Finite Group Databasebeta

← C2×#13082474 #15661846

Subgroups — C2×#13082474 #15661846

Order 2816.

7130 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082474C2132yesmaximal, direct product factor
2C2×#10623090C212yesmaximal, complemented
3C2×#10623098C212yesmaximal, complemented
4C2×#10623099C212yesmaximal, complemented
5C2×#10623073C212yesmaximal, complemented
6C2×#10623064C212yesmaximal, complemented
7C2×#10623042C212yesmaximal, complemented
8C2×#10623060C212yesmaximal, complemented
9C2×#10623044C212yesmaximal, complemented
10C2×#10623095C214yesmaximal, complemented
11C2×#10623057C211yesmaximal, characteristic, complemented
12C2×#10623356C211yesmaximal, characteristic, complemented
13C2×#10623048C211yesmaximal, characteristic, complemented
14C2×#10623363C211yesmaximal, characteristic
15C2×#10623069C214yesmaximal, complemented
16C2×#10623035C211yesmaximal, characteristic, complemented
17C22×#66940C211yesmaximal, characteristic, complemented
18C2×C11×#520C211yesmaximal, characteristic, complemented
19C22×C11×#41C2211yescharacteristic
20C22×#4339C2211yescharacteristic
21C23×Dic22C2211yescharacteristic
22C11×#520C22116yescomplemented
23C2×C4×Q8×C11C2212yes—
24C2×C4×D4×C11C2214yes—
25C2×C4×D4×C11C2212yes—
26C2×C11×#117C2212yes—
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2212yes—
29C22×C11×C4⋊C4C2211yescharacteristic
30#10623363C22116yes—
31#10623356C22116yescomplemented
32C2×#67000C2211yescharacteristic
33C2×#66997C2211yescharacteristic
34C2×#66997C2212yes—
35C2×#66993C2211yescharacteristic
36C2×#66992C2212yes—
37C2×#66992C2212yes—
38C2×#66989C2211yescharacteristic
39C2×#66989C2212yes—
40C2×#66988C2214yes—
41C2×#66982C2214yes—
42C2×C4×C22⋊D11C2212yes—
43C2×C4×C22⋊D11C2214yes—
44C2×C4×C22⋊D11C2214yes—
45C2×C4×C22⋊D11C2212yes—
46C2×#66979C2214yes—
47C2×#66979C2211yescharacteristic
48C2×#66977C2212yes—
49C2×#66977C2212yes—
50C2×#66977C2214yes—
51C22×Dic11⋊C4C2212yes—
52C22×C4×Dic11C2212yes—
53C22×C4×Dic11C2211yescharacteristic
54#10623099C22132yescomplemented
55#10623098C22132yescomplemented
56#10623095C22164yescomplemented
57#10623090C22132yescomplemented
58#10623073C22132yescomplemented
59#10623069C22164yescomplemented
60#10623064C22132yescomplemented
61#10623060C22132yescomplemented
62#10623057C22116yescomplemented
63#10623048C22116yescomplemented
64#10623044C22132yescomplemented
65C2×#66951C2214yes—
66#10623042C22132yescomplemented
67C2×#66950C2212yes—
68C2×#66950C2212yes—
69C2×#66949C2214yes—
70#10623035C22116yescomplemented
71C2×#66946C2212yes—
72C2×#66945C2212yes—
