Finite Group Databasebeta

← #46821247

Subgroups — #46821247

Order 34432.

372 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771232C211yesmaximal, characteristic, complemented
2#31771175C211yesmaximal, characteristic
3#31770974C211yesmaximal, characteristic, complemented
4#31770972C211yesmaximal, characteristic, complemented
5#31770963C211yesmaximal, characteristic, complemented
6#31770959C211yesmaximal, characteristic, complemented
7#31770958C211yesmaximal, characteristic, complemented
8#31770957C211yesmaximal, characteristic, complemented
9#31770954C211yesmaximal, characteristic, complemented
10#31770612C211yesmaximal, characteristic, complemented
11#31770603C211yesmaximal, characteristic
12#31770598C211yesmaximal, characteristic
13#103×D269C211yesmaximal, characteristic, complemented
14#31770562C211yesmaximal, characteristic, complemented
15#489×C269C211yesmaximal, characteristic, complemented
16C2×#16864401C2211yescharacteristic
17C2×Q8×D269C2211yescharacteristic
18C2×#16864385C2211yescharacteristic
19C2×C8×D269C2211yescharacteristic
20#22575453C2211yescharacteristic
21#22575452C2211yescharacteristic
22#22575451—21no—
23#22575451C2211yescharacteristic
24#22575445C2211yescharacteristic
25#22575444C2211yescharacteristic
26#22575443—21no—
27#22575440C2211yescharacteristic
28#22575435—21no—
29#22575435—21no—
30#22575431—21no—
31#22575430—21no—
32#22575430—21no—
33#22575429—21no—
34#22575411C2211yescharacteristic
35#22575410C2211yescharacteristic
36C4⋊C4×D269C2211yescharacteristic
37#22575378C2211yescharacteristic
38#22575378C2211yescharacteristic
39#22575378C2211yescharacteristic
40#22575378C2211yescharacteristic
41#22575377C2211yescharacteristic
42#22575377C2211yescharacteristic
43#22575376C2211yescharacteristic
44#22575376C2211yescharacteristic
45#22575376C2211yescharacteristic
46#22575376C2211yescharacteristic
47#22575374C2211yescharacteristic
48#22575374C2211yescharacteristic
49#22575363C2211yescharacteristic
50C4×#14524130C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C4⋊Q8×C269C2211yescharacteristic
53#124×C269C2211yescharacteristic
54#103×C269C2211yescharacteristic
55#103×C269C2211yescharacteristic
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#97×C269C2211yescharacteristic
59#16864401—22no—
60#16864401—22no—
61C2×Dic538—21no—
62C2×Dic538—21no—
63C2×Dic538C2311yescharacteristic
64C2×Dic538C2311yescharacteristic
65Q8×D269—22no—
66Q8×D269—22no—
67C2×C22⋊D269—21no—
68C22×Dic269—21no—
69C2×C4×D269—21no—
70C2×C4×D269—21no—
71C2×C4×D269C2311yescharacteristic
72#16864385—22no—
73C2×#14524130C2311yescharacteristic
74C2×#14524130C2311yescharacteristic
75C8×D269—22no—
76C4⋊Dic269—21no—
77C4⋊Dic269—21no—
78C4⋊Dic269—21no—
79C4⋊Dic269C2311yescharacteristic
80C4⋊Dic269C2311yescharacteristic
81#16864381—21no—
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85#16864381—21no—
86#16864381—21no—
87#16864381—21no—
88#16864381D411yescharacteristic
