Finite Group Databasebeta

← C2×#13074426 #14920117

Subgroups — C2×#13074426 #14920117

Order 2816.

4142 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D11C211yesmaximal, characteristic
3#13074426C2116yesmaximal, direct product factor
4C2×#10622562C211yesmaximal, characteristic, complemented
5C2×#10622605C211yesmaximal, characteristic, complemented
6C2×#10622561C211yesmaximal, characteristic, complemented
7C2×#10622607C211yesmaximal, characteristic, complemented
8C2×#10622607C211yesmaximal, characteristic, complemented
9C2×#10622286C211yesmaximal, characteristic, complemented
10C2×#10622560C211yesmaximal, characteristic, complemented
11C2×#10622281C211yesmaximal, characteristic, complemented
12C2×#10622602C211yesmaximal, characteristic, complemented
13C2×#10622600C211yesmaximal, characteristic, complemented
14C2×#10622568C211yesmaximal, characteristic
15C2×#10622568C211yesmaximal, characteristic
16C2×C11×#396C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×Dic22C2211yescharacteristic, complemented
21C22×C11×C4⋊C4C2211yescharacteristic, complemented
22C22×C11×C4⋊C4C2211yescharacteristic, complemented
23C22×C11×C4⋊C4C2211yescharacteristic, complemented
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic, complemented
41C22×C4⋊Dic11C2211yescharacteristic, complemented
42C22×Dic11⋊C4C2211yescharacteristic, complemented
43C22×Dic11⋊C4C2211yescharacteristic, complemented
44C22×Dic11⋊C4C2211yescharacteristic, complemented
45C22×Dic11⋊C4C2211yescharacteristic, complemented
46C2×#66949—28no—
47C2×#66949C2218yescomplemented
48C2×C22⋊C4×D11—28no—
49C2×C22⋊C4×D11C2218yes—
50C11×#396C2218yescomplemented
51C2×C11×#95C2211yescharacteristic, complemented
52C2×C11⋊#95C2211yescharacteristic, complemented
53C2×C11⋊#95C2211yescharacteristic, complemented
54C2×C11⋊#95C2211yescharacteristic, complemented
55C2×C11⋊#95C2211yescharacteristic, complemented
56C2×C11⋊#95C2211yescharacteristic, complemented
57#10622607C2218yescomplemented
58#10622607C2218yescomplemented
59#10622605C2218yescomplemented
60#10622602C2218yescomplemented
61#10622600C2218yescomplemented
62#10622568C2218yes—
63#10622568C2218yes—
64#10622562C2218yescomplemented
65#10622561C2218yescomplemented
66#10622560C2218yescomplemented
67#10622286C2218yescomplemented
68#10622281C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11—24no—
71C24×D11—24no—
72C24×D11—42no—
73C24×D11—42no—
74C24×D11—42no—
75C24×D11—42no—
76C24×D11Q818yescomplemented
77C24×D11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C24×D11C2314yes—
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
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×D11—42no—
96C22×C4×D11—42no—
97C22×C4×D11D418yes—
98C22×C4×D11C2314yes—
99C22×C4×D11C2314yes—
100C22×Dic22—24no—
101C22×Dic22—42no—
102C22×Dic22—42no—
103C22×Dic22C2314yescomplemented
104C2×C11×C4⋊C4—24no—
105C2×C11×C4⋊C4—42no—
106C2×C11×C4⋊C4—42no—
107C2×C11×C4⋊C4C2314yescomplemented
108C2×C11×C4⋊C4C2314yescomplemented
