Finite Group Databasebeta

← C2×#13082291 #15662176

Subgroups — C2×#13082291 #15662176

Order 2816.

11438 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67043C211yesmaximal, characteristic, complemented
2C22×#41×D11C211yesmaximal, characteristic, complemented
3#13082291C2132yesmaximal, direct product factor
4C2×#10623163C212yesmaximal, complemented
5C2×#10623129C212yesmaximal, complemented
6C2×#10623162C212yesmaximal, complemented
7C2×#10623142C214yesmaximal, complemented
8C2×#10623143C212yesmaximal, complemented
9C2×#10623141C214yesmaximal, complemented
10C2×#10623139C212yesmaximal, complemented
11C2×#10623159C212yesmaximal, complemented
12C2×#10623356C211yesmaximal, characteristic, complemented
13C2×#10623137C212yesmaximal, complemented
14C2×#10623359C211yesmaximal, characteristic, complemented
15C22×#66950C211yesmaximal, characteristic, complemented
16C2×D11×C22⋊Q8C212yesmaximal, complemented
17C2×#10623035C211yesmaximal, characteristic, complemented
18C2×C11×#537C211yesmaximal, characteristic, complemented
19C22×C11×#41C2211yescharacteristic
20C22×C11×#41C2211yescharacteristic, complemented
21C2×#67043—216no—
22C2×#67043C22116yescomplemented
23C2×#41×D11—216no—
24C2×#41×D11C22116yescomplemented
25C22×#4343C2211yescharacteristic
26C22×Q8×D11C2211yescharacteristic
27C22×Q8×D11C2212yescomplemented
28C22×#4341C2212yes—
29C22×#4341C2211yescharacteristic
30C22×#4341C2212yescomplemented
31C22×#4341C2214yescomplemented
32C22×D4×D11C2212yes—
33C22×D4×D11C2211yescharacteristic
34C22×#4339C2212yes—
35C22×#4339C2211yescharacteristic
36C22×#4339C2212yescomplemented
37C23×C4×D11C2212yes—
38C23×C4×D11C2211yescharacteristic
39C23×Dic22C2211yescharacteristic, complemented
40C23×Dic22C2212yescomplemented
41C11×#537C22116yescomplemented
42C2×C11×C22⋊Q8C2212yescomplemented
43C2×C11×C22⋊Q8C2212yescomplemented
44C2×C11×#121C2212yescomplemented
45C2×C11×#121C2214yescomplemented
46C2×C11×#121C2212yescomplemented
47C22×C11×C4⋊C4C2211yescharacteristic, complemented
48#10623359C22116yescomplemented
49#10623356C22116yescomplemented
50C2×#66999C2211yescharacteristic
51C2×#66999C2211yescharacteristic, complemented
52C2×#66997C2212yescomplemented
53C2×#66992C2214yescomplemented
54C2×#66991C2211yescharacteristic
55C2×#66991C2211yescharacteristic, complemented
56C2×#66991C2214yescomplemented
57C2×#66990C2214yes—
58C2×#66990C2212yes—
59C2×#66989C2212yescomplemented
60C2×#66988C2214yescomplemented
61C2×#66988C2212yescomplemented
62C2×D4×Dic11C2214yescomplemented
63C2×C4×C22⋊D11C2212yes—
64C2×C4×C22⋊D11C2214yescomplemented
65C2×C4×C22⋊D11C2212yescomplemented
66C22×(C2×D11)⋊C4C2212yes—
67C2×#66979C2211yescharacteristic, complemented
68C22×C4⋊Dic11C2212yescomplemented
69C2×#66977C2212yescomplemented
70C2×#66977C2212yescomplemented
71#10623163C22132yescomplemented
72#10623162C22132yescomplemented
73#10623159C22132yescomplemented
74D11×C22⋊Q8C22132yescomplemented
75#10623143C22132yescomplemented
76#10623142C22164yescomplemented
77#10623141C22164yescomplemented
78#10623139C22132yescomplemented
79#10623137C22132yescomplemented
80#10623129C22132yescomplemented
81C2×#66950C2212yes—
82C2×#66950C2212yes—
83C2×#66950C22116yescomplemented
84C2×#66950C2212yescomplemented
85C2×#66950C2212yescomplemented
86C2×#66949C2214yes—
87C2×#66947C2214yescomplemented
88#10623035C22116yescomplemented
89C2×#66946C2212yescomplemented
90C2×#66945C2212yescomplemented
91C2×C4⋊C4×D11C2212yescomplemented
92C2×C4⋊C4×D11C2214yescomplemented
93C2×#66941C2214yescomplemented
