Finite Group Databasebeta

← C2×#13073716 #14923883

Subgroups — C2×#13073716 #14923883

Order 2816.

3330 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67000C211yesmaximal, characteristic, complemented
2C22×#66939C211yesmaximal, characteristic, complemented
3#13073716C2116yesmaximal, direct product factor
4C2×#10622288C211yesmaximal, characteristic, complemented
5C2×#10622287C211yesmaximal, characteristic, complemented
6C2×#10622573C211yesmaximal, characteristic
7C2×#10622843C211yesmaximal, characteristic, complemented
8C2×#10622570C211yesmaximal, characteristic, complemented
9C2×#10622283C211yesmaximal, characteristic, complemented
10C2×#10622268C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622571C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#393C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C2×#67000—28no—
28C2×#67000C2218yescomplemented
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×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×#66939—28no—
45C2×#66939C2218yescomplemented
46C11×#393C2218yescomplemented
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49C2×C11×#95C2211yescharacteristic
50#10622843C2218yescomplemented
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58#10622573C2218yes—
59#10622571C2218yescomplemented
60#10622570C2218yescomplemented
61#10622569C2218yescomplemented
62C22⋊C4×Dic11C2218yescomplemented
63#10622288C2218yescomplemented
64#10622287C2218yescomplemented
65#10622283C2218yescomplemented
66#10622279C2218yescomplemented
67#10622278C2218yescomplemented
68#10622268C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C22×Q8×C11—24no—
73C22×Q8×C11—24no—
74C22×Q8×C11—42no—
75C22×Q8×C11C2314yes—
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—24no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—42no—
87C22×C22⋊D11—42no—
88C22×C22⋊D11C2314yes—
89C22×C22⋊D11C2314yes—
90C23×Dic11—24no—
91C23×Dic11—24no—
92C23×Dic11—42no—
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2314yes—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C22×D44—24no—
101C22×D44—24no—
102C22×D44—42no—
103C22×D44C2314yes—
104C22×C4×D11—24no—
105C22×C4×D11—42no—
106C22×C4×D11—42no—
107C22×C4×D11C2314yes—
108C2×C11×C22⋊C4—24no—
109C2×C11×C22⋊C4—24no—
110C2×C11×C22⋊C4—42no—
111C2×C11×C22⋊C4C2314yes—
112C2×C11×C22⋊C4C2314yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C22⋊Dic11—24no—
115C2×C22⋊Dic11C2314yes—
116#67000—232no—
117C2×(C2×D11)⋊C4—24no—
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—42no—
124C2×(C2×D11)⋊C4—42no—
125C2×(C2×D11)⋊C4D418yescomplemented
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×(C2×D11)⋊C4C2314yes—
135C2×C4⋊Dic11—24no—
136C2×C4⋊Dic11—24no—
137C2×C4⋊Dic11C2314yes—
138C2×C4⋊Dic11C2314yes—
139C2×Dic11⋊C4—24no—
140C2×Dic11⋊C4C2314yes—
141C2×C4×Dic11—24no—
142C2×C4×Dic11—42no—
143C2×C4×Dic11—42no—
144C2×C4×Dic11C2314yes—
145C2×C4×Dic11C2314yes—
146C2×C4×Dic11C2314yes—
147#66939—232no—
148C11×#95C2314yes—
149C11×#95C2314yes—
150C11×#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2557—111nomaximal, Sylow
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11#4114yes—
166C24×C11C2412yes—
167C24×C11C2411yescharacteristic
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×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—22no—
181C23×D11C2×D414yes—
182C23×D11C2412yes—
183C23×D11C2412yes—
184C2×Q8×C11—28no—
185C2×Q8×C11—28no—
186C2×Q8×C11—44no—
187C2×Q8×C11—416no—
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×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11C2×D414yes—
205C22×C4×C11#4114yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C2×C22⋊D11—28no—
213C2×C22⋊D11—28no—
214C2×C22⋊D11—28no—
