Finite Group Databasebeta

← C2×#13072461 #14921677

Subgroups — C2×#13072461 #14921677

Order 2816.

3614 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66997C211yesmaximal, characteristic, complemented
2C22×#66931C211yesmaximal, characteristic, complemented
3C22×#66999C211yesmaximal, characteristic, complemented
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
5#13072461C2116yesmaximal, direct product factor
6C2×#10622289C211yesmaximal, characteristic, complemented
7C2×#10622561C211yesmaximal, characteristic, complemented
8C2×#10622286C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic
10C2×#10622570C211yesmaximal, characteristic
11C2×#10622260C211yesmaximal, characteristic, complemented
12C2×#10622260C211yesmaximal, characteristic, complemented
13C2×#10622281C211yesmaximal, characteristic, complemented
14C2×#10622559C211yesmaximal, characteristic, complemented
15C2×#10622262C211yesmaximal, characteristic, complemented
16C2×C11×#393C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×Dic22C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C2×#66999—28no—
28C2×#66999C2218yescomplemented
29C2×#66997—28no—
30C2×#66997C2218yescomplemented
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×C4⋊Dic11C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×(C22⋊D11)⋊C4—28no—
51C2×(C22⋊D11)⋊C4C2218yes—
52C2×#66931—28no—
53C2×#66931C2218yescomplemented
54C11×#393C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57C2×C11×#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622570C2218yes—
62#10622570C2218yes—
63#10622561C2218yescomplemented
64#10622559C2218yescomplemented
65#10622289C2218yescomplemented
66#10622286C2218yescomplemented
67#10622281C2218yescomplemented
68#10622262C2218yescomplemented
69#10622260C2218yescomplemented
70#10622260C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C22×Q8×C11—24no—
74C22×Q8×C11—24no—
75C22×Q8×C11—42no—
76C22×Q8×C11C2314yes—
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11Q818yescomplemented
86C22×C22⋊D11C2314yes—
87C23×Dic11—24no—
88C23×Dic11—24no—
89C23×Dic11—42no—
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2314yes—
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C22×C4×D11—24no—
99C22×C4×D11—24no—
100C22×C4×D11—42no—
101C22×C4×D11C2314yes—
102C22×Dic22—24no—
103C22×Dic22—24no—
104C22×Dic22—42no—
105C22×Dic22C2314yes—
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4—24no—
108C2×C11×C22⋊C4—42no—
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2314yes—
112C2×C22⋊Dic11—24no—
113C2×C22⋊Dic11—24no—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2314yes—
116#66999—232no—
117#66997—232no—
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4—24no—
120C2×(C2×D11)⋊C4—24no—
121C2×(C2×D11)⋊C4—24no—
122C2×(C2×D11)⋊C4—42no—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×C4⋊Dic11—24no—
129C2×C4⋊Dic11—24no—
130C2×C4⋊Dic11C2314yes—
131C2×C4⋊Dic11C2314yes—
132C2×Dic11⋊C4—24no—
133C2×Dic11⋊C4—24no—
134C2×Dic11⋊C4—24no—
135C2×Dic11⋊C4—24no—
136C2×Dic11⋊C4—24no—
137C2×Dic11⋊C4—24no—
138C2×Dic11⋊C4—24no—
139C2×Dic11⋊C4D418yes—
