Finite Group Databasebeta

← #46823454

Subgroups — #46823454

Order 34432.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771295C211yesmaximal, characteristic
2#31771004C211yesmaximal, characteristic, complemented
3#31770946C211yesmaximal, characteristic, complemented
4#31770943C211yesmaximal, characteristic, complemented
5#31770940C211yesmaximal, characteristic, complemented
6#31770938C211yesmaximal, characteristic, complemented
7#31770912C211yesmaximal, characteristic, complemented
8#31770909C211yesmaximal, characteristic, complemented
9#31770861C211yesmaximal, characteristic, complemented
10#31770861C211yesmaximal, characteristic, complemented
11C4×#16864392C211yesmaximal, characteristic, complemented
12#31770683C211yesmaximal, characteristic
13#31770648C211yesmaximal, characteristic, complemented
14#31770645C211yesmaximal, characteristic, complemented
15#552×C269C211yesmaximal, characteristic
16C2×#16864392C2211yescharacteristic
17C2×#16864386C2211yescharacteristic
18C2×#16864386C2211yescharacteristic
19#22575446—21no—
20#22575445C2211yescharacteristic
21#22575443—21no—
22#22575434—21no—
23#22575432C2211yescharacteristic
24#22575432C2211yescharacteristic
25C4×Dic538C2211yescharacteristic
26#22575412C2211yescharacteristic
27#22575409—21no—
28C2×C4⋊Dic269C2211yescharacteristic
29#22575386C2211yescharacteristic
30#22575386C2211yescharacteristic
31#22575386C2211yescharacteristic
32#22575386C2211yescharacteristic
33#22575386C2211yescharacteristic
34#22575384C2211yescharacteristic
35#22575384C2211yescharacteristic
36#22575384C2211yescharacteristic
37#22575384C2211yescharacteristic
38C4⋊#14524130C2211yescharacteristic
39#22575377C2211yescharacteristic
40#22575377C2211yescharacteristic
41#22575377C2211yescharacteristic
42#22575376C2211yescharacteristic
43#22575376C2211yescharacteristic
44#22575376C2211yescharacteristic
45C22⋊#14524130C2211yescharacteristic
46C22⋊#14524130C2211yescharacteristic
47C4×#14524130C2211yescharacteristic
48#126×C269—21no—
49#125×C269—21no—
50#125×C269C2211yescharacteristic
51#123×C269—21no—
52C22⋊Q8×C269C2211yescharacteristic
53C22⋊Q8×C269C2211yescharacteristic
54C4×Q8×C269C2211yescharacteristic
55C4×D4×C269C2211yescharacteristic
56#117×C269—21no—
57#117×C269C2211yescharacteristic
58C2×C4⋊C4×C269C2211yescharacteristic
59C2×Dic538C2311yescharacteristic
60C22×Dic269—21no—
61#16864392—22no—
62#16864386—22no—
63#16864386—22no—
64C2×#14524130C2311yescharacteristic
65C2×#14524130C2311yescharacteristic
66C2×#14524130C2311yescharacteristic
67C2×#14524130C2311yescharacteristic
68C4⋊Dic269—21no—
69C4⋊Dic269C2311yescharacteristic
70C4⋊Dic269C2311yescharacteristic
71C4⋊Dic269C2311yescharacteristic
72#16864381—21no—
73#16864381—21no—
74#16864381—21no—
75#16864381—21no—
76#16864381—21no—
77C22⋊Dic269—21no—
78C22⋊Dic269—21no—
79C22⋊Dic269—21no—
80C4×Dic269—21no—
81C4×Dic269—21no—
82C2×Q8×C269C2311yescharacteristic
83C2×D4×C269D411yescharacteristic
84C22×C4×C269—21no—
85C22×C4×C269C2311yescharacteristic
86C22×C4×C269C2311yescharacteristic
87C4⋊C4×C269—21no—
88C4⋊C4×C269—21no—
89C4⋊C4×C269—21no—
90C4⋊C4×C269—21no—
91C4⋊C4×C269—21no—
92C4⋊C4×C269—21no—
93C4⋊C4×C269D411yescharacteristic
94C4⋊C4×C269C2311yescharacteristic
95C4⋊C4×C269C2311yescharacteristic
96C4⋊C4×C269C2311yescharacteristic
97C22⋊C4×C269—21no—
98C22⋊C4×C269—21no—
99C22⋊C4×C269—21no—
100C22⋊C4×C269D411yescharacteristic
101C22⋊C4×C269D411yescharacteristic
102C42×C269—21no—
103C42×C269—21no—
104C42×C269C2311yescharacteristic
105Dic538—21no—
106Dic538—21no—
107C2×Dic269—21no—
108C2×Dic269—21no—
109C2×Dic269—21no—
110C2×Dic269—21no—
111C2×Dic269—42no—
112#14524130—21no—
113#14524130—21no—
114#14524130—21no—
115#14524130#4112yes—
116C23×C269C2×D411yescharacteristic
117C23×C269C2×D411yescharacteristic
118Q8×C269—21no—
119Q8×C269—21no—
120D4×C269—41no—
121C2×C4×C269—21no—
122C2×C4×C269—21no—
123C2×C4×C269—21no—
124C2×C4×C269—21no—
125C2×C4×C269—21no—
126C2×C4×C269—21no—
127C2×C4×C269—21no—
128C2×C4×C269—21no—
129C2×C4×C269—42no—
130C2×C4×C269C2×D411yescharacteristic
131C2×C4×C269C2×D411yescharacteristic
132C2×C4×C269C2×D411yescharacteristic
133C2×C4×C269C2×D411yescharacteristic
134C2×C4×C269C2411yescharacteristic
135C22×C269—21no—
136C22×C269—21no—
137C22×C269—21no—
138C22×C269—21no—
