Finite Group Databasebeta

← C2×#13082593 #15661890

Subgroups — C2×#13082593 #15661890

Order 2816.

7142 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082593C2132yesmaximal, direct product factor
2C2×#10623110C211yesmaximal, characteristic, complemented
3C2×#10623110C211yesmaximal, characteristic, complemented
4C2×#10623226C212yesmaximal, complemented
5C2×#10623112C212yesmaximal, complemented
6C2×#10623112C212yesmaximal, complemented
7C2×#10623224C214yesmaximal, complemented
8C2×#10623257C212yesmaximal, complemented
9C2×#10623257C211yesmaximal, characteristic, complemented
10C2×#10623262C212yesmaximal, complemented
11C2×#10623223C214yesmaximal, complemented
12C2×#10623259C211yesmaximal, characteristic, complemented
13C2×#10623111C212yesmaximal, complemented
14C2×#10623111C211yesmaximal, characteristic, complemented
15C2×D11×#125C212yesmaximal, complemented
16C2×#10623105C212yesmaximal, complemented
17C2×C4×#4343C211yesmaximal, characteristic, complemented
18C2×C11×#557C211yesmaximal, characteristic, complemented
19C22×#4343C2211yescharacteristic
20C22×#4343C2212yes—
21C11×#557C22116yescomplemented
22C2×C11×C4⋊Q8C2211yescharacteristic
23C2×C11×C4⋊Q8C2212yes—
24C2×C11×#125C2214yes—
25C2×C11×#125C2212yes—
26C2×C4×Q8×C11C2212yes—
27C2×C4×Q8×C11C2212yes—
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×Q8×C11C2211yescharacteristic
30C2×#67000C2211yescharacteristic
31C2×#66999C2211yescharacteristic
32C2×#66999C2212yes—
33C2×#66999C2212yes—
34C2×#66999C2212yes—
35C2×#66999C2212yes—
36C2×Q8×Dic11C2212yes—
37C2×Q8×Dic11C2211yescharacteristic
38#10623262C22132yescomplemented
39#10623259C22116yescomplemented
40#10623257C22116yescomplemented
41#10623257C22132yescomplemented
42#10623226C22132yescomplemented
43#10623224C22164yescomplemented
44#10623223C22164yescomplemented
45D11×#125C22132yescomplemented
46#10623112C22132yescomplemented
47#10623112C22132yescomplemented
48#10623111C22116yescomplemented
49#10623111C22132yescomplemented
50#10623110C22116yescomplemented
51#10623110C22116yescomplemented
52#10623105C22132yescomplemented
53C4×#4343C22116yescomplemented
54C2×#66951C2212yes—
55C2×#66951C2214yes—
56C2×#66951C2214yes—
57C2×#66950C2212yes—
58C2×#66949C2214yes—
59C2×#66949C2214yes—
60C2×#66948C2211yescharacteristic
61C2×#66948C2212yes—
62C2×#66948C2214yes—
63C2×#66947C2214yes—
64C2×#66947C2214yes—
65C2×#66947C2214yes—
66C2×#66947C2214yes—
67C2×#66947C2212yes—
68C2×#66946C2214yes—
69C2×#66946C2212yes—
70C2×#66946C2211yescharacteristic
71C2×#66945C2212yes—
