Finite Group Databasebeta

← #14959882

Subgroups — #14959882

Order 2816.

2502 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C212yesmaximal
2#13077013C211yesmaximal, characteristic, complemented
3#13077012C211yesmaximal, characteristic, complemented
4#13076991C212yesmaximal, complemented
5#13076975C214yesmaximal, complemented
6#13076969C211yesmaximal, characteristic
7#13076967C214yesmaximal
8#13076965C212yesmaximal
9#13076963C211yesmaximal, characteristic
10C4×#66922C211yesmaximal, characteristic, complemented
11C4×#66941C214yesmaximal, complemented
12C4×#66997C212yesmaximal, complemented
13#13071020C214yesmaximal
14C43×D11C211yesmaximal, characteristic
15C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2212yes—
18C2×#66999C2212yes—
19C2×#66997C2212yes—
20C2×#66997C2212yes—
21#10623109—216no—
22C2×#66950C2212yes—
23C2×#66949C2214yes—
24C2×#66942C2214yes—
25C2×#66941C2212yes—
26C2×#66941C2214yes—
27C2×#66925C2214yes—
28C2×C42×D11C2211yescharacteristic
29C2×C42×D11C2211yescharacteristic
30C2×C42×D11C2212yes—
31C2×C42×D11C2211yescharacteristic
32C2×C42×D11C2212yes—
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22C2212yes—
35C2×C4×Dic22C2214yes—
36C11×#391C2212yes—
37C11×#389C2214yes—
38C11×#384C2211yescharacteristic
39C4×C11×C4⋊C4C2214yes—
40C43×C11C2211yescharacteristic
41#10622843C2212yes—
42#10622600C2214yes—
43#10622600C2214yes—
44#10622598C2214yes—
45#10622589C2214yes—
46#10622589C2214yes—
47#10622589C2212yes—
48#10622589C2214yes—
49#10622587C2212yes—
50#10622586C2214yes—
51#10622585C2218yes—
52#10622548C2211yescharacteristic
53C4×C4⋊Dic11C2214yes—
54C4×Dic11⋊C4C2218yes—
55C42×Dic11C2211yescharacteristic
56C42×Dic11C2211yescharacteristic
57C42×Dic11C2212yes—
58C42×Dic11C2212yes—
59C42×Dic11C2211yescharacteristic
60#10622542C2212yes—
61#10622541C2214yes—
62#10622280C2218yes—
63#10622263C2218yes—
64#10622260C2218yes—
65#10622259C2218yes—
66C22×Q8×C11C2312yes—
67C22×C4×D11C2311yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C22×C4×D11C2312yes—
70C22×C4×D11C2312yes—
71C22×C4×D11C2311yescharacteristic
72C22×Dic22C2312yes—
73C22×Dic22C2314yes—
74C11×C4⋊Q8—24no—
75C4×Q8×C11—28no—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C42×C11C2314yes—
81C2×C42×C11C2312yes—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2312yes—
85C2×C42×C11C2311yescharacteristic
86#66999—28no—
87#66997—28no—
88#66997—28no—
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2314yes—
91C2×C4⋊Dic11C2314yes—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2314yes—
94C2×C4⋊Dic11C2314yes—
95C2×Dic11⋊C4C2314yes—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2314yes—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2318yes—
101C2×Dic11⋊C4C2318yes—
102C2×C4×Dic11C2314yes—
103C2×C4×Dic11C2312yes—
104C2×C4×Dic11C2312yes—
105C2×C4×Dic11C2312yes—
106C2×C4×Dic11C2312yes—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2312yes—
113C2×C4×Dic11C2312yes—
114C2×C4×Dic11C2312yes—
115C2×C4×Dic11C2311yescharacteristic
116#66950—28no—
117#66949—216no—
118#66942—216no—
119#66941—28no—
120#66941—216no—
121#66925—216no—
122C42×D11—24no—
123C42×D11—28no—
124C42×D11—24no—
125C42×D11D418yes—
