Finite Group Databasebeta

← #99×Dic22 #14770321

Subgroups — #99×Dic22 #14770321

Order 2816.

1354 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic22C211yesmaximal, characteristic
2C22⋊C4×Dic22C212yesmaximal, complemented
3#13069601C212yesmaximal, complemented
4#13069599C214yesmaximal, complemented
5#13068604C211yesmaximal, characteristic
6#13068602C212yesmaximal
7#99×Dic11C212yesmaximal
8C4×C11×#99C211yesmaximal, characteristic
9C23×Dic22C411yescharacteristic, complemented
10C23×Dic22C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×D4×Dic11C2212yes—
13C2×#66977C411yescharacteristic, complemented
14C2×#66977C2211yescharacteristic
15D4×Dic22—22no—
16D4×Dic22—24no—
17D4×Dic22—22no—
18C2×#66941C412yescomplemented
19C2×#66931C412yescomplemented
20C2×#66931C2212yes—
21C2×#66922C411yescharacteristic, complemented
22C2×C4×Dic22—22no—
23C2×C4×Dic22C411yescharacteristic, complemented
24C2×C11×#99C2211yescharacteristic
25C2×C11×#99C2211yescharacteristic
26C4×C11×C22⋊C4C2212yes—
27C2×#66898C2212yes—
28#10622825C2212yes—
29#10622555C2214yes—
30C22⋊C4×Dic11C2214yes—
31#10622542—22no—
32#10622259—24no—
33C11×#342C2212yes—
34#10622165C2214yes—
35#10622165C2214yes—
36#10622164C2212yes—
37C22×D4×C11C2311yescharacteristic
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2×C412yes—
41C23×Dic11C2312yes—
42C22×Dic22—21no—
43C22×Dic22—22no—
44C22×Dic22—21no—
45C22×Dic22—44no—
46C22×Dic22—44no—
47C22×Dic22C2×C411yescharacteristic
48C22×Dic22C2×C411yescharacteristic
49C22×Dic22C2×C412yes—
50C22×Dic22C2×C411yescharacteristic
51C22×Dic22C2×C412yes—
52C22×Dic22D412yes—
53C22×Dic22D414yes—
54C22×Dic22D412yes—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C2×C11×C4⋊C4C2×C411yescharacteristic
58C2×C11×C22⋊C4C2×C411yescharacteristic
59C2×C11×C22⋊C4C2312yes—
60C2×C11×C22⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4C2312yes—
62C2×C42×C11—22no—
63C2×C42×C11C2×C411yescharacteristic
64C2×C22⋊Dic11C2×C412yes—
65C2×C22⋊Dic11C2314yes—
66C2×C22⋊Dic11C2312yes—
67D4×Dic11—24no—
68D4×Dic11—24no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11C2×C411yescharacteristic
71C2×C4⋊Dic11C2×C412yes—
72C2×C4⋊Dic11C2×C412yes—
73#66977—22no—
74#66977—22no—
75#66977—22no—
76#66977—22no—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4C2×C412yes—
79C2×Dic11⋊C4C2×C412yes—
80C2×Dic11⋊C4C2×C412yes—
81C2×C4×Dic11—24no—
82C2×C4×Dic11C2×C412yes—
83#66941—24no—
84#66941—24no—
85#66931—24no—
86#66931—24no—
87#66931—24no—
88#66931—24no—
89#66922—22no—
90#66922—22no—
91C4×Dic22—21no—
92C4×Dic22—22no—
93C4×Dic22—21no—
94C4×Dic22—48no—
95C11×#99—22no—
96C11×#99Q814yescomplemented
97C11×#95—22no—
98#66898—24no—
99C11⋊#95—22no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102Q8×#99—111nomaximal, Sylow
103C24×C11C22×C411yescharacteristic
104C24×C11C2411yescharacteristic
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11C2×Q812yes—
108C2×D4×C11#4112yes—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11C22×C411yescharacteristic
