Finite Group Databasebeta

← #28400824

Subgroups — #28400824

Order 14464.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299209C211yesmaximal, characteristic, complemented
2#20299070C211yesmaximal, characteristic
3#20298938C211yesmaximal, characteristic, complemented
4#20298937C211yesmaximal, characteristic, complemented
5#20298899C211yesmaximal, characteristic, complemented
6#20298898C211yesmaximal, characteristic, complemented
7#20298800C211yesmaximal, characteristic, complemented
8#20298747C211yesmaximal, characteristic
9#20298747C211yesmaximal, characteristic
10#20298701C211yesmaximal, characteristic, complemented
11#20298699C211yesmaximal, characteristic, complemented
12SD16×Dic113C211yesmaximal, characteristic, complemented
13#20298683C211yesmaximal, characteristic, complemented
14#20298658C211yesmaximal, characteristic, complemented
15#461×C113C211yesmaximal, characteristic, complemented
16C2×D4×D113C2211yescharacteristic
17C2×#14268634C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19#16813617—21no—
20#16813617—21no—
21#16813614C2211yescharacteristic, complemented
22#16813612—21no—
23#16813612—21no—
24#16813598C2211yescharacteristic
25#16813598C2211yescharacteristic
26Q8×Dic113C2211yescharacteristic, complemented
27Q8×Dic113C2211yescharacteristic, complemented
28C4×D452C2211yescharacteristic
29D4×Dic113C2211yescharacteristic
30#16813584C2211yescharacteristic
31C4×C22⋊D113—21no—
32#16813582—21no—
33#16813580C2211yescharacteristic
34#16813579C2211yescharacteristic
35C2×#14268624—21no—
36C22⋊C4×D113—21no—
37#16813556C2211yescharacteristic, complemented
38#16813555C2211yescharacteristic, complemented
39#16813554C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41C4⋊#11744751C2211yescharacteristic, complemented
42#16813546C2211yescharacteristic, complemented
43#16813546C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813532C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C2×SD16×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54C4⋊Q8×C113C2211yescharacteristic, complemented
55C4×D4×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58#103×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C2×D452C2311yescharacteristic
61C2×C22⋊D113—21no—
62D4×D113—22no—
63D4×D113—22no—
64C22×Dic113—21no—
65C2×C4×D113—21no—
66C2×C4×D113—21no—
67C2×C4×D113C2311yescharacteristic
68#14268634—22no—
69#14268634—22no—
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C4⋊Dic113—21no—
73C4⋊Dic113—21no—
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626D411yescharacteristic
82#14268626D411yescharacteristic
83C22⋊Dic113—21no—
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624D411yescharacteristic
90#14268624D411yescharacteristic
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113C2311yescharacteristic
95C2×Q8×C113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C2×D4×C113C2311yescharacteristic
98C22×C4×C113—21no—
99SD16×C113—22no—
100SD16×C113—22no—
101C2×C8×C113C2311yescharacteristic
102C2×C8×C113C2311yescharacteristic
103C4⋊C4×C113—21no—
104C4⋊C4×C113—21no—
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113—21no—
110C22×D113—24no—
111C22×D113—81no—
112C22×D113—81no—
113C22×D113C2×D411yescharacteristic
114Q8×C113—21no—
115Q8×C113—21no—
116Q8×C113—21no—
117Q8×C113—21no—
118D4×C113—21no—
119D4×C113#4112yes—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—81no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2411yescharacteristic
127C22⋊D113—24no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—81no—
132C2×Dic113C2×D411yescharacteristic
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135D452—21no—
136D452#4112yes—
137C4×D113—21no—
138C4×D113—21no—
139C4×D113—81no—
140C4×D113—81no—
141C8×C113—21no—
142C8×C113—21no—
143#11744751—21no—
144#11744751—21no—
145C22×C113—22no—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113C22×D411yescharacteristic
149C2×D113—21no—
150C2×D113—22no—
151C2×D113—21no—
152C2×D113—21no—
153C2×D113—41no—
154C2×D113—41no—
155C2×D113—84no—
156C4×C113—21no—
157C4×C113—21no—
158C4×C113—41no—
159C4×C113—41no—
160C4×C113—41no—
161C4×C113C2×#4111yescharacteristic
162C4×C113C2×#4111yescharacteristic
163Dic113—21no—
164Dic113—21no—
165Dic113—21no—
166Dic113—41no—
167Dic113—41no—
168Dic113—41no—
169C2×C113—42no—
170C2×C113#52511yescharacteristic
171C2×C113#57711yescharacteristic
172C2×C113#57711yescharacteristic
173D113—41no—
174D113—42no—
175#3123—1131nomaximal, Sylow
176C113#312311yescharacteristic, complemented, Sylow
177#541—1131no—
