Finite Group Databasebeta

← C2×#13082292 #15662172

Subgroups — C2×#13082292 #15662172

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×#67040C211yesmaximal, characteristic, complemented
2C23×#4339C211yesmaximal, characteristic, complemented
3#13082292C2132yesmaximal, direct product factor
4C2×#10623163C212yesmaximal, complemented
5C2×#10623164C212yesmaximal, complemented
6C2×#10623162C212yesmaximal, complemented
7C2×#10623038C214yesmaximal, complemented
8C2×#10623161C212yesmaximal, complemented
9C2×#10623021C214yesmaximal, complemented
10C2×#10623041C211yesmaximal, characteristic, complemented
11C2×#10623160C212yesmaximal, complemented
12C2×#10623347C211yesmaximal, characteristic, complemented
13C2×#10623159C212yesmaximal, complemented
14C2×#10623158C212yesmaximal, complemented
15C2×#10623322C211yesmaximal, characteristic, complemented
16C2×D11×C22⋊Q8C212yesmaximal, complemented
17C2×#10623035C211yesmaximal, characteristic, complemented
18C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
19C23×Q8×C11C2211yescharacteristic, complemented
20C24×C4×C11C2211yescharacteristic
21C23×C22⋊D11C2212yes—
22C2×#67040—216no—
23C2×#67040C22116yescomplemented
24C22×#4343C2212yescomplemented
25C22×#4343C2212yescomplemented
26C22×Q8×D11C2212yescomplemented
27C22×Q8×D11C2212yescomplemented
28C22×#4339—216no—
29C22×#4339C2212yes—
30C22×#4339C2211yescharacteristic
31C22×#4339C2212yes—
32C22×#4339C2211yescharacteristic
33C22×#4339C2211yescharacteristic
34C22×#4339C2211yescharacteristic
35C22×#4339C22116yescomplemented
36C22×#4339C2211yescharacteristic, complemented
37C22×#4339C2214yescomplemented
38C23×D44C2211yescharacteristic
39C23×C4×D11C2212yes—
40C23×Dic22C2211yescharacteristic
41C2×C11×C22⋊Q8C2212yes—
42C2×C11×C22⋊Q8C2212yes—
43C2×C11×C22⋊Q8C2212yescomplemented
44C2×C11×C22⋊Q8C2212yescomplemented
45C2×C11×C22⋊Q8C22116yescomplemented
46C22×C11×C4⋊C4C2211yescharacteristic, complemented
47C22×C11×C4⋊C4C2212yescomplemented
48C22×C11×C22⋊C4C2212yes—
49C2×#67006C2212yes—
50#10623347C22116yescomplemented
51C2×#67000C2212yescomplemented
52C2×#66999C2212yescomplemented
53C2×#66999C2212yescomplemented
54C2×#66997C2212yescomplemented
55#10623322C22116yescomplemented
56C2×#66983C2211yescharacteristic
57C2×#66983C2211yescharacteristic, complemented
58C2×#66983C2214yescomplemented
59C2×#66982C2212yescomplemented
60C2×#66982C2214yescomplemented
61C2×C4×C22⋊D11C2212yes—
62C2×C4×C22⋊D11C2212yescomplemented
63C2×C4×C22⋊D11C2214yescomplemented
64C2×#66979C2211yescharacteristic, complemented
65C2×#66977C2211yescharacteristic
66C2×#66977C2211yescharacteristic, complemented
67#10623164C22132yescomplemented
68#10623163C22132yescomplemented
69#10623162C22132yescomplemented
70#10623161C22132yescomplemented
71#10623160C22132yescomplemented
72#10623159C22132yescomplemented
73#10623158C22132yescomplemented
74D11×C22⋊Q8C22132yescomplemented
75#10623041C22116yescomplemented
76C2×#66950C2212yescomplemented
77C2×#66950C2212yescomplemented
78C2×#66949C2214yescomplemented
79C2×#66949C2214yescomplemented
80#10623038C22164yescomplemented
81C2×#66948C2212yescomplemented
82C2×#66948C2214yescomplemented
83C2×#66948C2212yescomplemented
84C2×#66947C2214yescomplemented
85C2×#66947C2214yescomplemented
86#10623035C22116yescomplemented
87C2×#66946C2214yescomplemented
88C2×#66946C2212yescomplemented
89C2×#66945C2212yescomplemented
90C2×C4⋊C4×D11C2212yescomplemented
