Finite Group Databasebeta

← C2×#13081050 #15632298

Subgroups — C2×#13081050 #15632298

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623072C211yesmaximal, characteristic, complemented
2#13081050C2116yesmaximal, direct product factor
3C2×#10622693C211yesmaximal, characteristic, complemented
4C2×#10622583C211yesmaximal, characteristic, complemented
5C2×#10622648C211yesmaximal, characteristic, complemented
6C2×#10622584C211yesmaximal, characteristic, complemented
7C2×#10622646C211yesmaximal, characteristic, complemented
8C2×#10622704C211yesmaximal, characteristic, complemented
9C2×#10622622C211yesmaximal, characteristic, complemented
10C2×#10622655C211yesmaximal, characteristic, complemented
11C2×#10622654C211yesmaximal, characteristic, complemented
12C2×#10622631C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622577C211yesmaximal, characteristic, complemented
15C22×#66871C211yesmaximal, characteristic, complemented
16C2×C11×#547C211yesmaximal, characteristic
17C22×C11×#41—21no—
18C11×#547—24no—
19C11×#547C2218yes—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8—21no—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C2×#66988—21no—
31C22×#4324C2211yescharacteristic
32C2×#66979C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36C22×#4318C2211yescharacteristic
37C23×C11⋊C8C2211yescharacteristic
38#10623072—24no—
39#10623072C2218yescomplemented
40C2×#66942—21no—
41C2×#66932—21no—
42C2×#66930—21no—
43C2×#66923C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46C2×#66896C2211yescharacteristic
47C2×#66896C2211yescharacteristic
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic
50#10622704C2218yescomplemented
51#10622693C2218yescomplemented
52#10622655C2218yescomplemented
53#10622654C2218yescomplemented
54#10622648C2218yescomplemented
55#10622646C2218yescomplemented
56#10622631C2218yescomplemented
57#10622624C2218yescomplemented
58#10622622C2218yescomplemented
59#10622584C2218yescomplemented
60#10622583C2218yescomplemented
61C2×#66874C2211yescharacteristic
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64#10622577C2218yescomplemented
65C2×#66872C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66871C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71C2×#66871C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73C2×#66871C2211yescharacteristic
74C2×#66871C2218yescomplemented
75C2×C4⋊(C11⋊C8)C2211yescharacteristic
76C2×#66867C2211yescharacteristic
77C2×C11×#41—28no—
78C2×C11×#41—48no—
79C22×Q8×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11D411yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×Dic11—21no—
90C22×Dic22C2311yescharacteristic
91C11×C4⋊Q8—22no—
92C11×C4⋊Q8C2314yes—
93C11×#123—28no—
94C11×#123—28no—
95C11×C22⋊Q8—28no—
96C11×#121—22no—
97C11×#121—22no—
98C11×#121C2314yes—
99C11×#121C2314yes—
100C4×D4×C11—22no—
101C4×D4×C11D414yes—
102C4×D4×C11C2314yes—
103C4×D4×C11C2314yes—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4—22no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2314yes—
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4D411yescharacteristic
119C2×C11×C22⋊C4D411yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C2×C22⋊Dic11—21no—
122C2×C22⋊Dic11—21no—
123C2×C22⋊Dic11—21no—
124#66988—28no—
125C2×#4324—24no—
126C2×#4324C2314yes—
127#66979—22no—
128#66979C2314yes—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11—22no—
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2314yes—
135#66977—22no—
136#66977—22no—
137#66977C2314yes—
138#66977C2314yes—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×C4×Dic11—21no—
145C2×C4×Dic11—21no—
146C2×#4318—24no—
147C2×#4318C2314yes—
148C22×C11⋊C8—24no—
149C22×C11⋊C8C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C22×C11⋊C8C2314yes—
