Finite Group Databasebeta

← C2×#13082589 #15661878

Subgroups — C2×#13082589 #15661878

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#13082589C2132yesmaximal, direct product factor
2C2×#10623252C211yesmaximal, characteristic, complemented
3C2×#10623261C211yesmaximal, characteristic, complemented
4C2×#10623261C211yesmaximal, characteristic, complemented
5C2×#10623061C212yesmaximal, complemented
6C2×#10623112C214yesmaximal, complemented
7C2×#10623060C212yesmaximal, complemented
8C2×#10623170C212yesmaximal, complemented
9C2×#10623257C211yesmaximal, characteristic, complemented
10C2×#10623162C212yesmaximal, complemented
11C2×#10623114C212yesmaximal, complemented
12C2×#10623169C214yesmaximal, complemented
13C2×#10623222C212yesmaximal, complemented
14C2×#10623010C211yesmaximal, characteristic, complemented
15C2×D11×#125C212yesmaximal, complemented
16C2×#10623105C212yesmaximal, complemented
17C2×C4×#4339C211yesmaximal, characteristic, complemented
18C2×C11×#533C211yesmaximal, characteristic, complemented
19C22×#4343C2212yes—
20C22×#4339C2211yescharacteristic
21C11×#533C22116yescomplemented
22C2×C11×C4⋊Q8C2211yescharacteristic
23C2×C11×C4⋊Q8C2211yescharacteristic
24C2×C11×#125C2212yes—
25C2×C11×C22⋊Q8C2212yes—
26C2×C11×C22⋊Q8C2212yes—
27C2×C4×Q8×C11C2212yes—
28C2×C4×Q8×C11C2212yes—
29C2×C11×#117C2212yes—
30C22×C42×C11C2211yescharacteristic
31C2×#66999C2212yes—
32C2×#66999C2214yes—
33C2×#66999C2214yes—
34C2×Q8×Dic11C2212yes—
35C2×#66997C2212yes—
36C2×#66983C2211yescharacteristic
37C2×#66982C2212yes—
38C2×C4×C22⋊D11C2212yes—
39C2×C4×C22⋊D11C2212yes—
40C2×C4×C22⋊D11C2212yes—
41C2×#66979C2211yescharacteristic
42C2×#66977C2211yescharacteristic
43#10623261C22116yescomplemented
44#10623261C22116yescomplemented
45#10623257C22116yescomplemented
46#10623252C22116yescomplemented
47#10623222C22132yescomplemented
48D11×#125C22132yescomplemented
49#10623170C22132yescomplemented
50#10623169C22164yescomplemented
51#10623162C22132yescomplemented
52#10623114C22132yescomplemented
53#10623112C22164yescomplemented
54#10623105C22132yescomplemented
55#10623061C22132yescomplemented
56#10623060C22132yescomplemented
57C2×#66951C2214yes—
58C2×#66950C2212yes—
59C2×#66950C2212yes—
60C2×#66948C2212yes—
61C2×#66947C2214yes—
62C2×#66947C2214yes—
63C2×#66946C2212yes—
64C2×#66946C2214yes—
65C2×#66946C2212yes—
66C2×#66945C2214yes—
67C2×C4⋊C4×D11C2212yes—
68C2×C4⋊C4×D11C2214yes—
69C2×C4⋊C4×D11C2212yes—
70C2×C4⋊C4×D11C2214yes—
71C2×C4⋊C4×D11C2212yes—
72C2×#66943C2212yes—
73C2×#66943C2212yes—