126C42×D11Q8116yescomplemented
127#66922—24no—
128C4×Dic22—28no—
129C4×Dic22—216no—
130C11×#95C2318yes—
131C11⋊#95C2318yes—
132C11⋊#95C2318yes—
133C11⋊#95C2318yes—
134#36645—111nomaximal, Sylow
135C23×D11C2411yescharacteristic
136C2×Q8×C11—24no—
137C2×Q8×C11—24no—
138C2×Q8×C11—24no—
139C22×C4×C11C2414yes—
140C22×C4×C11C2414yes—
141C22×C4×C11C2411yescharacteristic
142C22×C4×C11C2412yes—
143C22×C4×C11C2411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×C4×C11C2412yes—
146C22×Dic11C2414yes—
147C22×Dic11C2414yes—
148C22×Dic11C2411yescharacteristic
149C22×Dic11C2412yes—
150C22×Dic11C2411yescharacteristic
151C22×Dic11C2411yescharacteristic
152C22×Dic11C2412yes—
153C2×C4×D11—24no—
154C2×C4×D11—24no—
155C2×C4×D11—24no—
156C2×C4×D11—22no—
157C2×C4×D11—24no—
158C2×C4×D11—22no—
159C2×C4×D11—24no—
160C2×C4×D11C2×D414yes—
161C2×C4×D11C2×D414yes—
162C2×C4×D11C2×D414yes—
163C2×C4×D11C2×Q818yes—
164C2×C4×D11C2×Q818yes—
165C2×C4×D11C2×Q818yes—
166C2×Dic22—28no—
167C2×Dic22—216no—
168C2×Dic22—24no—
169C2×Dic22—24no—
170C2×Dic22—24no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—28no—
173C11×C4⋊C4—28no—
174C11×C4⋊C4—28no—
175C42×C11—28no—
176C42×C11—22no—
177C42×C11—24no—
178C42×C11C2×D414yes—
179C42×C11C2×Q818yes—
180C42×C11#4114yes—
181(C2×D11)⋊C4—28no—
182(C2×D11)⋊C4—28no—
183C4⋊Dic11—28no—
184C4⋊Dic11—24no—
185C4⋊Dic11—28no—
186C4⋊Dic11—28no—
187Dic11⋊C4—28no—
188Dic11⋊C4—28no—
189Dic11⋊C4—28no—
190Dic11⋊C4—28no—
191Dic11⋊C4—216no—
192Dic11⋊C4—216no—
193Dic11⋊C4—28no—
194C4×Dic11—24no—
195C4×Dic11—24no—
196C4×Dic11—24no—
197C4×Dic11—28no—
198C4×Dic11—22no—
199C4×Dic11—24no—
200C4×Dic11C2×D414yes—
201C4×Dic11C2×D414yes—
202C4×Dic11C2×D414yes—
203C4×Dic11C2×Q818yes—
204C4×Dic11C2×Q818yes—
205C4×Dic11C2×Q818yes—
206C4×Dic11#4118yes—
207C4×Dic11#4114yes—
208C2×#533—112no—
209#2868—111no—
210#2868—111no—
211#2862—112no—
212#2859—114no—
213#2857—112no—
214#2857—114no—
215#2857—111no—
216#2857—111no—
217C4×C4⋊Q8—114no—
218C4×C4⋊Q8—111no—
219C4×C4⋊Q8—112no—
220C4×C4⋊Q8D1111yescharacteristic, complemented
221#2285—114no—
222C2×C43—111no—
223C23×C11C2511yescharacteristic
224C22×D11—21no—
225C22×D11—22no—
226C22×D11—21no—
227C22×D11C22×D412yes—
228C22×D11C22×Q814yes—
229Q8×C11—48no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—28no—
237C2×C4×C11—24no—
238C2×C4×C11C22×D412yes—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D412yes—
241C2×C4×C11C22×Q814yes—
242C2×C4×C11C22×Q814yes—
243C2×C4×C11C22×Q814yes—
244C2×C4×C11C2×#4112yes—
245C2×C4×C11C2×#4114yes—
246C2×C4×C11C2×#4112yes—
247C2×C4×C11C2×#4114yes—
248C2×Dic11—21no—
249C2×Dic11—22no—
250C2×Dic11—21no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—28no—
256C2×Dic11—24no—
257C2×Dic11C22×D412yes—
258C2×Dic11C22×D412yes—
259C2×Dic11C22×D412yes—
260C2×Dic11C22×Q814yes—
261C2×Dic11C22×Q814yes—
262C2×Dic11C22×Q814yes—
263C2×Dic11C2×#4114yes—
264C2×Dic11C2×#4114yes—
265C2×Dic11C2×#4114yes—
266C4×D11—28no—
267C4×D11—216no—
268C4×D11—28no—
269C4×D11—216no—
270C4×D11C4⋊Q8116yescomplemented
271Dic22—48no—
272Dic22—416no—
273#533—2216no—
274C2×C4⋊Q8—112no—
275C2×C4⋊Q8—112no—
276C2×C4⋊Q8—114no—
277C2×C4⋊Q8—112no—
278C2×C4⋊Q8—111no—
279C2×C4⋊Q8C2×D1111yescharacteristic
