Finite Group Databasebeta

← C2×#13082480 #15661851

Subgroups — C2×#13082480 #15661851

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#13082480C2132yesmaximal, direct product factor
2C2×#10623212C212yesmaximal, complemented
3C2×#10623252C212yesmaximal, complemented
4C2×#10623263C212yesmaximal, complemented
5C2×#10623172C212yesmaximal, complemented
6C2×#10623202C212yesmaximal, complemented
7C2×#10623166C212yesmaximal, complemented
8C2×#10623173C212yesmaximal, complemented
9C2×#10623170C212yesmaximal, complemented
10C2×#10623196C214yesmaximal, complemented
11C2×#10623347C211yesmaximal, characteristic, complemented
12C2×#10623048C211yesmaximal, characteristic, complemented
13C2×#10623363C211yesmaximal, characteristic
14C2×#10623180C214yesmaximal, complemented
15C2×#10623358C211yesmaximal, characteristic, complemented
16C2×#10623054C211yesmaximal, characteristic, complemented
17C22×Q8×Dic11C211yesmaximal, characteristic, complemented
18C2×C11×#536C211yesmaximal, characteristic, complemented
19C22×C11×#41C2211yescharacteristic
20C23×Q8×C11C2211yescharacteristic
21C22×#4339C2211yescharacteristic
22C11×#536C22116yescomplemented
23C2×C11×C4⋊Q8C2212yes—
24C2×C11×#124C2212yes—
25C2×C11×#123C2214yes—
26C2×C11×C22⋊Q8C2212yes—
27C2×C11×C22⋊Q8C2212yes—
28C2×C11×#117C2211yescharacteristic
29#10623363C22116yes—
30#10623358C22116yescomplemented
31#10623347C22116yescomplemented
32C2×#67000C2211yescharacteristic
33C2×#67000C2212yes—
34C2×#66999C2212yes—
35C2×#66999C2212yes—
36C2×Q8×Dic11C2212yes—
37C2×Q8×Dic11C2212yes—
38C2×Q8×Dic11C2212yes—
39C2×Q8×Dic11C2212yes—
40C2×Q8×Dic11C2212yes—
41C2×Q8×Dic11C22116yescomplemented
42C2×#66997C2211yescharacteristic
43C2×#66997C2212yes—
44C2×#66993C2211yescharacteristic
45C2×#66992C2212yes—
46C2×#66992C2212yes—
47C2×#66989C2211yescharacteristic
48C2×D4×Dic11C2214yes—
49C2×D4×Dic11C2212yes—
50C2×#66982C2214yes—
51C2×C4×C22⋊D11C2212yes—
52C2×C4×C22⋊D11C2212yes—
53C2×#66979C2212yes—
54C2×#66979C2211yescharacteristic
55C22×C4⋊Dic11C2212yes—
56C22×C4⋊Dic11C2212yes—
57C22×C4⋊Dic11C2211yescharacteristic
58C22×C4×Dic11C2212yes—
59C22×C4×Dic11C2211yescharacteristic
60#10623263C22132yescomplemented
61#10623252C22132yescomplemented
62#10623212C22132yescomplemented
63#10623202C22132yescomplemented
64#10623196C22164yescomplemented
65#10623180C22164yescomplemented
66#10623173C22132yescomplemented
67#10623172C22132yescomplemented
68#10623170C22132yescomplemented
69#10623166C22132yescomplemented
70#10623054C22116yescomplemented
71#10623048C22116yescomplemented
72C2×#66951C2214yes—
73C2×#66951C2214yes—
74C2×#66950C2214yes—
75C2×#66945C2214yes—
