Finite Group Databasebeta

← C2×#13082525 #15662146

Subgroups — C2×#13082525 #15662146

Order 2816.

7758 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082525C2132yesmaximal, direct product factor
2C2×#10623172C212yesmaximal, complemented
3C2×#10623147C212yesmaximal, complemented
4C2×#10623166C212yesmaximal, complemented
5C2×#10623132C214yesmaximal, complemented
6C2×#10623129C214yesmaximal, complemented
7C2×#10623142C212yesmaximal, complemented
8C2×#10623174C212yesmaximal, complemented
9C2×#10623134C212yesmaximal, complemented
10C2×#10623364C211yesmaximal, characteristic, complemented
11C2×#10623153C212yesmaximal, complemented
12C2×#10623363C211yesmaximal, characteristic, complemented
13C2×#10623127C212yesmaximal, complemented
14C22×#66941C211yesmaximal, characteristic, complemented
15C2×#10623358C211yesmaximal, characteristic, complemented
16C2×#10623035C211yesmaximal, characteristic, complemented
17C2×#41×Dic11C211yesmaximal, characteristic, complemented
18C2×C11×#537C211yesmaximal, characteristic, complemented
19C22×C11×#41C2211yescharacteristic
20C22×C11×#41C2211yescharacteristic
21C22×#4341C2214yes—
22C22×#4339C2211yescharacteristic
23C23×Dic22C2212yes—
24C11×#537C22116yescomplemented
25C2×C11×C22⋊Q8C2212yes—
26C2×C11×C22⋊Q8C2212yes—
27C2×C11×#121C2214yes—
28C2×C11×#121C2212yes—
29C2×C11×#121C2212yes—
30C22×C11×C4⋊C4C2211yescharacteristic
31#10623364C22116yescomplemented
32#10623363C22116yescomplemented
33#10623358C22116yescomplemented
34#41×Dic11C22116yescomplemented
35C2×#67000C2211yescharacteristic
36C2×#66999C2212yes—
37C2×Q8×Dic11C2211yescharacteristic
38C2×Q8×Dic11C2212yes—
39C2×Q8×Dic11C2211yescharacteristic
40C2×#66997C2211yescharacteristic
41C2×#66993C2211yescharacteristic
42C2×#66992C2212yes—
43C2×#66992C2214yes—
44C2×#66992C2214yes—
45C2×#66992C2212yes—
46C2×#66991C2212yes—
47C2×#66989C2211yescharacteristic
48C2×#66989C2214yes—
49C2×#66988C2214yes—
50C2×D4×Dic11C2212yes—
51C2×D4×Dic11C2214yes—
52C2×D4×Dic11C2212yes—
53C2×D4×Dic11C2211yescharacteristic
54C2×D4×Dic11C2211yescharacteristic
55C2×D4×Dic11C2212yes—
56C2×#66983C2212yes—
57C2×C4×C22⋊D11C2214yes—
58C2×C4×C22⋊D11C2212yes—
59C2×C4×C22⋊D11C2212yes—
60C2×#66979C2212yes—
61C2×#66979C2212yes—
62C2×#66979C2211yescharacteristic
63C22×C4⋊Dic11C2211yescharacteristic
64C22×C4⋊Dic11C2212yes—
65C2×#66977C2212yes—
66C22×Dic11⋊C4C2212yes—
67C22×C4×Dic11C2211yescharacteristic
68C22×C4×Dic11C2212yes—
69#10623174C22132yescomplemented
70#10623172C22132yescomplemented
71#10623166C22132yescomplemented
72#10623153C22132yescomplemented
73#10623147C22132yescomplemented
74#10623142C22132yescomplemented
75#10623134C22132yescomplemented
