Finite Group Databasebeta

← C2×#13082585 #15661889

Subgroups — C2×#13082585 #15661889

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#13082585C2132yesmaximal, direct product factor
2C2×#10623252C211yesmaximal, characteristic, complemented
3C2×#10623074C211yesmaximal, characteristic, complemented
4C2×#10623074C211yesmaximal, characteristic, complemented
5C2×#10623149C212yesmaximal, complemented
6C2×#10623173C212yesmaximal, complemented
7C2×#10623181C214yesmaximal, complemented
8C2×#10623044C212yesmaximal, complemented
9C2×#10623355C212yesmaximal, complemented
10C2×#10623156C212yesmaximal, complemented
11C2×#10623196C214yesmaximal, complemented
12C2×#10623259C211yesmaximal, characteristic, complemented
13C2×#10623088C211yesmaximal, characteristic, complemented
14C2×#10623131C212yesmaximal, complemented
15C22×#66943C212yesmaximal, complemented
16C2×#10623358C212yesmaximal, complemented
17C2×C4×#4341C211yesmaximal, characteristic, complemented
18C2×C11×#547C211yesmaximal, characteristic, complemented
19C22×C11×#41C2212yes—
20C22×#4341C2211yescharacteristic
21C11×#547C22116yescomplemented
22C2×C11×C4⋊Q8C2211yescharacteristic
23C2×C11×#123C2214yes—
24C2×C11×C22⋊Q8C2212yes—
25C2×C11×#121C2212yes—
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C22×C11×C4⋊C4C2212yes—
29#10623358C22132yescomplemented
30#10623355C22132yescomplemented
31C2×#66999C2212yes—
32C2×Q8×Dic11C2212yes—
33C2×Q8×Dic11C2212yes—
34C2×#66997C2212yes—
35C2×#66992C2214yes—
36C2×#66991C2211yescharacteristic
37C2×#66989C2211yescharacteristic
38C2×#66988C2214yes—
39C2×D4×Dic11C2214yes—
40C2×D4×Dic11C2212yes—
41C2×D4×Dic11C2214yes—
42C2×D4×Dic11C2212yes—
43C2×D4×Dic11C2211yescharacteristic
44C2×#66982C2214yes—
45C2×C4×C22⋊D11C2212yes—
46C2×C4×C22⋊D11C2212yes—
47C2×#66979C2214yes—
48C2×#66979C2212yes—
49C22×C4⋊Dic11C2212yes—
50C22×C4⋊Dic11C2214yes—
51C22×C4⋊Dic11C2212yes—
52C2×#66977C2212yes—
53C2×#66977C2212yes—
54C22×Dic11⋊C4C2214yes—
55C22×C4×Dic11C2212yes—
56#10623259C22116yescomplemented
57#10623252C22116yescomplemented
58#10623196C22164yescomplemented
59#10623181C22164yescomplemented
60#10623173C22132yescomplemented
61#10623156C22132yescomplemented
62#10623149C22132yescomplemented
63#10623131C22132yescomplemented
64#10623088C22116yescomplemented
65#10623074C22116yescomplemented
66#10623074C22116yescomplemented
67C4×#4341C22116yescomplemented
68#10623044C22132yescomplemented
69C2×#66951C2214yes—
70C2×#66950C2211yescharacteristic
71C2×#66950C2212yes—
72C2×#66945C2212yes—
73C2×#66945C2211yescharacteristic