76C2×#66945C2212yes—
77C2×C4⋊C4×D11C2212yes—
78C2×#66943C2211yescharacteristic
79C2×#66943C2211yescharacteristic
80C2×#66943C2214yes—
81C2×#66942C2214yes—
82C2×#66942C2214yes—
83C2×#66941C2211yescharacteristic
84C2×#66941C2211yescharacteristic
85C2×#66940C2214yes—
86C2×#66939C2214yes—
87C2×#66938C2214yes—
88C2×#66936C2214yes—
89C2×(C22⋊D11)⋊C4C2214yes—
90C2×(C22⋊D11)⋊C4C2214yes—
91C2×#66932C2214yes—
92C2×#66932C2214yes—
93C2×#66931C2212yes—
94C2×#66931C2214yes—
95C2×#66931C2212yes—
96C2×#66930C2214yes—
97C2×C4×D44C2212yes—
98C2×C4×Dic22C2212yes—
99C2×C4×Dic22C2212yes—
100C2×C4×Dic22C2212yes—
101C2×C11×#41—28no—
102C2×C11×#41C2318yes—
103C22×Q8×C11—28no—
104C22×Q8×C11C2312yes—
105C22×Q8×C11C2311yescharacteristic
106C22×Q8×C11C2312yes—
107C22×Q8×C11C2318yes—
108C22×D4×C11C2311yescharacteristic
109C22×D4×C11C2312yes—
110C23×C4×C11C2312yes—
111C23×C4×C11C2312yes—
112C23×C4×C11C2311yescharacteristic
113C22×C22⋊D11C2312yes—
114C22×C22⋊D11C2312yes—
115C22×C22⋊D11C2312yes—
116C23×Dic11C2311yescharacteristic
117C23×Dic11C2314yes—
118C23×Dic11C2311yescharacteristic
119C23×Dic11C2312yes—
120C2×#4339—28no—
121C2×#4339C2318yes—
122C22×D44C2311yescharacteristic
123C22×C4×D11C2312yes—
124C22×C4×D11C2314yes—
125C22×Dic22C2311yescharacteristic
126C22×Dic22C2312yes—
127C22×Dic22C2312yes—
128C11×C4⋊Q8C23116yes—
129C11×#124C23116yes—
130C11×#123C23132yes—
131C11×C22⋊Q8C23116yes—
132C11×C22⋊Q8C23116yes—
133C11×#117C2318yes—
134C2×C11×C4⋊C4C2314yes—
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2314yes—
138C2×C11×C22⋊C4C2314yes—
139C2×C11×C22⋊C4C2312yes—
140C2×C11×C22⋊C4C2314yes—
141C2×C42×C11C2312yes—
142C2×C22⋊Dic11C2312yes—
143C2×C22⋊Dic11C2312yes—
144C2×C22⋊Dic11C2312yes—
145C2×C22⋊Dic11C2314yes—
146#67000C2318yes—
147#67000C23116yes—
148#66999C23116yes—
149#66999C23116yes—
150Q8×Dic11C23116yes—
151Q8×Dic11C23116yes—
152Q8×Dic11C23116yes—
153Q8×Dic11C23116yes—
154Q8×Dic11C23116yes—
155#66997C2318yes—
156#66997C23116yes—
157#66993C2318yes—
158#66992C23116yes—
159#66992C23116yes—
160#66989C2318yes—
161D4×Dic11C23132yes—
162D4×Dic11C23116yes—
163#66982C23132yes—
164C4×C22⋊D11C23116yes—
165C4×C22⋊D11C23116yes—
166C2×(C2×D11)⋊C4C2314yes—
167C2×(C2×D11)⋊C4C2314yes—
168C2×(C2×D11)⋊C4C2314yes—
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2312yes—
171#66979C2318yes—
172#66979C23116yes—
173C2×C4⋊Dic11C2312yes—
174C2×C4⋊Dic11C2312yes—
175C2×C4⋊Dic11C2312yes—
176C2×C4⋊Dic11C2314yes—
177C2×C4⋊Dic11C2314yes—
178C2×C4⋊Dic11C2311yescharacteristic
179C2×C4⋊Dic11C2311yescharacteristic
180C2×C4⋊Dic11C2314yes—
181C2×C4⋊Dic11C2312yes—
182C2×C4⋊Dic11C2318yes—