109C2×C11×C4⋊C4C2314yescomplemented
110C2×C11×C22⋊C4—24no—
111C2×C11×C22⋊C4—42no—
112C2×C11×C22⋊C4—42no—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—42no—
118C2×C22⋊Dic11—42no—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
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—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×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×C4⋊Dic11—42no—
143C2×C4⋊Dic11—42no—
144C2×C4⋊Dic11C2314yescomplemented
145C2×C4⋊Dic11C2314yescomplemented
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4—42no—
149C2×Dic11⋊C4—42no—
150C2×Dic11⋊C4C2314yescomplemented
151C2×Dic11⋊C4C2314yescomplemented
152C2×Dic11⋊C4C2314yescomplemented
153C2×Dic11⋊C4C2314yescomplemented
154#66949—232no—
155C22⋊C4×D11—232no—
156C11×#95C2314yescomplemented
157C11⋊#95C2314yescomplemented
158C11⋊#95C2314yescomplemented
159C11⋊#95C2314yescomplemented
160C11⋊#95C2314yescomplemented
161C11⋊#95C2314yescomplemented
162C2×#2626—111nomaximal, Sylow
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11C2×Q814yes—
170C24×C11C2412yes—
171C24×C11C2411yescharacteristic
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—232no—
183C23×D11—28no—
184C23×D11—28no—
185C23×D11—416no—
186C23×D11—416no—
187C23×D11—44no—
188C23×D11—44no—
189C23×D11—44no—
190C23×D11—44no—
191C23×D11—416no—
192C23×D11—416no—
193C23×D11—416no—
194C23×D11—416no—
195C23×D11C2×D414yes—
196C23×D11C2×Q814yes—
197C23×D11C2×Q814yes—
198C23×D11C2×Q8116yescomplemented
199C23×D11#4114yes—
200C23×D11C2412yes—
201C23×D11C2412yes—
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×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11C2×D414yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
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—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11C2×D414yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C2×C4×D11—28no—
251C2×C4×D11—416no—
252C2×C4×D11—44no—
253C2×C4×D11—44no—
254C2×C4×D11—44no—
255C2×C4×D11—44no—
256C2×C4×D11—416no—
257C2×C4×D11C2×D4116yes—
258C2×Dic22—28no—
259C2×Dic22—44no—
260C2×Dic22—44no—
261C2×Dic22—416no—
262C11×C4⋊C4—28no—
263C11×C4⋊C4—44no—
264C11×C4⋊C4—44no—
265C11×C22⋊C4—28no—
266C11×C22⋊C4—44no—
267C11×C22⋊C4—44no—
268C22⋊Dic11—28no—
269C22⋊Dic11—44no—
270C22⋊Dic11—44no—
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—44no—
278(C2×D11)⋊C4—44no—
279(C2×D11)⋊C4—44no—
280(C2×D11)⋊C4—44no—
281C4⋊Dic11—44no—
282C4⋊Dic11—44no—
283Dic11⋊C4—28no—
284Dic11⋊C4—28no—
285Dic11⋊C4—44no—
286Dic11⋊C4—44no—
287C22×C22⋊Q8—111no—
288C23×C22⋊C4—111no—
289#2626—1116no—
290C2×#399—111no—
291C2×#399—111no—
292C2×#396—111no—
293C2×#396—111no—
294C2×#396—111no—
295C2×#396D1111yescharacteristic, complemented
296C2×#393—111no—
297C2×#393—111no—
298C2×#385—111no—
299C2×#385—111no—
300C2×#380—111no—
301C2×#379—111no—
302C2×#379—111no—
303C23×C11—28no—
304C23×C11—28no—
305C23×C11—28no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11C22×D412yes—
