Finite Group Databasebeta

← C2×#13072440 #14921527

Subgroups — C2×#13072440 #14921527

Order 2816.

3374 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic
3#13072440C2116yesmaximal, direct product factor
4C2×#10622271C211yesmaximal, characteristic, complemented
5C2×#10622270C211yesmaximal, characteristic, complemented
6C2×#10622289C211yesmaximal, characteristic, complemented
7C2×#10622286C211yesmaximal, characteristic, complemented
8C2×#10622259C211yesmaximal, characteristic, complemented
9C2×#10622265C211yesmaximal, characteristic, complemented
10C2×#10622826C211yesmaximal, characteristic
11C2×#10622826C211yesmaximal, characteristic
12C2×#10622281C211yesmaximal, characteristic, complemented
13C2×#10622823C211yesmaximal, characteristic, complemented
14C2×#10622823C211yesmaximal, characteristic, complemented
15C2×#10622280C211yesmaximal, characteristic, complemented
16C22×C11×#95C211yesmaximal, characteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×Dic22C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C2×C4×C22⋊D11—28no—
27C2×C4×C22⋊D11C2218yes—
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C2×#66977—28no—
35C2×#66977C2218yescomplemented
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2218yescomplemented
49#10622826C2218yes—
50#10622826C2218yes—
51#10622823C2218yescomplemented
52#10622823C2218yescomplemented
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622289C2218yescomplemented
62#10622286C2218yescomplemented
63#10622281C2218yescomplemented
64#10622280C2218yescomplemented
65#10622271C2218yescomplemented
66#10622270C2218yescomplemented
67#10622265C2218yescomplemented
68#10622259C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C23×C4×C11—24no—
72C23×C4×C11—24no—
73C23×C4×C11—24no—
74C23×C4×C11—24no—
75C23×C4×C11—24no—
76C23×C4×C11—42no—
77C23×C4×C11—42no—
78C23×C4×C11—42no—
79C23×C4×C11—42no—
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2314yes—
85C23×C4×C11C2314yes—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2314yes—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11Q818yescomplemented
92C22×C22⋊D11C2314yes—
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C22×C4×D11—24no—
101C22×C4×D11—24no—
102C22×C4×D11—42no—
103C22×C4×D11C2314yes—
104C22×Dic22—24no—
105C22×Dic22—24no—
106C22×Dic22—42no—
107C22×Dic22C2314yes—
108C2×C22⋊Dic11—24no—
109C2×C22⋊Dic11—24no—
110C2×C22⋊Dic11D418yes—
111C2×C22⋊Dic11C2314yes—
112C2×C22⋊Dic11C2314yes—
113C2×C22⋊Dic11C2314yes—
114C4×C22⋊D11—232no—
115C2×(C2×D11)⋊C4—24no—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4—42no—
118C2×(C2×D11)⋊C4—42no—
119C2×(C2×D11)⋊C4—42no—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×C4⋊Dic11—24no—
126C2×C4⋊Dic11C2314yes—
127#66977—232no—
128C2×Dic11⋊C4—24no—
129C2×Dic11⋊C4—24no—
130C2×Dic11⋊C4—24no—
131C2×Dic11⋊C4—24no—
132C2×Dic11⋊C4—42no—
133C2×Dic11⋊C4—42no—
134C2×Dic11⋊C4—42no—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×C4×Dic11—24no—
143C2×C4×Dic11C2314yes—
144C11×#95C2314yes—
145C11×#95C2314yes—
146C11×#95C2314yes—
