Finite Group Databasebeta

← C2×#13080697 #15630299

Subgroups — C2×#13080697 #15630299

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×#10623074C211yesmaximal, characteristic, complemented
2#13080697C2116yesmaximal, direct product factor
3C2×#10622668C211yesmaximal, characteristic, complemented
4C2×#10622657C211yesmaximal, characteristic, complemented
5C2×#10622646C211yesmaximal, characteristic, complemented
6C2×#10622620C211yesmaximal, characteristic, complemented
7C2×#10622655C211yesmaximal, characteristic, complemented
8C2×#10622664C211yesmaximal, characteristic, complemented
9C2×#10622667C211yesmaximal, characteristic, complemented
10C2×#10622852C211yesmaximal, characteristic, complemented
11C2×#10622831C211yesmaximal, characteristic, complemented
12C2×#10622631C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622845C211yesmaximal, characteristic, complemented
15C22×#66896C211yesmaximal, characteristic, complemented
16C2×C11×#546C211yesmaximal, characteristic
17C22×C11×#41C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C11×#546—24no—
20C11×#546C2218yes—
21C2×C11×#124C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121—21no—
25C2×C11×#121C2211yescharacteristic
26C2×C11×#120—21no—
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C22×C11×C22⋊C4—21no—
30C22×#4326C2211yescharacteristic, complemented
31C2×D4×Dic11—21no—
32C22×#4324C2211yescharacteristic
33C22×#4324C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic, complemented
36C2×#66977C2211yescharacteristic
37C2×#66977C2211yescharacteristic, complemented
38C22×#4318C2211yescharacteristic, complemented
39C23×C11⋊C8C2211yescharacteristic
40#10623074—24no—
41#10623074C2218yescomplemented
42C2×#66943—21no—
43C2×#66931—21no—
44C2×#66931—21no—
45C2×#66922C2211yescharacteristic, complemented
46C2×C4×Dic22C2211yescharacteristic, complemented
47#10622852C2218yescomplemented
48#10622845C2218yescomplemented
49C2×#66899C2211yescharacteristic, complemented
50C2×#66899C2211yescharacteristic, complemented
51C2×#66899C2211yescharacteristic, complemented
52#10622831C2218yescomplemented
53C2×#66896C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57C2×#66896C2211yescharacteristic
58C2×#66896C2211yescharacteristic
59C2×#66896C2218yescomplemented
60C2×C22⋊(C11⋊C8)C2211yescharacteristic
61C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
62#10622668C2218yescomplemented
63#10622667C2218yescomplemented
64#10622664C2218yescomplemented
65#10622657C2218yescomplemented
66#10622655C2218yescomplemented
67#10622646C2218yescomplemented
68#10622631C2218yescomplemented
69#10622624C2218yescomplemented
70#10622620C2218yescomplemented
71C2×#66874C2211yescharacteristic, complemented
72C2×#66871C2211yescharacteristic, complemented
73C2×#66871C2211yescharacteristic, complemented
74C2×#66871C2211yescharacteristic, complemented
75C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
76C2×#66867C2211yescharacteristic, complemented
77C25×C11—21no—
78C2×C11×#41—22no—
79C2×C11×#41—24no—
80C2×C11×#41—42no—
81C2×C11×#41C2314yes—
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11—24no—
84C22×D4×C11—21no—
85C22×D4×C11—21no—
86C22×D4×C11—21no—
87C22×D4×C11—22no—
88C22×D4×C11—42no—
89C22×D4×C11D411yescharacteristic
90C22×D4×C11C2311yescharacteristic
