Finite Group Databasebeta

← C2×#13072974 #14922873

Subgroups — C2×#13072974 #14922873

Order 2816.

3678 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×#66997C211yesmaximal, characteristic, complemented
2C22×#67000C211yesmaximal, characteristic, complemented
3C22×#66938C211yesmaximal, characteristic, complemented
4C22×#66937C211yesmaximal, characteristic
5#13072974C2116yesmaximal, direct product factor
6C2×#10622285C211yesmaximal, characteristic, complemented
7C2×#10622572C211yesmaximal, characteristic, complemented
8C2×#10622286C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622570C211yesmaximal, characteristic, complemented
11C2×#10622558C211yesmaximal, characteristic, complemented
12C2×#10622282C211yesmaximal, characteristic, complemented
13C2×#10622280C211yesmaximal, characteristic, complemented
14C2×#10622262C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#393C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×Dic22C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C2×#67000—28no—
29C2×#67000C2218yescomplemented
30C2×#66997—28no—
31C2×#66997C2218yescomplemented
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×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×C4×Dic11C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×#66938—28no—
51C2×#66938C2218yescomplemented
52C2×#66937—28no—
53C2×#66937C2218yes—
54C11×#393C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57C2×C11×#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622572C2218yescomplemented
62#10622570C2218yescomplemented
63#10622570C2218yescomplemented
64#10622558C2218yescomplemented
65#10622286C2218yescomplemented
66#10622285C2218yescomplemented
67#10622282C2218yescomplemented
68#10622280C2218yescomplemented
69#10622279C2218yescomplemented
70#10622262C2218yescomplemented
71C25×C11C2311yescharacteristic
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
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—42no—
90C22×C22⋊D11C2314yes—
91C22×C22⋊D11C2314yes—
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C22×D44—24no—
99C22×D44—24no—
100C22×D44—42no—
101C22×D44C2314yes—
102C22×C4×D11—24no—
103C22×C4×D11—24no—
104C22×C4×D11—24no—
105C22×C4×D11C2314yes—
106C22×Dic22—24no—
107C22×Dic22—24no—
108C22×Dic22—42no—
109C22×Dic22C2314yes—
110C2×C11×C22⋊C4—24no—
111C2×C11×C22⋊C4—24no—
112C2×C11×C22⋊C4—42no—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—24no—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120#67000—232no—
121#66997—232no—
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—42no—
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×Dic11⋊C4—24no—
141C2×Dic11⋊C4—24no—
142C2×Dic11⋊C4—24no—
143C2×Dic11⋊C4—24no—
144C2×Dic11⋊C4D418yes—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×C4×Dic11—24no—
151C2×C4×Dic11—24no—
152C2×C4×Dic11—24no—
153C2×C4×Dic11—24no—
154C2×C4×Dic11C2314yes—
155C2×C4×Dic11C2314yes—
156C2×C4×Dic11C2314yes—
157C2×C4×Dic11C2314yes—
158#66938—232no—
159#66937—232no—
160C11×#95C2314yes—
161C11×#95C2314yes—
162C11×#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2491—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×D11—22no—
189C23×D11C2×D414yes—
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×C11C2×D414yes—
213C22×C4×C11C2×D414yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C2×C22⋊D11—28no—
221C2×C22⋊D11—28no—
222C2×C22⋊D11—28no—
223C2×C22⋊D11—28no—
224C2×C22⋊D11—28no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—416no—
227C2×C22⋊D11—416no—
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×Dic11C2×D414yes—
241C22×Dic11C2×D414yes—
242C22×Dic11C2×D414yes—
243C22×Dic11#4114yes—
244C22×Dic11#4114yes—
245C22×Dic11#4114yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C2×D44—28no—
253C2×D44—28no—
254C2×D44—44no—
255C2×D44—416no—
256C2×C4×D11—28no—
257C2×C4×D11—28no—
258C2×C4×D11—28no—
259C2×C4×D11—416no—
260C2×Dic22—28no—
261C2×Dic22—28no—
262C2×Dic22—44no—
263C2×Dic22—416no—
264C11×C22⋊C4—28no—
265C11×C22⋊C4—28no—
266C11×C22⋊C4—44no—
267C22⋊Dic11—28no—
268C22⋊Dic11—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—44no—
277(C2×D11)⋊C4C2×D4116yescomplemented
278Dic11⋊C4—28no—
279Dic11⋊C4—28no—
280Dic11⋊C4—28no—
281Dic11⋊C4—28no—
282Dic11⋊C4C2×D4116yes—
283C4×Dic11—28no—
284C4×Dic11—28no—
285C4×Dic11—28no—
286C4×Dic11—28no—
287C22×C4⋊Q8—111no—
288C22×#124—111no—
289C22×#124—111no—
290C22×#121—111no—
291#2491—1116no—
292C2×#394—111no—
293C2×#394—111no—