183C2×C4⋊Dic11C23116yes—
184C2×C4⋊Dic11C23116yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2314yes—
188C2×Dic11⋊C4C2312yes—
189C2×Dic11⋊C4C2312yes—
190C2×Dic11⋊C4C2314yes—
191C2×Dic11⋊C4C2314yes—
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2312yes—
197C2×C4×Dic11C2314yes—
198C2×C4×Dic11C2314yes—
199C2×C4×Dic11C2314yes—
200C2×C4×Dic11C2314yes—
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2318yes—
204C2×C4×Dic11C23116yes—
205#66951C23132yes—
206#66951C23132yes—
207#66950C23132yes—
208#66945C23132yes—
209#66945C23116yes—
210C4⋊C4×D11C23116yes—
211#66943C23132yes—
212#66943C2318yes—
213#66943C2318yes—
214#66942C23132yes—
215#66942C23132yes—
216#66941C2318yes—
217#66941C2318yes—
218#66940C23132yes—
219#66939C23132yes—
220#66938C23132yes—
221#66936C23132yes—
222(C22⋊D11)⋊C4C23132yes—
223(C22⋊D11)⋊C4C23132yes—
224#66932C23132yes—
225#66932C23132yes—
226#66931C23116yes—
227#66931C23116yes—
228#66931C23132yes—
229#66930C23132yes—
230C4×D44C23116yes—
231C4×Dic22C23116yes—
232C4×Dic22C23116yes—
233C4×Dic22C23116yes—
234C2×#3507—111nomaximal, Sylow
235C24×C11C2412yes—
236C24×C11C2411yescharacteristic
237C23×D11C2412yes—
238C11×#41—232no—
239C2×Q8×C11—28no—
240C2×Q8×C11—28no—
241C2×Q8×C11—232no—
242C2×Q8×C11—24no—
243C2×Q8×C11C2418yes—
244C2×Q8×C11C2414yes—
245C2×Q8×C11C2418yes—
246C2×D4×C11—28no—
247C2×D4×C11—24no—
248C2×D4×C11C2414yes—
249C2×D4×C11C2418yes—
250C22×C4×C11—28no—
251C22×C4×C11—28no—
252C22×C4×C11#4118yes—
253C22×C4×C11C2414yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2412yes—
256C22×C4×C11C2418yes—
257C22×C4×C11C2412yes—
258C22×C4×C11C2418yes—
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2414yes—
262C2×C22⋊D11—28no—
263C2×C22⋊D11—28no—
264C2×C22⋊D11—44no—
265C2×C22⋊D11C2418yes—
266C2×C22⋊D11C2418yes—
267C2×C22⋊D11C2418yes—
268C22×Dic11—24no—
269C22×Dic11—42no—
270C22×Dic11—44no—
271C22×Dic11—48no—
272C22×Dic11C2414yes—
273C22×Dic11C2411yescharacteristic
274C22×Dic11C2414yes—
275C22×Dic11C2412yes—
276C22×Dic11C2412yes—
277C22×Dic11C2411yescharacteristic
278C22×Dic11C2411yescharacteristic
279C22×Dic11C2412yes—
280C22×Dic11C24116yes—
281C22×Dic11C2414yes—
282C22×Dic11C2418yes—
283C22×Dic11C2411yescharacteristic
284#4339—232no—
285C2×D44—24no—
286C2×D44C2414yes—
287C2×C4×D11—28no—
288C2×C4×D11—48no—
289C2×C4×D11C2418yes—
290C2×C4×D11C24116yes—
291C2×Dic22—28no—
292C2×Dic22—24no—
293C2×Dic22—44no—
294C2×Dic22C2414yes—
295C2×Dic22C2418yes—
296C2×Dic22C2418yes—
297C11×C4⋊C4C24116yes—
298C11×C4⋊C4C2414yes—
299C11×C4⋊C4C2414yes—
300C11×C4⋊C4C24116yes—
301C11×C22⋊C4C24116yes—
302C11×C22⋊C4C2418yes—
303C11×C22⋊C4C24116yes—