76#10623132C22164yescomplemented
77#10623129C22164yescomplemented
78#10623127C22132yescomplemented
79C2×#66951C2214yes—
80C2×#66950C2214yes—
81#10623035C22116yescomplemented
82C2×#66946C2212yes—
83C2×#66945C2212yes—
84C2×C4⋊C4×D11C2212yes—
85C2×#66942C2214yes—
86C2×#66941C2212yes—
87C2×#66941C2212yes—
88C2×#66941C2212yes—
89C2×#66941C2212yes—
90C2×#66941C22116yescomplemented
91C2×#66940C2214yes—
92C2×#66940C2212yes—
93C2×#66938C2214yes—
94C2×#66938C2214yes—
95C2×#66936C2214yes—
96C2×(C22⋊D11)⋊C4C2214yes—
97C2×#66932C2214yes—
98C2×#66931C2214yes—
99C2×#66931C2214yes—
100C2×#66930C2214yes—
101C2×C11×#41—28no—
102C2×C11×#41—28no—
103C2×C11×#41C2318yes—
104C2×C11×#41C2318yes—
105C22×Q8×C11C2311yescharacteristic
106C22×Q8×C11C2311yescharacteristic
107C22×D4×C11C2311yescharacteristic
108C22×D4×C11C2311yescharacteristic
109C22×D4×C11C2312yes—
110C22×D4×C11C2312yes—
111C22×D4×C11C2314yes—
112C23×C4×C11C2312yes—
113C23×C4×C11C2312yes—
114C23×C4×C11C2312yes—
115C23×C4×C11C2311yescharacteristic
116C22×C22⋊D11C2312yes—
117C22×C22⋊D11C2312yes—
118C22×C22⋊D11C2312yes—
119C22×C22⋊D11C2314yes—
120C23×Dic11C2312yes—
121C23×Dic11C2312yes—
122C23×Dic11C2311yescharacteristic
123C23×Dic11C2311yescharacteristic
124C23×Dic11C2314yes—
125C23×Dic11C2312yes—
126C2×#4341—416no—
127C2×#4341C23132yes—
128C2×#4339—28no—
129C2×#4339C2318yes—
130C22×D44C2311yescharacteristic
131C22×C4×D11C2312yes—
132C22×C4×D11C2314yes—
133C22×Dic22—48no—
134C22×Dic22C2314yes—
135C22×Dic22C2311yescharacteristic
136C22×Dic22C2314yes—
137C22×Dic22C23116yes—
138C11×C22⋊Q8C23116yes—
139C11×C22⋊Q8C23116yes—
140C11×#121C23116yes—
141C11×#121C23132yes—
142C11×#121C23116yes—
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2314yes—
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2318yes—
147C2×C11×C22⋊C4C2314yes—
148C2×C11×C22⋊C4C2314yes—
149C2×C22⋊Dic11C2314yes—
150C2×C22⋊Dic11C2312yes—
151C2×C22⋊Dic11C2312yes—
152C2×C22⋊Dic11C2314yes—
153C2×C22⋊Dic11C2312yes—
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2312yes—
156#67000C2318yes—
157#66999C23116yes—
158Q8×Dic11C2318yes—
159Q8×Dic11C2318yes—
160Q8×Dic11C23116yes—
161#66997C2318yes—
162#66993C2318yes—
163#66992C23116yes—
164#66992C23116yes—
165#66992C23132yes—
166#66992C23132yes—
167#66991C23116yes—
168#66989C2318yes—
169#66989C23132yes—
170#66988C23132yes—
171D4×Dic11C23116yes—
172D4×Dic11C23116yes—
173D4×Dic11C2318yes—
174D4×Dic11C2318yes—
175D4×Dic11C23116yes—
176D4×Dic11C23132yes—
177#66983C23116yes—
178C4×C22⋊D11C23132yes—
179C4×C22⋊D11C23116yes—
180C4×C22⋊D11C23116yes—
181C2×(C2×D11)⋊C4C2314yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2314yes—
184C2×(C2×D11)⋊C4C2312yes—
185#66979C2318yes—