74C2×#66943C2212yes—
75C2×#66943C2211yescharacteristic
76C2×#66943C2214yes—
77C2×#66943C2212yes—
78C2×#66943C2212yes—
79C2×#66943C2214yes—
80C2×#66943C2212yes—
81C2×#66943C22132yescomplemented
82C2×#66942C2214yes—
83C2×#66942C2214yes—
84C2×#66940C2212yes—
85C2×#66940C2212yes—
86C2×#66940C2211yescharacteristic
87C2×#66939C2214yes—
88C2×#66936C2212yes—
89C2×(C22⋊D11)⋊C4C2212yes—
90C2×#66932C2212yes—
91C2×#66932C2214yes—
92C2×#66932C2214yes—
93C2×#66931C2214yes—
94C2×#66931C2214yes—
95C2×#66930C2212yes—
96C2×#66930C2214yes—
97C2×C42×D11C2211yescharacteristic
98C2×#66922C2211yescharacteristic
99C2×C4×Dic22C2211yescharacteristic
100C2×C4×Dic22C2211yescharacteristic
101C2×C11×#41—216no—
102C2×C11×#41C23116yes—
103C22×Q8×C11C2312yes—
104C22×D4×C11C2314yes—
105C22×D4×C11C2311yescharacteristic
106C22×D4×C11C2311yescharacteristic
107C23×C4×C11C2312yes—
108C23×C4×C11C2314yes—
109C23×C4×C11C2312yes—
110C22×C22⋊D11C2312yes—
111C22×C22⋊D11C2312yes—
112C23×Dic11C2312yes—
113C23×Dic11C2314yes—
114C23×Dic11C2314yes—
115C23×Dic11C2312yes—
116C2×#4341—28no—
117C2×#4341C2318yes—
118C22×C4×D11C2311yescharacteristic
119C22×C4×D11C2311yescharacteristic
120C22×C4×D11C2311yescharacteristic
121C22×Dic22C2311yescharacteristic
122C22×Dic22C2311yescharacteristic
123C22×Dic22C2312yes—
124C11×C4⋊Q8C2318yes—
125C11×#123C23132yes—
126C11×C22⋊Q8C23116yes—
127C11×#121C23116yes—
128C4×D4×C11C2318yes—
129C4×D4×C11C2318yes—
130C2×C11×C4⋊C4C2312yes—
131C2×C11×C4⋊C4C2312yes—
132C2×C11×C4⋊C4C2311yescharacteristic
133C2×C11×C4⋊C4C2314yes—
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C23116yes—
136C2×C11×C22⋊C4C2312yes—
137C2×C11×C22⋊C4C2314yes—
138C2×C11×C22⋊C4C2312yes—
139C2×C42×C11C2311yescharacteristic
140C2×C22⋊Dic11C2312yes—
141C2×C22⋊Dic11C2312yes—
142C2×C22⋊Dic11C2314yes—
143C2×C22⋊Dic11C2314yes—
144C2×C22⋊Dic11C2312yes—
145C2×C22⋊Dic11C2312yes—
146#66999C23116yes—
147Q8×Dic11C23116yes—
148Q8×Dic11C23116yes—
149#66997C23116yes—
150#66992C23132yes—
151#66991C2318yes—
152#66989C2318yes—
153#66988C23132yes—
154D4×Dic11C2318yes—
155D4×Dic11C23116yes—
156D4×Dic11C23116yes—
157D4×Dic11C23132yes—
158D4×Dic11C23132yes—
159#66982C23132yes—
160C4×C22⋊D11C23116yes—
161C4×C22⋊D11C23116yes—
162C2×(C2×D11)⋊C4C2312yes—
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2314yes—
165#66979C23132yes—
166#66979C23116yes—
167C2×C4⋊Dic11C2311yescharacteristic
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2312yes—
170C2×C4⋊Dic11C2312yes—
171C2×C4⋊Dic11C2314yes—
172C2×C4⋊Dic11C2314yes—
173C2×C4⋊Dic11C2312yes—
174C2×C4⋊Dic11C2314yes—
