Finite Group Databasebeta

← C2×#13082294 #15662177

Subgroups — C2×#13082294 #15662177

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
2C22×#41×D11C211yesmaximal, characteristic, complemented
3#13082294C2132yesmaximal, direct product factor
4C2×#10623258C212yesmaximal, complemented
5C2×#10623208C212yesmaximal, complemented
6C2×#10623257C212yesmaximal, complemented
7C2×#10623186C214yesmaximal, complemented
8C2×#10623207C212yesmaximal, complemented
9C2×#10623185C214yesmaximal, complemented
10C2×#10623160C212yesmaximal, complemented
11C2×#10623364C211yesmaximal, characteristic, complemented
12C2×#10623159C212yesmaximal, complemented
13C2×#10623158C212yesmaximal, complemented
14C2×#10623055C211yesmaximal, characteristic, complemented
15C22×#66999C211yesmaximal, characteristic, complemented
16C2×D11×C22⋊Q8C212yesmaximal, complemented
17C2×#10623054C211yesmaximal, characteristic, complemented
18C2×C11×#536C211yesmaximal, characteristic, complemented
19C22×C11×#41C2211yescharacteristic
20C23×Q8×C11C2211yescharacteristic, complemented
21C2×#41×D11—216no—
22C2×#41×D11C22116yescomplemented
23C2×#67040—216no—
24C2×#67040C22116yescomplemented
25C22×#4343C2211yescharacteristic
26C22×#4343C2212yescomplemented
27C22×#4343C2212yescomplemented
28C22×Q8×D11C2211yescharacteristic
29C22×Q8×D11C2212yescomplemented
30C22×Q8×D11C2212yescomplemented
31C22×#4341C2212yes—
32C22×#4341C2211yescharacteristic
33C22×D4×D11C2212yes—
34C22×D4×D11C2211yescharacteristic
35C22×#4339C2212yes—
36C22×#4339C2211yescharacteristic
37C22×#4339C2211yescharacteristic, complemented
38C22×#4339C2214yescomplemented
39C23×C4×D11C2211yescharacteristic
40C23×C4×D11C2212yes—
41C11×#536C22116yescomplemented
42C2×C11×C4⋊Q8C2212yescomplemented
43C2×C11×#124C2212yescomplemented
44C2×C11×#123C2214yescomplemented
45C2×C11×C22⋊Q8C2212yescomplemented
46C2×C11×C22⋊Q8C2212yescomplemented
47C2×C11×#117C2211yescharacteristic, complemented
48#10623364C22116yescomplemented
49C2×#66999C2212yes—
50C2×#66999C2212yes—
51C2×#66999C2212yescomplemented
52C2×#66999C2212yescomplemented
53C2×#66999C2212yescomplemented
54C2×#66999C22116yescomplemented
55C2×#66992C2214yescomplemented
56C2×#66991C2212yescomplemented
57C2×#66983C2212yescomplemented
58C22×(C2×D11)⋊C4C2212yes—
59C22×C4⋊Dic11C2211yescharacteristic, complemented
60C2×#66977C2212yescomplemented
61C22×Dic11⋊C4C2212yescomplemented
62#10623258C22132yescomplemented
63#10623257C22132yescomplemented
64#10623208C22132yescomplemented
65#10623207C22132yescomplemented
66#10623186C22164yescomplemented
67#10623185C22164yescomplemented
68#10623160C22132yescomplemented
69#10623159C22132yescomplemented
70#10623158C22132yescomplemented
71D11×C22⋊Q8C22132yescomplemented
72#10623055C22116yescomplemented
73#10623054C22116yescomplemented
74C2×#66950C2211yescharacteristic
75C2×#66950C2211yescharacteristic, complemented
76C2×#66949C2214yes—
77C2×#66949C2214yescomplemented
78C2×#66948C2211yescharacteristic
79C2×#66948C2211yescharacteristic, complemented
80C2×#66948C2214yescomplemented
81C2×#66947C2214yescomplemented
82C2×#66947C2214yescomplemented
83C2×#66946C2214yes—
84C2×#66945C2212yescomplemented
85C2×C4⋊C4×D11C2212yescomplemented
86C2×C4⋊C4×D11C2214yescomplemented
87C2×#66941C2214yescomplemented
88C2×#66939C2212yescomplemented
89C2×#66938C2214yescomplemented
90C2×#66937C2214yescomplemented
91C2×#66937C2214yescomplemented
92C2×#66936C2214yescomplemented
93C2×#66935C2212yes—
94C2×#66935C2214yes—