91C2×C4⋊C4×D11C2214yescomplemented
92C2×#66941C2214yescomplemented
93C2×#66940C2212yescomplemented
94C2×#66938C2214yescomplemented
95#10623021C22164yescomplemented
96C2×#66937C2214yescomplemented
97C2×#66937C2214yescomplemented
98C2×#66936C2214yescomplemented
99C2×#66935C2214yes—
100C2×(C22⋊D11)⋊C4C2214yes—
101C2×C22⋊C4×D11C2214yes—
102C2×#66931C2214yes—
103C25×C11C2311yescharacteristic
104C24×D11C2312yes—
105C22×Q8×C11—28no—
106C22×Q8×C11C2312yes—
107C22×Q8×C11C2312yes—
108C22×Q8×C11C2318yescomplemented
109C23×C4×C11—28no—
110C23×C4×C11C2311yescharacteristic
111C23×C4×C11C2311yescharacteristic
112C23×C4×C11C2311yescharacteristic
113C23×C4×C11C2311yescharacteristic
114C23×C4×C11C2312yes—
115C23×C4×C11C2311yescharacteristic
116C23×C4×C11C2318yes—
117C23×C4×C11C2312yes—
118C23×C4×C11C2311yescharacteristic
119C22×C22⋊D11—216no—
120C22×C22⋊D11C2312yes—
121C22×C22⋊D11C2312yes—
122C22×C22⋊D11C2312yes—
123C22×C22⋊D11C23116yes—
124C22×C22⋊D11C2312yes—
125C22×C22⋊D11C2312yes—
126C22×C22⋊D11C2312yes—
127C22×C22⋊D11C2312yes—
128C23×Dic11C2312yes—
129#67040—2128no—
130C2×#4343—216no—
131C2×#4343—216no—
132C2×#4343C23116yescomplemented
133C2×#4343C23116yescomplemented
134C2×Q8×D11—216no—
135C2×Q8×D11—216no—
136C2×Q8×D11C23116yescomplemented
137C2×Q8×D11C23116yescomplemented
138C2×#4339—28no—
139C2×#4339—28no—
140C2×#4339—216no—
141C2×#4339—232no—
142C2×#4339—2128no—
143C2×#4339—28no—
144C2×#4339—216no—
145C2×#4339—28no—
146C2×#4339D4116yescomplemented
147C2×#4339C23116yes—
148C2×#4339C2318yes—
149C2×#4339C23116yes—
150C2×#4339C2318yes—
151C2×#4339C2318yes—
152C2×#4339C2318yes—
153C2×#4339C23132yescomplemented
154C2×#4339C2318yescomplemented
155C22×D44—28no—
156C22×D44C2314yes—
157C22×D44C2312yes—
158C22×D44C2311yescharacteristic
159C22×D44C2311yescharacteristic
160C22×D44C2318yes—
161C22×D44C2314yes—
162C22×D44C2311yescharacteristic
163C22×C4×D11—216no—
164C22×C4×D11C2314yes—
165C22×C4×D11C2314yes—
166C22×C4×D11C2312yes—
167C22×C4×D11C2312yes—
168C22×C4×D11C2312yes—
169C22×C4×D11C2312yes—
170C22×C4×D11C23116yes—
171C22×C4×D11C2314yes—
172C22×C4×D11C2312yes—
173C22×Dic22—28no—
174C22×Dic22C2314yes—
175C22×Dic22C2312yes—
176C22×Dic22C2311yescharacteristic
177C22×Dic22C2311yescharacteristic
178C22×Dic22C2318yes—
179C22×Dic22C2311yescharacteristic
180C11×C22⋊Q8C23116yes—
181C11×C22⋊Q8C23116yes—
182C11×C22⋊Q8C23116yescomplemented
183C11×C22⋊Q8C23116yescomplemented
184C2×C11×C4⋊C4C2312yes—
185C2×C11×C4⋊C4C2314yes—
186C2×C11×C4⋊C4C2312yes—
187C2×C11×C4⋊C4C2314yes—
188C2×C11×C4⋊C4C2318yescomplemented
189C2×C11×C4⋊C4C23116yescomplemented
190C2×C11×C22⋊C4C2314yes—
191C2×C11×C22⋊C4C2314yes—
192C2×C11×C22⋊C4C23116yes—
193#67006C23116yes—
194C2×C22⋊Dic11C2312yes—
195C2×C22⋊Dic11C2312yes—
196C2×C22⋊Dic11C2312yes—
197#67000C23116yescomplemented
198#66999C23116yescomplemented
199#66999C23116yescomplemented
200#66997C23116yescomplemented
201#66983C2318yes—
202#66983C23132yescomplemented
203#66983C2318yescomplemented
204#66982C23132yescomplemented
205#66982C23116yescomplemented
206C4×C22⋊D11C23116yes—
207C4×C22⋊D11C23132yescomplemented
208C4×C22⋊D11C23116yescomplemented
209C2×(C2×D11)⋊C4C2314yes—
210C2×(C2×D11)⋊C4C2314yes—
211C2×(C2×D11)⋊C4C2314yes—
212C2×(C2×D11)⋊C4C2314yes—
213C2×(C2×D11)⋊C4C2314yes—
214C2×(C2×D11)⋊C4C2312yes—
215C2×(C2×D11)⋊C4C2312yes—
216#66979C2318yescomplemented
217C2×C4⋊Dic11C2314yes—
218C2×C4⋊Dic11C2311yescharacteristic
219C2×C4⋊Dic11C2311yescharacteristic