304C42×C11C2418yes—
305C22⋊Dic11C2418yes—
306C22⋊Dic11C2418yes—
307C22⋊Dic11C2418yes—
308C22⋊Dic11C24116yes—
309(C2×D11)⋊C4C24116yes—
310(C2×D11)⋊C4C24116yes—
311(C2×D11)⋊C4C24116yes—
312(C2×D11)⋊C4C2418yes—
313(C2×D11)⋊C4C2418yes—
314C4⋊Dic11C2418yes—
315C4⋊Dic11C2418yes—
316C4⋊Dic11C2418yes—
317C4⋊Dic11C24116yes—
318C4⋊Dic11C24116yes—
319C4⋊Dic11C2414yes—
320C4⋊Dic11C2414yes—
321C4⋊Dic11C24116yes—
322C4⋊Dic11C2418yes—
323Dic11⋊C4C2418yes—
324Dic11⋊C4C2418yes—
325Dic11⋊C4C24116yes—
326Dic11⋊C4C2418yes—
327Dic11⋊C4C2418yes—
328Dic11⋊C4C24116yes—
329Dic11⋊C4C24116yes—
330Dic11⋊C4C2418yes—
331Dic11⋊C4C2418yes—
332C4×Dic11C2414yes—
333C4×Dic11C2414yes—
334C4×Dic11C2418yes—
335C4×Dic11C24116yes—
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×#536D1111yescharacteristic, complemented
353C2×#533—111no—
354C2×#532—111no—
355C2×#529—114no—
356C2×#520—111no—
357C2×#520—111no—
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—216no—
373Q8×C11—216no—
374Q8×C11—28no—
375D4×C11—216no—
376D4×C11—28no—
377C2×C4×C11—24no—
378C2×C4×C11—216no—
379C2×C4×C11—28no—
380C2×C4×C11—24no—
381C2×C4×C11—24no—
382C2×C4×C11—216no—
383C2×C4×C11C2×#4114yes—
384C2×C4×C11C2×#4114yes—
385C2×C4×C11C2×#41116yes—
386C2×C4×C11C2518yes—
387C2×C4×C11C2514yes—
388C2×C4×C11C2514yes—
389C2×C4×C11C2514yes—
390C2×C4×C11C2512yes—
391C2×C4×C11C2512yes—
392C22⋊D11—216no—
393C22⋊D11—216no—
394C22⋊D11—48no—
395C2×Dic11—24no—
396C2×Dic11—24no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—24no—
400C2×Dic11—28no—
401C2×Dic11—22no—
402C2×Dic11—28no—
403C2×Dic11—44no—
404C2×Dic11—416no—
405C2×Dic11—48no—
406C2×Dic112−1+414yes—
407C2×Dic11C2512yes—
408C2×Dic11C2518yes—
409C2×Dic11C2514yes—
410C2×Dic11C2514yes—
411C2×Dic11C2512yes—
412C2×Dic11C2512yes—
413C2×Dic11C2514yes—
414C2×Dic11C2512yes—
415D44—28no—
416C4×D11—216no—
417C4×D11—416no—
418Dic22—28no—
419Dic22—216no—
420Dic22—48no—
421C22×#41—111no—
422C22×#41C2×D1111yescharacteristic
423C23×Q8C2×D1111yescharacteristic
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#536C2×D11116yescomplemented
435#533—1116no—
436#532—1116no—
437C2×C4⋊Q8—111no—
438C2×C4⋊Q8—112no—
439C2×C4⋊Q8—111no—
440C2×C4⋊Q8—111no—
441C2×C4⋊Q8C2×D1112yes—
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—112no—
455C2×#124—111no—
456C2×#124—114no—
457C2×#124C2×D1112yes—
458C2×#123—114no—
459C2×#123—114no—
460C2×#123—114no—
461C2×#123C2×D1114yes—
462C2×C22⋊Q8—112no—
463C2×C22⋊Q8—112no—
464C2×C22⋊Q8—114no—
465C2×C22⋊Q8—112no—
466C2×C22⋊Q8—112no—
467C2×C22⋊Q8—114no—
468C2×C22⋊Q8C2×D1112yes—
469C2×C22⋊Q8C2×D1112yes—
470C2×#121—112no—
471C2×#121—112no—
