Finite Group Databasebeta

← C2×#13071350 #14912596

Subgroups — C2×#13071350 #14912596

Order 2816.

2982 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic
2#13071350C2116yesmaximal, direct product factor
3C2×#10622587C211yesmaximal, characteristic, complemented
4C2×#10622259C211yesmaximal, characteristic, complemented
5C2×#10622585C211yesmaximal, characteristic, complemented
6C2×#10622268C211yesmaximal, characteristic, complemented
7C2×#10622594C211yesmaximal, characteristic, complemented
8C2×#10622546C211yesmaximal, characteristic, complemented
9C2×#10622591C211yesmaximal, characteristic, complemented
10C2×#10622602C211yesmaximal, characteristic
11C2×#10622602C211yesmaximal, characteristic
12C2×#10622600C211yesmaximal, characteristic
13C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
14C2×#10622279C211yesmaximal, characteristic
15C2×D11×#95C211yesmaximal, characteristic
16C2×C11×#389C211yesmaximal, characteristic, complemented
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C2×#66949C4116yescomplemented
39C2×#66949C2218yes—
40C11×#389C2218yescomplemented
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622602C2218yes—
56#10622602C2218yes—
57#10622600C2218yes—
58#10622594C2218yescomplemented
59#10622591C2218yescomplemented
60#10622587C2218yescomplemented
61#10622585C2218yescomplemented
62C4×(C2×D11)⋊C4C2218yes—
63#10622546C2218yescomplemented
64#10622279C2218yes—
65D11×#95C2218yes—
66#10622268C2218yescomplemented
67#10622259C2218yescomplemented
68C24×D11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C22×C4×D11—24no—
84C22×C4×D11—42no—
85C22×C4×D11—42no—
86C22×C4×D11—42no—
87C22×C4×D11—42no—
88C22×C4×D11—42no—
89C22×C4×D11—42no—
90C22×C4×D11C2×C418yes—
91C22×C4×D11Q818yescomplemented
92C22×C4×D11C2314yes—
93C22×C4×D11C2314yes—
94C22×C4×D11C2314yes—
95C22×Dic22—42no—
96C22×Dic22—42no—
97C22×Dic22C2×C418yescomplemented
98C22×Dic22C2314yes—
99C2×C11×C4⋊C4—42no—
100C2×C11×C4⋊C4—42no—
101C2×C11×C4⋊C4—42no—
102C2×C11×C4⋊C4C2×C418yescomplemented
103C2×C11×C4⋊C4C2314yes—
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2314yes—
107C2×C42×C11—42no—
108C2×C42×C11C2314yes—
109C2×(C2×D11)⋊C4—24no—
110C2×(C2×D11)⋊C4—24no—
111C2×(C2×D11)⋊C4C2×C418yes—
112C2×(C2×D11)⋊C4C2×C418yes—
113C2×(C2×D11)⋊C4C2314yes—
114C2×(C2×D11)⋊C4C2314yes—
115C2×(C2×D11)⋊C4C2314yes—
116C2×(C2×D11)⋊C4C2314yes—
117C2×C4⋊Dic11—42no—
118C2×C4⋊Dic11C2314yes—
119C2×Dic11⋊C4—42no—
120C2×Dic11⋊C4—42no—
121C2×Dic11⋊C4C2×C418yescomplemented
122C2×Dic11⋊C4C2×C418yescomplemented
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2314yes—
126C2×Dic11⋊C4C2314yes—
127C2×C4×Dic11—42no—
128C2×C4×Dic11—42no—
129C2×C4×Dic11—42no—
130C2×C4×Dic11C2314yes—
131C2×C4×Dic11C2314yes—
132C2×C4×Dic11C2314yes—
133#66949C2×C4164yescomplemented
134C11×#95C2314yes—