175C2×C4⋊Dic11C2312yes—
176C2×C4⋊Dic11C2314yes—
177C2×C4⋊Dic11C23116yes—
178C2×C4⋊Dic11C23132yes—
179C2×C4⋊Dic11C23116yes—
180#66977C23116yes—
181#66977C23116yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2314yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2314yes—
187C2×Dic11⋊C4C2314yes—
188C2×Dic11⋊C4C2314yes—
189C2×Dic11⋊C4C2314yes—
190C2×Dic11⋊C4C2312yes—
191C2×Dic11⋊C4C23132yes—
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2312yes—
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2312yes—
198C2×C4×Dic11C2314yes—
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2314yes—
201C2×C4×Dic11C23116yes—
202#66951C23132yes—
203#66950C23116yes—
204#66950C2318yes—
205#66945C23116yes—
206#66945C2318yes—
207#66943C23116yes—
208#66943C23116yes—
209#66943C2318yes—
210#66943C23116yes—
211#66943C23132yes—
212#66943C23132yes—
213#66943C23116yes—
214#66942C23132yes—
215#66942C23132yes—
216#66940C23116yes—
217#66940C23116yes—
218#66940C2318yes—
219#66939C23132yes—
220#66936C23116yes—
221(C22⋊D11)⋊C4C23116yes—
222#66932C23116yes—
223#66932C23132yes—
224#66932C23132yes—
225#66931C23132yes—
226#66931C23132yes—
227#66930C23116yes—
228#66930C23132yes—
229C42×D11C2318yes—
230#66922C2318yes—
231C4×Dic22C2318yes—
232C4×Dic22C2318yes—
233C2×#3515—111nomaximal, Sylow
234C24×C11C2412yes—
235C24×C11C2412yes—
236C23×D11C2411yescharacteristic
237C11×#41—264no—
238C2×Q8×C11—28no—
239C2×Q8×C11C2418yes—
240C2×D4×C11—216no—
241C2×D4×C11—24no—
242C2×D4×C11#4118yes—
243C2×D4×C11C24116yes—
244C2×D4×C11C2414yes—
245C2×D4×C11C2414yes—
246C22×C4×C11—216no—
247C22×C4×C11—28no—
248C22×C4×C11—28no—
249C22×C4×C11C2412yes—
250C22×C4×C11C2414yes—
251C22×C4×C11C2418yes—
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2412yes—
254C22×C4×C11C24116yes—
255C22×C4×C11C2418yes—
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C2×C22⋊D11—28no—
259C2×C22⋊D11—44no—
260C2×C22⋊D11C2418yes—
261C2×C22⋊D11C2418yes—
262C22×Dic11—28no—
263C22×Dic11—48no—
264C22×Dic11—44no—
265C22×Dic11—48no—
266C22×Dic11C2418yes—
267C22×Dic11C2411yescharacteristic
268C22×Dic11C2411yescharacteristic
269C22×Dic11C2412yes—
270C22×Dic11C2411yescharacteristic
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C22×Dic11C2414yes—
275C22×Dic11C24116yes—
276C22×Dic11C24116yes—
277C22×Dic11C2418yes—
278#4341—232no—
279C2×C4×D11—24no—
280C2×C4×D11—24no—
281C2×C4×D11—42no—
282C2×C4×D11C2414yes—
283C2×C4×D11C2414yes—
284C2×C4×D11C2414yes—
285C2×Dic22—24no—
286C2×Dic22—24no—
287C2×Dic22—44no—
288C2×Dic22C2414yes—
289C2×Dic22C2414yes—