186#66979C23116yes—
187#66979C23116yes—
188C2×C4⋊Dic11C2312yes—
189C2×C4⋊Dic11C2314yes—
190C2×C4⋊Dic11C2312yes—
191C2×C4⋊Dic11C2312yes—
192C2×C4⋊Dic11C2312yes—
193C2×C4⋊Dic11C2318yes—
194C2×C4⋊Dic11C2311yescharacteristic
195C2×C4⋊Dic11C2311yescharacteristic
196C2×C4⋊Dic11C23116yes—
197#66977C23116yes—
198C2×Dic11⋊C4C2312yes—
199C2×Dic11⋊C4C2314yes—
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2314yes—
202C2×Dic11⋊C4C2314yes—
203C2×Dic11⋊C4C2314yes—
204C2×Dic11⋊C4C23116yes—
205C2×C4×Dic11C2314yes—
206C2×C4×Dic11C2314yes—
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2312yes—
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2318yes—
215C2×C4×Dic11C23116yes—
216#66951C23132yes—
217#66950C23132yes—
218#66946C23116yes—
219#66945C23116yes—
220C4⋊C4×D11C23116yes—
221#66942C23132yes—
222#66941C23116yes—
223#66941C23116yes—
224#66941C23116yes—
225#66941C23116yes—
226#66940C23116yes—
227#66940C23132yes—
228#66938C23132yes—
229#66938C23132yes—
230#66936C23132yes—
231(C22⋊D11)⋊C4C23132yes—
232#66932C23132yes—
233#66931C23132yes—
234#66931C23132yes—
235#66930C23132yes—
236C2×#3511—111nomaximal, Sylow
237C24×C11C2412yes—
238C24×C11C2412yes—
239C24×C11C2411yescharacteristic
240C23×D11C2412yes—
241C11×#41—232no—
242C11×#41—232no—
243C2×Q8×C11—24no—
244C2×Q8×C11—24no—
245C2×Q8×C11C2414yes—
246C2×Q8×C11C2414yes—
247C2×D4×C11—28no—
248C2×D4×C11—28no—
249C2×D4×C11—24no—
250C2×D4×C11—24no—
251C2×D4×C11—48no—
252C2×D4×C11C2414yes—
253C2×D4×C11C2414yes—
254C2×D4×C11C2418yes—
255C2×D4×C11C2418yes—
256C2×D4×C11C24116yes—
257C22×C4×C11—28no—
258C22×C4×C11—28no—
259C22×C4×C11—44no—
260C22×C4×C11#4118yescomplemented
261C22×C4×C11C2412yes—
262C22×C4×C11C2412yes—
263C22×C4×C11C2418yes—
264C22×C4×C11C2414yes—
265C22×C4×C11C2418yes—
266C22×C4×C11C2418yes—
267C22×C4×C11C2411yescharacteristic
268C22×C4×C11C2411yescharacteristic
269C22×C4×C11C2414yes—
270C2×C22⋊D11—28no—
271C2×C22⋊D11—28no—
272C2×C22⋊D11—28no—
273C2×C22⋊D11—48no—
274C2×C22⋊D11C2418yes—
275C2×C22⋊D11C2418yes—
276C2×C22⋊D11C2418yes—
277C2×C22⋊D11C24116yes—
278C22×Dic11—24no—
279C22×Dic11—28no—
280C22×Dic11—24no—
281C22×Dic11—28no—
282C22×Dic11—44no—
283C22×Dic11—48no—
284C22×Dic11C2418yes—
285C22×Dic11C2418yes—
286C22×Dic11C2412yes—
287C22×Dic11C2412yes—
288C22×Dic11C2411yescharacteristic
289C22×Dic11C2414yes—
290C22×Dic11C2412yes—
291C22×Dic11C2411yescharacteristic
292C22×Dic11C2414yes—
293C22×Dic11C2414yes—
294C22×Dic11C24116yes—
295C22×Dic11C2418yes—
296C22×Dic11C2411yescharacteristic
297C22×Dic11C2411yescharacteristic
298#4341—464no—
299#4339—232no—
300C2×D44—24no—
301C2×D44C2414yes—
302C2×C4×D11—28no—
303C2×C4×D11—48no—
304C2×C4×D11C2418yes—
