Finite Group Databasebeta

← #46820739

Subgroups — #46820739

Order 34432.

376 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771235C211yesmaximal, characteristic, complemented
2#31771087C211yesmaximal, characteristic
3#31770914C211yesmaximal, characteristic, complemented
4#31770904C211yesmaximal, characteristic, complemented
5#31770902C211yesmaximal, characteristic, complemented
6#31770900C211yesmaximal, characteristic, complemented
7#31770898C211yesmaximal, characteristic, complemented
8#31770886C211yesmaximal, characteristic, complemented
9#31770884C211yesmaximal, characteristic, complemented
10#31770644C211yesmaximal, characteristic, complemented
11#107×D269C211yesmaximal, characteristic, complemented
12#31770630C211yesmaximal, characteristic, complemented
13#31770605C211yesmaximal, characteristic
14#31770600C211yesmaximal, characteristic
15#479×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic
17C2×#16864385C2211yescharacteristic
18C2×C8×D269C2211yescharacteristic
19#22575453C2211yescharacteristic
20#22575452—21no—
21#22575452C2211yescharacteristic
22#22575444C2211yescharacteristic
23#22575443—21no—
24#22575433—21no—
25#22575431—21no—
26Q8×Dic269C2211yescharacteristic
27C4×D1076—21no—
28C4×D1076C2211yescharacteristic
29#22575415—21no—
30#22575415C2211yescharacteristic
31#22575411C2211yescharacteristic
32#22575410—21no—
33#22575410C2211yescharacteristic
34C4⋊C4×D269—21no—
35C4⋊C4×D269C2211yescharacteristic
36C4⋊C4×D269C2211yescharacteristic
37#22575387C2211yescharacteristic
38#22575387C2211yescharacteristic
39#22575386C2211yescharacteristic
40#22575386C2211yescharacteristic
41#22575386C2211yescharacteristic
42#22575384C2211yescharacteristic
43C4⋊#14524130C2211yescharacteristic
44#22575382C2211yescharacteristic
45#22575382C2211yescharacteristic
46#22575377C2211yescharacteristic
47#22575377C2211yescharacteristic
48#22575375C2211yescharacteristic
49#22575375C2211yescharacteristic
50#22575373C2211yescharacteristic
51#22575373C2211yescharacteristic
52#125×C269C2211yescharacteristic
53C4×Q8×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#103×C269C2211yescharacteristic
59#16864403—22no—
60#16864403Q814yescomplemented
61C2×Dic538—21no—
62C2×Dic538—21no—
63C2×D1076—21no—
64C2×D1076C2311yescharacteristic
65C2×C4×D269—21no—
66C2×C4×D269—21no—
67C2×C4×D269—21no—
68C2×C4×D269—21no—
69C2×C4×D269—21no—
70C2×C4×D269C2311yescharacteristic
71#16864385—22no—
72C2×#14524130C2311yescharacteristic
73C2×#14524130C2311yescharacteristic
74C8×D269—22no—
75C4⋊Dic269—21no—
76C4⋊Dic269—21no—
77C4⋊Dic269—21no—
78C4⋊Dic269C2311yescharacteristic
79C4⋊Dic269C2311yescharacteristic
80C4⋊Dic269C2311yescharacteristic
81#16864381—21no—
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85#16864381D411yescharacteristic
86#16864381D411yescharacteristic
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379D411yescharacteristic
