Finite Group Databasebeta

← C2×#13073973 #14924986

Subgroups — C2×#13073973 #14924986

Order 2816.

3222 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66940C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic
3#13073973C2116yesmaximal, direct product factor
4C2×#10622562C211yesmaximal, characteristic, complemented
5C2×#10622605C211yesmaximal, characteristic, complemented
6C2×#10622286C211yesmaximal, characteristic, complemented
7C2×#10622560C211yesmaximal, characteristic, complemented
8C2×#10622570C211yesmaximal, characteristic
9C2×#10622570C211yesmaximal, characteristic
10C2×#10622260C211yesmaximal, characteristic, complemented
11C2×#10622585C211yesmaximal, characteristic, complemented
12C2×#10622281C211yesmaximal, characteristic, complemented
13C2×#10622823C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, characteristic, complemented
15C2×#10622263C211yesmaximal, characteristic, complemented
16C2×C11×#385C211yesmaximal, characteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C2×C4×C22⋊D11—28no—
29C2×C4×C22⋊D11C2218yes—
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×#66940—28no—
47C2×#66940C2218yescomplemented
48C11×#385C2218yescomplemented
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51#10622823C2218yescomplemented
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58#10622605C2218yescomplemented
59#10622602C2218yescomplemented
60#10622585C2218yescomplemented
61#10622570C2218yes—
62#10622570C2218yes—
63#10622562C2218yescomplemented
64#10622560C2218yescomplemented
65#10622286C2218yescomplemented
66#10622281C2218yescomplemented
67#10622263C2218yescomplemented
68#10622260C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C23×C4×C11—24no—
72C23×C4×C11—42no—
73C23×C4×C11—42no—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2314yes—
81C22×C22⋊D11—24no—
82C22×C22⋊D11—24no—
83C22×C22⋊D11Q818yescomplemented
84C22×C22⋊D11C2314yes—
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C22×C4×D11—24no—
93C22×C4×D11—42no—
94C22×C4×D11—42no—
95C22×C4×D11C2314yes—
96C22×Dic22—24no—
97C22×Dic22—24no—
98C22×Dic22—24no—
99C22×Dic22C2314yes—
100C2×C11×C4⋊C4—24no—
101C2×C11×C4⋊C4—42no—
102C2×C11×C4⋊C4C2314yes—
103C2×C11×C4⋊C4C2314yes—
104C2×C11×C22⋊C4—24no—
105C2×C11×C22⋊C4—42no—
106C2×C11×C22⋊C4C2314yes—
107C2×C11×C22⋊C4C2314yes—
108C2×C22⋊Dic11—24no—
109C2×C22⋊Dic11—24no—
110C2×C22⋊Dic11—42no—
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—24no—
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—42no—
126C2×C4⋊Dic11C2314yes—
127C2×Dic11⋊C4—24no—
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⋊C4C2314yes—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×C4×Dic11—24no—
142C2×C4×Dic11—24no—
143C2×C4×Dic11D418yes—
144C2×C4×Dic11C2314yes—
145C2×C4×Dic11C2314yes—
146C2×C4×Dic11C2314yes—
147#66940—232no—
148C11×#95C2314yes—
149C11×#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C2×#2580—111nomaximal, Sylow
157C24×C11—22no—
158C24×C11—22no—
