Finite Group Databasebeta

← C2×#13080691 #15630293

Subgroups — C2×#13080691 #15630293

Order 2816.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623081C211yesmaximal, characteristic
2#13080691C2116yesmaximal, direct product factor
3C2×#10622702C211yesmaximal, characteristic, complemented
4C2×#10622583C211yesmaximal, characteristic, complemented
5C2×#10622580C211yesmaximal, characteristic, complemented
6C2×#10622700C211yesmaximal, characteristic, complemented
7C2×#10622662C211yesmaximal, characteristic, complemented
8C2×#10622664C211yesmaximal, characteristic, complemented
9C2×#10622641C211yesmaximal, characteristic, complemented
10C2×#10622660C211yesmaximal, characteristic, complemented
11C2×#10622659C211yesmaximal, characteristic, complemented
12C2×#10622639C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622579C211yesmaximal, characteristic, complemented
15C22×#66873C211yesmaximal, characteristic, complemented
16C2×C11×#554C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C11×#554—24no—
20C11×#554C2218yescomplemented
21C2×C11×C4⋊Q8C2211yescharacteristic, complemented
22C2×C11×#125—21no—
23C2×C11×C22⋊Q8—21no—
24C2×C11×C22⋊Q8—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic, complemented
27C2×C4×Q8×C11C2211yescharacteristic, complemented
28C2×C4×D4×C11—21no—
29C2×C4×D4×C11C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C22×C11×C4⋊C4C2211yescharacteristic, complemented
32C22×#4326C2211yescharacteristic, complemented
33C22×#4325C2211yescharacteristic
34C22×#4325C2211yescharacteristic
35C2×#66990—21no—
36C2×#66983C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38C22×#4318C2211yescharacteristic, complemented
39C23×C11⋊C8C2211yescharacteristic
40#10623081—24no—
41#10623081C2218yes—
42C2×#66947—21no—
43C2×#66937—21no—
44C2×C22⋊C4×D11—21no—
45C2×#66928C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic
47C2×#66899C2211yescharacteristic, complemented
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
50#10622702C2218yescomplemented
51#10622700C2218yescomplemented
52#10622664C2218yescomplemented
53#10622662C2218yescomplemented
54#10622660C2218yescomplemented
55#10622659C2218yescomplemented
56#10622641C2218yescomplemented
57#10622639C2218yescomplemented
58#10622624C2218yescomplemented
59#10622583C2218yescomplemented
60C2×#66874C2211yescharacteristic, complemented
61C2×#66874C2211yescharacteristic, complemented
62C2×#66874C2211yescharacteristic, complemented
63#10622580C2218yescomplemented
64#10622579C2218yescomplemented
65C2×#66873C2211yescharacteristic
66C2×#66873C2211yescharacteristic
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66873C2211yescharacteristic
70C2×#66873C2211yescharacteristic
71C2×#66873C2218yescomplemented
72C2×#66871C2211yescharacteristic, complemented
73C2×#66871C2211yescharacteristic, complemented
74C2×#66871C2211yescharacteristic, complemented
75C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
76C2×#66867C2211yescharacteristic, complemented
77C24×D11—21no—
78C22×Q8×C11—21no—
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11D411yescharacteristic
81C23×C4×C11—21no—
82C23×C4×C11—21no—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C2×#4339—22no—