140C2×Dic11⋊C4D418yescomplemented
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×C4×Dic11—24no—
151C2×C4×Dic11—24no—
152C2×C4×Dic11—24no—
153C2×C4×Dic11C2314yes—
154C2×C4×Dic11C2314yes—
155C2×C4×Dic11C2314yes—
156(C22⋊D11)⋊C4—232no—
157#66931—232no—
158C11×#95C2314yes—
159C11×#95C2314yes—
160C11×#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C2×#2452—111nomaximal, Sylow
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11C2×Q814yes—
172C24×C11C2412yes—
173C24×C11C2411yescharacteristic
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11C2×Q814yes—
181C23×D11C2412yes—
182C2×Q8×C11—28no—
183C2×Q8×C11—28no—
184C2×Q8×C11—44no—
185C2×Q8×C11—416no—
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×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11C2×D414yes—
203C22×C4×C11C2×D414yes—
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—28no—
215C22×Dic11—28no—
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—44no—
231C22×Dic11—416no—
232C22×Dic11C2×D414yes—
233C22×Dic11C2×D414yes—
234C22×Dic11C2×D414yes—
235C22×Dic11C2×D414yes—
236C22×Dic11C2×Q814yes—
237C22×Dic11#4114yes—
238C22×Dic11#4114yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C2×C4×D11—28no—
247C2×C4×D11—28no—
248C2×C4×D11—44no—
249C2×C4×D11—416no—
250C2×Dic22—28no—
251C2×Dic22—28no—
252C2×Dic22—44no—
253C2×Dic22—416no—
254C11×C22⋊C4—28no—
255C11×C22⋊C4—28no—
256C11×C22⋊C4—44no—
257C22⋊Dic11—28no—
258C22⋊Dic11—28no—
259(C2×D11)⋊C4—28no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—44no—
264C4⋊Dic11—28no—
265C4⋊Dic11—28no—
266Dic11⋊C4—28no—
267Dic11⋊C4—28no—
268Dic11⋊C4—28no—
269Dic11⋊C4—28no—
270Dic11⋊C4—28no—
271Dic11⋊C4—28no—
272Dic11⋊C4—28no—
273Dic11⋊C4C2×D4116yes—
274Dic11⋊C4C2×D4116yescomplemented
275C4×Dic11—28no—
276C4×Dic11—28no—
277C4×Dic11—28no—
278C22×C4⋊Q8—111no—
279C22×C22⋊Q8—111no—
280C22×C22⋊Q8—111no—
281C22×C4×D4—111no—
282#2452—1116no—
283C2×#396—111no—
284C2×#396—111no—
285C2×#393—111no—
286C2×#393D1111yescharacteristic, complemented
287C2×#390—111no—
288C2×#390—111no—
289C2×#389—111no—
290C2×#389—111no—
291C2×#385—111no—
292C2×#385—111no—
293C2×C4×C4⋊C4—111no—
294C23×C11—28no—
295C23×C11—28no—
296C23×C11—28no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—44no—
304C23×C11—44no—
305C23×C11—44no—
306C23×C11—44no—
307C23×C11C22×D412yes—
308C23×C11C22×D412yes—
309C23×C11C22×Q814yes—
310C23×C11C22×Q812yes—
311C23×C11C2×#4112yes—
312C23×C11C2×#4112yes—
313C23×C11H(5,𝔽2)12yes—
314C23×C112−1+412yes—
315C23×C11C2511yescharacteristic
316C22×D11—28no—
317C22×D11—28no—
318C22×D11—28no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—44no—
326C22×D11—44no—
327C22×D11—44no—
328C22×D11—44no—
329C22×D11C22×Q814yes—
330Q8×C11—416no—
331C2×C4×C11—28no—
332C2×C4×C11—28no—
333C2×C4×C11—22no—
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—44no—
350C2×C4×C11—44no—
351C2×C4×C11—44no—
352C2×C4×C11—44no—
353C2×C4×C11C22×D414yes—
354C2×C4×C11C22×D414yes—
355C22⋊D11—232no—
356C2×Dic11—28no—
357C2×Dic11—28no—
358C2×Dic11—28no—
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—416no—
375C2×Dic11—44no—
376C2×Dic11—44no—
