Finite Group Databasebeta

← C2×#13072062 #14921726

Subgroups — C2×#13072062 #14921726

Order 2816.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic, complemented
2C22×#66949C211yesmaximal, characteristic, complemented
3C22×#66946C211yesmaximal, characteristic
4C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
5#13072062C2116yesmaximal, direct product factor
6C2×#10622597C211yesmaximal, characteristic, complemented
7C2×#10622607C211yesmaximal, characteristic, complemented
8C2×#10622607C211yesmaximal, characteristic, complemented
9C2×#10622259C211yesmaximal, characteristic, complemented
10C2×#10622260C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic
12C2×#10622278C211yesmaximal, characteristic
13C2×#10622280C211yesmaximal, characteristic, complemented
14C2×#10622280C211yesmaximal, characteristic, complemented
15C2×#10622600C211yesmaximal, characteristic, complemented
16C2×C11×#398C211yesmaximal, characteristic, complemented
17C23×D44C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×Dic22C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C22×C4⋊Dic11C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×#66949—28no—
45C2×#66949—28no—
46C2×#66949C2218yescomplemented
47C2×#66949C2218yescomplemented
48C2×#66946—28no—
49C2×#66946C2218yes—
50C2×C4⋊C4×D11—28no—
51C2×C4⋊C4×D11C2218yescomplemented
52C11×#398C2218yescomplemented
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#10622607C2218yescomplemented
62#10622607C2218yescomplemented
63#10622600C2218yescomplemented
64#10622597C2218yescomplemented
65#10622280C2218yescomplemented
66#10622280C2218yescomplemented
67#10622278C2218yes—
68#10622278C2218yes—
69#10622260C2218yescomplemented
70#10622259C2218yescomplemented
71C24×D11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C22×D44—24no—
87C22×D44—24no—
88C22×D44Q818yescomplemented
89C22×D44C2314yes—
90C22×C4×D11—24no—
91C22×C4×D11—24no—
92C22×C4×D11—24no—
93C22×C4×D11—24no—
94C22×C4×D11—24no—
95C22×C4×D11—24no—
96C22×C4×D11—24no—
97C22×C4×D11—24no—
98C22×C4×D11—24no—
99C22×C4×D11—42no—
100C22×C4×D11—42no—
101C22×C4×D11D418yes—
102C22×C4×D11C2314yes—
103C22×C4×D11C2314yes—
104C22×C4×D11C2314yes—
105C22×C4×D11C2314yes—
106C22×Dic22—24no—
107C22×Dic22—24no—
108C22×Dic22—24no—
109C22×Dic22C2314yes—
110C2×C11×C4⋊C4—24no—
111C2×C11×C4⋊C4—24no—
112C2×C11×C4⋊C4—24no—
113C2×C11×C4⋊C4—24no—
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C4⋊C4C2314yes—
116C2×C11×C4⋊C4C2314yes—
117C2×C11×C4⋊C4C2314yes—
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4—24no—
120C2×(C2×D11)⋊C4—24no—
121C2×(C2×D11)⋊C4—24no—
122C2×(C2×D11)⋊C4—24no—
123C2×(C2×D11)⋊C4—24no—
124C2×(C2×D11)⋊C4—42no—
125C2×(C2×D11)⋊C4—42no—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×C4⋊Dic11—24no—
135C2×C4⋊Dic11—42no—
136C2×C4⋊Dic11C2314yes—
137C2×C4⋊Dic11C2314yes—
138C2×Dic11⋊C4—24no—
139C2×Dic11⋊C4—24no—
140C2×Dic11⋊C4—24no—
141C2×Dic11⋊C4—24no—
142C2×Dic11⋊C4—42no—
143C2×Dic11⋊C4D418yescomplemented
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×C4×Dic11—24no—
151C2×C4×Dic11C2314yes—
152#66949—232no—
153#66949—232no—
154#66946—232no—
155C4⋊C4×D11—232no—