215C2×C22⋊D11—28no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—416no—
219C2×C22⋊D11—416no—
220C22×Dic11—28no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—28no—
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—44no—
238C22×Dic11—416no—
239C22×Dic11C2×D414yes—
240C22×Dic11#4114yes—
241C22×Dic11#4114yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C2×D44—28no—
249C2×D44—28no—
250C2×D44—44no—
251C2×D44—416no—
252C2×C4×D11—28no—
253C2×C4×D11—44no—
254C2×C4×D11—44no—
255C2×C4×D11—416no—
256C11×C22⋊C4—28no—
257C11×C22⋊C4—28no—
258C11×C22⋊C4—44no—
259C22⋊Dic11—28no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊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—44no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4C2×D4116yescomplemented
269C4⋊Dic11—28no—
270C4⋊Dic11—28no—
271Dic11⋊C4—28no—
272C4×Dic11—28no—
273C4×Dic11—44no—
274C4×Dic11—44no—
275C22×#124—111no—
276C22×#123—111no—
277#2557—1116no—
278C2×#397—111no—
279C2×#397—111no—
280C2×#393D1111yescharacteristic, complemented
281C2×#392—111no—
282C2×#391—111no—
283C2×#390—111no—
284C2×#388—111no—
285C2×#387—111no—
286C2×#386—111no—
287C2×#386—111no—
288C2×#386—111no—
289C2×C4×C22⋊C4—111no—
290C2×C4×C22⋊C4—111no—
291C23×C11—28no—
292C23×C11—28no—
293C23×C11—28no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—44no—
301C23×C11—44no—
302C23×C11—44no—
303C23×C11—44no—
304C23×C11C22×D412yes—
305C23×C11C2×#4112yes—
306C23×C11C2×#4114yes—
307C23×C11C2×#4112yes—
308C23×C11C2×#4112yes—
309C23×C11C2×#4112yes—
310C23×C11H(5,𝔽2)12yes—
311C23×C11H(5,𝔽2)12yes—
312C23×C11C2511yescharacteristic
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—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—44no—
330C22×D11—44no—
331C22×D11—44no—
332C22×D11—44no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11—44no—
340C22×D11C22×D414yes—
341Q8×C11—416no—
342C2×C4×C11—28no—
343C2×C4×C11—28no—
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—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—44no—
361C2×C4×C11—44no—
362C2×C4×C11—44no—
363C2×C4×C11—44no—
364C2×C4×C11C22×D414yes—
365C2×C4×C11C2×#4114yes—
366C22⋊D11—416no—
367C22⋊D11—416no—
368C2×Dic11—28no—
369C2×Dic11—28no—
370C2×Dic11—28no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—416no—
387C2×Dic11—44no—
388C2×Dic11—44no—
389C2×Dic11—44no—
390C2×Dic11C22×D414yes—
391C2×Dic11C2×#4114yes—
392C2×Dic11C2×#4114yes—
393D44—416no—
394C4×D11—416no—
395C23×Q8C2×D1111yescharacteristic
396C23×D4—111no—
397C23×D4—111no—
398C23×D4—111no—
399C24×C4—111no—
400C24×C4—111no—
401C2×#124—118no—
402C2×#124—228no—
403C2×#123—118no—
404C2×#123—228no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407C22×C4⋊C4—111no—
408C22×C22⋊C4—111no—
409C22×C22⋊C4—111no—
410C22×C22⋊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#397—118no—
425#397—118no—
426#393C2×D1118yescomplemented
427#392—118no—
428#391—118no—
429#390—118no—
430#388—118no—
431#387—118no—
432#386—118no—
433#386—118no—
434#386—118no—
435C4×C22⋊C4—118no—
436C4×C22⋊C4—118no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95—111no—
444C2×#95C2×D1111yescharacteristic
445C2×#95C2×D1111yescharacteristic
446C2×#95C2×D1111yescharacteristic
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—416no—
455C22×C11#52914yes—
456C22×C11#53214yes—
457C22×C11#53814yes—
458C22×C11#54614yes—
459C22×C11#54614yes—
460C22×C11#55114yes—
461C22×C11#55914yes—
462C22×C11C23×D411yescharacteristic
463C22×C11C22×#4111yescharacteristic
464C22×C11C22×#4111yescharacteristic
465C22×C11C22×#4111yescharacteristic
466C22×C11C22×#4111yescharacteristic
467C22×C11C2×H(5,𝔽2)11yescharacteristic
468C22×C11C2×H(5,𝔽2)11yescharacteristic
469C2×D11—24no—
470C2×D11—24no—