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11C2×Q814yes—
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—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
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—28no—
191C22×C4×C11—44no—
192C22×C4×C11—44no—
193C22×C4×C11—416no—
194C22×C4×C11C2×D414yes—
195C22×C4×C11#4114yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2412yes—
202C2×C22⋊D11—232no—
203C2×C22⋊D11—28no—
204C2×C22⋊D11—28no—
205C2×C22⋊D11C2×Q8116yescomplemented
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
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×Dic11C2×D414yes—
223C22×Dic11C2×D414yes—
224C22×Dic11C2×Q814yes—
225C22×Dic11#4114yes—
226C22×Dic11#4114yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C2×C4×D11—28no—
235C2×C4×D11—44no—
236C2×C4×D11—44no—
237C2×C4×D11—416no—
238C2×Dic22—232no—
239C2×Dic22—28no—
240C2×Dic22—28no—
241C2×Dic22—28no—
242C11×C4⋊C4—28no—
243C11×C4⋊C4—44no—
244C11×C22⋊C4—28no—
245C11×C22⋊C4—44no—
246C22⋊Dic11—28no—
247C22⋊Dic11—28no—
248C22⋊Dic11—44no—
249(C2×D11)⋊C4—28no—
250(C2×D11)⋊C4—28no—
251(C2×D11)⋊C4—28no—
252(C2×D11)⋊C4—44no—
253(C2×D11)⋊C4—44no—
254C4⋊Dic11—44no—
255Dic11⋊C4—28no—
256Dic11⋊C4—28no—
257Dic11⋊C4—28no—
258Dic11⋊C4—28no—
259Dic11⋊C4—28no—
260Dic11⋊C4—44no—
261Dic11⋊C4—44no—
262C4×Dic11—28no—
263C4×Dic11—28no—
264C4×Dic11C2×D4116yes—
265C22×C4×Q8—111no—
266C22×C4×D4—111no—
267#2580—1116no—
268C2×#399—111no—
269C2×#399—111no—
270C2×#393—111no—
271C2×#393—111no—
272C2×#390—111no—
273C2×#390—111no—
274C2×#389—111no—
275C2×#389—111no—
276C2×#385—111no—
277C2×#385—111no—
278C2×#385—111no—
279C2×#385D1111yescharacteristic, complemented
280C2×#382—111no—
281C23×C11—28no—
282C23×C11—28no—
283C23×C11—28no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—44no—
291C23×C11—44no—
292C23×C11—44no—
293C23×C11—44no—
294C23×C11C22×D412yes—
295C23×C11C22×Q814yes—
296C23×C11C22×Q812yes—
297C23×C11C2×#4112yes—
298C23×C11C2×#4112yes—
299C23×C11C2×#4112yes—
300C23×C11H(5,𝔽2)12yes—
301C23×C11H(5,𝔽2)12yes—
302C23×C11C2511yescharacteristic
303C22×D11—28no—
304C22×D11—28no—
305C22×D11—28no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—44no—
313C22×D11—44no—
314C22×D11—44no—
315C22×D11—44no—
316C22×D11C22×Q814yes—
317C2×C4×C11—28no—
318C2×C4×C11—28no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
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—416no—
336C2×C4×C11—44no—
337C2×C4×C11—44no—
338C2×C4×C11—44no—
339C2×C4×C11—44no—
340C2×C4×C11C22×D414yes—
341C2×C4×C11C2×#4114yes—
342C22⋊D11—232no—
343C2×Dic11—28no—
344C2×Dic11—28no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
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—44no—
362C2×Dic11—44no—
363C2×Dic11—44no—
364C2×Dic11—44no—
365C2×Dic11C22⋊Q8116yes—
366C2×Dic11C22×D414yes—
367C2×Dic11C22×D414yes—
368C2×Dic11C22×Q814yes—
369C2×Dic11C2×#4114yes—
370C2×Dic11C2×#4114yes—
371C4×D11—416no—
372Dic22—232no—
373C23×Q8—111no—
374C23×D4—111no—
375C24×C4—111no—