290C2×Dic22C2418yes—
291C11×C4⋊C4C2418yes—
292C11×C4⋊C4C2418yes—
293C11×C4⋊C4C2414yes—
294C11×C4⋊C4C24116yes—
295C11×C4⋊C4C2414yes—
296C11×C22⋊C4C2418yes—
297C11×C22⋊C4C24116yes—
298C11×C22⋊C4C2418yes—
299C42×C11C2414yes—
300C22⋊Dic11C2418yes—
301C22⋊Dic11C2418yes—
302C22⋊Dic11C24116yes—
303C22⋊Dic11C24116yes—
304C22⋊Dic11C2418yes—
305C22⋊Dic11C2418yes—
306(C2×D11)⋊C4C2418yes—
307(C2×D11)⋊C4C2418yes—
308(C2×D11)⋊C4C24116yes—
309C4⋊Dic11C2414yes—
310C4⋊Dic11C2414yes—
311C4⋊Dic11C2418yes—
312C4⋊Dic11C2418yes—
313C4⋊Dic11C24116yes—
314C4⋊Dic11C24116yes—
315C4⋊Dic11C2418yes—
316C4⋊Dic11C24116yes—
317C4⋊Dic11C2418yes—
318C4⋊Dic11C24116yes—
319Dic11⋊C4C2418yes—
320Dic11⋊C4C2418yes—
321Dic11⋊C4C24116yes—
322Dic11⋊C4C2418yes—
323Dic11⋊C4C24116yes—
324Dic11⋊C4C24116yes—
325Dic11⋊C4C24116yes—
326Dic11⋊C4C24116yes—
327Dic11⋊C4C2418yes—
328C4×Dic11C2418yes—
329C4×Dic11C2418yes—
330C4×Dic11C2414yes—
331C4×Dic11C2414yes—
332C4×Dic11C2414yes—
333C4×Dic11C2418yes—
334C4×Dic11C24116yes—
335C4×Dic11C2418yes—
336C4×Dic11C24116yes—
337#3515—1132no—
338C2×#557—111no—
339C2×#554—111no—
340C2×#554—111no—
341C2×#553—112no—
342C2×#552—114no—
343C2×#552—112no—
344C2×#552—112no—
345C2×#547—112no—
346C2×#547D1111yescharacteristic, complemented
347C2×#541—112no—
348C2×#539—114no—
349C2×#533—111no—
350C2×#529—112no—
351C2×#529—111no—
352C22×#125—112no—
353C2×#520—112no—
354C2×C4×#41—111no—
355C23×C11—24no—
356C23×C11—24no—
357C23×C11—24no—
358C23×C11—24no—
359C23×C11—24no—
360C23×C11C2×#4118yes—
361C23×C11C2514yes—
362C23×C11C2514yes—
363C23×C11C2511yescharacteristic
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11C2512yes—
368Q8×C11—216no—
369D4×C11—232no—
370D4×C11—28no—
371D4×C11C2×#41116yes—
372C2×C4×C11—24no—
373C2×C4×C11—28no—
374C2×C4×C11—232no—
375C2×C4×C11—24no—
376C2×C4×C11—22no—
377C2×C4×C11—216no—
378C2×C4×C11—216no—
379C2×C4×C11C2×#4114yes—
380C2×C4×C112−1+414yes—
381C2×C4×C11C2514yes—
382C2×C4×C11C2518yes—
383C2×C4×C11C2512yes—
384C2×C4×C11C2514yes—
385C2×C4×C11C2512yes—
386C2×C4×C11C2512yes—
387C22⋊D11—216no—
388C22⋊D11—48no—
389C2×Dic11—24no—
390C2×Dic11—22no—
391C2×Dic11—216no—
392C2×Dic11—24no—
393C2×Dic11—22no—
394C2×Dic11—28no—
395C2×Dic11—22no—
396C2×Dic11—24no—
397C2×Dic11—24no—
398C2×Dic11—416no—
399C2×Dic11—416no—
400C2×Dic11—48no—
401C2×Dic11C2512yes—
402C2×Dic11C2512yes—
403C2×Dic11C2514yes—
404C2×Dic11C2512yes—
405C2×Dic11C2514yes—
406C2×Dic11C2514yes—
407C2×Dic11C2514yes—
408C2×Dic11C2518yes—
409C4×D11—28no—
410C4×D11—28no—
411C4×D11—44no—
412Dic22—28no—
413Dic22—28no—