95C2×(C22⋊D11)⋊C4C2214yescomplemented
96C2×(C22⋊D11)⋊C4C2214yescomplemented
97C2×C22⋊C4×D11C2214yes—
98C2×#66931C2214yescomplemented
99C2×C4×D44C2212yes—
100C2×C4×D44C2212yescomplemented
101C2×C4×D44C2212yescomplemented
102C2×C4×Dic22C2212yescomplemented
103C24×D11C2312yes—
104C24×D11C2311yescharacteristic
105C2×C11×#41—28no—
106C2×C11×#41C2318yes—
107C22×Q8×C11—28no—
108C22×Q8×C11C2312yes—
109C22×Q8×C11C2312yes—
110C22×Q8×C11C2311yescharacteristic
111C22×Q8×C11C2318yescomplemented
112C22×D4×C11C2311yescharacteristic
113C22×D4×C11C2312yes—
114C23×C4×C11C2312yes—
115C23×C4×C11C2312yes—
116C23×C4×C11C2311yescharacteristic
117C22×C22⋊D11C2312yes—
118C22×C22⋊D11C2312yes—
119C22×C22⋊D11C2312yes—
120C22×C22⋊D11C2314yes—
121C22×C22⋊D11C2312yes—
122C23×Dic11C2312yes—
123C23×Dic11C2311yescharacteristic
124C23×Dic11C2312yes—
125#41×D11—2128no—
126#67040—2128no—
127C2×#4343—28no—
128C2×#4343—216no—
129C2×#4343—216no—
130C2×#4343C2318yes—
131C2×#4343C23116yescomplemented
132C2×#4343C23116yescomplemented
133C2×Q8×D11—216no—
134C2×Q8×D11—28no—
135C2×Q8×D11—216no—
136C2×Q8×D11C2318yes—
137C2×Q8×D11C23116yescomplemented
138C2×Q8×D11C23116yescomplemented
139C2×#4341—216no—
140C2×#4341—28no—
141C2×#4341C23116yes—
142C2×#4341C2318yes—
143C2×D4×D11—216no—
144C2×D4×D11—28no—
145C2×D4×D11C23116yes—
146C2×D4×D11C2318yes—
147C2×#4339—28no—
148C2×#4339—232no—
149C2×#4339—216no—
150C2×#4339D4116yescomplemented
151C2×#4339C23116yes—
152C2×#4339C2318yes—
153C2×#4339C2318yescomplemented
154C2×#4339C23132yescomplemented
155C22×D44C2312yes—
156C22×D44C2314yes—
157C22×D44C2312yes—
158C22×D44C2311yescharacteristic
159C22×D44C2312yes—
160C22×D44C2311yescharacteristic
161C22×C4×D11—28no—
162C22×C4×D11—216no—
163C22×C4×D11C2311yescharacteristic
164C22×C4×D11C2312yes—
165C22×C4×D11C2311yescharacteristic
166C22×C4×D11C2314yes—
167C22×C4×D11C2314yes—
168C22×C4×D11C2312yes—
169C22×C4×D11C2312yes—
170C22×C4×D11C2311yescharacteristic
171C22×C4×D11C2311yescharacteristic
172C22×C4×D11C2318yes—
173C22×C4×D11C23116yes—
174C22×C4×D11C2314yes—
175C22×C4×D11C2312yes—
176C22×Dic22C2314yes—
177C22×Dic22C2312yes—
178C22×Dic22C2311yescharacteristic
179C22×Dic22C2311yescharacteristic
180C11×C4⋊Q8C23116yescomplemented
181C11×#124C23116yescomplemented
182C11×#123C23132yescomplemented
183C11×C22⋊Q8C23116yescomplemented
184C11×C22⋊Q8C23116yescomplemented
185C11×#117C2318yescomplemented
186C2×C11×C4⋊C4C2314yes—
187C2×C11×C4⋊C4C2311yescharacteristic
188C2×C11×C4⋊C4C2314yes—
189C2×C11×C4⋊C4C2311yescharacteristic
190C2×C11×C22⋊C4C2314yes—
191C2×C11×C22⋊C4C2312yes—
192C2×C11×C22⋊C4C2314yes—
193C2×C42×C11C2312yes—
194C2×C22⋊Dic11C2314yes—
195#66999C23116yes—
196#66999C23116yes—
197#66999C23116yescomplemented
198#66999C23116yescomplemented
199#66999C23116yescomplemented
200#66992C23132yescomplemented
201#66991C23116yescomplemented
202#66983C23116yescomplemented
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2314yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2314yes—
209C2×(C2×D11)⋊C4C2314yes—
210C2×(C2×D11)⋊C4C2314yes—
211C2×(C2×D11)⋊C4C23116yes—
212C2×C4⋊Dic11C2312yes—
213C2×C4⋊Dic11C2312yes—
214C2×C4⋊Dic11C2312yes—
215C2×C4⋊Dic11C2312yes—
216C2×C4⋊Dic11C2318yescomplemented
217#66977C23116yescomplemented
218C2×Dic11⋊C4C2314yes—
219C2×Dic11⋊C4C2314yes—
220C2×Dic11⋊C4C2314yes—
221C2×Dic11⋊C4C2314yes—
222C2×Dic11⋊C4C23116yescomplemented
223C2×C4×Dic11C2314yes—
224#66950C2318yes—
225#66950C2318yescomplemented
226#66949C23132yes—