220#66977C2318yes—
221#66977C2318yescomplemented
222C2×Dic11⋊C4C2314yes—
223C2×Dic11⋊C4C2314yes—
224C2×Dic11⋊C4C2314yes—
225C2×Dic11⋊C4C2312yes—
226C2×Dic11⋊C4C2312yes—
227C2×C4×Dic11C2314yes—
228C2×C4×Dic11C2312yes—
229#66950C23116yescomplemented
230#66950C23116yescomplemented
231#66949C23132yescomplemented
232#66949C23132yescomplemented
233#66948C23132yescomplemented
234#66948C23116yescomplemented
235#66948C23116yescomplemented
236#66947C23132yescomplemented
237#66947C23132yescomplemented
238#66946C23116yescomplemented
239#66946C23132yescomplemented
240#66945C23116yescomplemented
241C4⋊C4×D11C23116yescomplemented
242C4⋊C4×D11C23132yescomplemented
243#66941C23132yescomplemented
244#66940C23116yescomplemented
245#66938C23132yescomplemented
246#66937C23132yescomplemented
247#66937C23132yescomplemented
248#66936C23132yescomplemented
249#66935C23132yes—
250(C22⋊D11)⋊C4C23132yes—
251C22⋊C4×D11C23132yes—
252#66931C23132yes—
253C2×#3489—111nomaximal, Sylow
254C24×C11—24no—
255C24×C11—24no—
256C24×C11—42no—
257C24×C11C2411yescharacteristic
258C24×C11C2414yes—
259C24×C11C2411yescharacteristic
260C24×C11C2411yescharacteristic
261C23×D11—28no—
262C23×D11—28no—
263C23×D11—44no—
264C23×D11C2412yes—
265C23×D11C2412yes—
266C23×D11C2418yes—
267C23×D11C2412yes—
268C2×Q8×C11—28no—
269C2×Q8×C11—28no—
270C2×Q8×C11—232no—
271C2×Q8×C11C2418yes—
272C2×Q8×C11C2418yes—
273C22×C4×C11—24no—
274C22×C4×C11—28no—
275C22×C4×C11—24no—
276C22×C4×C11—24no—
277C22×C4×C11—24no—
278C22×C4×C11—24no—
279C22×C4×C11—232no—
280C22×C4×C11—44no—
281C22×C4×C11C2×D418yes—
282C22×C4×C11C2414yes—
283C22×C4×C11C2414yes—
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2414yes—
287C22×C4×C11C2414yes—
288C22×C4×C11C2414yes—
289C22×C4×C11C2414yes—
290C22×C4×C11C2418yes—
291C22×C4×C11C2414yes—
292C22×C4×C11C2418yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2414yes—
296C2×C22⋊D11—264no—
297C2×C22⋊D11—28no—
298C2×C22⋊D11—28no—
299C2×C22⋊D11—28no—
300C2×C22⋊D11—28no—
301C2×C22⋊D11—28no—
302C2×C22⋊D11—44no—
303C2×C22⋊D11C2×D4116yes—
304C2×C22⋊D11C2418yes—
305C2×C22⋊D11C2418yes—
306C2×C22⋊D11C2418yes—
307C2×C22⋊D11C2418yes—
308C2×C22⋊D11C2418yes—
309C2×C22⋊D11C2418yes—
310C2×C22⋊D11C2418yes—
311C22×Dic11—28no—
312C22×Dic11C2418yes—
313C22×Dic11C2412yes—
314C22×Dic11C2412yes—
315C22×Dic11C2412yes—
316C22×Dic11C2412yes—
317C22×Dic11C2412yes—
318#4343—264no—
319#4343—264no—
320Q8×D11—264no—
321Q8×D11—264no—
322#4339—264no—
323#4339—2128no—
324#4339—232no—
325#4339—264no—
326#4339—232no—
327#4339—232no—
328#4339—232no—
329#4339C2×D4164yescomplemented
330C2×D44—232no—
331C2×D44—28no—
332C2×D44—216no—
333C2×D44—24no—
334C2×D44—24no—
335C2×D44—48no—
336C2×D44C2×D418yes—
337C2×D44C24116yes—
338C2×D44C2418yes—
339C2×D44C2414yes—
340C2×D44C2414yes—
341C2×D44C24116yes—
342C2×D44C2414yes—
343C2×C4×D11—28no—
344C2×C4×D11—216no—
345C2×C4×D11—264no—
346C2×C4×D11—28no—
347C2×C4×D11—216no—
348C2×C4×D11—28no—
349C2×C4×D11—28no—
350C2×C4×D11—48no—
351C2×C4×D11C2×D4116yes—
352C2×C4×D11C24116yes—
353C2×C4×D11C24116yes—
354C2×C4×D11C2418yes—
355C2×C4×D11C2418yes—
356C2×C4×D11C2418yes—
357C2×C4×D11C2418yes—
358C2×C4×D11C24116yes—
359C2×C4×D11C2418yes—
360C2×Dic22—28no—
361C2×Dic22—216no—
362C2×Dic22—232no—
363C2×Dic22—24no—
364C2×Dic22—24no—
365C2×Dic22C2×D418yes—
366C2×Dic22C24116yes—
367C2×Dic22C2418yes—
368C2×Dic22C2414yes—
369C2×Dic22C2414yes—
370C2×Dic22C2414yes—
371C11×C4⋊C4C2418yes—