414Dic22—48no—
415C22×#41—111no—
416C22×#41C2×D1112yes—
417#557—1116no—
418#554—1116no—
419#554—1116no—
420#553—1132no—
421#552—1164no—
422#552—1132no—
423#552—1132no—
424#547—1132no—
425#547C2×D11116yescomplemented
426#541—1132no—
427#539—1164no—
428#533—1116no—
429C2×C4⋊Q8—112no—
430C2×C4⋊Q8—111no—
431C2×C4⋊Q8C2×D1111yescharacteristic
432#529—1132no—
433#529—1116no—
434C2×#126—114no—
435C2×#126—114no—
436C2×#126—112no—
437C2×#126—114no—
438C2×#125—114no—
439C2×#125—114no—
440C2×#125—111no—
441C2×#125—112no—
442C2×#125—114no—
443C2×#125—114no—
444C2×#125—112no—
445C2×#125—112no—
446C2×#125—112no—
447C2×#125—1132no—
448C2×#124—111no—
449C2×#123—114no—
450C2×#123—114no—
451C2×#123—112no—
452C2×#123—114no—
453C2×#123C2×D1114yes—
454C2×C22⋊Q8—112no—
455C2×C22⋊Q8—112no—
456C2×C22⋊Q8—112no—
457C2×C22⋊Q8—111no—
458C2×C22⋊Q8—112no—
459C2×C22⋊Q8—114no—
460C2×C22⋊Q8—114no—
461C2×C22⋊Q8C2×D1112yes—
462C2×#121—111no—
463C2×#121—114no—
464C2×#121C2×D1112yes—
465#520—1132no—
466C4×#41—1116no—
467C2×C4×Q8—112no—
468C2×C4×Q8—112no—
469C2×C4×Q8—111no—
470C2×C4×Q8—112no—
471C2×C4×Q8—112no—
472C2×C4×Q8—111no—
473C2×C4×Q8—111no—
474C2×C4×D4—111no—
475C2×C4×D4—114no—
476C2×C4×D4—112no—
477C2×C4×D4—114no—
478C2×C4×D4—112no—
479C2×C4×D4—112no—
480C2×C4×D4—112no—
481C2×C4×D4—112no—
482C2×C4×D4C2×D1111yescharacteristic
483C2×C4×D4C2×D1111yescharacteristic
484C2×#117—112no—
485C2×#117—114no—
486C2×#117—111no—
487C2×#117—112no—
488C2×#117—112no—
489C2×#117—114no—
490C22×C4⋊C4—114no—
491C22×C4⋊C4—114no—
492C22×C4⋊C4—112no—
493C22×C4⋊C4—112no—
494C22×C4⋊C4C2×D1112yes—
495C22×C42—112no—
496C22×C42—111no—
497C22×C11—24no—
498C22×C11—24no—
499C22×C11—216no—
500C22×C11—24no—
501C22×C11—24no—
502C22×C11—24no—
503C22×C11—48no—
504C22×C11C22×#4118yes—
505C22×C11C22×#4112yes—
506C22×C11C2×2−1+412yes—
507C22×C11#58512yes—
508C22×C11C2611yescharacteristic
509C2×D11—22no—
510C2×D11—22no—
511C2×D11—22no—
512C2×D11—44no—
513C4×C11—24no—
514C4×C11—28no—
515C4×C11—24no—
516C4×C11—22no—
517C4×C11C22×#4114yes—
518C4×C11C2×2−1+414yes—
519Dic11—24no—
520Dic11—22no—
521Dic11—24no—
522Dic11—22no—
523Dic11—28no—
524Dic11—22no—
525Dic11—24no—
526Dic11—24no—
527C2×#41—216no—
528C2×#41—118no—
529C2×#41—228no—
530C2×#41C22×D11116yes—
531C22×Q8—111no—
532C22×Q8—111no—
533C22×Q8—112no—
534C22×Q8C22×D1112yes—
535C22×D4—112no—
536C22×D4—112no—
537C22×D4C22×D1111yescharacteristic
538C22×D4C22×D1114yes—
539C22×D4C22×D1111yescharacteristic
540C23×C4—112no—
541C23×C4—114no—
542C23×C4—112no—
543C23×C4—114no—