135C11×#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C2×#2329—111nomaximal, Sylow
149C24×C11C2411yescharacteristic
150C23×D11—22no—
151C23×D11—22no—
152C23×D11—22no—
153C23×D11—22no—
154C23×D11C22×C414yes—
155C23×D11C2×Q814yes—
156C23×D11#4114yes—
157C23×D11C2412yes—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11C22×C414yes—
176C22×C4×C11C22×C414yes—
177C22×C4×C11C22×C414yes—
178C22×C4×C11C2×Q814yes—
179C22×C4×C11C2412yes—
180C22×C4×C11C2412yes—
181C22×C4×C11C2412yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2412yes—
185C22×C4×C11C2412yes—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11C22×C414yes—
204C22×Dic11C22×C414yes—
205C22×Dic11C22×C414yes—
206C22×Dic11C2×Q814yes—
207C22×Dic11C2412yes—
208C22×Dic11C2412yes—
209C22×Dic11C2412yes—
210C22×Dic11C2412yes—
211C22×Dic11C2412yes—
212C22×Dic11C2412yes—
213C22×Dic11C2412yes—
214C2×C4×D11—28no—
215C2×C4×D11—416no—
216C2×C4×D11—416no—
217C2×C4×D11—44no—
218C2×C4×D11—44no—
219C2×C4×D11—44no—
220C2×C4×D11—44no—
221C2×C4×D11—44no—
222C2×C4×D11—44no—
223C2×C4×D11—416no—
224C2×C4×D11C22×C4116yes—
225C2×C4×D11C2×Q8116yescomplemented
226C2×Dic22—416no—
227C2×Dic22—44no—
228C2×Dic22—44no—
229C2×Dic22C22×C4116yescomplemented
230C11×C4⋊C4—44no—
231C11×C4⋊C4—44no—
232C11×C4⋊C4—44no—
233C11×C4⋊C4C22×C4116yescomplemented
234C42×C11—44no—
235(C2×D11)⋊C4—28no—
236(C2×D11)⋊C4—28no—
237(C2×D11)⋊C4C22×C4116yes—
238(C2×D11)⋊C4C22×C4116yes—
239C4⋊Dic11—44no—
240Dic11⋊C4—44no—
241Dic11⋊C4—44no—
242Dic11⋊C4C22×C4116yescomplemented
243Dic11⋊C4C22×C4116yescomplemented
244C4×Dic11—44no—
245C4×Dic11—44no—
246C4×Dic11—44no—
247C22×C22⋊Q8—111no—
248#2329—1116no—
249C2×#391—111no—
250C2×#391—111no—
251C2×#389—111no—
252C2×#389D1111yescharacteristic, complemented
253C2×#387—111no—
254C2×#387—111no—
255C2×#387—111no—
256C2×#387—111no—
257C2×#385—111no—
258C2×#385—111no—
259C2×#380—111no—
260C2×C4×C22⋊C4—111no—
261C2×C4×C22⋊C4—111no—
262C22×#95—111no—
263C23×C11C23×C412yes—
264C23×C11C22×Q812yes—
265C23×C11C2×#4112yes—
266C23×C11H(5,𝔽2)12yes—
267C23×C11H(5,𝔽2)12yes—
268C23×C11H(5,𝔽2)12yes—
269C23×C112−1+412yes—
270C23×C11C2511yescharacteristic
271C22×D11—28no—
272C22×D11—28no—
273C22×D11—28no—
274C22×D11—28no—
275C22×D11—28no—
276C22×D11—28no—
277C22×D11—22no—
278C22×D11—22no—
279C22×D11—22no—
280C22×D11—22no—
281C22×D11C4×Q8116yes—
282C22×D11C23×C414yes—
283C22×D11C22×Q814yes—
284C22×D11C2×#4114yes—
285C2×C4×C11—28no—
286C2×C4×C11—28no—
287C2×C4×C11—28no—
288C2×C4×C11—28no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—44no—
307C2×C4×C11—44no—
308C2×C4×C11—44no—
309C2×C4×C11C23×C414yes—
310C2×C4×C11C23×C414yes—
311C2×C4×C11C23×C414yes—
312C2×C4×C11C22×Q814yes—
313C2×Dic11—28no—
314C2×Dic11—28no—
315C2×Dic11—28no—
316C2×Dic11—28no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—44no—