91C22×D4×C11C2314yes—
92C22×D4×C11C2311yescharacteristic
93C23×C4×C11—21no—
94C23×C4×C11—21no—
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C23×Dic11—21no—
98C23×Dic11—21no—
99C22×Dic22—21no—
100C22×Dic22C2311yescharacteristic
101C11×#124—22no—
102C11×#124C2314yes—
103C11×#123—28no—
104C11×C22⋊Q8—22no—
105C11×C22⋊Q8C2314yes—
106C11×#121—22no—
107C11×#121—28no—
108C11×#121C2314yes—
109C11×#120—28no—
110C4×D4×C11—22no—
111C4×D4×C11D414yes—
112C4×D4×C11C2314yes—
113C4×D4×C11C2314yes—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4D411yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—28no—
123C2×C11×C22⋊C4D411yescharacteristic
124C2×C11×C22⋊C4D411yescharacteristic
125C2×C42×C11C2311yescharacteristic
126C2×C22⋊Dic11—21no—
127C2×C22⋊Dic11—21no—
128C2×#4326—42no—
129C2×#4326C2314yescomplemented
130D4×Dic11—28no—
131C2×#4324—24no—
132C2×#4324—42no—
133C2×#4324C2314yes—
134C2×#4324C2314yes—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11—21no—
137C2×C4⋊Dic11—21no—
138C2×C4⋊Dic11—22no—
139C2×C4⋊Dic11—22no—
140C2×C4⋊Dic11C2311yescharacteristic
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2314yes—
144C2×C4⋊Dic11C2314yescomplemented
145#66977—22no—
146#66977—22no—
147#66977C2314yes—
148#66977C2314yescomplemented
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×C4×Dic11—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#66943—28no—
162#66931—28no—
163#66931—28no—
164#66922—22no—
165#66922C2314yescomplemented
166C4×Dic22—22no—
167C4×Dic22C2314yescomplemented
168#66899C2314yescomplemented
169#66899C2314yescomplemented
170#66899C2314yescomplemented
171#66896C2314yes—
172#66896C2314yes—
173#66896C2314yes—
174#66896C2314yes—
175#66896C2314yes—
176#66896C2314yes—
177C22⋊(C11⋊C8)C2314yes—
178C22⋊(C11⋊C8)C2314yescomplemented
179#66874C2314yescomplemented
180#66871C2314yescomplemented
181#66871C2314yescomplemented
182#66871C2314yescomplemented
183C4⋊(C11⋊C8)C2314yescomplemented
184#66867C2314yescomplemented
185C2×#3314—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—24no—
189C24×C11—44no—
190C24×C11—44no—
191C24×C11—82no—
192C24×C11C2×D411yescharacteristic
193C24×C11C2×D411yescharacteristic
194C11×#41—28no—
195C11×#41—44no—
196C11×#41—48no—
197C2×Q8×C11—21no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C2×Q8×C11C2412yes—
201C2×D4×C11—24no—
202C2×D4×C11—28no—
203C2×D4×C11—24no—
204C2×D4×C11—24no—
205C2×D4×C11—21no—
206C2×D4×C11—24no—
207C2×D4×C11—21no—
208C2×D4×C11—22no—
209C2×D4×C11—22no—
210C2×D4×C11—22no—
211C2×D4×C11—44no—
212C2×D4×C11—48no—
213C2×D4×C11—44no—
214C2×D4×C11—44no—
215C2×D4×C11—82no—
216C2×D4×C11C2×D414yes—
217C2×D4×C11#4114yes—
218C2×D4×C11C2412yes—
219C2×D4×C11C2412yes—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—24no—
227C22×C4×C11—24no—
228C22×C4×C11—44no—
229C22×C4×C11—82no—
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2412yes—
237C22×C4×C11C2412yes—
238C22×C4×C11C2411yescharacteristic
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—24no—
244C22×Dic11—24no—
245C22×Dic11—82no—
246C22×Dic11—82no—
247C2×Dic22—21no—
248C2×Dic22—24no—
249C2×Dic22—22no—
250C2×Dic22—22no—
251C2×Dic22—82no—
252C2×Dic22C2412yes—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4C2×D414yes—
256C11×C4⋊C4C2412yes—