147C11×#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C2×#2450—111nomaximal, Sylow
157C24×C11—22no—
158C24×C11—22no—
159C24×C11—22no—
160C24×C11—22no—
161C24×C11C2×D414yes—
162C24×C11C2×Q814yes—
163C24×C11#4114yes—
164C24×C11C2412yes—
165C24×C11C2411yescharacteristic
166C23×D11—22no—
167C23×D11—22no—
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—22no—
172C23×D11C2×Q814yes—
173C23×D11C2412yes—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—28no—
181C22×C4×C11—28no—
182C22×C4×C11—28no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—28no—
194C22×C4×C11—28no—
195C22×C4×C11—44no—
196C22×C4×C11—44no—
197C22×C4×C11—44no—
198C22×C4×C11—44no—
199C22×C4×C11—416no—
200C22×C4×C11—416no—
201C22×C4×C11—416no—
202C22×C4×C11#4114yes—
203C22×C4×C11#4114yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C2×C22⋊D11—232no—
211C2×C22⋊D11—28no—
212C2×C22⋊D11—28no—
213C2×C22⋊D11C2×Q8116yescomplemented
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
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×Dic11—22no—
232C22×Dic11C2×D414yes—
233C22×Dic11C2×D414yes—
234C22×Dic11C2×Q814yes—
235C22×Dic11C2412yes—
236C22×Dic11C2412yes—
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C2×C4×D11—28no—
243C2×C4×D11—28no—
244C2×C4×D11—44no—
245C2×C4×D11—416no—
246C2×Dic22—28no—
247C2×Dic22—28no—
248C2×Dic22—44no—
249C2×Dic22—416no—
250C22⋊Dic11—28no—
251C22⋊Dic11—28no—
252C22⋊Dic11C2×D4116yes—
253(C2×D11)⋊C4—28no—
254(C2×D11)⋊C4—28no—
255(C2×D11)⋊C4—44no—
256(C2×D11)⋊C4—44no—
257(C2×D11)⋊C4—44no—
258C4⋊Dic11—28no—
259Dic11⋊C4—28no—
260Dic11⋊C4—28no—
261Dic11⋊C4—28no—
262Dic11⋊C4—28no—
263Dic11⋊C4—44no—
264Dic11⋊C4—44no—
265Dic11⋊C4—44no—
266C4×Dic11—28no—
267C22×C22⋊Q8—111no—
268C22×C4×D4—111no—
269#2450—1116no—
270C2×#400—111no—
271C2×#398—111no—
272C2×#396—111no—
273C2×#393—111no—
274C2×#391—111no—
275C2×#387—111no—
276C2×#386—111no—
277C2×#386—111no—
278C2×#385—111no—
279C2×#385—111no—
280C2×#385—111no—
281C2×#380—111no—
282C22×#95D1111yescharacteristic, complemented
283C23×C11—28no—
284C23×C11—28no—
285C23×C11—28no—
286C23×C11—28no—
287C23×C11—28no—
288C23×C11—28no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11C22⋊Q8116yes—
294C23×C11C22×D414yes—
295C23×C11C22×D412yes—
296C23×C11C22×Q814yes—
297C23×C11C22×Q812yes—
298C23×C11C2×#4114yes—
299C23×C11C2×#4112yes—
300C23×C11C2×#4112yes—
301C23×C11C2×#4112yes—
302C23×C11H(5,𝔽2)12yes—
303C23×C11H(5,𝔽2)12yes—
304C23×C11C2511yescharacteristic
305C22×D11—28no—
306C22×D11—28no—
307C22×D11—28no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—44no—
315C22×D11—44no—
316C22×D11—44no—
317C22×D11—44no—
318C22×D11C22×Q814yes—
319C2×C4×C11—28no—
320C2×C4×C11—28no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—416no—
338C2×C4×C11—416no—
339C2×C4×C11—416no—
340C2×C4×C11—44no—
341C2×C4×C11—44no—
342C2×C4×C11—44no—
343C2×C4×C11—44no—
344C2×C4×C11C2×#4114yes—
345C2×C4×C11C2×#4114yes—
346C22⋊D11—232no—
347C2×Dic11—28no—
348C2×Dic11—28no—
349C2×Dic11—28no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—44no—