227#66949C23132yescomplemented
228#66948C2318yes—
229#66948C23132yescomplemented
230#66948C2318yescomplemented
231#66947C23132yescomplemented
232#66947C23132yescomplemented
233#66946C23132yes—
234#66945C23116yescomplemented
235C4⋊C4×D11C23132yescomplemented
236C4⋊C4×D11C23116yescomplemented
237#66941C23132yescomplemented
238#66939C23116yescomplemented
239#66938C23132yescomplemented
240#66937C23132yescomplemented
241#66937C23132yescomplemented
242#66936C23132yescomplemented
243#66935C23116yes—
244#66935C23132yes—
245(C22⋊D11)⋊C4C23132yescomplemented
246(C22⋊D11)⋊C4C23132yescomplemented
247C22⋊C4×D11C23132yes—
248#66931C23132yescomplemented
249C4×D44C23116yes—
250C4×D44C23116yescomplemented
251C4×D44C23116yescomplemented
252C4×Dic22C23116yescomplemented
253C2×#3489—111nomaximal, Sylow
254C24×C11C2412yes—
255C24×C11C2411yescharacteristic
256C23×D11—24no—
257C23×D11—28no—
258C23×D11—28no—
259C23×D11—24no—
260C23×D11—44no—
261C23×D11—42no—
262C23×D11C2411yescharacteristic
263C23×D11C2412yes—
264C23×D11C2418yes—
265C23×D11C2414yes—
266C23×D11C2412yes—
267C23×D11C2411yescharacteristic
268C11×#41—232no—
269C2×Q8×C11—28no—
270C2×Q8×C11—28no—
271C2×Q8×C11—24no—
272C2×Q8×C11—232no—
273C2×Q8×C11C2418yes—
274C2×Q8×C11C2418yes—
275C2×Q8×C11C2414yes—
276C2×D4×C11—28no—
277C2×D4×C11—24no—
278C2×D4×C11C2414yes—
279C2×D4×C11C2418yes—
280C22×C4×C11—28no—
281C22×C4×C11—28no—
282C22×C4×C11C2×D418yes—
283C22×C4×C11C2412yes—
284C22×C4×C11C2412yes—
285C22×C4×C11C2414yes—
286C22×C4×C11C2412yes—
287C22×C4×C11C2418yes—
288C22×C4×C11C2418yes—
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2414yes—
292C2×C22⋊D11—28no—
293C2×C22⋊D11—28no—
294C2×C22⋊D11—28no—
295C2×C22⋊D11—48no—
296C2×C22⋊D11C2×D4116yes—
297C2×C22⋊D11C2418yes—
298C2×C22⋊D11C2418yes—
299C2×C22⋊D11C2418yes—
300C2×C22⋊D11C24116yes—
301C2×C22⋊D11C2418yes—
302C22×Dic11—28no—
303C22×Dic11—24no—
304C22×Dic11—44no—
305C22×Dic11C2418yes—
306C22×Dic11C2414yes—
307C22×Dic11C2414yes—
308C22×Dic11C2411yescharacteristic
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2412yes—
311C22×Dic11C2418yes—
312C22×Dic11C2412yes—
313#4343—232no—
314#4343—264no—
315#4343—264no—
316Q8×D11—264no—
317Q8×D11—232no—
318Q8×D11—264no—
319#4341—264no—
320#4341—232no—
321D4×D11—264no—
322D4×D11—232no—
323#4339—2128no—
324#4339—264no—
325#4339—232no—
326#4339C2×D4164yescomplemented
327C2×D44—28no—
328C2×D44—216no—
329C2×D44—28no—
330C2×D44—24no—
331C2×D44—44no—
332C2×D44C2×D418yes—
333C2×D44C2418yes—
334C2×D44C24116yes—
335C2×D44C2418yes—
336C2×D44C2414yes—
337C2×D44C2418yes—
338C2×D44C2414yes—
339C2×C4×D11—28no—
340C2×C4×D11—216no—
341C2×C4×D11—264no—
342C2×C4×D11—28no—
343C2×C4×D11—216no—
344C2×C4×D11—24no—
345C2×C4×D11—24no—
346C2×C4×D11—24no—
347C2×C4×D11—24no—
348C2×C4×D11—232no—
349C2×C4×D11—28no—
350C2×C4×D11—48no—
351C2×C4×D11C2×D4116yes—
352C2×C4×D11C2414yes—
353C2×C4×D11C2418yes—
354C2×C4×D11C2414yes—
355C2×C4×D11C24116yes—
356C2×C4×D11C24116yes—
357C2×C4×D11C2418yes—
358C2×C4×D11C2418yes—
359C2×C4×D11C2414yes—
360C2×C4×D11C2414yes—
361C2×C4×D11C24116yes—
362C2×C4×D11C2418yes—
363C2×Dic22—28no—
364C2×Dic22—216no—
365C2×Dic22—24no—
366C2×Dic22C2×D418yes—
367C2×Dic22C24116yes—
368C2×Dic22C2418yes—
369C2×Dic22C2414yes—
370C2×Dic22C2414yes—
371C11×C4⋊C4C24116yes—
372C11×C4⋊C4C2414yes—
373C11×C4⋊C4C24116yes—
374C11×C4⋊C4C2414yes—
375C11×C22⋊C4C24116yes—
376C11×C22⋊C4C2418yes—
377C11×C22⋊C4C24116yes—
378C42×C11C2418yes—
379C22⋊Dic11C24116yes—
380(C2×D11)⋊C4C2418yes—