257C11×C22⋊C4—24no—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—24no—
262C11×C22⋊C4C2×D414yes—
263C11×C22⋊C4C2×D414yes—
264C42×C11C2×D412yes—
265C42×C11C2412yes—
266C22⋊Dic11—24no—
267C22⋊Dic11—24no—
268#4326—44no—
269#4324—28no—
270#4324—44no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11—24no—
275C4⋊Dic11—24no—
276C4⋊Dic11—24no—
277C4⋊Dic11C2412yes—
278C4⋊Dic11C2412yes—
279C4⋊Dic11C2412yes—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283C4×Dic11—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×#554—111no—
295C2×#546D1111yescharacteristic
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—24no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—48no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11—48no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11—84no—
326C23×C11—816no—
327C23×C11#13714yes—
328C23×C11C22×D412yes—
329C23×C11C22×D412yes—
330C23×C11C22×D411yescharacteristic
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—42no—
334D4×C11—28no—
335D4×C11—24no—
336D4×C11—22no—
337D4×C11—22no—
338D4×C11—22no—
339D4×C11—48no—
340D4×C11—48no—
341D4×C11—42no—
342D4×C11—84no—
343D4×C11C2×#4114yes—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—24no—
349C2×C4×C11—24no—
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—48no—
357C2×C4×C11—42no—
358C2×C4×C11—42no—
359C2×C4×C11—84no—
360C2×C4×C11C22×D412yes—
361C2×C4×C11C22×D412yes—
362C2×C4×C11C22×D412yes—
363C2×C4×C11C22×D412yes—
364C2×C4×C11C22×D411yescharacteristic
365C2×C4×C11C2×#4112yes—
366C2×C4×C11H(5,𝔽2)12yes—
367C2×C4×C11C2511yescharacteristic
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—42no—
373C2×Dic11—42no—
374C2×Dic11—42no—
375C2×Dic11—42no—
376C2×Dic11—84no—
377C2×Dic11—84no—
378Dic22—22no—
379Dic22—22no—
380Dic22—42no—
381Dic22—84no—
382C11⋊C8—22no—
383C11⋊C8—22no—
384C11⋊C8—22no—
385C11⋊C8—22no—
386C22×#41C2×D1111yescharacteristic
387C23×D4C2×D1111yescharacteristic
388C22×Q16—111no—
389C22×SD16—111no—
390C22×SD16—111no—
391C22×M16—111no—
392C23×C8—111no—
393#554—118no—
394#554—224no—
395#546—24no—
396#546C2×D1118yes—
397C2×C4⋊Q8—111no—
398C2×#125—221no—
399C2×#124C2×D1111yescharacteristic
400C2×#123—21no—
401C2×C22⋊Q8—111no—
402C2×C22⋊Q8—111no—
403C2×C22⋊Q8—221no—
404C2×C22⋊Q8—221no—
405C2×C22⋊Q8C2×D1111yescharacteristic
406C2×#121—21no—
407C2×#121C2×D1111yescharacteristic
408C2×#120—21no—
409C2×C4×Q8—111no—
410C2×C4×D4—221no—
411C2×C4×D4C2×D1111yescharacteristic
412C2×C4×D4C2×D1111yescharacteristic
413C22×C4⋊C4—111no—
414C22×C4⋊C4—111no—
415C22×C22⋊C4—21no—
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—24no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—44no—
454C22×C11—48no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—816no—
461C22×C11—84no—
462C22×C11#54612yes—
463C22×C11C2×#13714yes—
464C22×C11C2×#13712yes—
465C22×C11#57612yes—
466C22×C11C23×D411yescharacteristic
467C4×C11—22no—
468C4×C11—22no—
469C4×C11—22no—
470C4×C11—22no—
471C4×C11—42no—
472C4×C11—42no—
473C4×C11#54612yes—
474C4×C11C22×#4111yescharacteristic
475C4×C11C2×H(5,𝔽2)11yescharacteristic
476Dic11—42no—
477Dic11—42no—
478Dic11—42no—
479Dic11—42no—
480C25—21no—
481C2×#41—22no—
482C2×#41—24no—
483C2×#41—42no—
484C2×#41C22×D1114yes—
485C22×Q8—111no—
486C22×Q8—221no—
487C22×Q8C22×D1111yescharacteristic