372C11×C4⋊C4C24116yes—
373C11×C4⋊C4C2418yes—
374C11×C4⋊C4C24116yes—
375C11×C22⋊C4C24116yes—
376C11×C22⋊C4C24116yes—
377C22⋊Dic11C2418yes—
378C22⋊Dic11C2418yes—
379C22⋊Dic11C2418yes—
380(C2×D11)⋊C4C24116yes—
381(C2×D11)⋊C4C24116yes—
382(C2×D11)⋊C4C24116yes—
383(C2×D11)⋊C4C24116yes—
384(C2×D11)⋊C4C24116yes—
385(C2×D11)⋊C4C2418yes—
386(C2×D11)⋊C4C2418yes—
387C4⋊Dic11C24116yes—
388C4⋊Dic11C2414yes—
389C4⋊Dic11C2414yes—
390Dic11⋊C4C24116yes—
391Dic11⋊C4C24116yes—
392Dic11⋊C4C24116yes—
393Dic11⋊C4C2418yes—
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—112no—
405C2×#546—114no—
406C2×#537—112no—
407C2×#537—111no—
408C2×#536—111no—
409C2×#536—112no—
410C2×#525—111no—
411C2×#525—112no—
412C22×C22⋊Q8—112no—
413C22×C22⋊Q8D1111yescharacteristic, complemented
414C2×#520—111no—
415C23×C11—22no—
416C23×C11—22no—
417C23×C11—22no—
418C23×C11—22no—
419C23×C11—28no—
420C23×C11—22no—
421C23×C11—22no—
422C23×C11—28no—
423C23×C11—22no—
424C23×C11—44no—
425C23×C11—416no—
426C23×C11C22×D414yes—
427C23×C112−1+414yescomplemented
428C23×C11C2512yes—
429C23×C11C2512yes—
430C23×C11C2512yes—
431C23×C11C2511yescharacteristic
432C22×D11—24no—
433C22×D11—24no—
434C22×D11—24no—
435C22×D11—24no—
436C22×D11—24no—
437C22×D11—24no—
438C22×D11—216no—
439C22×D11—24no—
440C22×D11—24no—
441C22×D11—216no—
442C22×D11—48no—
443C22×D11—432no—
444C22×D11C22×D418yes—
445C22×D11C2514yes—
446C22×D11C2514yes—
447C22×D11C2514yes—
448Q8×C11—216no—
449Q8×C11—216no—
450C2×C4×C11—22no—
451C2×C4×C11—28no—
452C2×C4×C11—22no—
453C2×C4×C11—28no—
454C2×C4×C11—216no—
455C2×C4×C11—28no—
456C2×C4×C11—28no—
457C2×C4×C11—28no—
458C2×C4×C11—28no—
459C2×C4×C11—28no—
460C2×C4×C11—48no—
461C2×C4×C11C22×D414yes—
462C2×C4×C11C22×D414yes—
463C2×C4×C11C22×D4116yes—
464C2×C4×C11C2518yes—
465C2×C4×C11C2518yes—
466C2×C4×C11C2512yes—
467C2×C4×C11C2512yes—
468C2×C4×C11C2512yes—
469C2×C4×C11C2512yes—
470C22⋊D11—216no—
471C22⋊D11—216no—
472C22⋊D11—216no—
473C22⋊D11—216no—
474C22⋊D11—216no—
475C22⋊D11—48no—
476C22⋊D11C22×D4132yes—
477C2×Dic11—24no—
478C2×Dic11—24no—
479C2×Dic11—24no—
480C2×Dic11—24no—
481C2×Dic11—216no—
482C2×Dic11C22×D418yes—
483C2×Dic11C2514yes—
484C2×Dic11C2514yes—
485C2×Dic11C2514yes—
486C2×Dic11C2514yes—
487C2×Dic11C2514yes—
488D44—216no—
489D44—232no—
490D44—28no—
491D44—28no—
492D44—416no—
493D44C22×D4116yes—
494C4×D11—216no—
495C4×D11—232no—
496C4×D11—216no—
497C4×D11—216no—
498C4×D11—216no—
499C4×D11—232no—
500C4×D11—416no—
501C4×D11C22×D4132yes—
502Dic22—28no—
503Dic22—28no—
504Dic22—216no—
505Dic22—232no—
506Dic22C22×D4116yes—
507C2×2−1+4—1116no—
508C2×2−1+4—2216no—
509C22×#41—112no—
510C22×#41—112no—
511C22×#41—111no—
512C22×#41—112no—
513C22×#41—111no—
514C22×#41—111no—
515C22×#41—112no—
516C22×#41—111no—
517C22×#41—1116no—
518C22×#41—111no—
519C22×#41—114no—
520C22×#41—2216no—
521C23×Q8—112no—
522C23×Q8—112no—
523C23×Q8—111no—
524C23×Q8C2×D1111yescharacteristic, complemented
525C23×D4—112no—
526C23×D4—111no—
527C24×C4—112no—
528C24×C4C2×D1111yescharacteristic
529D4×Q8—1132no—
530#548—1132no—
531#547—1132no—
532#547—1164no—
533#546—1132no—
534#546—1164no—
535#537—1132no—
536#537—1116no—
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—112no—
551C2×C22⋊Q8—112no—
552C2×C22⋊Q8—111no—
553C2×C22⋊Q8—111no—
554C2×C22⋊Q8—1132no—
555C2×C22⋊Q8—114no—
556C2×C22⋊Q8—114no—
557C2×C22⋊Q8—112no—
558C2×C22⋊Q8—112no—
559C2×C22⋊Q8—114no—
560C2×C22⋊Q8C2×D1112yes—
561C2×C22⋊Q8C2×D1112yes—