472#520—1116no—
473#520—1116no—
474C2×C4×Q8—112no—
475C2×C4×Q8—112no—
476C2×C4×Q8—112no—
477C2×C4×Q8—112no—
478C2×C4×Q8—1116no—
479C2×C4×Q8—112no—
480C2×C4×Q8—114no—
481C2×C4×Q8—112no—
482C2×C4×Q8—112no—
483C2×C4×Q8—112no—
484C2×C4×D4—114no—
485C2×C4×D4—112no—
486C2×C4×D4—112no—
487C2×C4×D4—112no—
488C2×C4×D4—114no—
489C2×C4×D4—114no—
490C2×C4×D4—112no—
491C2×#117—111no—
492C2×#117—112no—
493C2×#117—112no—
494C2×#117—114no—
495C2×#117—114no—
496C2×#117C2×D1111yescharacteristic
497C22×C4⋊C4—111no—
498C22×C4⋊C4—112no—
499C22×C4⋊C4—112no—
500C22×C4⋊C4—112no—
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—28no—
521C4×C11—24no—
522C4×C11—24no—
523C4×C11C22×#4114yes—
524C4×C11C22×#4114yes—
525Dic11—24no—
526Dic11—24no—
527Dic11—22no—
528Dic11—22no—
529Dic11—24no—
530Dic11—28no—
531Dic11—22no—
532Dic11C2×2−1+414yes—
533C2×#41—28no—
534C2×#41—118no—
535C2×#41—228no—
536C2×#41C22×D1118yes—
537C22×Q8—28no—
538C22×Q8—112no—
539C22×Q8—111no—
540C22×Q8—112no—
541C22×Q8C22×D1112yes—
542C22×Q8C22×D1112yes—
543C22×Q8C22×D1111yescharacteristic
544C22×Q8C22×D1118yes—
545C22×D4—112no—
546C22×D4—112no—
547C22×D4—112no—
548C22×D4—111no—
549C22×D4C22×D1112yes—
550C22×D4C22×D1111yescharacteristic
551C23×C4—111no—
552C23×C4—112no—
553C23×C4—111no—
554C23×C4—114no—
555C23×C4—112no—
556C23×C4—114no—
557C23×C4C22×D1112yes—
558C23×C4C22×D1112yes—
559C23×C4C22×D1111yescharacteristic
560C4⋊Q8—118no—
561C4⋊Q8—1116no—
562C4⋊Q8—118no—
563C4⋊Q8—118no—
564C4⋊Q8C22×D11116yes—
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—1116no—
577#124—118no—
578#124—1132no—
579#124C22×D11116yes—
580#123—1132no—
581#123—1132no—
582#123—1132no—
583#123C22×D11132yes—
584C22⋊Q8—1116no—
585C22⋊Q8—1116no—
586C22⋊Q8—1132no—
587C22⋊Q8—1116no—
588C22⋊Q8—1116no—
589C22⋊Q8—1132no—
590C22⋊Q8C22×D11116yes—
591C22⋊Q8C22×D11116yes—
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×Q8—1116no—
603C4×D4—1132no—
604C4×D4—1116no—
605C4×D4—1116no—
606C4×D4—1116no—
607C4×D4—1132no—
608C4×D4—1132no—
609C4×D4—1116no—
610#117—118no—
611#117—1116no—
612#117—1116no—
613#117—1132no—
614#117—1132no—
615#117C22×D1118yes—
616C2×C4⋊C4—112no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—112no—
619C2×C4⋊C4—114no—
620C2×C4⋊C4—114no—
621C2×C4⋊C4—118no—
622C2×C4⋊C4—114no—
623C2×C4⋊C4—114no—
624C2×C4⋊C4—1116no—
625C2×C4⋊C4—1116no—
626C2×C4⋊C4—111no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4—114no—
630C2×C4⋊C4—112no—
631C2×C4⋊C4—112no—
632C2×C4⋊C4—112no—
633C2×C4⋊C4—112no—
634C2×C4⋊C4—112no—
635C2×C4⋊C4—114no—
636C2×C4⋊C4—112no—
637C2×C4⋊C4—1116no—
638C2×C4⋊C4C22×D1111yescharacteristic