72C2×#66945C2211yescharacteristic
73C2×#66945C2212yes—
74C2×C4⋊C4×D11C2214yes—
75C2×C4⋊C4×D11C2212yes—
76C2×C4⋊C4×D11C2212yes—
77C2×C4⋊C4×D11C2214yes—
78C2×C4⋊C4×D11C2212yes—
79C2×#66943C2211yescharacteristic
80C2×#66943C2212yes—
81C2×#66942C2214yes—
82C2×#66942C2214yes—
83C2×#66942C2214yes—
84C2×#66940C2212yes—
85C2×#66929C2214yes—
86C2×C4×D44C2212yes—
87C2×C4×D44C2212yes—
88C2×C4×D44C2212yes—
89C2×C4×D44C2211yescharacteristic
90C2×C4×D44C2214yes—
91C2×C4×D44C2211yescharacteristic
92C2×C4×D44C2212yes—
93C2×#66925C2214yes—
94C2×#66925C2214yes—
95C2×#66925C2212yes—
96C2×C42×D11C2212yes—
97C2×C42×D11C2211yescharacteristic
98C2×#66923C2212yes—
99C2×#66923C2212yes—
100C2×#66922C2211yescharacteristic
101C22×Q8×C11C2312yes—
102C22×Q8×C11C2311yescharacteristic
103C22×Q8×C11C2311yescharacteristic
104C2×#4343—28no—
105C2×#4343—216no—
106C2×#4343C2318yes—
107C2×#4343C23116yes—
108C22×D44C2311yescharacteristic
109C22×D44C2312yes—
110C22×D44C2314yes—
111C22×D44C2312yes—
112C22×D44C2311yescharacteristic
113C22×C4×D11C2312yes—
114C22×C4×D11C2311yescharacteristic
115C22×C4×D11C2311yescharacteristic
116C22×C4×D11C2312yes—
117C22×C4×D11C2312yes—
118C22×C4×D11C2314yes—
119C22×C4×D11C2312yes—
120C22×C4×D11C2311yescharacteristic
121C22×C4×D11C2314yes—
122C22×C4×D11C2314yes—
123C22×Dic22C2312yes—
124C11×C4⋊Q8C2318yes—
125C11×C4⋊Q8C23116yes—
126C11×#125C23116yes—
127C11×#125C23132yes—
128C4×Q8×C11C2318yes—
129C4×Q8×C11C23116yes—
130C4×Q8×C11C2318yes—
131C4×Q8×C11C23116yes—
132C2×C11×C4⋊C4C2312yes—
133C2×C11×C4⋊C4C2314yes—
134C2×C11×C4⋊C4C2314yes—
135C2×C11×C4⋊C4C2314yes—
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2312yes—
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2312yes—
140C2×C11×C4⋊C4C2312yes—
141C2×C42×C11C2311yescharacteristic
142C2×C42×C11C2312yes—
143C2×C42×C11C2312yes—
144C2×C42×C11C2314yes—
145#67000C2318yes—
146#66999C23116yes—
147#66999C23116yes—
148#66999C23116yes—
149#66999C23116yes—
150#66999C2318yes—
151Q8×Dic11C23116yes—
152Q8×Dic11C2318yes—
153C2×(C2×D11)⋊C4C2312yes—
154C2×(C2×D11)⋊C4C2312yes—
155C2×(C2×D11)⋊C4C2314yes—
156C2×(C2×D11)⋊C4C2312yes—
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2314yes—
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2312yes—
162C2×(C2×D11)⋊C4C2312yes—
163C2×(C2×D11)⋊C4C2314yes—
164C2×(C2×D11)⋊C4C2314yes—
165C2×C4⋊Dic11C2312yes—
166C2×C4⋊Dic11C2312yes—
167C2×C4⋊Dic11C2311yescharacteristic
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2312yes—
170C2×C4⋊Dic11C2312yes—
171C2×C4⋊Dic11C2314yes—