381(C2×D11)⋊C4C2418yes—
382(C2×D11)⋊C4C2418yes—
383(C2×D11)⋊C4C24116yes—
384(C2×D11)⋊C4C2418yes—
385(C2×D11)⋊C4C24116yes—
386(C2×D11)⋊C4C24116yes—
387(C2×D11)⋊C4C24116yes—
388C4⋊Dic11C2418yes—
389C4⋊Dic11C2418yes—
390C4⋊Dic11C2418yes—
391C4⋊Dic11C2418yes—
392Dic11⋊C4C24116yes—
393Dic11⋊C4C24116yes—
394Dic11⋊C4C24116yes—
395Dic11⋊C4C24116yes—
396C4×Dic11C24116yes—
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—111no—
407C2×#537—112no—
408C2×#536—112no—
409C2×#536D1111yescharacteristic, complemented
410C2×#525—112no—
411C2×#525—111no—
412C22×C22⋊Q8—111no—
413C22×C22⋊Q8—112no—
414C2×#520—111no—
415C23×C11—22no—
416C23×C11—22no—
417C23×C11—24no—
418C23×C11—24no—
419C23×C11—24no—
420C23×C11C22×D414yes—
421C23×C11C2514yes—
422C23×C11C2512yes—
423C23×C11C2511yescharacteristic
424C22×D11—22no—
425C22×D11—24no—
426C22×D11—24no—
427C22×D11—22no—
428C22×D11—24no—
429C22×D11—22no—
430C22×D11—28no—
431C22×D11—24no—
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—24no—
435C22×D11—216no—
436C22×D11—216no—
437C22×D11—28no—
438C22×D11—48no—
439C22×D11—44no—
440C22×D11—432no—
441C22×D11—416no—
442C22×D11C22×D418yes—
443C22×D112−1+414yescomplemented
444C22×D11C2512yes—
445C22×D11C2514yes—
446C22×D11C2514yes—
447C22×D11C2512yes—
448Q8×C11—216no—
449Q8×C11—216no—
450Q8×C11—28no—
451D4×C11—216no—
452D4×C11—28no—
453C2×C4×C11—24no—
454C2×C4×C11—28no—
455C2×C4×C11—216no—
456C2×C4×C11—24no—
457C2×C4×C11—24no—
458C2×C4×C11—216no—
459C2×C4×C11C22×D414yes—
460C2×C4×C11C22×D414yes—
461C2×C4×C11C22×D4116yes—
462C2×C4×C11C2514yes—
463C2×C4×C11C2514yes—
464C2×C4×C11C2518yes—
465C2×C4×C11C2514yes—
466C2×C4×C11C2512yes—
467C2×C4×C11C2512yes—
468C22⋊D11—216no—
469C22⋊D11—216no—
470C22⋊D11—216no—
471C22⋊D11—416no—
472C22⋊D11C22×D4132yes—
473C2×Dic11—24no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—28no—
477C2×Dic11—28no—
478C2×Dic11—216no—
479C2×Dic11—48no—
480C2×Dic11C22×D418yes—
481C2×Dic11C2518yes—
482C2×Dic11C2512yes—
483C2×Dic11C2512yes—
484C2×Dic11C2514yes—
485C2×Dic11C2514yes—
486D44—216no—
487D44—232no—
488D44—216no—
489D44—28no—
490D44—48no—
491D44C22×D4116yes—
492C4×D11—216no—
493C4×D11—232no—
494C4×D11—28no—
495C4×D11—28no—
496C4×D11—28no—
497C4×D11—28no—
498C4×D11—216no—
499C4×D11—216no—
500C4×D11—232no—
501C4×D11—416no—
502C4×D11C22×D4132yes—
503Dic22—28no—
504Dic22—216no—
505Dic22—232no—
506Dic22C22×D4116yes—
507C2×2−1+4—1116no—
508C2×2−1+4—2216no—
509C22×#41—1116no—
510C22×#41—111no—
511C22×#41—112no—
512C22×#41—112no—
513C22×#41—112no—
514C22×#41—111no—
515C22×#41—111no—
516C22×#41—112no—
517C22×#41—111no—
518C22×#41—114no—
519C22×#41—2216no—
520C22×#41C2×D1111yescharacteristic
521C23×Q8—111no—
522C23×Q8—112no—
523C23×Q8—112no—
524C23×Q8C2×D1111yescharacteristic, complemented
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—1132no—
534#546—1164no—
535#537—1116no—
536#537—1132no—
537#536—1132no—
538#536C2×D11116yescomplemented
539C2×C4⋊Q8—114no—
540C2×C4⋊Q8C2×D1112yescomplemented
541C2×#124—114no—
542C2×#124C2×D1112yescomplemented
543#525—1132no—
544#525—1116no—
545C2×#123—114no—
546C2×#123—114no—
547C2×#123—114no—
548C2×#123—112no—
549C2×#123C2×D1114yescomplemented
550C2×C22⋊Q8—112no—
551C2×C22⋊Q8—112no—
552C2×C22⋊Q8—112no—
553C2×C22⋊Q8—112no—
554C2×C22⋊Q8—112no—
555C2×C22⋊Q8—1116no—
556C2×C22⋊Q8—112no—
557C2×C22⋊Q8—1132no—
558C2×C22⋊Q8—114no—
559C2×C22⋊Q8—114no—
560C2×C22⋊Q8—111no—
561C2×C22⋊Q8—111no—
562C2×C22⋊Q8—114no—
563C2×C22⋊Q8C2×D1112yescomplemented