94C2×#66940C2212yescomplemented
95C2×#66938C2214yescomplemented
96C2×#66937C2214yescomplemented
97C2×#66936C2214yescomplemented
98C2×#66936C2214yescomplemented
99C2×(C22⋊D11)⋊C4C2214yes—
100C2×C22⋊C4×D11C2214yes—
101C2×#66931C2214yescomplemented
102C2×#66931C2214yescomplemented
103C24×D11C2312yes—
104C24×D11C2311yescharacteristic
105C2×C11×#41—28no—
106C2×C11×#41—28no—
107C2×C11×#41C2318yes—
108C2×C11×#41C2318yescomplemented
109C22×Q8×C11C2311yescharacteristic
110C22×Q8×C11C2311yescharacteristic
111C22×D4×C11C2312yes—
112C22×D4×C11C2312yes—
113C22×D4×C11C2311yescharacteristic
114C22×D4×C11C2311yescharacteristic
115C22×D4×C11C2314yes—
116C23×C4×C11C2312yes—
117C23×C4×C11C2312yes—
118C23×C4×C11C2312yes—
119C23×C4×C11C2311yescharacteristic
120C22×C22⋊D11C2312yes—
121C22×C22⋊D11C2312yes—
122C22×C22⋊D11C2314yes—
123C22×C22⋊D11C2312yes—
124C22×C22⋊D11C2312yes—
125C22×C22⋊D11C2312yes—
126C23×Dic11C2312yes—
127C23×Dic11C2314yes—
128C23×Dic11C2311yescharacteristic
129C23×Dic11C2312yes—
130#67043—2128no—
131#41×D11—2128no—
132C2×#4343—28no—
133C2×#4343C2318yes—
134C2×Q8×D11—216no—
135C2×Q8×D11—28no—
136C2×Q8×D11C2318yes—
137C2×Q8×D11C23116yescomplemented
138C2×#4341—216no—
139C2×#4341—232no—
140C2×#4341—216no—
141C2×#4341—28no—
142C2×#4341C2318yes—
143C2×#4341C23116yes—
144C2×#4341C23116yescomplemented
145C2×#4341C23132yescomplemented
146C2×D4×D11—216no—
147C2×D4×D11—28no—
148C2×D4×D11C23116yes—
149C2×D4×D11C2318yes—
150C2×#4339—216no—
151C2×#4339—216no—
152C2×#4339D4116yescomplemented
153C2×#4339C23116yes—
154C2×#4339C2318yes—
155C2×#4339C23116yescomplemented
156C22×D44C2312yes—
157C22×D44C2311yescharacteristic
158C22×C4×D11—28no—
159C22×C4×D11—216no—
160C22×C4×D11C2314yes—
161C22×C4×D11C2312yes—
162C22×C4×D11C2312yes—
163C22×C4×D11C2311yescharacteristic
164C22×C4×D11C2311yescharacteristic
165C22×C4×D11C2311yescharacteristic
166C22×C4×D11C2311yescharacteristic
167C22×C4×D11C2318yes—
168C22×C4×D11C23116yes—
169C22×C4×D11C2314yes—
170C22×C4×D11C2312yes—
171C22×Dic22—28no—
172C22×Dic22—216no—
173C22×Dic22C2312yes—
174C22×Dic22C2314yes—
175C22×Dic22C2312yes—
176C22×Dic22C2312yes—
177C22×Dic22C2311yescharacteristic
178C22×Dic22C2318yescomplemented
179C22×Dic22C23116yescomplemented
180C11×C22⋊Q8C23116yescomplemented
181C11×C22⋊Q8C23116yescomplemented
182C11×#121C23116yescomplemented
183C11×#121C23116yescomplemented
184C11×#121C23132yescomplemented
185C2×C11×C4⋊C4C2312yes—
186C2×C11×C4⋊C4C2314yes—
187C2×C11×C4⋊C4C2312yes—
188C2×C11×C4⋊C4C2318yescomplemented
189C2×C11×C22⋊C4C2314yes—
190C2×C11×C22⋊C4C2314yes—
191C2×C22⋊Dic11C2312yes—
192C2×C22⋊Dic11C2314yes—
193C2×C22⋊Dic11C2312yes—
194C2×C22⋊Dic11C2314yes—
195C2×C22⋊Dic11C2312yes—
196#66999C2318yes—
197#66999C2318yescomplemented
198#66997C23116yescomplemented
199#66992C23132yescomplemented
200#66991C2318yes—
201#66991C2318yescomplemented
202#66991C23132yescomplemented
203#66990C23116yes—
204#66990C23132yes—
205#66989C23116yescomplemented
206#66988C23132yescomplemented
207#66988C23116yescomplemented
208D4×Dic11C23132yescomplemented
209C4×C22⋊D11C23116yes—
210C4×C22⋊D11C23132yescomplemented
211C4×C22⋊D11C23116yescomplemented
212C2×(C2×D11)⋊C4C2312yes—
213C2×(C2×D11)⋊C4C2314yes—
214C2×(C2×D11)⋊C4C2314yes—
215C2×(C2×D11)⋊C4C2314yes—
216C2×(C2×D11)⋊C4C2312yes—
217C2×(C2×D11)⋊C4C23116yes—
218#66979C2318yescomplemented
219C2×C4⋊Dic11C2314yes—
220C2×C4⋊Dic11C2314yes—
221C2×C4⋊Dic11C2311yescharacteristic
222C2×C4⋊Dic11C2311yescharacteristic
223C2×C4⋊Dic11C23116yescomplemented
224#66977C23116yescomplemented
