Finite Group Databasebeta

← #46819988

Subgroups — #46819988

Order 34432.

314 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771159C211yesmaximal, characteristic
2#31770736C211yesmaximal, characteristic, complemented
3#31770735C211yesmaximal, characteristic, complemented
4#31770734C211yesmaximal, characteristic, complemented
5#31770734C211yesmaximal, characteristic, complemented
6#31770733C211yesmaximal, characteristic, complemented
7#31770733C211yesmaximal, characteristic, complemented
8#31770732C211yesmaximal, characteristic, complemented
9#31770667C211yesmaximal, characteristic
10#31770665C211yesmaximal, characteristic
11#31770665C211yesmaximal, characteristic
12#31770664C211yesmaximal, characteristic
13#31770661C211yesmaximal, characteristic
14#31770660C211yesmaximal, characteristic
15#446×C269C211yesmaximal, characteristic, complemented
16#22575452C411yescharacteristic
17#22575451C411yescharacteristic
18#22575443C411yescharacteristic
19#22575443C411yescharacteristic
20#22575433C411yescharacteristic
21#22575431C411yescharacteristic
22#22575431C411yescharacteristic
23#22575429C411yescharacteristic
24C4×Dic538C2211yescharacteristic
25C4×Dic538C2211yescharacteristic
26C4×Dic538C2211yescharacteristic
27#22575410C2211yescharacteristic
28#22575410C2211yescharacteristic
29C42×D269C2211yescharacteristic
30C4⋊#14524130C2211yescharacteristic
31C4⋊#14524130C2211yescharacteristic
32C4⋊#14524130C2211yescharacteristic
33#22575382C2211yescharacteristic
34#22575382C2211yescharacteristic
35#22575382C2211yescharacteristic
36#22575382C2211yescharacteristic
37#22575382C2211yescharacteristic
38#22575382C2211yescharacteristic
39#22575365C2211yescharacteristic
40#22575365C2211yescharacteristic
41#22575365C2211yescharacteristic
42#22575365C2211yescharacteristic
43#22575364C2211yescharacteristic
44#22575364C2211yescharacteristic
45#22575363C2211yescharacteristic
46#22575363C2211yescharacteristic
47#22575363C2211yescharacteristic
48#22575363C2211yescharacteristic
49C4×#14524130C2211yescharacteristic
50C8×Dic269C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C4×Q8×C269C2211yescharacteristic
53C4⋊C8×C269C2211yescharacteristic
54C4⋊C8×C269C2211yescharacteristic
55C4⋊C8×C269C2211yescharacteristic
56#97×C269C2211yescharacteristic
57#97×C269C2211yescharacteristic
58C4×C8×C269C2211yescharacteristic
59C2×Dic538C2×C411yescharacteristic
60C2×Dic538C2×C411yescharacteristic
61C2×Dic538C2×C411yescharacteristic
62C2×C4×D269C2×C411yescharacteristic
63C2×C4×D269C2×C411yescharacteristic
64C2×C4×D269C2311yescharacteristic
65C2×#14524130C2311yescharacteristic
66C2×#14524130C2311yescharacteristic
67C2×#14524130C2311yescharacteristic
68C2×#14524130C2311yescharacteristic
69C4⋊Dic269C2×C411yescharacteristic
70C4⋊Dic269C2×C411yescharacteristic
71C4⋊Dic269C2×C411yescharacteristic
72#16864381C2×C411yescharacteristic
73#16864381C2×C411yescharacteristic
74#16864381C2×C411yescharacteristic
75#16864381C2×C411yescharacteristic
76#16864381C2×C411yescharacteristic
77#16864381C2×C411yescharacteristic
78#16864381C2×C411yescharacteristic