562C2×C22⋊Q8C2×D1112yescomplemented
563C2×C22⋊Q8C2×D1112yescomplemented
564C2×C22⋊Q8C2×D11116yescomplemented
565C2×#121—111no—
566C2×#121—111no—
567C2×#121—114no—
568C2×#121—112no—
569C2×#121—114no—
570C2×#121—112no—
571C2×#121—114no—
572C2×#121—114no—
573C2×#120—112no—
574C2×#120—114no—
575#520—1116no—
576C2×C4×Q8—112no—
577C2×C4×D4—112no—
578C2×C4×D4—114no—
579C2×C4×D4—112no—
580C2×C4×D4—112no—
581C2×C4×D4—114no—
582C2×C4×D4—114no—
583C2×#117—111no—
584C2×#117—112no—
585C22×C4⋊C4—112no—
586C22×C4⋊C4—114no—
587C22×C4⋊C4C2×D1111yescharacteristic, complemented
588C22×C4⋊C4C2×D1112yescomplemented
589C22×C22⋊C4—114no—
590C22×C22⋊C4C2×D1112yes—
591C22×C11—22no—
592C22×C11—22no—
593C22×C11—22no—
594C22×C11—22no—
595C22×C11—28no—
596C22×C11—28no—
597C22×C11—22no—
598C22×C11—22no—
599C22×C11—22no—
600C22×C11—416no—
601C22×C11—44no—
602C22×C11C23×D414yes—
603C22×C11C23×D412yes—
604C22×C11C2×2−1+412yes—
605C22×C11C2×2−1+414yescomplemented
606C22×C11#58512yes—
607C22×C11C2611yescharacteristic
608C2×D11—24no—
609C2×D11—24no—
610C2×D11—216no—
611C2×D11—24no—
612C2×D11—24no—
613C2×D11—24no—
614C2×D11—24no—
615C2×D11—24no—
616C2×D11—24no—
617C2×D11—432no—
618C2×D11—48no—
619C2×D11—48no—
620C2×D11C23×D418yes—
621C4×C11—22no—
622C4×C11—22no—
623C4×C11—28no—
624C4×C11—28no—
625C4×C11C23×D414yes—
626C4×C11C23×D414yes—
627Dic11—24no—
628Dic11—24no—
629Dic11—24no—
630Dic11—24no—
631Dic11C23×D418yes—
632C25—112no—
633C25C22×D1111yescharacteristic
6342−1+4—22128no—
635C2×#41—1116no—
636C2×#41—1116no—
637C2×#41—1116no—
638C2×#41—118no—
639C2×#41—118no—
640C2×#41—1116no—
641C2×#41—118no—
642C2×#41—1132no—
643C2×#41—118no—
644C2×#41—1116no—
645C2×#41—118no—
646C2×#41—2216no—
647C2×#41—2216no—
648C2×#41—228no—
649C2×#41—2232no—
650C2×#41—228no—
651C2×#41—22128no—
652C2×#41—2216no—
653C2×#41—2216no—
654C2×#41—228no—
655C2×#41—228no—
656C22×Q8—28no—
657C22×Q8—1116no—
658C22×Q8—1116no—
659C22×Q8—111no—
660C22×Q8—111no—
661C22×Q8—114no—
662C22×Q8—112no—
663C22×Q8—111no—
664C22×Q8—118no—
665C22×Q8—228no—
666C22×Q8—2216no—
667C22×Q8—2216no—
668C22×Q8C22×D1112yes—
669C22×Q8C22×D1112yes—
670C22×Q8C22×D1118yescomplemented
671C22×D4—112no—
672C22×D4—112no—
673C22×D4—112no—
674C22×D4—112no—
675C22×D4—112no—
676C22×D4—112no—
677C22×D4—1116no—
678C22×D4—112no—
679C22×D4—111no—
680C22×D4—114no—
681C22×D4—111no—
682C22×D4—112no—
683C22×D4—111no—
684C22×D4—118no—
685C22×D4—114no—
686C22×D4—228no—
687C22×D4—2216no—
688C23×C4—28no—
689C23×C4—112no—
690C23×C4—112no—
691C23×C4—114no—
692C23×C4—112no—
693C23×C4—114no—
694C23×C4—112no—
695C23×C4—112no—
696C23×C4—112no—
697C23×C4—1116no—
698C23×C4—114no—
699C23×C4—2216no—
700C23×C4C22×D1112yes—
701C23×C4C22×D1111yescharacteristic
702C23×C4C22×D1111yescharacteristic
703C23×C4C22×D1111yescharacteristic
704C23×C4C22×D1111yescharacteristic
705C23×C4C22×D1111yescharacteristic
706C23×C4C22×D1118yes—
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—1116no—
719C22⋊Q8—1116no—
720C22⋊Q8—118no—
721C22⋊Q8—118no—
722C22⋊Q8—1116no—
723C22⋊Q8—1132no—
724C22⋊Q8—1132no—
725C22⋊Q8—1116no—
726C22⋊Q8—1132no—
727C22⋊Q8C22×D11116yes—
728C22⋊Q8C22×D11116yes—
729C22⋊Q8C22×D11116yescomplemented
730C22⋊Q8C22×D11116yescomplemented
731#121—118no—
732#121—118no—
733#121—1132no—
734#121—1116no—
735#121—1132no—
736#121—1116no—
737#121—1132no—
738#121—1132no—
739#120—1116no—
740#120—1132no—
741C4×Q8—1116no—
742C4×D4—1132no—
743C4×D4—1116no—
744C4×D4—1116no—
745C4×D4—1116no—