471C2×D11—24no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—416no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—88no—
485C4×C11—24no—
486C4×C11—24no—
487C4×C11—42no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11—42no—
491Dic11—24no—
492Dic11—24no—
493Dic11—24no—
494Dic11—42no—
495Dic11—42no—
496Dic11—42no—
497C25—111no—
498C25—111no—
499C25C22×D1111yescharacteristic
500C22×Q8—24no—
501C22×Q8—24no—
502C22×Q8—42no—
503C22×Q8C22×D1114yes—
504C22×D4—114no—
505C22×D4—114no—
506C22×D4—114no—
507C22×D4—224no—
508C22×D4—224no—
509C22×D4—224no—
510C22×D4—224no—
511C22×D4—224no—
512C22×D4—224no—
513C22×D4—442no—
514C22×D4—442no—
515C22×D4—442no—
516C23×C4—111no—
517C23×C4—111no—
518C23×C4—111no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—114no—
523C23×C4—114no—
524C23×C4—224no—
525C23×C4—224no—
526C23×C4—224no—
527C23×C4—442no—
528C23×C4—442no—
529C23×C4—442no—
530C23×C4C22×D1111yescharacteristic
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C23×C4C22×D1111yescharacteristic
535C23×C4C22×D1111yescharacteristic
536#124—2232no—
537#123—2232no—
538C2×C4⋊C4—114no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—224no—
542C2×C4⋊C4—224no—
543C2×C4⋊C4—224no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—118no—
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—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—114no—
558C2×C22⋊C4—224no—
559C2×C22⋊C4—224no—
560C2×C22⋊C4—224no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—442no—
566C2×C22⋊C4—442no—
567C2×C22⋊C4C22×D1114yes—
568C2×C22⋊C4C22×D1114yes—
569C2×C22⋊C4C22×D1114yes—
570C2×C42—114no—
571C2×C42—114no—
572C2×C42—114no—
573C2×C42—224no—
574C2×C42—442no—
575C2×C42—442no—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95—114no—
582#95—114no—
583#95C22×D1114yes—
584#95C22×D1114yes—
585#95C22×D1114yes—
586C2×C11—44no—
587C2×C11#255718yescomplemented
588C2×C11C2×#52911yescharacteristic
589C2×C11C2×#53211yescharacteristic
590C2×C11C2×#53811yescharacteristic
591C2×C11C2×#54611yescharacteristic
592C2×C11C2×#54611yescharacteristic
593C2×C11C2×#55111yescharacteristic
594C2×C11C2×#55911yescharacteristic
595D11—44no—
596D11—82no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—114no—
604C24—112no—
605C24—112no—
606C24—222no—
607C24—222no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24—222no—
617C24—222no—
618C24—222no—
619C24#434314yes—
620C24C23×D1112yes—
621C24C23×D1111yescharacteristic
622C2×Q8—28no—
623C2×Q8—28no—
624C2×Q8—44no—
625C2×Q8—416no—
626C2×D4—228no—
627C2×D4—228no—
628C2×D4—228no—
629C2×D4—228no—
630C2×D4—228no—
631C2×D4—228no—
632C2×D4—444no—
633C2×D4—4416no—
634C2×D4—444no—
635C2×D4—444no—
636C2×D4—4416no—
637C2×D4—4416no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—114no—
655C22×C4—114no—
656C22×C4—114no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—112no—
662C22×C4—112no—
663C22×C4—228no—
664C22×C4—228no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—222no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—222no—
674C22×C4—228no—
675C22×C4—222no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4—222no—
679C22×C4—222no—
680C22×C4—222no—
681C22×C4—444no—
682C22×C4—444no—
683C22×C4—4416no—
684C22×C4—444no—
685C22×C4—4416no—
686C22×C4D4×D1114yes—
687C22×C4#434114yes—
688C22×C4C23×D1112yes—
689C22×C4C23×D1112yes—
690C22×C4C23×D1112yes—
691C22×C4C23×D1112yes—
692C22×C4C23×D1112yes—
693C22×C4C23×D1112yes—
694C4⋊C4—228no—
695C4⋊C4—228no—
696C4⋊C4—228no—
697C22⋊C4—28no—
698C22⋊C4—28no—
699C22⋊C4—44no—
700C22⋊C4—1116no—
701C22⋊C4—228no—
702C22⋊C4—228no—
703C22⋊C4—228no—
704C22⋊C4—228no—
705C22⋊C4—228no—
706C22⋊C4—228no—
707C22⋊C4—228no—
708C22⋊C4—444no—
709C22⋊C4—444no—
710C42—228no—
711C42—444no—
712C42—444no—
