Finite Group Databasebeta

← C2×#13074546 #14920207

Subgroups — C2×#13074546 #14920207

Order 2816.

3326 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic
3#13074546C2116yesmaximal, direct product factor
4C2×#10622273C211yesmaximal, characteristic, complemented
5C2×#10622271C211yesmaximal, characteristic, complemented
6C2×#10622288C211yesmaximal, characteristic, complemented
7C2×#10622565C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622572C211yesmaximal, characteristic, complemented
10C2×#10622286C211yesmaximal, characteristic, complemented
11C2×#10622560C211yesmaximal, characteristic, complemented
12C2×#10622833C211yesmaximal, characteristic, complemented
13C2×#10622826C211yesmaximal, characteristic, complemented
14C2×#10622571C211yesmaximal, characteristic, complemented
15C22×C11⋊#95C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C23×Dic22C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C2×#66992—28no—
32C2×#66992C2218yes—
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×Dic11⋊C4C2211yescharacteristic
42C2×#66931—28no—
43C2×#66931C2218yescomplemented
44C11×#386C2218yescomplemented
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47#10622833C2218yescomplemented
48#10622826C2218yescomplemented
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
59C2×C11⋊#95C2218yescomplemented
60#10622574C2218yescomplemented
61#10622572C2218yescomplemented
62#10622571C2218yescomplemented
63#10622565C2218yescomplemented
64#10622560C2218yescomplemented
65#10622288C2218yescomplemented
66#10622286C2218yescomplemented
67#10622273C2218yescomplemented
68#10622271C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C22×D4×C11—24no—
73C22×D4×C11—24no—
74C22×D4×C11—24no—
75C22×D4×C11C2314yes—
76C23×C4×C11—24no—
77C23×C4×C11—42no—
78C23×C4×C11—42no—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2314yes—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—42no—
90C22×C22⋊D11—42no—
91C22×C22⋊D11C2314yes—
92C22×C22⋊D11C2314yes—
93C23×Dic11—24no—
94C23×Dic11—42no—
95C23×Dic11—42no—
96C23×Dic11—42no—
97C23×Dic11—42no—
98C23×Dic11D418yes—
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2314yes—
107C23×Dic11C2314yes—
108C22×Dic22—24no—
109C22×Dic22—42no—
110C22×Dic22—42no—
111C22×Dic22C2314yes—
112C2×C11×C22⋊C4—24no—
113C2×C11×C22⋊C4—42no—
114C2×C11×C22⋊C4—42no—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C22⋊Dic11—24no—
119C2×C22⋊Dic11—24no—
120C2×C22⋊Dic11—42no—
121C2×C22⋊Dic11—42no—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126#66992—232no—
127C2×(C2×D11)⋊C4—24no—
128C2×(C2×D11)⋊C4—42no—
129C2×(C2×D11)⋊C4—42no—
130C2×(C2×D11)⋊C4—42no—
131C2×(C2×D11)⋊C4—42no—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×C4⋊Dic11—24no—
138C2×C4⋊Dic11C2314yes—
139C2×Dic11⋊C4—24no—
140C2×Dic11⋊C4—24no—
141C2×Dic11⋊C4—24no—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145#66931—232no—
146C11×#95C2314yes—
147C11×#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2639—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×C11C2×D414yes—
171C24×C11#4114yes—
172C24×C11#4114yes—
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—28no—
186C2×D4×C11—28no—
187C2×D4×C11—416no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—28no—
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—44no—
205C22×C4×C11—44no—
206C22×C4×C11—416no—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C2×C22⋊D11—28no—
213C2×C22⋊D11—28no—
214C2×C22⋊D11—28no—
215C2×C22⋊D11—28no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—416no—
219C2×C22⋊D11—416no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—28no—
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×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—416no—
241C22×Dic11—44no—