79#16864381C2×C411yescharacteristic
80#16864381C2×C411yescharacteristic
81#16864381C2×C411yescharacteristic
82#16864379C2×C411yescharacteristic
83#16864379C2×C411yescharacteristic
84#16864379C2×C411yescharacteristic
85#16864379C2×C411yescharacteristic
86C4×Dic269C2×C411yescharacteristic
87C4×Dic269C2×C411yescharacteristic
88C4×Dic269C2311yescharacteristic
89C4×Dic269C2311yescharacteristic
90C4×Dic269C2311yescharacteristic
91C2×Q8×C269C2×C411yescharacteristic
92C2×C8×C269C2311yescharacteristic
93C2×C8×C269C2311yescharacteristic
94C2×C8×C269C2311yescharacteristic
95C2×C8×C269C2311yescharacteristic
96C4⋊C4×C269C2×C411yescharacteristic
97C4⋊C4×C269C2×C411yescharacteristic
98C4⋊C4×C269C2×C411yescharacteristic
99C42×C269C2311yescharacteristic
100C42×C269C2311yescharacteristic
101C42×C269C2311yescharacteristic
102C22×D269C22×C411yescharacteristic
103Dic538—41no—
104Dic538—41no—
105Dic538—41no—
106C2×Dic269C22×C411yescharacteristic
107C2×Dic269C22×C411yescharacteristic
108C2×Dic269C22×C411yescharacteristic
109C2×Dic269C22×C411yescharacteristic
110C2×Dic269C22×C411yescharacteristic
111C2×Dic269C22×C411yescharacteristic
112C2×Dic269C22×C411yescharacteristic
113C4×D269—21no—
114C4×D269—21no—
115C4×D269—41no—
116C4×D269—41no—
117#14524130—21no—
118#14524130—21no—
119#14524130—21no—
120#14524130—21no—
121Q8×C269—41no—
122C2×C4×C269C22×C411yescharacteristic
123C2×C4×C269C22×C411yescharacteristic
124C2×C4×C269C22×C411yescharacteristic
125C2×C4×C269C22×C411yescharacteristic
126C2×C4×C269C22×C411yescharacteristic
127C2×C4×C269C22×C411yescharacteristic
128C2×C4×C269C2411yescharacteristic
129C8×C269—21no—
130C8×C269—21no—
131C8×C269—21no—
132C8×C269—21no—
133C22×C269C23×C411yescharacteristic
134C2×D269—21no—
135C2×D269—21no—
136C2×D269—21no—
137C4×C269—21no—
138C4×C269—21no—
139C4×C269—21no—
140C4×C269—21no—
141C4×C269—21no—
142C4×C269—21no—
143C4×C2692−1+411yescharacteristic
144C4×C2692−1+411yescharacteristic
145Dic269—21no—
146Dic269—21no—
147Dic269—21no—
148Dic269—21no—
149Dic269—21no—
150Dic269—21no—
151Dic269—21no—
152C2×C269#51911yescharacteristic
153C2×C269#56811yescharacteristic
154C2×C269#56811yescharacteristic
155D269—41no—
156C269#298711yescharacteristic, complemented, Sylow
157#2987—2691nomaximal, Sylow
158#533—2691no—
159#446—2691no—
160#446—2691no—
161#446—2691no—
162#446—2691no—
163#446—2691no—
164#446—2691no—
165#446—2691no—
166#446D26911yescharacteristic, complemented
167#433—2691no—
168#433—2691no—
169#433—2691no—
170#433—2691no—
171#432—2691no—
172#432—2691no—
173C4⋊Q8—2691no—
174C4⋊Q8—2691no—
175#125—2691no—
176#125—2691no—
177C22⋊Q8—2691no—
178C22⋊Q8—2691no—
179C22⋊Q8—2691no—
180C22⋊Q8—2691no—
181C4×Q8—2691no—
182C4×Q8—2691no—
183C4×Q8—2691no—
184C4×Q8C2×D26911yescharacteristic
185#117—2691no—
186#117—2691no—
187C2×C42—2691no—
188C4⋊C8—2691no—
189C4⋊C8—2691no—
190C4⋊C8—2691no—
191C4⋊C8—2691no—
192C4⋊C8—2691no—
193C4⋊C8—2691no—
194C4⋊C8—2691no—
195C4⋊C8—2691no—
196C4⋊C8—2691no—
197C4⋊C8C2×D26911yescharacteristic
198C4⋊C8C2×D26911yescharacteristic
199C4⋊C8C2×D26911yescharacteristic
200C22⋊C8—2691no—