172C2×Dic11⋊C4C2314yes—
173C2×Dic11⋊C4C2314yes—
174C2×Dic11⋊C4C2314yes—
175C2×Dic11⋊C4C2314yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2314yes—
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2314yes—
180C2×C4×Dic11C2311yescharacteristic
181C2×C4×Dic11C2312yes—
182C2×C4×Dic11C2311yescharacteristic
183C2×C4×Dic11C2311yescharacteristic
184C2×C4×Dic11C2312yes—
185C2×C4×Dic11C2314yes—
186#66951C23132yes—
187#66951C23132yes—
188#66951C23116yes—
189#66950C23116yes—
190#66949C23132yes—
191#66949C23132yes—
192#66948C23116yes—
193#66948C23132yes—
194#66948C2318yes—
195#66947C23132yes—
196#66947C23132yes—
197#66947C23132yes—
198#66947C23116yes—
199#66947C23132yes—
200#66946C2318yes—
201#66946C23116yes—
202#66946C23132yes—
203#66945C23116yes—
204#66945C2318yes—
205#66945C23116yes—
206C4⋊C4×D11C23116yes—
207C4⋊C4×D11C23132yes—
208C4⋊C4×D11C23116yes—
209C4⋊C4×D11C23132yes—
210C4⋊C4×D11C23116yes—
211#66943C23116yes—
212#66943C2318yes—
213#66942C23132yes—
214#66942C23132yes—
215#66942C23132yes—
216#66940C23116yes—
217#66929C23132yes—
218C4×D44C2318yes—
219C4×D44C23116yes—
220C4×D44C2318yes—
221C4×D44C23116yes—
222C4×D44C23116yes—
223C4×D44C23132yes—
224C4×D44C23116yes—
225#66925C23116yes—
226#66925C23132yes—
227#66925C23132yes—
228C42×D11C2318yes—
229C42×D11C23116yes—
230#66923C23116yes—
231#66923C23116yes—
232#66922C2318yes—
233C2×#3515—111nomaximal, Sylow
234C23×D11C2411yescharacteristic
235C23×D11C2412yes—
236C23×D11C2412yes—
237C2×Q8×C11—24no—
238C2×Q8×C11—28no—
239C2×Q8×C11—24no—
240C2×Q8×C11C2418yes—
241C2×Q8×C11C2414yes—
242C2×Q8×C11C2414yes—
243C22×C4×C11C2412yes—
244C22×C4×C11C2414yes—
245C22×C4×C11C2412yes—
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2412yes—
248C22×C4×C11C2412yes—
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×Dic11C2411yescharacteristic
252C22×Dic11C2411yescharacteristic
253C22×Dic11C2411yescharacteristic
254C22×Dic11C2412yes—
255C22×Dic11C2414yes—
256C22×Dic11C2412yes—
257#4343—232no—
258#4343—264no—
259C2×D44—28no—
260C2×D44—216no—
261C2×D44—24no—
262C2×D44—44no—
263C2×D44#4118yes—
264C2×D44C2414yes—
265C2×D44C2418yes—
266C2×D44C24116yes—
267C2×D44C2418yes—
268C2×D44C2414yes—
269C2×C4×D11—28no—
270C2×C4×D11—216no—
271C2×C4×D11—24no—
272C2×C4×D11—28no—
273C2×C4×D11—28no—
274C2×C4×D11—24no—
275C2×C4×D11—42no—
276C2×C4×D11—44no—
277C2×C4×D11—48no—
278C2×C4×D11—48no—
279C2×C4×D11C2418yes—
280C2×C4×D11C2414yes—
281C2×C4×D11C2414yes—
282C2×C4×D11C2418yes—
283C2×C4×D11C2418yes—
284C2×C4×D11C24116yes—
285C2×C4×D11C2418yes—