73C2×C4⋊C4×D11C2212yes—
74C2×#66943C2211yescharacteristic
75C2×#66943C2211yescharacteristic
76C2×#66942C2214yes—
77C2×#66942C2214yes—
78C2×#66941C2211yescharacteristic
79C2×#66941C2211yescharacteristic
80C2×#66940C2212yes—
81C2×#66940C2212yes—
82C2×#66940C2212yes—
83C2×#66940C2212yes—
84C2×#66940C2212yes—
85C2×#66940C22116yescomplemented
86C2×#66939C2214yes—
87C2×#66938C2214yes—
88C2×#66936C2214yes—
89C2×#66932C2214yes—
90C2×#66932C2214yes—
91C2×#66931C2212yes—
92C2×#66931C2212yes—
93C2×#66929C2214yes—
94C2×#66928C2212yes—
95C2×#66925C2214yes—
96C2×#66923C2214yes—
97C2×#66922C2212yes—
98C2×C4×Dic22C2214yes—
99C2×C4×Dic22C2212yes—
100C2×C4×Dic22C2212yes—
101C2×C11×#41—28no—
102C2×C11×#41C2318yes—
103C22×Q8×C11C2311yescharacteristic
104C22×D4×C11C2312yes—
105C22×D4×C11C2311yescharacteristic
106C23×C4×C11C2312yes—
107C23×C4×C11C2312yes—
108C23×C4×C11C2314yes—
109C23×C4×C11C2311yescharacteristic
110C22×C22⋊D11C2312yes—
111C22×C22⋊D11C2312yes—
112C22×C22⋊D11C2312yes—
113C23×Dic11C2311yescharacteristic
114C23×Dic11C2312yes—
115C23×Dic11C2311yescharacteristic
116C2×#4339—28no—
117C2×#4339C2318yes—
118C22×D44C2311yescharacteristic
119C22×C4×D11C2312yes—
120C22×C4×D11C2314yes—
121C22×Dic22—28no—
122C22×Dic22C2312yes—
123C22×Dic22C2311yescharacteristic
124C22×Dic22C2312yes—
125C22×Dic22C2312yes—
126C22×Dic22C2318yes—
127C22×Dic22C2312yes—
128C4×Q8×C11C23116yes—
129C4×D4×C11C23132yes—
130C4×D4×C11C23116yes—
131C11×#117C2318yes—
132C11×#117C23116yes—
133C2×C11×C4⋊C4C2312yes—
134C2×C11×C4⋊C4C2312yes—
135C2×C11×C4⋊C4C2318yes—
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2314yes—
139C2×C11×C4⋊C4C23116yes—
140C2×C11×C22⋊C4C2312yes—
141C2×C11×C22⋊C4C2314yes—
142C2×C42×C11C2312yes—
143C2×C42×C11C2314yes—
144C2×C22⋊Dic11C2312yes—
145C2×C22⋊Dic11C2312yes—
146C2×C22⋊Dic11C2312yes—
147C2×C22⋊Dic11C2314yes—
148C2×C22⋊Dic11C2314yes—
149#67000C2318yes—
150#66997C2318yes—
151#66997C23116yes—
152#66993C2318yes—
153#66992C23116yes—
154#66992C23116yes—
155#66989C2318yes—
156#66989C23116yes—
157#66988C23132yes—
158#66982C23132yes—
159C4×C22⋊D11C23132yes—
160C4×C22⋊D11C23116yes—
161C4×C22⋊D11C23132yes—
162C4×C22⋊D11C23116yes—
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2314yes—
165C2×(C2×D11)⋊C4C2314yes—
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2314yes—
168#66979C2318yes—
169#66979C23132yes—
170C2×C4⋊Dic11C2314yes—
171C2×C4⋊Dic11C2312yes—
172C2×C4⋊Dic11C2312yes—
173C2×C4⋊Dic11C2314yes—
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2311yescharacteristic
176#66977C23116yes—
177#66977C23132yes—