225#66977C23116yescomplemented
226C2×Dic11⋊C4C2314yes—
227C2×Dic11⋊C4C2312yes—
228C2×Dic11⋊C4C2314yes—
229C2×Dic11⋊C4C2314yes—
230C2×Dic11⋊C4C2312yes—
231C2×C4×Dic11C2314yes—
232C2×C4×Dic11C2312yes—
233#66950C23116yes—
234#66950C23116yes—
235#66950C23116yescomplemented
236#66950C23116yescomplemented
237#66949C23132yes—
238#66947C23132yescomplemented
239#66946C23116yescomplemented
240#66945C23116yescomplemented
241C4⋊C4×D11C23116yescomplemented
242C4⋊C4×D11C23132yescomplemented
243#66941C23132yescomplemented
244#66940C23116yescomplemented
245#66938C23132yescomplemented
246#66937C23132yescomplemented
247#66936C23132yescomplemented
248#66936C23132yescomplemented
249(C22⋊D11)⋊C4C23132yes—
250C22⋊C4×D11C23132yes—
251#66931C23132yescomplemented
252#66931C23132yescomplemented
253C2×#3489—111nomaximal, Sylow
254C24×C11C2412yes—
255C24×C11C2412yes—
256C24×C11C2411yescharacteristic
257C23×D11—24no—
258C23×D11—28no—
259C23×D11—28no—
260C23×D11—24no—
261C23×D11—44no—
262C23×D11—42no—
263C23×D11C2411yescharacteristic
264C23×D11C2418yes—
265C23×D11C2414yes—
266C23×D11C2412yes—
267C23×D11C2411yescharacteristic
268C11×#41—232no—
269C11×#41—232no—
270C2×Q8×C11—24no—
271C2×Q8×C11—24no—
272C2×Q8×C11C2414yes—
273C2×Q8×C11C2414yes—
274C2×D4×C11—28no—
275C2×D4×C11—28no—
276C2×D4×C11—24no—
277C2×D4×C11—24no—
278C2×D4×C11—48no—
279C2×D4×C11C2418yes—
280C2×D4×C11C2418yes—
281C2×D4×C11C2414yes—
282C2×D4×C11C2414yes—
283C2×D4×C11C24116yes—
284C22×C4×C11—28no—
285C22×C4×C11—28no—
286C22×C4×C11—44no—
287C22×C4×C11C2×D418yes—
288C22×C4×C11C2414yes—
289C22×C4×C11C2412yes—
290C22×C4×C11C2412yes—
291C22×C4×C11C2418yes—
292C22×C4×C11C2418yes—
293C22×C4×C11C2418yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2414yes—
297C2×C22⋊D11—28no—
298C2×C22⋊D11—28no—
299C2×C22⋊D11—216no—
300C2×C22⋊D11—28no—
301C2×C22⋊D11—44no—
302C2×C22⋊D11C2×D4116yes—
303C2×C22⋊D11C2418yes—
304C2×C22⋊D11C2418yes—
305C2×C22⋊D11C24116yes—
306C2×C22⋊D11C2418yes—
307C2×C22⋊D11C2418yes—
308C2×C22⋊D11C2418yes—
309C22×Dic11—216no—
310C22×Dic11—28no—
311C22×Dic11—28no—
312C22×Dic11—24no—
313C22×Dic11C2418yes—
314C22×Dic11C24116yes—
315C22×Dic11C2412yes—
316C22×Dic11C2412yes—
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2414yes—
320C22×Dic11C2414yes—
321C22×Dic11C2418yes—
322C22×Dic11C2412yes—
323#4343—232no—
324Q8×D11—264no—
325Q8×D11—232no—
326#4341—264no—
327#4341—2128no—
328#4341—264no—
329#4341—232no—
330D4×D11—264no—
331D4×D11—232no—
332#4339—264no—
333#4339—264no—
334#4339C2×D4164yescomplemented
335C2×D44—28no—
336C2×D44C2×D418yes—
337C2×D44C2418yes—
338C2×D44C2414yes—
339C2×C4×D11—28no—
340C2×C4×D11—264no—
341C2×C4×D11—28no—
342C2×C4×D11—216no—
343C2×C4×D11—24no—
344C2×C4×D11—24no—
345C2×C4×D11—24no—
346C2×C4×D11—24no—
347C2×C4×D11—232no—
348C2×C4×D11—48no—
349C2×C4×D11C2×D4116yes—
350C2×C4×D11C24116yes—
351C2×C4×D11C2418yes—
352C2×C4×D11C2418yes—
353C2×C4×D11C2414yes—
354C2×C4×D11C2414yes—
355C2×C4×D11C2414yes—
356C2×C4×D11C2414yes—
357C2×C4×D11C24116yes—
358C2×C4×D11C2418yes—
359C2×Dic22—216no—
360C2×Dic22—28no—
361C2×Dic22—264no—
362C2×Dic22—28no—
363C2×Dic22—28no—
364C2×Dic22—232no—
365C2×Dic22C2×D418yes—
366C2×Dic22C2418yes—
367C2×Dic22C24116yes—
368C2×Dic22C2418yes—
369C2×Dic22C2418yes—
370C2×Dic22C2414yes—
371C11×C4⋊C4C2418yes—
372C11×C4⋊C4C24116yes—
373C11×C4⋊C4C2418yes—
374C11×C22⋊C4C24116yes—
375C11×C22⋊C4C24116yes—
376C22⋊Dic11C2418yes—
377C22⋊Dic11C24116yes—
378C22⋊Dic11C2418yes—
379C22⋊Dic11C24116yes—
380C22⋊Dic11C2418yes—
381(C2×D11)⋊C4C2418yes—