286C2×C4×D11C2414yes—
287C2×C4×D11C24116yes—
288C2×C4×D11C24116yes—
289C2×Dic22—44no—
290C2×Dic22C2418yes—
291C11×C4⋊C4C2418yes—
292C11×C4⋊C4C24116yes—
293C11×C4⋊C4C24116yes—
294C11×C4⋊C4C24116yes—
295C11×C4⋊C4C2414yes—
296C11×C4⋊C4C2418yes—
297C11×C4⋊C4C2414yes—
298C11×C4⋊C4C2418yes—
299C11×C4⋊C4C2418yes—
300C42×C11C2414yes—
301C42×C11C2418yes—
302C42×C11C2418yes—
303C42×C11C24116yes—
304(C2×D11)⋊C4C2418yes—
305(C2×D11)⋊C4C2418yes—
306(C2×D11)⋊C4C24116yes—
307(C2×D11)⋊C4C2418yes—
308(C2×D11)⋊C4C2418yes—
309(C2×D11)⋊C4C24116yes—
310(C2×D11)⋊C4C2418yes—
311(C2×D11)⋊C4C2418yes—
312(C2×D11)⋊C4C2418yes—
313(C2×D11)⋊C4C2418yes—
314(C2×D11)⋊C4C24116yes—
315(C2×D11)⋊C4C24116yes—
316C4⋊Dic11C2418yes—
317C4⋊Dic11C2418yes—
318C4⋊Dic11C2414yes—
319C4⋊Dic11C2414yes—
320C4⋊Dic11C2418yes—
321C4⋊Dic11C2418yes—
322C4⋊Dic11C24116yes—
323Dic11⋊C4C24116yes—
324Dic11⋊C4C24116yes—
325Dic11⋊C4C24116yes—
326Dic11⋊C4C24116yes—
327Dic11⋊C4C2418yes—
328Dic11⋊C4C24116yes—
329Dic11⋊C4C2418yes—
330Dic11⋊C4C24116yes—
331C4×Dic11C2414yes—
332C4×Dic11C2418yes—
333C4×Dic11C2414yes—
334C4×Dic11C2414yes—
335C4×Dic11C2418yes—
336C4×Dic11C24116yes—
337#3515—1132no—
338C2×#557D1111yescharacteristic, complemented
339C2×#554—111no—
340C2×#554—111no—
341C2×#553—112no—
342C2×#552—114no—
343C2×#552—112no—
344C2×#552—112no—
345C2×#547—111no—
346C2×#547—112no—
347C2×#541—112no—
348C2×#539—114no—
349C2×#533—111no—
350C2×#529—111no—
351C2×#529—112no—
352C22×#125—112no—
353C2×#520—112no—
354C2×C4×#41—111no—
355C23×C11C2511yescharacteristic
356C22×D11—24no—
357C22×D11—24no—
358C22×D11—22no—
359C22×D11—24no—
360C22×D11—22no—
361C22×D11—24no—
362C22×D11—24no—
363C22×D11—22no—
364C22×D11C2×#4118yes—
365C22×D11C2512yes—
366C22×D11C2514yes—
367C22×D11C2514yes—
368Q8×C11—28no—
369Q8×C11—216no—
370Q8×C11—28no—
371C2×C4×C11—24no—
372C2×C4×C11—28no—
373C2×C4×C11—24no—
374C2×C4×C11—22no—
375C2×C4×C11—24no—
376C2×C4×C11—24no—
377C2×C4×C11C2×#4114yes—
378C2×C4×C112−1+414yes—
379C2×C4×C11C2514yes—
380C2×C4×C11C2518yes—
381C2×C4×C11C2514yes—
382C2×C4×C11C2512yes—
383C2×C4×C11C2514yes—
384C2×C4×C11C2514yes—
385C2×C4×C11C2512yes—
386C2×C4×C11C2512yes—
387C2×Dic11—22no—
388C2×Dic11—24no—
389C2×Dic11—22no—
390C2×Dic11—24no—
391C2×Dic11—28no—
392C2×Dic11—22no—
393C2×Dic11C2512yes—
394C2×Dic11C2512yes—
395C2×Dic11C2512yes—
396C2×Dic11C2514yes—
397C2×Dic11C2518yes—
398C2×Dic11C2514yes—
399D44—216no—
400D44—232no—
401D44—28no—
402D44—48no—
403D44C2×#41116yes—
404C4×D11—216no—
405C4×D11—232no—
406C4×D11—28no—
407C4×D11—216no—