178#66977C23116yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2314yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2314yes—
187C2×Dic11⋊C4C2314yes—
188C2×Dic11⋊C4C2314yes—
189C2×Dic11⋊C4C2314yes—
190C2×Dic11⋊C4C23116yes—
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2312yes—
194C2×C4×Dic11C2314yes—
195C2×C4×Dic11C2314yes—
196C2×C4×Dic11C2314yes—
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2318yes—
200C2×C4×Dic11C23116yes—
201#66951C23132yes—
202#66950C23116yes—
203#66950C23116yes—
204#66949C23132yes—
205#66946C23116yes—
206#66945C23116yes—
207C4⋊C4×D11C23116yes—
208#66943C2318yes—
209#66943C2318yes—
210#66942C23132yes—
211#66942C23132yes—
212#66941C2318yes—
213#66941C2318yes—
214#66940C23116yes—
215#66940C23116yes—
216#66940C23116yes—
217#66940C23116yes—
218#66940C23116yes—
219#66939C23132yes—
220#66938C23132yes—
221#66936C23132yes—
222#66932C23132yes—
223#66932C23132yes—
224#66931C23116yes—
225#66931C23116yes—
226#66929C23132yes—
227#66928C23116yes—
228#66925C23132yes—
229#66923C23132yes—
230#66922C23116yes—
231C4×Dic22C23116yes—
232C4×Dic22C23116yes—
233C4×Dic22C23132yes—
234C2×#3507—111nomaximal, Sylow
235C24×C11C2412yes—
236C24×C11C2411yescharacteristic
237C23×D11C2412yes—
238C11×#41—232no—
239C2×Q8×C11—24no—
240C2×Q8×C11C2414yes—
241C2×D4×C11—28no—
242C2×D4×C11—24no—
243C2×D4×C11C2418yes—
244C2×D4×C11C2414yes—
245C22×C4×C11—28no—
246C22×C4×C11—48no—
247C22×C4×C11—44no—
248C22×C4×C11#4118yes—
249C22×C4×C11C2414yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C2412yes—
252C22×C4×C11C2412yes—
253C22×C4×C11C2418yes—
254C22×C4×C11C2418yes—
255C22×C4×C11C24116yes—
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2414yes—
259C2×C22⋊D11—28no—
260C2×C22⋊D11—28no—
261C2×C22⋊D11—44no—
262C2×C22⋊D11C2418yes—
263C2×C22⋊D11C2418yes—
264C2×C22⋊D11C2418yes—
265C22×Dic11—24no—
266C22×Dic11—28no—
267C22×Dic11—42no—
268C22×Dic11C2414yes—
269C22×Dic11C2418yes—
270C22×Dic11C2411yescharacteristic
271C22×Dic11C2412yes—
272C22×Dic11C2411yescharacteristic
273C22×Dic11C2411yescharacteristic
274C22×Dic11C2412yes—
275C22×Dic11C2414yes—
276C22×Dic11C2412yes—
277C22×Dic11C2414yes—
278C22×Dic11C2411yescharacteristic
279#4339—232no—
280C2×D44—24no—
281C2×D44C2414yes—
282C2×C4×D11—28no—
283C2×C4×D11—48no—
284C2×C4×D11C2418yes—
285C2×C4×D11C24116yes—
286C2×Dic22—28no—
287C2×Dic22—28no—
288C2×Dic22—28no—
289C2×Dic22—232no—
290C2×Dic22—24no—
291C2×Dic22—44no—
292C2×Dic22C2418yes—
293C2×Dic22C2414yes—
294C2×Dic22C2418yes—
295C2×Dic22C2418yes—
296C2×Dic22C2418yes—