746C4×D4—1132no—
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—111no—
756C2×C4⋊C4—112no—
757C2×C4⋊C4—114no—
758C2×C4⋊C4—1116no—
759C2×C4⋊C4—1132no—
760C2×C4⋊C4C22×D1112yes—
761C2×C4⋊C4C22×D1114yes—
762C2×C4⋊C4C22×D1112yes—
763C2×C4⋊C4C22×D1114yes—
764C2×C4⋊C4C22×D1118yescomplemented
765C2×C4⋊C4C22×D11116yescomplemented
766C2×C22⋊C4—112no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—114no—
770C2×C22⋊C4—114no—
771C2×C22⋊C4—114no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—114no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—114no—
776C2×C22⋊C4—1132no—
777C2×C22⋊C4C22×D1114yes—
778C2×C22⋊C4C22×D1114yes—
779C2×C22⋊C4C22×D11116yes—
780C2×C42—114no—
781C2×C42—112no—
782C2×C11—24no—
783C2×C11—24no—
784C2×C11—42no—
785C2×C11#348914yescomplemented
786C2×C11C24×D411yescharacteristic
787C2×C11C22×2−1+411yescharacteristic
788C2×C11C2×#58511yescharacteristic
789D11—28no—
790D11—44no—
791D11—44no—
792C24—24no—
793C24—24no—
794C24—42no—
795C24—112no—
796C24—112no—
797C24—112no—
798C24—118no—
799C24—228no—
800C24—228no—
801C24—444no—
802C24C23×D1111yescharacteristic
803C24C23×D1114yes—
804C24C23×D1111yescharacteristic
805C24C23×D1111yescharacteristic
806#41—1164no—
807#41—2264no—
808#41—2264no—
809#41—2232no—
810#41—22128no—
811#41—2232no—
812#41—2264no—
813#41—2264no—
814#41—2232no—
815#41—2232no—
816C2×Q8—28no—
817C2×Q8—28no—
818C2×Q8—232no—
819C2×Q8—118no—
820C2×Q8—114no—
821C2×Q8—114no—
822C2×Q8—1116no—
823C2×Q8—118no—
824C2×Q8—114no—
825C2×Q8—2216no—
826C2×Q8—228no—
827C2×Q8—2232no—
828C2×Q8—2264no—
829C2×Q8—2264no—
830C2×Q8—224no—
831C2×Q8—224no—
832C2×Q8C23×D1118yes—
833C2×Q8C23×D1118yes—
834C2×D4—1116no—
835C2×D4—118no—
836C2×D4—118no—
837C2×D4—118no—
838C2×D4—118no—
839C2×D4—118no—
840C2×D4—118no—
841C2×D4—118no—
842C2×D4—118no—
843C2×D4—114no—
844C2×D4—1116no—
845C2×D4—114no—
846C2×D4—118no—
847C2×D4—114no—
848C2×D4—1116no—
849C2×D4—2232no—
850C2×D4—228no—
851C2×D4—2216no—
852C2×D4—228no—
853C2×D4—2264no—
854C2×D4—228no—
855C2×D4—228no—
856C2×D4—228no—
857C2×D4—228no—
858C2×D4—224no—
859C2×D4—224no—
860C2×D4—448no—
861C2×D4—444no—
862C22×C4—24no—
863C22×C4—28no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—232no—
869C22×C4—44no—
870C22×C4—112no—
871C22×C4—1116no—
872C22×C4—118no—
873C22×C4—118no—
874C22×C4—112no—
875C22×C4—112no—
876C22×C4—112no—
877C22×C4—112no—
878C22×C4—1116no—
879C22×C4—118no—
880C22×C4—1116no—
881C22×C4—118no—
882C22×C4—118no—
883C22×C4—118no—
884C22×C4—1116no—
885C22×C4—228no—
886C22×C4—2264no—
887C22×C4—2216no—
888C22×C4—228no—
889C22×C4—2216no—
890C22×C4—228no—
891C22×C4—228no—
892C22×C4—228no—
893C22×C4—448no—
894C22×C4D4×D1118yes—
895C22×C4C23×D1118yes—
896C22×C4C23×D1114yes—
897C22×C4C23×D1114yes—
898C22×C4C23×D1114yes—
899C22×C4C23×D1114yes—
900C22×C4C23×D1114yes—
901C22×C4C23×D1114yes—
902C22×C4C23×D1114yes—
903C22×C4C23×D1111yescharacteristic
904C22×C4C23×D1111yescharacteristic
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—114no—
915C4⋊C4—118no—
916C4⋊C4—1116no—
917C4⋊C4C23×D1118yes—
918C4⋊C4C23×D11116yes—
919C4⋊C4C23×D1118yes—
920C4⋊C4C23×D11116yes—
921C22⋊C4—118no—
922C22⋊C4—118no—
923C22⋊C4—118no—
924C22⋊C4—1116no—
925C22⋊C4—1116no—
926C22⋊C4—1116no—
927C22⋊C4—118no—
928C22⋊C4—1116no—
929C22⋊C4—118no—
930C22⋊C4—1116no—
931C22⋊C4C23×D11116yes—
932C22⋊C4C23×D11116yes—
933C42—1116no—
934C42—118no—
935C11C2×#348911yescharacteristic, complemented, Sylow