305C2×C4×D11C24116yes—
306C2×Dic22—216no—
307C2×Dic22—24no—
308C2×Dic22—48no—
309C2×Dic22—432no—
310C2×Dic22C24116yes—
311C2×Dic22C2414yes—
312C2×Dic22C24116yes—
313C11×C4⋊C4C2418yes—
314C11×C4⋊C4C24116yes—
315C11×C4⋊C4C2418yes—
316C11×C22⋊C4C24116yes—
317C11×C22⋊C4C24116yes—
318C22⋊Dic11C24116yes—
319C22⋊Dic11C2418yes—
320C22⋊Dic11C2418yes—
321C22⋊Dic11C24116yes—
322C22⋊Dic11C2418yes—
323C22⋊Dic11C2418yes—
324C22⋊Dic11C2418yes—
325(C2×D11)⋊C4C24116yes—
326(C2×D11)⋊C4C2418yes—
327(C2×D11)⋊C4C24116yes—
328(C2×D11)⋊C4C2418yes—
329C4⋊Dic11C2418yes—
330C4⋊Dic11C24116yes—
331C4⋊Dic11C2418yes—
332C4⋊Dic11C2418yes—
333C4⋊Dic11C2418yes—
334C4⋊Dic11C2414yes—
335C4⋊Dic11C2414yes—
336Dic11⋊C4C2418yes—
337Dic11⋊C4C24116yes—
338Dic11⋊C4C2418yes—
339Dic11⋊C4C24116yes—
340Dic11⋊C4C24116yes—
341Dic11⋊C4C24116yes—
342C4×Dic11C24116yes—
343C4×Dic11C24116yes—
344C4×Dic11C2418yes—
345C4×Dic11C2418yes—
346C4×Dic11C2418yes—
347C4×Dic11C2414yes—
348C4×Dic11C2414yes—
349C4×Dic11C2414yes—
350C4×Dic11C2414yes—
351#3511—1132no—
352C2×#556—112no—
353C2×#555—112no—
354C2×#554—112no—
355C2×#553—114no—
356C2×#548—114no—
357C2×#547—112no—
358C2×#542—112no—
359C2×#542—112no—
360C2×#537—111no—
361C2×#537D1111yescharacteristic, complemented
362C2×#533—112no—
363C2×#532—111no—
364C2×#532—112no—
365C22×C4⋊Q8—111no—
366C2×#520—111no—
367C2×#520—111no—
368C2×C4×#41—111no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—24no—
372C23×C11—24no—
373C23×C11—24no—
374C23×C11—24no—
375C23×C11—24no—
376C23×C11—24no—
377C23×C11C2×#4114yes—
378C23×C11C2514yes—
379C23×C11C2514yes—
380C23×C11C2512yes—
381C23×C11C2511yescharacteristic
382C22×D11—24no—
383C22×D11—24no—
384C22×D11—24no—
385C22×D11C2514yes—
386Q8×C11—28no—
387Q8×C11—28no—
388D4×C11—216no—
389D4×C11—216no—
390D4×C11—28no—
391D4×C11—28no—
392D4×C11—416no—
393C2×C4×C11—24no—
394C2×C4×C11—24no—
395C2×C4×C11—28no—
396C2×C4×C11—216no—
397C2×C4×C11—216no—
398C2×C4×C11—48no—
399C2×C4×C11C2×#4114yes—
400C2×C4×C11C2×#4114yes—
401C2×C4×C11C2×#41116yescomplemented
402C2×C4×C11C2514yes—
403C2×C4×C11C2514yes—
404C2×C4×C11C2518yes—
405C2×C4×C11C2512yes—
406C2×C4×C11C2512yes—
407C22⋊D11—216no—
408C22⋊D11—216no—
409C22⋊D11—216no—
410C22⋊D11—416no—
411C2×Dic11—24no—
412C2×Dic11—28no—
413C2×Dic11—22no—
414C2×Dic11—24no—
415C2×Dic11—24no—
416C2×Dic11—22no—
417C2×Dic11—28no—
418C2×Dic11—216no—
419C2×Dic11—28no—
420C2×Dic11—216no—
421C2×Dic11—48no—
422C2×Dic11—416no—
423C2×Dic11H(5,𝔽2)14yes—
424C2×Dic112−1+414yes—
425C2×Dic11C2514yes—
426C2×Dic11C2514yes—
427C2×Dic11C2512yes—
428C2×Dic11C2514yes—
429C2×Dic11C2512yes—
430C2×Dic11C2518yes—
431C2×Dic11C2512yes—
432C2×Dic11C2512yes—
433D44—28no—
434C4×D11—216no—
435C4×D11—416no—