153C22×C11⋊C8C2311yescharacteristic
154#66942—28no—
155#66932—28no—
156#66930—28no—
157#66923—22no—
158#66923C2314yes—
159C4×Dic22—22no—
160C4×Dic22C2314yes—
161#66896C2314yes—
162#66896C2314yes—
163#66896C2314yes—
164C22⋊(C11⋊C8)C2314yes—
165C22⋊(C11⋊C8)C2314yes—
166#66874C2314yes—
167#66874C2314yes—
168#66874C2314yes—
169#66872C2314yes—
170#66872C2314yes—
171#66872C2314yes—
172#66871C2314yes—
173#66871C2314yes—
174#66871C2314yes—
175#66871C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178C4⋊(C11⋊C8)C2314yes—
179#66867C2314yes—
180C2×#3343—111nomaximal, Sylow
181C24×C11—21no—
182C24×C11C2×D411yescharacteristic
183C24×C11C2×D411yescharacteristic
184C11×#41—432no—
185C2×Q8×C11—24no—
186C2×Q8×C11—44no—
187C2×D4×C11—24no—
188C2×D4×C11—24no—
189C2×D4×C11—24no—
190C2×D4×C11—21no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—44no—
194C2×D4×C11—44no—
195C2×D4×C11C2×D414yes—
196C2×D4×C11C2412yes—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—24no—
205C22×C4×C11—24no—
206C22×C4×C11—24no—
207C22×C4×C11—44no—
208C22×C4×C11—44no—
209C22×C4×C11—44no—
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2411yescharacteristic
219C22×Dic11—24no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—44no—
225C2×Dic22—21no—
226C2×Dic22—22no—
227C2×Dic22—22no—
228C2×Dic22C2412yes—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—24no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4C2×D414yes—
236C11×C4⋊C4C2412yes—
237C11×C4⋊C4C2412yes—
238C11×C4⋊C4C2412yes—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—24no—
242C11×C22⋊C4C2×D414yes—
243C11×C22⋊C4C2×D414yes—
244C42×C11C2×D412yes—
245C42×C11C2412yes—
246C22⋊Dic11—24no—
247C22⋊Dic11—24no—
248C22⋊Dic11—24no—
249#4324—28no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11—24no—
254C4⋊Dic11C2412yes—
255C4⋊Dic11C2412yes—
256C4⋊Dic11C2412yes—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262C4×Dic11—24no—
263C4×Dic11—24no—
264#4318—28no—
265C2×C11⋊C8—28no—
266C2×C11⋊C8—22no—
267C2×C11⋊C8—22no—
268C2×C11⋊C8—22no—
269C2×C11⋊C8#4114yescomplemented
270C2×C11⋊C8C2412yes—
271C2×C11⋊C8C2412yes—
272C2×C11⋊C8C2412yes—
273C2×C11⋊C8C2412yes—
274C2×#552—111no—
275C2×#547D1111yescharacteristic
276#3343—1116no—
277C2×#501—111no—
278C2×#484—111no—
279C2×#482—111no—
280C2×#483—111no—
281C2×#480—111no—
282C2×#477—111no—
283C2×#478—111no—
284C2×#468—111no—
285C2×#465—111no—
286C2×#440—111no—
287C2×#435—111no—
288C2×#428—111no—
289C22×#107—111no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11—42no—
299C23×C11AGL(1,ℤ/8)14yes—
300C23×C11C22×D412yes—
301C23×C11C22×D412yes—
302C23×C11C22×D411yescharacteristic
303Q8×C11—48no—
304D4×C11—28no—
305D4×C11—22no—
306D4×C11—22no—
307D4×C11—48no—
308D4×C11—48no—
309D4×C11—42no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—24no—
315C2×C4×C11—24no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—48no—
324C2×C4×C11—48no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—48no—
329C2×C4×C11C22×D412yes—
330C2×C4×C11C22×D412yes—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×D412yes—
333C2×C4×C11C22×D411yescharacteristic
334C2×C4×C11C2×#4112yes—
335C2×C4×C112−1+412yes—
336C2×C4×C11C2511yescharacteristic
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—42no—
342C2×Dic11—48no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346Dic22—22no—
347Dic22—22no—
348Dic22—42no—
349C11⋊C8—22no—
350C11⋊C8—22no—
351C11⋊C8—22no—
352C11⋊C8C2×#4114yescomplemented
353C22×#41—21no—
354C22×SD16—111no—
355C22×M16—111no—
356C23×C8—111no—
357#552—118no—
358#552—224no—
359#547—24no—
360#547C2×D1118yes—
361C2×C4⋊Q8C2×D1111yescharacteristic
362C2×#126—221no—
363C2×#125—111no—
364C2×#125—221no—
365C2×#123—21no—
366C2×#123—21no—
367C2×#123—221no—
368C2×C22⋊Q8—21no—
369C2×C22⋊Q8—111no—
370C2×C22⋊Q8—111no—