139C22×C269—21no—
140C22×C269—21no—
141C22×C269C22×D411yescharacteristic
142C4×C269—21no—
143C4×C269—21no—
144C4×C269—21no—
145C4×C269—21no—
146C4×C269—41no—
147C4×C269—41no—
148C4×C269—41no—
149C4×C269—41no—
150C4×C269C2×#4111yescharacteristic
151C4×C2692−1+411yescharacteristic
152Dic269—41no—
153Dic269—41no—
154Dic269—41no—
155Dic269—41no—
156C2×C269—41no—
157C2×C269—41no—
158C2×C269#54711yescharacteristic
159C2×C269#57511yescharacteristic
160C2×C269#57811yescharacteristic
161C269#335211yescharacteristic, complemented, Sylow
162#3352—2691nomaximal, Sylow
163#552—2691no—
164#552D26911yescharacteristic
165#499—2691no—
166#485—2691no—
167#485—2691no—
168#484—2691no—
169#484—2691no—
170#479—2691no—
171#479—2691no—
172#470—2691no—
173#470—2691no—
174C4×Q16—2691no—
175#436—2691no—
176#428—2691no—
177#428—2691no—
178C2×Q16—2691no—
179C2×M16—2691no—
180C2×M16—2691no—
181#126—21no—
182#126—5381no—
183#125—21no—
184#125—2691no—
185#125—5381no—
186#125C2×D26911yescharacteristic
187#123—21no—
188#123—5381no—
189C22⋊Q8—2691no—
190C22⋊Q8—2691no—
191C22⋊Q8C2×D26911yescharacteristic
192C22⋊Q8C2×D26911yescharacteristic
193C4×Q8—2691no—
194C4×Q8C2×D26911yescharacteristic
195C4×D4C2×D26911yescharacteristic
196#117—21no—
197#117—2691no—
198#117—5381no—
199#117C2×D26911yescharacteristic
200C2×C4⋊C4—2691no—
201C2×C4⋊C4C2×D26911yescharacteristic
202#107—2691no—
203#107—2691no—
204#107—2691no—
205#107—2691no—
206#107—2691no—
207#106—2691no—
208#106—2691no—
209#106—2691no—
210#106—2691no—
211C4⋊C8—2691no—
212#103—2691no—
213#103—2691no—
214#103—2691no—
215#103—2691no—
216#103—2691no—
217#103—2691no—
218C22⋊C8—2691no—
219C22⋊C8—2691no—
220C4×C8—2691no—
221C2×Q8—2691no—
222C2×Q8C22×D26911yescharacteristic
223C2×D4C22⋊D26911yescharacteristic
224C22×C4—21no—
225C22×C4—5381no—
226C22×C4C22×D26911yescharacteristic
227C22×C4C22×D26911yescharacteristic
228Q16—5382no—
229M16—5382no—
230M16—5382no—
231C2×C8—2691no—
232C2×C8—2691no—
233C2×C8—2691no—
234C2×C8—2691no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—2691no—
242C4⋊C4—2691no—
243C4⋊C4—2691no—
244C4⋊C4—5381no—
245C4⋊C4—5381no—
246C4⋊C4—5381no—
247C4⋊C4—5381no—
248C4⋊C4—5381no—
249C4⋊C4—5381no—
250C4⋊C4C22⋊D26911yescharacteristic
251C4⋊C4C22×D26911yescharacteristic
252C4⋊C4C22×D26911yescharacteristic
253C4⋊C4C22×D26911yescharacteristic
254C22⋊C4—21no—
255C22⋊C4—21no—
256C22⋊C4—21no—
257C22⋊C4—5381no—
258C22⋊C4—5381no—
259C22⋊C4—5381no—
260C22⋊C4C22⋊D26911yescharacteristic
261C22⋊C4C22⋊D26911yescharacteristic
262C42—21no—
263C42—21no—
264C42—5381no—
265C42—5381no—
266C42C22×D26911yescharacteristic
267C23C2×C22⋊D26911yescharacteristic
268C23C2×C22⋊D26911yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—5381no—
272Q8—5381no—
273D4—41no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—5381no—
284C2×C4—5381no—
285C2×C4—5381no—
286C2×C4—5381no—
287C2×C4—10762no—
288C2×C4C2×C22⋊D26911yescharacteristic
289C2×C4C2×C22⋊D26911yescharacteristic
290C2×C4C2×C22⋊D26911yescharacteristic
291C2×C4C2×C22⋊D26911yescharacteristic
292C2×C4C23×D26911yescharacteristic
293C8—2692no—
294C8—5381no—
295C8—5381no—
296C8—5381no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22C22×C22⋊D26911yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—10761no—
313C4—10761no—
314C4—10761no—
315C4—10761no—
316C4#41×D26911yescharacteristic
317C4#2257550011yescharacteristic
318C2—41no—
319C2—41no—
320C2#3177125411yescharacteristic
321C2#3177140311yescharacteristic
322C2#3177142011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#552×C269C2
socleC22×C269C22×D4
prime radicalC2×D4×C269D4
hypercenter#552D269
hypocenterC269#3352
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #31771004C2semidirect
3. #31770946C2semidirect
4. #31770943C2semidirect
5. #31770940C2semidirect
6. #31770938C2semidirect
7. #31770912C2semidirect
8. #31770909C2semidirect
9. #31770861C2semidirect
10. #31770861C2semidirect
11. C4×#16864392C2semidirect
13. #31770648C2semidirect
14. #31770645C2semidirect
161. C269#3352semidirect

Maximal subgroups

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

subgroupindex
#317712952
#317710042
#317709462
#317709432
#317709402
#317709382
#317709122
#317709092
#317708612
C4×#168643922
#317706832
#317706482
#317706452
#552×C2692
#3352269