382(C2×D11)⋊C4C24116yes—
383(C2×D11)⋊C4C24116yes—
384(C2×D11)⋊C4C24116yes—
385(C2×D11)⋊C4C2418yes—
386C4⋊Dic11C24116yes—
387C4⋊Dic11C24116yes—
388C4⋊Dic11C2414yes—
389C4⋊Dic11C2414yes—
390Dic11⋊C4C24116yes—
391Dic11⋊C4C2418yes—
392Dic11⋊C4C24116yes—
393Dic11⋊C4C24116yes—
394Dic11⋊C4C2418yes—
395C4×Dic11C24116yes—
396C4×Dic11C2418yes—
397C22×2−1+4—111no—
398C23×#41—111no—
399#3489—1132no—
400C2×D4×Q8—112no—
401C2×#548—112no—
402C2×#547—112no—
403C2×#547—114no—
404C2×#546—114no—
405C2×#546—112no—
406C2×#537—112no—
407C2×#537D1111yescharacteristic, complemented
408C2×#536—111no—
409C2×#536—112no—
410C2×#525—111no—
411C2×#525—112no—
412C22×C22⋊Q8—112no—
413C22×C22⋊Q8—111no—
414C2×#520—111no—
415C23×C11—22no—
416C23×C11—22no—
417C23×C11—24no—
418C23×C11—24no—
419C23×C11—24no—
420C23×C11—24no—
421C23×C11—24no—
422C23×C11—24no—
423C23×C11C22×D414yes—
424C23×C11C2514yes—
425C23×C11C2514yes—
426C23×C11C2512yes—
427C23×C11C2511yescharacteristic
428C22×D11—22no—
429C22×D11—24no—
430C22×D11—24no—
431C22×D11—22no—
432C22×D11—22no—
433C22×D11—28no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—216no—
437C22×D11—216no—
438C22×D11—28no—
439C22×D11—48no—
440C22×D11—44no—
441C22×D11—432no—
442C22×D11—416no—
443C22×D11C22×D418yes—
444C22×D112−1+414yescomplemented
445C22×D11C2512yes—
446C22×D11C2514yes—
447C22×D11C2512yes—
448Q8×C11—28no—
449Q8×C11—28no—
450D4×C11—216no—
451D4×C11—216no—
452D4×C11—28no—
453D4×C11—28no—
454D4×C11—416no—
455C2×C4×C11—24no—
456C2×C4×C11—24no—
457C2×C4×C11—28no—
458C2×C4×C11—216no—
459C2×C4×C11—216no—
460C2×C4×C11—48no—
461C2×C4×C11C22×D414yes—
462C2×C4×C11C22×D414yes—
463C2×C4×C11C22×D4116yes—
464C2×C4×C11C2518yes—
465C2×C4×C11C2514yes—
466C2×C4×C11C2514yes—
467C2×C4×C11C2512yes—
468C2×C4×C11C2512yes—
469C22⋊D11—216no—
470C22⋊D11—232no—
471C22⋊D11—216no—
472C22⋊D11—216no—
473C22⋊D11—48no—
474C22⋊D11C22×D4132yes—
475C2×Dic11—28no—
476C2×Dic11—22no—
477C2×Dic11—216no—
478C2×Dic11—22no—
479C2×Dic11—28no—
480C2×Dic11—24no—
481C2×Dic11—24no—
482C2×Dic11—232no—
483C2×Dic11—216no—
484C2×Dic11C22×D418yes—
485C2×Dic11C2514yes—
486C2×Dic11C2514yes—
487C2×Dic11C2512yes—
488C2×Dic11C2512yes—
489C2×Dic11C2518yes—
490C2×Dic11C2514yes—
491D44—216no—
492D44C22×D4116yes—
493C4×D11—216no—
494C4×D11—232no—
495C4×D11—28no—
496C4×D11—28no—
497C4×D11—28no—
498C4×D11—28no—
499C4×D11—216no—
500C4×D11—416no—
501C4×D11C22×D4132yes—
502Dic22—216no—
503Dic22—216no—
504Dic22—232no—
505Dic22—216no—
506Dic22C22×D4116yes—
507C2×2−1+4—1116no—
508C2×2−1+4—2216no—
509C22×#41—1116no—
510C22×#41—111no—
511C22×#41—112no—
512C22×#41—111no—
513C22×#41—112no—
514C22×#41—114no—
515C22×#41—111no—
516C22×#41—112no—
517C22×#41—112no—
518C22×#41—2216no—
519C22×#41C2×D1111yescharacteristic
520C22×#41C2×D1111yescharacteristic, complemented
521C23×Q8—111no—
522C23×Q8—112no—
523C23×Q8—111no—
524C23×Q8—112no—
525C23×D4—112no—
526C23×D4—111no—
527C24×C4—112no—
528C24×C4—111no—
529D4×Q8—1132no—
530#548—1132no—
531#547—1132no—
532#547—1164no—
533#546—1164no—
534#546—1132no—
535#537—1132no—
536#537C2×D11116yescomplemented
537#536—1116no—
538#536—1132no—
539C2×C4⋊Q8—112no—
540C2×C4⋊Q8—114no—
541C2×#124—112no—
542C2×#124—114no—
543#525—1116no—
544#525—1132no—
545C2×#123—112no—
546C2×#123—114no—
547C2×#123—114no—
548C2×#123—114no—
549C2×#123—114no—
550C2×C22⋊Q8—111no—
551C2×C22⋊Q8—111no—
552C2×C22⋊Q8—112no—
553C2×C22⋊Q8—112no—
554C2×C22⋊Q8—1132no—
555C2×C22⋊Q8—114no—
556C2×C22⋊Q8—112no—
557C2×C22⋊Q8—112no—
558C2×C22⋊Q8—112no—
559C2×C22⋊Q8—112no—
560C2×C22⋊Q8—1116no—