297C11×C4⋊C4C2418yes—
298C11×C4⋊C4C2418yes—
299C11×C4⋊C4C2414yes—
300C11×C4⋊C4C2414yes—
301C11×C4⋊C4C24116yes—
302C11×C22⋊C4C2418yes—
303C11×C22⋊C4C24116yes—
304C42×C11C2418yes—
305C42×C11C24116yes—
306C22⋊Dic11C2418yes—
307C22⋊Dic11C2418yes—
308C22⋊Dic11C2418yes—
309C22⋊Dic11C24116yes—
310C22⋊Dic11C24116yes—
311(C2×D11)⋊C4C2418yes—
312(C2×D11)⋊C4C24116yes—
313(C2×D11)⋊C4C24116yes—
314(C2×D11)⋊C4C2418yes—
315(C2×D11)⋊C4C24116yes—
316C4⋊Dic11C24116yes—
317C4⋊Dic11C2418yes—
318C4⋊Dic11C2418yes—
319C4⋊Dic11C24116yes—
320C4⋊Dic11C2414yes—
321C4⋊Dic11C2414yes—
322Dic11⋊C4C2418yes—
323Dic11⋊C4C2418yes—
324Dic11⋊C4C2418yes—
325Dic11⋊C4C24116yes—
326Dic11⋊C4C2418yes—
327Dic11⋊C4C2418yes—
328Dic11⋊C4C2418yes—
329Dic11⋊C4C24116yes—
330Dic11⋊C4C24116yes—
331Dic11⋊C4C24116yes—
332Dic11⋊C4C24116yes—
333C4×Dic11C2414yes—
334C4×Dic11C2414yes—
335C4×Dic11C2418yes—
336C4×Dic11C24116yes—
337C4×Dic11C24116yes—
338C4×Dic11C24116yes—
339C4×Dic11C2414yes—
340C4×Dic11C2414yes—
341#3507—1132no—
342C2×#559—112no—
343C2×#557—112no—
344C2×#556—112no—
345C2×#556—112no—
346C2×#556—112no—
347C2×#554—112no—
348C2×#552—112no—
349C2×#552—112no—
350C2×#539—114no—
351C2×#536—111no—
352C2×#536—111no—
353C2×#533—111no—
354C2×#532—111no—
355C2×#529—114no—
356C2×#520—111no—
357C2×#520D1111yescharacteristic, complemented
358C22×C4×Q8—111no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—24no—
362C23×C11—24no—
363C23×C11—24no—
364C23×C11C2×#4114yes—
365C23×C11C2514yes—
366C23×C11C2512yes—
367C23×C11C2511yescharacteristic
368C22×D11—24no—
369C22×D11—24no—
370C22×D11—24no—
371C22×D11C2514yes—
372Q8×C11—28no—
373D4×C11—216no—
374D4×C11—28no—
375C2×C4×C11—24no—
376C2×C4×C11—24no—
377C2×C4×C11—24no—
378C2×C4×C11—28no—
379C2×C4×C11—216no—
380C2×C4×C11—416no—
381C2×C4×C11—48no—
382C2×C4×C11C2×#4114yes—
383C2×C4×C11C2×#4114yes—
384C2×C4×C11C2×#41116yes—
385C2×C4×C11C2518yes—
386C2×C4×C11C2514yes—
387C2×C4×C11C2514yes—
388C2×C4×C11C2514yes—
389C2×C4×C11C2512yes—
390C2×C4×C11C2512yes—
391C22⋊D11—216no—
392C22⋊D11—216no—
393C22⋊D11—48no—
394C2×Dic11—216no—
395C2×Dic11—28no—
396C2×Dic11—24no—
397C2×Dic11—24no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—24no—
401C2×Dic11—22no—
402C2×Dic11—28no—
403C2×Dic11—44no—
404C2×Dic112−1+414yes—
405C2×Dic11C2512yes—
406C2×Dic11C2514yes—
407C2×Dic11C2512yes—
408C2×Dic11C2512yes—
409C2×Dic11C2514yes—
410C2×Dic11C2518yes—
411C2×Dic11C2514yes—
412C2×Dic11C2512yes—
413D44—28no—
414C4×D11—216no—
415C4×D11—416no—
416Dic22—216no—
417Dic22—216no—
418Dic22—28no—
419Dic22—216no—
420Dic22—48no—
421C22×#41—111no—