371C2×#121C2×D1111yescharacteristic
372C2×#121C2×D1111yescharacteristic
373C2×C4×Q8—111no—
374C2×C4×D4C2×D1111yescharacteristic
375C2×C4×D4C2×D1111yescharacteristic
376C2×#117—111no—
377C2×#117—221no—
378C22×C4⋊C4—111no—
379C22×C4⋊C4C2×D1111yescharacteristic
380C22×C4⋊C4C2×D1111yescharacteristic
381#501—118no—
382#484—118no—
383#483—118no—
384#482—118no—
385#480—118no—
386#478—118no—
387#477—118no—
388#468—118no—
389#465—118no—
390#440—118no—
391#435—118no—
392#428—118no—
393C2×#107—111no—
394C2×#107—111no—
395C2×#107—111no—
396C2×#107—111no—
397C2×#107—118no—
398C2×#107—111no—
399C2×#107—111no—
400C2×#106—111no—
401C2×#106—111no—
402C2×#106—111no—
403C2×C4⋊C8—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#102—111no—
408C2×#102—111no—
409C2×#102—111no—
410C2×C22⋊C8—111no—
411C2×C22⋊C8—111no—
412C2×#97—111no—
413C22×C11—28no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—44no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—84no—
424C22×C11#54712yes—
425C22×C11C2×AGL(1,ℤ/8)14yes—
426C22×C11C2×AGL(1,ℤ/8)12yes—
427C22×C11#57812yes—
428C22×C11C23×D411yescharacteristic
429C4×C11—22no—
430C4×C11—22no—
431C4×C11—22no—
432C4×C11—22no—
433C4×C11—42no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11#54712yes—
437C4×C11C22×#4111yescharacteristic
438C4×C11C2×2−1+411yescharacteristic
439Dic11—42no—
440Dic11—42no—
441Dic11—42no—
442Dic11—42no—
443C2×#41—28no—
444C2×#41—48no—
445C22×Q8—21no—
446C22×Q8—111no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4C22⋊D1111yescharacteristic
450C22×D4C22×D1111yescharacteristic
451C23×C4—21no—
452C23×C4—21no—
453C23×C4—21no—
454C23×C4—221no—
455C23×C4C22×D1111yescharacteristic
456C23×C4C22×D1111yescharacteristic
457C2×SD16—114no—
458C2×SD16—224no—
459C2×M16—114no—
460C2×M16—224no—
461C22×C8—111no—
462C22×C8—111no—
463C22×C8—114no—
464C22×C8—111no—
465C22×C8—111no—
466C22×C8—224no—
467C4⋊Q8—22no—
468C4⋊Q8C22×D1114yes—
469#126—228no—
470#125—114no—
471#125—228no—
472#125—222no—
473#123—28no—
474#123—28no—
475#123—228no—
476C22⋊Q8—28no—
477C22⋊Q8—114no—
478C22⋊Q8—114no—
479C22⋊Q8—222no—
480C22⋊Q8—222no—
481#121—22no—
482#121—22no—
483#121C22×D1114yes—
484#121C22×D1114yes—
485C4×Q8—114no—
486C4×Q8—222no—
487C4×D4—22no—
488C4×D4C22⋊D1114yes—
489C4×D4C22×D1114yes—
490C4×D4C22×D1114yes—
491#117—114no—
492#117—222no—
493#117—228no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—114no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—222no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4C22⋊D1111yescharacteristic
511C2×C4⋊C4C22×D1111yescharacteristic
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C4⋊C4C22×D1111yescharacteristic
514C2×C4⋊C4C22×D1114yes—
515C2×C4⋊C4C22×D1114yes—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4C22⋊D1111yescharacteristic
523C2×C22⋊C4C22⋊D1111yescharacteristic
524C2×C42—221no—
525C2×C42—221no—
526C2×C42C22×D1111yescharacteristic
527#107—114no—
528#107—114no—
529#107—114no—
530#107—114no—
531#107—114no—
532#107—114no—
533#106—114no—
534#106—114no—
535#106—114no—
536C4⋊C8—114no—
537#103—114no—
538#103—114no—
539#103—114no—
540#102—114no—
541#102—114no—
542#102—114no—
543C22⋊C8—114no—
544C22⋊C8—114no—
545#97—114no—
546C2×C11—24no—
547C2×C11—42no—
548C2×C11—82no—
549C2×C11#334314yescomplemented
550C2×C11C2×#54711yescharacteristic
551C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
552C2×C11C2×#57811yescharacteristic
553C24—21no—
554C24C2×C22⋊D1111yescharacteristic
555C24C2×C22⋊D1111yescharacteristic
556#41—432no—
557C2×Q8—24no—
558C2×Q8—44no—
559C2×Q8—112no—
560C2×Q8—221no—
561C2×Q8—222no—
562C2×Q8—222no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4C2×C22⋊D1114yes—
572C2×D4C23×D1112yes—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—224no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—444no—