436Dic22—28no—
437Dic22—232no—
438Dic22—416no—
439C22×#41—114no—
440C22×#41—111no—
441C22×#41C2×D1111yescharacteristic
442C22×#41C2×D1111yescharacteristic
443C23×Q8—112no—
444#556—1132no—
445#555—1132no—
446#554—1132no—
447#553—1164no—
448#548—1164no—
449#547—1132no—
450#542—1132no—
451#542—1132no—
452#537—1116no—
453#537C2×D11116yescomplemented
454#533—1132no—
455#532—1116no—
456#532—1132no—
457C2×C4⋊Q8—111no—
458C2×C4⋊Q8—112no—
459C2×C4⋊Q8—112no—
460C2×C4⋊Q8—112no—
461C2×C4⋊Q8—112no—
462C2×C4⋊Q8—1116no—
463C2×#127—111no—
464C2×#126—114no—
465C2×#126—114no—
466C2×#125—114no—
467C2×#124—111no—
468C2×#124—111no—
469C2×#124—114no—
470C2×#124—114no—
471C2×#124—114no—
472C2×#123—114no—
473C2×#123—114no—
474C2×C22⋊Q8—112no—
475C2×C22⋊Q8—112no—
476C2×C22⋊Q8—114no—
477C2×C22⋊Q8—114no—
478C2×C22⋊Q8—114no—
479C2×C22⋊Q8C2×D1112yes—
480C2×C22⋊Q8C2×D1112yes—
481C2×#121—112no—
482C2×#121—112no—
483C2×#121—112no—
484C2×#121—114no—
485C2×#121—114no—
486C2×#121—112no—
487C2×#121C2×D1112yes—
488C2×#121C2×D1112yes—
489C2×#121C2×D1114yes—
490#520—1116no—
491#520—1116no—
492C4×#41—1116no—
493C2×C4×Q8—111no—
494C2×C4×Q8—111no—
495C2×C4×Q8—112no—
496C2×C4×Q8—112no—
497C2×C4×Q8—114no—
498C2×C4×D4—111no—
499C2×C4×D4—112no—
500C2×C4×D4—112no—
501C2×C4×D4—111no—
502C2×C4×D4—112no—
503C2×C4×D4—114no—
504C2×C4×D4—114no—
505C2×C4×D4—112no—
506C2×C4×D4—112no—
507C2×C4×D4—112no—
508C2×C4×D4—114no—
509C2×#117—111no—
510C2×#117—112no—
511C2×#117—112no—
512C2×#117—112no—
513C2×#117—114no—
514C22×C4⋊C4—112no—
515C22×C4⋊C4—111no—
516C22×C4⋊C4—112no—
517C22×C4⋊C4—112no—
518C22×C4⋊C4C2×D1111yescharacteristic
519C22×C42—111no—
520C22×C42—112no—
521C22×C11—22no—
522C22×C11—22no—
523C22×C11—28no—
524C22×C11—24no—
525C22×C11—24no—
526C22×C11—24no—
527C22×C11—24no—
528C22×C11—24no—
529C22×C11—24no—
530C22×C11—48no—
531C22×C11—48no—
532C22×C11C22×#4114yes—
533C22×C11C22×#4112yes—
534C22×C11C2×H(5,𝔽2)12yes—
535C22×C11C2×2−1+412yes—
536C22×C11C2611yescharacteristic
537C2×D11—24no—
538C2×D11—24no—
539C2×D11—24no—
540C2×D11—48no—
541C4×C11—24no—
542C4×C11—24no—
543C4×C11—28no—
544C4×C11C22×#4114yes—
545C4×C11C22×#4114yes—
546Dic11—24no—
547Dic11—28no—
548Dic11—22no—
549Dic11—24no—
550Dic11—24no—
551Dic11—22no—
552Dic11C2×H(5,𝔽2)14yes—
553Dic11C2×2−1+414yes—
554C2×#41—28no—
555C2×#41—28no—
556C2×#41—1132no—
557C2×#41—118no—
558C2×#41—228no—
559C2×#41—4416no—
560C2×#41C22×D1118yes—
561C2×#41C22×D1118yes—
562C22×Q8—111no—
563C22×Q8—114no—
564C22×Q8—114no—
565C22×Q8—1116no—
566C22×Q8—448no—
567C22×Q8C22×D1111yescharacteristic
568C22×Q8C22×D1111yescharacteristic
569C22×D4—112no—
570C22×D4—112no—
571C22×D4—112no—
572C22×D4—114no—
573C22×D4—111no—