74C2×#66943C2212yes—
75C2×#66942C2214yes—
76C2×#66942C2214yes—
77C2×#66942C2214yes—
78C2×#66940C2212yes—
79C2×#66937C2214yes—
80C2×#66936C2214yes—
81C2×#66936C2214yes—
82C2×#66932C2214yes—
83#10623010C22116yescomplemented
84C2×#66929C2212yes—
85C2×#66929C2214yes—
86C2×#66928C2211yescharacteristic
87C4×#4339C22116yescomplemented
88C2×C4×D44C2214yes—
89C2×C4×D44C2211yescharacteristic
90C2×C4×D44C2211yescharacteristic
91C2×C4×D44C2211yescharacteristic
92C2×#66925C2214yes—
93C2×#66925C2212yes—
94C2×#66925C2212yes—
95C2×C42×D11C2212yes—
96C2×#66923C2211yescharacteristic
97C2×#66923C2214yes—
98C2×C4×Dic22C2211yescharacteristic
99C2×C4×Dic22C2211yescharacteristic
100C2×C4×Dic22C2211yescharacteristic
101C22×Q8×C11C2312yes—
102C22×Q8×C11C2312yes—
103C23×C4×C11C2311yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C22×C22⋊D11C2312yes—
107C22×C22⋊D11C2312yes—
108C2×#4343—216no—
109C2×#4343C23116yes—
110C2×#4339—28no—
111C2×#4339C2318yes—
112C22×D44C2311yescharacteristic
113C22×D44C2314yes—
114C22×D44C2311yescharacteristic
115C22×C4×D11C2312yes—
116C22×C4×D11C2312yes—
117C22×C4×D11C2312yes—
118C22×C4×D11C2314yes—
119C22×C4×D11C2312yes—
120C22×C4×D11C2314yes—
121C22×C4×D11C2314yes—
122C22×Dic22C2311yescharacteristic
123C22×Dic22C2311yescharacteristic
124C11×C4⋊Q8C2318yes—
125C11×C4⋊Q8C2318yes—
126C11×#125C23116yes—
127C11×C22⋊Q8C23116yes—
128C11×C22⋊Q8C23116yes—
129C4×Q8×C11C23116yes—
130C4×Q8×C11C23116yes—
131C11×#117C23116yes—
132C2×C11×C4⋊C4C2312yes—
133C2×C11×C4⋊C4C2312yes—
134C2×C11×C4⋊C4C2314yes—
135C2×C11×C4⋊C4C2314yes—
136C2×C11×C4⋊C4C2312yes—
137C2×C11×C4⋊C4C2312yes—
138C2×C11×C22⋊C4C2314yes—
139C2×C42×C11C2311yescharacteristic
140C2×C42×C11C2311yescharacteristic
141C2×C42×C11C2311yescharacteristic
142C2×C42×C11C2314yes—
143C2×C42×C11C2311yescharacteristic
144C2×C42×C11C2318yes—
145C2×C22⋊Dic11C2312yes—
146C2×C22⋊Dic11C2312yes—
147#66999C23116yes—
148#66999C23132yes—
149#66999C23132yes—
150Q8×Dic11C23116yes—
151#66997C23116yes—
152#66983C2318yes—
153#66982C23116yes—
154C4×C22⋊D11C23116yes—
155C4×C22⋊D11C23116yes—
156C4×C22⋊D11C23116yes—
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2312yes—
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2314yes—
162C2×(C2×D11)⋊C4C2312yes—
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2314yes—
165C2×(C2×D11)⋊C4C2314yes—
166#66979C2318yes—
167C2×C4⋊Dic11C2311yescharacteristic
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2311yescharacteristic
170C2×C4⋊Dic11C2311yescharacteristic
171C2×C4⋊Dic11C2314yes—