376C24×C4C2×D1111yescharacteristic
377C2×C4×Q8—118no—
378C2×C4×Q8—228no—
379C2×C4×D4—118no—
380C2×C4×D4—228no—
381C22×C4⋊C4—111no—
382C22×C4⋊C4—111no—
383C22×C4⋊C4—111no—
384C22×C4⋊C4—111no—
385C22×C4⋊C4—111no—
386C22×C4⋊C4—111no—
387C22×C4⋊C4—111no—
388C22×C4⋊C4—111no—
389C22×C4⋊C4C2×D1111yescharacteristic
390C22×C4⋊C4C2×D1111yescharacteristic
391C22×C22⋊C4—111no—
392C22×C22⋊C4—111no—
393C22×C22⋊C4—111no—
394C22×C22⋊C4—111no—
395C22×C22⋊C4—111no—
396C22×C22⋊C4—111no—
397C22×C22⋊C4—111no—
398C22×C22⋊C4—111no—
399C22×C22⋊C4C2×D1111yescharacteristic
400C22×C22⋊C4C2×D1111yescharacteristic
401C22×C42—111no—
402C22×C42—111no—
403C22×C42—111no—
404#399—118no—
405#399—118no—
406#393—118no—
407#393—118no—
408#390—118no—
409#390—118no—
410#389—118no—
411#389—118no—
412#385—118no—
413#385—118no—
414#385—118no—
415#385C2×D1118yescomplemented
416#382—118no—
417C2×#95—111no—
418C2×#95—111no—
419C2×#95—111no—
420C2×#95—111no—
421C2×#95—111no—
422C2×#95—111no—
423C2×#95C2×D1111yescharacteristic
424C2×#95C2×D1111yescharacteristic
425C22×C11—24no—
426C22×C11—24no—
427C22×C11—24no—
428C22×C11—416no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11C2×C22⋊Q814yes—
434C22×C11#52514yes—
435C22×C11#53514yes—
436C22×C11#55414yes—
437C22×C11#55414yes—
438C22×C11#55914yes—
439C22×C11#55914yes—
440C22×C11C23×D411yescharacteristic
441C22×C11C23×Q811yescharacteristic
442C22×C11C22×#4111yescharacteristic
443C22×C11C22×#4111yescharacteristic
444C22×C11C22×#4111yescharacteristic
445C22×C11C2×H(5,𝔽2)11yescharacteristic
446C22×C11C2×H(5,𝔽2)11yescharacteristic
447C2×D11—24no—
448C2×D11—24no—
449C2×D11—24no—
450C2×D11—416no—
451C2×D11—42no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—42no—
455C4×C11—24no—
456C4×C11—24no—
457C4×C11—42no—
458C4×C11—42no—
459C4×C11—42no—
460C4×C11—42no—
461Dic11—24no—
462Dic11—24no—
463Dic11—42no—
464Dic11—42no—
465Dic11—42no—
466Dic11—42no—
467Dic11C2×C22⋊Q818yes—
468C25—111no—
469C25C22×D1111yescharacteristic
470C22×Q8—114no—
471C22×Q8—224no—
472C22×Q8—224no—
473C22×Q8—224no—
474C22×D4—118no—
475C22×D4—114no—
476C22×D4—224no—
477C22×D4—224no—
478C23×C4—24no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4—111no—
482C23×C4—111no—
483C23×C4—111no—
484C23×C4—111no—
485C23×C4—111no—
486C23×C4—111no—
487C23×C4—111no—
488C23×C4—114no—
489C23×C4—224no—
490C23×C4—442no—
491C23×C4—442no—
492C23×C4C22×D1111yescharacteristic
493C23×C4C22×D1111yescharacteristic
494C23×C4C22×D1111yescharacteristic
495C23×C4C22×D1111yescharacteristic
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C23×C4C22×D1114yes—
499C4×Q8—2232no—
500C4×D4—2232no—
501C2×C4⋊C4—24no—
502C2×C4⋊C4—42no—
503C2×C4⋊C4—114no—
504C2×C4⋊C4—114no—
505C2×C4⋊C4—114no—
506C2×C4⋊C4—114no—
507C2×C4⋊C4—114no—
508C2×C4⋊C4—114no—
509C2×C4⋊C4—114no—
510C2×C4⋊C4—114no—
511C2×C4⋊C4—224no—
512C2×C4⋊C4—224no—
513C2×C4⋊C4—224no—
514C2×C4⋊C4—224no—
515C2×C4⋊C4—224no—
516C2×C4⋊C4—442no—
517C2×C4⋊C4—442no—
518C2×C4⋊C4—442no—
519C2×C4⋊C4C22×D1114yes—