242C22×Dic11—44no—
243C22×Dic11—44no—
244C22×Dic11—44no—
245C22×Dic11—416no—
246C22×Dic11C2×D414yes—
247C22×Dic11C2×D414yes—
248C22×Dic11C2×D4116yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C2×Dic22—28no—
257C2×Dic22—44no—
258C2×Dic22—44no—
259C2×Dic22—416no—
260C11×C22⋊C4—28no—
261C11×C22⋊C4—44no—
262C11×C22⋊C4—44no—
263C22⋊Dic11—28no—
264C22⋊Dic11—28no—
265C22⋊Dic11—44no—
266C22⋊Dic11—44no—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4—44no—
270(C2×D11)⋊C4—44no—
271(C2×D11)⋊C4—44no—
272C4⋊Dic11—28no—
273Dic11⋊C4—28no—
274Dic11⋊C4—28no—
275Dic11⋊C4—28no—
276C22×C22⋊Q8—111no—
277C22×#121—111no—
278#2639—1116no—
279C2×#400—111no—
280C2×#400—111no—
281C2×#397—111no—
282C2×#397—111no—
283C2×#394—111no—
284C2×#394—111no—
285C2×#393—111no—
286C2×#393—111no—
287C2×#386—111no—
288C2×#386—111no—
289C2×#386—111no—
290C2×#386D1111yescharacteristic, complemented
291C22×#95—111no—
292C23×C11—28no—
293C23×C11—28no—
294C23×C11—28no—
295C23×C11—28no—
296C23×C11—28no—
297C23×C11—28no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—44no—
310C23×C11—44no—
311C23×C11—44no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11#124116yes—
317C23×C11C22×D414yes—
318C23×C11C22×D412yes—
319C23×C11C2×#4114yes—
320C23×C11C2×#4112yes—
321C23×C11C2×#4114yes—
322C23×C11C2×#4112yes—
323C23×C11H(5,𝔽2)12yes—
324C23×C11H(5,𝔽2)12yes—
325C23×C11H(5,𝔽2)12yes—
326C23×C112−1+412yes—
327C23×C11C2511yescharacteristic
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11—44no—
340C22×D11—44no—
341C22×D11—44no—
342D4×C11—416no—
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—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—416no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C2×C4×C11—44no—
362C2×C4×C11—44no—
363C2×C4×C11—44no—
364C22⋊D11—416no—
365C22⋊D11—416no—
366C2×Dic11—28no—
367C2×Dic11—28no—
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—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—416no—
388C2×Dic11—416no—
389C2×Dic11—44no—
390C2×Dic11—44no—
391C2×Dic11—44no—
392C2×Dic11—44no—
393C2×Dic11—44no—
394C2×Dic11C22×D414yes—
395C2×Dic11C22×D414yes—
396Dic22—416no—
397C23×Q8—111no—
398C23×D4—111no—
399C23×D4—111no—
400C23×D4C2×D1111yescharacteristic
401C24×C4—111no—
402C24×C4—111no—
403C24×C4C2×D1111yescharacteristic
404C2×C22⋊Q8—118no—
405C2×C22⋊Q8—228no—
406C2×#121—118no—
407C2×#121—228no—
408C22×C4⋊C4—111no—
409C22×C4⋊C4—111no—
410C22×C4⋊C4—111no—
411C22×C4⋊C4—111no—
412C22×C22⋊C4—111no—
413C22×C22⋊C4—111no—
414C22×C22⋊C4—111no—
415C22×C22⋊C4—111no—
416C22×C22⋊C4—111no—
417C22×C22⋊C4—111no—
418C22×C22⋊C4—111no—
419C22×C22⋊C4—111no—
420C22×C22⋊C4—111no—
421C22×C22⋊C4C2×D1111yescharacteristic
422C22×C22⋊C4C2×D1111yescharacteristic
423C22×C22⋊C4C2×D1111yescharacteristic
424#400—118no—
425#400—118no—
426#397—118no—
427#397—118no—
428#394—118no—
429#394—118no—
430#393—118no—
431#393—118no—
432#386—118no—
433#386—118no—
434#386—118no—
435#386C2×D1118yescomplemented
436C2×#95—118no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95—111no—
444C2×#95—111no—
445C2×#95—111no—
446C2×#95—111no—
447C2×#95C2×D1111yescharacteristic
448C2×#95C2×D1111yescharacteristic
449C22×C11—232no—
450C22×C11—24no—
451C22×C11—24no—
452C22×C11—24no—
453C22×C11—24no—
454C22×C11—24no—
455C22×C11—24no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—88no—
464C22×C11C2×#12418yes—
465C22×C11C2×#12414yes—
466C22×C11#53414yes—
467C22×C11#53714yes—
468C22×C11#53814yes—
469C22×C11#53814yes—
470C22×C11#53914yes—
471C22×C11#53914yes—
472C22×C11C23×D411yescharacteristic
473C22×C11C22×#4111yescharacteristic
474C22×C11C22×#4111yescharacteristic
475C22×C11C2×H(5,𝔽2)11yescharacteristic
476C22×C11C2×H(5,𝔽2)11yescharacteristic
477C22×C11C2×H(5,𝔽2)11yescharacteristic