544C23×C4—111no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4C22×D1114yes—
548C23×C4C22×D1112yes—
549C23×C4C22×D1112yes—
550C4⋊Q8—1116no—
551C4⋊Q8—118no—
552C4⋊Q8C22×D1118yes—
553#126—1132no—
554#126—1132no—
555#126—1116no—
556#126—1132no—
557#125—118no—
558#125—1116no—
559#125—1132no—
560#125—1132no—
561#125—1116no—
562#125—1116no—
563#125—1132no—
564#125—1132no—
565#125—1116no—
566#124—118no—
567#123—1132no—
568#123—1132no—
569#123—1116no—
570#123—1132no—
571#123C22×D11132yes—
572C22⋊Q8—1116no—
573C22⋊Q8—1116no—
574C22⋊Q8—1116no—
575C22⋊Q8—118no—
576C22⋊Q8—1116no—
577C22⋊Q8—1132no—
578C22⋊Q8—1132no—
579C22⋊Q8C22×D11116yes—
580#121—118no—
581#121—1132no—
582#121C22×D11116yes—
583C4×Q8—1116no—
584C4×Q8—1116no—
585C4×Q8—118no—
586C4×Q8—1116no—
587C4×Q8—1116no—
588C4×Q8—118no—
589C4×Q8—118no—
590C4×D4—118no—
591C4×D4—1132no—
592C4×D4—1116no—
593C4×D4—1132no—
594C4×D4—1116no—
595C4×D4—1116no—
596C4×D4—1116no—
597C4×D4—1116no—
598C4×D4C22×D1118yes—
599C4×D4C22×D1118yes—
600#117—1116no—
601#117—1132no—
602#117—118no—
603#117—1116no—
604#117—1116no—
605#117—1132no—
606C2×C4⋊C4—111no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—112no—
609C2×C4⋊C4—112no—
610C2×C4⋊C4—111no—
611C2×C4⋊C4—112no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—112no—
614C2×C4⋊C4—114no—
615C2×C4⋊C4—114no—
616C2×C4⋊C4—1132no—
617C2×C4⋊C4—1116no—
618C2×C4⋊C4—114no—
619C2×C4⋊C4—114no—
620C2×C4⋊C4—114no—
621C2×C4⋊C4—1132no—
622C2×C4⋊C4—1116no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—112no—
625C2×C4⋊C4—112no—
626C2×C4⋊C4—114no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—114no—
629C2×C4⋊C4C22×D1111yescharacteristic
630C2×C4⋊C4C22×D1112yes—
631C2×C4⋊C4C22×D1114yes—
632C2×C4⋊C4C22×D11116yes—
633C2×C4⋊C4C22×D1111yescharacteristic
634C2×C4⋊C4C22×D1112yes—
635C2×C22⋊C4—112no—
636C2×C22⋊C4—112no—
637C2×C22⋊C4—112no—
638C2×C22⋊C4—114no—
639C2×C22⋊C4—112no—
640C2×C22⋊C4—114no—
641C2×C22⋊C4—112no—
642C2×C22⋊C4—114no—
643C2×C22⋊C4—112no—
644C2×C22⋊C4C22×D1112yes—
645C2×C22⋊C4C22×D1114yes—
646C2×C22⋊C4C22×D1112yes—
647C2×C42—112no—
648C2×C42—111no—
649C2×C42—114no—
650C2×C42—114no—
651C2×C42—111no—
652C2×C42—112no—
653C2×C42—112no—
654C2×C42—112no—
655C2×C42—1116no—
656C2×C42—111no—
657C2×C42—118no—
658C2×C42C22×D1111yescharacteristic
659C2×C11—28no—
660C2×C11—44no—
661C2×C11#351514yescomplemented
662C2×C11C23×#4111yescharacteristic
663C2×C11C22×2−1+411yescharacteristic
664C2×C11C2×#58511yescharacteristic
665D11—42no—
666C24—111no—
667C24C23×D1112yes—
668C24C23×D1112yes—
669#41—264no—
670#41—2232no—
671C2×Q8—28no—