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—24no—
125C22×Dic11—44no—
126C22×Dic11—44no—
127C22×Dic11C22×C412yes—
128C22×Dic11C22×C412yes—
129C22×Dic11C22×C412yes—
130C22×Dic11C22×C412yes—
131C22×Dic11C2×D414yes—
132C22×Dic11C2×D414yes—
133C2×Dic22—28no—
134C2×Dic22—24no—
135C2×Dic22—22no—
136C2×Dic22—22no—
137C2×Dic22—21no—
138C2×Dic22—21no—
139C2×Dic22—42no—
140C2×Dic22—44no—
141C2×Dic22—42no—
142C2×Dic22—44no—
143C2×Dic22—48no—
144C2×Dic22—48no—
145C2×Dic22—44no—
146C2×Dic22—44no—
147C2×Dic22—44no—
148C2×Dic22C22⋊C412yes—
149C2×Dic22C22⋊C411yescharacteristic
150C2×Dic22C22⋊C412yes—
151C2×Dic22C22⋊C414yes—
152C2×Dic22C22⋊C412yes—
153C2×Dic22C22⋊C414yes—
154C2×Dic22C22⋊C411yescharacteristic
155C11×C4⋊C4—22no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4C2×Q814yescomplemented
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—44no—
165C22⋊Dic11—24no—
166C22⋊Dic11—24no—
167C22⋊Dic11—24no—
168C22⋊Dic11—24no—
169C4⋊Dic11—24no—
170C4⋊Dic11—24no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—44no—
174Dic11⋊C4—22no—
175Dic11⋊C4—22no—
176Dic11⋊C4—24no—
177Dic11⋊C4—24no—
178Dic11⋊C4—48no—
179C4×Dic11—22no—
180C4×Dic11—22no—
181C4×Dic11—48no—
182C2×D4×Q8—111no—
183Q8×C22⋊C4—112no—
184#1996—112no—
185#1996—114no—
186#1799—112no—
187#1799—111no—
188C4×#99—112no—
189C4×#99D1111yescharacteristic
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11C4×Q812yescomplemented
197C23×C11C23×C411yescharacteristic
198C23×C11C22×D412yes—
199C23×C11C22×Q811yescharacteristic
200C23×C11C2×#4111yescharacteristic
201C23×C112−1+412yes—
202D4×C11—24no—
203D4×C11—24no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—24no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11C2×C22⋊C412yes—
223C2×C4×C11C2×C22⋊C411yescharacteristic
224C2×C4×C11C2×C22⋊C411yescharacteristic
225C2×C4×C11C4×Q812yescomplemented
226C2×Dic11—28no—
227C2×Dic11—24no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—42no—
231C2×Dic11—44no—
232C2×Dic11—44no—
233C2×Dic11—44no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—44no—
237C2×Dic11—44no—
238C2×Dic11—44no—
239C2×Dic11C2×C22⋊C412yes—
240C2×Dic11C2×C22⋊C414yes—
241C2×Dic11C2×C22⋊C412yes—
242Dic22—22no—
243Dic22—24no—
244Dic22—24no—
245Dic22—28no—
246Dic22—44no—
247Dic22—42no—
248Dic22—44no—
249Dic22—42no—
250Dic22—42no—
251Dic22—44no—
252Dic22#9914yesdirect product factor
253C23×Q8—111no—
254C23×Q8—111no—
255D4×Q8—222no—
256D4×Q8—222no—
257D4×Q8—224no—
258C2×C4⋊Q8—112no—
259C2×C4⋊Q8—111no—
260C2×C22⋊Q8—111no—
261C2×C22⋊Q8—111no—
262C2×C22⋊Q8—112no—
263C2×C22⋊Q8—112no—
264C2×C4×Q8—111no—
265C2×C4×Q8—222no—
266C2×C4×D4—112no—
267C2×C4×D4C2×D1111yescharacteristic
268C2×#99—112no—
269C2×#99C2×D1111yescharacteristic
270C2×#99C2×D1111yescharacteristic
271#391—224no—
272#391—222no—
273#380—112no—
274#380—114no—
275C4×C22⋊C4—114no—
276C4×C22⋊C4C2×D1112yes—
277#342—112no—
278#342—114no—
279#342—114no—
280#342C2×D1112yes—
281C22×C11—22no—
282C22×C11—21no—
