Finite Group Databasebeta

← #46820023

Subgroups — #46820023

Order 34432.

356 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771142C211yesmaximal, characteristic
2#31770736C211yesmaximal, characteristic, complemented
3#31770678C211yesmaximal, characteristic, complemented
4#31770678C211yesmaximal, characteristic, complemented
5#31770675C211yesmaximal, characteristic, complemented
6#31770675C211yesmaximal, characteristic, complemented
7C8×D1076C211yesmaximal, characteristic, complemented
8#31770670C211yesmaximal, characteristic, complemented
9#31770667C211yesmaximal, characteristic, complemented
10#31770664C211yesmaximal, characteristic, complemented
11#31770660C211yesmaximal, characteristic, complemented
12#31770630C211yesmaximal, characteristic, complemented
13#31770630C211yesmaximal, characteristic, complemented
14C4⋊C8×D269C211yesmaximal, characteristic, complemented
15#446×C269C211yesmaximal, characteristic, complemented
16C2×#16864385C2211yescharacteristic
17C2×#16864385C2211yescharacteristic
18C2×C8×D269C2211yescharacteristic
19C2×C8×D269C2211yescharacteristic
20C2×C8×D269C2211yescharacteristic
21C2×C8×D269C2211yescharacteristic
22#22575448C411yescharacteristic
23#22575448C411yescharacteristic
24#22575444C411yescharacteristic
25#22575442C411yescharacteristic
26#22575438C411yescharacteristic
27#22575438C411yescharacteristic
28#22575429C411yescharacteristic
29#22575428C411yescharacteristic
30C4×D1076C2211yescharacteristic
31C4×D1076C2211yescharacteristic
32C4×D1076C2211yescharacteristic
33#22575410C2211yescharacteristic
34#22575410C2211yescharacteristic
35C42×D269C2211yescharacteristic
36C4⋊#14524130C2211yescharacteristic
37C4⋊#14524130C2211yescharacteristic
38C4⋊#14524130C2211yescharacteristic
39#22575382C2211yescharacteristic
40#22575382C2211yescharacteristic
41#22575382C2211yescharacteristic
42#22575382C2211yescharacteristic
43#22575365C2211yescharacteristic
44#22575365C2211yescharacteristic
45#22575365C2211yescharacteristic
46#22575365C2211yescharacteristic
47#22575365C2211yescharacteristic
48#22575365C2211yescharacteristic
49#22575364C2211yescharacteristic
50#22575364C2211yescharacteristic
51C4×#14524130C2211yescharacteristic
52C4×Q8×C269C2211yescharacteristic
53C4⋊C8×C269C2211yescharacteristic
54C4⋊C8×C269C2211yescharacteristic
55C4⋊C8×C269C2211yescharacteristic
56#97×C269C2211yescharacteristic
57#97×C269C2211yescharacteristic
58C4×C8×C269C2211yescharacteristic
59C2×D1076C2×C411yescharacteristic
60C2×D1076C2×C411yescharacteristic
61C2×D1076C2×C411yescharacteristic
62C2×C4×D269C2×C411yescharacteristic
63C2×C4×D269C2×C411yescharacteristic
64C2×C4×D269C2311yescharacteristic
65C2×C4×D269C2311yescharacteristic
66C2×C4×D269C2311yescharacteristic
67#16864385—41no—
68#16864385—41no—
69C2×#14524130C2311yescharacteristic
70C2×#14524130C2311yescharacteristic
71C2×#14524130C2311yescharacteristic
72C2×#14524130C2311yescharacteristic
73C8×D269—41no—
74C8×D269—41no—
75C8×D269—41no—
76C8×D269—41no—
77C4⋊Dic269C2×C411yescharacteristic
78C4⋊Dic269C2×C411yescharacteristic
79C4⋊Dic269C2×C411yescharacteristic
80#16864381C2×C411yescharacteristic
81#16864381C2×C411yescharacteristic
82#16864381C2×C411yescharacteristic
83#16864381C2×C411yescharacteristic
84#16864379C2×C411yescharacteristic
85#16864379C2×C411yescharacteristic