408C4×D11—216no—
409C4×D11—28no—
410C4×D11—416no—
411C4×D11—416no—
412C4×D11—44no—
413C4×D11—48no—
414Dic22—48no—
415C22×#41—111no—
416C22×#41—112no—
417#557C2×D11116yescomplemented
418#554—1116no—
419#554—1116no—
420#553—1132no—
421#552—1164no—
422#552—1132no—
423#552—1132no—
424#547—1116no—
425#547—1132no—
426#541—1132no—
427#539—1164no—
428#533—1116no—
429C2×C4⋊Q8—111no—
430C2×C4⋊Q8C2×D1111yescharacteristic
431C2×C4⋊Q8C2×D1112yes—
432#529—1132no—
433#529—1116no—
434C2×#126—114no—
435C2×#126—112no—
436C2×#126—114no—
437C2×#126—114no—
438C2×#125—1132no—
439C2×#125—114no—
440C2×#125—114no—
441C2×#125—114no—
442C2×#125—111no—
443C2×#125—112no—
444C2×#125—112no—
445C2×#125—112no—
446C2×#125C2×D1112yes—
447C2×#125C2×D1114yes—
448C2×#124—111no—
449C2×#123—112no—
450C2×#123—114no—
451C2×#123—114no—
452C2×#123—114no—
453C2×#123—114no—
454C2×C22⋊Q8—111no—
455C2×C22⋊Q8—112no—
456C2×C22⋊Q8—112no—
457C2×C22⋊Q8—112no—
458C2×C22⋊Q8—112no—
459C2×C22⋊Q8—114no—
460C2×C22⋊Q8—114no—
461C2×C22⋊Q8—112no—
462C2×#121—112no—
463C2×#121—111no—
464C2×#121—114no—
465#520—1132no—
466C4×#41—1116no—
467C2×C4×Q8—111no—
468C2×C4×Q8—112no—
469C2×C4×Q8—112no—
470C2×C4×Q8C2×D1111yescharacteristic
471C2×C4×Q8C2×D1112yes—
472C2×C4×Q8C2×D1112yes—
473C2×C4×Q8C2×D1111yescharacteristic
474C2×C4×D4—111no—
475C2×C4×D4—112no—
476C2×C4×D4—114no—
477C2×C4×D4—111no—
478C2×C4×D4—112no—
479C2×C4×D4—114no—
480C2×C4×D4—112no—
481C2×C4×D4—112no—
482C2×C4×D4—111no—
483C2×C4×D4—112no—
484C2×#117—111no—
485C2×#117—112no—
486C2×#117—112no—
487C2×#117—112no—
488C2×#117—114no—
489C2×#117—114no—
490C22×C4⋊C4—114no—
491C22×C4⋊C4—112no—
492C22×C4⋊C4—112no—
493C22×C4⋊C4—114no—
494C22×C4⋊C4—112no—
495C22×C42—112no—
496C22×C42—111no—
497C22×C11C22×#4112yes—
498C22×C11C2×2−1+412yes—
499C22×C11#58512yes—
500C22×C11C2611yescharacteristic
501C2×D11—24no—
502C2×D11—24no—
503C2×D11—216no—
504C2×D11—22no—
505C2×D11—24no—
506C2×D11—22no—
507C2×D11—24no—
508C2×D11—24no—
509C2×D11—22no—
510C2×D11—44no—
511C2×D11—48no—
512C2×D11C22×#4118yes—
513C4×C11—24no—
514C4×C11—28no—
515C4×C11—24no—
516C4×C11—22no—
517C4×C11—24no—
518C4×C11—24no—
519C4×C11C22×#4114yes—
520C4×C11C2×2−1+414yes—
521Dic11—22no—
522Dic11—24no—
523Dic11—22no—
524Dic11—24no—
525Dic11—28no—
526Dic11—22no—
527C2×#41—118no—
528C2×#41—1116no—
529C2×#41—228no—
530C2×#41—2216no—
531C22×Q8—112no—
532C22×Q8C22×D1111yescharacteristic
533C22×Q8C22×D1112yes—
534C22×Q8C22×D1111yescharacteristic
535C22×D4—111no—
536C22×D4—111no—
537C22×D4—112no—
538C22×D4—114no—
539C22×D4—112no—