639C2×C4⋊C4C22×D1111yescharacteristic
640C2×C4⋊C4C22×D1114yes—
641C2×C4⋊C4C22×D1114yes—
642C2×C22⋊C4—112no—
643C2×C22⋊C4—112no—
644C2×C22⋊C4—114no—
645C2×C22⋊C4—112no—
646C2×C22⋊C4—112no—
647C2×C22⋊C4—114no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4—112no—
650C2×C22⋊C4—114no—
651C2×C22⋊C4C22×D1114yes—
652C2×C22⋊C4C22×D1112yes—
653C2×C22⋊C4C22×D1114yes—
654C2×C42—114no—
655C2×C42—114no—
656C2×C42—114no—
657C2×C42—112no—
658C2×C42—111no—
659C2×C42—111no—
660C2×C42—114no—
661C2×C42—111no—
662C2×C42—111no—
663C2×C42—1116no—
664C2×C42—118no—
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—28no—
679C2×Q8—28no—
680C2×Q8—232no—
681C2×Q8—24no—
682C2×Q8—118no—
683C2×Q8—114no—
684C2×Q8—118no—
685C2×Q8—228no—
686C2×Q8—224no—
687C2×Q8—444no—
688C2×Q8C23×D1118yes—
689C2×Q8C23×D1118yes—
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—28no—
705C22×C4—111no—
706C22×C4—114no—
707C22×C4—111no—
708C22×C4—114no—
709C22×C4—112no—
710C22×C4—111no—
711C22×C4—112no—
712C22×C4—111no—
713C22×C4—112no—
714C22×C4—118no—
715C22×C4—114no—
716C22×C4—1116no—
717C22×C4—118no—
718C22×C4—1116no—
719C22×C4—224no—
720C22×C4—228no—
721C22×C4—448no—
722C22×C4—444no—
723C22×C4—448no—
724C22×C4—442no—
725C22×C4#434118yes—
726C22×C4C23×D1118yes—
727C22×C4C23×D1118yes—
728C22×C4C23×D1112yes—
729C22×C4C23×D1114yes—
730C22×C4C23×D1112yes—
731C22×C4C23×D1112yes—
732C22×C4C23×D1114yes—
733C22×C4C23×D1111yescharacteristic
734C22×C4C23×D1111yescharacteristic
735C4⋊C4—118no—
736C4⋊C4—114no—
737C4⋊C4—118no—
738C4⋊C4—1116no—
739C4⋊C4—1116no—
740C4⋊C4—1116no—
741C4⋊C4—1116no—
742C4⋊C4—114no—
743C4⋊C4—118no—
744C4⋊C4—118no—
745C4⋊C4—1116no—
746C4⋊C4—118no—
747C4⋊C4—118no—
748C4⋊C4—118no—
749C4⋊C4—118no—
750C4⋊C4—118no—
751C4⋊C4—1116no—
752C4⋊C4—118no—
753C4⋊C4C23×D1114yes—
754C4⋊C4C23×D1114yes—
755C4⋊C4C23×D11116yes—
756C4⋊C4C23×D11116yes—
757C22⋊C4—118no—
758C22⋊C4—118no—
759C22⋊C4—1116no—
760C22⋊C4—118no—
761C22⋊C4—118no—
762C22⋊C4—1116no—
763C22⋊C4—1116no—
764C22⋊C4—118no—
765C22⋊C4—1116no—
766C22⋊C4C23×D11116yes—
767C22⋊C4C23×D1118yes—
768C22⋊C4C23×D11116yes—
769C42—1116no—
770C42—114no—
771C42—114no—
772C42—1116no—
773C42—114no—
774C42—114no—
775C42—1116no—
776C42—1116no—
777C42—118no—
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×#434114yes—
790C23C24×D1114yes—
791C23C24×D1112yes—
792C23C24×D1111yescharacteristic
793Q8—216no—
794Q8—216no—
795Q8—28no—
796Q8—2216no—
797Q8—228no—
798Q8—448no—
799D4—216no—
800D4—28no—
801D4—2216no—
802D4—2216no—
803D4—228no—
804D4—448no—
805C2×C4—24no—
806C2×C4—216no—
807C2×C4—28no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—216no—