172C2×C4⋊Dic11C2314yes—
173C2×C4⋊Dic11C2314yes—
174#66977C2318yes—
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2314yes—
182C2×Dic11⋊C4C2314yes—
183C2×Dic11⋊C4C2314yes—
184C2×Dic11⋊C4C2314yes—
185C2×Dic11⋊C4C2314yes—
186C2×C4×Dic11C2312yes—
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2312yes—
189C2×C4×Dic11C2312yes—
190C2×C4×Dic11C2314yes—
191#66951C23132yes—
192#66950C23116yes—
193#66950C23116yes—
194#66948C23116yes—
195#66947C23132yes—
196#66947C23132yes—
197#66946C23116yes—
198#66946C23116yes—
199#66946C23132yes—
200#66945C23132yes—
201C4⋊C4×D11C23116yes—
202C4⋊C4×D11C23116yes—
203C4⋊C4×D11C23116yes—
204C4⋊C4×D11C23132yes—
205C4⋊C4×D11C23132yes—
206#66943C23116yes—
207#66943C23116yes—
208#66943C23116yes—
209#66942C23132yes—
210#66942C23132yes—
211#66942C23132yes—
212#66940C23116yes—
213#66937C23132yes—
214#66936C23132yes—
215#66936C23132yes—
216#66932C23132yes—
217#66929C23116yes—
218#66929C23132yes—
219#66928C2318yes—
220C4×D44C2318yes—
221C4×D44C2318yes—
222C4×D44C2318yes—
223C4×D44C23132yes—
224#66925C23116yes—
225#66925C23116yes—
226#66925C23132yes—
227C42×D11C23116yes—
228#66923C2318yes—
229#66923C23132yes—
230C4×Dic22C2318yes—
231C4×Dic22C2318yes—
232C4×Dic22C2318yes—
233C2×#3515—111nomaximal, Sylow
234C24×C11C2411yescharacteristic
235C23×D11C2412yes—
236C23×D11C2412yes—
237C2×Q8×C11—28no—
238C2×Q8×C11—44no—
239C2×Q8×C11C2418yes—
240C2×Q8×C11C2418yes—
241C22×C4×C11—24no—
242C22×C4×C11—24no—
243C22×C4×C11—42no—
244C22×C4×C11C2411yescharacteristic
245C22×C4×C11C2411yescharacteristic
246C22×C4×C11C2414yes—
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2414yes—
250C22×C4×C11C2414yes—
251C22×C4×C11C2414yes—
252C22×C4×C11C2414yes—
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C2×C22⋊D11—28no—
256C2×C22⋊D11—44no—
257C2×C22⋊D11C2418yes—
258C2×C22⋊D11C2418yes—
259C22×Dic11C2412yes—
260C22×Dic11C2412yes—
261C22×Dic11C2412yes—
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265#4343—264no—
266#4339—232no—
267C2×D44—216no—
268C2×D44—24no—
269C2×D44#4118yes—
270C2×D44C2414yes—
271C2×D44C24116yes—
272C2×D44C2414yes—
273C2×C4×D11—28no—
274C2×C4×D11—216no—
275C2×C4×D11—28no—
276C2×C4×D11—28no—
277C2×C4×D11—44no—
278C2×C4×D11—48no—
279C2×C4×D11—48no—
280C2×C4×D11C2418yes—
281C2×C4×D11C2418yes—
282C2×C4×D11C2418yes—
283C2×C4×D11C24116yes—
284C2×C4×D11C2418yes—
285C2×C4×D11C24116yes—
286C2×C4×D11C24116yes—
287C2×Dic22—24no—
288C2×Dic22—24no—
289C2×Dic22C2414yes—
290C2×Dic22C2414yes—
291C11×C4⋊C4C2418yes—
292C11×C4⋊C4C2418yes—