564C2×C22⋊Q8C2×D1112yescomplemented
565C2×#121—112no—
566C2×#121—114no—
567C2×#121—112no—
568C2×#121—111no—
569C2×#121—111no—
570C2×#121—114no—
571C2×#121—114no—
572C2×#121—114no—
573C2×#120—114no—
574C2×#120—112no—
575#520—1116no—
576C2×C4×Q8—112no—
577C2×C4×D4—114no—
578C2×C4×D4—114no—
579C2×C4×D4—114no—
580C2×C4×D4—112no—
581C2×C4×D4—112no—
582C2×C4×D4—112no—
583C2×#117—112no—
584C2×#117C2×D1111yescharacteristic, complemented
585C22×C4⋊C4—112no—
586C22×C4⋊C4—111no—
587C22×C4⋊C4—112no—
588C22×C4⋊C4—114no—
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—48no—
598C22×C11C23×D414yes—
599C22×C11C23×D412yes—
600C22×C11C2×2−1+412yes—
601C22×C11#58512yes—
602C22×C11C2611yescharacteristic
603C2×D11—22no—
604C2×D11—24no—
605C2×D11—22no—
606C2×D11—24no—
607C2×D11—28no—
608C2×D11—216no—
609C2×D11—22no—
610C2×D11—24no—
611C2×D11—22no—
612C2×D11—24no—
613C2×D11—22no—
614C2×D11—24no—
615C2×D11—432no—
616C2×D11—416no—
617C2×D11—48no—
618C2×D11—44no—
619C2×D11C23×D418yes—
620C2×D11C2×2−1+414yescomplemented
621C4×C11—24no—
622C4×C11—28no—
623C4×C11—24no—
624C4×C11—24no—
625C4×C11C23×D414yes—
626C4×C11C23×D414yes—
627Dic11—24no—
628Dic11—22no—
629Dic11—22no—
630Dic11—28no—
631Dic11C23×D418yes—
632C25—112no—
633C25—111no—
6342−1+4—22128no—
635C2×#41—28no—
636C2×#41—1116no—
637C2×#41—1116no—
638C2×#41—118no—
639C2×#41—1116no—
640C2×#41—118no—
641C2×#41—1116no—
642C2×#41—118no—
643C2×#41—118no—
644C2×#41—1116no—
645C2×#41—1132no—
646C2×#41—2216no—
647C2×#41—2232no—
648C2×#41—2216no—
649C2×#41—2216no—
650C2×#41—228no—
651C2×#41—228no—
652C2×#41—2216no—
653C2×#41—22128no—
654C2×#41—228no—
655C2×#41C22×D1118yes—
656C22×Q8—28no—
657C22×Q8—1116no—
658C22×Q8—1116no—
659C22×Q8—118no—
660C22×Q8—111no—
661C22×Q8—111no—
662C22×Q8—114no—
663C22×Q8—112no—
664C22×Q8—2216no—
665C22×Q8—228no—
666C22×Q8—2216no—
667C22×Q8C22×D1112yes—
668C22×Q8C22×D1112yes—
669C22×Q8C22×D1111yescharacteristic
670C22×Q8C22×D1118yescomplemented
671C22×D4—112no—
672C22×D4—112no—
673C22×D4—112no—
674C22×D4—112no—
675C22×D4—114no—
676C22×D4—1116no—
677C22×D4—118no—
678C22×D4—111no—
679C22×D4—112no—
680C22×D4—114no—
681C22×D4—111no—
682C22×D4—112no—
683C22×D4—112no—
684C22×D4—2216no—
685C22×D4—228no—
686C22×D4C22×D1112yes—
687C22×D4C22×D1111yescharacteristic
688C23×C4—112no—
689C23×C4—111no—
690C23×C4—112no—
691C23×C4—112no—
692C23×C4—114no—
693C23×C4—112no—
694C23×C4—114no—
695C23×C4—112no—
696C23×C4—112no—
697C23×C4—111no—
698C23×C4—111no—
699C23×C4—111no—
700C23×C4—111no—
701C23×C4—1116no—
702C23×C4—118no—
703C23×C4—114no—
704C23×C4—2216no—
705C23×C4—228no—
706C23×C4C22×D1112yes—
707C23×C4C22×D1112yes—
708C23×C4C22×D1111yescharacteristic
709C4⋊Q8—1132no—
710C4⋊Q8C22×D11116yescomplemented
711#124—1132no—
712#124C22×D11116yescomplemented
713#123—1132no—
714#123—1132no—
715#123—1116no—
716#123—1132no—
717#123C22×D11132yescomplemented
718C22⋊Q8—1116no—
719C22⋊Q8—1116no—
720C22⋊Q8—1116no—
721C22⋊Q8—1116no—
722C22⋊Q8—1116no—
723C22⋊Q8—1116no—
724C22⋊Q8—118no—
725C22⋊Q8—1132no—
726C22⋊Q8—118no—
727C22⋊Q8—1132no—
728C22⋊Q8—1132no—
729C22⋊Q8C22×D11116yescomplemented
730C22⋊Q8C22×D11116yescomplemented
731#121—1132no—
732#121—1116no—
733#121—1116no—
734#121—118no—
735#121—118no—
736#121—1132no—
737#121—1132no—
738#121—1132no—
739#120—1132no—
740#120—1116no—
741C4×Q8—1116no—
742C4×D4—1132no—
743C4×D4—1132no—
744C4×D4—1132no—
745C4×D4—1116no—
746C4×D4—1116no—
747C4×D4—1116no—
748#117—1116no—
749#117C22×D1118yescomplemented
750C2×C4⋊C4—112no—
751C2×C4⋊C4—114no—