811C2×C4—114no—
812C2×C4—112no—
813C2×C4—112no—
814C2×C4—118no—
815C2×C4—114no—
816C2×C4—112no—
817C2×C4—114no—
818C2×C4—112no—
819C2×C4—114no—
820C2×C4—228no—
821C2×C4—224no—
822C2×C4—222no—
823C2×C4—224no—
824C2×C4—228no—
825C2×C4—224no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—2216no—
829C2×C4—4416no—
830C2×C4—448no—
831C2×C4—4416no—
832C2×C4—444no—
833C2×C4C2×#434114yes—
834C2×C4C2×#434114yes—
835C2×C4C2×#4341116yes—
836C2×C4C24×D1114yes—
837C2×C4C24×D1118yes—
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×#434114yes—
854C22C22×#434112yes—
855C22D11×2−1+412yes—
856C22#1062345712yes—
857C22C25×D1111yescharacteristic
858C4—24no—
859C4—28no—
860C4—24no—
861C4—24no—
862C4—114no—
863C4—224no—
864C4—222no—
865C4—224no—
866C4—228no—
867C4—224no—
868C4—222no—
869C4—222no—
870C4C22×#434114yes—
871C4C22×#434114yes—
872C2—24no—
873C2—44no—
874C2—444no—
875C2#1308248014yesdirect product factor
876C2C23×#434111yescharacteristic
877C2C2×D11×2−1+411yescharacteristic
878C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#536C2
socleC23×C11C25
prime radicalC2×#10623363C2
hypercenterC2×#536D11
hypocenterC11C2×#3507
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. #13082480C2direct (N × H)
2. C2×#10623212C2semidirect
3. C2×#10623252C2semidirect
4. C2×#10623263C2semidirect
5. C2×#10623172C2semidirect
6. C2×#10623202C2semidirect
7. C2×#10623166C2semidirect
8. C2×#10623173C2semidirect
9. C2×#10623170C2semidirect
10. C2×#10623196C2semidirect
11. C2×#10623347C2semidirect
12. C2×#10623048C2semidirect
14. C2×#10623180C2semidirect
15. C2×#10623358C2semidirect
16. C2×#10623054C2semidirect
17. C22×Q8×Dic11C2semidirect
18. C2×C11×#536C2semidirect
22. C11×#536C22semidirect
30. #10623358C22semidirect
31. #10623347C22semidirect
41. C2×Q8×Dic11C22semidirect
60. #10623263C22semidirect
61. #10623252C22semidirect
62. #10623212C22semidirect
63. #10623202C22semidirect
64. #10623196C22semidirect
65. #10623180C22semidirect
66. #10623173C22semidirect
67. #10623172C22semidirect
68. #10623170C22semidirect
69. #10623166C22semidirect
70. #10623054C22semidirect
71. #10623048C22semidirect
352. C2×#536D11semidirect
434. #536C2×D11semidirect
668. C2×C11#3507semidirect
779. C11C2×#3507semidirect
875. C2#13082480direct (N × H)

Maximal subgroups

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

subgroupindex
#130824802
C2×#106232122
C2×#106232522
C2×#106232632
C2×#106231722
C2×#106232022
C2×#106231662
C2×#106231732
C2×#106231702
C2×#106231962
C2×#106233472
C2×#106230482
C2×#106233632
C2×#106231802
C2×#106233582
C2×#106230542
C22×Q8×Dic112
C2×C11×#5362
C2×#350711