377C2×Dic11C22⋊Q8116yescomplemented
378C2×Dic11C22×D414yes—
379C2×Dic11C22×D414yes—
380C2×Dic11C22×D414yes—
381C2×Dic11C22×D414yes—
382C2×Dic11C22×Q814yes—
383C2×Dic11C2×#4114yes—
384C2×Dic11C2×#4114yes—
385C4×D11—416no—
386Dic22—416no—
387C23×Q8—111no—
388C23×Q8C2×D1111yescharacteristic
389C23×D4—111no—
390C24×C4—111no—
391C24×C4—111no—
392C2×C4⋊Q8—118no—
393C2×C4⋊Q8—228no—
394C2×C22⋊Q8—118no—
395C2×C22⋊Q8—118no—
396C2×C22⋊Q8—228no—
397C2×C22⋊Q8—228no—
398C2×C4×D4—118no—
399C2×C4×D4—228no—
400C22×C4⋊C4—111no—
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—111no—
410C22×C4⋊C4—111no—
411C22×C22⋊C4—111no—
412C22×C22⋊C4—111no—
413C22×C22⋊C4—111no—
414C22×C22⋊C4—111no—
415C22×C22⋊C4—111no—
416C22×C22⋊C4—111no—
417C22×C22⋊C4—111no—
418C22×C22⋊C4C2×D1111yescharacteristic
419C22×C22⋊C4C2×D1111yescharacteristic
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C42—111no—
422C22×C42—111no—
423C22×C42—111no—
424#396—118no—
425#396—118no—
426#393—118no—
427#393C2×D1118yescomplemented
428#390—118no—
429#390—118no—
430#389—118no—
431#389—118no—
432#385—118no—
433#385—118no—
434C4×C4⋊C4—118no—
435C2×#95—111no—
436C2×#95—111no—
437C2×#95—111no—
438C2×#95C2×D1111yescharacteristic
439C2×#95C2×D1111yescharacteristic
440C2×#95C2×D1111yescharacteristic
441C22×C11—24no—
442C22×C11—24no—
443C22×C11—24no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—416no—
449C22×C11C2×C22⋊Q814yes—
450C22×C11#53214yes—
451C22×C11#54214yes—
452C22×C11D4214yes—
453C22×C11#54814yes—
454C22×C11D4×Q814yes—
455C22×C11#55414yes—
456C22×C11C23×D411yescharacteristic
457C22×C11C23×D411yescharacteristic
458C22×C11C23×Q811yescharacteristic
459C22×C11C22×#4111yescharacteristic
460C22×C11C22×#4111yescharacteristic
461C22×C11C2×H(5,𝔽2)11yescharacteristic
462C22×C11C2×2−1+411yescharacteristic
463C2×D11—24no—
464C2×D11—24no—
465C2×D11—24no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—416no—
471C4×C11—24no—
472C4×C11—24no—
473C4×C11—42no—
474C4×C11—42no—
475C4×C11—42no—
476C4×C11—42no—
477Dic11—24no—
478Dic11—24no—
479Dic11—24no—
480Dic11—24no—
481Dic11—42no—
482Dic11—42no—
483Dic11C2×C22⋊Q818yescomplemented
484C25—111no—
485C25C22×D1111yescharacteristic
486C22×Q8—24no—
487C22×Q8—24no—
488C22×Q8—42no—
489C22×Q8—114no—
490C22×Q8—224no—
491C22×Q8—224no—
492C22×Q8—442no—
493C22×Q8C22×D1114yes—
494C22×D4—118no—
495C22×D4—114no—
496C22×D4—224no—
497C22×D4—224no—
498C23×C4—111no—
499C23×C4—111no—
500C23×C4—111no—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4—111no—
505C23×C4—114no—
506C23×C4—114no—
507C23×C4—224no—
508C23×C4—224no—
509C23×C4—224no—
510C23×C4—224no—
511C23×C4—442no—
512C23×C4—442no—
513C23×C4C22×D1111yescharacteristic
514C23×C4C22×D1111yescharacteristic
515C23×C4C22×D1111yescharacteristic
516C23×C4C22×D1111yescharacteristic
517C23×C4C22×D1111yescharacteristic
518C23×C4C22×D1111yescharacteristic
519C4⋊Q8—2232no—
520C22⋊Q8—2232no—
521C22⋊Q8—2232no—
522C4×D4—2232no—
523C2×C4⋊C4—118no—
524C2×C4⋊C4—118no—
525C2×C4⋊C4—114no—
526C2×C4⋊C4—114no—
527C2×C4⋊C4—114no—
528C2×C4⋊C4—114no—
529C2×C4⋊C4—114no—
530C2×C4⋊C4—114no—
531C2×C4⋊C4—114no—