752C2×C4⋊C4—112no—
753C2×C4⋊C4—114no—
754C2×C4⋊C4—112no—
755C2×C4⋊C4—118no—
756C2×C4⋊C4—114no—
757C2×C4⋊C4—114no—
758C2×C4⋊C4—1116no—
759C2×C4⋊C4—112no—
760C2×C4⋊C4—1116no—
761C2×C4⋊C4—1132no—
762C2×C4⋊C4C22×D1111yescharacteristic
763C2×C4⋊C4C22×D1114yes—
764C2×C4⋊C4C22×D1111yescharacteristic
765C2×C4⋊C4C22×D1114yes—
766C2×C22⋊C4—114no—
767C2×C22⋊C4—114no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—114no—
770C2×C22⋊C4—1116no—
771C2×C22⋊C4—114no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—114no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—1132no—
777C2×C22⋊C4C22×D1114yes—
778C2×C22⋊C4C22×D1112yes—
779C2×C22⋊C4C22×D1114yes—
780C2×C42—114no—
781C2×C42C22×D1112yes—
782C2×C11—24no—
783C2×C11—44no—
784C2×C11#348914yescomplemented
785C2×C11C24×D411yescharacteristic
786C2×C11C22×2−1+411yescharacteristic
787C2×C11C2×#58511yescharacteristic
788D11—24no—
789D11—28no—
790D11—44no—
791D11—42no—
792C24—111no—
793C24—112no—
794C24—111no—
795C24—112no—
796C24—118no—
797C24—114no—
798C24—228no—
799C24—224no—
800C24—228no—
801C24—224no—
802C24—442no—
803C24—444no—
804C24C23×D1112yes—
805C24C23×D1111yescharacteristic
806#41—232no—
807#41—1164no—
808#41—2264no—
809#41—22128no—
810#41—2264no—
811#41—2264no—
812#41—2232no—
813#41—2232no—
814#41—2264no—
815#41—2232no—
816C2×Q8—28no—
817C2×Q8—28no—
818C2×Q8—232no—
819C2×Q8—24no—
820C2×Q8—118no—
821C2×Q8—114no—
822C2×Q8—114no—
823C2×Q8—1116no—
824C2×Q8—118no—
825C2×Q8—2216no—
826C2×Q8—228no—
827C2×Q8—2264no—
828C2×Q8—2232no—
829C2×Q8—2264no—
830C2×Q8—224no—
831C2×Q8C23×D1118yes—
832C2×Q8C23×D1118yes—
833C2×Q8C23×D1114yes—
834C2×D4—28no—
835C2×D4—24no—
836C2×D4—1116no—
837C2×D4—118no—
838C2×D4—118no—
839C2×D4—118no—
840C2×D4—118no—
841C2×D4—1116no—
842C2×D4—118no—
843C2×D4—114no—
844C2×D4—118no—
845C2×D4—1116no—
846C2×D4—114no—
847C2×D4—118no—
848C2×D4—118no—
849C2×D4—228no—
850C2×D4—2216no—
851C2×D4—228no—
852C2×D4—228no—
853C2×D4—2264no—
854C2×D4—2232no—
855C2×D4—228no—
856C2×D4—228no—
857C2×D4—224no—
858C2×D4—444no—
859C2×D4—448no—
860C2×D4C23×D1118yes—
861C2×D4C23×D1114yes—
862C22×C4—28no—
863C22×C4—28no—
864C22×C4—112no—
865C22×C4—1116no—
866C22×C4—118no—
867C22×C4—114no—
868C22×C4—118no—
869C22×C4—114no—
870C22×C4—112no—
871C22×C4—111no—
872C22×C4—111no—
873C22×C4—118no—
874C22×C4—1116no—
875C22×C4—118no—
876C22×C4—1116no—
877C22×C4—118no—
878C22×C4—118no—
879C22×C4—114no—
880C22×C4—114no—
881C22×C4—114no—
882C22×C4—114no—
883C22×C4—1116no—
884C22×C4—228no—
885C22×C4—2264no—
886C22×C4—2216no—
887C22×C4—228no—
888C22×C4—2216no—
889C22×C4—228no—
890C22×C4—224no—
891C22×C4—224no—
892C22×C4—224no—
893C22×C4—224no—
894C22×C4—224no—
895C22×C4—2232no—
896C22×C4—228no—
897C22×C4—448no—
898C22×C4—444no—
899C22×C4D4×D1118yes—
900C22×C4C23×D1118yes—
901C22×C4C23×D1118yes—
902C22×C4C23×D1112yes—
903C22×C4C23×D1112yes—
904C22×C4C23×D1114yes—
905C22×C4C23×D1112yes—
906C22×C4C23×D1114yes—
907C22×C4C23×D1111yescharacteristic
908C22×C4C23×D1111yescharacteristic
909C4⋊C4—118no—
910C4⋊C4—1116no—
911C4⋊C4—118no—
912C4⋊C4—1116no—
913C4⋊C4—118no—
914C4⋊C4—1116no—
915C4⋊C4—1116no—
916C4⋊C4—118no—
917C4⋊C4C23×D1114yes—
918C4⋊C4C23×D11116yes—
919C4⋊C4C23×D1114yes—
920C4⋊C4C23×D11116yes—
921C22⋊C4—1116no—
922C22⋊C4—1116no—
923C22⋊C4—118no—
924C22⋊C4—1116no—
925C22⋊C4—1116no—
926C22⋊C4—118no—
927C22⋊C4—118no—
928C22⋊C4—1116no—
929C22⋊C4—118no—
930C22⋊C4C23×D11116yes—
931C22⋊C4C23×D1118yes—
932C22⋊C4C23×D11116yes—
933C42—1116no—
934C42C23×D1118yes—