178#518—1131no—
179#485—1131no—
180#485—1131no—
181#478—1131no—
182#478—1131no—
183#461—1131no—
184#461D11311yescharacteristic, complemented
185#450—1131no—
186#450—1131no—
187#440—1131no—
188#440—1131no—
189C4×SD16—1131no—
190C4×SD16—1131no—
191#433—1131no—
192C22×D4—1131no—
193C2×SD16—1131no—
194C2×SD16—1131no—
195C2×SD16C2×D11311yescharacteristic
196C2×SD16C2×D11311yescharacteristic
197C4⋊Q8C2×D11311yescharacteristic, complemented
198#126—2261no—
199#126—2261no—
200#125—1131no—
201#125—2261no—
202#125—2261no—
203C22⋊Q8—1131no—
204C22⋊Q8—1131no—
205C4×Q8—1131no—
206C4×Q8—1131no—
207C4×D4—1131no—
208C4×D4—1131no—
209C4×D4—1131no—
210C4×D4—2261no—
211C4×D4—2261no—
212C4×D4C2×D11311yescharacteristic
213#117—1131no—
214#117—1131no—
215C2×C22⋊C4—2261no—
216C2×C22⋊C4—2261no—
217#107—1131no—
218#107—1131no—
219#106—1131no—
220#106—1131no—
221C4⋊C8—1131no—
222C4⋊C8C2×D11311yescharacteristic, complemented
223#103—1131no—
224#103—1131no—
225#103C2×D11311yescharacteristic, complemented
226#103C2×D11311yescharacteristic, complemented
227#102—1131no—
228#102—1131no—
229#102—1131no—
230#102—1131no—
231C22⋊C8—1131no—
232C22⋊C8—1131no—
233#97—1131no—
234C4×C8—1131no—
235C24—2261no—
236C2×Q8C22×D11311yescharacteristic
237C2×Q8C22×D11311yescharacteristic
238C2×D4—1131no—
239C2×D4—2261no—
240C2×D4—2262no—
241C2×D4—2262no—
242C2×D4C22×D11311yescharacteristic
243C22×C4—21no—
244C22×C4—1131no—
245C22×C4—2261no—
246C22×C4—2261no—
247C22×C4—2261no—
248SD16—22no—
249SD16—22no—
250SD16—2262no—
251SD16—2262no—
252C2×C8—1131no—
253C2×C8—1131no—
254C2×C8C22×D11311yescharacteristic
255C2×C8C22×D11311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—1131no—
259C4⋊C4—1131no—
260C4⋊C4—1131no—
261C4⋊C4—1131no—
262C4⋊C4—1131no—
263C4⋊C4—2261no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4—2261no—
269C4⋊C4C22×D11311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—1131no—
272C22⋊C4—1131no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4—2261no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C42—1131no—
280C42—2261no—
281C42—2261no—
282C42—2261no—
283C42C22×D11311yescharacteristic
284C23—21no—
285C23—1131no—
286C23—9041no—
287C23—9041no—
288C23—2264no—
289C23—2261no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294D4—21no—
295D4—1132no—
296D4—2264no—
297D4—2261no—
298D4#1426864612yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—1131no—
304C2×C4—1131no—
305C2×C4—1131no—
306C2×C4—9041no—
307C2×C4—9041no—
308C2×C4—9041no—
309C2×C4—2261no—
310C2×C4—2261no—
311C2×C4—2261no—
312C2×C4—2261no—
313C2×C4—2261no—
314C2×C4D4×D11311yescharacteristic
315C2×C4D4×D11311yescharacteristic
316C2×C4C23×D11311yescharacteristic
317C8—21no—
318C8—21no—
319C8—2261no—
320C8—2261no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—9044no—
325C22—4521no—
326C22—4521no—
327C22—2261no—
328C22—2262no—
329C22—2261no—
330C22—2261no—
331C22C2×D4×D11311yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—4521no—
338C4—4521no—
339C4—4521no—
340C4—2261no—
341C4—2261no—
342C4—2261no—
343C4#41×D11311yescharacteristic
344C4C2×#1426864611yescharacteristic
345C2—42no—
346C2—4521no—
347C2—4522no—
348C2#2029910811yescharacteristic
349C2#2029940411yescharacteristic
350C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#461×C113C2
socleC22×C113C22×D4
prime radicalC2×D4×D113C22
hypercenter#461D113
hypocenterC113#3123
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #20299209C2semidirect
3. #20298938C2semidirect
4. #20298937C2semidirect
5. #20298899C2semidirect
6. #20298898C2semidirect
7. #20298800C2semidirect
10. #20298701C2semidirect
11. #20298699C2semidirect
12. SD16×Dic113C2semidirect
13. #20298683C2semidirect
14. #20298658C2semidirect
15. #461×C113C2semidirect
21. #16813614C22semidirect
26. Q8×Dic113C22semidirect
27. Q8×Dic113C22semidirect
37. #16813556C22semidirect
38. #16813555C22semidirect
39. #16813554C22semidirect
40. #16813553C22semidirect
41. C4⋊#11744751C22semidirect
42. #16813546C22semidirect
43. #16813546C22semidirect
50. #16813532C22semidirect
51. C8×Dic113C22semidirect
54. C4⋊Q8×C113C22semidirect
56. C4⋊C8×C113C22semidirect
57. #103×C113C22semidirect
58. #103×C113C22semidirect
176. C113#3123semidirect
184. #461D113semidirect
197. C4⋊Q8C2×D113semidirect
222. C4⋊C8C2×D113semidirect
225. #103C2×D113semidirect
226. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992092
#202990702
#202989382
#202989372
#202988992
#202988982
#202988002
#202987472
#202987012
#202986992
SD16×Dic1132
#202986832
#202986582
#461×C1132
#3123113