422C22×#41C2×D1111yescharacteristic
423C23×Q8—111no—
424#559—1132no—
425#557—1132no—
426#556—1132no—
427#556—1132no—
428#556—1132no—
429#554—1132no—
430#552—1132no—
431#552—1132no—
432#539—1164no—
433#536—1116no—
434#536—1116no—
435#533—1116no—
436#532—1116no—
437C2×C4⋊Q8—111no—
438C2×C4⋊Q8—112no—
439C2×C4⋊Q8—111no—
440C2×C4⋊Q8—111no—
441C2×C4⋊Q8—112no—
442C2×#127—111no—
443#529—1164no—
444C2×#126—114no—
445C2×#126—114no—
446C2×#126—114no—
447C2×#126—114no—
448C2×#125—114no—
449C2×#125—114no—
450C2×#125—111no—
451C2×#125—111no—
452C2×#125—114no—
453C2×#124—111no—
454C2×#124—111no—
455C2×#124—112no—
456C2×#124—114no—
457C2×#124—112no—
458C2×#123—114no—
459C2×#123—114no—
460C2×#123—114no—
461C2×#123—114no—
462C2×C22⋊Q8—112no—
463C2×C22⋊Q8—112no—
464C2×C22⋊Q8—114no—
465C2×C22⋊Q8—114no—
466C2×C22⋊Q8—112no—
467C2×C22⋊Q8—112no—
468C2×C22⋊Q8—112no—
469C2×C22⋊Q8—112no—
470C2×#121—112no—
471C2×#121—112no—
472#520—1116no—
473#520C2×D11116yescomplemented
474C2×C4×Q8—112no—
475C2×C4×Q8—112no—
476C2×C4×Q8—112no—
477C2×C4×Q8—112no—
478C2×C4×Q8—112no—
479C2×C4×Q8—1116no—
480C2×C4×Q8—114no—
481C2×C4×Q8—112no—
482C2×C4×Q8—112no—
483C2×C4×Q8C2×D1112yes—
484C2×C4×D4—114no—
485C2×C4×D4—114no—
486C2×C4×D4—112no—
487C2×C4×D4—112no—
488C2×C4×D4—112no—
489C2×C4×D4C2×D1114yes—
490C2×C4×D4C2×D1112yes—
491C2×#117—111no—
492C2×#117—114no—
493C2×#117—112no—
494C2×#117—114no—
495C2×#117C2×D1111yescharacteristic
496C2×#117C2×D1112yes—
497C22×C4⋊C4—112no—
498C22×C4⋊C4—112no—
499C22×C4⋊C4C2×D1111yescharacteristic
500C22×C4⋊C4C2×D1112yes—
501C22×C42—112no—
502C22×C42—111no—
503C22×C11—22no—
504C22×C11—22no—
505C22×C11—28no—
506C22×C11—24no—
507C22×C11—24no—
508C22×C11—24no—
509C22×C11—48no—
510C22×C11C22×#4114yes—
511C22×C11C22×#4112yes—
512C22×C11C2×2−1+412yes—
513C22×C11#58512yes—
514C22×C11C2611yescharacteristic
515C2×D11—24no—
516C2×D11—24no—
517C2×D11—24no—
518C2×D11—48no—
519C4×C11—24no—
520C4×C11—24no—
521C4×C11—24no—
522C4×C11—28no—
523C4×C11C22×#4114yes—
524C4×C11C22×#4114yes—
525Dic11—28no—
526Dic11—24no—
527Dic11—24no—
528Dic11—22no—
529Dic11—22no—
530Dic11—24no—
531Dic11—22no—
532Dic11C2×2−1+414yes—
533C2×#41—28no—
534C2×#41—118no—
535C2×#41—228no—
536C2×#41C22×D1118yes—
537C22×Q8—112no—
538C22×Q8—112no—
539C22×Q8—112no—
540C22×Q8—111no—
541C22×Q8—118no—
542C22×Q8—112no—
543C22×Q8—228no—
544C22×Q8C22×D1111yescharacteristic
545C22×D4—112no—
546C22×D4—112no—
547C22×D4—112no—
548C22×D4—111no—
549C22×D4C22×D1112yes—
550C22×D4C22×D1111yescharacteristic
551C23×C4—112no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—112no—