935C11C2×#348911yescharacteristic, complemented, Sylow
936C23—22no—
937C23—22no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—118no—
942C23—114no—
943C23—112no—
944C23—114no—
945C23—112no—
946C23—114no—
947C23—2216no—
948C23—228no—
949C23—2216no—
950C23—222no—
951C23—224no—
952C23—224no—
953C23—222no—
954C23—224no—
955C23—228no—
956C23—222no—
957C23—224no—
958C23—222no—
959C23—224no—
960C23—222no—
961C23—444no—
962C23—448no—
963C23—4416no—
964C23—4432no—
965C23C2×D4×D1114yes—
966C23C24×D1114yes—
967C23C24×D1112yes—
968C23C24×D1111yescharacteristic
969Q8—216no—
970Q8—216no—
971Q8—28no—
972Q8—1116no—
973Q8—2232no—
974Q8—2216no—
975Q8—228no—
976D4—216no—
977D4—28no—
978D4—1132no—
979D4—1116no—
980D4—2216no—
981D4—2232no—
982D4—2216no—
983D4—2216no—
984D4—2216no—
985D4—2216no—
986D4—228no—
987D4—448no—
988D4—4416no—
989C2×C4—24no—
990C2×C4—28no—
991C2×C4—216no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—216no—
995C2×C4—118no—
996C2×C4—114no—
997C2×C4—1132no—
998C2×C4—118no—
999C2×C4—114no—
1000C2×C4—112no—
1001C2×C4—112no—
1002C2×C4—2216no—
1003C2×C4—2232no—
1004C2×C4—2216no—
1005C2×C4—2232no—
1006C2×C4—2216no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—224no—
1010C2×C4—228no—
1011C2×C4—228no—
1012C2×C4—228no—
1013C2×C4—228no—
1014C2×C4—228no—
1015C2×C4—228no—
1016C2×C4—2216no—
1017C2×C4—4416no—
1018C2×C4—448no—
1019C2×C4C2×D4×D1114yes—
1020C2×C4C2×D4×D1114yes—
1021C2×C4C2×D4×D11116yes—
1022C2×C4C24×D1114yes—
1023C2×C4C24×D1114yes—
1024C2×C4C24×D1118yes—
1025C2×C4C24×D1114yes—
1026C2×C4C24×D1112yes—
1027C2×C4C24×D1112yes—
1028C22—22no—
1029C22—22no—
1030C22—28no—
1031C22—24no—
1032C22—24no—
1033C22—24no—
1034C22—48no—
1035C22—118no—
1036C22—114no—
1037C22—222no—
1038C22—224no—
1039C22—224no—
1040C22—222no—
1041C22—228no—
1042C22—2216no—
1043C22—224no—
1044C22—222no—
1045C22—224no—
1046C22—222no—
1047C22—224no—
1048C22—222no—
1049C22—4416no—
1050C22—4432no—
1051C22—444no—
1052C22—448no—
1053C22C22×D4×D1114yes—
1054C22C22×D4×D1112yes—
1055C22D11×2−1+412yes—
1056C22#1062345712yes—
1057C22C25×D1111yescharacteristic
1058C4—24no—
1059C4—28no—
1060C4—24no—
1061C4—24no—
1062C4—118no—
1063C4—222no—
1064C4—222no—
1065C4—224no—
1066C4—228no—
1067C4C22×D4×D1114yes—
1068C4C22×D4×D1114yes—
1069C2—24no—
1070C2—44no—
1071C2—224no—
1072C2—228no—
1073C2—442no—
1074C2—444no—
1075C2#1308229414yesdirect product factor
1076C2C23×D4×D1111yescharacteristic
1077C2C2×D11×2−1+411yescharacteristic
1078C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#536C2
socleC23×C11C25
hypercenterC2×#536D11
hypocenterC11C2×#3489
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C22×#67040C2semidirect
2. C22×#41×D11C2semidirect
3. #13082294C2direct (N × H)
4. C2×#10623258C2semidirect
5. C2×#10623208C2semidirect
6. C2×#10623257C2semidirect
7. C2×#10623186C2semidirect
8. C2×#10623207C2semidirect
9. C2×#10623185C2semidirect
10. C2×#10623160C2semidirect
11. C2×#10623364C2semidirect
12. C2×#10623159C2semidirect
13. C2×#10623158C2semidirect
14. C2×#10623055C2semidirect
15. C22×#66999C2semidirect
16. C2×D11×C22⋊Q8C2semidirect
17. C2×#10623054C2semidirect
18. C2×C11×#536C2semidirect
20. C23×Q8×C11C22semidirect
22. C2×#41×D11C22semidirect
24. C2×#67040C22semidirect
26. C22×#4343C22semidirect
27. C22×#4343C22semidirect
29. C22×Q8×D11C22semidirect
30. C22×Q8×D11C22semidirect
37. C22×#4339C22semidirect
38. C22×#4339C22semidirect
41. C11×#536C22semidirect
42. C2×C11×C4⋊Q8C22semidirect