488C22×D4—24no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—22no—
493C22×D4—42no—
494C22×D4C22⋊D1111yescharacteristic
495C22×D4C22×D1111yescharacteristic
496C22×D4C22×D1114yes—
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—114no—
519C4⋊Q8—222no—
520#125—228no—
521#124—22no—
522#124C22×D1114yes—
523#123—28no—
524C22⋊Q8—22no—
525C22⋊Q8—114no—
526C22⋊Q8—114no—
527C22⋊Q8—222no—
528C22⋊Q8—222no—
529C22⋊Q8—228no—
530C22⋊Q8—228no—
531C22⋊Q8C22×D1114yes—
532#121—22no—
533#121—28no—
534#121C22×D1114yes—
535#120—28no—
536C4×Q8—114no—
537C4×Q8—222no—
538C4×D4—22no—
539C4×D4—228no—
540C4×D4C22⋊D1114yes—
541C4×D4C22×D1114yes—
542C4×D4C22×D1114yes—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—111no—
547C2×C4⋊C4—114no—
548C2×C4⋊C4—114no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4—221no—
551C2×C4⋊C4—222no—
552C2×C4⋊C4—222no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—221no—
556C2×C4⋊C4—221no—
557C2×C4⋊C4C22⋊D1111yescharacteristic
558C2×C4⋊C4C22×D1111yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—28no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4C22⋊D1111yescharacteristic
568C2×C22⋊C4C22⋊D1111yescharacteristic
569C2×C42—221no—
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—44no—
591C2×C11—82no—
592C2×C11#331414yescomplemented
593C2×C11C2×#54611yescharacteristic
594C2×C11C22×#13711yescharacteristic
595C2×C11C2×#57611yescharacteristic
596C24—21no—
597C24—21no—
598C24—24no—
599C24—44no—
600C24—44no—
601C24—82no—
602C24C2×C22⋊D1111yescharacteristic
603C24C2×C22⋊D1111yescharacteristic
604#41—28no—
605#41—44no—
606#41—48no—
607C2×Q8—21no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—112no—
611C2×Q8—221no—
612C2×Q8—224no—
613C2×Q8—222no—
614C2×Q8—222no—
615C2×Q8—882no—
616C2×Q8C23×D1112yes—
617C2×D4—24no—
618C2×D4—28no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—21no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—44no—
628C2×D4—48no—
629C2×D4—44no—
630C2×D4—44no—
631C2×D4—82no—
632C2×D4#434114yes—
633C2×D4C2×C22⋊D1114yes—
634C2×D4C23×D1112yes—
635C2×D4C23×D1112yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—44no—
645C22×C4—82no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—221no—
650C22×C4—224no—
651C22×C4—224no—
652C22×C4—882no—
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—24no—
677C4⋊C4—21no—
678C4⋊C4—112no—
679C4⋊C4—112no—
680C4⋊C4—112no—
681C4⋊C4—221no—
682C4⋊C4—224no—
683C4⋊C4—224no—
684C4⋊C4—221no—
685C4⋊C4—221no—
686C4⋊C4—224no—
687C4⋊C4—224no—
688C4⋊C4—224no—
689C4⋊C4—224no—
690C4⋊C4C2×C22⋊D1114yes—
691C4⋊C4C23×D1112yes—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—224no—
698C22⋊C4—224no—
699C22⋊C4C2×C22⋊D1114yes—
700C22⋊C4C2×C22⋊D1114yes—
701C42—224no—
702C42C2×C22⋊D1112yes—
703C42C23×D1112yes—
704C11C2×#331411yescharacteristic, complemented, Sylow
705C23—22no—
706C23—22no—
707C23—22no—
708C23—24no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—48no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—48no—
718C23—42no—
719C23—42no—
720C23—84no—
721C23—816no—
722C23#6700414yes—
723C23C22×C22⋊D1112yes—
724C23C22×C22⋊D1112yes—
725C23C22×C22⋊D1111yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—222no—
730Q8—222no—
731Q8—442no—
732Q8—884no—
733D4—28no—
734D4—24no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—48no—