555C23×C4—114no—
556C23×C4C22×D1112yes—
557C23×C4C22×D1112yes—
558C23×C4C22×D1114yes—
559C23×C4C22×D1111yescharacteristic
560C4⋊Q8—118no—
561C4⋊Q8—1116no—
562C4⋊Q8—118no—
563C4⋊Q8—118no—
564C4⋊Q8—1116no—
565#127—118no—
566#126—1132no—
567#126—1132no—
568#126—1132no—
569#126—1132no—
570#125—1132no—
571#125—118no—
572#125—118no—
573#125—1132no—
574#125—1132no—
575#124—118no—
576#124—118no—
577#124—1116no—
578#124—1132no—
579#124—1116no—
580#123—1132no—
581#123—1132no—
582#123—1132no—
583#123—1132no—
584C22⋊Q8—1116no—
585C22⋊Q8—1116no—
586C22⋊Q8—1132no—
587C22⋊Q8—1116no—
588C22⋊Q8—1116no—
589C22⋊Q8—1132no—
590C22⋊Q8—1116no—
591C22⋊Q8—1116no—
592#121—1116no—
593#121—1116no—
594C4×Q8—1116no—
595C4×Q8—1116no—
596C4×Q8—1116no—
597C4×Q8—1116no—
598C4×Q8—1116no—
599C4×Q8—1132no—
600C4×Q8—1116no—
601C4×Q8—1116no—
602C4×Q8C22×D11116yes—
603C4×D4—1132no—
604C4×D4—1132no—
605C4×D4—1116no—
606C4×D4—1116no—
607C4×D4—1116no—
608C4×D4C22×D11132yes—
609C4×D4C22×D11116yes—
610#117—118no—
611#117—1132no—
612#117—1116no—
613#117—1132no—
614#117C22×D1118yes—
615#117C22×D11116yes—
616C2×C4⋊C4—111no—
617C2×C4⋊C4—114no—
618C2×C4⋊C4—114no—
619C2×C4⋊C4—114no—
620C2×C4⋊C4—1116no—
621C2×C4⋊C4—111no—
622C2×C4⋊C4—112no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—114no—
625C2×C4⋊C4—114no—
626C2×C4⋊C4—112no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4—112no—
630C2×C4⋊C4—112no—
631C2×C4⋊C4—114no—
632C2×C4⋊C4—114no—
633C2×C4⋊C4—112no—
634C2×C4⋊C4—1116no—
635C2×C4⋊C4C22×D1112yes—
636C2×C4⋊C4C22×D1111yescharacteristic
637C2×C4⋊C4C22×D1112yes—
638C2×C4⋊C4C22×D1114yes—
639C2×C4⋊C4C22×D1118yes—
640C2×C4⋊C4C22×D11116yes—
641C2×C4⋊C4C22×D1111yescharacteristic
642C2×C22⋊C4—112no—
643C2×C22⋊C4—112no—
644C2×C22⋊C4—114no—
645C2×C22⋊C4—112no—
646C2×C22⋊C4—114no—
647C2×C22⋊C4—112no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4—114no—
650C2×C22⋊C4—112no—
651C2×C22⋊C4—114no—
652C2×C22⋊C4C22×D1112yes—
653C2×C22⋊C4C22×D1114yes—
654C2×C42—114no—
655C2×C42—114no—
656C2×C42—112no—
657C2×C42—111no—
658C2×C42—111no—
659C2×C42—114no—
660C2×C42—111no—
661C2×C42—111no—
662C2×C42—1116no—
663C2×C42—118no—
664C2×C42C22×D1114yes—
665C2×C42C22×D1112yes—
666C2×C11—24no—
667C2×C11—44no—
668C2×C11#350714yescomplemented
669C2×C11C23×#4111yescharacteristic
670C2×C11C22×2−1+411yescharacteristic
671C2×C11C2×#58511yescharacteristic
672D11—44no—
673C24—112no—
674C24C23×D1112yes—
675C24C23×D1111yescharacteristic
676#41—232no—
677#41—2232no—
678C2×Q8—24no—
679C2×Q8—118no—
680C2×Q8—118no—
681C2×Q8—118no—
682C2×Q8—114no—