574C22×D4C22×D1112yes—
575C22×D4C22×D1112yes—
576C22×D4C22×D1111yescharacteristic
577C22×D4C22×D1111yescharacteristic
578C22×D4C22×D1114yes—
579C23×C4—111no—
580C23×C4—112no—
581C23×C4—111no—
582C23×C4—112no—
583C23×C4—112no—
584C23×C4—114no—
585C23×C4—112no—
586C23×C4—114no—
587C23×C4C22×D1112yes—
588C23×C4C22×D1112yes—
589C23×C4C22×D1112yes—
590C23×C4C22×D1111yescharacteristic
591C4⋊Q8—118no—
592C4⋊Q8—1116no—
593C4⋊Q8—1116no—
594C4⋊Q8—1116no—
595C4⋊Q8—1116no—
596#127—118no—
597#126—1132no—
598#126—1132no—
599#125—1132no—
600#124—118no—
601#124—118no—
602#124—1132no—
603#124—1132no—
604#124—1132no—
605#123—1132no—
606#123—1132no—
607C22⋊Q8—1116no—
608C22⋊Q8—1116no—
609C22⋊Q8—1132no—
610C22⋊Q8—1132no—
611C22⋊Q8—1132no—
612C22⋊Q8C22×D11116yes—
613C22⋊Q8C22×D11116yes—
614#121—1116no—
615#121—1116no—
616#121—1132no—
617#121—1116no—
618#121—1132no—
619#121—1116no—
620#121C22×D11116yes—
621#121C22×D11116yes—
622#121C22×D11132yes—
623C4×Q8—118no—
624C4×Q8—118no—
625C4×Q8—1116no—
626C4×Q8—1116no—
627C4×Q8—1132no—
628C4×D4—118no—
629C4×D4—1116no—
630C4×D4—1116no—
631C4×D4—118no—
632C4×D4—1116no—
633C4×D4—1132no—
634C4×D4—1132no—
635C4×D4—1116no—
636C4×D4—1116no—
637C4×D4—1116no—
638C4×D4—1132no—
639#117—118no—
640#117—1116no—
641#117—1116no—
642#117—1116no—
643#117—1132no—
644C2×C4⋊C4—111no—
645C2×C4⋊C4—112no—
646C2×C4⋊C4—114no—
647C2×C4⋊C4—112no—
648C2×C4⋊C4—114no—
649C2×C4⋊C4—114no—
650C2×C4⋊C4—118no—
651C2×C4⋊C4—1116no—
652C2×C4⋊C4—114no—
653C2×C4⋊C4—1116no—
654C2×C4⋊C4—111no—
655C2×C4⋊C4—112no—
656C2×C4⋊C4—112no—
657C2×C4⋊C4—112no—
658C2×C4⋊C4—112no—
659C2×C4⋊C4—114no—
660C2×C4⋊C4—1116no—
661C2×C4⋊C4C22×D1112yes—
662C2×C4⋊C4C22×D1112yes—
663C2×C4⋊C4C22×D1118yes—
664C2×C4⋊C4C22×D1114yes—
665C2×C22⋊C4—112no—
666C2×C22⋊C4—114no—
667C2×C22⋊C4—112no—
668C2×C22⋊C4—112no—
669C2×C22⋊C4—114no—
670C2×C22⋊C4—112no—
671C2×C22⋊C4—112no—
672C2×C22⋊C4—114no—
673C2×C22⋊C4—114no—
674C2×C22⋊C4—112no—
675C2×C22⋊C4—112no—
676C2×C22⋊C4C22×D1114yes—
677C2×C22⋊C4C22×D1114yes—
678C2×C42—112no—
679C2×C42—114no—
680C2×C42—114no—
681C2×C42—111no—
682C2×C42—112no—
683C2×C42—111no—
684C2×C42—111no—
685C2×C42—112no—
686C2×C42—118no—
687C2×C42—1116no—
688C2×C42—111no—
689C2×C11—24no—
690C2×C11—44no—
691C2×C11—44no—
692C2×C11#351114yescomplemented
693C2×C11C23×#4111yescharacteristic
694C2×C11C22×H(5,𝔽2)11yescharacteristic
695C2×C11C22×2−1+411yescharacteristic
696D11—44no—
697C24—112no—
698C24C23×D1112yes—
699C24C23×D1112yes—
700C24C23×D1111yescharacteristic
701#41—232no—
702#41—232no—
703#41—2232no—
704#41—4464no—
705C2×Q8—24no—
706C2×Q8—24no—
707C2×Q8—114no—
708C2×Q8—1116no—
709C2×Q8—1116no—
710C2×Q8—2216no—
711C2×Q8—224no—
712C2×Q8—448no—
