Finite Group Databasebeta

← #102×Dic22 #14770360

Subgroups — #102×Dic22 #14770360

Order 2816.

1314 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic22C211yesmaximal, characteristic
2C2×C8×Dic22C211yesmaximal, characteristic, complemented
3C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
4#13069577C211yesmaximal, characteristic, complemented
5#13069575C212yesmaximal, complemented
6#13069568C211yesmaximal, characteristic, complemented
7#13069566C212yesmaximal, complemented
8#13068616C211yesmaximal, characteristic
9#13068614C212yesmaximal
10#102×Dic11C212yesmaximal
11C4×C11×#102C211yesmaximal, characteristic
12C23×Dic22—21no—
13C2×C4×D4×C11C2211yescharacteristic
14C2×D4×Dic11C2212yes—
15C2×#66977—21no—
16D4×Dic22—24no—
17D4×Dic22C418yescomplemented
18C2×#66941C2212yes—
19C2×#66931—22no—
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22—21no—
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C2×#66896C2212yes—
28C2×Dic11⋊C8C2212yes—
29C2×C8×Dic11C2212yes—
30#10622589C2212yes—
31C4⋊C4×Dic11C2212yes—
32#10622548C2211yescharacteristic
33#10622541—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C8×Dic22—24no—
36#10622260—22no—
37C11×#340C2211yescharacteristic
38C11×#340C2211yescharacteristic
39#10622189C2212yes—
40#10622189C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×Dic11—22no—
47C22×Dic22—21no—
48C22×Dic22—22no—
49C22×Dic22—28no—
50C22×Dic22—44no—
51C22×Dic22—44no—
52C22×Dic22D411yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C4×D4×C11—22no—
56C4×D4×C11C2×C414yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11—22no—
64D4×Dic11—24no—
65D4×Dic11C2×C418yes—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11D411yescharacteristic
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2312yes—
72#66977—28no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4D412yes—
77C2×C4×Dic11—22no—
78C2×C4×Dic11C2312yes—
79C22×C11⋊C8C2312yes—
80#66941—24no—
81#66941C2×C418yes—
82#66931—216no—
83#66922—22no—
84#66922C2×C414yes—
85C4×Dic22—44no—
86C4×Dic22C2×C414yes—
87C4×Dic22D414yes—
88C11×#102—22no—
89C11×#102Q814yescomplemented
90C4×C8×C11—22no—
91C11×#95—21no—
92#66896—24no—
93C11⋊#95—22no—
94Dic11⋊C8—24no—
95C8×Dic11—24no—
96C4⋊(C11⋊C8)—22no—
97Q8×#102—111nomaximal, Sylow
98C24×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11C22×C412yes—
103C2×D4×C11C2×Q812yes—
104C2×D4×C11#4112yes—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—24no—
108C22×C4×C11—21no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—28no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—44no—
118C22×Dic11—44no—
119C22×Dic11C2×D412yes—
120C22×Dic11C2×D412yes—
121C2×Dic22—28no—
122C2×Dic22—24no—
123C2×Dic22—44no—
124C2×Dic22—44no—
125C2×Dic22—432no—
126C2×Dic22—42no—
127C2×Dic22—42no—
128C2×Dic22C22⋊C414yes—
129C2×Dic22D814yes—
130C2×Dic22SD1614yes—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11C2×Q812yescomplemented
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4C22×C412yes—
142C11×C4⋊C4C2×Q812yescomplemented
143C11×C22⋊C4—24no—
144C42×C11—42no—
145C42×C11C22×C412yes—
146C42×C11C2×D412yes—
147C22⋊Dic11—28no—
148C4⋊Dic11—24no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—42no—
153C4⋊Dic11—81no—
154C4⋊Dic11C22⋊C414yes—
155C4⋊Dic11C22×C414yes—
156Dic11⋊C4—28no—
157Dic11⋊C4—44no—
158Dic11⋊C4—82no—
159Dic11⋊C4C22⋊C418yes—
160C4×Dic11—44no—
161C4×Dic11C22×C414yes—
162C4×Dic11C2×D414yes—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×D4×Q8—111no—
167C2×C8×Q8—111no—
168Q8×C4⋊C4—111no—
169#1990—111no—
170#1990—112no—
171#1988—111no—
172#1988—112no—
173#1802—112no—
174#1802—111no—