293C11×C4⋊C4C24116yes—
294C11×C4⋊C4C24116yes—
295C11×C4⋊C4C2418yes—
296C11×C4⋊C4C2418yes—
297C11×C22⋊C4C24116yes—
298C42×C11C2414yes—
299C42×C11C2414yes—
300C42×C11C2414yes—
301C42×C11C24116yes—
302C42×C11C2414yes—
303C22⋊Dic11C2418yes—
304C22⋊Dic11C2418yes—
305(C2×D11)⋊C4C2418yes—
306(C2×D11)⋊C4C2418yes—
307(C2×D11)⋊C4C2418yes—
308(C2×D11)⋊C4C2418yes—
309(C2×D11)⋊C4C24116yes—
310(C2×D11)⋊C4C2418yes—
311(C2×D11)⋊C4C2418yes—
312(C2×D11)⋊C4C24116yes—
313(C2×D11)⋊C4C24116yes—
314C4⋊Dic11C2414yes—
315C4⋊Dic11C2414yes—
316C4⋊Dic11C2414yes—
317C4⋊Dic11C2414yes—
318C4⋊Dic11C24116yes—
319C4⋊Dic11C24116yes—
320C4⋊Dic11C24116yes—
321Dic11⋊C4C2418yes—
322Dic11⋊C4C2418yes—
323Dic11⋊C4C2418yes—
324Dic11⋊C4C2418yes—
325Dic11⋊C4C2418yes—
326Dic11⋊C4C2418yes—
327Dic11⋊C4C24116yes—
328Dic11⋊C4C24116yes—
329Dic11⋊C4C24116yes—
330Dic11⋊C4C24116yes—
331Dic11⋊C4C24116yes—
332C4×Dic11C2418yes—
333C4×Dic11C2418yes—
334C4×Dic11C2418yes—
335C4×Dic11C2418yes—
336C4×Dic11C24116yes—
337#3515—1132no—
338C2×#557—111no—
339C2×#554—111no—
340C2×#554—111no—
341C2×#553—112no—
342C2×#552—112no—
343C2×#552—114no—
344C2×#552—112no—
345C2×#547—111no—
346C2×#547—112no—
347C2×#541—112no—
348C2×#539—114no—
349C2×#533D1111yescharacteristic, complemented
350C2×#529—111no—
351C2×#529—112no—
352C22×#125—112no—
353C2×#520—112no—
354C2×C4×#41—111no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11C2512yes—
359C23×C11C2511yescharacteristic
360C22×D11—24no—
361C22×D11—24no—
362C22×D11—24no—
363C22×D11—24no—
364C22×D11—24no—
365C22×D11C2×#4118yes—
366C22×D11C2514yes—
367C22×D11C2514yes—
368Q8×C11—216no—
369Q8×C11—48no—
370C2×C4×C11—22no—
371C2×C4×C11—28no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—28no—
375C2×C4×C11—22no—
376C2×C4×C11—28no—
377C2×C4×C11—28no—
378C2×C4×C11—44no—
379C2×C4×C11C2×#4114yes—
380C2×C4×C112−1+414yes—
381C2×C4×C11C2512yes—
382C2×C4×C11C2512yes—
383C2×C4×C11C2518yes—
384C2×C4×C11C2512yes—
385C2×C4×C11C2512yes—
386C2×C4×C11C2518yes—
387C2×C4×C11C2512yes—
388C2×C4×C11C2512yes—
389C22⋊D11—216no—
390C22⋊D11—48no—
391C2×Dic11—24no—
392C2×Dic11—24no—
393C2×Dic11—24no—
394C2×Dic11—24no—
395C2×Dic11—24no—
396C2×Dic11—24no—
397C2×Dic11C2514yes—
398C2×Dic11C2514yes—
399C2×Dic11C2514yes—
400C2×Dic11C2514yes—
401C2×Dic11C2514yes—
402C2×Dic11C2514yes—
403D44—232no—
404D44—28no—
405D44C2×#41116yes—
406C4×D11—216no—
407C4×D11—232no—
408C4×D11—216no—
409C4×D11—216no—
410C4×D11—48no—
411C4×D11—416no—
412C4×D11—416no—
413Dic22—28no—
414Dic22—28no—
415C22×#41—112no—
416C22×#41—111no—
417#557—1116no—