713C2×Q8—4432no—
714C2×Q8C23×D1114yes—
715C2×Q8C23×D1114yes—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—48no—
721C2×D4—118no—
722C2×D4—118no—
723C2×D4—118no—
724C2×D4—1116no—
725C2×D4—114no—
726C2×D4—228no—
727C2×D4—228no—
728C2×D4—228no—
729C2×D4—224no—
730C2×D4—448no—
731C2×D4C23×D1118yes—
732C2×D4C23×D1118yes—
733C2×D4C23×D1114yes—
734C2×D4C23×D1114yes—
735C2×D4C23×D11116yes—
736C22×C4—28no—
737C22×C4—28no—
738C22×C4—44no—
739C22×C4—111no—
740C22×C4—111no—
741C22×C4—114no—
742C22×C4—118no—
743C22×C4—114no—
744C22×C4—118no—
745C22×C4—112no—
746C22×C4—111no—
747C22×C4—111no—
748C22×C4—112no—
749C22×C4—112no—
750C22×C4—114no—
751C22×C4—118no—
752C22×C4—1116no—
753C22×C4—118no—
754C22×C4—1116no—
755C22×C4—224no—
756C22×C4—228no—
757C22×C4—224no—
758C22×C4—228no—
759C22×C4—228no—
760C22×C4—448no—
761C22×C4—444no—
762C22×C4—448no—
763C22×C4#434118yescomplemented
764C22×C4C23×D1118yes—
765C22×C4C23×D1118yes—
766C22×C4C23×D1112yes—
767C22×C4C23×D1112yes—
768C22×C4C23×D1114yes—
769C22×C4C23×D1118yes—
770C22×C4C23×D1111yescharacteristic
771C22×C4C23×D1111yescharacteristic
772C22×C4C23×D1114yes—
773C4⋊C4—114no—
774C4⋊C4—118no—
775C4⋊C4—1116no—
776C4⋊C4—118no—
777C4⋊C4—1116no—
778C4⋊C4—1116no—
779C4⋊C4—1116no—
780C4⋊C4—114no—
781C4⋊C4—118no—
782C4⋊C4—118no—
783C4⋊C4—118no—
784C4⋊C4—118no—
785C4⋊C4—1116no—
786C4⋊C4C23×D1118yes—
787C4⋊C4C23×D1118yes—
788C4⋊C4C23×D11116yes—
789C22⋊C4—118no—
790C22⋊C4—1116no—
791C22⋊C4—118no—
792C22⋊C4—118no—
793C22⋊C4—1116no—
794C22⋊C4—118no—
795C22⋊C4—118no—
796C22⋊C4—1116no—
797C22⋊C4—1116no—
798C22⋊C4—118no—
799C22⋊C4—118no—
800C22⋊C4C23×D11116yes—
801C22⋊C4C23×D11116yes—
802C42—114no—
803C42—118no—
804C42—114no—
805C42—118no—
806C42—114no—
807C42—114no—
808C42—118no—
809C42—1116no—
810C42—1116no—
811C11C2×#351111yescharacteristic, complemented, Sylow
812C23—22no—
813C23—22no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—114no—
821C23—224no—
822C23—224no—
823C23—224no—
824C23C2×#434114yes—
825C23C24×D1114yes—
826C23C24×D1114yes—
827C23C24×D1112yes—
828C23C24×D1111yescharacteristic
829Q8—28no—
830Q8—28no—
831Q8—2232no—
832Q8—228no—
833Q8—4416no—
834D4—216no—
835D4—216no—
836D4—28no—
837D4—28no—
838D4—416no—
839D4—2216no—
840D4—2216no—
841D4—2216no—
842D4—228no—
843D4—4416no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—216no—
848C2×C4—216no—
849C2×C4—48no—
850C2×C4—114no—
851C2×C4—114no—
852C2×C4—112no—
853C2×C4—112no—
854C2×C4—114no—
855C2×C4—112no—
856C2×C4—112no—
857C2×C4—114no—
858C2×C4—114no—
859C2×C4—118no—
860C2×C4—228no—
861C2×C4—2216no—
862C2×C4—228no—
863C2×C4—2216no—
864C2×C4—224no—
865C2×C4—224no—
866C2×C4—222no—
867C2×C4—228no—
868C2×C4—224no—