156C11×#95C2314yes—
157C11×#95C2314yes—
158C11×#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C2×#2417—111nomaximal, Sylow
165C24×C11C2411yescharacteristic
166C23×D11—22no—
167C23×D11—22no—
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—22no—
176C23×D11C2×D414yes—
177C23×D11C2×Q814yes—
178C23×D11C2×Q814yes—
179C23×D11#4114yes—
180C23×D11C2412yes—
181C23×D11C2412yes—
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—22no—
191C22×C4×C11—22no—
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×C11C2×D414yes—
201C22×C4×C11C2×D414yes—
202C22×C4×C11C2×Q814yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
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×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11C2×D414yes—
225C22×Dic11C2×D414yes—
226C22×Dic11C2×D414yes—
227C22×Dic11#4114yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C2×D44—232no—
235C2×D44—28no—
236C2×D44—28no—
237C2×D44C2×Q8116yescomplemented
238C2×C4×D11—232no—
239C2×C4×D11—28no—
240C2×C4×D11—28no—
241C2×C4×D11—28no—
242C2×C4×D11—28no—
243C2×C4×D11—28no—
244C2×C4×D11—28no—
245C2×C4×D11—28no—
246C2×C4×D11—28no—
247C2×C4×D11—28no—
248C2×C4×D11—44no—
249C2×C4×D11—44no—
250C2×C4×D11—416no—
251C2×C4×D11—416no—
252C2×C4×D11—416no—
253C2×C4×D11C2×D4116yes—
254C2×Dic22—28no—
255C2×Dic22—28no—
256C2×Dic22—28no—
257C2×Dic22—416no—
258C11×C4⋊C4—28no—
259C11×C4⋊C4—28no—
260C11×C4⋊C4—28no—
261C11×C4⋊C4—28no—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—28no—
264(C2×D11)⋊C4—28no—
265(C2×D11)⋊C4—28no—
266(C2×D11)⋊C4—28no—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4—44no—
270C4⋊Dic11—28no—
271C4⋊Dic11—44no—
272Dic11⋊C4—28no—
273Dic11⋊C4—28no—
274Dic11⋊C4—28no—
275Dic11⋊C4—28no—
276Dic11⋊C4—44no—
277Dic11⋊C4C2×D4116yescomplemented
278C4×Dic11—28no—
279C22×C22⋊Q8—111no—
280C22×C22⋊Q8—111no—
281C22×C4×D4—111no—
282C23×C4⋊C4—111no—
283#2417—1116no—
284C2×#398—111no—
285C2×#398D1111yescharacteristic, complemented
286C2×#396—111no—
287C2×#396—111no—
288C2×#391—111no—
289C2×#389—111no—
290C2×#386—111no—
291C2×#386—111no—
292C2×#380—111no—
293C2×#380—111no—
294C2×#380—111no—
295C23×C11C22×D412yes—
296C23×C11C22×D412yes—
297C23×C11C22×Q812yes—
298C23×C11C2×#4112yes—
299C23×C11C2×#4112yes—
300C23×C11H(5,𝔽2)12yes—
301C23×C112−1+412yes—
302C23×C11C2511yescharacteristic
303C22×D11—28no—
304C22×D11—28no—
305C22×D11—28no—
306C22×D11—28no—
307C22×D11—28no—
308C22×D11—28no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—28no—
314C22×D11—28no—
315C22×D11—28no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—44no—
323C22×D11—44no—
324C22×D11—44no—
325C22×D11—44no—
326C22×D11C22⋊Q8116yescomplemented
327C22×D11C22×D414yes—
328C22×D11C22×Q814yes—
329C22×D11C22×Q814yes—
330C22×D11C2×#4114yes—
331C2×C4×C11—28no—
332C2×C4×C11—28no—
333C2×C4×C11—28no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
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—44no—
353C2×C4×C11—44no—
354C2×C4×C11—44no—
355C2×C4×C11—44no—
356C2×C4×C11C22×D414yes—
357C2×C4×C11C22×D414yes—
358C2×C4×C11C22×Q814yes—
359C2×Dic11—28no—
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—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—44no—