317C23×C11C22×Q814yes—
318C23×C11C22×Q812yes—
319C23×C11C2×#4112yes—
320C23×C11H(5,𝔽2)12yes—
321C23×C11H(5,𝔽2)12yes—
322C23×C11H(5,𝔽2)12yes—
323C23×C11H(5,𝔽2)12yes—
324C23×C11C2511yescharacteristic
325C22×D11—28no—
326C22×D11—28no—
327C22×D11—28no—
328C22×D11—28no—
329C22×D11—28no—
330C22×D11—28no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—28no—
336C22×D11—28no—
337C22×D11—28no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—232no—
345C22×D11—416no—
346C22×D11—416no—
347C22×D11—4128no—
348C22×D11—416no—
349C22×D11—416no—
350C22×D11—416no—
351C22×D11—416no—
352C22×D11—44no—
353C22×D11—44no—
354C22×D11—44no—
355C22×D11—44no—
356C22×D11C22⋊Q8116yes—
357C22×D11C22×D414yes—
358C22×D11C22×Q814yes—
359C22×D11C22×Q814yes—
360C22×D11C2×#4114yes—
361C2×C4×C11—28no—
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—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—44no—
380C2×C4×C11—44no—
381C2×C4×C11—44no—
382C2×C4×C11—44no—
383C2×C4×C11—44no—
384C2×C4×C11C22×D414yes—
385C2×Dic11—28no—
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—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—44no—
404C2×Dic11—44no—
405C2×Dic11—44no—
406C2×Dic11—44no—
407C2×Dic11—44no—
408C2×Dic11C22×D414yes—
409C4×D11—416no—
410C4×D11—416no—
411Dic22—416no—
412C26—111no—
413C23×Q8—111no—
414C24×C4—111no—
415C24×C4—111no—
416C2×C22⋊Q8—118no—
417C2×C22⋊Q8—228no—
418C22×C4⋊C4—111no—
419C22×C4⋊C4—111no—
420C22×C4⋊C4—111no—
421C22×C4⋊C4—111no—
422C22×C4⋊C4—111no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4C2×D1111yescharacteristic, complemented
425C22×C4⋊C4C2×D1111yescharacteristic, complemented
426C22×C4⋊C4C2×D1111yescharacteristic, complemented
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⋊C4—111no—
438C22×C22⋊C4—111no—
439C22×C22⋊C4—111no—
440C22×C22⋊C4—118no—
441C22×C22⋊C4—228no—
442C22×C22⋊C4C2×D1111yescharacteristic
443C22×C22⋊C4C2×D1111yescharacteristic
444C22×C22⋊C4C2×D1111yescharacteristic
445#399—118no—
446#399—118no—
447#396—118no—
448#396—118no—
449#396—118no—
450#396C2×D1118yescomplemented
451#393—118no—
452#393—118no—
453#385—118no—
454#385—118no—
455#380—118no—
456#379—118no—
457#379—118no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95—111no—
461C2×#95—111no—
462C2×#95—111no—
463C2×#95C2×D1111yescharacteristic, complemented
464C22×C11—24no—
465C22×C11—24no—
466C22×C11—24no—
467C22×C11—416no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11C2×C22⋊Q814yes—
473C22×C11#53414yes—
474C22×C11#53514yes—
475C22×C11#53814yes—
476C22×C11#53814yes—
477C22×C11#54314yes—
478C22×C11#54314yes—
479C22×C11C23×D411yescharacteristic
480C22×C11C23×Q811yescharacteristic
481C22×C11C22×#4111yescharacteristic
482C22×C11C2×H(5,𝔽2)11yescharacteristic
483C22×C11C2×H(5,𝔽2)11yescharacteristic
484C22×C11C2×H(5,𝔽2)11yescharacteristic
485C22×C11C2×H(5,𝔽2)11yescharacteristic
486C2×D11—232no—
487C2×D11—24no—
488C2×D11—24no—
489C2×D11—24no—
490C2×D11—24no—