540C23×C4—114no—
541C23×C4—112no—
542C23×C4—112no—
543C23×C4—112no—
544C23×C4—111no—
545C23×C4—111no—
546C23×C4—114no—
547C23×C4—112no—
548C23×C4—114no—
549C23×C4—111no—
550C4⋊Q8—118no—
551C4⋊Q8C22×D1118yes—
552C4⋊Q8C22×D11116yes—
553#126—1132no—
554#126—1116no—
555#126—1132no—
556#126—1132no—
557#125—118no—
558#125—1116no—
559#125—1132no—
560#125—1132no—
561#125—1132no—
562#125—1116no—
563#125—1116no—
564#125C22×D11116yes—
565#125C22×D11132yes—
566#124—118no—
567#123—1116no—
568#123—1132no—
569#123—1132no—
570#123—1132no—
571#123—1132no—
572C22⋊Q8—118no—
573C22⋊Q8—1116no—
574C22⋊Q8—1116no—
575C22⋊Q8—1116no—
576C22⋊Q8—1116no—
577C22⋊Q8—1116no—
578C22⋊Q8—1132no—
579C22⋊Q8—1132no—
580#121—1116no—
581#121—118no—
582#121—1132no—
583C4×Q8—118no—
584C4×Q8—1116no—
585C4×Q8—1116no—
586C4×Q8C22×D1118yes—
587C4×Q8C22×D11116yes—
588C4×Q8C22×D11116yes—
589C4×Q8C22×D1118yes—
590C4×D4—118no—
591C4×D4—1116no—
592C4×D4—1132no—
593C4×D4—118no—
594C4×D4—1116no—
595C4×D4—1132no—
596C4×D4—1116no—
597C4×D4—1116no—
598C4×D4—118no—
599C4×D4—1116no—
600#117—118no—
601#117—1116no—
602#117—1116no—
603#117—1116no—
604#117—1132no—
605#117—1132no—
606C2×C4⋊C4—114no—
607C2×C4⋊C4—112no—
608C2×C4⋊C4—111no—
609C2×C4⋊C4—112no—
610C2×C4⋊C4—112no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—112no—
613C2×C4⋊C4—114no—
614C2×C4⋊C4—114no—
615C2×C4⋊C4—114no—
616C2×C4⋊C4—114no—
617C2×C4⋊C4—112no—
618C2×C4⋊C4—111no—
619C2×C4⋊C4—112no—
620C2×C4⋊C4—114no—
621C2×C4⋊C4—1132no—
622C2×C4⋊C4—1116no—
623C2×C4⋊C4—1116no—
624C2×C4⋊C4—1132no—
625C2×C4⋊C4—1116no—
626C2×C4⋊C4C22×D1111yescharacteristic
627C2×C4⋊C4C22×D1111yescharacteristic
628C2×C4⋊C4C22×D1112yes—
629C2×C4⋊C4C22×D1114yes—
630C2×C4⋊C4C22×D1114yes—
631C2×C4⋊C4C22×D1112yes—
632C2×C4⋊C4C22×D1112yes—
633C2×C4⋊C4C22×D1112yes—
634C2×C4⋊C4C22×D1114yes—
635C2×C22⋊C4—112no—
636C2×C22⋊C4—112no—
637C2×C22⋊C4—112no—
638C2×C22⋊C4—112no—
639C2×C22⋊C4—114no—
640C2×C22⋊C4—112no—
641C2×C22⋊C4—112no—
642C2×C22⋊C4—114no—
643C2×C22⋊C4—114no—
644C2×C22⋊C4—114no—
645C2×C22⋊C4—112no—
646C2×C22⋊C4—112no—
647C2×C42—112no—
648C2×C42—111no—
649C2×C42—114no—
650C2×C42—111no—
651C2×C42—112no—
652C2×C42—111no—
653C2×C42—1116no—
654C2×C42—118no—
655C2×C42C22×D1114yes—
656C2×C42C22×D1112yes—
657C2×C42C22×D1112yes—
658C2×C42C22×D1111yescharacteristic
659C2×C11#351514yescomplemented
660C2×C11C23×#4111yescharacteristic
661C2×C11C22×2−1+411yescharacteristic
662C2×C11C2×#58511yescharacteristic
663D11—28no—
664D11—42no—
665D11—44no—
666C24—112no—
667C24—111no—
668C24—112no—