672C2×Q8—114no—
673C2×Q8—114no—
674C2×Q8—118no—
675C2×Q8—224no—
676C2×Q8—224no—
677C2×Q8—444no—
678C2×Q8C23×D1118yes—
679C2×D4—216no—
680C2×D4—24no—
681C2×D4—118no—
682C2×D4—118no—
683C2×D4—228no—
684C2×D4—444no—
685C2×D4#434118yes—
686C2×D4C23×D1114yes—
687C2×D4C23×D11116yes—
688C2×D4C23×D1114yes—
689C22×C4—216no—
690C22×C4—28no—
691C22×C4—28no—
692C22×C4—118no—
693C22×C4—111no—
694C22×C4—111no—
695C22×C4—112no—
696C22×C4—111no—
697C22×C4—112no—
698C22×C4—112no—
699C22×C4—114no—
700C22×C4—112no—
701C22×C4—118no—
702C22×C4—1116no—
703C22×C4—1116no—
704C22×C4—114no—
705C22×C4—114no—
706C22×C4—114no—
707C22×C4—228no—
708C22×C4—224no—
709C22×C4—224no—
710C22×C4—442no—
711C22×C4—444no—
712C22×C4—448no—
713C22×C4—448no—
714C22×C4C23×D1118yes—
715C22×C4C23×D11116yes—
716C22×C4C23×D1118yes—
717C22×C4C23×D1112yes—
718C22×C4C23×D1114yes—
719C22×C4C23×D1111yescharacteristic
720C22×C4C23×D1112yes—
721C22×C4C23×D1111yescharacteristic
722C22×C4C23×D1111yescharacteristic
723C4⋊C4—114no—
724C4⋊C4—1116no—
725C4⋊C4—118no—
726C4⋊C4—118no—
727C4⋊C4—114no—
728C4⋊C4—118no—
729C4⋊C4—1116no—
730C4⋊C4—118no—
731C4⋊C4—1116no—
732C4⋊C4—1116no—
733C4⋊C4—1116no—
734C4⋊C4—1116no—
735C4⋊C4—1116no—
736C4⋊C4—118no—
737C4⋊C4—118no—
738C4⋊C4—118no—
739C4⋊C4—1116no—
740C4⋊C4—118no—
741C4⋊C4—1116no—
742C4⋊C4C23×D1114yes—
743C4⋊C4C23×D1118yes—
744C4⋊C4C23×D11116yes—
745C4⋊C4C23×D1114yes—
746C4⋊C4C23×D1118yes—
747C22⋊C4—118no—
748C22⋊C4—118no—
749C22⋊C4—118no—
750C22⋊C4—1116no—
751C22⋊C4—118no—
752C22⋊C4—1116no—
753C22⋊C4—118no—
754C22⋊C4—1116no—
755C22⋊C4—118no—
756C22⋊C4C23×D1118yes—
757C22⋊C4C23×D11116yes—
758C22⋊C4C23×D1118yes—
759C42—114no—
760C42—118no—
761C42—114no—
762C42—114no—
763C42—118no—
764C42—118no—
765C42—1116no—
766C42—1116no—
767C42—118no—
768C42C23×D1114yes—
769C11C2×#351511yescharacteristic, complemented, Sylow
770C23—24no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—112no—
776C23—222no—
777C23—222no—
778C23—222no—
779C23C2×#434118yes—
780C23C24×D1114yes—
781C23C24×D1114yes—
782C23C24×D1111yescharacteristic
783Q8—216no—
784Q8—228no—
785Q8—228no—
786Q8—448no—
787D4—232no—
788D4—28no—
789D4—2216no—
790D4—448no—
791D4C2×#4341116yes—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—232no—
795C2×C4—24no—
796C2×C4—22no—
797C2×C4—216no—
798C2×C4—216no—
799C2×C4—112no—
800C2×C4—112no—
801C2×C4—112no—
802C2×C4—114no—
803C2×C4—114no—
804C2×C4—114no—
805C2×C4—118no—
806C2×C4—114no—
807C2×C4—222no—
808C2×C4—224no—
809C2×C4—2216no—
810C2×C4—222no—
811C2×C4—224no—
812C2×C4—222no—
813C2×C4—224no—