88C2×#4339—24no—
89C2×#4339—42no—
90C2×#4339C2314yes—
91C22×D44—24no—
92C22×D44—21no—
93C22×D44—22no—
94C22×D44—42no—
95C22×D44C2311yescharacteristic
96C22×D44C2314yes—
97C22×D44C2311yescharacteristic
98C22×C4×D11—21no—
99C22×C4×D11—21no—
100C22×Dic22C2311yescharacteristic
101C11×C4⋊Q8—22no—
102C11×C4⋊Q8C2314yescomplemented
103C11×#125—28no—
104C11×C22⋊Q8—22no—
105C11×C22⋊Q8—22no—
106C11×C22⋊Q8—28no—
107C11×C22⋊Q8—28no—
108C11×C22⋊Q8C2314yes—
109C11×C22⋊Q8C2314yescomplemented
110C4×Q8×C11—22no—
111C4×Q8×C11C2314yescomplemented
112C4×D4×C11—28no—
113C4×D4×C11D414yes—
114C4×D4×C11C2314yes—
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4—22no—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—22no—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4—21no—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4D411yescharacteristic
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C4⋊C4C2311yescharacteristic
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C11×C4⋊C4C2314yes—
128C2×C11×C4⋊C4C2314yescomplemented
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4D411yescharacteristic
132C2×C11×C22⋊C4D411yescharacteristic
133C2×C42×C11—21no—
134C2×C42×C11C2311yescharacteristic
135C2×C22⋊Dic11—21no—
136C2×#4326—42no—
137C2×#4326C2314yescomplemented
138C2×#4325—24no—
139C2×#4325—42no—
140C2×#4325C2314yes—
141C2×#4325C2314yes—
142#66990—28no—
143#66983—22no—
144#66983C2314yes—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4—21no—
149C2×C4⋊Dic11C2311yescharacteristic
150#66977—22no—
151#66977C2314yes—
152C2×Dic11⋊C4—21no—
153C2×#4318—42no—
154C2×#4318C2314yescomplemented
155C22×C11⋊C8—42no—
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2314yes—
161#66947—28no—
162#66937—28no—
163C22⋊C4×D11—28no—
164#66928—22no—
165#66928C2314yes—
166C4×D44—22no—
167C4×D44C2314yes—
168#66899C2314yescomplemented
169C22⋊(C11⋊C8)C2314yes—
170C22⋊(C11⋊C8)C2314yescomplemented
171#66874C2314yescomplemented
172#66874C2314yescomplemented
173#66874C2314yescomplemented
174#66873C2314yes—
175#66873C2314yes—
176#66873C2314yes—
177#66873C2314yes—
178#66873C2314yes—
179#66873C2314yes—
180#66871C2314yescomplemented
181#66871C2314yescomplemented
182#66871C2314yescomplemented
183C4⋊(C11⋊C8)C2314yescomplemented
184#66867C2314yescomplemented
185C2×#3314—111nomaximal, Sylow
186C24×C11C2×D411yescharacteristic
187C24×C11C2×D411yescharacteristic
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—24no—
191C23×D11—44no—
192C23×D11—44no—
193C23×D11—82no—
194C2×Q8×C11—21no—
195C2×Q8×C11—24no—
196C2×Q8×C11—22no—
197C2×Q8×C11—22no—
198C2×Q8×C11—82no—
199C2×Q8×C11C2412yes—
200C2×D4×C11—24no—
201C2×D4×C11C2×D414yes—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—24no—
211C22×C4×C11—24no—
212C22×C4×C11—82no—
213C22×C4×C11—82no—
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2411yescharacteristic
223C2×C22⋊D11—24no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—82no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229#4339—28no—
230#4339—44no—
231#4339—48no—
232C2×D44—28no—
233C2×D44—21no—
234C2×D44—21no—
235C2×D44—24no—
236C2×D44—22no—
237C2×D44—22no—
238C2×D44—22no—
239C2×D44—44no—