335C2×Dic11—44no—
336C2×Dic11—44no—
337C2×Dic11C23×C414yes—
338C2×Dic11C23×C414yes—
339C2×Dic11C23×C414yes—
340C2×Dic11C22×Q814yes—
341C4×D11—416no—
342C4×D11—416no—
343C4×D11—416no—
344Dic22—416no—
345C23×Q8—111no—
346C24×C4—111no—
347C24×C4—111no—
348C24×C4—111no—
349C2×C22⋊Q8—118no—
350C2×C22⋊Q8—1116no—
351C22×C4⋊C4—111no—
352C22×C4⋊C4—111no—
353C22×C4⋊C4—111no—
354C22×C4⋊C4—111no—
355C22×C4⋊C4—111no—
356C22×C4⋊C4C2×D1111yescharacteristic
357C22×C4⋊C4C2×D1111yescharacteristic
358C22×C4⋊C4C2×D1111yescharacteristic
359C22×C4⋊C4C2×D1111yescharacteristic
360C22×C22⋊C4—111no—
361C22×C22⋊C4—111no—
362C22×C22⋊C4—111no—
363C22×C22⋊C4—111no—
364C22×C42—111no—
365C22×C42—111no—
366C22×C42—111no—
367C22×C42C2×D1111yescharacteristic
368#391—118no—
369#391—118no—
370#389—118no—
371#389C2×D1118yescomplemented
372#387—118no—
373#387—118no—
374#387—118no—
375#387—118no—
376#385—118no—
377#385—118no—
378#380—118no—
379C4×C22⋊C4—118no—
380C4×C22⋊C4—118no—
381C2×#95—111no—
382C2×#95—111no—
383C2×#95—111no—
384C2×#95—111no—
385C2×#95—111no—
386C2×#95—111no—
387C2×#95—111no—
388C2×#95—111no—
389C2×#95—111no—
390C2×#95—111no—
391C2×#95—111no—
392C2×#95—111no—
393C2×#95—118no—
394C2×#95C2×D1111yescharacteristic
395C2×#95C2×D1111yescharacteristic
396C22×C11C2×C4×Q814yes—
397C22×C11#51814yes—
398C22×C11#52014yes—
399C22×C11#53814yes—
400C22×C11#53914yes—
401C22×C11#54314yes—
402C22×C11#54414yes—
403C22×C11C24×C411yescharacteristic
404C22×C11C23×Q811yescharacteristic
405C22×C11C22×#4111yescharacteristic
406C22×C11C2×H(5,𝔽2)11yescharacteristic
407C22×C11C2×H(5,𝔽2)11yescharacteristic
408C22×C11C2×H(5,𝔽2)11yescharacteristic
409C22×C11C2×2−1+411yescharacteristic
410C2×D11—232no—
411C2×D11—24no—
412C2×D11—24no—
413C2×D11—24no—
414C2×D11—24no—
415C2×D11—24no—
416C2×D11—24no—
417C2×D11C2×C4×Q818yes—
418C4×C11—24no—
419C4×C11—24no—
420C4×C11—24no—
421C4×C11—24no—
422C4×C11—42no—
423C4×C11—42no—
424C4×C11—42no—
425Dic11—24no—
426Dic11—24no—
427Dic11—24no—
428Dic11—24no—
429Dic11—42no—
430Dic11—42no—
431Dic11—42no—
432C25—111no—
433C22×Q8—118no—
434C22×Q8—114no—
435C22×Q8—442no—
436C22×Q8—442no—
437C23×C4—111no—
438C23×C4—111no—
439C23×C4—111no—
440C23×C4—111no—
441C23×C4—118no—
442C23×C4—118no—
443C23×C4—114no—
444C23×C4—114no—
445C23×C4—111no—
446C23×C4—111no—
447C23×C4—111no—
448C23×C4—114no—
449C23×C4—224no—
450C23×C4—442no—
451C23×C4—442no—
452C23×C4—442no—
453C23×C4—442no—
454C23×C4—442no—
455C23×C4—442no—
456C23×C4C22×D1111yescharacteristic
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C23×C4C22×D1111yescharacteristic
460C23×C4C22×D1111yescharacteristic
461C23×C4C22×D1111yescharacteristic
462C23×C4C22×D1111yescharacteristic
463C22⋊Q8—1164no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—118no—
468C2×C4⋊C4—118no—
469C2×C4⋊C4—114no—
470C2×C4⋊C4—114no—