532C2×C4⋊C4—114no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—224no—
537C2×C4⋊C4—224no—
538C2×C4⋊C4—224no—
539C2×C4⋊C4—224no—
540C2×C4⋊C4—224no—
541C2×C4⋊C4—224no—
542C2×C4⋊C4—224no—
543C2×C4⋊C4—224no—
544C2×C4⋊C4—224no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—114no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—224no—
556C2×C22⋊C4—224no—
557C2×C22⋊C4—224no—
558C2×C22⋊C4—224no—
559C2×C22⋊C4—224no—
560C2×C22⋊C4—224no—
561C2×C22⋊C4—442no—
562C2×C22⋊C4C22×D1114yes—
563C2×C22⋊C4C22×D1114yes—
564C2×C22⋊C4C22×D1114yes—
565C2×C42—114no—
566C2×C42—114no—
567C2×C42—114no—
568C2×C42—224no—
569C2×C42—224no—
570C2×C42—224no—
571#95—114no—
572#95—114no—
573#95—114no—
574#95C22×D1114yes—
575#95C22×D1114yes—
576#95C22×D1114yes—
577C2×C11—44no—
578C2×C11#245218yescomplemented
579C2×C11C22×C22⋊Q811yescharacteristic
580C2×C11C2×#53211yescharacteristic
581C2×C11C2×#54211yescharacteristic
582C2×C11C2×D4211yescharacteristic
583C2×C11C2×#54811yescharacteristic
584C2×C11C2×D4×Q811yescharacteristic
585C2×C11C2×#55411yescharacteristic
586D11—44no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—114no—
594C24—112no—
595C24—222no—
596C24—222no—
597C24—222no—
598C24—222no—
599C24—222no—
600C24—222no—
601C24Q8×D1114yes—
602C24C23×D1112yes—
603C24C23×D1111yescharacteristic
604C2×Q8—28no—
605C2×Q8—28no—
606C2×Q8—44no—
607C2×Q8—416no—
608C2×Q8—228no—
609C2×Q8—228no—
610C2×Q8—444no—
611C2×Q8—4416no—
612C2×D4—1116no—
613C2×D4—228no—
614C2×D4—2232no—
615C2×D4—228no—
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—114no—
638C22×C4—114no—
639C22×C4—114no—
640C22×C4—112no—
641C22×C4—112no—
642C22×C4—112no—
643C22×C4—112no—
644C22×C4—112no—
645C22×C4—112no—
646C22×C4—228no—
647C22×C4—228no—
648C22×C4—228no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4—222no—
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—228no—
664C22×C4—444no—
665C22×C4—4416no—
666C22×C4—444no—
667C22×C4—4416no—
668C22×C4D4×D1114yes—
669C22×C4D4×D1114yes—
670C22×C4C23×D1112yes—
671C22×C4C23×D1112yes—
672C22×C4C23×D1112yes—
673C22×C4C23×D1112yes—
674C22×C4C23×D1112yes—
675C22×C4C23×D1112yes—
676C4⋊C4—1116no—
677C4⋊C4—1116no—
678C4⋊C4—228no—
679C4⋊C4—228no—
680C4⋊C4—228no—
681C4⋊C4—228no—
682C4⋊C4—228no—
683C4⋊C4—228no—
684C4⋊C4—228no—
685C4⋊C4—228no—
686C4⋊C4—228no—
687C22⋊C4—28no—
688C22⋊C4—28no—
689C22⋊C4—44no—
690C22⋊C4—228no—
691C22⋊C4—228no—
692C22⋊C4—228no—
693C22⋊C4—228no—
694C22⋊C4—228no—
695C22⋊C4—228no—
696C22⋊C4—444no—
697C42—228no—
698C42—228no—
699C42—228no—
700C11C2×#245211yescharacteristic, complemented, Sylow
701C23—28no—
702C23—28no—
703C23—28no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—114no—
715C23—228no—
716C23—228no—
717C23—228no—
718C23—222no—
719C23—222no—
720C23—222no—
721C23—222no—
722C23—222no—
723C23—222no—
724C23—444no—
725C23—444no—
726C23—444no—
727C23—444no—
728C23C2×D4×D1112yes—
729C23C2×D4×D1112yes—
730C23#6703712yes—
731C23C2×Q8×D1114yes—
732C23C2×Q8×D1112yes—
733C23#41×D1112yes—
734C23#41×D1112yes—
735C23#6704312yes—
736C23C24×D1111yescharacteristic
737Q8—416no—
738Q8—4416no—
739D4—2232no—