375C2×Dic11—44no—
376C2×Dic11—44no—
377C2×Dic11—44no—
378C2×Dic11#121116yes—
379C2×Dic11C22×D414yes—
380C2×Dic11C22×D414yes—
381C2×Dic11C22×D414yes—
382C2×Dic11C2×#4114yes—
383D44—232no—
384C4×D11—232no—
385C4×D11—416no—
386C4×D11—416no—
387C4×D11—416no—
388Dic22—416no—
389C23×Q8—111no—
390C23×D4—111no—
391C24×C4—111no—
392C24×C4—111no—
393C24×C4—111no—
394C24×C4—111no—
395C2×C22⋊Q8—118no—
396C2×C22⋊Q8—118no—
397C2×C22⋊Q8—228no—
398C2×C22⋊Q8—228no—
399C2×C4×D4—118no—
400C2×C4×D4—228no—
401C22×C4⋊C4—111no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4—111no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407C22×C4⋊C4—111no—
408C22×C4⋊C4—111no—
409C22×C4⋊C4—118no—
410C22×C4⋊C4—228no—
411C22×C4⋊C4C2×D1111yescharacteristic
412C22×C4⋊C4C2×D1111yescharacteristic
413C22×C4⋊C4C2×D1111yescharacteristic
414C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
422C22×C22⋊C4—111no—
423C22×C42—111no—
424#398—118no—
425#398C2×D1118yescomplemented
426#396—118no—
427#396—118no—
428#391—118no—
429#389—118no—
430#386—118no—
431#386—118no—
432#380—118no—
433#380—118no—
434#380—118no—
435C2×#95—111no—
436C2×#95—111no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95C2×D1111yescharacteristic
441C2×#95C2×D1111yescharacteristic
442C2×#95C2×D1111yescharacteristic
443C22×C11C2×#12114yes—
444C22×C11C2×C22⋊Q814yes—
445C22×C11#53714yes—
446C22×C11#54614yes—
447C22×C11D4×Q814yes—
448C22×C11#55214yes—
449C22×C11#55414yes—
450C22×C11C23×D411yescharacteristic
451C22×C11C23×D411yescharacteristic
452C22×C11C23×Q811yescharacteristic
453C22×C11C22×#4111yescharacteristic
454C22×C11C22×#4111yescharacteristic
455C22×C11C2×H(5,𝔽2)11yescharacteristic
456C22×C11C2×2−1+411yescharacteristic
457C2×D11—24no—
458C2×D11—232no—
459C2×D11—24no—
460C2×D11—24no—
461C2×D11—24no—
462C2×D11—24no—
463C2×D11—24no—
464C2×D11—24no—
465C2×D11—24no—
466C2×D11—24no—
467C2×D11—42no—
468C2×D11—416no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11C2×C22⋊Q818yescomplemented
473C4×C11—24no—
474C4×C11—24no—
475C4×C11—24no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11—42no—
479C4×C11—42no—
480Dic11—24no—
481Dic11—42no—
482Dic11—42no—
483Dic11—42no—
484Dic11—42no—
485Dic11C2×#12118yes—
486C25—111no—
487C25—111no—
488C22×Q8—114no—
489C22×Q8—224no—
490C22×Q8—224no—
491C22×Q8—224no—
492C22×D4—118no—
493C22×D4—114no—
494C22×D4—224no—
495C22×D4—224no—
496C23×C4—111no—
497C23×C4—111no—
498C23×C4—118no—
499C23×C4—114no—
500C23×C4—111no—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4—114no—
505C23×C4—114no—
506C23×C4—114no—
507C23×C4—224no—
508C23×C4—224no—
509C23×C4—224no—
510C23×C4—224no—
511C23×C4—224no—
512C23×C4—224no—
513C23×C4—224no—
514C23×C4—224no—
515C23×C4—224no—
516C23×C4—442no—
517C23×C4—442no—
518C23×C4C22×D1111yescharacteristic
519C23×C4C22×D1111yescharacteristic
520C23×C4C22×D1111yescharacteristic
521C23×C4C22×D1111yescharacteristic
522C23×C4C22×D1111yescharacteristic
523C23×C4C22×D1111yescharacteristic
524C23×C4C22×D1111yescharacteristic
525C22⋊Q8—2232no—
526C22⋊Q8—2232no—
527C4×D4—2232no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—24no—