369C2×Dic11—44no—
370C2×Dic11—44no—
371C2×Dic11—44no—
372C2×Dic11C22×D414yes—
373C2×Dic11C22×D414yes—
374C2×Dic11C22×Q814yes—
375C4×D11—416no—
376Dic22—416no—
377C23×Q8—111no—
378C23×D4—111no—
379C24×C4—111no—
380C24×C4C2×D1111yescharacteristic
381C24×C4C2×D1111yescharacteristic
382C24×C4C2×D1111yescharacteristic
383C2×C22⋊Q8—118no—
384C2×C22⋊Q8—228no—
385C2×C4×D4—118no—
386C2×C4×D4—228no—
387C22×C4⋊C4—111no—
388C22×C4⋊C4—111no—
389C22×C4⋊C4—111no—
390C22×C4⋊C4—111no—
391C22×C4⋊C4—111no—
392C22×C4⋊C4—111no—
393C22×C4⋊C4—111no—
394C22×C4⋊C4—111no—
395C22×C22⋊C4—111no—
396C22×C22⋊C4—111no—
397C22×C22⋊C4—111no—
398C22×C22⋊C4—111no—
399C22×C22⋊C4—111no—
400C22×C22⋊C4—111no—
401C22×C22⋊C4—111no—
402C22×C22⋊C4—111no—
403C22×C42—111no—
404#400—118no—
405#398—118no—
406#396—118no—
407#393—118no—
408#391—118no—
409#387—118no—
410#386—118no—
411#386—118no—
412#385—118no—
413#385—118no—
414#385—118no—
415#380—118no—
416C2×#95—111no—
417C2×#95—111no—
418C2×#95—111no—
419C2×#95—111no—
420C2×#95—111no—
421C2×#95—111no—
422C2×#95—111no—
423C2×#95—111no—
424C2×#95C2×D1111yescharacteristic
425C2×#95C2×D1111yescharacteristic
426C2×#95C2×D1111yescharacteristic
427C2×#95C2×D1111yescharacteristic
428C2×#95C2×D1118yescomplemented
429C22×C11—24no—
430C22×C11—24no—
431C22×C11—24no—
432C22×C11—24no—
433C22×C11—24no—
434C22×C11—24no—
435C22×C11—232no—
436C22×C11C2×C22⋊Q818yes—
437C22×C11C2×C22⋊Q814yes—
438C22×C11#52914yes—
439C22×C11#53814yes—
440C22×C11#54614yes—
441C22×C11#54614yes—
442C22×C11#55414yes—
443C22×C11#55414yes—
444C22×C11C23×D411yescharacteristic
445C22×C11C23×Q811yescharacteristic
446C22×C11C22×#4111yescharacteristic
447C22×C11C22×#4111yescharacteristic
448C22×C11C22×#4111yescharacteristic
449C22×C11C2×H(5,𝔽2)11yescharacteristic
450C22×C11C2×H(5,𝔽2)11yescharacteristic
451C2×D11—24no—
452C2×D11—24no—
453C2×D11—24no—
454C2×D11—42no—
455C2×D11—42no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—416no—
459C4×C11—24no—
460C4×C11—24no—
461C4×C11—42no—
462C4×C11—42no—
463C4×C11—42no—
464C4×C11—42no—
465Dic11—24no—
466Dic11—24no—
467Dic11—24no—
468Dic11—42no—
469Dic11—42no—
470Dic11—42no—
471Dic11—42no—
472C25—111no—
473C25C22×D1111yescharacteristic
474C22×Q8—114no—
475C22×Q8—224no—
476C22×Q8—224no—
477C22×Q8—442no—
478C22×D4—118no—
479C22×D4—114no—
480C22×D4—224no—
481C22×D4—224no—
482C23×C4—24no—
483C23×C4—24no—
484C23×C4—24no—
485C23×C4—24no—
486C23×C4—24no—
487C23×C4—42no—
488C23×C4—42no—
489C23×C4—42no—
490C23×C4—42no—
491C23×C4—111no—
492C23×C4—111no—
493C23×C4—111no—
494C23×C4—111no—
495C23×C4—111no—
496C23×C4—111no—
497C23×C4—111no—
498C23×C4—114no—
499C23×C4—224no—
500C23×C4—224no—
501C23×C4—442no—
502C23×C4C22×D1111yescharacteristic
503C23×C4C22×D1111yescharacteristic
504C23×C4C22×D1111yescharacteristic
505C23×C4C22×D1111yescharacteristic
506C23×C4C22×D1114yes—
507C23×C4C22×D1114yes—
508C23×C4C22×D1111yescharacteristic
509C23×C4C22×D1111yescharacteristic
510C23×C4C22×D1114yes—
511C22⋊Q8—2232no—
512C4×D4—2232no—
513C2×C4⋊C4—114no—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—114no—