418#554—1116no—
419#554—1116no—
420#553—1132no—
421#552—1132no—
422#552—1164no—
423#552—1132no—
424#547—1116no—
425#547—1132no—
426#541—1132no—
427#539—1164no—
428#533C2×D11116yescomplemented
429C2×C4⋊Q8—112no—
430C2×C4⋊Q8C2×D1111yescharacteristic
431C2×C4⋊Q8C2×D1111yescharacteristic
432#529—1132no—
433#529—1116no—
434C2×#126—114no—
435C2×#126—114no—
436C2×#126—112no—
437C2×#126—114no—
438C2×#125—1132no—
439C2×#125—114no—
440C2×#125—114no—
441C2×#125—114no—
442C2×#125—112no—
443C2×#125—112no—
444C2×#125—112no—
445C2×#125—111no—
446C2×#125—114no—
447C2×#125C2×D1112yes—
448C2×#124—111no—
449C2×#123—112no—
450C2×#123—114no—
451C2×#123—114no—
452C2×#123—114no—
453C2×#123—114no—
454C2×C22⋊Q8—114no—
455C2×C22⋊Q8—114no—
456C2×C22⋊Q8—112no—
457C2×C22⋊Q8—111no—
458C2×C22⋊Q8—112no—
459C2×C22⋊Q8—112no—
460C2×C22⋊Q8C2×D1112yes—
461C2×C22⋊Q8C2×D1112yes—
462C2×#121—111no—
463C2×#121—112no—
464C2×#121—114no—
465#520—1132no—
466C4×#41—1116no—
467C2×C4×Q8—112no—
468C2×C4×Q8—112no—
469C2×C4×Q8—111no—
470C2×C4×Q8—111no—
471C2×C4×Q8—111no—
472C2×C4×Q8C2×D1112yes—
473C2×C4×Q8C2×D1112yes—
474C2×C4×D4—112no—
475C2×C4×D4—112no—
476C2×C4×D4—112no—
477C2×C4×D4—114no—
478C2×C4×D4—112no—
479C2×C4×D4—112no—
480C2×C4×D4—111no—
481C2×C4×D4—111no—
482C2×C4×D4—114no—
483C2×C4×D4—111no—
484C2×#117—111no—
485C2×#117—114no—
486C2×#117—112no—
487C2×#117—112no—
488C2×#117—114no—
489C2×#117C2×D1112yes—
490C22×C4⋊C4—114no—
491C22×C4⋊C4—112no—
492C22×C4⋊C4—112no—
493C22×C4⋊C4—114no—
494C22×C4⋊C4—112no—
495C22×C42—112no—
496C22×C42C2×D1111yescharacteristic
497C22×C11—22no—
498C22×C11—22no—
499C22×C11—22no—
500C22×C11—44no—
501C22×C11C22×#4112yes—
502C22×C11C2×2−1+412yes—
503C22×C11#58512yes—
504C22×C11C2611yescharacteristic
505C2×D11—24no—
506C2×D11—24no—
507C2×D11—216no—
508C2×D11—24no—
509C2×D11—24no—
510C2×D11—24no—
511C2×D11—48no—
512C2×D11C22×#4118yes—
513C4×C11—22no—
514C4×C11—28no—
515C4×C11—22no—
516C4×C11—22no—
517C4×C11—22no—
518C4×C11—28no—
519C4×C11C22×#4114yes—
520C4×C11C2×2−1+414yes—
521Dic11—24no—
522Dic11—24no—
523Dic11—24no—
524Dic11—24no—
525Dic11—24no—
526Dic11—24no—
527C2×#41—1116no—
528C2×#41—118no—
529C2×#41—228no—
530C2×#41—2216no—
531C22×Q8—111no—
532C22×Q8—111no—
533C22×Q8C22×D1112yes—
534C22×Q8C22×D1112yes—
535C22×D4—112no—
536C22×D4—112no—
537C22×D4—111no—
538C22×D4—111no—
539C22×D4—114no—
540C23×C4—114no—
541C23×C4—112no—
542C23×C4—112no—
543C23×C4—112no—
544C23×C4—114no—
545C23×C4—112no—
546C23×C4—114no—
547C23×C4C22×D1111yescharacteristic