478C22×C11C2×2−1+411yescharacteristic
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—88no—
487C4×C11—42no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11—42no—
491C4×C11—42no—
492Dic11—24no—
493Dic11—24no—
494Dic11—42no—
495Dic11—42no—
496Dic11—42no—
497Dic11—42no—
498Dic11—42no—
499C25—111no—
500C25C22×D1111yescharacteristic
501C25C22×D1111yescharacteristic
502C22×Q8—114no—
503C22×Q8—224no—
504C22×Q8—442no—
505C22×Q8—442no—
506C22×D4—24no—
507C22×D4—24no—
508C22×D4—24no—
509C22×D4—114no—
510C22×D4—114no—
511C22×D4—224no—
512C22×D4—224no—
513C22×D4—224no—
514C22×D4—224no—
515C22×D4—442no—
516C22×D4—442no—
517C22×D4C22×D1114yes—
518C23×C4—24no—
519C23×C4—42no—
520C23×C4—42no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—118no—
524C23×C4—114no—
525C23×C4—111no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—111no—
529C23×C4—111no—
530C23×C4—114no—
531C23×C4—224no—
532C23×C4—442no—
533C23×C4—442no—
534C23×C4—442no—
535C23×C4—442no—
536C23×C4C22×D1111yescharacteristic
537C23×C4C22×D1111yescharacteristic
538C23×C4C22×D1111yescharacteristic
539C23×C4C22×D1111yescharacteristic
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1114yes—
542C22⋊Q8—2232no—
543#121—2232no—
544C2×C4⋊C4—114no—
545C2×C4⋊C4—114no—
546C2×C4⋊C4—114no—
547C2×C4⋊C4—114no—
548C2×C4⋊C4—224no—
549C2×C4⋊C4—224no—
550C2×C4⋊C4—224no—
551C2×C4⋊C4—224no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—114no—
558C2×C22⋊C4—114no—
559C2×C22⋊C4—114no—
560C2×C22⋊C4—114no—
561C2×C22⋊C4—114no—
562C2×C22⋊C4—114no—
563C2×C22⋊C4—114no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—224no—
566C2×C22⋊C4—224no—
567C2×C22⋊C4—442no—
568C2×C22⋊C4—442no—
569C2×C22⋊C4—442no—
570C2×C22⋊C4—442no—
571C2×C22⋊C4—442no—
572C2×C22⋊C4—442no—
573C2×C22⋊C4C22×D1114yes—
574C2×C22⋊C4C22×D1114yes—
575C2×C22⋊C4C22×D1114yes—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95—114no—
582#95—114no—
583#95—114no—
584#95—114no—
585#95—114no—
586#95C22×D1114yes—
587#95C22×D1114yes—
588C2×C11—28no—
589C2×C11—82no—
590C2×C11#263918yescomplemented
591C2×C11C22×#12411yescharacteristic
592C2×C11C2×#53411yescharacteristic
593C2×C11C2×#53711yescharacteristic
594C2×C11C2×#53811yescharacteristic
595C2×C11C2×#53811yescharacteristic
596C2×C11C2×#53911yescharacteristic
597C2×C11C2×#53911yescharacteristic
598D11—82no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—112no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24—222no—
617C24—222no—
618C24#433914yes—
619C24D4×D1114yes—
620C24#434114yes—
621C24C23×D1112yes—
622C24C23×D1112yes—
623C24C23×D1111yescharacteristic
624C2×Q8—228no—
625C2×Q8—444no—
626C2×Q8—444no—
627C2×Q8—4416no—
628C2×D4—28no—
629C2×D4—28no—
630C2×D4—28no—
631C2×D4—416no—
632C2×D4—228no—
633C2×D4—228no—
634C2×D4—228no—
635C2×D4—228no—
636C2×D4—444no—
637C2×D4—444no—
638C2×D4—4416no—
639C2×D4—4416no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—28no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—416no—
659C22×C4—114no—
660C22×C4—114no—
661C22×C4—112no—
662C22×C4—112no—
663C22×C4—1116no—
664C22×C4—112no—
665C22×C4—112no—
666C22×C4—112no—
667C22×C4—112no—
668C22×C4—112no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—228no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4—222no—
679C22×C4—222no—
680C22×C4—222no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—4416no—
690C22×C4—444no—
691C22×C4—444no—
692C22×C4—444no—
693C22×C4—444no—
694C22×C4—4416no—
695C22×C4C23×D1112yes—
696C22×C4C23×D1112yes—
697C22×C4C23×D1112yes—
698C22×C4C23×D1112yes—
699C22×C4C23×D1112yes—
700C4⋊C4—228no—
701C4⋊C4—228no—
702C4⋊C4—228no—
703C4⋊C4—228no—
704C22⋊C4—28no—
705C22⋊C4—44no—
706C22⋊C4—44no—
707C22⋊C4—228no—
708C22⋊C4—228no—
709C22⋊C4—228no—
710C22⋊C4—444no—