683C2×Q8—118no—
684C2×Q8—228no—
685C2×Q8—228no—
686C2×Q8—228no—
687C2×Q8—2232no—
688C2×Q8—224no—
689C2×Q8—444no—
690C2×Q8C23×D1114yes—
691C2×D4—28no—
692C2×D4—24no—
693C2×D4—118no—
694C2×D4—118no—
695C2×D4—118no—
696C2×D4—114no—
697C2×D4—228no—
698C2×D4—228no—
699C2×D4—224no—
700C2×D4—444no—
701C2×D4C23×D1118yes—
702C2×D4C23×D1114yes—
703C22×C4—28no—
704C22×C4—44no—
705C22×C4—48no—
706C22×C4—111no—
707C22×C4—114no—
708C22×C4—118no—
709C22×C4—111no—
710C22×C4—112no—
711C22×C4—114no—
712C22×C4—111no—
713C22×C4—112no—
714C22×C4—111no—
715C22×C4—112no—
716C22×C4—114no—
717C22×C4—118no—
718C22×C4—1116no—
719C22×C4—224no—
720C22×C4—228no—
721C22×C4—228no—
722C22×C4—448no—
723C22×C4—442no—
724C22×C4#433918yes—
725C22×C4C23×D1118yes—
726C22×C4C23×D1114yes—
727C22×C4C23×D1112yes—
728C22×C4C23×D1112yes—
729C22×C4C23×D1112yes—
730C22×C4C23×D1118yes—
731C22×C4C23×D11116yes—
732C22×C4C23×D1114yes—
733C22×C4C23×D1111yescharacteristic
734C22×C4C23×D1111yescharacteristic
735C4⋊C4—114no—
736C4⋊C4—1116no—
737C4⋊C4—1116no—
738C4⋊C4—1116no—
739C4⋊C4—114no—
740C4⋊C4—118no—
741C4⋊C4—118no—
742C4⋊C4—1116no—
743C4⋊C4—1116no—
744C4⋊C4—118no—
745C4⋊C4—118no—
746C4⋊C4—118no—
747C4⋊C4—118no—
748C4⋊C4—118no—
749C4⋊C4—1116no—
750C4⋊C4—1116no—
751C4⋊C4—118no—
752C4⋊C4C23×D1118yes—
753C4⋊C4C23×D1114yes—
754C4⋊C4C23×D1118yes—
755C4⋊C4C23×D11116yes—
756C4⋊C4C23×D1114yes—
757C22⋊C4—118no—
758C22⋊C4—118no—
759C22⋊C4—1116no—
760C22⋊C4—118no—
761C22⋊C4—1116no—
762C22⋊C4—118no—
763C22⋊C4—1116no—
764C22⋊C4—1116no—
765C22⋊C4—118no—
766C22⋊C4—1116no—
767C22⋊C4C23×D1118yes—
768C22⋊C4C23×D11116yes—
769C42—1116no—
770C42—114no—
771C42—114no—
772C42—1116no—
773C42—114no—
774C42—114no—
775C42—1116no—
776C42—118no—
777C42C23×D11116yes—
778C42C23×D1118yes—
779C11C2×#350711yescharacteristic, complemented, Sylow
780C23—22no—
781C23—22no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—114no—
786C23—224no—
787C23—224no—
788C23—224no—
789C23C2×#433914yes—
790C23C24×D1114yes—
791C23C24×D1112yes—
792C23C24×D1111yescharacteristic
793Q8—28no—
794Q8—2216no—
795Q8—2216no—
796Q8—2216no—
797Q8—228no—
798Q8—448no—
799D4—216no—
800D4—28no—
801D4—2216no—
802D4—2216no—
803D4—228no—
804D4—448no—
805C2×C4—24no—
806C2×C4—28no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—216no—
810C2×C4—48no—
811C2×C4—416no—
812C2×C4—114no—
813C2×C4—112no—
814C2×C4—112no—
815C2×C4—114no—
816C2×C4—118no—
817C2×C4—112no—
818C2×C4—114no—
819C2×C4—112no—
820C2×C4—114no—
821C2×C4—228no—
822C2×C4—224no—
823C2×C4—2216no—
824C2×C4—228no—