740C2×C4—28no—
741C2×C4—28no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
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—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—1116no—
763C2×C4—114no—
764C2×C4—114no—
765C2×C4—114no—
766C2×C4—114no—
767C2×C4—114no—
768C2×C4—114no—
769C2×C4—114no—
770C2×C4—228no—
771C2×C4—228no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—228no—
781C2×C4—228no—
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—444no—
791C2×C4—444no—
792C2×C4C2×D4×D1114yes—
793C2×C4C2×D4×D1114yes—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—42no—
798C22—416no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—224no—
803C22—224no—
804C22—224no—
805C22—442no—
806C22—4416no—
807C22—442no—
808C22—442no—
809C22—442no—
810C22#1062312114yes—
811C22D11×C22⋊Q814yes—
812C22#1062316314yes—
813C22#1062316714yes—
814C22#1062319914yes—
815C22#1062320014yes—
816C22#1062320814yes—
817C22C22×D4×D1111yescharacteristic
818C22C22×D4×D1111yescharacteristic
819C22C2×#6703711yescharacteristic
820C22C22×Q8×D1111yescharacteristic
821C22C2×#41×D1111yescharacteristic
822C22C2×#41×D1111yescharacteristic
823C22C2×#6704311yescharacteristic
824C4—24no—
825C4—24no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—118no—
831C4—224no—
832C4—224no—
833C4—224no—
834C4—224no—
835C4—442no—
836C4—442no—
837C2—44no—
838C2—444no—
839C2#1307246118yesdirect product factor
840C2C2×D11×C22⋊Q811yescharacteristic
841C2C2×#1062319911yescharacteristic
842C2C2×#1062320011yescharacteristic
843C2C2×#1062312111yescharacteristic
844C2C2×#1062320811yescharacteristic
845C2C2×#1062316311yescharacteristic
846C2C2×#1062316711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#393C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#393D11
hypocenterC11C2×#2452
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#66997C2semidirect
2. C22×#66931C2semidirect
3. C22×#66999C2semidirect
5. #13072461C2direct (N × H)
6. C2×#10622289C2semidirect
7. C2×#10622561C2semidirect
8. C2×#10622286C2semidirect
11. C2×#10622260C2semidirect
12. C2×#10622260C2semidirect
13. C2×#10622281C2semidirect
14. C2×#10622559C2semidirect
15. C2×#10622262C2semidirect
16. C2×C11×#393C2semidirect
28. C2×#66999C22semidirect
30. C2×#66997C22semidirect
53. C2×#66931C22semidirect
54. C11×#393C22semidirect
63. #10622561C22semidirect
64. #10622559C22semidirect
65. #10622289C22semidirect
66. #10622286C22semidirect
67. #10622281C22semidirect
68. #10622262C22semidirect
69. #10622260C22semidirect
70. #10622260C22semidirect
85. C22×C22⋊D11Q8semidirect
140. C2×Dic11⋊C4D4semidirect
213. C2×C22⋊D11C2×Q8semidirect
274. Dic11⋊C4C2×D4semidirect
286. C2×#393D11semidirect
377. C2×Dic11C22⋊Q8semidirect
427. #393C2×D11semidirect
483. Dic11C2×C22⋊Q8semidirect
578. C2×C11#2452semidirect
700. C11C2×#2452semidirect
839. C2#13072461direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669972
C22×#669312
C22×#669992
C22×(C22⋊D11)⋊C42
#130724612
C2×#106222892
C2×#106225612
C2×#106222862
C2×#106225702
C2×#106222602
C2×#106222812
C2×#106225592
C2×#106222622
C2×C11×#3932
C2×#245211