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—28no—
941C23—22no—
942C23—22no—
943C23—28no—
944C23—22no—
945C23—44no—
946C23—416no—
947C23—118no—
948C23—114no—
949C23—114no—
950C23—114no—
951C23—2216no—
952C23—224no—
953C23—224no—
954C23—224no—
955C23—224no—
956C23—224no—
957C23—224no—
958C23—2216no—
959C23—224no—
960C23—224no—
961C23—448no—
962C23—4432no—
963C23C2×D4×D1114yes—
964C23#6704014yescomplemented
965C23C24×D1112yes—
966C23C24×D1112yes—
967C23C24×D1112yes—
968C23C24×D1111yescharacteristic
969Q8—216no—
970Q8—216no—
971Q8—1116no—
972Q8—2232no—
973Q8—2216no—
974Q8—228no—
975Q8—228no—
976D4—1132no—
977D4—1116no—
978D4—2216no—
979D4—2232no—
980D4—2216no—
981D4—2216no—
982D4—2216no—
983D4—2216no—
984D4—2216no—
985D4—228no—
986D4—228no—
987D4—4416no—
988D4—448no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—28no—
992C2×C4—28no—
993C2×C4—216no—
994C2×C4—28no—
995C2×C4—28no—
996C2×C4—28no—
997C2×C4—28no—
998C2×C4—28no—
999C2×C4—48no—
1000C2×C4—118no—
1001C2×C4—114no—
1002C2×C4—1132no—
1003C2×C4—114no—
1004C2×C4—114no—
1005C2×C4—114no—
1006C2×C4—114no—
1007C2×C4—2216no—
1008C2×C4—2232no—
1009C2×C4—2216no—
1010C2×C4—2232no—
1011C2×C4—2216no—
1012C2×C4—224no—
1013C2×C4—224no—
1014C2×C4—224no—
1015C2×C4—224no—
1016C2×C4—2216no—
1017C2×C4—2216no—
1018C2×C4—4416no—
1019C2×C4C2×D4×D1114yes—
1020C2×C4C2×D4×D1114yes—
1021C2×C4C2×D4×D11116yes—
1022C2×C4C24×D1118yes—
1023C2×C4C24×D1118yes—
1024C2×C4C24×D1112yes—
1025C2×C4C24×D1112yes—
1026C2×C4C24×D1112yes—
1027C2×C4C24×D1112yes—
1028C22—22no—
1029C22—22no—
1030C22—22no—
1031C22—22no—
1032C22—28no—
1033C22—28no—
1034C22—22no—
1035C22—22no—
1036C22—22no—
1037C22—416no—
1038C22—44no—
1039C22—118no—
1040C22—224no—
1041C22—224no—
1042C22—2216no—
1043C22—224no—
1044C22—224no—
1045C22—224no—
1046C22—224no—
1047C22—224no—
1048C22—224no—
1049C22—4432no—
1050C22—448no—
1051C22—448no—
1052C22C22×D4×D1114yes—
1053C22C22×D4×D1112yes—
1054C22C2×#6704012yes—
1055C22C2×#6704014yescomplemented
1056C22#1062345312yes—
1057C22C25×D1111yescharacteristic
1058C4—22no—
1059C4—22no—
1060C4—28no—
1061C4—28no—
1062C4—118no—
1063C4—224no—
1064C4—224no—
1065C4—224no—
1066C4—224no—
1067C4C22×D4×D1114yes—
1068C4C22×D4×D1114yes—
1069C2—24no—
1070C2—24no—
1071C2—42no—
1072C2—228no—
1073C2—444no—
1074C2—444no—
1075C2#1308229214yesdirect product factor
1076C2C23×D4×D1111yescharacteristic
1077C2C22×#6704011yescharacteristic
1078C2C2×#1062345311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×C22⋊Q8C2
socleC23×C11C25
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#3489
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#67040C2semidirect
2. C23×#4339C2semidirect
3. #13082292C2direct (N × H)
4. C2×#10623163C2semidirect
5. C2×#10623164C2semidirect
6. C2×#10623162C2semidirect
7. C2×#10623038C2semidirect
8. C2×#10623161C2semidirect
9. C2×#10623021C2semidirect
10. C2×#10623041C2semidirect
11. C2×#10623160C2semidirect
12. C2×#10623347C2semidirect
13. C2×#10623159C2semidirect
14. C2×#10623158C2semidirect
15. C2×#10623322C2semidirect
16. C2×D11×C22⋊Q8C2semidirect
17. C2×#10623035C2semidirect
18. C22×C11×C22⋊Q8C2semidirect
19. C23×Q8×C11C22semidirect
23. C2×#67040C22semidirect
24. C22×#4343C22semidirect
25. C22×#4343C22semidirect
26. C22×Q8×D11C22semidirect
27. C22×Q8×D11C22semidirect
35. C22×#4339C22semidirect
36. C22×#4339C22semidirect
37. C22×#4339C22semidirect
43. C2×C11×C22⋊Q8C22semidirect
44. C2×C11×C22⋊Q8C22semidirect