825C2×C4—224no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—224no—
830C2×C4—2216no—
831C2×C4—4416no—
832C2×C4—444no—
833C2×C4C2×#433914yes—
834C2×C4C2×#433914yes—
835C2×C4C2×#4339116yes—
836C2×C4C24×D1118yes—
837C2×C4C24×D1114yes—
838C2×C4C24×D1114yes—
839C2×C4C24×D1114yes—
840C2×C4C24×D1112yes—
841C2×C4C24×D1112yes—
842C22—22no—
843C22—22no—
844C22—28no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—48no—
849C22—224no—
850C22—224no—
851C22—224no—
852C22—448no—
853C22C22×#433914yes—
854C22C22×#433912yes—
855C22#1062345512yes—
856C22D11×2−1+412yes—
857C22C25×D1111yescharacteristic
858C4—24no—
859C4—24no—
860C4—28no—
861C4—24no—
862C4—114no—
863C4—224no—
864C4—228no—
865C4—222no—
866C4—224no—
867C4—224no—
868C4—222no—
869C4—222no—
870C4C22×#433914yes—
871C4C22×#433914yes—
872C2—24no—
873C2—44no—
874C2—444no—
875C2#1308247414yesdirect product factor
876C2C23×#433911yescharacteristic
877C2C2×D11×2−1+411yescharacteristic
878C2C2×#1062345511yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#520C2
socleC23×C11C25
prime radicalC2×#10623363C2
hypercenterC2×#520D11
hypocenterC11C2×#3507
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #13082474C2direct (N × H)
2. C2×#10623090C2semidirect
3. C2×#10623098C2semidirect
4. C2×#10623099C2semidirect
5. C2×#10623073C2semidirect
6. C2×#10623064C2semidirect
7. C2×#10623042C2semidirect
8. C2×#10623060C2semidirect
9. C2×#10623044C2semidirect
10. C2×#10623095C2semidirect
11. C2×#10623057C2semidirect
12. C2×#10623356C2semidirect
13. C2×#10623048C2semidirect
15. C2×#10623069C2semidirect
16. C2×#10623035C2semidirect
17. C22×#66940C2semidirect
18. C2×C11×#520C2semidirect
22. C11×#520C22semidirect
31. #10623356C22semidirect
54. #10623099C22semidirect
55. #10623098C22semidirect
56. #10623095C22semidirect
57. #10623090C22semidirect
58. #10623073C22semidirect
59. #10623069C22semidirect
60. #10623064C22semidirect
61. #10623060C22semidirect
62. #10623057C22semidirect
63. #10623048C22semidirect
64. #10623044C22semidirect
66. #10623042C22semidirect
70. #10623035C22semidirect
85. C2×#66940C22semidirect
357. C2×#520D11semidirect
473. #520C2×D11semidirect
668. C2×C11#3507semidirect
779. C11C2×#3507semidirect
875. C2#13082474direct (N × H)

Maximal subgroups

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

subgroupindex
#130824742
C2×#106230902
C2×#106230982
C2×#106230992
C2×#106230732
C2×#106230642
C2×#106230422
C2×#106230602
C2×#106230442
C2×#106230952
C2×#106230572
C2×#106233562
C2×#106230482
C2×#106233632
C2×#106230692
C2×#106230352
C22×#669402
C2×C11×#5202
C2×#350711