561C2×C22⋊Q8—114no—
562C2×C22⋊Q8—114no—
563C2×C22⋊Q8C2×D1112yescomplemented
564C2×C22⋊Q8C2×D1112yescomplemented
565C2×#121—111no—
566C2×#121—111no—
567C2×#121—114no—
568C2×#121—114no—
569C2×#121—114no—
570C2×#121C2×D1112yescomplemented
571C2×#121C2×D1114yescomplemented
572C2×#121C2×D1112yescomplemented
573C2×#120—112no—
574C2×#120—114no—
575#520—1116no—
576C2×C4×Q8—112no—
577C2×C4×D4—114no—
578C2×C4×D4—112no—
579C2×C4×D4—114no—
580C2×C4×D4—112no—
581C2×C4×D4—112no—
582C2×C4×D4—114no—
583C2×#117—111no—
584C2×#117—112no—
585C22×C4⋊C4—112no—
586C22×C4⋊C4—112no—
587C22×C4⋊C4—114no—
588C22×C4⋊C4C2×D1111yescharacteristic, complemented
589C22×C22⋊C4—112no—
590C22×C22⋊C4—114no—
591C22×C11—22no—
592C22×C11—22no—
593C22×C11—28no—
594C22×C11—24no—
595C22×C11—24no—
596C22×C11—24no—
597C22×C11—24no—
598C22×C11—24no—
599C22×C11—24no—
600C22×C11—48no—
601C22×C11—48no—
602C22×C11C23×D414yes—
603C22×C11C23×D412yes—
604C22×C11C2×2−1+412yes—
605C22×C11#58512yes—
606C22×C11C2611yescharacteristic
607C2×D11—22no—
608C2×D11—24no—
609C2×D11—22no—
610C2×D11—24no—
611C2×D11—28no—
612C2×D11—216no—
613C2×D11—22no—
614C2×D11—22no—
615C2×D11—22no—
616C2×D11—432no—
617C2×D11—416no—
618C2×D11—44no—
619C2×D11C23×D418yes—
620C2×D11C2×2−1+414yescomplemented
621C4×C11—24no—
622C4×C11—24no—
623C4×C11—28no—
624C4×C11C23×D414yes—
625C4×C11C23×D414yes—
626Dic11—28no—
627Dic11—22no—
628Dic11—22no—
629Dic11—24no—
630Dic11—24no—
631Dic11C23×D418yes—
632C25—112no—
633C25—111no—
6342−1+4—22128no—
635C2×#41—28no—
636C2×#41—28no—
637C2×#41—118no—
638C2×#41—1116no—
639C2×#41—1132no—
640C2×#41—1116no—
641C2×#41—118no—
642C2×#41—1116no—
643C2×#41—118no—
644C2×#41—1116no—
645C2×#41—1116no—
646C2×#41—2216no—
647C2×#41—2216no—
648C2×#41—2216no—
649C2×#41—2216no—
650C2×#41—2232no—
651C2×#41—228no—
652C2×#41—228no—
653C2×#41—22128no—
654C2×#41C22×D1118yes—
655C2×#41C22×D1118yescomplemented
656C22×Q8—1116no—
657C22×Q8—118no—
658C22×Q8—111no—
659C22×Q8—112no—
660C22×Q8—114no—
661C22×Q8—112no—
662C22×Q8—112no—
663C22×Q8—118no—
664C22×Q8—1116no—
665C22×Q8—2216no—
666C22×Q8—2216no—
667C22×Q8—228no—
668C22×Q8—228no—
669C22×Q8C22×D1111yescharacteristic
670C22×Q8C22×D1111yescharacteristic
671C22×D4—112no—
672C22×D4—112no—
673C22×D4—114no—
674C22×D4—112no—
675C22×D4—112no—
676C22×D4—112no—
677C22×D4—1116no—
678C22×D4—118no—
679C22×D4—111no—
680C22×D4—112no—
681C22×D4—2216no—
682C22×D4—228no—
683C22×D4C22×D1112yes—
684C22×D4C22×D1111yescharacteristic
685C22×D4C22×D1112yes—
686C22×D4C22×D1111yescharacteristic
687C22×D4C22×D1114yes—
688C23×C4—112no—
689C23×C4—112no—
690C23×C4—111no—
691C23×C4—114no—
692C23×C4—112no—
693C23×C4—114no—
694C23×C4—112no—
695C23×C4—112no—
696C23×C4—111no—
697C23×C4—111no—
698C23×C4—111no—
699C23×C4—111no—
700C23×C4—1116no—
701C23×C4—118no—
702C23×C4—114no—
703C23×C4—2216no—
704C23×C4—228no—
705C23×C4C22×D1112yes—
706C23×C4C22×D1112yes—
707C23×C4C22×D1112yes—
708C23×C4C22×D1111yescharacteristic
709C4⋊Q8—1116no—
710C4⋊Q8—1132no—
711#124—1116no—
712#124—1132no—
713#123—1116no—
714#123—1132no—
715#123—1132no—
716#123—1132no—
717#123—1132no—
718C22⋊Q8—118no—
719C22⋊Q8—118no—
720C22⋊Q8—1116no—
721C22⋊Q8—1116no—
722C22⋊Q8—1116no—
723C22⋊Q8—1116no—
724C22⋊Q8—1132no—
725C22⋊Q8—1116no—
726C22⋊Q8—1116no—
727C22⋊Q8—1132no—
728C22⋊Q8—1132no—
729C22⋊Q8C22×D11116yescomplemented
730C22⋊Q8C22×D11116yescomplemented
731#121—118no—
732#121—118no—
733#121—1132no—
734#121—1132no—
735#121—1132no—
736#121C22×D11116yescomplemented
737#121C22×D11132yescomplemented
738#121C22×D11116yescomplemented
