemented
66#10622284C2218yes—
67#10622283C2218yescomplemented
68#10622282C2218yescomplemented
69#10622278C2218yescomplemented
70#10622262C2218yescomplemented
71C24×D11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C22×Q8×C11—24no—
75C22×Q8×C11—24no—
76C22×Q8×C11—42no—
77C22×Q8×C11C2314yes—
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C22×D44—24no—
91C22×D44—24no—
92C22×D44—24no—
93C22×D44—24no—
94C22×D44—24no—
95C22×D44—24no—
96C22×D44—24no—
97C22×D44—42no—
98C22×D44—42no—
99C22×D44C2314yes—
100C22×D44C2314yes—
101C22×D44C2314yes—
102C22×C4×D11—24no—
103C22×C4×D11—24no—
104C22×C4×D11—24no—
105C22×C4×D11—24no—
106C22×C4×D11—42no—
107C22×C4×D11—42no—
108C22×C4×D11C2314yes—
109C22×C4×D11C2314yes—
110C2×C11×C4⋊C4—24no—
111C2×C11×C4⋊C4—24no—
112C2×C11×C4⋊C4—42no—
113C2×C11×C4⋊C4C2314yes—
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C4⋊C4C2314yes—
116#67000—232no—
117#66999—232no—
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4—24no—
120C2×(C2×D11)⋊C4—24no—
121C2×(C2×D11)⋊C4—24no—
122C2×(C2×D11)⋊C4—24no—
123C2×(C2×D11)⋊C4—24no—
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)⋊C4D418yescomplemented
131C2×(C2×D11)⋊C4C2314yes—
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×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×C4⋊Dic11—24no—
145C2×C4⋊Dic11C2314yes—
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4D418yescomplemented
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×C4×Dic11—24no—
153C2×C4×Dic11—24no—
154C2×C4×Dic11—24no—
155C2×C4×Dic11C2314yes—
156C2×C4×Dic11C2314yes—
157C2×C4×Dic11C2314yes—
158#66947—232no—
159#66946—232no—
160C11×#95C2314yes—
161C11×#95C2314yes—
162C11×#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2461—111nomaximal, Sylow
167C24×C11C2411yescharacteristic
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×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11C2×D414yes—
188C23×D11#4114yes—
189C23×D11C2412yes—
190C23×D11C2412yes—
191C23×D11C2412yes—
192C2×Q8×C11—28no—
193C2×Q8×C11—28no—
194C2×Q8×C11—44no—
195C2×Q8×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—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11C2×D414yes—
214C22×C4×C11C2×D414yes—
215C22×C4×C11#4114yes—
216C22×C4×C11#4114yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
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×Dic11C2×D414yes—
237C22×Dic11C2×D414yes—
238C22×Dic11C2×D414yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C2×D44—232no—
245C2×D44—28no—
246C2×D44—28no—
247C2×D44—28no—
248C2×D44—28no—
249C2×D44—28no—
250C2×D44—28no—
251C2×D44—28no—
252C2×D44—44no—
253C2×D44—44no—
254C2×D44—416no—
255C2×D44—416no—
256C2×C4×D11—28no—
257C2×C4×D11—28no—
258C2×C4×D11—28no—
259C2×C4×D11—28no—
260C2×C4×D11—44no—
261C2×C4×D11—44no—
262C2×C4×D11—416no—
263C2×C4×D11—416no—
264C11×C4⋊C4—28no—
265C11×C4⋊C4—28no—
266C11×C4⋊C4—44no—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—28no—
269(C2×D11)⋊C4—28no—
270(C2×D11)⋊C4—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)⋊C4—28no—
279(C2×D11)⋊C4C2×D4116yescomplemented
280C4⋊Dic11—28no—
281Dic11⋊C4—28no—
282Dic11⋊C4—28no—
283Dic11⋊C4C2×D4116yescomplemented
284C4×Dic11—28no—
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×#395D1111yescharacteristic, complemented
294C2×#394—111no—
295C2×#392—111no—
296C2×#390—111no—
297C2×#388—111no—
298C2×#388—111no—
299C2×#388—111no—
300C2×#386—111no—
301C2×#385—111no—
302C2×C4×C4⋊C4—111no—
303C23×C11C22×D412yes—
304C23×C11C22×D412yes—
305C23×C11C2×#4112yes—
306C23×C11C2×#4112yes—
307C23×C11C2×#4112yes—
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—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
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—44no—
337C22×D11—44no—
338C22×D11—44no—
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×D11—44no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11C22×D414yes—
352C22×D11C2×#4114yes—
353Q8×C11—416no—
354C2×C4×C11—28no—
355C2×C4×C11—28no—
356C2×C4×C11—28no—
357C2×C4×C11—28no—
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—22no—