491C2×D11—24no—
492C2×D11—24no—
493C2×D11—24no—
494C2×D11—24no—
495C2×D11—24no—
496C2×D11—464no—
497C2×D11—416no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11C2×C22⋊Q818yes—
503C4×C11—24no—
504C4×C11—42no—
505C4×C11—42no—
506C4×C11—42no—
507C4×C11—42no—
508C4×C11—42no—
509Dic11—24no—
510Dic11—42no—
511Dic11—42no—
512Dic11—42no—
513Dic11—42no—
514Dic11—42no—
515C25—111no—
516C25—111no—
517C25—118no—
518C25—114no—
519C25—224no—
520C25—224no—
521C25—442no—
522C25—442no—
523C25—442no—
524C25—442no—
525C25C22×D1111yescharacteristic
526C22×Q8—114no—
527C22×Q8—224no—
528C22×Q8—442no—
529C22×Q8—442no—
530C23×C4—111no—
531C23×C4—118no—
532C23×C4—114no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—114no—
539C23×C4—224no—
540C23×C4—442no—
541C23×C4—442no—
542C23×C4—442no—
543C23×C4—442no—
544C23×C4C22×D1111yescharacteristic
545C23×C4C22×D1111yescharacteristic
546C23×C4C22×D1111yescharacteristic
547C23×C4C22×D1111yescharacteristic
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550C22⋊Q8—2232no—
551C2×C4⋊C4—24no—
552C2×C4⋊C4—42no—
553C2×C4⋊C4—42no—
554C2×C4⋊C4—114no—
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—442no—
563C2×C4⋊C4—442no—
564C2×C4⋊C4—442no—
565C2×C4⋊C4—442no—
566C2×C4⋊C4C22×D1114yescomplemented
567C2×C4⋊C4C22×D1114yescomplemented
568C2×C4⋊C4C22×D1114yescomplemented
569C2×C22⋊C4—24no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
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—114no—
583C2×C22⋊C4—114no—
584C2×C22⋊C4—114no—
585C2×C22⋊C4—2232no—
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—442no—
594C2×C22⋊C4—442no—
595C2×C22⋊C4—442no—
596C2×C22⋊C4—442no—
597C2×C22⋊C4—442no—
598C2×C22⋊C4—442no—
599C2×C22⋊C4C22×D1114yes—
600C2×C22⋊C4C22×D1114yes—
601C2×C22⋊C4C22×D1114yes—
602#95—114no—
603#95—114no—
604#95—114no—
605#95—114no—
606#95—114no—
607#95C22×D1114yescomplemented
608C2×C11—44no—
609C2×C11#262618yescomplemented
610C2×C11C22×C22⋊Q811yescharacteristic
611C2×C11C2×#53411yescharacteristic
612C2×C11C2×#53511yescharacteristic
613C2×C11C2×#53811yescharacteristic
614C2×C11C2×#53811yescharacteristic
615C2×C11C2×#54311yescharacteristic
616C2×C11C2×#54311yescharacteristic
617D11—28no—
618D11—44no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—114no—
626C24—114no—
627C24—114no—
628C24—112no—
629C24—114no—
630C24—112no—
631C24—1116no—
632C24—228no—
633C24—2232no—
634C24—228no—
635C24—222no—
636C24—222no—
637C24—222no—
638C24—222no—
639C24—222no—
640C24—222no—
641C24—222no—
642C24—222no—
643C24—222no—
644C24—222no—
645C24—4416no—
646C24—4416no—
647C24—444no—
648C24—444no—
649C24—444no—
650C24—444no—
651C24—4416no—
652C24—4416no—
653C24—4416no—
654C24—4416no—
655C24Q8×D1114yes—
656C24C23×D1112yes—
657C24C23×D1111yescharacteristic
658C2×Q8—228no—
659C2×Q8—444no—
660C2×Q8—444no—
661C2×Q8—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—22no—
679C22×C4—114no—
680C22×C4—112no—
681C22×C4—1116no—
682C22×C4—112no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—112no—