280C2×#125—114no—
281C2×C22⋊Q8—112no—
282C2×C22⋊Q8—114no—
283C2×C22⋊Q8—112no—
284C2×C4×Q8—114no—
285C2×C4×Q8—112no—
286C2×C4×Q8C2×D1112yes—
287C2×#117—114no—
288C22×C42—111no—
289C22×C42—112no—
290C22×C42—111no—
291C22×C42—112no—
292C22×C42—111no—
293#391—112no—
294#391—112no—
295#391—112no—
296#391—118no—
297#391C2×D1112yes—
298#389—118no—
299#389—114no—
300#389—114no—
301#389—114no—
302#389—118no—
303#389C2×D1114yes—
304#384—114no—
305#384—112no—
306#384—114no—
307#384—114no—
308#384—111no—
309#384C2×D1111yescharacteristic
310#382—118no—
311#380—114no—
312#380—114no—
313#380—118no—
314C4×C4⋊C4—118no—
315C4×C4⋊C4—114no—
316C4×C4⋊C4C2×D1114yes—
317C43—112no—
318C43—111no—
319C43—112no—
320C43—111no—
321C43—111no—
322C43C2×D1111yescharacteristic
323C22×C11C23×D411yescharacteristic
324C22×C11C23×Q812yes—
325C22×C11C22×#4111yescharacteristic
326C22×C11C22×#4112yes—
327C22×C11C22×#4111yescharacteristic
328C2×D11—22no—
329C2×D11—22no—
330C2×D11—24no—
331C2×D11—24no—
332C2×D11C2×C4⋊Q814yes—
333C4×C11—22no—
334C4×C11—24no—
335C4×C11—44no—
336C4×C11—44no—
337C4×C11C2×C4⋊Q814yes—
338C4×C11#53214yes—
339C4×C11#53318yescomplemented
340Dic11—22no—
341Dic11—24no—
342Dic11—44no—
343Dic11—44no—
344Dic11C2×C4⋊Q814yes—
345Dic11#53214yes—
346Dic11#53318yescomplemented
347C22×Q8—114no—
348C22×Q8—112no—
349C22×Q8C22×D1112yes—
350C23×C4—111no—
351C23×C4—111no—
352C23×C4—111no—
353C23×C4—112no—
354C23×C4—112no—
355C4⋊Q8—24no—
356C4⋊Q8—228no—
357C4⋊Q8—2216no—
358C4⋊Q8—228no—
359C4⋊Q8—228no—
360C4⋊Q8—224no—
361#125—2216no—
362C22⋊Q8—2216no—
363C22⋊Q8—228no—
364C22⋊Q8—228no—
365C4×Q8—28no—
366C4×Q8—2216no—
367C4×Q8—228no—
368#117—2216no—
369C2×C4⋊C4—114no—
370C2×C4⋊C4—114no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—114no—
373C2×C4⋊C4—114no—
374C2×C4⋊C4—114no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4—118no—
377C2×C4⋊C4—118no—
378C2×C4⋊C4—114no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4C22×D1114yes—
381C2×C4⋊C4C22×D1112yes—
382C2×C4⋊C4C22×D1114yes—
383C2×C4⋊C4C22×D1114yes—
384C2×C22⋊C4—114no—
385C2×C22⋊C4—114no—
386C2×C42—111no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—112no—
390C2×C42—112no—
391C2×C42—112no—
392C2×C42—111no—
393C2×C42—112no—
394C2×C42—118no—
395C2×C42—1116no—
396C2×C42—112no—
397C2×C42—112no—
398C2×C42—112no—
399C2×C42—112no—
400C2×C42—111no—
401C2×C42—114no—
402C2×C42—224no—
403C2×C42—228no—
404C2×C42—224no—
405C2×C42C22×D1112yes—
406C2×C42C22×D1111yescharacteristic
407C2×C42C22×D1114yes—
408C2×C42C22×D1111yescharacteristic
409C2×C42C22×D1111yescharacteristic
410C2×C42C22×D1112yes—
411#95—118no—
412#95—118no—
413#95—118no—
414#95C22×D1118yes—
415C2×C11C22×C4⋊Q811yescharacteristic
416C2×C11C2×#53211yescharacteristic
417C2×C11C2×#53211yescharacteristic
418C2×C11C2×#53312yes—
419C2×C11C2×#53312yes—
420D11—24no—
421C24—111no—
422C2×Q8—24no—
423C2×Q8—24no—
424C2×Q8—24no—
425C2×Q8—228no—
426C2×Q8—2216no—
427C2×Q8—224no—
428C2×Q8—224no—
429C2×Q8—224no—
430C22×C4—111no—
431C22×C4—112no—
432C22×C4—111no—
433C22×C4—114no—
434C22×C4—118no—
435C22×C4—112no—
436C22×C4—111no—
437C22×C4—114no—
438C22×C4—114no—
439C22×C4—118no—
440C22×C4—118no—
441C22×C4—114no—