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550C4⋊Q8—1116no—
551C4⋊Q8C22×D1118yes—
552C4⋊Q8C22×D1118yes—
553#126—1132no—
554#126—1132no—
555#126—1116no—
556#126—1132no—
557#125—1132no—
558#125—1132no—
559#125—1116no—
560#125—1116no—
561#125—1132no—
562#125—1116no—
563#125—118no—
564#125—1132no—
565#125C22×D11116yes—
566#124—118no—
567#123—1116no—
568#123—1132no—
569#123—1132no—
570#123—1132no—
571#123—1132no—
572C22⋊Q8—1132no—
573C22⋊Q8—1132no—
574C22⋊Q8—1116no—
575C22⋊Q8—118no—
576C22⋊Q8—1116no—
577C22⋊Q8—1116no—
578C22⋊Q8C22×D11116yes—
579C22⋊Q8C22×D11116yes—
580#121—118no—
581#121—1116no—
582#121—1132no—
583C4×Q8—1116no—
584C4×Q8—1116no—
585C4×Q8—118no—
586C4×Q8—118no—
587C4×Q8—118no—
588C4×Q8C22×D11116yes—
589C4×Q8C22×D11116yes—
590C4×D4—1116no—
591C4×D4—1116no—
592C4×D4—1116no—
593C4×D4—1132no—
594C4×D4—1116no—
595C4×D4—1116no—
596C4×D4—118no—
597C4×D4—118no—
598C4×D4—1132no—
599C4×D4—118no—
600#117—118no—
601#117—1132no—
602#117—1116no—
603#117—1116no—
604#117—1132no—
605#117C22×D11116yes—
606C2×C4⋊C4—111no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—112no—
609C2×C4⋊C4—111no—
610C2×C4⋊C4—112no—
611C2×C4⋊C4—111no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—114no—
614C2×C4⋊C4—114no—
615C2×C4⋊C4—114no—
616C2×C4⋊C4—114no—
617C2×C4⋊C4—112no—
618C2×C4⋊C4—112no—
619C2×C4⋊C4—111no—
620C2×C4⋊C4—112no—
621C2×C4⋊C4—114no—
622C2×C4⋊C4—112no—
623C2×C4⋊C4—114no—
624C2×C4⋊C4—1132no—
625C2×C4⋊C4—1116no—
626C2×C4⋊C4—1116no—
627C2×C4⋊C4—1132no—
628C2×C4⋊C4—1116no—
629C2×C4⋊C4C22×D1114yes—
630C2×C4⋊C4C22×D1112yes—
631C2×C4⋊C4C22×D1112yes—
632C2×C4⋊C4C22×D1112yes—
633C2×C4⋊C4C22×D1114yes—
634C2×C4⋊C4C22×D1112yes—
635C2×C22⋊C4—112no—
636C2×C22⋊C4—112no—
637C2×C22⋊C4—112no—
638C2×C22⋊C4—112no—
639C2×C22⋊C4—112no—
640C2×C22⋊C4—114no—
641C2×C22⋊C4—112no—
642C2×C22⋊C4—112no—
643C2×C22⋊C4—114no—
644C2×C22⋊C4—114no—
645C2×C22⋊C4—112no—
646C2×C22⋊C4C22×D1114yes—
647C2×C42—112no—
648C2×C42—114no—
649C2×C42—112no—
650C2×C42—112no—
651C2×C42—112no—
652C2×C42—1116no—
653C2×C42C22×D1111yescharacteristic
654C2×C42C22×D1111yescharacteristic
655C2×C42C22×D1114yes—
656C2×C42C22×D1111yescharacteristic
657C2×C42C22×D1118yes—
658C2×C42C22×D1111yescharacteristic
659C2×C11—42no—
660C2×C11#351514yescomplemented
661C2×C11C23×#4111yescharacteristic
662C2×C11C22×2−1+411yescharacteristic
663C2×C11C2×#58511yescharacteristic
664D11—28no—
665D11—44no—
666C24—112no—
667C24—112no—
668C24C23×D1111yescharacteristic
669#41—2232no—
670#41—2264no—
671C2×Q8—28no—
672C2×Q8—44no—
673C2×Q8—114no—
674C2×Q8—114no—