45. C2×C11×C22⋊Q8C22semidirect
46. C22×C11×C4⋊C4C22semidirect
47. C22×C11×C4⋊C4C22semidirect
50. #10623347C22semidirect
51. C2×#67000C22semidirect
52. C2×#66999C22semidirect
53. C2×#66999C22semidirect
54. C2×#66997C22semidirect
55. #10623322C22semidirect
57. C2×#66983C22semidirect
58. C2×#66983C22semidirect
59. C2×#66982C22semidirect
60. C2×#66982C22semidirect
62. C2×C4×C22⋊D11C22semidirect
63. C2×C4×C22⋊D11C22semidirect
64. C2×#66979C22semidirect
66. C2×#66977C22semidirect
67. #10623164C22semidirect
68. #10623163C22semidirect
69. #10623162C22semidirect
70. #10623161C22semidirect
71. #10623160C22semidirect
72. #10623159C22semidirect
73. #10623158C22semidirect
74. D11×C22⋊Q8C22semidirect
75. #10623041C22semidirect
76. C2×#66950C22semidirect
77. C2×#66950C22semidirect
78. C2×#66949C22semidirect
79. C2×#66949C22semidirect
80. #10623038C22semidirect
81. C2×#66948C22semidirect
82. C2×#66948C22semidirect
83. C2×#66948C22semidirect
84. C2×#66947C22semidirect
85. C2×#66947C22semidirect
86. #10623035C22semidirect
87. C2×#66946C22semidirect
88. C2×#66946C22semidirect
89. C2×#66945C22semidirect
90. C2×C4⋊C4×D11C22semidirect
91. C2×C4⋊C4×D11C22semidirect
92. C2×#66941C22semidirect
93. C2×#66940C22semidirect
94. C2×#66938C22semidirect
95. #10623021C22semidirect
96. C2×#66937C22semidirect
97. C2×#66937C22semidirect
98. C2×#66936C22semidirect
108. C22×Q8×C11C23semidirect
132. C2×#4343C23semidirect
133. C2×#4343C23semidirect
136. C2×Q8×D11C23semidirect
137. C2×Q8×D11C23semidirect
146. C2×#4339D4semidirect
153. C2×#4339C23semidirect
154. C2×#4339C23semidirect
182. C11×C22⋊Q8C23semidirect
183. C11×C22⋊Q8C23semidirect
188. C2×C11×C4⋊C4C23semidirect
189. C2×C11×C4⋊C4C23semidirect
197. #67000C23semidirect
198. #66999C23semidirect
199. #66999C23semidirect
200. #66997C23semidirect
202. #66983C23semidirect
203. #66983C23semidirect
204. #66982C23semidirect
205. #66982C23semidirect
207. C4×C22⋊D11C23semidirect
208. C4×C22⋊D11C23semidirect
216. #66979C23semidirect
221. #66977C23semidirect
229. #66950C23semidirect
230. #66950C23semidirect
231. #66949C23semidirect
232. #66949C23semidirect
233. #66948C23semidirect
234. #66948C23semidirect
235. #66948C23semidirect
236. #66947C23semidirect
237. #66947C23semidirect
238. #66946C23semidirect
239. #66946C23semidirect
240. #66945C23semidirect
241. C4⋊C4×D11C23semidirect
242. C4⋊C4×D11C23semidirect
243. #66941C23semidirect
244. #66940C23semidirect
245. #66938C23semidirect
246. #66937C23semidirect
247. #66937C23semidirect
248. #66936C23semidirect
329. #4339C2×D4semidirect
413. C22×C22⋊Q8D11semidirect
427. C23×C112−1+4semidirect
524. C23×Q8C2×D11semidirect
562. C2×C22⋊Q8C2×D11semidirect
563. C2×C22⋊Q8C2×D11semidirect
564. C2×C22⋊Q8C2×D11semidirect
587. C22×C4⋊C4C2×D11semidirect
588. C22×C4⋊C4C2×D11semidirect
605. C22×C11C2×2−1+4semidirect
670. C22×Q8C22×D11semidirect
729. C22⋊Q8C22×D11semidirect
730. C22⋊Q8C22×D11semidirect
764. C2×C4⋊C4C22×D11semidirect
765. C2×C4⋊C4C22×D11semidirect
785. C2×C11#3489semidirect
935. C11C2×#3489semidirect
964. C23#67040semidirect
1055. C22C2×#67040semidirect
1075. C2#13082292direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670402
C23×#43392
#130822922
C2×#106231632
C2×#106231642
C2×#106231622
C2×#106230382
C2×#106231612
C2×#106230212
C2×#106230412
C2×#106231602
C2×#106233472
C2×#106231592
C2×#106231582
C2×#106233222
C2×D11×C22⋊Q82
C2×#106230352
C22×C11×C22⋊Q82
C2×#348911