294C2×#393—111no—
295C2×#393D1111yescharacteristic, complemented
296C2×#390—111no—
297C2×#390—111no—
298C2×#388—111no—
299C2×#388—111no—
300C2×#380—111no—
301C2×C4×C4⋊C4—111no—
302C2×C4×C22⋊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—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—22no—
340C22×D11—22no—
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×D11—44no—
352C22×D11C22×D414yes—
353Q8×C11—416no—
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—22no—
372C2×C4×C11—44no—
373C2×C4×C11—44no—
374C2×C4×C11—44no—
375C2×C4×C11—44no—
376C2×C4×C11C22×D414yes—
377C2×C4×C11C22×D414yes—
378C22⋊D11—416no—
379C22⋊D11—416no—
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—44no—
396C2×Dic11—44no—
397C2×Dic11#124116yescomplemented
398C2×Dic11C22×D414yes—
399C2×Dic11C22×D414yes—
400C2×Dic11C22×D414yes—
401C2×Dic11C2×#4114yes—
402C2×Dic11C2×#4114yes—
403C2×Dic11C2×#4114yes—
404D44—416no—
405C4×D11—416no—
406Dic22—416no—
407C23×Q8—111no—
408C23×Q8C2×D1111yescharacteristic
409C23×D4—111no—
410C23×D4—111no—
411C23×D4—111no—
412C24×C4—111no—
413C2×C4⋊Q8—118no—
414C2×C4⋊Q8—228no—
415C2×#124—118no—
416C2×#124—118no—
417C2×#124—228no—
418C2×#124—228no—
419C2×#121—118no—
420C2×#121—228no—
421C22×C4⋊C4—111no—
422C22×C4⋊C4—111no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C4⋊C4—111no—
426C22×C22⋊C4—111no—
427C22×C22⋊C4—111no—
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⋊C4C2×D1111yescharacteristic
438C22×C22⋊C4C2×D1111yescharacteristic
439C22×C22⋊C4C2×D1111yescharacteristic
440C22×C42—111no—
441C22×C42—111no—
442C22×C42—111no—
443C22×C42—111no—
444#394—118no—
445#394—118no—
446#393—118no—
447#393C2×D1118yescomplemented
448#390—118no—
449#390—118no—
450#388—118no—
451#388—118no—
452#380—118no—
453C4×C4⋊C4—118no—
454C4×C22⋊C4—118no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95C2×D1111yescharacteristic
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×C11C2×#12414yes—
470C22×C11#53214yes—
471C22×C11#54214yes—
472C22×C11D4214yes—
473C22×C11#54714yes—
474C22×C11#54814yes—
475C22×C11#55514yes—
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—42no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—42no—
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—42no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11—42no—
505Dic11—24no—
506Dic11—24no—
507Dic11—24no—
508Dic11—42no—
509Dic11—42no—
510Dic11C2×#12418yescomplemented
511C25—111no—
512C25—111no—
513C25C22×D1111yescharacteristic
514C22×Q8—24no—
515C22×Q8—24no—
516C22×Q8—42no—
517C22×Q8—114no—
518C22×Q8—224no—
519C22×Q8—224no—
520C22×Q8—442no—
521C22×Q8C22×D1114yes—
522C22×D4—114no—
523C22×D4—114no—
524C22×D4—114no—
525C22×D4—224no—
526C22×D4—224no—
527C22×D4—224no—
528C22×D4—224no—
529C22×D4—224no—
530C22×D4—224no—
531C22×D4—224no—
532C22×D4—442no—
533C22×D4—442no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—111no—
539C23×C4—111no—
540C23×C4—114no—
541C23×C4—224no—
542C23×C4—224no—
543C23×C4—224no—
544C23×C4C22×D1111yescharacteristic
545C23×C4C22×D1111yescharacteristic
546C23×C4C22×D1111yescharacteristic
547C23×C4C22×D1111yescharacteristic
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550C4⋊Q8—2232no—
551#124—2232no—
552#124—2232no—
553#121—2232no—
554C2×C4⋊C4—118no—
555C2×C4⋊C4—114no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—114no—
558C2×C4⋊C4—114no—
559C2×C4⋊C4—114no—
560C2×C4⋊C4—224no—
561C2×C4⋊C4—224no—
562C2×C4⋊C4—224no—
563C2×C4⋊C4—224no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—118no—
568C2×C22⋊C4—114no—
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—224no—
580C2×C22⋊C4—224no—
581C2×C22⋊C4—224no—
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—442no—
589C2×C22⋊C4C22×D1114yes—
590C2×C22⋊C4C22×D1114yes—
591C2×C22⋊C4C22×D1114yes—
592C2×C42—114no—
593C2×C42—114no—
594C2×C42—114no—
595C2×C42—114no—
596C2×C42—224no—
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—82no—
607C2×C11#249118yescomplemented
608C2×C11C22×#12411yescharacteristic
609C2×C11C2×#53211yescharacteristic
610C2×C11C2×#54211yescharacteristic
611C2×C11C2×D4211yescharacteristic
612C2×C11C2×#54711yescharacteristic
613C2×C11C2×#54811yescharacteristic
614C2×C11C2×#55511yescharacteristic
615D11—44no—
616D11—82no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—114no—
625C24—112no—
626C24—112no—
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—
640C24C23×D1112yes—
641C24C23×D1111yescharacteristic
642C2×Q8—28no—
643C2×Q8—28no—