89#16864381D411yescharacteristic
90C22⋊Dic269—21no—
91C22⋊Dic269—21no—
92#16864379—21no—
93#16864379D411yescharacteristic
94#16864379D411yescharacteristic
95C4×Dic269—21no—
96C4×Dic269C2311yescharacteristic
97C2×Q8×C269—21no—
98C2×Q8×C269C2311yescharacteristic
99C2×D4×C269C2311yescharacteristic
100C2×C8×C269C2311yescharacteristic
101C2×C8×C269C2311yescharacteristic
102C4⋊C4×C269—21no—
103C4⋊C4×C269C2311yescharacteristic
104C4⋊C4×C269C2311yescharacteristic
105C22⋊C4×C269—21no—
106C22⋊C4×C269—21no—
107C42×C269C2311yescharacteristic
108C22×D269C2×D411yescharacteristic
109Dic538—21no—
110Dic538—21no—
111Dic538—21no—
112Dic538—21no—
113Dic538—42no—
114Dic538—81no—
115C22⋊D269—42no—
116C2×Dic269—21no—
117C2×Dic269—21no—
118C2×Dic269—21no—
119C2×Dic269—21no—
120C2×Dic269—42no—
121C2×Dic269C2×D411yescharacteristic
122C2×Dic269C2×D411yescharacteristic
123C2×Dic269C2×D411yescharacteristic
124C4×D269—42no—
125C4×D269—81no—
126C4×D269#4112yes—
127C4×D269#4112yes—
128#14524130—21no—
129#14524130—21no—
130C23×C269—21no—
131Q8×C269—21no—
132Q8×C269—21no—
133Q8×C269—81no—
134D4×C269—21no—
135D4×C269—21no—
136C2×C4×C269—21no—
137C2×C4×C269—21no—
138C2×C4×C269—21no—
139C2×C4×C269C2×D411yescharacteristic
140C2×C4×C269C2×D411yescharacteristic
141C2×C4×C269C2411yescharacteristic
142C8×C269—21no—
143C8×C269—21no—
144C22×C269—41no—
145C22×C269—41no—
146C22×C269—41no—
147C22×C269C22×D411yescharacteristic
148C2×D269—21no—
149C2×D269—21no—
150C2×D269#12412yes—
151C4×C269—21no—
152C4×C269—21no—
153C4×C269—41no—
154C4×C269—41no—
155C4×C269—41no—
156C4×C269C2×#4111yescharacteristic
157C4×C269C2×#4111yescharacteristic
158Dic269—21no—
159Dic269—21no—
160Dic269—41no—
161Dic269—41no—
162Dic269—41no—
163Dic269—41no—
164Dic269#12412yes—
165C2×C269—81no—
166C2×C269C2×#12411yescharacteristic
167C2×C269#57711yescharacteristic
168C2×C269#57811yescharacteristic
169D269—22no—
170C269#313711yescharacteristic, complemented, Sylow
171#3137—2691nomaximal, Sylow
172#544—2691no—
173#536—2691no—
174#491—2691no—
175#491—2691no—
176#489—2691no—
177#489D26911yescharacteristic, complemented
178#488—2691no—
179#488—2691no—
180#487—2691no—
181#487—2691no—
182#419—2691no—
183#417—2691no—
184#416—2691no—
185C2×#103—2691no—
186#405—2691no—
187C2×#41—2691no—
188C22×Q8—2691no—
189C2×M16—2691no—
190C22×C8—2691no—
191C4⋊Q8—2691no—
192C4⋊Q8—2691no—
193C4⋊Q8—2691no—
194C4⋊Q8—5381no—
195C4⋊Q8C2×D26911yescharacteristic
196#125—2691no—
197#125—2691no—
198#125—5381no—
199#124—2691no—
200#124C2×D26911yescharacteristic
201#123—5381no—
202#123—5381no—
203C22⋊Q8—5381no—
204C22⋊Q8—5381no—
205C22⋊Q8—5381no—
206C22⋊Q8—5381no—
207#117—2691no—
208#117—2691no—
209C2×C4⋊C4—2691no—
210#103—2691no—
211#103—2691no—
212#103—2691no—
213#103—2691no—
214#103—2691no—
215#103—2691no—
216#103—2691no—
217#103—2691no—
218#103—2691no—
219#103—2691no—
220#103C2×D26911yescharacteristic
221#103C2×D26911yescharacteristic
222#102—2691no—
223#102—2691no—
224#102C2×D26911yescharacteristic