91#16864379D411yescharacteristic
92C4×Dic269—21no—
93C4×Dic269—21no—
94C4×Dic269C2311yescharacteristic
95C2×Q8×C269C2311yescharacteristic
96C2×C8×C269C2311yescharacteristic
97C2×C8×C269C2311yescharacteristic
98C4⋊C4×C269—21no—
99C4⋊C4×C269—21no—
100C4⋊C4×C269—21no—
101C4⋊C4×C269C2311yescharacteristic
102C4⋊C4×C269C2311yescharacteristic
103C4⋊C4×C269C2311yescharacteristic
104C42×C269—21no—
105C42×C269C2311yescharacteristic
106C22×D269—21no—
107C22×D269C2×D411yescharacteristic
108Dic538—81no—
109Dic538—81no—
110D1076—24no—
111D1076—21no—
112D1076C2×Q812yes—
113C2×Dic269—21no—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269C2×D411yescharacteristic
117C2×Dic269C2×D411yescharacteristic
118C2×Dic269C2×D411yescharacteristic
119C4×D269—24no—
120C4×D269—81no—
121C4×D269—81no—
122C4×D269—81no—
123C4×D269—81no—
124C4×D269C2×Q812yes—
125C4×D269#4112yes—
126#14524130—21no—
127#14524130—21no—
128Q8×C269—21no—
129Q8×C269C2×Q812yes—
130C2×C4×C269—21no—
131C2×C4×C269—21no—
132C2×C4×C269—21no—
133C2×C4×C269—21no—
134C2×C4×C269C2×D411yescharacteristic
135C2×C4×C269C2×D411yescharacteristic
136C2×C4×C269C2411yescharacteristic
137C8×C269—21no—
138C8×C269—21no—
139C22×C269C22×D411yescharacteristic
140C2×D269—21no—
141C2×D269—21no—
142C2×D269—22no—
143C2×D269—41no—
144C2×D269—41no—
145C2×D269C22⋊Q812yes—
146C4×C269—22no—
147C4×C269—21no—
148C4×C269—21no—
149C4×C269—41no—
150C4×C269—41no—
151C4×C269—41no—
152C4×C269C22×Q811yescharacteristic
153C4×C269C2×#4111yescharacteristic
154Dic269—21no—
155Dic269—21no—
156Dic269—41no—
157Dic269—41no—
158Dic269—41no—
159Dic269C22⋊Q812yes—
160C2×C269C2×C22⋊Q811yescharacteristic
161C2×C269#57611yescharacteristic
162C2×C269#57811yescharacteristic
163D269—22no—
164D269—42no—
165C269#308311yescharacteristic, complemented, Sylow
166#3083—2691nomaximal, Sylow
167#544—2691no—
168#520—2691no—
169#479—2691no—
170#479D26911yescharacteristic, complemented
171#478—2691no—
172#478—2691no—
173#477—2691no—
174#477—2691no—
175#474—2691no—
176#474—2691no—
177#428—2691no—
178C2×#107—2691no—
179#424—2691no—
180#417—2691no—
181#416—2691no—
182C2×#41—2691no—
183C2×M16—2691no—
184C22×C8—2691no—
185C4⋊Q8—2691no—
186C4⋊Q8—2691no—
187C4⋊Q8—5381no—
188#125—2691no—
189#125—5381no—
190#125C2×D26911yescharacteristic
191C22⋊Q8—5381no—
192C22⋊Q8—5381no—
193C4×Q8—2691no—
194C4×Q8C2×D26911yescharacteristic
195C4×D4—2691no—
196C4×D4—2691no—
197C4×D4—5381no—
198C4×D4—5381no—
199#117—2691no—
200#117—2691no—
201#117—5381no—
202C2×C4⋊C4—2691no—
203C2×C4⋊C4—2691no—
204C2×C4⋊C4—5381no—
205#107—2691no—
206#107—2691no—
207#107—2691no—
208#107—2691no—
209#107—2691no—
210#107C2×D26911yescharacteristic
211#106—2691no—
212#106C2×D26911yescharacteristic
213C4⋊C8—2691no—
214C4⋊C8—2691no—
215C4⋊C8—2691no—
216C4⋊C8C2×D26911yescharacteristic
217#103—2691no—
218#103—2691no—
219#103C2×D26911yescharacteristic