644C2×Q8—44no—
645C2×Q8—416no—
646C2×Q8—228no—
647C2×Q8—228no—
648C2×Q8—444no—
649C2×Q8—4416no—
650C2×D4—228no—
651C2×D4—228no—
652C2×D4—228no—
653C2×D4—228no—
654C2×D4—228no—
655C2×D4—228no—
656C2×D4—228no—
657C2×D4—444no—
658C2×D4—4416no—
659C2×D4—4416no—
660C2×D4—444no—
661C2×D4—4416no—
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—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—114no—
679C22×C4—114no—
680C22×C4—114no—
681C22×C4—112no—
682C22×C4—114no—
683C22×C4—114no—
684C22×C4—114no—
685C22×C4—112no—
686C22×C4—112no—
687C22×C4—112no—
688C22×C4—112no—
689C22×C4—112no—
690C22×C4—228no—
691C22×C4—228no—
692C22×C4—228no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—222no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—222no—
703C22×C4—222no—
704C22×C4—222no—
705C22×C4—4416no—
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—1116no—
715C4⋊C4—228no—
716C4⋊C4—228no—
717C4⋊C4—228no—
718C4⋊C4—228no—
719C22⋊C4—28no—
720C22⋊C4—28no—
721C22⋊C4—44no—
722C22⋊C4—1116no—
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—444no—
733C42—228no—
734C42—228no—
735C42—228no—
736C42—228no—
737C11C2×#249111yescharacteristic, 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—228no—
754C23—228no—
755C23—222no—
756C23—222no—
757C23—222no—
758C23—222no—
759C23—222no—
760C23—222no—
761C23—228no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—222no—
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—
783C23#6704012yes—
784C23#41×D1112yes—
785C23#41×D1112yes—
786C23#41×D1112yes—
787C23C24×D1111yescharacteristic
788Q8—416no—
789Q8—4416no—
790D4—4416no—
791D4—4416no—
792D4—4416no—
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—22no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—114no—
816C2×C4—114no—
817C2×C4—114no—
818C2×C4—1116no—
819C2×C4—114no—
820C2×C4—114no—
821C2×C4—114no—
822C2×C4—228no—
823C2×C4—228no—
824C2×C4—228no—
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—222no—
836C2×C4—222no—
837C2×C4—4416no—
838C2×C4—444no—
839C2×C4—444no—
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—442no—
854C22—442no—
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#1062316214yes—
868C22#1062316414yes—
869C22#1062317114yes—
870C22#1062319914yes—
871C22#1062320114yes—
872C22D11×#12414yes—
873C22C22×D4×D1111yescharacteristic
874C22C22×D4×D1111yescharacteristic
875C22C2×#6703711yescharacteristic
876C22C2×#6704011yescharacteristic
877C22C2×#41×D1111yescharacteristic
878C22C2×#41×D1111yescharacteristic
879C22C2×#41×D1111yescharacteristic
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—118no—
887C4—224no—
888C4—224no—
889C4—224no—
890C4—442no—
891C4—442no—
892C2—82no—
893C2—444no—
894C2—882no—
895C2#1307297418yesdirect product factor
896C2C2×D11×#12411yescharacteristic
897C2C2×#1062319911yescharacteristic
898C2C2×#1062317111yescharacteristic
899C2C2×#1062312111yescharacteristic
900C2C2×#1062316211yescharacteristic
901C2C2×#1062316411yescharacteristic
902C2C2×#1062320111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#393C2
socleC24×C11C24
prime radicalC22×#66937C2
hypercenterC2×#393D11
hypocenterC11C2×#2491
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#66997C2semidirect
2. C22×#67000C2semidirect
3. C22×#66938C2semidirect
5. #13072974C2direct (N × H)
6. C2×#10622285C2semidirect
7. C2×#10622572C2semidirect
8. C2×#10622286C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622558C2semidirect
12. C2×#10622282C2semidirect
13. C2×#10622280C2semidirect
14. C2×#10622262C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#393C2semidirect
29. C2×#67000C22semidirect
31. C2×#66997C22semidirect
51. C2×#66938C22semidirect
54. C11×#393C22semidirect
61. #10622572C22semidirect
62. #10622570C22semidirect
63. #10622570C22semidirect
64. #10622558C22semidirect
65. #10622286C22semidirect
66. #10622285C22semidirect
67. #10622282C22semidirect
68. #10622280C22semidirect
69. #10622279C22semidirect
70. #10622262C22semidirect
130. C2×(C2×D11)⋊C4D4semidirect
277. (C2×D11)⋊C4C2×D4semidirect
295. C2×#393D11semidirect
397. C2×Dic11#124semidirect
447. #393C2×D11semidirect
510. Dic11C2×#124semidirect
607. C2×C11#2491semidirect
737. C11C2×#2491semidirect
895. C2#13072974direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669972
C22×#670002
C22×#669382
C22×#669372
#130729742
C2×#106222852
C2×#106225722
C2×#106222862
C2×#106225702
C2×#106225582
C2×#106222822
C2×#106222802
C2×#106222622
C2×#106222792
C2×C11×#3932
C2×#249111