Finite Group Databasebeta

← #28400732

Subgroups — #28400732

Order 14464.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299152C211yesmaximal, characteristic, complemented
2C4×#14268646C211yesmaximal, characteristic
3#20298941C211yesmaximal, characteristic, complemented
4#20298937C211yesmaximal, characteristic, complemented
5#20298892C211yesmaximal, characteristic, complemented
6#20298886C211yesmaximal, characteristic, complemented
7#20298807C211yesmaximal, characteristic, complemented
8#20298801C211yesmaximal, characteristic, complemented
9#20298761C211yesmaximal, characteristic
10#20298757C211yesmaximal, characteristic
11#20298706C211yesmaximal, characteristic, complemented
12#20298703C211yesmaximal, characteristic, complemented
13#20298698C211yesmaximal, characteristic, complemented
14#20298653C211yesmaximal, characteristic, complemented
15#440×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20#16813621C2211yescharacteristic
21#16813620C2211yescharacteristic
22#16813612—21no—
23#16813602C2211yescharacteristic
24#16813600—21no—
25#16813598C2211yescharacteristic
26C4×Dic226—21no—
27C4×Dic226C2211yescharacteristic
28C4×Dic226C2211yescharacteristic
29#16813587C2211yescharacteristic
30D4×Dic113C2211yescharacteristic
31C4×C22⋊D113—21no—
32#16813582—21no—
33#16813580C2211yescharacteristic
34#16813579—21no—
35#16813578—21no—
36C2×C4×Dic113—21no—
37C42×D113C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813533C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59#14268646—22no—
60#14268646—22no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63C2×Dic226C2311yescharacteristic
64C2×C22⋊D113—21no—
65C22×Dic113—21no—
66C22×Dic113—21no—
67C2×C4×D113D411yescharacteristic
68C2×C4×D113D411yescharacteristic
69C2×C4×D113C2311yescharacteristic
70Dic452—22no—
71#14268637—22no—
72#14268635—22no—
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C4⋊Dic113—21no—
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85C22⋊Dic113—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89C4×Dic113—21no—
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113D411yescharacteristic
94C4×Dic113D411yescharacteristic
95C4×Dic113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C2×D4×C113C2311yescharacteristic
98C22×C4×C113—21no—
99SD16×C113—22no—
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
106C42×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113C2×D411yescharacteristic
110Q8×C113—21no—
111Q8×C113—21no—
112D4×C113—21no—
113D4×C113#4112yes—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—42no—
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2411yescharacteristic
121C22⋊D113—24no—
122C2×Dic113—24no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—42no—
128C2×Dic113C2×D411yescharacteristic
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131C4×D113—21no—
132C4×D113—21no—
133C4×D113—22no—
134C4×D113—41no—
135Dic226—21no—
136Dic226—21no—
137Dic226—21no—
138Dic226—42no—
139Dic226#4112yes—
140C8×C113—21no—
141C8×C113—21no—
142#11744751—21no—
143#11744751—21no—
144C22×C113—22no—
145C22×C113—41no—
146C22×C113—41no—
147C22×C113C22×D411yescharacteristic
148C2×D113—21no—
149C2×D113—21no—
150C2×D113—21no—
151C4×C113—21no—
152C4×C113—21no—
153C4×C113—41no—
154C4×C113—41no—
155C4×C113—41no—
156C4×C113C2×#4111yescharacteristic
157C4×C113C2×#4111yescharacteristic
158Dic113—22no—
159Dic113—21no—
160Dic113—21no—
161Dic113—41no—
162Dic113—41no—
163Dic113—41no—
164Dic113#13712yes—
165C2×C113—42no—
166C2×C113#52511yescharacteristic
167C2×C113C2×#13711yescharacteristic
168C2×C113#57511yescharacteristic
169D113—41no—
170#3116—1131nomaximal, Sylow
171C113#311611yescharacteristic, complemented, Sylow
172#533—1131no—
173C4×#41—1131no—
174#485—1131no—
175#485—1131no—