283C22×C11—22no—
284C22×C11—21no—
285C22×C11—22no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—41no—
292C22×C11—41no—
293C22×C11C22×C22⋊C411yescharacteristic
294C22×C11C2×C4×Q811yescharacteristic
295C22×C11#51911yescharacteristic
296C22×C11#54812yes—
297C22×C11D4×Q812yes—
298C4×C11—22no—
299C4×C11—21no—
300C4×C11—22no—
301C4×C11—44no—
302C4×C11—41no—
303C4×C11—41no—
304C4×C11—82no—
305C4×C11C2×#9912yes—
306Dic11—22no—
307Dic11—24no—
308Dic11—42no—
309Dic11—42no—
310Dic11—84no—
311Dic11C2×#9914yes—
312C22×Q8—111no—
313C22×Q8—112no—
314C22×Q8—111no—
315C22×Q8—112no—
316C22×Q8—111no—
317C22×Q8—112no—
318C22×Q8—114no—
319C22×Q8—112no—
320C22×Q8—221no—
321C22×Q8—222no—
322C22×Q8—221no—
323C22×Q8—444no—
324C22×Q8—444no—
325C22×D4C22×D1111yescharacteristic
326C23×C4—112no—
327C23×C4—112no—
328C23×C4C4×D1111yescharacteristic
329C23×C4C22×D1111yescharacteristic
330C4⋊Q8—222no—
331C4⋊Q8—222no—
332C4⋊Q8—224no—
333C4⋊Q8—224no—
334C22⋊Q8—224no—
335C22⋊Q8—224no—
336C22⋊Q8—224no—
337C22⋊Q8—224no—
338C22⋊Q8—222no—
339C22⋊Q8—222no—
340C22⋊Q8—222no—
341C22⋊Q8—222no—
342C4×Q8—221no—
343C4×Q8—222no—
344C4×Q8—221no—
345C4×Q8—448no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—224no—
349C4×D4—224no—
350C2×C4⋊C4—112no—
351C2×C4⋊C4—112no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—112no—
354C2×C4⋊C4—112no—
355C2×C4⋊C4—112no—
356C2×C4⋊C4—224no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4C4×D1111yescharacteristic
359C2×C22⋊C4—112no—
360C2×C22⋊C4—112no—
361C2×C22⋊C4—114no—
362C2×C22⋊C4C4×D1111yescharacteristic
363C2×C22⋊C4C22×D1112yes—
364C2×C22⋊C4C22×D1111yescharacteristic
365C2×C22⋊C4C22×D1112yes—
366C2×C42—22no—
367C2×C42—112no—
368C2×C42—224no—
369C2×C42C4×D1111yescharacteristic
370#99—22no—
371#99—224no—
372#99Dic2214yesdirect product factor
373#95—22no—
374#95—224no—
375#95—224no—
376#95—222no—
377C2×C11—22no—
378C2×C11—22no—
379C2×C11—21no—
380C2×C11—21no—
381C2×C11—42no—
382C2×C11Q8×C22⋊C411yescharacteristic
383C2×C11C22×#9911yescharacteristic
384C2×C11#288411yescharacteristic
385C24C2×C4×D1111yescharacteristic
386C24C23×D1111yescharacteristic
387C2×Q8—111no—
388C2×Q8—112no—
389C2×Q8—111no—
390C2×Q8—114no—
391C2×Q8—112no—
392C2×Q8—114no—
393C2×Q8—112no—
394C2×Q8—222no—
395C2×Q8—222no—
396C2×Q8—228no—
397C2×Q8—224no—
398C2×Q8—221no—
399C2×Q8—221no—
400C2×Q8—444no—
401C2×Q8—442no—
402C2×Q8—442no—
403C2×Q8—444no—
404C2×Q8—448no—
405C2×Q8—444no—
406C2×Q8—444no—
407C2×Q8—448no—
408C2×Q8—444no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4C2×Dic2212yes—
412C2×D4#433912yes—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—112no—
420C22×C4—114no—
421C22×C4—112no—
422C22×C4—114no—
423C22×C4—112no—
424C22×C4—112no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—224no—
428C22×C4—444no—
429C22×C4—444no—
430C22×C4C2×C4×D1111yescharacteristic
431C22×C4C2×C4×D1111yescharacteristic
432C22×C4C2×C4×D1111yescharacteristic
433C22×C4C2×C4×D1111yescharacteristic
434C22×C4C2×C4×D1111yescharacteristic