530C2×C4⋊C4—24no—
531C2×C4⋊C4—24no—
532C2×C4⋊C4—118no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—114no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—2232no—
542C2×C4⋊C4—224no—
543C2×C4⋊C4—224no—
544C2×C4⋊C4—224no—
545C2×C4⋊C4—224no—
546C2×C4⋊C4—224no—
547C2×C4⋊C4—442no—
548C2×C4⋊C4—442no—
549C2×C4⋊C4C22×D1114yes—
550C2×C4⋊C4C22×D1114yes—
551C2×C4⋊C4C22×D1114yes—
552C2×C4⋊C4C22×D1114yes—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—114no—
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—224no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—224no—
566C2×C22⋊C4—224no—
567C2×C22⋊C4—442no—
568C2×C22⋊C4—442no—
569C2×C42—114no—
570C2×C42—224no—
571#95—114no—
572#95—114no—
573#95—114no—
574#95—114no—
575#95—114no—
576#95C22×D1114yes—
577#95C22×D1114yes—
578#95C22×D1114yes—
579C2×C11#241718yescomplemented
580C2×C11C22×#12111yescharacteristic
581C2×C11C22×C22⋊Q811yescharacteristic
582C2×C11C2×#53711yescharacteristic
583C2×C11C2×#54611yescharacteristic
584C2×C11C2×D4×Q811yescharacteristic
585C2×C11C2×#55211yescharacteristic
586C2×C11C2×#55411yescharacteristic
587D11—28no—
588D11—44no—
589C24—114no—
590C24—114no—
591C24—114no—
592C24—112no—
593C24—114no—
594C24—112no—
595C24—222no—
596C24—222no—
597C24—222no—
598C24—222no—
599C24—222no—
600C24—222no—
601C24—222no—
602C24—222no—
603C24—222no—
604C24—222no—
605C24C23×D1111yescharacteristic
606C2×Q8—228no—
607C2×Q8—228no—
608C2×Q8—228no—
609C2×Q8—4416no—
610C2×D4—1116no—
611C2×D4—228no—
612C2×D4—2232no—
613C2×D4—228no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—114no—
633C22×C4—114no—
634C22×C4—114no—
635C22×C4—112no—
636C22×C4—114no—
637C22×C4—112no—
638C22×C4—1116no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—112no—
642C22×C4—112no—
643C22×C4—228no—
644C22×C4—2232no—
645C22×C4—228no—
646C22×C4—228no—
647C22×C4—228no—
648C22×C4—228no—
649C22×C4—228no—
650C22×C4—228no—
651C22×C4—228no—
652C22×C4—222no—
653C22×C4—222no—
654C22×C4—222no—
655C22×C4—222no—
656C22×C4—222no—
657C22×C4—222no—
658C22×C4—222no—
659C22×C4—222no—
660C22×C4—222no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—222no—
666C22×C4—228no—
667C22×C4—444no—
668C22×C4—444no—
669C22×C4—4416no—
670C22×C4—4416no—
671C22×C4—4416no—
672C22×C4D4×D1114yes—
673C22×C4D4×D1114yes—
674C22×C4Q8×D1114yes—
675C22×C4C23×D1112yes—
676C22×C4C23×D1112yes—
677C22×C4C23×D1112yes—
678C22×C4C23×D1112yes—
679C22×C4C23×D1112yes—
680C22×C4C23×D1112yes—
681C22×C4C23×D1112yes—
682C4⋊C4—28no—
683C4⋊C4—28no—
684C4⋊C4—28no—
685C4⋊C4—28no—
686C4⋊C4—1116no—
687C4⋊C4—228no—
688C4⋊C4—228no—
689C4⋊C4—228no—
690C4⋊C4—228no—
691C4⋊C4—228no—
692C4⋊C4—444no—
693C4⋊C4—444no—
694C22⋊C4—228no—
695C22⋊C4—228no—
696C22⋊C4—228no—
697C22⋊C4—228no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C22⋊C4—444no—
701C22⋊C4—444no—
702C42—228no—
703C11C2×#241711yescharacteristic, complemented, Sylow
704C23—1116no—
705C23—114no—
706C23—114no—
707C23—114no—
708C23—114no—
709C23—228no—
710C23—228no—
711C23—228no—
712C23—228no—
713C23—222no—
714C23—222no—
715C23—222no—
716C23—222no—
717C23—228no—
718C23—228no—
719C23—228no—
720C23—228no—
721C23—222no—