175C4×#102—112no—
176C4×#102D1111yescharacteristic
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11C22×D411yescharacteristic
185D4×C11—22no—
186D4×C11—22no—
187D4×C11—22no—
188D4×C11C4×Q814yescomplemented
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—48no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11C2×C22⋊C412yes—
202C2×C4×C11C2×C22⋊C412yes—
203C2×C4×C11C2×D812yes—
204C2×C4×C11C2×SD1612yes—
205C2×C4×C11C23×C411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×Q811yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C112−1+411yescharacteristic
210C2×C4×C112−1+411yescharacteristic
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—24no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—416no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11C2×C22⋊C414yes—
221C2×Dic11C2×C22⋊C414yes—
222C2×Dic11C2×D814yes—
223C2×Dic11C2×SD1614yes—
224Dic22—48no—
225Dic22—416no—
226Dic22#102116yesdirect product factor
227C8×C11—22no—
228C8×C11—41no—
229C11⋊C8—42no—
230C23×Q8—221no—
231D4×Q8—118no—
232D4×Q8—224no—
233C2×C4⋊Q8—112no—
234C2×C4⋊Q8—111no—
235C2×C22⋊Q8—222no—
236C2×C22⋊Q8—221no—
237C2×C4×Q8—111no—
238C2×C4×Q8—221no—
239C2×C4×D4—112no—
240C2×C4×D4C2×D1111yescharacteristic
241C8×Q8—224no—
242C2×C4⋊C8—112no—
243C2×C4⋊C8—111no—
244C2×#102—112no—
245C2×#102C2×D1111yescharacteristic
246C2×#102C2×D1111yescharacteristic
247C2×C4×C8—112no—
248C2×C4×C8C2×D1111yescharacteristic
249#389—222no—
250#389—221no—
251#384—112no—
252#384—111no—
253C4×C4⋊C4—112no—
254C4×C4⋊C4C2×D1111yescharacteristic
255#340—112no—
256#340—112no—
257#340—112no—
258#340—112no—
259#340—112no—
260#340C2×D1111yescharacteristic
261#340C2×D1111yescharacteristic
262C22×C11—24no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11C22×C22⋊C411yescharacteristic
270C22×C11#54811yescharacteristic
271C22×C11D4×Q811yescharacteristic
272C22×C11C22×D811yescharacteristic
273C22×C11C22×SD1611yescharacteristic
274C22×C11#57711yescharacteristic
275C22×C11#57811yescharacteristic
276C4×C11—22no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11—81no—
280C4×C11C2×#10214yes—
281C4×C11C2×C4×Q811yescharacteristic
282C4×C11#51911yescharacteristic
283C4×C11#54811yescharacteristic
284C4×C11D4×Q811yescharacteristic
285Dic11—24no—
286Dic11—44no—
287Dic11—82no—
288Dic11C2×#10218yes—
289C22×Q8—111no—
290C22×Q8—222no—
291C22×Q8—228no—
292C22×Q8—221no—
293C22×Q8—444no—
294C22×Q8—444no—
295C22×D4C22×D1111yescharacteristic
296C23×C4—21no—
297C23×C4—222no—
298C22×C8—112no—
299C22×C8C22×D1111yescharacteristic
300C22×C8C22×D1111yescharacteristic
301C4⋊Q8—118no—
302C4⋊Q8—114no—
303C4⋊Q8—224no—
304C4⋊Q8—222no—
305C22⋊Q8—2216no—
306C22⋊Q8—228no—
307C4×Q8—114no—
308C4×Q8—114no—
309C4×Q8—444no—
310C4×D4—22no—
311C4×D4—118no—
312C4×D4—224no—
313C4×D4C4×D1114yes—
314C2×C4⋊C4—112no—
315C2×C4⋊C4—111no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4—222no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4C22×D1111yescharacteristic
325C2×C4⋊C4C22×D1111yescharacteristic
326C2×C4⋊C4C22×D1111yescharacteristic
327C2×C22⋊C4—21no—
328C2×C22⋊C4—222no—
329C2×C42—21no—
330C2×C42—112no—
331C2×C42—222no—
332C2×C42C22×D1111yescharacteristic
333C4⋊C8—224no—
334C4⋊C8—222no—
335#102—22no—
336#102—224no—
337#102Dic2214yesdirect product factor
338C4×C8—22no—
339C4×C8—224no—
340#95—21no—
341#95—222no—
342C2×C11—44no—
343C2×C11Q8×C22⋊C411yescharacteristic
344C2×C11C22×#10211yescharacteristic
345C2×C11#289811yescharacteristic
346C2×C11#335811yescharacteristic
347C2×C11#335911yescharacteristic
348C2×C11Q8×D811yescharacteristic
349C2×C11Q8×SD1611yescharacteristic
350C24—21no—
351C2×Q8—114no—