739#120—1116no—
740#120—1132no—
741C4×Q8—1116no—
742C4×D4—1132no—
743C4×D4—1132no—
744C4×D4—1116no—
745C4×D4—1116no—
746C4×D4—1116no—
747C4×D4—1132no—
748#117—118no—
749#117—1116no—
750C2×C4⋊C4—111no—
751C2×C4⋊C4—112no—
752C2×C4⋊C4—114no—
753C2×C4⋊C4—114no—
754C2×C4⋊C4—114no—
755C2×C4⋊C4—114no—
756C2×C4⋊C4—1116no—
757C2×C4⋊C4—111no—
758C2×C4⋊C4—114no—
759C2×C4⋊C4—112no—
760C2×C4⋊C4—1116no—
761C2×C4⋊C4—1132no—
762C2×C4⋊C4C22×D1112yes—
763C2×C4⋊C4C22×D1114yes—
764C2×C4⋊C4C22×D1112yes—
765C2×C4⋊C4C22×D1118yescomplemented
766C2×C22⋊C4—114no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—114no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—114no—
773C2×C22⋊C4—114no—
774C2×C22⋊C4—1116no—
775C2×C22⋊C4—114no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—1132no—
778C2×C22⋊C4C22×D1114yes—
779C2×C22⋊C4C22×D1114yes—
780C2×C42—114no—
781C2×C42—112no—
782C2×C11—24no—
783C2×C11—44no—
784C2×C11—44no—
785C2×C11#348914yescomplemented
786C2×C11C24×D411yescharacteristic
787C2×C11C22×2−1+411yescharacteristic
788C2×C11C2×#58511yescharacteristic
789D11—24no—
790D11—28no—
791D11—42no—
792C24—111no—
793C24—112no—
794C24—111no—
795C24—118no—
796C24—114no—
797C24—228no—
798C24—224no—
799C24—228no—
800C24—224no—
801C24—442no—
802C24—444no—
803C24C23×D1112yes—
804C24C23×D1112yes—
805C24C23×D1111yescharacteristic
806#41—232no—
807#41—232no—
808#41—1164no—
809#41—2264no—
810#41—2264no—
811#41—2264no—
812#41—2264no—
813#41—22128no—
814#41—2232no—
815#41—2232no—
816C2×Q8—24no—
817C2×Q8—24no—
818C2×Q8—118no—
819C2×Q8—114no—
820C2×Q8—118no—
821C2×Q8—1116no—
822C2×Q8—118no—
823C2×Q8—118no—
824C2×Q8—2216no—
825C2×Q8—228no—
826C2×Q8—2264no—
827C2×Q8—2264no—
828C2×Q8—2232no—
829C2×Q8—228no—
830C2×Q8—228no—
831C2×Q8—2232no—
832C2×Q8C23×D1114yes—
833C2×Q8C23×D1114yes—
834C2×D4—28no—
835C2×D4—28no—
836C2×D4—24no—
837C2×D4—24no—
838C2×D4—48no—
839C2×D4—1116no—
840C2×D4—118no—
841C2×D4—118no—
842C2×D4—1116no—
843C2×D4—118no—
844C2×D4—118no—
845C2×D4—118no—
846C2×D4—118no—
847C2×D4—114no—
848C2×D4—118no—
849C2×D4—228no—
850C2×D4—228no—
851C2×D4—2264no—
852C2×D4—2232no—
853C2×D4—228no—
854C2×D4—2216no—
855C2×D4—228no—
856C2×D4—444no—
857C2×D4C23×D1118yes—
858C2×D4C23×D1114yes—
859C2×D4C23×D1118yes—
860C2×D4C23×D1114yes—
861C2×D4C23×D11116yes—
862C22×C4—28no—
863C22×C4—28no—
864C22×C4—44no—
865C22×C4—112no—
866C22×C4—1116no—
867C22×C4—118no—
868C22×C4—118no—
869C22×C4—114no—
870C22×C4—1116no—
871C22×C4—118no—
872C22×C4—112no—
873C22×C4—112no—
874C22×C4—114no—
875C22×C4—111no—
876C22×C4—111no—
877C22×C4—1116no—
878C22×C4—118no—
879C22×C4—118no—
880C22×C4—114no—
881C22×C4—114no—
882C22×C4—114no—
883C22×C4—114no—
884C22×C4—1116no—
885C22×C4—228no—
886C22×C4—2264no—
887C22×C4—228no—
888C22×C4—2216no—
889C22×C4—228no—
890C22×C4—2216no—
891C22×C4—224no—
892C22×C4—228no—
893C22×C4—224no—
894C22×C4—224no—
895C22×C4—224no—
896C22×C4—224no—
897C22×C4—2232no—
898C22×C4—448no—
899C22×C4D4×D1118yes—
900C22×C4C23×D1118yes—
901C22×C4C23×D1118yes—
902C22×C4C23×D1114yes—
903C22×C4C23×D1112yes—
904C22×C4C23×D1112yes—
905C22×C4C23×D1118yes—
906C22×C4C23×D1114yes—
907C22×C4C23×D1111yescharacteristic
908C22×C4C23×D1111yescharacteristic
909C4⋊C4—114no—
910C4⋊C4—118no—
911C4⋊C4—1116no—
912C4⋊C4—1116no—
913C4⋊C4—1116no—
914C4⋊C4—1116no—
915C4⋊C4—114no—
916C4⋊C4—1116no—
917C4⋊C4—118no—
918C4⋊C4C23×D1118yes—
919C4⋊C4C23×D11116yes—
920C4⋊C4C23×D1118yes—
921C22⋊C4—1116no—
922C22⋊C4—118no—
923C22⋊C4—118no—
924C22⋊C4—1116no—
925C22⋊C4—118no—
926C22⋊C4—118no—
