Finite Group Databasebeta

← #28401101

Subgroups — #28401101

Order 14464.

340 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299228C211yesmaximal, characteristic
2#20299225C211yesmaximal, characteristic
3#20299007C211yesmaximal, characteristic, complemented
4#20299006C211yesmaximal, characteristic, complemented
5#20299005C211yesmaximal, characteristic, complemented
6#20298999C211yesmaximal, characteristic, complemented
7#20298997C211yesmaximal, characteristic, complemented
8#20298995C211yesmaximal, characteristic, complemented
9#20298994C211yesmaximal, characteristic, complemented
10#20298639C211yesmaximal, characteristic
11#20298637C211yesmaximal, characteristic
12#20298635C211yesmaximal, characteristic
13#106×D113C211yesmaximal, characteristic
14#20298555C211yesmaximal, characteristic
15#501×C113C211yesmaximal, characteristic, complemented
16C2×#14268630C2211yescharacteristic
17C2×C8×D113C2211yescharacteristic
18#16813622C2211yescharacteristic
19#16813621—21no—
20#16813621C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813620—21no—
23#16813614C2211yescharacteristic
24#16813613C2211yescharacteristic
25#16813613C2211yescharacteristic
26#16813612—21no—
27#16813612—21no—
28#16813602—21no—
29#16813600—21no—
30#16813600—21no—
31#16813598—21no—
32#16813580C2211yescharacteristic
33#16813580C2211yescharacteristic
34#16813579C2211yescharacteristic
35C4⋊C4×D113C2211yescharacteristic
36C4⋊C4×D113C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813554C2211yescharacteristic
42#16813554C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813553C2211yescharacteristic
45#16813553C2211yescharacteristic
46#16813553C2211yescharacteristic
47#16813553C2211yescharacteristic
48#16813553C2211yescharacteristic
49#16813532C2211yescharacteristic
50C4×#11744751C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C4⋊Q8×C113C2211yescharacteristic
53#125×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic
57#106×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226—21no—
61C2×Dic226—21no—
62C2×C4×D113—21no—
63C2×C4×D113—21no—
64C2×C4×D113C2311yescharacteristic
65#14268630Q814yescomplemented
66C2×#11744751C2311yescharacteristic
67C2×#11744751C2311yescharacteristic
68C8×D113Q814yescomplemented
69C4⋊Dic113—21no—
70C4⋊Dic113—21no—
71C4⋊Dic113—21no—
72C4⋊Dic113C2311yescharacteristic
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626D411yescharacteristic
85#14268626D411yescharacteristic
86#14268624—21no—
87#14268624—21no—
88#14268624D411yescharacteristic
89#14268624D411yescharacteristic
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113C2311yescharacteristic
93C2×Q8×C113—21no—
94C2×C8×C113C2311yescharacteristic
95C2×C8×C113C2311yescharacteristic
96C4⋊C4×C113—21no—
97C4⋊C4×C113—21no—
98C4⋊C4×C113—21no—
99C4⋊C4×C113C2311yescharacteristic
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C42×C113C2311yescharacteristic
104C22×D113C2×D411yescharacteristic
105Q8×C113—81no—
106C2×C4×C113—21no—
107C2×C4×C113—21no—
108C2×C4×C113—21no—
109C2×C4×C113—21no—
110C2×C4×C113C2×D411yescharacteristic
111C2×C4×C113C2×D411yescharacteristic
112C2×C4×C113C2411yescharacteristic
113C2×Dic113—21no—
114C2×Dic113—21no—
115C2×Dic113—21no—
116C2×Dic113—21no—
117C2×Dic113C2×D411yescharacteristic
118C2×Dic113C2×D411yescharacteristic
119C2×Dic113C2×D411yescharacteristic
120C4×D113—81no—
121C4×D113—81no—
122C4×D113C2×Q812yes—
123C4×D113C2×Q812yes—
124Dic226—81no—
125Dic226—81no—
126Dic226—81no—
127C8×C113C2×Q812yes—
128C8×C113C2×Q812yes—
129#11744751C2×Q812yes—
130#11744751C2×Q812yes—
131C22×C113C22×D411yescharacteristic
132C2×D113—21no—
133C2×D113—21no—
134C2×D113C4⋊Q812yes—
135C4×C113—21no—
136C4×C113—21no—
137C4×C113—41no—
138C4×C113—41no—
139C4×C113—41no—
140C4×C113—41no—
141C4×C113C22×Q811yescharacteristic
142C4×C113C22×Q811yescharacteristic
143Dic113—21no—
144Dic113—21no—
145Dic113—41no—
146Dic113—41no—
147Dic113—41no—