86#16864379C2×C411yescharacteristic
87#16864379C2×C411yescharacteristic
88#16864379C2×C411yescharacteristic
89#16864379C2×C411yescharacteristic
90#16864379C2×C411yescharacteristic
91#16864379C2×C411yescharacteristic
92#16864379C2×C411yescharacteristic
93#16864379C2×C411yescharacteristic
94C4×Dic269C2×C411yescharacteristic
95C4×Dic269C2×C411yescharacteristic
96C4×Dic269C2311yescharacteristic
97C2×Q8×C269C2×C411yescharacteristic
98C2×C8×C269C2311yescharacteristic
99C2×C8×C269C2311yescharacteristic
100C2×C8×C269C2311yescharacteristic
101C2×C8×C269C2311yescharacteristic
102C4⋊C4×C269C2×C411yescharacteristic
103C4⋊C4×C269C2×C411yescharacteristic
104C4⋊C4×C269C2×C411yescharacteristic
105C42×C269C2311yescharacteristic
106C42×C269C2311yescharacteristic
107C42×C269C2311yescharacteristic
108C22×D269C22×C411yescharacteristic
109C22×D269C22×C411yescharacteristic
110C22×D269C22×C411yescharacteristic
111D1076—22no—
112D1076—22no—
113D1076—41no—
114C2×Dic269C22×C411yescharacteristic
115C2×Dic269C22×C411yescharacteristic
116C2×Dic269C22×C411yescharacteristic
117C2×Dic269C22×C411yescharacteristic
118C2×Dic269C22×C411yescharacteristic
119C4×D269—22no—
120C4×D269—21no—
121C4×D269—21no—
122C4×D269—21no—
123C4×D269—21no—
124C4×D269—21no—
125C4×D269—21no—
126C4×D269—41no—
127#14524130—21no—
128#14524130—21no—
129#14524130—21no—
130#14524130—21no—
131Q8×C269—41no—
132C2×C4×C269C22×C411yescharacteristic
133C2×C4×C269C22×C411yescharacteristic
134C2×C4×C269C22×C411yescharacteristic
135C2×C4×C269C22×C411yescharacteristic
136C2×C4×C269C22×C411yescharacteristic
137C2×C4×C269C22×C411yescharacteristic
138C2×C4×C269C2411yescharacteristic
139C8×C269—21no—
140C8×C269—21no—
141C8×C269—21no—
142C8×C269—21no—
143C22×C269C23×C411yescharacteristic
144C2×D269—21no—
145C2×D269—21no—
146C2×D269—21no—
147C2×D269—21no—
148C2×D269—21no—
149C2×D269—21no—
150C2×D269—21no—
151C2×D269—21no—
152C2×D269#13112yes—
153C4×C269—21no—
154C4×C269—21no—
155C4×C269—21no—
156C4×C269—21no—
157C4×C269—21no—
158C4×C269—21no—
159C4×C269H(5,𝔽2)11yescharacteristic
160C4×C2692−1+411yescharacteristic
161Dic269—21no—
162Dic269—21no—
163Dic269—21no—
164Dic269—21no—
165Dic269—21no—
166C2×C269#52011yescharacteristic
167C2×C269C2×#13111yescharacteristic
168C2×C269#56811yescharacteristic
169D269—22no—
170D269—41no—
171D269—41no—
172C269#299211yescharacteristic, complemented, Sylow
173#2992—2691nomaximal, Sylow
174#529—2691no—
175#446—2691no—
176#446D26911yescharacteristic, complemented
177#435—2691no—
178#435—2691no—
179#435—2691no—
180#435—2691no—
181C8×D4—2691no—
182C8×D4—2691no—
183#433—2691no—
184#433—2691no—
185#432—2691no—
186#424—2691no—
187#424—2691no—
188C2×C4⋊C8—2691no—
189C2×M16—2691no—
190C2×M16—2691no—
191C22×C8—2691no—
192C22×C8—2691no—
193C22×C8—2691no—
194C22×C8—2691no—
195#126—2691no—
196#126—2691no—
197#125—2691no—
198#124—2691no—
199#123—2691no—
200#123—2691no—
201C22⋊Q8—2691no—
202#121—2691no—
203C4×Q8C2×D26911yescharacteristic
204C4×D4—2691no—
205C4×D4—2691no—
206C4×D4—2691no—
207#117—2691no—
208#117—2691no—
209C2×C42—2691no—
210C4⋊C8—2691no—
211C4⋊C8—2691no—
212C4⋊C8—2691no—
213C4⋊C8—2691no—
214C4⋊C8—2691no—
215C4⋊C8—2691no—
216C4⋊C8—2691no—
217C4⋊C8C2×D26911yescharacteristic
218C4⋊C8C2×D26911yescharacteristic
219C4⋊C8C2×D26911yescharacteristic
220C22⋊C8—2691no—
221C22⋊C8—2691no—