739D4—48no—
740D4—42no—
741D4—84no—
742D4C2×#434114yes—
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—48no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—84no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—442no—
764C2×C4—442no—
765C2×C4—442no—
766C2×C4—442no—
767C2×C4—884no—
768C2×C4—884no—
769C2×C4C2×#434112yes—
770C2×C4#6703712yes—
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—24no—
786C22—22no—
787C22—22no—
788C22—44no—
789C22—48no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—816no—
796C22—84no—
797C22#1062333712yes—
798C22C2×#6700414yes—
799C22C2×#6700412yes—
800C22#1062336612yes—
801C22C23×C22⋊D1111yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—42no—
807C4—42no—
808C4—442no—
809C4—442no—
810C4—442no—
811C4—442no—
812C4#1062333712yes—
813C4C22×#434111yescharacteristic
814C4C2×#6703711yescharacteristic
815C2—24no—
816C2—42no—
817C2—44no—
818C2—82no—
819C2#1308069714yesdirect product factor
820C2C2×#1062333711yescharacteristic
821C2C22×#6700411yescharacteristic
822C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#546C2
socleC23×C11C22×D4
hypercenterC2×#546D11
hypocenterC11C2×#3314
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#10623074C2semidirect
2. #13080697C2direct (N × H)
3. C2×#10622668C2semidirect
4. C2×#10622657C2semidirect
5. C2×#10622646C2semidirect
6. C2×#10622620C2semidirect
7. C2×#10622655C2semidirect
8. C2×#10622664C2semidirect
9. C2×#10622667C2semidirect
10. C2×#10622852C2semidirect
11. C2×#10622831C2semidirect
12. C2×#10622631C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622845C2semidirect
15. C22×#66896C2semidirect
30. C22×#4326C22semidirect
35. C22×C4⋊Dic11C22semidirect
37. C2×#66977C22semidirect
38. C22×#4318C22semidirect
41. #10623074C22semidirect
45. C2×#66922C22semidirect
46. C2×C4×Dic22C22semidirect
47. #10622852C22semidirect
48. #10622845C22semidirect
49. C2×#66899C22semidirect
50. C2×#66899C22semidirect
51. C2×#66899C22semidirect
52. #10622831C22semidirect
59. C2×#66896C22semidirect
61. C2×C22⋊(C11⋊C8)C22semidirect
62. #10622668C22semidirect
63. #10622667C22semidirect
64. #10622664C22semidirect
65. #10622657C22semidirect
66. #10622655C22semidirect
67. #10622646C22semidirect
68. #10622631C22semidirect
69. #10622624C22semidirect
70. #10622620C22semidirect
71. C2×#66874C22semidirect
72. C2×#66871C22semidirect
73. C2×#66871C22semidirect
74. C2×#66871C22semidirect
75. C2×C4⋊(C11⋊C8)C22semidirect
76. C2×#66867C22semidirect
129. C2×#4326C23semidirect
144. C2×C4⋊Dic11C23semidirect
148. #66977C23semidirect
154. C2×#4318C23semidirect
165. #66922C23semidirect
167. C4×Dic22C23semidirect
168. #66899C23semidirect
169. #66899C23semidirect
170. #66899C23semidirect
178. C22⋊(C11⋊C8)C23semidirect
179. #66874C23semidirect
180. #66871C23semidirect
181. #66871C23semidirect
182. #66871C23semidirect
183. C4⋊(C11⋊C8)C23semidirect
184. #66867C23semidirect
592. C2×C11#3314semidirect
704. C11C2×#3314semidirect
819. C2#13080697direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230742
#130806972
C2×#106226682
C2×#106226572
C2×#106226462
C2×#106226202
C2×#106226552
C2×#106226642
C2×#106226672
C2×#106228522
C2×#106228312
C2×#106226312
C2×#106226242
C2×#106228452
C22×#668962
C2×C11×#5462
C2×#331411