220#103C2×D26911yescharacteristic
221#102—2691no—
222#102—2691no—
223#102—2691no—
224#102—2691no—
225#41—2694no—
226#41—5382no—
227C2×Q8—5381no—
228C2×Q8—5381no—
229C2×Q8C22×D26911yescharacteristic
230C2×D4—2691no—
231C2×D4—5381no—
232C22×C4—2691no—
233C22×C4—5381no—
234C22×C4—5381no—
235C22×C4—5381no—
236C22×C4—5381no—
237C22×C4—5381no—
238M16—5382no—
239C2×C8—2691no—
240C2×C8—2691no—
241C2×C8—5382no—
242C2×C8C22×D26911yescharacteristic
243C2×C8C22×D26911yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—2691no—
248C4⋊C4—2691no—
249C4⋊C4—2691no—
250C4⋊C4—2691no—
251C4⋊C4—2691no—
252C4⋊C4—5381no—
253C4⋊C4—5381no—
254C4⋊C4—5381no—
255C4⋊C4—5381no—
256C4⋊C4—5381no—
257C4⋊C4—5381no—
258C4⋊C4—5381no—
259C4⋊C4C22×D26911yescharacteristic
260C4⋊C4C22×D26911yescharacteristic
261C4⋊C4C22×D26911yescharacteristic
262C22⋊C4—2691no—
263C22⋊C4—2691no—
264C22⋊C4—5381no—
265C22⋊C4—5381no—
266C22⋊C4—5381no—
267C42—21no—
268C42—2691no—
269C42—5381no—
270C42—5381no—
271C42C22×D26911yescharacteristic
272C23—2691no—
273C23—5381no—
274Q8—21no—
275Q8—21521no—
276Q8—21521no—
277Q8Q8×D26912yes—
278D4—2692no—
279D4—5384no—
280D4—5381no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—2691no—
286C2×C4—2692no—
287C2×C4—2692no—
288C2×C4—2691no—
289C2×C4—2691no—
290C2×C4—5384no—
291C2×C4—5381no—
292C2×C4—5381no—
293C2×C4—5381no—
294C2×C4—21521no—
295C2×C4—21521no—
296C2×C4—21521no—
297C2×C4—21521no—
298C2×C4D4×D26911yescharacteristic
299C2×C4D4×D26911yescharacteristic
300C2×C4C23×D26911yescharacteristic
301C8—21no—
302C8—21no—
303C8—5381no—
304C8—5381no—
305C22—2692no—
306C22—5381no—
307C22—5381no—
308C22—5382no—
309C22—10761no—
310C22—10761no—
311C22C2×D4×D26911yescharacteristic
312C4—21no—
313C4—21no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—2692no—
319C4—5381no—
320C4—5381no—
321C4—10761no—
322C4—10761no—
323C4—10761no—
324C4C2×Q8×D26911yescharacteristic
325C4#41×D26911yescharacteristic
326C2—5382no—
327C2—10762no—
328C2C22⋊Q8×D26911yescharacteristic
329C2#3177140711yescharacteristic
330C2#3177142111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#479×C269C2
socleC22×C269C22×D4
prime radicalC2×#16864403C22
hypercenter#479D269
hypocenterC269#3083
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #31771235C2semidirect
3. #31770914C2semidirect
4. #31770904C2semidirect
5. #31770902C2semidirect
6. #31770900C2semidirect
7. #31770898C2semidirect
8. #31770886C2semidirect
9. #31770884C2semidirect
10. #31770644C2semidirect
11. #107×D269C2semidirect
12. #31770630C2semidirect
15. #479×C269C2semidirect
60. #16864403Q8semidirect
165. C269#3083semidirect
170. #479D269semidirect

Maximal subgroups

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

subgroupindex
#317712352
#317710872
#317709142
#317709042
#317709022
#317709002
#317708982
#317708862
#317708842
#317706442
#107×D2692
#317706302
#317706052
#317706002
#479×C2692
#3083269