Finite Group Databasebeta

← #46820049

Subgroups — #46820049

Order 34432.

346 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#31771135C211yesmaximal, characteristic
2#31770735C211yesmaximal, characteristic, complemented
3#31770734C211yesmaximal, characteristic, complemented
4#31770681C211yesmaximal, characteristic, complemented
5#31770679C211yesmaximal, characteristic, complemented
6#31770677C211yesmaximal, characteristic, complemented
7#31770674C211yesmaximal, characteristic, complemented
8#31770673C211yesmaximal, characteristic, complemented
9#31770664C211yesmaximal, characteristic, complemented
10#31770663C211yesmaximal, characteristic, complemented
11#31770659C211yesmaximal, characteristic, complemented
12#31770633C211yesmaximal, characteristic, complemented
13#31770630C211yesmaximal, characteristic, complemented
14#31770628C211yesmaximal, characteristic, complemented
15#436×C269C211yesmaximal, characteristic, complemented
16C2×#16864386C2211yescharacteristic
17C2×#16864385C2211yescharacteristic
18C22×#14524130C2211yescharacteristic
19C2×C8×D269C2211yescharacteristic
20#22575448C411yescharacteristic
21#22575446C411yescharacteristic
22#22575443C411yescharacteristic
23#22575439C411yescharacteristic
24#22575437C411yescharacteristic
25#22575434C411yescharacteristic
26#22575430C411yescharacteristic
27#22575425C411yescharacteristic
28C4×Dic538C2211yescharacteristic
29C4×C22⋊D269C2211yescharacteristic
30C4×C22⋊D269C2211yescharacteristic
31#22575412C2211yescharacteristic
32#22575410C2211yescharacteristic
33C2×C4×Dic269C2211yescharacteristic
34C4⋊#14524130C2211yescharacteristic
35#22575382C2211yescharacteristic
36#22575382C2211yescharacteristic
37#22575382C2211yescharacteristic
38#22575382C2211yescharacteristic
39#22575382C2211yescharacteristic
40#22575382C2211yescharacteristic
41#22575382C2211yescharacteristic
42#22575382C2211yescharacteristic
43C22⋊#14524130C2211yescharacteristic
44C22⋊#14524130C2211yescharacteristic
45#22575365C2211yescharacteristic
46#22575365C2211yescharacteristic
47#22575364C2211yescharacteristic
48#22575363C2211yescharacteristic
49#22575363C2211yescharacteristic
50#22575363C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C2×M16×C269C2211yescharacteristic
53C2×M16×C269C2211yescharacteristic
54C4×D4×C269C2211yescharacteristic
55C4⋊C8×C269C2211yescharacteristic
56C22⋊C8×C269C2211yescharacteristic
57C22⋊C8×C269C2211yescharacteristic
58C4×C8×C269C2211yescharacteristic
59C2×Dic538C2×C411yescharacteristic
60C2×C22⋊D269C2×C411yescharacteristic
61C2×C22⋊D269C2×C411yescharacteristic
62C22×Dic269C2×C411yescharacteristic
63C22×Dic269C2×C411yescharacteristic
64C2×C4×D269C2311yescharacteristic
65#16864386—41no—
66#16864385—41no—
67C2×#14524130—41no—
68C2×#14524130C2311yescharacteristic
69C2×#14524130C2311yescharacteristic
70C2×#14524130C2311yescharacteristic
71C2×#14524130C2311yescharacteristic
72C8×D269—41no—
73C4⋊Dic269C2×C411yescharacteristic
74C4⋊Dic269C2×C411yescharacteristic
75C4⋊Dic269C2×C411yescharacteristic
76#16864381C2×C411yescharacteristic
77#16864381C2×C411yescharacteristic
78#16864381C2×C411yescharacteristic
79#16864381C2×C411yescharacteristic
80#16864381C2×C411yescharacteristic
81#16864381C2×C411yescharacteristic
82C22⋊Dic269C2×C411yescharacteristic
83C22⋊Dic269C2×C411yescharacteristic
84C22⋊Dic269C2×C411yescharacteristic
85C22⋊Dic269C2×C411yescharacteristic
86#16864379C2×C411yescharacteristic
87#16864379C2×C411yescharacteristic
88#16864379C2×C411yescharacteristic
89#16864379C2×C411yescharacteristic
90C4×Dic269C2×C411yescharacteristic
91C4×Dic269C2×C411yescharacteristic
92C4×Dic269C2311yescharacteristic
93C4×Dic269C2311yescharacteristic
94C4×Dic269C2311yescharacteristic
95C2×D4×C269C2×C411yescharacteristic
96C22×C4×C269C2311yescharacteristic
97C22×C4×C269C2311yescharacteristic
98M16×C269—41no—
99M16×C269—41no—
100C2×C8×C269C2311yescharacteristic
101C2×C8×C269C2311yescharacteristic
102C2×C8×C269C2311yescharacteristic
103C2×C8×C269C2311yescharacteristic
104C4⋊C4×C269C2×C411yescharacteristic
105C22⋊C4×C269C2×C411yescharacteristic
106C22⋊C4×C269C2×C411yescharacteristic
107C42×C269C2311yescharacteristic
108C22×D269C22×C411yescharacteristic
109Dic538—41no—
110C22⋊D269—41no—
111C22⋊D269—41no—
112C2×Dic269—41no—
113C2×Dic269—41no—
114C2×Dic269C22×C411yescharacteristic
115C2×Dic269C22×C411yescharacteristic
116C2×Dic269C22×C411yescharacteristic
117C2×Dic269C22×C411yescharacteristic
118C2×Dic269C22×C411yescharacteristic
119C2×Dic269C22×C411yescharacteristic