592C22×C4C2×C22⋊D1112yes—
593C22×C4C2×C22⋊D1112yes—
594C22×C4C2×C22⋊D1111yescharacteristic
595C22×C4C2×C22⋊D1111yescharacteristic
596C22×C4C2×C22⋊D1111yescharacteristic
597C22×C4C2×C22⋊D1111yescharacteristic
598C22×C4C23×D1112yes—
599C22×C4C23×D1112yes—
600C22×C4C23×D1111yescharacteristic
601SD16—228no—
602M16—228no—
603C2×C8—114no—
604C2×C8—112no—
605C2×C8—112no—
606C2×C8—112no—
607C2×C8—112no—
608C2×C8—228no—
609C2×C8—222no—
610C2×C8—222no—
611C2×C8—222no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—112no—
619C4⋊C4—112no—
620C4⋊C4—112no—
621C4⋊C4—221no—
622C4⋊C4—221no—
623C4⋊C4—224no—
624C4⋊C4—221no—
625C4⋊C4—224no—
626C4⋊C4—224no—
627C4⋊C4—224no—
628C4⋊C4—224no—
629C4⋊C4—224no—
630C4⋊C4C2×C22⋊D1114yes—
631C4⋊C4C23×D1112yes—
632C4⋊C4C23×D1112yes—
633C4⋊C4C23×D1112yes—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—224no—
638C22⋊C4—224no—
639C22⋊C4—224no—
640C22⋊C4C2×C22⋊D1114yes—
641C22⋊C4C2×C22⋊D1114yes—
642C42—224no—
643C42—224no—
644C42C2×C22⋊D1112yes—
645C42C23×D1112yes—
646C11C2×#334311yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23#6698514yes—
657C23C22×C22⋊D1112yes—
658C23C22×C22⋊D1112yes—
659C23C22×C22⋊D1111yescharacteristic
660Q8—48no—
661Q8—222no—
662Q8—222no—
663Q8—442no—
664D4—28no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—48no—
669D4—42no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—48no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—48no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—448no—
694C2×C4—442no—
695C2×C4—442no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4#41×D1112yes—
699C2×C4#6704312yes—
700C2×C4C22×C22⋊D1112yes—
701C2×C4C22×C22⋊D1112yes—
702C2×C4C22×C22⋊D1112yes—
703C2×C4C22×C22⋊D1112yes—
704C2×C4C22×C22⋊D1111yescharacteristic
705C2×C4C24×D1111yescharacteristic
706C8—114no—
707C8—222no—
708C8—222no—
709C8—222no—
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—84no—
721C22C2×#6698514yes—
722C22C2×#6698512yes—
723C22#1062335512yes—
724C22#1062336912yes—
725C22C23×C22⋊D1111yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—442no—
734C4—442no—
735C4—442no—
736C4—442no—
737C4#1062335512yes—
738C4C2×#41×D1111yescharacteristic
739C4C2×#6704311yescharacteristic
740C2—24no—
741C2—42no—
742C2—82no—
743C2#1308105014yesdirect product factor
744C2C2×#1062335511yescharacteristic
745C2C22×#6698511yescharacteristic
746C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#547C2
socleC23×C11C22×D4
hypercenterC2×#547D11
hypocenterC11C2×#3343
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#10623072C2semidirect
2. #13081050C2direct (N × H)
3. C2×#10622693C2semidirect
4. C2×#10622583C2semidirect
5. C2×#10622648C2semidirect
6. C2×#10622584C2semidirect
7. C2×#10622646C2semidirect
8. C2×#10622704C2semidirect
9. C2×#10622622C2semidirect
10. C2×#10622655C2semidirect
11. C2×#10622654C2semidirect
12. C2×#10622631C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622577C2semidirect
15. C22×#66871C2semidirect
39. #10623072C22semidirect
50. #10622704C22semidirect
51. #10622693C22semidirect
52. #10622655C22semidirect
53. #10622654C22semidirect
54. #10622648C22semidirect
55. #10622646C22semidirect
56. #10622631C22semidirect
57. #10622624C22semidirect
58. #10622622C22semidirect
59. #10622584C22semidirect
60. #10622583C22semidirect
64. #10622577C22semidirect
74. C2×#66871C22semidirect
269. C2×C11⋊C8#41semidirect
352. C11⋊C8C2×#41semidirect
549. C2×C11#3343semidirect
646. C11C2×#3343semidirect
743. C2#13081050direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230722
#130810502
C2×#106226932
C2×#106225832
C2×#106226482
C2×#106225842
C2×#106226462
C2×#106227042
C2×#106226222
C2×#106226552
C2×#106226542
C2×#106226312
C2×#106226242
C2×#106225772
C22×#668712
C2×C11×#5472
C2×#334311