240C2×D44—44no—
241C2×D44—48no—
242C2×D44#4114yes—
243C2×D44C2412yes—
244C2×D44C2412yes—
245C2×C4×D11—24no—
246C2×C4×D11—24no—
247C2×C4×D11—44no—
248C2×C4×D11—82no—
249C2×Dic22—21no—
250C2×Dic22—22no—
251C2×Dic22—22no—
252C2×Dic22C2412yes—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—24no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—24no—
258C11×C4⋊C4—24no—
259C11×C4⋊C4—24no—
260C11×C4⋊C4—24no—
261C11×C4⋊C4—24no—
262C11×C4⋊C4C2×D414yes—
263C11×C4⋊C4C2412yes—
264C11×C4⋊C4C2412yes—
265C11×C4⋊C4C2412yes—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—24no—
268C11×C22⋊C4C2×D414yes—
269C11×C22⋊C4C2×D414yes—
270C42×C11—24no—
271C42×C11C2×D412yes—
272C42×C11C2412yes—
273C22⋊Dic11—24no—
274#4326—44no—
275#4325—28no—
276#4325—44no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281C4⋊Dic11—21no—
282C4⋊Dic11C2412yes—
283Dic11⋊C4—24no—
284#4318—44no—
285C2×C11⋊C8—22no—
286C2×C11⋊C8—22no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8—22no—
289C2×C11⋊C8—44no—
290C2×C11⋊C8C2412yes—
291C2×C11⋊C8C2412yes—
292C2×C11⋊C8C2412yes—
293C2×C11⋊C8C2412yes—
294C2×#554D1111yescharacteristic, complemented
295C2×#546—111no—
296#3314—1116no—
297C2×#489—111no—
298C2×#484—111no—
299C2×#480—111no—
300C2×#474—111no—
301C2×#468—111no—
302C2×#467—111no—
303C2×#464—111no—
304C2×#452—111no—
305C2×#450—111no—
306C2×#440—111no—
307C2×#435—111no—
308C2×#417—111no—
309C22×#102—111no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11#13714yes—
316C23×C11C22×D412yes—
317C23×C11C22×D412yes—
318C23×C11C22×D411yescharacteristic
319C22×D11—24no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—48no—
323C22×D11—42no—
324C22×D11—42no—
325C22×D11—42no—
326C22×D11—48no—
327C22×D11—42no—
328C22×D11—42no—
329C22×D11—84no—
330C22×D11—816no—
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—42no—
334Q8×C11—84no—
335D4×C11—28no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—24no—
341C2×C4×C11—24no—
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—42no—
351C2×C4×C11—42no—
352C2×C4×C11—42no—
353C2×C4×C11—42no—
354C2×C4×C11—84no—
355C2×C4×C11—84no—
356C2×C4×C11C22×D412yes—
357C2×C4×C11C22×D412yes—
358C2×C4×C11C22×D412yes—
359C2×C4×C11C22×D412yes—
360C2×C4×C11C22×D411yescharacteristic
361C2×C4×C11C2×#4112yes—
362C2×C4×C11H(5,𝔽2)12yes—
363C2×C4×C11C2511yescharacteristic
364C22⋊D11—48no—
365C22⋊D11—84no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—42no—
369C2×Dic11—42no—
370D44—24no—
371D44—22no—
372D44—22no—
373D44—22no—
374D44—48no—
375D44—42no—
376D44C2×#4114yes—
377C4×D11—48no—
378C4×D11—84no—
379Dic22—22no—
380Dic22—22no—
381Dic22—42no—
382C11⋊C8—22no—
383C11⋊C8—22no—
384C11⋊C8—22no—
385C11⋊C8—22no—
386C22×#41—111no—
387C23×D4—111no—
388C22×Q16—111no—
389C22×SD16—111no—
390C22×SD16—111no—
391C22×M16—111no—
392C23×C8—111no—
393#554—24no—
394#554C2×D1118yescomplemented
395#546—118no—
396#546—224no—
397C2×C4⋊Q8C2×D1111yescharacteristic, complemented
398C2×#125—21no—
399C2×#124—111no—
400C2×#123—221no—
401C2×C22⋊Q8—21no—
402C2×C22⋊Q8—21no—
403C2×C22⋊Q8—111no—
404C2×C22⋊Q8C2×D1111yescharacteristic
405C2×C22⋊Q8C2×D1111yescharacteristic, complemented
406C2×#121—111no—
407C2×#121—221no—
408C2×#120—221no—