927C22⋊C4—1116no—
928C22⋊C4—1116no—
929C22⋊C4—1116no—
930C22⋊C4—118no—
931C22⋊C4C23×D11116yes—
932C22⋊C4C23×D11116yes—
933C42—1116no—
934C42—118no—
935C11C2×#348911yescharacteristic, complemented, Sylow
936C23—22no—
937C23—22no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—118no—
945C23—114no—
946C23—112no—
947C23—114no—
948C23—112no—
949C23—2216no—
950C23—228no—
951C23—2216no—
952C23—222no—
953C23—224no—
954C23—222no—
955C23—224no—
956C23—228no—
957C23—222no—
958C23—222no—
959C23—222no—
960C23—444no—
961C23—448no—
962C23—4416no—
963C23—4432no—
964C23C2×D4×D1114yes—
965C23C24×D1114yes—
966C23C24×D1114yes—
967C23C24×D1112yes—
968C23C24×D1111yescharacteristic
969Q8—28no—
970Q8—28no—
971Q8—1116no—
972Q8—2232no—
973Q8—2216no—
974Q8—2216no—
975Q8—2216no—
976D4—216no—
977D4—216no—
978D4—28no—
979D4—28no—
980D4—416no—
981D4—1132no—
982D4—1116no—
983D4—2216no—
984D4—2216no—
985D4—2216no—
986D4—2232no—
987D4—2216no—
988D4—448no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—28no—
992C2×C4—216no—
993C2×C4—216no—
994C2×C4—48no—
995C2×C4—118no—
996C2×C4—114no—
997C2×C4—1132no—
998C2×C4—114no—
999C2×C4—114no—
1000C2×C4—118no—
1001C2×C4—112no—
1002C2×C4—112no—
1003C2×C4—2216no—
1004C2×C4—2216no—
1005C2×C4—2232no—
1006C2×C4—2216no—
1007C2×C4—2232no—
1008C2×C4—222no—
1009C2×C4—222no—
1010C2×C4—228no—
1011C2×C4—228no—
1012C2×C4—2216no—
1013C2×C4—224no—
1014C2×C4—224no—
1015C2×C4—228no—
1016C2×C4—228no—
1017C2×C4—228no—
1018C2×C4—228no—
1019C2×C4—4416no—
1020C2×C4C2×D4×D1114yes—
1021C2×C4C2×D4×D1114yes—
1022C2×C4C2×D4×D11116yes—
1023C2×C4C24×D1118yes—
1024C2×C4C24×D1114yes—
1025C2×C4C24×D1114yes—
1026C2×C4C24×D1112yes—
1027C2×C4C24×D1112yes—
1028C22—22no—
1029C22—22no—
1030C22—28no—
1031C22—24no—
1032C22—24no—
1033C22—24no—
1034C22—24no—
1035C22—24no—
1036C22—24no—
1037C22—48no—
1038C22—48no—
1039C22—118no—
1040C22—114no—
1041C22—222no—
1042C22—224no—
1043C22—224no—
1044C22—222no—
1045C22—228no—
1046C22—2216no—
1047C22—222no—
1048C22—222no—
1049C22—222no—
1050C22—4416no—
1051C22—4432no—
1052C22—444no—
1053C22C22×D4×D1114yes—
1054C22C22×D4×D1112yes—
1055C22#1062345512yes—
1056C22D11×2−1+412yes—
1057C22C25×D1111yescharacteristic
1058C4—24no—
1059C4—24no—
1060C4—28no—
1061C4—118no—
1062C4—222no—
1063C4—222no—
1064C4—228no—
1065C4—224no—
1066C4—224no—
1067C4C22×D4×D1114yes—
1068C4C22×D4×D1114yes—
1069C2—24no—
1070C2—44no—
1071C2—44no—
1072C2—224no—
1073C2—228no—
1074C2—442no—
1075C2#1308229114yesdirect product factor
1076C2C23×D4×D1111yescharacteristic
1077C2C2×D11×2−1+411yescharacteristic
1078C2C2×#1062345511yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#537C2
socleC23×C11C25
hypercenterC2×#537D11
hypocenterC11C2×#3489
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C22×#67043C2semidirect
2. C22×#41×D11C2semidirect
3. #13082291C2direct (N × H)
4. C2×#10623163C2semidirect
5. C2×#10623129C2semidirect
6. C2×#10623162C2semidirect
7. C2×#10623142C2semidirect
8. C2×#10623143C2semidirect
9. C2×#10623141C2semidirect
10. C2×#10623139C2semidirect
11. C2×#10623159C2semidirect
12. C2×#10623356C2semidirect
13. C2×#10623137C2semidirect
14. C2×#10623359C2semidirect
15. C22×#66950C2semidirect
16. C2×D11×C22⋊Q8C2semidirect
17. C2×#10623035C2semidirect
18. C2×C11×#537C2semidirect
20. C22×C11×#41C22semidirect
22. C2×#67043C22semidirect
24. C2×#41×D11C22semidirect
27. C22×Q8×D11C22semidirect
30. C22×#4341C22semidirect
31. C22×#4341C22semidirect
36. C22×#4339C22semidirect
39. C23×Dic22C22semidirect
40. C23×Dic22C22semidirect
41. C11×#537C22semidirect