669#41—2232no—
670#41—2264no—
671C2×Q8—24no—
672C2×Q8—24no—
673C2×Q8—28no—
674C2×Q8—118no—
675C2×Q8—444no—
676C2×Q8C23×D1114yes—
677C2×Q8C23×D1118yes—
678C2×Q8C23×D1114yes—
679C2×D4—118no—
680C2×D4—114no—
681C2×D4—114no—
682C2×D4—118no—
683C2×D4—1116no—
684C2×D4—118no—
685C2×D4—228no—
686C2×D4—2216no—
687C2×D4—224no—
688C2×D4—444no—
689C22×C4—111no—
690C22×C4—111no—
691C22×C4—111no—
692C22×C4—112no—
693C22×C4—114no—
694C22×C4—112no—
695C22×C4—118no—
696C22×C4—118no—
697C22×C4—114no—
698C22×C4—114no—
699C22×C4—1116no—
700C22×C4—118no—
701C22×C4—118no—
702C22×C4—114no—
703C22×C4—1116no—
704C22×C4—1116no—
705C22×C4—2216no—
706C22×C4—228no—
707C22×C4—228no—
708C22×C4—224no—
709C22×C4—228no—
710C22×C4—224no—
711C22×C4—444no—
712C22×C4—448no—
713C22×C4—448no—
714C22×C4—442no—
715C22×C4C23×D1112yes—
716C22×C4C23×D1111yescharacteristic
717C22×C4C23×D1114yes—
718C22×C4C23×D1112yes—
719C22×C4C23×D1112yes—
720C22×C4C23×D1112yes—
721C22×C4C23×D1111yescharacteristic
722C22×C4C23×D1111yescharacteristic
723C4⋊C4—1116no—
724C4⋊C4—118no—
725C4⋊C4—114no—
726C4⋊C4—118no—
727C4⋊C4—118no—
728C4⋊C4—1116no—
729C4⋊C4—118no—
730C4⋊C4—1116no—
731C4⋊C4—1116no—
732C4⋊C4—1116no—
733C4⋊C4—1116no—
734C4⋊C4—118no—
735C4⋊C4—114no—
736C4⋊C4—118no—
737C4⋊C4—1116no—
738C4⋊C4C23×D1114yes—
739C4⋊C4C23×D1114yes—
740C4⋊C4C23×D1118yes—
741C4⋊C4C23×D11116yes—
742C4⋊C4C23×D11116yes—
743C4⋊C4C23×D1118yes—
744C4⋊C4C23×D1118yes—
745C4⋊C4C23×D1118yes—
746C4⋊C4C23×D11116yes—
747C22⋊C4—118no—
748C22⋊C4—118no—
749C22⋊C4—118no—
750C22⋊C4—118no—
751C22⋊C4—1116no—
752C22⋊C4—118no—
753C22⋊C4—118no—
754C22⋊C4—1116no—
755C22⋊C4—1116no—
756C22⋊C4—1116no—
757C22⋊C4—118no—
758C22⋊C4—118no—
759C42—114no—
760C42—118no—
761C42—114no—
762C42—114no—
763C42—118no—
764C42—1116no—
765C42C23×D1118yes—
766C42C23×D1114yes—
767C42C23×D11116yes—
768C42C23×D1118yes—
769C11C2×#351511yescharacteristic, complemented, Sylow
770C23—118no—
771C23—114no—
772C23—112no—
773C23—114no—
774C23—224no—
775C23—224no—
776C23—222no—
777C23—224no—
778C23—222no—
779C23—224no—
780C23—224no—
781C23—222no—
782C23C24×D1111yescharacteristic
783Q8—28no—
784Q8—28no—
785Q8—216no—
786Q8—448no—
787D4—1116no—
788D4—2216no—
789D4—2232no—
790D4—228no—
791D4—448no—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—112no—
799C2×C4—112no—
800C2×C4—112no—
801C2×C4—114no—
802C2×C4—118no—
803C2×C4—114no—
804C2×C4—2216no—
805C2×C4—2232no—
806C2×C4—222no—
807C2×C4—224no—
808C2×C4—222no—
809C2×C4—224no—
810C2×C4—222no—
811C2×C4—228no—
812C2×C4—2216no—
813C2×C4—228no—