409C2×C4×Q8C2×D1111yescharacteristic, complemented
410C2×C4×D4—21no—
411C2×C4×D4—111no—
412C2×C4×D4C2×D1111yescharacteristic
413C22×C4⋊C4C2×D1111yescharacteristic
414C22×C4⋊C4C2×D1111yescharacteristic, complemented
415C22×C22⋊C4—221no—
416#489—118no—
417#484—118no—
418#480—118no—
419#474—118no—
420#468—118no—
421#467—118no—
422#464—118no—
423#452—118no—
424#450—118no—
425#440—118no—
426#435—118no—
427C2×#107—111no—
428C2×#107—111no—
429C2×#107—111no—
430C2×C4⋊C8—111no—
431#417—118no—
432C2×#103—111no—
433C2×#103—111no—
434C2×#103—111no—
435C2×#103—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×#102—111no—
439C2×#102—111no—
440C2×#102—111no—
441C2×#102—118no—
442C2×#102—111no—
443C2×C22⋊C8—111no—
444C2×C22⋊C8—111no—
445C2×#97—111no—
446C22×C11—22no—
447C22×C11—28no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—44no—
453C22×C11#54612yes—
454C22×C11C2×#13714yes—
455C22×C11C2×#13712yes—
456C22×C11#57612yes—
457C22×C11C23×D411yescharacteristic
458C2×D11—24no—
459C2×D11—48no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—42no—
465C2×D11—816no—
466C2×D11—84no—
467C4×C11—22no—
468C4×C11—22no—
469C4×C11—22no—
470C4×C11—22no—
471C4×C11—42no—
472C4×C11—42no—
473C4×C11—42no—
474C4×C11—42no—
475C4×C11#54612yes—
476C4×C11C22×#4111yescharacteristic
477C4×C11C2×H(5,𝔽2)11yescharacteristic
478Dic11—42no—
479Dic11—42no—
480C25—221no—
481C2×#41—114no—
482C2×#41—224no—
483C2×#41—222no—
484C2×#41—442no—
485C22×Q8—21no—
486C22×Q8—111no—
487C22×Q8C22×D1111yescharacteristic
488C22×D4—111no—
489C22×D4—111no—
490C22×D4—114no—
491C22×D4—224no—
492C22×D4—221no—
493C22×D4—221no—
494C22×D4—221no—
495C22×D4—222no—
496C22×D4—442no—
497C22×D4C22⋊D1111yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—221no—
501C23×C4—221no—
502C23×C4C22×D1111yescharacteristic
503C23×C4C22×D1111yescharacteristic
504C2×Q16—114no—
505C2×Q16—442no—
506C2×SD16—114no—
507C2×SD16—114no—
508C2×SD16—224no—
509C2×SD16—442no—
510C2×M16—114no—
511C2×M16—442no—
512C22×C8—111no—
513C22×C8—111no—
514C22×C8—111no—
515C22×C8—111no—
516C22×C8—114no—
517C22×C8—442no—
518C4⋊Q8—22no—
519C4⋊Q8C22×D1114yescomplemented
520#125—28no—
521#124—114no—
522#124—222no—
523#123—228no—
524C22⋊Q8—22no—
525C22⋊Q8—22no—
526C22⋊Q8—28no—
527C22⋊Q8—28no—
528C22⋊Q8—114no—
529C22⋊Q8—222no—
530C22⋊Q8C22×D1114yes—
531C22⋊Q8C22×D1114yescomplemented
532#121—114no—
533#121—222no—
534#121—228no—
535#120—228no—
536C4×Q8—22no—
537C4×Q8C22×D1114yescomplemented
538C4×D4—28no—
539C4×D4—114no—
540C4×D4—222no—
541C4×D4C22⋊D1114yes—
542C4×D4C22×D1114yes—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4C22⋊D1111yescharacteristic
554C2×C4⋊C4C22×D1111yescharacteristic
555C2×C4⋊C4C22×D1111yescharacteristic
556C2×C4⋊C4C22×D1114yes—
557C2×C4⋊C4C22×D1111yescharacteristic
558C2×C4⋊C4C22×D1114yescomplemented
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—228no—
567C2×C22⋊C4C22⋊D1111yescharacteristic
568C2×C22⋊C4C22⋊D1111yescharacteristic
569C2×C42—21no—
570C2×C42C22×D1111yescharacteristic
571#107—114no—
572#107—114no—
573#107—114no—
574C4⋊C8—114no—
575#103—114no—
576#103—114no—
577#103—114no—
578#103—114no—
579#102—114no—
580#102—114no—
581#102—114no—
582#102—114no—
583#102—114no—