814C2×C4—224no—
815C2×C4—228no—
816C2×C4—228no—
817C2×C4—228no—
818C2×C4—444no—
819C2×C4—448no—
820C2×C4—4416no—
821C2×C4—4416no—
822C2×C4C2×#434114yes—
823C2×C4#6704314yes—
824C2×C4C24×D1114yes—
825C2×C4C24×D1118yes—
826C2×C4C24×D1112yes—
827C2×C4C24×D1114yes—
828C2×C4C24×D1112yes—
829C2×C4C24×D1112yes—
830C22—24no—
831C22—24no—
832C22—216no—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—48no—
837C22—222no—
838C22—222no—
839C22—222no—
840C22—444no—
841C22C22×#434118yes—
842C22C22×#434112yes—
843C22C2×#6704312yes—
844C22#1062345712yes—
845C22C25×D1111yescharacteristic
846C4—24no—
847C4—28no—
848C4—24no—
849C4—22no—
850C4—222no—
851C4—224no—
852C4—222no—
853C4—224no—
854C4—222no—
855C4—224no—
856C4—224no—
857C4—228no—
858C4C22×#434114yes—
859C4C2×#6704314yes—
860C2—28no—
861C2—44no—
862C2—442no—
863C2#1308258514yesdirect product factor
864C2C23×#434111yescharacteristic
865C2C22×#6704311yescharacteristic
866C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#547C2
socleC23×C11C25
hypercenterC2×#547D11
hypocenterC11C2×#3515
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #13082585C2direct (N × H)
2. C2×#10623252C2semidirect
3. C2×#10623074C2semidirect
4. C2×#10623074C2semidirect
5. C2×#10623149C2semidirect
6. C2×#10623173C2semidirect
7. C2×#10623181C2semidirect
8. C2×#10623044C2semidirect
9. C2×#10623355C2semidirect
10. C2×#10623156C2semidirect
11. C2×#10623196C2semidirect
12. C2×#10623259C2semidirect
13. C2×#10623088C2semidirect
14. C2×#10623131C2semidirect
15. C22×#66943C2semidirect
16. C2×#10623358C2semidirect
17. C2×C4×#4341C2semidirect
18. C2×C11×#547C2semidirect
21. C11×#547C22semidirect
29. #10623358C22semidirect
30. #10623355C22semidirect
56. #10623259C22semidirect
57. #10623252C22semidirect
58. #10623196C22semidirect
59. #10623181C22semidirect
60. #10623173C22semidirect
61. #10623156C22semidirect
62. #10623149C22semidirect
63. #10623131C22semidirect
64. #10623088C22semidirect
65. #10623074C22semidirect
66. #10623074C22semidirect
67. C4×#4341C22semidirect
68. #10623044C22semidirect
81. C2×#66943C22semidirect
346. C2×#547D11semidirect
425. #547C2×D11semidirect
661. C2×C11#3515semidirect
769. C11C2×#3515semidirect
863. C2#13082585direct (N × H)

Maximal subgroups

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

subgroupindex
#130825852
C2×#106232522
C2×#106230742
C2×#106231492
C2×#106231732
C2×#106231812
C2×#106230442
C2×#106233552
C2×#106231562
C2×#106231962
C2×#106232592
C2×#106230882
C2×#106231312
C22×#669432
C2×#106233582
C2×C4×#43412
C2×C11×#5472
C2×#351511