435C22×C4D4×D1112yes—
436C22×C4D4×D1112yes—
437C4⋊C4—22no—
438C4⋊C4—224no—
439C4⋊C4—222no—
440C4⋊C4—222no—
441C4⋊C4—224no—
442C4⋊C4—224no—
443C4⋊C4—221no—
444C4⋊C4—221no—
445C4⋊C4—224no—
446C4⋊C4—444no—
447C4⋊C4—448no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—224no—
454C22⋊C4—224no—
455C22⋊C4—224no—
456C22⋊C4—224no—
457C22⋊C4C2×Dic2214yescomplemented
458C42—21no—
459C42—21no—
460C42—44no—
461C42—222no—
462C42—222no—
463C42—448no—
464C11Q8×#9911yescharacteristic, complemented, Sylow
465C23—21no—
466C23—21no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23C4×Dic2212yescomplemented
472C23C22×Dic2211yescharacteristic
473C23C22×C4×D1111yescharacteristic
474C23C2×#433911yescharacteristic
475C23C2×D4×D1112yes—
476C23#6704312yes—
477Q8—114no—
478Q8—224no—
479Q8—228no—
480Q8—222no—
481Q8—224no—
482Q8—442no—
483Q8—444no—
484Q8—442no—
485Q8—444no—
486Q8—444no—
487Q8—442no—
488D4—24no—
489D4—24no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—24no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—112no—
509C2×C4—112no—
510C2×C4—114no—
511C2×C4—228no—
512C2×C4—224no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—444no—
516C2×C4—444no—
517C2×C4—442no—
518C2×C4—444no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—444no—
522C2×C4—444no—
523C2×C4—444no—
524C2×C4C4×Dic2212yescomplemented
525C2×C4C22⋊C4×D1111yescharacteristic
526C2×C4C22⋊C4×D1112yes—
527C2×C4C22⋊C4×D1111yescharacteristic
528C22—22no—
529C22—21no—
530C22—22no—
531C22—21no—
532C22—22no—
533C22—41no—
534C22—41no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—41no—
539C22—41no—
540C22C2×C4×Dic2211yescharacteristic
541C22C2×C22⋊C4×D1111yescharacteristic
542C22#1062304711yescharacteristic
543C22D4×Dic2212yes—
544C22#1062308312yes—
545C4—21no—
546C4—22no—
547C4—22no—
548C4—44no—
549C4—41no—
550C4—41no—
551C4—82no—
552C4—114no—
553C4—222no—
554C4—224no—
555C4—442no—
556C4—442no—
557C4—884no—
558C4D11×#9912yes—
559C2—22no—
560C2—22no—
561C2—21no—
562C2—21no—
563C2—42no—
564C2C22⋊C4×Dic2211yescharacteristic
565C2C2×D11×#9911yescharacteristic
566C2#1307707811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC4×C11×#99C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×C11C23
cosocleC24×C11C24
hypercenterC4×#99D11
hypocenterC11Q8×#99
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×Dic22C2semidirect
3. #13069601C2semidirect
4. #13069599C2semidirect
9. C23×Dic22C4semidirect
13. C2×#66977C4semidirect
18. C2×#66941C4semidirect
19. C2×#66931C4semidirect
21. C2×#66922C4semidirect
23. C2×C4×Dic22C4semidirect
96. C11×#99Q8semidirect
161. C11×C22⋊C4C2×Q8semidirect
196. C23×C11C4×Q8semidirect
225. C2×C4×C11C4×Q8semidirect
252. Dic22#99direct (N × H)
372. #99Dic22direct (N × H)
457. C22⋊C4C2×Dic22semidirect
464. C11Q8×#99semidirect
471. C23C4×Dic22semidirect
524. C2×C4C4×Dic22semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic222
C22⋊C4×Dic222
#130696012
#130695992
#130686042
#130686022
#99×Dic112
C4×C11×#992
Q8×#9911