442C22×C4—114no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—224no—
446C22×C4—222no—
447C22×C4—224no—
448C22×C4—222no—
449C22×C4—224no—
450C22×C4C23×D1114yes—
451C22×C4C23×D1114yes—
452C22×C4C23×D1111yescharacteristic
453C22×C4C23×D1112yes—
454C22×C4C23×D1111yescharacteristic
455C22×C4C23×D1112yes—
456C22×C4C23×D1111yescharacteristic
457C4⋊C4—28no—
458C4⋊C4—28no—
459C4⋊C4—24no—
460C4⋊C4—28no—
461C4⋊C4—228no—
462C4⋊C4—228no—
463C4⋊C4—228no—
464C4⋊C4—228no—
465C4⋊C4—228no—
466C4⋊C4—2216no—
467C4⋊C4—2216no—
468C4⋊C4—228no—
469C4⋊C4—228no—
470C4⋊C4—224no—
471C4⋊C4—228no—
472C22⋊C4—228no—
473C22⋊C4—228no—
474C42—28no—
475C42—22no—
476C42—24no—
477C42—114no—
478C42—114no—
479C42—114no—
480C42—118no—
481C42—118no—
482C42—118no—
483C42—114no—
484C42—118no—
485C42—224no—
486C42—224no—
487C42—224no—
488C42—222no—
489C42—224no—
490C42—228no—
491C42#433914yes—
492C42D4×D1114yes—
493C42Q8×D1118yes—
494C11#3664511yescharacteristic, complemented, Sylow
495C23—112no—
496C23—114no—
497C23—221no—
498C23—222no—
499C23—221no—
500C23C24×D1111yescharacteristic
501Q8—48no—
502Q8—4416no—
503Q8—448no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—28no—
511C2×C4—24no—
512C2×C4—112no—
513C2×C4—112no—
514C2×C4—114no—
515C2×C4—114no—
516C2×C4—114no—
517C2×C4—114no—
518C2×C4—114no—
519C2×C4—1116no—
520C2×C4—112no—
521C2×C4—114no—
522C2×C4—228no—
523C2×C4—2216no—
524C2×C4—221no—
525C2×C4—222no—
526C2×C4—221no—
527C2×C4—222no—
528C2×C4—228no—
529C2×C4—2216no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—228no—
534C2×C4—224no—
535C2×C4C2×#433912yes—
536C2×C4C2×#433914yes—
537C2×C4C2×D4×D1112yes—
538C2×C4C2×D4×D1112yes—
539C2×C4C2×D4×D1112yes—
540C2×C4C2×Q8×D1114yes—
541C2×C4C2×Q8×D1114yes—
542C2×C4C2×Q8×D1114yes—
543C2×C4#41×D1112yes—
544C2×C4#41×D1114yes—
545C22—114no—
546C22—222no—
547C22—222no—
548C22—224no—
549C22—224no—
550C22C22×#433911yescharacteristic
551C22C22×D4×D1111yescharacteristic
552C22C22×Q8×D1112yes—
553C22C2×#41×D1112yes—
554C22C2×#41×D1111yescharacteristic
555C4—22no—
556C4—24no—
557C4—44no—
558C4—44no—
559C4—114no—
560C4—114no—
561C4—118no—
562C4—222no—
563C4—224no—
564C4—444no—
565C4—444no—
566C4#1062307914yes—
567C4#1062310918yescomplemented
568C4D11×C4⋊Q814yes—
569C2—224no—
570C2C2×D11×C4⋊Q811yescharacteristic
571C2D11×#53211yescharacteristic
572C2C2×#1062307911yescharacteristic
573C2D11×#53312yes—
574C2C2×#1062310912yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×C4⋊Q8C2
prime radicalC23×D11C24
hypercenterC4×C4⋊Q8D11
hypocenterC11#36645
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13077013C2semidirect
3. #13077012C2semidirect
4. #13076991C2semidirect
5. #13076975C2semidirect
10. C4×#66922C2semidirect
11. C4×#66941C2semidirect
12. C4×#66997C2semidirect
15. C4×C11×C4⋊Q8C2semidirect
126. C42×D11Q8semidirect
220. C4×C4⋊Q8D11semidirect
270. C4×D11C4⋊Q8semidirect
339. C4×C11#533semidirect
346. Dic11#533semidirect
494. C11#36645semidirect
567. C4#10623109semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
#130770132
#130770122
#130769912
#130769752
#130769692
#130769672
#130769652
#130769632
C4×#669222
C4×#669412
C4×#669972
#130710202
C43×D112
C4×C11×C4⋊Q82
#3664511