201C22⋊C8—2691no—
202C22⋊C8—2691no—
203C22⋊C8—2691no—
204#97—2691no—
205#97—2691no—
206#97—2691no—
207#97—2691no—
208#97—2691no—
209#97—2691no—
210#97C2×D26911yescharacteristic
211#97C2×D26911yescharacteristic
212C4×C8—2691no—
213C4×C8—2691no—
214C4×C8—2691no—
215C4×C8C2×D26911yescharacteristic
216C2×Q8—2691no—
217C2×Q8—2691no—
218C2×Q8—2691no—
219C2×Q8C4×D26911yescharacteristic
220C22×C4—2691no—
221C22×C4—2691no—
222C22×C4—2691no—
223C2×C8—2691no—
224C2×C8—2691no—
225C2×C8—2691no—
226C2×C8—2691no—
227C2×C8C22×D26911yescharacteristic
228C2×C8C22×D26911yescharacteristic
229C2×C8C22×D26911yescharacteristic
230C2×C8C22×D26911yescharacteristic
231C4⋊C4—2691no—
232C4⋊C4—2691no—
233C4⋊C4—2691no—
234C4⋊C4—2691no—
235C4⋊C4—2691no—
236C4⋊C4—2691no—
237C4⋊C4—2691no—
238C4⋊C4—2691no—
239C4⋊C4—2691no—
240C4⋊C4—2691no—
241C4⋊C4—2691no—
242C4⋊C4—2691no—
243C4⋊C4—2691no—
244C4⋊C4C4×D26911yescharacteristic
245C4⋊C4C4×D26911yescharacteristic
246C4⋊C4C4×D26911yescharacteristic
247C22⋊C4—2691no—
248C22⋊C4—2691no—
249C22⋊C4—2691no—
250C22⋊C4—2691no—
251C42—2691no—
252C42—2691no—
253C42—2691no—
254C42—2691no—
255C42—2691no—
256C42C22×D26911yescharacteristic
257C42C22×D26911yescharacteristic
258C42C22×D26911yescharacteristic
259C23—2691no—
260Q8—41no—
261Q8—10761no—
262Q8—10761no—
263Q8—10761no—
264C2×C4—2691no—
265C2×C4—2691no—
266C2×C4—2691no—
267C2×C4—2691no—
268C2×C4—2691no—
269C2×C4—2691no—
270C2×C4—2691no—
271C2×C4—5381no—
272C2×C4—5381no—
273C2×C4—10761no—
274C2×C4—10761no—
275C2×C4C2×C4×D26911yescharacteristic
276C2×C4C2×C4×D26911yescharacteristic
277C2×C4C2×C4×D26911yescharacteristic
278C2×C4C2×C4×D26911yescharacteristic
279C2×C4C2×C4×D26911yescharacteristic
280C2×C4C2×C4×D26911yescharacteristic
281C2×C4C23×D26911yescharacteristic
282C8—21no—
283C8—21no—
284C8—21no—
285C8—21no—
286C8—5381no—
287C8—5381no—
288C8—5381no—
289C8—5381no—
290C22—5381no—
291C22—5381no—
292C22—5381no—
293C22C22×C4×D26911yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—5381no—
301C4—5381no—
302C4—5381no—
303C4—5381no—
304C4—5381no—
305C4—5381no—
306C4—5381no—
307C4#2257550011yescharacteristic
308C4#2257550111yescharacteristic
309C2—10761no—
310C2#3177108111yescharacteristic
311C2#3177137011yescharacteristic
312C2#3177137111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D269
commutator, socleC22×C269C23×C4
Fitting#446×C269C2
prime radicalC22×D269C22×C4
cosocleC2×C4×C269C24
hypercenter#446D269
hypocenterC269#2987
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C2×C4 ◁ #446

Complements

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

NH ≅ G/Ntype
2. #31770736C2semidirect
3. #31770735C2semidirect
4. #31770734C2semidirect
5. #31770734C2semidirect
6. #31770733C2semidirect
7. #31770733C2semidirect
8. #31770732C2semidirect
15. #446×C269C2semidirect
156. C269#2987semidirect
166. #446D269semidirect

Maximal subgroups

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

subgroupindex
#317711592
#317707362
#317707352
#317707342
#317707332
#317707322
#317706672
#317706652
#317706642
#317706612
#317706602
#446×C2692
#2987269