675C2×Q8—224no—
676C2×Q8—224no—
677C2×Q8C23×D1118yes—
678C2×Q8C23×D1118yes—
679C2×D4—118no—
680C2×D4—118no—
681C2×D4—118no—
682C2×D4—114no—
683C2×D4—114no—
684C2×D4—1116no—
685C2×D4—2216no—
686C2×D4—228no—
687C2×D4—224no—
688C2×D4—444no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—42no—
692C22×C4—112no—
693C22×C4—112no—
694C22×C4—112no—
695C22×C4—112no—
696C22×C4—112no—
697C22×C4—112no—
698C22×C4—118no—
699C22×C4—118no—
700C22×C4—1116no—
701C22×C4—118no—
702C22×C4—118no—
703C22×C4—1116no—
704C22×C4—1116no—
705C22×C4—228no—
706C22×C4—2216no—
707C22×C4—228no—
708C22×C4—228no—
709C22×C4—444no—
710C22×C4—448no—
711C22×C4—448no—
712C22×C4C23×D1114yes—
713C22×C4C23×D1114yes—
714C22×C4C23×D1111yescharacteristic
715C22×C4C23×D1111yescharacteristic
716C22×C4C23×D1114yes—
717C22×C4C23×D1111yescharacteristic
718C22×C4C23×D1111yescharacteristic
719C22×C4C23×D1114yes—
720C22×C4C23×D1114yes—
721C22×C4C23×D1111yescharacteristic
722C22×C4C23×D1111yescharacteristic
723C4⋊C4—114no—
724C4⋊C4—1116no—
725C4⋊C4—118no—
726C4⋊C4—114no—
727C4⋊C4—118no—
728C4⋊C4—114no—
729C4⋊C4—1116no—
730C4⋊C4—1116no—
731C4⋊C4—1116no—
732C4⋊C4—1116no—
733C4⋊C4—1116no—
734C4⋊C4—118no—
735C4⋊C4—118no—
736C4⋊C4—114no—
737C4⋊C4—118no—
738C4⋊C4—1116no—
739C4⋊C4—118no—
740C4⋊C4—1116no—
741C4⋊C4C23×D11116yes—
742C4⋊C4C23×D1118yes—
743C4⋊C4C23×D1118yes—
744C4⋊C4C23×D1118yes—
745C4⋊C4C23×D11116yes—
746C4⋊C4C23×D1118yes—
747C22⋊C4—118no—
748C22⋊C4—118no—
749C22⋊C4—118no—
750C22⋊C4—118no—
751C22⋊C4—118no—
752C22⋊C4—1116no—
753C22⋊C4—118no—
754C22⋊C4—118no—
755C22⋊C4—1116no—
756C22⋊C4—1116no—
757C22⋊C4—118no—
758C22⋊C4C23×D11116yes—
759C42—118no—
760C42—118no—
761C42—118no—
762C42—1116no—
763C42—118no—
764C42C23×D1114yes—
765C42C23×D1114yes—
766C42C23×D1114yes—
767C42C23×D1114yes—
768C42C23×D11116yes—
769C11C2×#351511yescharacteristic, complemented, Sylow
770C23—22no—
771C23—22no—
772C23—22no—
773C23—118no—
774C23—114no—
775C23—114no—
776C23—224no—
777C23—224no—
778C23—224no—
779C23—224no—
780C23—224no—
781C23C24×D1112yes—
782C23C24×D1111yescharacteristic
783Q8—216no—
784Q8—48no—
785Q8—228no—
786Q8—228no—
787D4—1116no—
788D4—2232no—
789D4—2216no—
790D4—228no—
791D4—448no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—28no—
800C2×C4—44no—
801C2×C4—114no—
802C2×C4—114no—
803C2×C4—114no—
804C2×C4—114no—
805C2×C4—114no—
806C2×C4—114no—
807C2×C4—2216no—
808C2×C4—2232no—
809C2×C4—224no—
810C2×C4—224no—
811C2×C4—224no—
812C2×C4—224no—
813C2×C4—224no—
814C2×C4—224no—
815C2×C4—2216no—
816C2×C4—2216no—