176#477—1131no—
177#476—1131no—
178#462—1131no—
179#461—1131no—
180#452—1131no—
181#452—1131no—
182#441—1131no—
183#441—1131no—
184#440—1131no—
185#440D11311yescharacteristic, complemented
186#432—1131no—
187C2×#41—1131no—
188C2×Q16—1131no—
189C2×Q16—1131no—
190C2×SD16—1131no—
191C2×SD16C2×D11311yescharacteristic
192C4⋊Q8—1131no—
193C4⋊Q8—1131no—
194#125—2261no—
195C22⋊Q8—1131no—
196C22⋊Q8—1131no—
197C22⋊Q8—2261no—
198C4×Q8—1131no—
199C4×Q8—1131no—
200C4×Q8—1131no—
201C4×Q8—2261no—
202C4×Q8C2×D11311yescharacteristic
203C4×D4—1131no—
204C4×D4—2261no—
205C4×D4—2261no—
206C4×D4C2×D11311yescharacteristic
207#117—1131no—
208#117—2261no—
209#117—2261no—
210C2×C42—1131no—
211C2×C42—2261no—
212#107—1131no—
213#107C2×D11311yescharacteristic
214#106—1131no—
215#106—1131no—
216C4⋊C8—1131no—
217C4⋊C8—1131no—
218#103—1131no—
219#103—1131no—
220#103—1131no—
221#103—1131no—
222#103—1131no—
223#103C2×D11311yescharacteristic
224#102—1131no—
225#102C2×D11311yescharacteristic
226C22⋊C8—1131no—
227C22⋊C8—1131no—
228#97—1131no—
229#97C2×D11311yescharacteristic
230#41—2262no—
231#41—2262no—
232C2×Q8—1131no—
233C2×Q8—1131no—
234C2×Q8—2261no—
235C2×Q8C22×D11311yescharacteristic
236C2×D4—2261no—
237C2×D4C22×D11311yescharacteristic
238C22×C4—21no—
239C22×C4—1131no—
240C22×C4—1131no—
241C22×C4—1131no—
242C22×C4—2261no—
243C22×C4—2261no—
244Q16—2262no—
245Q16—2262no—
246SD16—22no—
247SD16—2262no—
248C2×C8—1131no—
249C2×C8—1131no—
250C2×C8C22×D11311yescharacteristic
251C2×C8C22×D11311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—1131no—
254C4⋊C4—1131no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4—2261no—
263C4⋊C4C22×D11311yescharacteristic
264C4⋊C4C22×D11311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C42—21no—
271C42—1131no—
272C42—1131no—
273C42—1131no—
274C42—2261no—
275C42—2261no—
276C42—2261no—
277C42—2261no—
278C42C22×D11311yescharacteristic
279C23—21no—
280C23—1131no—
281Q8—21no—
282Q8—21no—
283Q8—1132no—
284Q8—4522no—
285Q8—2261no—
286Q8—2261no—
287Q8—2261no—
288D4—21no—
289D4—2264no—
290D4#1426864712yes—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—1131no—
296C2×C4—1131no—
297C2×C4—1131no—
298C2×C4—4521no—
299C2×C4—4522no—
300C2×C4—2262no—
301C2×C4—2261no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4—2264no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4D4×D11311yescharacteristic
309C2×C4D4×D11311yescharacteristic
310C2×C4C23×D11311yescharacteristic
311C8—21no—
312C8—21no—
313C8—2261no—
314C8—2261no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—2261no—
319C22—2261no—
320C22—2261no—
321C22C2×D4×D11311yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—1132no—
328C4—4521no—
329C4—4521no—
330C4—4521no—
331C4—2261no—
332C4—2262no—
333C4—2261no—
334C4#41×D11311yescharacteristic
335C4C2×#1426864711yescharacteristic
336C2—42no—
337C2—4521no—
338C2#2029910711yescharacteristic
339C2#137×D11311yescharacteristic
340C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#440×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268646C22
hypercenter#440D113
hypocenterC113#3116
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #20299152C2semidirect
3. #20298941C2semidirect
4. #20298937C2semidirect
5. #20298892C2semidirect
6. #20298886C2semidirect
7. #20298807C2semidirect
8. #20298801C2semidirect
11. #20298706C2semidirect
12. #20298703C2semidirect
13. #20298698C2semidirect
14. #20298653C2semidirect
15. #440×C113C2semidirect
171. C113#3116semidirect
185. #440D113semidirect

Maximal subgroups

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

subgroupindex
#202991522
C4×#142686462
#202989412
#202989372
#202988922
#202988862
#202988072
#202988012
#202987612
#202987572
#202987062
#202987032
#202986982
#202986532
#440×C1132
#3116113