686C22×C4—112no—
687C22×C4—228no—
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—222no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—222no—
703C22×C4—222no—
704C22×C4—222no—
705C22×C4—4416no—
706C22×C4—444no—
707C22×C4—444no—
708C22×C4—444no—
709C22×C4—444no—
710C22×C4—4416no—
711C22×C4D4×D1114yes—
712C22×C4C23×D1112yes—
713C22×C4C23×D1112yes—
714C22×C4C23×D1112yes—
715C22×C4C23×D1112yes—
716C22×C4C23×D1112yes—
717C22×C4C23×D1112yes—
718C4⋊C4—28no—
719C4⋊C4—44no—
720C4⋊C4—44no—
721C4⋊C4—228no—
722C4⋊C4—228no—
723C4⋊C4—444no—
724C4⋊C4—444no—
725C4⋊C4—444no—
726C4⋊C4—444no—
727C22⋊C4—28no—
728C22⋊C4—44no—
729C22⋊C4—44no—
730C22⋊C4—228no—
731C22⋊C4—228no—
732C22⋊C4—228no—
733C22⋊C4—228no—
734C22⋊C4—228no—
735C22⋊C4—228no—
736C22⋊C4—228no—
737C22⋊C4—444no—
738C22⋊C4—444no—
739C22⋊C4—444no—
740C22⋊C4—444no—
741C22⋊C4—444no—
742C22⋊C4—444no—
743C11C2×#262611yescharacteristic, complemented, Sylow
744C23—28no—
745C23—28no—
746C23—28no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—1116no—
758C23—114no—
759C23—114no—
760C23—114no—
761C23—114no—
762C23—2232no—
763C23—228no—
764C23—228no—
765C23—228no—
766C23—228no—
767C23—228no—
768C23—228no—
769C23—222no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—228no—
774C23—228no—
775C23—228no—
776C23—222no—
777C23—222no—
778C23—222no—
779C23—222no—
780C23—222no—
781C23—222no—
782C23—4416no—
783C23—4416no—
784C23—4416no—
785C23—4416no—
786C23—4416no—
787C23—4416no—
788C23—44128no—
789C23—444no—
790C23—444no—
791C23—444no—
792C23—444no—
793C23C2×D4×D1112yes—
794C23#6703712yes—
795C23#6703712yes—
796C23C2×Q8×D1114yes—
797C23C2×Q8×D1112yes—
798C23#41×D1112yes—
799C23#6704212yes—
800C23#6704212yes—
801C23C24×D1111yescharacteristic
802Q8—4416no—
803C2×C4—28no—
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—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—114no—
827C2×C4—228no—
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—222no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—222no—
841C2×C4—222no—
842C2×C4—222no—
843C2×C4—222no—
844C2×C4—222no—
845C2×C4—4416no—
846C2×C4—4416no—
847C2×C4—444no—
848C2×C4—444no—
849C2×C4—444no—
850C2×C4—444no—
851C2×C4—444no—
852C2×C4C2×D4×D1114yes—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—416no—
861C22—118no—
862C22—224no—
863C22—224no—
864C22—224no—
865C22—224no—
866C22—224no—
867C22—224no—
868C22—2232no—
869C22—224no—
870C22—224no—
871C22—224no—
872C22—4464no—
873C22—442no—
874C22—442no—
875C22—442no—
876C22—442no—
877C22—4416no—
878C22#1062313614yes—
879C22#1062313814yes—
880C22#1062314414yes—
881C22D11×C22⋊Q814yes—
882C22#1062316514yes—
883C22#1062316514yes—
884C22#1062323514yes—
885C22C22×D4×D1111yescharacteristic
886C22C2×#6703711yescharacteristic
887C22C2×#6703711yescharacteristic
888C22C22×Q8×D1111yescharacteristic
889C22C2×#41×D1111yescharacteristic
890C22C2×#6704211yescharacteristic
891C22C2×#6704211yescharacteristic