42. C2×C11×C22⋊Q8C22semidirect
43. C2×C11×C22⋊Q8C22semidirect
44. C2×C11×#121C22semidirect
45. C2×C11×#121C22semidirect
46. C2×C11×#121C22semidirect
47. C22×C11×C4⋊C4C22semidirect
48. #10623359C22semidirect
49. #10623356C22semidirect
51. C2×#66999C22semidirect
52. C2×#66997C22semidirect
53. C2×#66992C22semidirect
55. C2×#66991C22semidirect
56. C2×#66991C22semidirect
59. C2×#66989C22semidirect
60. C2×#66988C22semidirect
61. C2×#66988C22semidirect
62. C2×D4×Dic11C22semidirect
64. C2×C4×C22⋊D11C22semidirect
65. C2×C4×C22⋊D11C22semidirect
67. C2×#66979C22semidirect
68. C22×C4⋊Dic11C22semidirect
69. C2×#66977C22semidirect
70. C2×#66977C22semidirect
71. #10623163C22semidirect
72. #10623162C22semidirect
73. #10623159C22semidirect
74. D11×C22⋊Q8C22semidirect
75. #10623143C22semidirect
76. #10623142C22semidirect
77. #10623141C22semidirect
78. #10623139C22semidirect
79. #10623137C22semidirect
80. #10623129C22semidirect
83. C2×#66950C22semidirect
84. C2×#66950C22semidirect
85. C2×#66950C22semidirect
87. C2×#66947C22semidirect
88. #10623035C22semidirect
89. C2×#66946C22semidirect
90. C2×#66945C22semidirect
91. C2×C4⋊C4×D11C22semidirect
92. C2×C4⋊C4×D11C22semidirect
93. C2×#66941C22semidirect
94. C2×#66940C22semidirect
95. C2×#66938C22semidirect
96. C2×#66937C22semidirect
97. C2×#66936C22semidirect
98. C2×#66936C22semidirect
101. C2×#66931C22semidirect
102. C2×#66931C22semidirect
108. C2×C11×#41C23semidirect
137. C2×Q8×D11C23semidirect
144. C2×#4341C23semidirect
145. C2×#4341C23semidirect
152. C2×#4339D4semidirect
155. C2×#4339C23semidirect
178. C22×Dic22C23semidirect
179. C22×Dic22C23semidirect
180. C11×C22⋊Q8C23semidirect
181. C11×C22⋊Q8C23semidirect
182. C11×#121C23semidirect
183. C11×#121C23semidirect
184. C11×#121C23semidirect
188. C2×C11×C4⋊C4C23semidirect
197. #66999C23semidirect
198. #66997C23semidirect
199. #66992C23semidirect
201. #66991C23semidirect
202. #66991C23semidirect
205. #66989C23semidirect
206. #66988C23semidirect
207. #66988C23semidirect
208. D4×Dic11C23semidirect
210. C4×C22⋊D11C23semidirect
211. C4×C22⋊D11C23semidirect
218. #66979C23semidirect
223. C2×C4⋊Dic11C23semidirect
224. #66977C23semidirect
225. #66977C23semidirect
235. #66950C23semidirect
236. #66950C23semidirect
238. #66947C23semidirect
239. #66946C23semidirect
240. #66945C23semidirect
241. C4⋊C4×D11C23semidirect
242. C4⋊C4×D11C23semidirect
243. #66941C23semidirect
244. #66940C23semidirect
245. #66938C23semidirect
246. #66937C23semidirect
247. #66936C23semidirect
248. #66936C23semidirect
251. #66931C23semidirect
252. #66931C23semidirect
334. #4339C2×D4semidirect
407. C2×#537D11semidirect
444. C22×D112−1+4semidirect
520. C22×#41C2×D11semidirect
536. #537C2×D11semidirect
563. C2×C22⋊Q8C2×D11semidirect
564. C2×C22⋊Q8C2×D11semidirect
570. C2×#121C2×D11semidirect
571. C2×#121C2×D11semidirect
572. C2×#121C2×D11semidirect
588. C22×C4⋊C4C2×D11semidirect
620. C2×D11C2×2−1+4semidirect
655. C2×#41C22×D11semidirect
729. C22⋊Q8C22×D11semidirect
730. C22⋊Q8C22×D11semidirect
736. #121C22×D11semidirect
737. #121C22×D11semidirect
738. #121C22×D11semidirect
765. C2×C4⋊C4C22×D11semidirect
785. C2×C11#3489semidirect
935. C11C2×#3489semidirect
1075. C2#13082291direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670432
C22×#41×D112
#130822912
C2×#106231632
C2×#106231292
C2×#106231622
C2×#106231422
C2×#106231432
C2×#106231412
C2×#106231392
C2×#106231592
C2×#106233562
C2×#106231372
C2×#106233592
C22×#669502
C2×D11×C22⋊Q82
C2×#106230352
C2×C11×#5372
C2×#348911