520C2×C4⋊C4C22×D1114yes—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—114no—
524C2×C22⋊C4—114no—
525C2×C22⋊C4—114no—
526C2×C22⋊C4—114no—
527C2×C22⋊C4—114no—
528C2×C22⋊C4—114no—
529C2×C22⋊C4—114no—
530C2×C22⋊C4—114no—
531C2×C22⋊C4—224no—
532C2×C22⋊C4—224no—
533C2×C22⋊C4—224no—
534C2×C22⋊C4—224no—
535C2×C22⋊C4—224no—
536C2×C22⋊C4—442no—
537C2×C22⋊C4—442no—
538C2×C22⋊C4—442no—
539C2×C22⋊C4C22×D1114yes—
540C2×C22⋊C4C22×D1114yes—
541C2×C42—118no—
542C2×C42—114no—
543C2×C42—114no—
544C2×C42—114no—
545C2×C42—224no—
546C2×C42—224no—
547#95—114no—
548#95—114no—
549#95—114no—
550#95—114no—
551#95—114no—
552#95—114no—
553#95C22×D1114yes—
554#95C22×D1114yes—
555C2×C11—44no—
556C2×C11#258018yescomplemented
557C2×C11C22×C22⋊Q811yescharacteristic
558C2×C11C2×#52511yescharacteristic
559C2×C11C2×#53511yescharacteristic
560C2×C11C2×#55411yescharacteristic
561C2×C11C2×#55411yescharacteristic
562C2×C11C2×#55911yescharacteristic
563C2×C11C2×#55911yescharacteristic
564D11—44no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—114no—
572C24—112no—
573C24—222no—
574C24—222no—
575C24—222no—
576C24—222no—
577C24—222no—
578C24—222no—
579C24Q8×D1114yes—
580C24C23×D1112yes—
581C24C23×D1111yescharacteristic
582C2×Q8—228no—
583C2×Q8—228no—
584C2×Q8—2232no—
585C2×Q8—228no—
586C2×D4—1116no—
587C2×D4—228no—
588C2×D4—2232no—
589C2×D4—228no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—28no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—416no—
610C22×C4—114no—
611C22×C4—114no—
612C22×C4—114no—
613C22×C4—112no—
614C22×C4—114no—
615C22×C4—114no—
616C22×C4—112no—
617C22×C4—112no—
618C22×C4—112no—
619C22×C4—112no—
620C22×C4—112no—
621C22×C4—112no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—222no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—222no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—228no—
639C22×C4—444no—
640C22×C4—444no—
641C22×C4—4416no—
642C22×C4#433914yes—
643C22×C4D4×D1114yes—
644C22×C4C23×D1112yes—
645C22×C4C23×D1112yes—
646C22×C4C23×D1112yes—
647C22×C4C23×D1112yes—
648C22×C4C23×D1112yes—
649C22×C4C23×D1112yes—
650C4⋊C4—28no—
651C4⋊C4—44no—
652C4⋊C4—228no—
653C4⋊C4—228no—
654C4⋊C4—228no—
655C4⋊C4—228no—
656C4⋊C4—228no—
657C4⋊C4—444no—
658C4⋊C4—444no—
659C4⋊C4—444no—
660C22⋊C4—28no—
661C22⋊C4—44no—
662C22⋊C4—228no—
663C22⋊C4—228no—
664C22⋊C4—228no—
665C22⋊C4—228no—
666C22⋊C4—228no—
667C22⋊C4—444no—
668C22⋊C4—444no—
669C22⋊C4—444no—
670C42—1116no—
671C42—228no—
672C42—228no—
673C11C2×#258011yescharacteristic, complemented, Sylow
674C23—28no—
675C23—28no—
676C23—28no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—114no—
688C23—228no—
689C23—228no—
690C23—228no—
691C23—222no—
692C23—222no—
693C23—222no—
694C23—222no—
695C23—222no—
696C23—222no—
697C23—444no—
698C23—444no—
699C23—444no—
700C23—444no—
701C23C2×#433912yes—
702C23C2×D4×D1112yes—
703C23#6703712yes—
704C23#6703712yes—
705C23C2×Q8×D1114yes—
706C23C2×Q8×D1112yes—
707C23#41×D1112yes—
708C23#41×D1112yes—
709C23C24×D1111yescharacteristic
710Q8—2232no—