892C4—24no—
893C4—42no—
894C4—42no—
895C4—42no—
896C4—42no—
897C4—42no—
898C4—224no—
899C4—442no—
900C4—442no—
901C4—442no—
902C4—442no—
903C4—442no—
904C2—44no—
905C2—228no—
906C2—444no—
907C2#1307442618yesdirect product factor
908C2C2×D11×C22⋊Q811yescharacteristic
909C2C2×#1062313611yescharacteristic
910C2C2×#1062313811yescharacteristic
911C2C2×#1062314411yescharacteristic
912C2C2×#1062323511yescharacteristic
913C2C2×#1062316511yescharacteristic
914C2C2×#1062316511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#396C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#396D11
hypocenterC11C2×#2626
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#66949C2semidirect
3. #13074426C2direct (N × H)
4. C2×#10622562C2semidirect
5. C2×#10622605C2semidirect
6. C2×#10622561C2semidirect
7. C2×#10622607C2semidirect
8. C2×#10622607C2semidirect
9. C2×#10622286C2semidirect
10. C2×#10622560C2semidirect
11. C2×#10622281C2semidirect
12. C2×#10622602C2semidirect
13. C2×#10622600C2semidirect
16. C2×C11×#396C2semidirect
20. C23×Dic22C22semidirect
21. C22×C11×C4⋊C4C22semidirect
22. C22×C11×C4⋊C4C22semidirect
23. C22×C11×C4⋊C4C22semidirect
40. C22×C4⋊Dic11C22semidirect
41. C22×C4⋊Dic11C22semidirect
42. C22×Dic11⋊C4C22semidirect
43. C22×Dic11⋊C4C22semidirect
44. C22×Dic11⋊C4C22semidirect
45. C22×Dic11⋊C4C22semidirect
47. C2×#66949C22semidirect
50. C11×#396C22semidirect
51. C2×C11×#95C22semidirect
52. C2×C11⋊#95C22semidirect
53. C2×C11⋊#95C22semidirect
54. C2×C11⋊#95C22semidirect
55. C2×C11⋊#95C22semidirect
56. C2×C11⋊#95C22semidirect
57. #10622607C22semidirect
58. #10622607C22semidirect
59. #10622605C22semidirect
60. #10622602C22semidirect
61. #10622600C22semidirect
64. #10622562C22semidirect
65. #10622561C22semidirect
66. #10622560C22semidirect
67. #10622286C22semidirect
68. #10622281C22semidirect
76. C24×D11Q8semidirect
103. C22×Dic22C23semidirect
107. C2×C11×C4⋊C4C23semidirect
108. C2×C11×C4⋊C4C23semidirect
109. C2×C11×C4⋊C4C23semidirect
144. C2×C4⋊Dic11C23semidirect
145. C2×C4⋊Dic11C23semidirect
150. C2×Dic11⋊C4C23semidirect
151. C2×Dic11⋊C4C23semidirect
152. C2×Dic11⋊C4C23semidirect
153. C2×Dic11⋊C4C23semidirect
156. C11×#95C23semidirect
157. C11⋊#95C23semidirect
158. C11⋊#95C23semidirect
159. C11⋊#95C23semidirect
160. C11⋊#95C23semidirect
161. C11⋊#95C23semidirect
198. C23×D11C2×Q8semidirect
295. C2×#396D11semidirect
424. C22×C4⋊C4C2×D11semidirect
425. C22×C4⋊C4C2×D11semidirect
426. C22×C4⋊C4C2×D11semidirect
450. #396C2×D11semidirect
463. C2×#95C2×D11semidirect
566. C2×C4⋊C4C22×D11semidirect
567. C2×C4⋊C4C22×D11semidirect
568. C2×C4⋊C4C22×D11semidirect
607. #95C22×D11semidirect
609. C2×C11#2626semidirect
743. C11C2×#2626semidirect
907. C2#13074426direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669492
C22×C22⋊C4×D112
#130744262
C2×#106225622
C2×#106226052
C2×#106225612
C2×#106226072
C2×#106222862
C2×#106225602
C2×#106222812
C2×#106226022
C2×#106226002
C2×#106225682
C2×C11×#3962
C2×#262611