711C22⋊C4—444no—
712C22⋊C4—444no—
713C22⋊C4—444no—
714C22⋊C4—444no—
715C22⋊C4—444no—
716C11C2×#263911yescharacteristic, complemented, Sylow
717C23—28no—
718C23—28no—
719C23—28no—
720C23—28no—
721C23—28no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—28no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—222no—
746C23—222no—
747C23—222no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23—444no—
753C23—444no—
754C23—444no—
755C23#66938116yes—
756C23C2×#433914yes—
757C23C2×#433912yes—
758C23C2×D4×D1114yes—
759C23C2×D4×D1112yes—
760C23C2×#434114yes—
761C23C2×#434112yes—
762C23#6703712yes—
763C23#6703712yes—
764C23#6704212yes—
765C23#6704312yes—
766C23C24×D1111yescharacteristic
767Q8—4416no—
768D4—416no—
769D4—4416no—
770D4—4416no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—416no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—114no—
793C2×C4—114no—
794C2×C4—228no—
795C2×C4—228no—
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—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—222no—
812C2×C4—222no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—4416no—
816C2×C4—4416no—
817C2×C4—444no—
818C2×C4—444no—
819C2×C4—444no—
820C2×C4—444no—
821C2×C4—444no—
822C22—24no—
823C22—24no—
824C22—24no—
825C22—24no—
826C22—24no—
827C22—24no—
828C22—232no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—88no—
837C22—442no—
838C22—442no—
839C22—442no—
840C22—442no—
841C22—442no—
842C22—442no—
843C22—442no—
844C22—888no—
845C22C2×#6693818yes—
846C22C2×#6693814yes—
847C22#1062309114yes—
848C22#1062309514yes—
849C22#1062312414yes—
850C22#1062312814yes—
851C22#1062313614yes—
852C22#1062319614yes—
853C22C22×#433911yescharacteristic
854C22C22×D4×D1111yescharacteristic
855C22C22×#434111yescharacteristic
856C22C2×#6703711yescharacteristic
857C22C2×#6703711yescharacteristic
858C22C2×#6704211yescharacteristic
859C22C2×#6704311yescharacteristic
860C4—42no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—224no—
866C4—224no—
867C4—442no—
868C4—442no—
869C4—442no—
870C4—442no—
871C4—442no—
872C2—28no—
873C2—82no—
874C2—882no—
875C2#1307454618yesdirect product factor
876C2C22×#6693811yescharacteristic
877C2C2×#1062313611yescharacteristic
878C2C2×#1062312811yescharacteristic
879C2C2×#1062309111yescharacteristic
880C2C2×#1062312411yescharacteristic
881C2C2×#1062309511yescharacteristic
882C2C2×#1062319611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC22×#66992C2
hypercenterC2×#386D11
hypocenterC11C2×#2639
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#66931C2semidirect
3. #13074546C2direct (N × H)
4. C2×#10622273C2semidirect
5. C2×#10622271C2semidirect
6. C2×#10622288C2semidirect
7. C2×#10622565C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622572C2semidirect
10. C2×#10622286C2semidirect
11. C2×#10622560C2semidirect
12. C2×#10622833C2semidirect
13. C2×#10622826C2semidirect
14. C2×#10622571C2semidirect
15. C22×C11⋊#95C2semidirect
16. C2×C11×#386C2semidirect
43. C2×#66931C22semidirect
44. C11×#386C22semidirect
47. #10622833C22semidirect
48. #10622826C22semidirect
59. C2×C11⋊#95C22semidirect
60. #10622574C22semidirect
61. #10622572C22semidirect
62. #10622571C22semidirect
63. #10622565C22semidirect
64. #10622560C22semidirect
65. #10622288C22semidirect
66. #10622286C22semidirect
67. #10622273C22semidirect
68. #10622271C22semidirect
290. C2×#386D11semidirect
435. #386C2×D11semidirect
590. C2×C11#2639semidirect
716. C11C2×#2639semidirect
875. C2#13074546direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669312
C22×#669922
#130745462
C2×#106222732
C2×#106222712
C2×#106222882
C2×#106225652
C2×#106225742
C2×#106225722
C2×#106222862
C2×#106225602
C2×#106228332
C2×#106228262
C2×#106225712
C22×C11⋊#952
C2×C11×#3862
C2×#263911