711D4—2232no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
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—416no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—1116no—
736C2×C4—114no—
737C2×C4—114no—
738C2×C4—114no—
739C2×C4—114no—
740C2×C4—114no—
741C2×C4—228no—
742C2×C4—228no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—222no—
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—4416no—
760C2×C4—444no—
761C2×C4—444no—
762C2×C4—444no—
763C2×C4—444no—
764C2×C4C2×#433914yes—
765C2×C4C2×D4×D1114yes—
766C22—24no—
767C22—24no—
768C22—24no—
769C22—42no—
770C22—416no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—224no—
775C22—224no—
776C22—224no—
777C22—442no—
778C22—4416no—
779C22—442no—
780C22—442no—
781C22—442no—
782C22#1062304214yes—
783C22#1062307814yes—
784C22#1062309014yes—
785C22#1062312314yes—
786C22D11×C22⋊Q814yes—
787C22#1062316714yes—
788C22#1062319514yes—
789C22C22×#433911yescharacteristic
790C22C22×D4×D1111yescharacteristic
791C22C2×#6703711yescharacteristic
792C22C2×#6703711yescharacteristic
793C22C22×Q8×D1111yescharacteristic
794C22C2×#41×D1111yescharacteristic
795C22C2×#41×D1111yescharacteristic
796C4—24no—
797C4—24no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—118no—
803C4—224no—
804C4—224no—
805C4—442no—
806C4—442no—
807C4—442no—
808C4—442no—
809C2—44no—
810C2—444no—
811C2#1307397318yesdirect product factor
812C2C2×D11×C22⋊Q811yescharacteristic
813C2C2×#1062307811yescharacteristic
814C2C2×#1062312311yescharacteristic
815C2C2×#1062316711yescharacteristic
816C2C2×#1062304211yescharacteristic
817C2C2×#1062309011yescharacteristic
818C2C2×#1062319511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#385C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#385D11
hypocenterC11C2×#2580
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#66940C2semidirect
3. #13073973C2direct (N × H)
4. C2×#10622562C2semidirect
5. C2×#10622605C2semidirect
6. C2×#10622286C2semidirect
7. C2×#10622560C2semidirect
10. C2×#10622260C2semidirect
11. C2×#10622585C2semidirect
12. C2×#10622281C2semidirect
13. C2×#10622823C2semidirect
14. C2×#10622602C2semidirect
15. C2×#10622263C2semidirect
16. C2×C11×#385C2semidirect
47. C2×#66940C22semidirect
48. C11×#385C22semidirect
51. #10622823C22semidirect
58. #10622605C22semidirect
59. #10622602C22semidirect
60. #10622585C22semidirect
63. #10622562C22semidirect
64. #10622560C22semidirect
65. #10622286C22semidirect
66. #10622281C22semidirect
67. #10622263C22semidirect
68. #10622260C22semidirect
83. C22×C22⋊D11Q8semidirect
205. C2×C22⋊D11C2×Q8semidirect
279. C2×#385D11semidirect
415. #385C2×D11semidirect
556. C2×C11#2580semidirect
673. C11C2×#2580semidirect
811. C2#13073973direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669402
C22×C4×C22⋊D112
#130739732
C2×#106225622
C2×#106226052
C2×#106222862
C2×#106225602
C2×#106225702
C2×#106222602
C2×#106225852
C2×#106222812
C2×#106228232
C2×#106226022
C2×#106222632
C2×C11×#3852
C2×#258011