375C2×C4×C11—44no—
376C2×C4×C11—44no—
377C2×C4×C11—44no—
378C2×C4×C11C22×D414yes—
379C2×C4×C11C22×D414yes—
380C2×C4×C11C2×#4114yes—
381C2×C4×C11C2×#4114yes—
382C2×Dic11—28no—
383C2×Dic11—28no—
384C2×Dic11—28no—
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—
402D44—232no—
403D44—416no—
404D44—416no—
405C4×D11—416no—
406C4×D11—416no—
407C23×Q8C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
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×C22⋊C4—111no—
439C22×C22⋊C4—111no—
440C22×C22⋊C4—111no—
441C22×C42—111no—
442C22×C42—111no—
443C22×C42—111no—
444#396—118no—
445#395C2×D1118yescomplemented
446#394—118no—
447#392—118no—
448#390—118no—
449#388—118no—
450#388—118no—
451#388—118no—
452#386—118no—
453#385—118no—
454C4×C4⋊C4—118no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95C2×D1111yescharacteristic
459C2×#95C2×D1111yescharacteristic
460C2×#95C2×D1111yescharacteristic
461C22×C11#52514yes—
462C22×C11#53214yes—
463C22×C11#54214yes—
464C22×C11D4214yes—
465C22×C11#54714yes—
466C22×C11#54814yes—
467C22×C11#55114yes—
468C22×C11C23×D411yescharacteristic
469C22×C11C23×D411yescharacteristic
470C22×C11C22×#4111yescharacteristic
471C22×C11C22×#4111yescharacteristic
472C22×C11C22×#4111yescharacteristic
473C22×C11C2×H(5,𝔽2)11yescharacteristic
474C22×C11C2×2−1+411yescharacteristic
475C2×D11—24no—
476C2×D11—24no—
477C2×D11—24no—
478C2×D11—24no—
479C2×D11—24no—
480C2×D11—24no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—42no—
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—88no—
499C4×C11—24no—
500C4×C11—24no—
501C4×C11—24no—
502C4×C11—24no—
503C4×C11—42no—
504C4×C11—42no—
505C4×C11—42no—
506Dic11—24no—
507Dic11—24no—
508Dic11—24no—
509Dic11—42no—
510Dic11—42no—
511C25—111no—
512C25—111no—
513C25—111no—
514C22×Q8—24no—
515C22×Q8—24no—
516C22×Q8—42no—
517C22×Q8C22×D1114yes—
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—114no—
536C23×C4—114no—
537C23×C4—224no—
538C23×C4—224no—
539C23×C4—224no—
540C23×C4—224no—
541C23×C4—442no—
542C23×C4—442no—
543C23×C4C22×D1111yescharacteristic
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—24no—
556C2×C4⋊C4—42no—
557C2×C4⋊C4—118no—
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⋊C4C22×D1114yes—
566C2×C4⋊C4C22×D1114yes—
567C2×C4⋊C4C22×D1114yes—
568C2×C22⋊C4—118no—
569C2×C22⋊C4—114no—
570C2×C22⋊C4—114no—
571C2×C22⋊C4—114no—
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⋊C4—224no—
592C2×C22⋊C4—224no—
593C2×C22⋊C4—224no—
594C2×C42—114no—
595C2×C42—114no—
596C2×C42—114no—
597C2×C42—224no—
598C2×C42—224no—
599C2×C42—224no—
600#95—114no—
601#95—114no—
602#95—114no—
603#95C22×D1114yes—
604#95C22×D1114yes—
605#95C22×D1114yes—
606C2×C11#246118yescomplemented
607C2×C11C2×#52511yescharacteristic
608C2×C11C2×#53211yescharacteristic
609C2×C11C2×#54211yescharacteristic
610C2×C11C2×D4211yescharacteristic
611C2×C11C2×#54711yescharacteristic
612C2×C11C2×#54811yescharacteristic
613C2×C11C2×#55111yescharacteristic
614D11—44no—
615D11—44no—
616D11—82no—
617C24—114no—
618C24—114no—
619C24—112no—
620C24—112no—
621C24—112no—
622C24—222no—
623C24—222no—
624C24—222no—
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×Q8—28no—
643C2×Q8—28no—
644C2×Q8—44no—
645C2×Q8—416no—
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—22no—
674C22×C4—22no—
675C22×C4—114no—
676C22×C4—114no—
677C22×C4—114no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—228no—
684C22×C4—228no—
685C22×C4—228no—
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—228no—
699C22×C4—444no—
700C22×C4—444no—
701C22×C4—4416no—
702C22×C4—4416no—
703C22×C4D4×D1114yes—
704C22×C4D4×D1114yes—
705C22×C4#434314yes—
706C22×C4#434314yes—
707C22×C4C23×D1112yes—
708C22×C4C23×D1112yes—
709C22×C4C23×D1112yes—
710C22×C4C23×D1112yes—
711C22×C4C23×D1112yes—
712C22×C4C23×D1112yes—
713C22×C4C23×D1112yes—
714C4⋊C4—28no—
715C4⋊C4—28no—
716C4⋊C4—44no—
717C4⋊C4—1116no—
718C4⋊C4—228no—
719C4⋊C4—228no—
720C4⋊C4—228no—
721C22⋊C4—1116no—
722C22⋊C4—228no—
723C22⋊C4—228no—
724C22⋊C4—228no—
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—228no—