869C2×C4—222no—
870C2×C4—2216no—
871C2×C4—4416no—
872C2×C4—448no—
873C2×C4—4416no—
874C2×C4C2×#434114yes—
875C2×C4C2×#434114yes—
876C2×C4C2×#4341116yescomplemented
877C2×C4C24×D1114yes—
878C2×C4C24×D1114yes—
879C2×C4C24×D1118yes—
880C2×C4C24×D1112yes—
881C2×C4C24×D1112yes—
882C22—22no—
883C22—22no—
884C22—28no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—48no—
892C22—48no—
893C22—224no—
894C22—224no—
895C22—224no—
896C22—448no—
897C22C22×#434114yes—
898C22C22×#434112yes—
899C22D11×H(5,𝔽2)12yes—
900C22D11×2−1+412yes—
901C22C25×D1111yescharacteristic
902C4—24no—
903C4—24no—
904C4—28no—
905C4—114no—
906C4—114no—
907C4—224no—
908C4—224no—
909C4—222no—
910C4—228no—
911C4—224no—
912C4—222no—
913C4C22×#434114yes—
914C4C22×#434114yes—
915C2—24no—
916C2—44no—
917C2—44no—
918C2—444no—
919C2#1308252514yesdirect product factor
920C2C23×#434111yescharacteristic
921C2C2×D11×H(5,𝔽2)11yescharacteristic
922C2C2×D11×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#537C2
socleC23×C11C25
hypercenterC2×#537D11
hypocenterC11C2×#3511
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. #13082525C2direct (N × H)
2. C2×#10623172C2semidirect
3. C2×#10623147C2semidirect
4. C2×#10623166C2semidirect
5. C2×#10623132C2semidirect
6. C2×#10623129C2semidirect
7. C2×#10623142C2semidirect
8. C2×#10623174C2semidirect
9. C2×#10623134C2semidirect
10. C2×#10623364C2semidirect
11. C2×#10623153C2semidirect
12. C2×#10623363C2semidirect
13. C2×#10623127C2semidirect
14. C22×#66941C2semidirect
15. C2×#10623358C2semidirect
16. C2×#10623035C2semidirect
17. C2×#41×Dic11C2semidirect
18. C2×C11×#537C2semidirect
24. C11×#537C22semidirect
31. #10623364C22semidirect
32. #10623363C22semidirect
33. #10623358C22semidirect
34. #41×Dic11C22semidirect
69. #10623174C22semidirect
70. #10623172C22semidirect
71. #10623166C22semidirect
72. #10623153C22semidirect
73. #10623147C22semidirect
74. #10623142C22semidirect
75. #10623134C22semidirect
76. #10623132C22semidirect
77. #10623129C22semidirect
78. #10623127C22semidirect
81. #10623035C22semidirect
90. C2×#66941C22semidirect
260. C22×C4×C11#41semidirect
361. C2×#537D11semidirect
401. C2×C4×C11C2×#41semidirect
453. #537C2×D11semidirect
692. C2×C11#3511semidirect
763. C22×C4#4341semidirect
811. C11C2×#3511semidirect
876. C2×C4C2×#4341semidirect
919. C2#13082525direct (N × H)

Maximal subgroups

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

subgroupindex
#130825252
C2×#106231722
C2×#106231472
C2×#106231662
C2×#106231322
C2×#106231292
C2×#106231422
C2×#106231742
C2×#106231342
C2×#106233642
C2×#106231532
C2×#106233632
C2×#106231272
C22×#669412
C2×#106233582
C2×#106230352
C2×#41×Dic112
C2×C11×#5372
C2×#351111