814C2×C4—228no—
815C2×C4—2216no—
816C2×C4—448no—
817C2×C4—4416no—
818C2×C4—4416no—
819C2×C4—444no—
820C2×C4#6704014yes—
821C2×C4#41×D1114yes—
822C2×C4C24×D1114yes—
823C2×C4C24×D1112yes—
824C2×C4C24×D1114yes—
825C2×C4C24×D1118yes—
826C2×C4C24×D1114yes—
827C2×C4C24×D1114yes—
828C2×C4C24×D1112yes—
829C2×C4C24×D1112yes—
830C22—118no—
831C22—224no—
832C22—224no—
833C22—2216no—
834C22—222no—
835C22—224no—
836C22—222no—
837C22—224no—
838C22—224no—
839C22—222no—
840C22—444no—
841C22—448no—
842C22C2×#6704012yes—
843C22C2×#41×D1112yes—
844C22#1062345712yes—
845C22C25×D1111yescharacteristic
846C4—24no—
847C4—28no—
848C4—24no—
849C4—24no—
850C4—24no—
851C4—22no—
852C4—222no—
853C4—224no—
854C4—222no—
855C4—224no—
856C4—222no—
857C4—228no—
858C4C2×#6704014yes—
859C4C2×#41×D1114yes—
860C2—228no—
861C2—442no—
862C2—444no—
863C2#1308259314yesdirect product factor
864C2C22×#41×D1111yescharacteristic
865C2C22×#6704011yescharacteristic
866C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#557C2
socleC23×C11C25
hypercenterC2×#557D11
hypocenterC11C2×#3515
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #13082593C2direct (N × H)
2. C2×#10623110C2semidirect
3. C2×#10623110C2semidirect
4. C2×#10623226C2semidirect
5. C2×#10623112C2semidirect
6. C2×#10623112C2semidirect
7. C2×#10623224C2semidirect
8. C2×#10623257C2semidirect
9. C2×#10623257C2semidirect
10. C2×#10623262C2semidirect
11. C2×#10623223C2semidirect
12. C2×#10623259C2semidirect
13. C2×#10623111C2semidirect
14. C2×#10623111C2semidirect
15. C2×D11×#125C2semidirect
16. C2×#10623105C2semidirect
17. C2×C4×#4343C2semidirect
18. C2×C11×#557C2semidirect
21. C11×#557C22semidirect
38. #10623262C22semidirect
39. #10623259C22semidirect
40. #10623257C22semidirect
41. #10623257C22semidirect
42. #10623226C22semidirect
43. #10623224C22semidirect
44. #10623223C22semidirect
45. D11×#125C22semidirect
46. #10623112C22semidirect
47. #10623112C22semidirect
48. #10623111C22semidirect
49. #10623111C22semidirect
50. #10623110C22semidirect
51. #10623110C22semidirect
52. #10623105C22semidirect
53. C4×#4343C22semidirect
338. C2×#557D11semidirect
417. #557C2×D11semidirect
659. C2×C11#3515semidirect
769. C11C2×#3515semidirect
863. C2#13082593direct (N × H)

Maximal subgroups

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

subgroupindex
#130825932
C2×#106231102
C2×#106232262
C2×#106231122
C2×#106232242
C2×#106232572
C2×#106232622
C2×#106232232
C2×#106232592
C2×#106231112
C2×D11×#1252
C2×#106231052
C2×C4×#43432
C2×C11×#5572
C2×#351511