735C42—228no—
736C42—228no—
737C11C2×#246111yescharacteristic, complemented, Sylow
738C23—114no—
739C23—114no—
740C23—228no—
741C23—228no—
742C23—228no—
743C23—228no—
744C23—228no—
745C23—228no—
746C23—222no—
747C23—222no—
748C23—222no—
749C23—222no—
750C23—222no—
751C23—222no—
752C23—222no—
753C23—222no—
754C23—222no—
755C23—222no—
756C23—222no—
757C23—222no—
758C23—222no—
759C23—222no—
760C23—222no—
761C23—222no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—444no—
766C23—444no—
767C23—444no—
768C23—444no—
769C23—444no—
770C23—444no—
771C23—444no—
772C23—444no—
773C23—444no—
774C23—444no—
775C23—444no—
776C23—444no—
777C23—444no—
778C23—444no—
779C23—444no—
780C23C2×D4×D1112yes—
781C23C2×D4×D1112yes—
782C23#6703712yes—
783C23C2×#434312yes—
784C23C2×#434312yes—
785C23#6704012yes—
786C23#41×D1112yes—
787C23C24×D1111yescharacteristic
788Q8—416no—
789D4—2232no—
790D4—4416no—
791D4—4416no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
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—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—114no—
817C2×C4—114no—
818C2×C4—114no—
819C2×C4—228no—
820C2×C4—228no—
821C2×C4—228no—
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—444no—
837C2×C4—444no—
838C2×C4C2×D4×D1114yes—
839C2×C4C2×D4×D1114yes—
840C2×C4C2×#434314yes—
841C2×C4C2×#434314yes—
842C22—224no—
843C22—224no—
844C22—224no—
845C22—224no—
846C22—224no—
847C22—224no—
848C22—442no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22—442no—
853C22—442no—
854C22—4416no—
855C22—4416no—
856C22—442no—
857C22—442no—
858C22—442no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—888no—
866C22#1062312114yes—
867C22#1062315814yes—
868C22#1062316414yes—
869C22#1062316814yes—
870C22#1062325614yes—
871C22#1062325714yes—
872C22#1062326414yes—
873C22C22×D4×D1111yescharacteristic
874C22C22×D4×D1111yescharacteristic
875C22C2×#6703711yescharacteristic
876C22C22×#434311yescharacteristic
877C22C22×#434311yescharacteristic
878C22C2×#6704011yescharacteristic
879C22C2×#41×D1111yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—42no—
885C4—42no—
886C4—42no—
887C4—224no—
888C4—224no—
889C4—224no—
890C4—442no—
891C4—442no—
892C2—444no—
893C2—444no—
894C2—882no—
895C2#1307258618yesdirect product factor
896C2C2×#1062315811yescharacteristic
897C2C2×#1062325611yescharacteristic
898C2C2×#1062326411yescharacteristic
899C2C2×#1062312111yescharacteristic
900C2C2×#1062325711yescharacteristic
901C2C2×#1062316411yescharacteristic
902C2C2×#1062316811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#395C2
socleC24×C11C24
prime radicalC2×#10622284C2
hypercenterC2×#395D11
hypocenterC11C2×#2461
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
1. C22×#67000C2semidirect
2. C22×#66947C2semidirect
3. C22×#66999C2semidirect
4. C22×#66946C2semidirect
5. #13072586C2direct (N × H)
6. C2×#10622607C2semidirect
7. C2×#10622285C2semidirect
9. C2×#10622601C2semidirect
10. C2×#10622283C2semidirect
11. C2×#10622603C2semidirect
12. C2×#10622282C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622602C2semidirect
15. C2×#10622262C2semidirect
16. C2×C11×#395C2semidirect
27. C2×#67000C22semidirect
29. C2×#66999C22semidirect
51. C2×#66947C22semidirect
53. C2×#66946C22semidirect
54. C11×#395C22semidirect
61. #10622607C22semidirect
62. #10622603C22semidirect
63. #10622602C22semidirect
64. #10622601C22semidirect
65. #10622285C22semidirect
67. #10622283C22semidirect
68. #10622282C22semidirect
69. #10622278C22semidirect
70. #10622262C22semidirect
130. C2×(C2×D11)⋊C4D4semidirect
148. C2×Dic11⋊C4D4semidirect
279. (C2×D11)⋊C4C2×D4semidirect
283. Dic11⋊C4C2×D4semidirect
293. C2×#395D11semidirect
445. #395C2×D11semidirect
606. C2×C11#2461semidirect
737. C11C2×#2461semidirect
895. C2#13072586direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670002
C22×#669472
C22×#669992
C22×#669462
#130725862
C2×#106226072
C2×#106222852
C2×#106222842
C2×#106226012
C2×#106222832
C2×#106226032
C2×#106222822
C2×#106222782
C2×#106226022
C2×#106222622
C2×C11×#3952
C2×#246111