43. C2×C11×#124C22semidirect
44. C2×C11×#123C22semidirect
45. C2×C11×C22⋊Q8C22semidirect
46. C2×C11×C22⋊Q8C22semidirect
47. C2×C11×#117C22semidirect
48. #10623364C22semidirect
51. C2×#66999C22semidirect
52. C2×#66999C22semidirect
53. C2×#66999C22semidirect
54. C2×#66999C22semidirect
55. C2×#66992C22semidirect
56. C2×#66991C22semidirect
57. C2×#66983C22semidirect
59. C22×C4⋊Dic11C22semidirect
60. C2×#66977C22semidirect
61. C22×Dic11⋊C4C22semidirect
62. #10623258C22semidirect
63. #10623257C22semidirect
64. #10623208C22semidirect
65. #10623207C22semidirect
66. #10623186C22semidirect
67. #10623185C22semidirect
68. #10623160C22semidirect
69. #10623159C22semidirect
70. #10623158C22semidirect
71. D11×C22⋊Q8C22semidirect
72. #10623055C22semidirect
73. #10623054C22semidirect
75. C2×#66950C22semidirect
77. C2×#66949C22semidirect
79. C2×#66948C22semidirect
80. C2×#66948C22semidirect
81. C2×#66947C22semidirect
82. C2×#66947C22semidirect
84. C2×#66945C22semidirect
85. C2×C4⋊C4×D11C22semidirect
86. C2×C4⋊C4×D11C22semidirect
87. C2×#66941C22semidirect
88. C2×#66939C22semidirect
89. C2×#66938C22semidirect
90. C2×#66937C22semidirect
91. C2×#66937C22semidirect
92. C2×#66936C22semidirect
95. C2×(C22⋊D11)⋊C4C22semidirect
96. C2×(C22⋊D11)⋊C4C22semidirect
98. C2×#66931C22semidirect
100. C2×C4×D44C22semidirect
101. C2×C4×D44C22semidirect
102. C2×C4×Dic22C22semidirect
111. C22×Q8×C11C23semidirect
131. C2×#4343C23semidirect
132. C2×#4343C23semidirect
137. C2×Q8×D11C23semidirect
138. C2×Q8×D11C23semidirect
150. C2×#4339D4semidirect
153. C2×#4339C23semidirect
154. C2×#4339C23semidirect
180. C11×C4⋊Q8C23semidirect
181. C11×#124C23semidirect
182. C11×#123C23semidirect
183. C11×C22⋊Q8C23semidirect
184. C11×C22⋊Q8C23semidirect
185. C11×#117C23semidirect
197. #66999C23semidirect
198. #66999C23semidirect
199. #66999C23semidirect
200. #66992C23semidirect
201. #66991C23semidirect
202. #66983C23semidirect
216. C2×C4⋊Dic11C23semidirect
217. #66977C23semidirect
222. C2×Dic11⋊C4C23semidirect
225. #66950C23semidirect
227. #66949C23semidirect
229. #66948C23semidirect
230. #66948C23semidirect
231. #66947C23semidirect
232. #66947C23semidirect
234. #66945C23semidirect
235. C4⋊C4×D11C23semidirect
236. C4⋊C4×D11C23semidirect
237. #66941C23semidirect
238. #66939C23semidirect
239. #66938C23semidirect
240. #66937C23semidirect
241. #66937C23semidirect
242. #66936C23semidirect
245. (C22⋊D11)⋊C4C23semidirect
246. (C22⋊D11)⋊C4C23semidirect
248. #66931C23semidirect
250. C4×D44C23semidirect
251. C4×D44C23semidirect
252. C4×Dic22C23semidirect
326. #4339C2×D4semidirect
409. C2×#536D11semidirect
443. C22×D112−1+4semidirect
524. C23×Q8C2×D11semidirect
538. #536C2×D11semidirect
540. C2×C4⋊Q8C2×D11semidirect
542. C2×#124C2×D11semidirect
549. C2×#123C2×D11semidirect
563. C2×C22⋊Q8C2×D11semidirect
564. C2×C22⋊Q8C2×D11semidirect
584. C2×#117C2×D11semidirect
620. C2×D11C2×2−1+4semidirect
670. C22×Q8C22×D11semidirect
710. C4⋊Q8C22×D11semidirect
712. #124C22×D11semidirect
717. #123C22×D11semidirect
729. C22⋊Q8C22×D11semidirect
730. C22⋊Q8C22×D11semidirect
749. #117C22×D11semidirect
784. C2×C11#3489semidirect
935. C11C2×#3489semidirect
1075. C2#13082294direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670402
C22×#41×D112
#130822942
C2×#106232582
C2×#106232082
C2×#106232572
C2×#106231862
C2×#106232072
C2×#106231852
C2×#106231602
C2×#106233642
C2×#106231592
C2×#106231582
C2×#106230552
C22×#669992
C2×D11×C22⋊Q82
C2×#106230542
C2×C11×#5362
C2×#348911