471C2×C4⋊C4—114no—
472C2×C4⋊C4—114no—
473C2×C4⋊C4—114no—
474C2×C4⋊C4—442no—
475C2×C4⋊C4—442no—
476C2×C4⋊C4—442no—
477C2×C4⋊C4C4×D1118yescomplemented
478C2×C4⋊C4C22×D1114yes—
479C2×C4⋊C4C22×D1114yes—
480C2×C4⋊C4C22×D1114yes—
481C2×C4⋊C4C22×D1114yes—
482C2×C22⋊C4—118no—
483C2×C22⋊C4—118no—
484C2×C22⋊C4—114no—
485C2×C22⋊C4—114no—
486C2×C22⋊C4—114no—
487C2×C22⋊C4—114no—
488C2×C22⋊C4—224no—
489C2×C22⋊C4—224no—
490C2×C42—42no—
491C2×C42—114no—
492C2×C42—114no—
493C2×C42—114no—
494C2×C42—442no—
495C2×C42—442no—
496C2×C42—442no—
497C2×C42C22×D1114yes—
498#95—114no—
499#95—114no—
500#95—114no—
501#95—114no—
502#95—114no—
503#95—114no—
504#95—114no—
505#95—114no—
506#95—114no—
507#95—114no—
508#95—114no—
509#95—114no—
510#95C22×D1114yes—
511#95C22×D1114yes—
512C2×C11#232918yescomplemented
513C2×C11C22×C4×Q811yescharacteristic
514C2×C11C2×#51811yescharacteristic
515C2×C11C2×#52011yescharacteristic
516C2×C11C2×#53811yescharacteristic
517C2×C11C2×#53911yescharacteristic
518C2×C11C2×#54311yescharacteristic
519C2×C11C2×#54411yescharacteristic
520D11—28no—
521C24—114no—
522C24—114no—
523C24—114no—
524C24—112no—
525C24—222no—
526C24—222no—
527C24—222no—
528C24—222no—
529C24C23×D1111yescharacteristic
530C2×Q8—1116no—
531C2×Q8—4416no—
532C2×Q8—444no—
533C2×Q8—444no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—114no—
552C22×C4—114no—
553C22×C4—114no—
554C22×C4—114no—
555C22×C4—112no—
556C22×C4—112no—
557C22×C4—112no—
558C22×C4—112no—
559C22×C4—1116no—
560C22×C4—1116no—
561C22×C4—112no—
562C22×C4—112no—
563C22×C4—112no—
564C22×C4—228no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—4416no—
583C22×C4—4416no—
584C22×C4—444no—
585C22×C4—444no—
586C22×C4—444no—
587C22×C4—444no—
588C22×C4—444no—
589C22×C4—444no—
590C22×C4—4416no—
591C22×C4C2×C4×D1114yes—
592C22×C4C2×C4×D1114yes—
593C22×C4C2×C4×D1114yes—
594C22×C4Q8×D1114yes—
595C22×C4C23×D1112yes—
596C22×C4C23×D1112yes—
597C22×C4C23×D1112yes—
598C22×C4C23×D1112yes—
599C22×C4C23×D1112yes—
600C22×C4C23×D1112yes—
601C22×C4C23×D1112yes—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—1116no—
606C4⋊C4—1116no—
607C4⋊C4—444no—
608C4⋊C4—444no—
609C4⋊C4—444no—
610C4⋊C4C2×C4×D11116yescomplemented
611C22⋊C4—1116no—
612C22⋊C4—1116no—
613C22⋊C4—228no—
614C22⋊C4—228no—
615C42—44no—
616C42—444no—
617C42—444no—
618C42—444no—
619C11C2×#232911yescharacteristic, complemented, Sylow
620C23—1116no—
621C23—114no—
622C23—114no—
623C23—114no—
624C23—228no—
625C23—228no—
626C23—228no—
627C23—228no—
628C23—228no—
629C23—222no—
630C23—222no—
631C23—222no—
632C23—222no—
633C23—228no—
634C23C22×C4×D1112yes—
635C23#6703712yes—
636C23#6703712yes—
637C23C2×Q8×D1112yes—
638C23#6704012yes—
639C23#41×D1112yes—
640C23#6704212yes—
641C23C24×D1111yescharacteristic
642Q8—4416no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—114no—