584#102—114no—
585C22⋊C8—114no—
586C22⋊C8—114no—
587#97—114no—
588C2×C11—24no—
589C2×C11—42no—
590C2×C11#331414yescomplemented
591C2×C11C2×#54611yescharacteristic
592C2×C11C22×#13711yescharacteristic
593C2×C11C2×#57611yescharacteristic
594D11—44no—
595D11—82no—
596C24—221no—
597C24—221no—
598C24—224no—
599C24—444no—
600C24—444no—
601C24—882no—
602C24C2×C22⋊D1111yescharacteristic
603C24C2×C22⋊D1111yescharacteristic
604#41—228no—
605#41—444no—
606#41—448no—
607C2×Q8—21no—
608C2×Q8—24no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—82no—
612C2×Q8—112no—
613C2×Q8—221no—
614C2×Q8—222no—
615C2×Q8—222no—
616C2×Q8C23×D1112yes—
617C2×D4—24no—
618C2×D4—114no—
619C2×D4—112no—
620C2×D4—112no—
621C2×D4—228no—
622C2×D4—224no—
623C2×D4—224no—
624C2×D4—222no—
625C2×D4—222no—
626C2×D4—222no—
627C2×D4—221no—
628C2×D4—224no—
629C2×D4—221no—
630C2×D4—444no—
631C2×D4—448no—
632C2×D4—444no—
633C2×D4—444no—
634C2×D4—882no—
635C2×D4C2×C22⋊D1114yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—82no—
647C22×C4—82no—
648C22×C4—221no—
649C22×C4—221no—
650C22×C4—224no—
651C22×C4—224no—
652C22×C4—444no—
653C22×C4—882no—
654C22×C4C2×C22⋊D1112yes—
655C22×C4C2×C22⋊D1112yes—
656C22×C4C2×C22⋊D1111yescharacteristic
657C22×C4C2×C22⋊D1111yescharacteristic
658C22×C4C2×C22⋊D1111yescharacteristic
659C22×C4C2×C22⋊D1111yescharacteristic
660C22×C4C23×D1112yes—
661C22×C4C23×D1112yes—
662C22×C4C23×D1111yescharacteristic
663Q16—444no—
664SD16—228no—
665SD16—444no—
666M16—444no—
667C2×C8—112no—
668C2×C8—112no—
669C2×C8—112no—
670C2×C8—112no—
671C2×C8—222no—
672C2×C8—222no—
673C2×C8—222no—
674C2×C8—222no—
675C2×C8—444no—
676C4⋊C4—21no—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—24no—
681C4⋊C4—24no—
682C4⋊C4—24no—
683C4⋊C4—24no—
684C4⋊C4—24no—
685C4⋊C4—112no—
686C4⋊C4—221no—
687C4⋊C4—224no—
688C4⋊C4C2×C22⋊D1114yes—
689C4⋊C4C23×D1112yes—
690C4⋊C4C23×D1112yes—
691C4⋊C4C23×D1112yes—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—224no—
695C22⋊C4—224no—
696C22⋊C4—224no—
697C22⋊C4—224no—
698C22⋊C4—224no—
699C22⋊C4C2×C22⋊D1114yes—
700C22⋊C4C2×C22⋊D1114yes—
701C42—24no—
702C42C2×C22⋊D1112yes—
703C42C23×D1112yes—
704C11C2×#331411yescharacteristic, complemented, Sylow
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—224no—
711C23—222no—
712C23—222no—
713C23—448no—
714C23—442no—
715C23—442no—
716C23—448no—
717C23—442no—
718C23—442no—
719C23—442no—
720C23—884no—
721C23—8816no—
722C23#6699514yes—
723C23C22×C22⋊D1112yes—
724C23C22×C22⋊D1112yes—
725C23C22×C22⋊D1111yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—84no—
730Q8—222no—
731Q8—222no—
732Q8—442no—
733D4—28no—
734D4—114no—
735D4—224no—
736D4—222no—
737D4—222no—
738D4—222no—
739D4—448no—
740D4—448no—
741D4—442no—
742D4—884no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
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—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—448no—
766C2×C4—442no—
767C2×C4—442no—
768C2×C4—884no—
769C2×C4#41×D1112yes—
770C2×C4#6704212yes—
771C2×C4C22×C22⋊D1112yes—
772C2×C4C22×C22⋊D1112yes—
773C2×C4C22×C22⋊D1112yes—
774C2×C4C22×C22⋊D1112yes—
775C2×C4C22×C22⋊D1111yescharacteristic
776C2×C4C24×D1111yescharacteristic
777C8—222no—
778C8—222no—