817C2×C4—448no—
818C2×C4—4416no—
819C2×C4—4416no—
820C2×C4#6704014yes—
821C2×C4#41×D1114yes—
822C2×C4C24×D1112yes—
823C2×C4C24×D1112yes—
824C2×C4C24×D1118yes—
825C2×C4C24×D1112yes—
826C2×C4C24×D1112yes—
827C2×C4C24×D1118yes—
828C2×C4C24×D1112yes—
829C2×C4C24×D1112yes—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—44no—
834C22—118no—
835C22—224no—
836C22—224no—
837C22—2216no—
838C22—224no—
839C22—224no—
840C22—224no—
841C22—448no—
842C22C2×#6704012yes—
843C22C2×#41×D1112yes—
844C22#1062345312yes—
845C22C25×D1111yescharacteristic
846C4—22no—
847C4—28no—
848C4—22no—
849C4—22no—
850C4—22no—
851C4—28no—
852C4—224no—
853C4—224no—
854C4—224no—
855C4—224no—
856C4—224no—
857C4—224no—
858C4C2×#6704014yes—
859C4C2×#41×D1114yes—
860C2—42no—
861C2—228no—
862C2—444no—
863C2#1308258914yesdirect product factor
864C2C22×#41×D1111yescharacteristic
865C2C22×#6704011yescharacteristic
866C2C2×#1062345311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#533C2
socleC23×C11C25
hypercenterC2×#533D11
hypocenterC11C2×#3515
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #13082589C2direct (N × H)
2. C2×#10623252C2semidirect
3. C2×#10623261C2semidirect
4. C2×#10623261C2semidirect
5. C2×#10623061C2semidirect
6. C2×#10623112C2semidirect
7. C2×#10623060C2semidirect
8. C2×#10623170C2semidirect
9. C2×#10623257C2semidirect
10. C2×#10623162C2semidirect
11. C2×#10623114C2semidirect
12. C2×#10623169C2semidirect
13. C2×#10623222C2semidirect
14. C2×#10623010C2semidirect
15. C2×D11×#125C2semidirect
16. C2×#10623105C2semidirect
17. C2×C4×#4339C2semidirect
18. C2×C11×#533C2semidirect
21. C11×#533C22semidirect
43. #10623261C22semidirect
44. #10623261C22semidirect
45. #10623257C22semidirect
46. #10623252C22semidirect
47. #10623222C22semidirect
48. D11×#125C22semidirect
49. #10623170C22semidirect
50. #10623169C22semidirect
51. #10623162C22semidirect
52. #10623114C22semidirect
53. #10623112C22semidirect
54. #10623105C22semidirect
55. #10623061C22semidirect
56. #10623060C22semidirect
83. #10623010C22semidirect
87. C4×#4339C22semidirect
349. C2×#533D11semidirect
428. #533C2×D11semidirect
660. C2×C11#3515semidirect
769. C11C2×#3515semidirect
863. C2#13082589direct (N × H)

Maximal subgroups

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

subgroupindex
#130825892
C2×#106232522
C2×#106232612
C2×#106230612
C2×#106231122
C2×#106230602
C2×#106231702
C2×#106232572
C2×#106231622
C2×#106231142
C2×#106231692
C2×#106232222
C2×#106230102
C2×D11×#1252
C2×#106231052
C2×C4×#43392
C2×C11×#5332
C2×#351511