352C2×Q8—114no—
353C2×Q8—114no—
354C2×Q8—228no—
355C2×Q8—224no—
356C2×Q8—444no—
357C2×Q8—444no—
358C2×Q8—4432no—
359C2×Q8—442no—
360C2×Q8—442no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4C2×Dic2212yes—
365C2×D4C2×C4×D1112yes—
366C2×D4#433912yes—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—24no—
370C22×C4—21no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—228no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—444no—
379C22×C4—444no—
380C22×C4D4×D1111yescharacteristic
381C22×C4D4×D1111yescharacteristic
382C22×C4C23×D1111yescharacteristic
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—222no—
389C2×C8—222no—
390C2×C8—222no—
391C2×C8C2×Dic2212yescomplemented
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—118no—
397C4⋊C4—114no—
398C4⋊C4—114no—
399C4⋊C4—228no—
400C4⋊C4—224no—
401C4⋊C4—222no—
402C4⋊C4—222no—
403C4⋊C4—222no—
404C4⋊C4—444no—
405C4⋊C4—442no—
406C4⋊C4—881no—
407C4⋊C4—882no—
408C4⋊C4C2×Dic2212yescomplemented
409C4⋊C4C2×C4×D1112yes—
410C22⋊C4—24no—
411C22⋊C4—228no—
412C42—42no—
413C42—114no—
414C42—114no—
415C42—444no—
416C42C2×C4×D1112yes—
417C42D4×D1112yes—
418C11Q8×#10211yescharacteristic, complemented, Sylow
419C23—22no—
420C23—22no—
421C23—22no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23C2×D4×D1111yescharacteristic
427Q8—1116no—
428Q8—4416no—
429Q8—448no—
430D4—22no—
431D4—22no—
432D4—22no—
433D4C4×Dic2214yescomplemented
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—48no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—114no—
447C2×C4—114no—
448C2×C4—114no—
449C2×C4—114no—
450C2×C4—222no—
451C2×C4—222no—
452C2×C4—224no—
453C2×C4—4416no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4C22⋊C4×D1112yes—
460C2×C4C22⋊C4×D1112yes—
461C2×C4D8×D1112yes—
462C2×C4SD16×D1112yes—
463C2×C4C22×Dic2211yescharacteristic
464C2×C4C22×C4×D1111yescharacteristic
465C2×C4C2×#433911yescharacteristic
466C2×C4C2×D4×D1111yescharacteristic
467C2×C4#6704311yescharacteristic
468C2×C4#6704311yescharacteristic
469C8—22no—
470C8—41no—
471C8—442no—
472C22—24no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22C2×C22⋊C4×D1111yescharacteristic
480C22D4×Dic2211yescharacteristic
481C22#1062308311yescharacteristic
482C22C2×D8×D1111yescharacteristic
483C22C2×SD16×D1111yescharacteristic
484C22#1062330111yescharacteristic
485C22#1062330211yescharacteristic
486C4—22no—
487C4—42no—
488C4—42no—
489C4—81no—
490C4—118no—
491C4—224no—
492C4—444no—
493C4—882no—
494C4D11×#10214yes—
495C4C2×C4×Dic2211yescharacteristic
496C4#1062304711yescharacteristic
497C4D4×Dic2211yescharacteristic
498C4#1062308311yescharacteristic
499C2—44no—
500C2C22⋊C4×Dic2211yescharacteristic
501C2C2×D11×#10211yescharacteristic
502C2#1307714511yescharacteristic
503C2#1308124911yescharacteristic
504C2#1308125611yescharacteristic
505C2D8×Dic2211yescharacteristic
506C2SD16×Dic2211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC4×#102D11
hypocenterC11Q8×#102
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic22C2semidirect
3. C4⋊C4×Dic22C2semidirect
4. #13069577C2semidirect
5. #13069575C2semidirect
6. #13069568C2semidirect
7. #13069566C2semidirect
17. D4×Dic22C4semidirect
89. C11×#102Q8semidirect
136. C2×C8×C11C2×Q8semidirect
142. C11×C4⋊C4C2×Q8semidirect
188. D4×C11C4×Q8semidirect
226. Dic22#102direct (N × H)
337. #102Dic22direct (N × H)
391. C2×C8C2×Dic22semidirect
408. C4⋊C4C2×Dic22semidirect
418. C11Q8×#102semidirect
433. D4C4×Dic22semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic222
C2×C8×Dic222
C4⋊C4×Dic222
#130695772
#130695752
#130695682
#130695662
#130686162
#130686142
#102×Dic112
C4×C11×#1022
Q8×#10211