713C11C2×#255711yescharacteristic, complemented, Sylow
714C23—28no—
715C23—28no—
716C23—28no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—114no—
728C23—228no—
729C23—228no—
730C23—222no—
731C23—222no—
732C23—222no—
733C23—222no—
734C23—222no—
735C23—222no—
736C23—228no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—444no—
745C23—444no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23—444no—
753C23—444no—
754C23—444no—
755C23C2×D4×D1112yes—
756C23C2×#434112yes—
757C23#6703712yes—
758C23C2×#434314yes—
759C23C2×#434312yes—
760C23#41×D1112yes—
761C23#41×D1112yes—
762C23#6704212yes—
763C23C24×D1111yescharacteristic
764Q8—416no—
765D4—4416no—
766D4—4416no—
767D4—4416no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—114no—
791C2×C4—114no—
792C2×C4—114no—
793C2×C4—228no—
794C2×C4—228no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—228no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—4416no—
812C2×C4—4416no—
813C2×C4—444no—
814C2×C4—444no—
815C2×C4—444no—
816C2×C4C2×D4×D1114yes—
817C2×C4C2×#434114yes—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—42no—
822C22—416no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—224no—
827C22—224no—
828C22—224no—
829C22—442no—
830C22—442no—
831C22—4416no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—442no—
838C22—442no—
839C22—442no—
840C22—442no—
841C22—888no—
842C22#1062312214yes—
843C22#1062315514yes—
844C22#1062316114yes—
845C22#1062316814yes—
846C22#1062319914yes—
847C22#1062320914yes—
848C22#1062321214yes—
849C22C22×D4×D1111yescharacteristic
850C22C22×#434111yescharacteristic
851C22C2×#6703711yescharacteristic
852C22C22×#434311yescharacteristic
853C22C2×#41×D1111yescharacteristic
854C22C2×#41×D1111yescharacteristic
855C22C2×#6704211yescharacteristic
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—224no—
863C4—224no—
864C4—224no—
865C4—442no—
866C4—442no—
867C4—442no—
868C2—44no—
869C2—444no—
870C2—882no—
871C2#1307371618yesdirect product factor
872C2C2×#1062315511yescharacteristic
873C2C2×#1062319911yescharacteristic
874C2C2×#1062320911yescharacteristic
875C2C2×#1062312211yescharacteristic
876C2C2×#1062316111yescharacteristic
877C2C2×#1062316811yescharacteristic
878C2C2×#1062321211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#393C2
socleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×#393D11
hypocenterC11C2×#2557
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#67000C2semidirect
2. C22×#66939C2semidirect
3. #13073716C2direct (N × H)
4. C2×#10622288C2semidirect
5. C2×#10622287C2semidirect
7. C2×#10622843C2semidirect
8. C2×#10622570C2semidirect
9. C2×#10622283C2semidirect
10. C2×#10622268C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622571C2semidirect
13. C2×#10622569C2semidirect
14. C2×C22⋊C4×Dic11C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#393C2semidirect
28. C2×#67000C22semidirect
45. C2×#66939C22semidirect
46. C11×#393C22semidirect
50. #10622843C22semidirect
59. #10622571C22semidirect
60. #10622570C22semidirect
61. #10622569C22semidirect
62. C22⋊C4×Dic11C22semidirect
63. #10622288C22semidirect
64. #10622287C22semidirect
65. #10622283C22semidirect
66. #10622279C22semidirect
67. #10622278C22semidirect
68. #10622268C22semidirect
125. C2×(C2×D11)⋊C4D4semidirect
268. (C2×D11)⋊C4C2×D4semidirect
280. C2×#393D11semidirect
426. #393C2×D11semidirect
587. C2×C11#2557semidirect
713. C11C2×#2557semidirect
871. C2#13073716direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670002
C22×#669392
#130737162
C2×#106222882
C2×#106222872
C2×#106225732
C2×#106228432
C2×#106225702
C2×#106222832
C2×#106222682
C2×#106222782
C2×#106225712
C2×#106225692
C2×C22⋊C4×Dic112
C2×#106222792
C2×C11×#3932
C2×#255711