148Dic113—41no—
149Dic113C4⋊Q812yes—
150C2×C113C2×C4⋊Q811yescharacteristic
151C2×C113#57711yescharacteristic
152C2×C113#57711yescharacteristic
153D113—22no—
154#3163—1131nomaximal, Sylow
155C113#316311yescharacteristic, complemented, Sylow
156#544—1131no—
157#544—1131no—
158#501—1131no—
159#501—1131no—
160#501—1131no—
161#501D11311yescharacteristic, complemented
162#499—1131no—
163#499—1131no—
164#498—1131no—
165#498—1131no—
166#428—1131no—
167#428—1131no—
168#427—1131no—
169C2×#106—1131no—
170#405—1131no—
171C2×M16—1131no—
172C22×C8—1131no—
173C4⋊Q8—1131no—
174C4⋊Q8—1131no—
175C4⋊Q8—1131no—
176C4⋊Q8—2261no—
177C4⋊Q8—2261no—
178C4⋊Q8C2×D11311yescharacteristic
179#125—1131no—
180#125—1131no—
181#125—1131no—
182#125—2261no—
183#125—2261no—
184#125C2×D11311yescharacteristic
185C22⋊Q8—2261no—
186C22⋊Q8—2261no—
187C22⋊Q8—2261no—
188C22⋊Q8—2261no—
189#117—1131no—
190#117—1131no—
191#117—1131no—
192C2×C4⋊C4—1131no—
193C2×C4⋊C4—1131no—
194#107—1131no—
195#107—1131no—
196#107—1131no—
197#107—1131no—
198#107C2×D11311yescharacteristic
199#107C2×D11311yescharacteristic
200#106—1131no—
201#106—1131no—
202#106—1131no—
203#106—1131no—
204#106—1131no—
205#106—1131no—
206#106—1131no—
207#106—1131no—
208#106C2×D11311yescharacteristic
209#106C2×D11311yescharacteristic
210#97—1131no—
211#97C2×D11311yescharacteristic
212C4×C8—1131no—
213C4×C8—1131no—
214C2×Q8—21no—
215C2×Q8—2261no—
216C2×Q8—2261no—
217C2×Q8—2261no—
218C22×C4—1131no—
219C22×C4—2261no—
220C22×C4—2261no—
221M16—1134no—
222C2×C8—1131no—
223C2×C8—1131no—
224C2×C8—1134no—
225C2×C8C22×D11311yescharacteristic
226C2×C8C22×D11311yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—1131no—
231C4⋊C4—1131no—
232C4⋊C4—1131no—
233C4⋊C4—1131no—
234C4⋊C4—1131no—
235C4⋊C4—1131no—
236C4⋊C4—2261no—
237C4⋊C4—2261no—
238C4⋊C4—2261no—
239C4⋊C4—2261no—
240C4⋊C4—2261no—
241C4⋊C4—2261no—
242C4⋊C4—2261no—
243C4⋊C4—2261no—
244C4⋊C4—2261no—
245C4⋊C4—2261no—
246C4⋊C4—2261no—
247C4⋊C4C22×D11311yescharacteristic
248C4⋊C4C22×D11311yescharacteristic
249C4⋊C4C22×D11311yescharacteristic
250C4⋊C4C22×D11311yescharacteristic
251C22⋊C4—1131no—
252C22⋊C4—1131no—
253C22⋊C4—2261no—
254C22⋊C4—2261no—
255C42—1131no—
256C42—2261no—
257C42—2261no—
258C42C22×D11311yescharacteristic
259C23—1131no—
260Q8—81no—
261Q8—9041no—
262Q8—9041no—
263Q8—9041no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—1131no—
269C2×C4—1132no—
270C2×C4—1132no—
271C2×C4—1131no—
272C2×C4—1131no—
273C2×C4—9041no—
274C2×C4—9041no—
275C2×C4—2261no—
276C2×C4—2261no—
277C2×C4—2261no—
278C2×C4—2261no—
279C2×C4D4×D11311yescharacteristic
280C2×C4D4×D11311yescharacteristic
281C2×C4C23×D11311yescharacteristic
282C8—1132no—
283C8—1132no—
284C8Q8×D11312yes—
285C8Q8×D11312yes—
286C22—1132no—
287C22—2261no—
288C22—2261no—
289C22C2×D4×D11311yescharacteristic
290C4—21no—
291C4—21no—
292C4—41no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—1132no—
297C4—4521no—
298C4—4521no—
299C4—4521no—
300C4—4521no—
301C4—2261no—
302C4—2261no—
303C4C2×Q8×D11311yescharacteristic
304C4C2×Q8×D11311yescharacteristic
305C2—2262no—
306C2C4⋊Q8×D11311yescharacteristic
307C2#2029940711yescharacteristic
308C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#501×C113C2
socleC22×C113C22×D4
prime radicalC22×D113C2×D4
hypercenter#501D113
hypocenterC113#3163
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #20299007C2semidirect
4. #20299006C2semidirect
5. #20299005C2semidirect
6. #20298999C2semidirect
7. #20298997C2semidirect
8. #20298995C2semidirect
9. #20298994C2semidirect
15. #501×C113C2semidirect
65. #14268630Q8semidirect
68. C8×D113Q8semidirect
155. C113#3163semidirect
161. #501D113semidirect

Maximal subgroups

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

subgroupindex
#202992282
#202992252
#202990072
#202990062
#202990052
#202989992
#202989972
#202989952
#202989942
#202986392
#202986372
#202986352
#106×D1132
#202985552
#501×C1132
#3163113