120C2×Dic269C22×C411yescharacteristic
121C4×D269—21no—
122C4×D269—21no—
123#14524130—21no—
124#14524130—21no—
125#14524130—21no—
126#14524130—21no—
127C23×C269C22×C411yescharacteristic
128C23×C269C22×C411yescharacteristic
129D4×C269—41no—
130C2×C4×C269—21no—
131C2×C4×C269—21no—
132C2×C4×C269—21no—
133C2×C4×C269—21no—
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×C269—21no—
144C22×C269—21no—
145C22×C269—21no—
146C22×C269—21no—
147C22×C269—21no—
148C22×C269—21no—
149C22×C269C23×C411yescharacteristic
150C2×D269—21no—
151C2×D269—21no—
152C2×D269—21no—
153C4×C269—21no—
154C4×C269—21no—
155C4×C269—21no—
156C4×C269—21no—
157C4×C269H(5,𝔽2)11yescharacteristic
158C4×C2692−1+411yescharacteristic
159Dic269—21no—
160Dic269—21no—
161Dic269—21no—
162Dic269—21no—
163Dic269—21no—
164Dic269—21no—
165Dic269—21no—
166C2×C269—41no—
167C2×C269—41no—
168C2×C269#52011yescharacteristic
169C2×C269#56811yescharacteristic
170C2×C269#56811yescharacteristic
171D269—41no—
172C269#299511yescharacteristic, complemented, Sylow
173#2995—2691nomaximal, Sylow
174#529—2691no—
175#446—2691no—
176#446—2691no—
177#436—2691no—
178#436D26911yescharacteristic, complemented
179#435—2691no—
180#435—2691no—
181#435—2691no—
182#435—2691no—
183#433—2691no—
184#433—2691no—
185#432—2691no—
186#424—2691no—
187#424—2691no—
188#423—2691no—
189C2×M16—2691no—
190C2×M16—2691no—
191C2×M16C2×D26911yescharacteristic
192C2×M16C2×D26911yescharacteristic
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×Q8—2691no—
204C4×D4—2691no—
205C4×D4—2691no—
206C4×D4C2×D26911yescharacteristic
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⋊C8—2691no—
218C4⋊C8—2691no—
219C4⋊C8C2×D26911yescharacteristic
220C22⋊C8—2691no—
221C22⋊C8—2691no—
222C22⋊C8—2691no—
223C22⋊C8—2691no—
224C22⋊C8C2×D26911yescharacteristic
225C22⋊C8C2×D26911yescharacteristic
226#97—2691no—
227#97—2691no—
228#97—2691no—
229#97—2691no—
230C4×C8—2691no—
231C4×C8C2×D26911yescharacteristic
232C2×Q8—2691no—
233C2×D4—2691no—
234C2×D4—2691no—
235C2×D4C4×D26911yescharacteristic
236C22×C4—2691no—
237C22×C4—2691no—
238C22×C4—2691no—
239C22×C4C22×D26911yescharacteristic
240C22×C4C22×D26911yescharacteristic
241M16—41no—
242M16—41no—
243M16—10761no—
244M16—10761no—
245C2×C8—2691no—
246C2×C8—2691no—
247C2×C8—2691no—
248C2×C8—2691no—
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⋊C4—2691no—
263C4⋊C4—2691no—
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⋊C4C4×D26911yescharacteristic
274C22⋊C4C4×D26911yescharacteristic
275C42—2691no—
276C42—2691no—
277C42—2691no—
278C42—2691no—
279C42—2691no—
280C42C22×D26911yescharacteristic
281C23—2691no—
282C23C2×C4×D26911yescharacteristic
283C23C2×C4×D26911yescharacteristic
284Q8—10761no—
285D4—41no—
286D4—10761no—
287D4—10761no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—2691no—
293C2×C4—2691no—
294C2×C4—2691no—
295C2×C4—2691no—
296C2×C4—2691no—
297C2×C4—2691no—
298C2×C4—2691no—
299C2×C4—5381no—
300C2×C4—5381no—
301C2×C4—10761no—
302C2×C4—10761no—
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—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—5381no—
323C22—5381no—
324C22—5381no—
325C22C22×C4×D26911yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—5381no—
331C4—5381no—
332C4—5381no—
333C4—5381no—
334C4—5381no—
335C4—5381no—
336C4—5381no—
337C4#2257549811yescharacteristic
338C4#2257550011yescharacteristic
339C2—41no—
340C2—41no—
341C2—10761no—
342C2#3177108411yescharacteristic
343C2#3177137011yescharacteristic
344C2#3177137111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D269
commutator, socleC22×C269C23×C4
Fitting#436×C269C2
prime radical#22575425C4
cosocleC2×C4×C269C24
hypercenter#436D269
hypocenterC269#2995
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C2×C4 ◁ #436

Complements

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

NH ≅ G/Ntype
2. #31770735C2semidirect
3. #31770734C2semidirect
4. #31770681C2semidirect
5. #31770679C2semidirect
6. #31770677C2semidirect
7. #31770674C2semidirect
8. #31770673C2semidirect
9. #31770664C2semidirect
10. #31770663C2semidirect
11. #31770659C2semidirect
12. #31770633C2semidirect
13. #31770630C2semidirect
14. #31770628C2semidirect
15. #436×C269C2semidirect
172. C269#2995semidirect
178. #436D269semidirect

Maximal subgroups

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

subgroupindex
#317711352
#317707352
#317707342
#317706812
#317706792
#317706772
#317706742
#317706732
#317706642
#317706632
#317706592
#317706332
#317706302
#317706282
#436×C2692
#2995269