668C2×C4—114no—
669C2×C4—114no—
670C2×C4—114no—
671C2×C4—228no—
672C2×C4—228no—
673C2×C4—228no—
674C2×C4—228no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—4416no—
693C2×C4—4416no—
694C2×C4—4416no—
695C2×C4—444no—
696C2×C4—444no—
697C2×C4—444no—
698C2×C4C22×C4×D1114yes—
699C2×C4C22×C4×D1114yes—
700C2×C4C22×C4×D1114yes—
701C2×C4C2×Q8×D1114yes—
702C22—118no—
703C22—224no—
704C22—224no—
705C22—224no—
706C22—224no—
707C22—224no—
708C22—224no—
709C22—2232no—
710C22#1062303514yes—
711C22#1062307614yes—
712C22C4×Q8×D1114yes—
713C22#1062314414yes—
714C22#1062316514yes—
715C22#1062322314yes—
716C22#1062326014yes—
717C22C23×C4×D1111yescharacteristic
718C22C2×#6703711yescharacteristic
719C22C2×#6703711yescharacteristic
720C22C22×Q8×D1111yescharacteristic
721C22C2×#6704011yescharacteristic
722C22C2×#41×D1111yescharacteristic
723C22C2×#6704211yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—224no—
732C4—224no—
733C4—224no—
734C4—224no—
735C4—442no—
736C4—442no—
737C4—442no—
738C2—228no—
739C2#1307135018yesdirect product factor
740C2C2×C4×Q8×D1111yescharacteristic
741C2C2×#1062307611yescharacteristic
742C2C2×#1062303511yescharacteristic
743C2C2×#1062314411yescharacteristic
744C2C2×#1062322311yescharacteristic
745C2C2×#1062316511yescharacteristic
746C2C2×#1062326011yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#389C2
socleC24×C11C24
prime radicalC24×D11C23
cosocleC23×C11C25
hypercenterC2×#389D11
hypocenterC11C2×#2329
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. #13071350C2direct (N × H)
3. C2×#10622587C2semidirect
4. C2×#10622259C2semidirect
5. C2×#10622585C2semidirect
6. C2×#10622268C2semidirect
7. C2×#10622594C2semidirect
8. C2×#10622546C2semidirect
9. C2×#10622591C2semidirect
16. C2×C11×#389C2semidirect
38. C2×#66949C4semidirect
40. C11×#389C22semidirect
58. #10622594C22semidirect
59. #10622591C22semidirect
60. #10622587C22semidirect
61. #10622585C22semidirect
63. #10622546C22semidirect
66. #10622268C22semidirect
67. #10622259C22semidirect
91. C22×C4×D11Q8semidirect
97. C22×Dic22C2×C4semidirect
102. C2×C11×C4⋊C4C2×C4semidirect
121. C2×Dic11⋊C4C2×C4semidirect
122. C2×Dic11⋊C4C2×C4semidirect
133. #66949C2×C4semidirect
225. C2×C4×D11C2×Q8semidirect
229. C2×Dic22C22×C4semidirect
233. C11×C4⋊C4C22×C4semidirect
242. Dic11⋊C4C22×C4semidirect
243. Dic11⋊C4C22×C4semidirect
252. C2×#389D11semidirect
371. #389C2×D11semidirect
477. C2×C4⋊C4C4×D11semidirect
512. C2×C11#2329semidirect
610. C4⋊C4C2×C4×D11semidirect
619. C11C2×#2329semidirect
739. C2#13071350direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669492
#130713502
C2×#106225872
C2×#106222592
C2×#106225852
C2×#106222682
C2×#106225942
C2×#106225462
C2×#106225912
C2×#106226022
C2×#106226002
C2×C4×(C2×D11)⋊C42
C2×#106222792
C2×D11×#952
C2×C11×#3892
C2×#232911