517C2×C4⋊C4—114no—
518C2×C4⋊C4—114no—
519C2×C4⋊C4—114no—
520C2×C4⋊C4—114no—
521C2×C4⋊C4—224no—
522C2×C4⋊C4—224no—
523C2×C4⋊C4—224no—
524C2×C4⋊C4—224no—
525C2×C4⋊C4—224no—
526C2×C4⋊C4—442no—
527C2×C4⋊C4—442no—
528C2×C4⋊C4—442no—
529C2×C22⋊C4—118no—
530C2×C22⋊C4—114no—
531C2×C22⋊C4—114no—
532C2×C22⋊C4—114no—
533C2×C22⋊C4—114no—
534C2×C22⋊C4—114no—
535C2×C22⋊C4—114no—
536C2×C22⋊C4—114no—
537C2×C22⋊C4—114no—
538C2×C22⋊C4—224no—
539C2×C22⋊C4—224no—
540C2×C22⋊C4—224no—
541C2×C22⋊C4—224no—
542C2×C22⋊C4—442no—
543C2×C22⋊C4—442no—
544C2×C22⋊C4—442no—
545C2×C42—114no—
546C2×C42—224no—
547#95—114no—
548#95—114no—
549#95—114no—
550#95—114no—
551#95—114no—
552#95—114no—
553#95—114no—
554#95—114no—
555#95C22×D1114yes—
556#95C22×D1114yes—
557#95C22×D1114yes—
558#95C22×D1114yes—
559C2×C11—28no—
560C2×C11#245018yescomplemented
561C2×C11C22×C22⋊Q811yescharacteristic
562C2×C11C2×#52911yescharacteristic
563C2×C11C2×#53811yescharacteristic
564C2×C11C2×#54611yescharacteristic
565C2×C11C2×#54611yescharacteristic
566C2×C11C2×#55411yescharacteristic
567C2×C11C2×#55411yescharacteristic
568D11—44no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—114no—
574C24—112no—
575C24—222no—
576C24—222no—
577C24—222no—
578C24—222no—
579C24—222no—
580C24—222no—
581C24#433914yes—
582C24D4×D1114yes—
583C24Q8×D1114yes—
584C24C23×D1112yes—
585C24C23×D1111yescharacteristic
586C2×Q8—228no—
587C2×Q8—228no—
588C2×Q8—444no—
589C2×Q8—4416no—
590C2×D4—1116no—
591C2×D4—2232no—
592C2×D4—228no—
593C2×D4—228no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—28no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—28no—
614C22×C4—28no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—416no—
620C22×C4—416no—
621C22×C4—416no—
622C22×C4—114no—
623C22×C4—114no—
624C22×C4—114no—
625C22×C4—112no—
626C22×C4—112no—
627C22×C4—112no—
628C22×C4—112no—
629C22×C4—112no—
630C22×C4—112no—
631C22×C4—112no—
632C22×C4—228no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—222no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—222no—
648C22×C4—222no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4—228no—
652C22×C4—444no—
653C22×C4—4416no—
654C22×C4#433914yes—
655C22×C4#433914yes—
656C22×C4C23×D1112yes—
657C22×C4C23×D1112yes—
658C22×C4C23×D1112yes—
659C22×C4C23×D1112yes—
660C22×C4C23×D1112yes—
661C22×C4C23×D1112yes—
662C4⋊C4—228no—
663C4⋊C4—228no—
664C4⋊C4—228no—
665C4⋊C4—228no—
666C4⋊C4—228no—
667C4⋊C4—444no—
668C4⋊C4—444no—
669C4⋊C4—444no—
670C22⋊C4—1116no—
671C22⋊C4—228no—
672C22⋊C4—228no—
673C22⋊C4—228no—
674C22⋊C4—228no—
675C22⋊C4—444no—
676C22⋊C4—444no—
677C22⋊C4—444no—
678C42—228no—
679C11C2×#245011yescharacteristic, complemented, Sylow
680C23—28no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—114no—
691C23—228no—
692C23—228no—
693C23—228no—
694C23—222no—
695C23—222no—
696C23—222no—
697C23—222no—
698C23—222no—
699C23—222no—
700C23—444no—
701C23—444no—
702C23—444no—
703C23—444no—
704C23#66949116yes—
705C23C2×#433914yes—
706C23C2×#433912yes—
707C23C2×#433912yes—