722C23—222no—
723C23—222no—
724C23—222no—
725C23—222no—
726C23—222no—
727C23—228no—
728C23—444no—
729C23—444no—
730C23—444no—
731C23—444no—
732C23C2×D4×D1112yes—
733C23C2×D4×D1112yes—
734C23C2×Q8×D1112yes—
735C23#6704012yes—
736C23#41×D1112yes—
737C23#41×D1112yes—
738C23#6704212yes—
739C23C24×D1111yescharacteristic
740Q8—4416no—
741D4—2232no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—1116no—
768C2×C4—114no—
769C2×C4—114no—
770C2×C4—114no—
771C2×C4—114no—
772C2×C4—2232no—
773C2×C4—228no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—4416no—
789C2×C4—4416no—
790C2×C4—4416no—
791C2×C4—444no—
792C2×C4—444no—
793C2×C4—444no—
794C2×C4—444no—
795C2×C4C2×D4×D1114yes—
796C2×C4C2×D4×D1114yes—
797C2×C4C2×Q8×D1114yes—
798C22—118no—
799C22—224no—
800C22—224no—
801C22—224no—
802C22—2232no—
803C22—224no—
804C22—224no—
805C22—224no—
806C22—224no—
807C22—224no—
808C22—224no—
809C22—442no—
810C22—442no—
811C22—4416no—
812C22—442no—
813C22—442no—
814C22D11×#12114yes—
815C22D11×C22⋊Q814yes—
816C22#1062316014yes—
817C22#1062318514yes—
818C22#1062322114yes—
819C22#1062322414yes—
820C22#1062325814yes—
821C22C22×D4×D1111yescharacteristic
822C22C22×D4×D1111yescharacteristic
823C22C22×Q8×D1111yescharacteristic
824C22C2×#6704011yescharacteristic
825C22C2×#41×D1111yescharacteristic
826C22C2×#41×D1111yescharacteristic
827C22C2×#6704211yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—118no—
836C4—224no—
837C4—442no—
838C4—442no—
839C4—442no—
840C4—442no—
841C2—228no—
842C2—444no—
843C2#1307206218yesdirect product factor
844C2C2×D11×#12111yescharacteristic
845C2C2×D11×C22⋊Q811yescharacteristic
846C2C2×#1062316011yescharacteristic
847C2C2×#1062318511yescharacteristic
848C2C2×#1062325811yescharacteristic
849C2C2×#1062322411yescharacteristic
850C2C2×#1062322111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#398D11
hypocenterC11C2×#2417
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#66949C2semidirect
2. C22×#66949C2semidirect
4. C22×C4⋊C4×D11C2semidirect
5. #13072062C2direct (N × H)
6. C2×#10622597C2semidirect
7. C2×#10622607C2semidirect
8. C2×#10622607C2semidirect
9. C2×#10622259C2semidirect
10. C2×#10622260C2semidirect
13. C2×#10622280C2semidirect
14. C2×#10622280C2semidirect
15. C2×#10622600C2semidirect
16. C2×C11×#398C2semidirect
46. C2×#66949C22semidirect
47. C2×#66949C22semidirect
51. C2×C4⋊C4×D11C22semidirect
52. C11×#398C22semidirect
61. #10622607C22semidirect
62. #10622607C22semidirect
63. #10622600C22semidirect
64. #10622597C22semidirect
65. #10622280C22semidirect
66. #10622280C22semidirect
69. #10622260C22semidirect
70. #10622259C22semidirect
88. C22×D44Q8semidirect
143. C2×Dic11⋊C4D4semidirect
237. C2×D44C2×Q8semidirect
277. Dic11⋊C4C2×D4semidirect
285. C2×#398D11semidirect
326. C22×D11C22⋊Q8semidirect
425. #398C2×D11semidirect
472. C2×D11C2×C22⋊Q8semidirect
579. C2×C11#2417semidirect
703. C11C2×#2417semidirect
843. C2#13072062direct (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×#669462
C22×C4⋊C4×D112
#130720622
C2×#106225972
C2×#106226072
C2×#106222592
C2×#106222602
C2×#106222782
C2×#106222802
C2×#106226002
C2×C11×#3982
C2×#241711