225#102C2×D26911yescharacteristic
226#97—2691no—
227#97C2×D26911yescharacteristic
228C4×C8—2691no—
229C4×C8—2691no—
230#41—5382no—
231#41—5382no—
232C2×Q8—21no—
233C2×Q8—2691no—
234C2×Q8—2691no—
235C2×Q8—5381no—
236C2×Q8—5381no—
237C2×Q8—5382no—
238C2×Q8—5382no—
239C2×Q8C22×D26911yescharacteristic
240C2×D4—5381no—
241C2×D4C22×D26911yescharacteristic
242C22×C4—2691no—
243C22×C4—5381no—
244C22×C4—5381no—
245C22×C4—5381no—
246M16—5382no—
247C2×C8—2691no—
248C2×C8—2691no—
249C2×C8—5382no—
250C2×C8C22×D26911yescharacteristic
251C2×C8C22×D26911yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—2691no—
254C4⋊C4—2691no—
255C4⋊C4—2691no—
256C4⋊C4—2691no—
257C4⋊C4—5381no—
258C4⋊C4—5381no—
259C4⋊C4—5381no—
260C4⋊C4—5381no—
261C4⋊C4—5381no—
262C4⋊C4—5381no—
263C4⋊C4—5381no—
264C4⋊C4—5381no—
265C4⋊C4—5381no—
266C4⋊C4—5381no—
267C4⋊C4C22×D26911yescharacteristic
268C4⋊C4C22×D26911yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—2691no—
272C22⋊C4—2691no—
273C22⋊C4—5381no—
274C22⋊C4—5381no—
275C22⋊C4—5381no—
276C42—2691no—
277C42—5381no—
278C42C22×D26911yescharacteristic
279C23—21no—
280C23—2691no—
281Q8—21no—
282Q8—21no—
283Q8—81no—
284Q8—5381no—
285Q8—5381no—
286Q8—5381no—
287Q8—5381no—
288Q8—10762no—
289Q8—21521no—
290D4—21no—
291D4—21no—
292D4—10762no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—2691no—
297C2×C4—2692no—
298C2×C4—2692no—
299C2×C4—2691no—
300C2×C4—2691no—
301C2×C4—5381no—
302C2×C4—5381no—
303C2×C4—5381no—
304C2×C4—5381no—
305C2×C4—10762no—
306C2×C4—10762no—
307C2×C4—21521no—
308C2×C4D4×D26911yescharacteristic
309C2×C4D4×D26911yescharacteristic
310C2×C4C23×D26911yescharacteristic
311C8—21no—
312C8—21no—
313C8—5381no—
314C8—5381no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—2692no—
319C22—5381no—
320C22—5381no—
321C22C2×D4×D26911yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—2692no—
328C4—5381no—
329C4—5381no—
330C4—10761no—
331C4—10761no—
332C4—10761no—
333C4—10761no—
334C4#41×D26911yescharacteristic
335C4#41×D26911yescharacteristic
336C2—81no—
337C2—5382no—
338C2#124×D26911yescharacteristic
339C2#3177141511yescharacteristic
340C2#3177142111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#489×C269C2
socleC22×C269C22×D4
prime radicalC2×#16864401C22
hypercenter#489D269
hypocenterC269#3137
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #31771232C2semidirect
3. #31770974C2semidirect
4. #31770972C2semidirect
5. #31770963C2semidirect
6. #31770959C2semidirect
7. #31770958C2semidirect
8. #31770957C2semidirect
9. #31770954C2semidirect
10. #31770612C2semidirect
13. #103×D269C2semidirect
14. #31770562C2semidirect
15. #489×C269C2semidirect
170. C269#3137semidirect
177. #489D269semidirect

Maximal subgroups

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

subgroupindex
#317712322
#317711752
#317709742
#317709722
#317709632
#317709592
#317709582
#317709572
#317709542
#317706122
#317706032
#317705982
#103×D2692
#317705622
#489×C2692
#3137269