779C8—222no—
780C8—222no—
781C22—28no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—44no—
788C22—224no—
789C22—448no—
790C22—442no—
791C22—442no—
792C22—442no—
793C22—442no—
794C22—442no—
795C22—8816no—
796C22—884no—
797C22C2×#6699514yes—
798C22C2×#6699512yes—
799C22#1062336012yes—
800C22#1062336612yes—
801C22C23×C22⋊D1111yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—442no—
811C4—442no—
812C4#1062336012yes—
813C4C2×#41×D1111yescharacteristic
814C4C2×#6704211yescharacteristic
815C2—24no—
816C2—42no—
817C2—444no—
818C2—882no—
819C2#1308069114yesdirect product factor
820C2C2×#1062336011yescharacteristic
821C2C22×#6699511yescharacteristic
822C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC2×#10623081C2
hypercenterC2×#554D11
hypocenterC11C2×#3314
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #13080691C2direct (N × H)
3. C2×#10622702C2semidirect
4. C2×#10622583C2semidirect
5. C2×#10622580C2semidirect
6. C2×#10622700C2semidirect
7. C2×#10622662C2semidirect
8. C2×#10622664C2semidirect
9. C2×#10622641C2semidirect
10. C2×#10622660C2semidirect
11. C2×#10622659C2semidirect
12. C2×#10622639C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622579C2semidirect
15. C22×#66873C2semidirect
16. C2×C11×#554C2semidirect
20. C11×#554C22semidirect
21. C2×C11×C4⋊Q8C22semidirect
26. C2×C11×C22⋊Q8C22semidirect
27. C2×C4×Q8×C11C22semidirect
31. C22×C11×C4⋊C4C22semidirect
32. C22×#4326C22semidirect
38. C22×#4318C22semidirect
47. C2×#66899C22semidirect
49. C2×C22⋊(C11⋊C8)C22semidirect
50. #10622702C22semidirect
51. #10622700C22semidirect
52. #10622664C22semidirect
53. #10622662C22semidirect
54. #10622660C22semidirect
55. #10622659C22semidirect
56. #10622641C22semidirect
57. #10622639C22semidirect
58. #10622624C22semidirect
59. #10622583C22semidirect
60. C2×#66874C22semidirect
61. C2×#66874C22semidirect
62. C2×#66874C22semidirect
63. #10622580C22semidirect
64. #10622579C22semidirect
71. C2×#66873C22semidirect
72. C2×#66871C22semidirect
73. C2×#66871C22semidirect
74. C2×#66871C22semidirect
75. C2×C4⋊(C11⋊C8)C22semidirect
76. C2×#66867C22semidirect
102. C11×C4⋊Q8C23semidirect
109. C11×C22⋊Q8C23semidirect
111. C4×Q8×C11C23semidirect
128. C2×C11×C4⋊C4C23semidirect
137. C2×#4326C23semidirect
154. C2×#4318C23semidirect
168. #66899C23semidirect
170. C22⋊(C11⋊C8)C23semidirect
171. #66874C23semidirect
172. #66874C23semidirect
173. #66874C23semidirect
180. #66871C23semidirect
181. #66871C23semidirect
182. #66871C23semidirect
183. C4⋊(C11⋊C8)C23semidirect
184. #66867C23semidirect
294. C2×#554D11semidirect
394. #554C2×D11semidirect
397. C2×C4⋊Q8C2×D11semidirect
405. C2×C22⋊Q8C2×D11semidirect
409. C2×C4×Q8C2×D11semidirect
414. C22×C4⋊C4C2×D11semidirect
519. C4⋊Q8C22×D11semidirect
531. C22⋊Q8C22×D11semidirect
537. C4×Q8C22×D11semidirect
558. C2×C4⋊C4C22×D11semidirect
590. C2×C11#3314semidirect
704. C11C2×#3314semidirect
819. C2#13080691direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230812
#130806912
C2×#106227022
C2×#106225832
C2×#106225802
C2×#106227002
C2×#106226622
C2×#106226642
C2×#106226412
C2×#106226602
C2×#106226592
C2×#106226392
C2×#106226242
C2×#106225792
C22×#668732
C2×C11×#5542
C2×#331411