222C22⋊C8—2691no—
223C22⋊C8—2691no—
224C22⋊C8—2691no—
225C22⋊C8—2691no—
226#97—2691no—
227#97—2691no—
228#97C2×D26911yescharacteristic
229#97C2×D26911yescharacteristic
230C4×C8—2691no—
231C4×C8C2×D26911yescharacteristic
232C2×Q8C4×D26911yescharacteristic
233C2×D4—2691no—
234C2×D4—2691no—
235C2×D4—2691no—
236C22×C4—2691no—
237C22×C4—2691no—
238C22×C4—2691no—
239C22×C4—2691no—
240C22×C4—2691no—
241M16—10761no—
242M16—10761no—
243C2×C8—2691no—
244C2×C8—2691no—
245C2×C8—2691no—
246C2×C8—2691no—
247C2×C8—10761no—
248C2×C8—10761no—
249C2×C8—10761no—
250C2×C8—10761no—
251C2×C8C22×D26911yescharacteristic
252C2×C8C22×D26911yescharacteristic
253C2×C8C22×D26911yescharacteristic
254C2×C8C22×D26911yescharacteristic
255C4⋊C4—2691no—
256C4⋊C4—2691no—
257C4⋊C4—2691no—
258C4⋊C4—2691no—
259C4⋊C4—2691no—
260C4⋊C4—2691no—
261C4⋊C4—2691no—
262C4⋊C4C4×D26911yescharacteristic
263C4⋊C4C4×D26911yescharacteristic
264C4⋊C4C4×D26911yescharacteristic
265C22⋊C4—2691no—
266C22⋊C4—2691no—
267C22⋊C4—2691no—
268C22⋊C4—2691no—
269C22⋊C4—2691no—
270C22⋊C4—2691no—
271C22⋊C4—2691no—
272C22⋊C4—2691no—
273C22⋊C4—2691no—
274C22⋊C4—2691no—
275C42—2691no—
276C42—2691no—
277C42—2691no—
278C42C22×D26911yescharacteristic
279C42C22×D26911yescharacteristic
280C42C22×D26911yescharacteristic
281C23—2691no—
282C23—2691no—
283C23—2691no—
284Q8—41no—
285D4—5382no—
286D4—5382no—
287D4—10761no—
288C2×C4—2691no—
289C2×C4—2691no—
290C2×C4—2691no—
291C2×C4—2691no—
292C2×C4—2691no—
293C2×C4—5382no—
294C2×C4—5381no—
295C2×C4—5381no—
296C2×C4—5381no—
297C2×C4—5381no—
298C2×C4—5381no—
299C2×C4—5381no—
300C2×C4—10761no—
301C2×C4C2×C4×D26911yescharacteristic
302C2×C4C2×C4×D26911yescharacteristic
303C2×C4C2×C4×D26911yescharacteristic
304C2×C4C2×C4×D26911yescharacteristic
305C2×C4C2×C4×D26911yescharacteristic
306C2×C4C2×C4×D26911yescharacteristic
307C2×C4C23×D26911yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—21no—
312C8—5381no—
313C8—5381no—
314C8—5381no—
315C8—5381no—
316C22—2692no—
317C22—5381no—
318C22—5381no—
319C22—5381no—
320C22—5381no—
321C22—5381no—
322C22—5381no—
323C22—5381no—
324C22—5381no—
325C22C22×C4×D26911yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—5381no—
333C4—5381no—
334C4—5381no—
335C4—5381no—
336C4—5381no—
337C4#2257549911yescharacteristic
338C4#2257550111yescharacteristic
339C2—5382no—
340C2—10761no—
341C2—10761no—
342C2#3177108711yescharacteristic
343C2#131×D26911yescharacteristic
344C2#3177137111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D269
commutator, socleC22×C269C23×C4
Fitting#446×C269C2
prime radical#22575428C4
cosocleC2×C4×C269C24
hypercenter#446D269
hypocenterC269#2992
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. #31770678C2semidirect
4. #31770678C2semidirect
5. #31770675C2semidirect
6. #31770675C2semidirect
7. C8×D1076C2semidirect
8. #31770670C2semidirect
9. #31770667C2semidirect
10. #31770664C2semidirect
11. #31770660C2semidirect
12. #31770630C2semidirect
13. #31770630C2semidirect
14. C4⋊C8×D269C2semidirect
15. #446×C269C2semidirect
172. C269#2992semidirect
176. #446D269semidirect

Maximal subgroups

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

subgroupindex
#317711422
#317707362
#317706782
#317706752
C8×D10762
#317706702
#317706672
#317706642
#317706602
#317706302
C4⋊C8×D2692
#446×C2692
#2992269