708C23C2×#433912yes—
709C23C2×D4×D1114yes—
710C23C2×D4×D1112yes—
711C23#6703712yes—
712C23#6703712yes—
713C23C2×Q8×D1114yes—
714C23C2×Q8×D1112yes—
715C23C24×D1111yescharacteristic
716Q8—4416no—
717D4—2232no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—416no—
737C2×C4—416no—
738C2×C4—416no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—114no—
744C2×C4—114no—
745C2×C4—114no—
746C2×C4—228no—
747C2×C4—228no—
748C2×C4—228no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—4416no—
768C2×C4—444no—
769C2×C4—444no—
770C2×C4—444no—
771C2×C4—444no—
772C2×C4C2×#433914yes—
773C2×C4C2×#433914yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—232no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—224no—
782C22—224no—
783C22—224no—
784C22—442no—
785C22—4416no—
786C22—442no—
787C22—442no—
788C22—442no—
789C22#1062301014yes—
790C22#1062302114yes—
791C22#1062302114yes—
792C22#1062302514yes—
793C22C2×#6694918yes—
794C22C2×#6694914yes—
795C22#1062304214yes—
796C22#1062304214yes—
797C22C22×#433911yescharacteristic
798C22C22×#433911yescharacteristic
799C22C22×#433911yescharacteristic
800C22C22×D4×D1111yescharacteristic
801C22C2×#6703711yescharacteristic
802C22C2×#6703711yescharacteristic
803C22C22×Q8×D1111yescharacteristic
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—224no—
811C4—224no—
812C4—224no—
813C4—442no—
814C4—442no—
815C4—442no—
816C4—442no—
817C2—28no—
818C2—444no—
819C2#1307244018yesdirect product factor
820C2C22×#6694911yescharacteristic
821C2C2×#1062301011yescharacteristic
822C2C2×#1062302511yescharacteristic
823C2C2×#1062302111yescharacteristic
824C2C2×#1062302111yescharacteristic
825C2C2×#1062304211yescharacteristic
826C2C2×#1062304211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#95C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22×#95D11
hypocenterC11C2×#2450
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
1. C22×#66977C2semidirect
3. #13072440C2direct (N × H)
4. C2×#10622271C2semidirect
5. C2×#10622270C2semidirect
6. C2×#10622289C2semidirect
7. C2×#10622286C2semidirect
8. C2×#10622259C2semidirect
9. C2×#10622265C2semidirect
12. C2×#10622281C2semidirect
13. C2×#10622823C2semidirect
14. C2×#10622823C2semidirect
15. C2×#10622280C2semidirect
16. C22×C11×#95C2semidirect
35. C2×#66977C22semidirect
48. C2×C11×#95C22semidirect
51. #10622823C22semidirect
52. #10622823C22semidirect
61. #10622289C22semidirect
62. #10622286C22semidirect
63. #10622281C22semidirect
64. #10622280C22semidirect
65. #10622271C22semidirect
66. #10622270C22semidirect
67. #10622265C22semidirect
68. #10622259C22semidirect
91. C22×C22⋊D11Q8semidirect
213. C2×C22⋊D11C2×Q8semidirect
282. C22×#95D11semidirect
428. C2×#95C2×D11semidirect
560. C2×C11#2450semidirect
679. C11C2×#2450semidirect
819. C2#13072440direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669772
C22×C4×C22⋊D112
#130724402
C2×#106222712
C2×#106222702
C2×#106222892
C2×#106222862
C2×#106222592
C2×#106222652
C2×#106228262
C2×#106222812
C2×#106228232
C2×#106222802
C22×C11×#952
C2×#245011