Finite Group Databasebeta

← #46821251

Subgroups — #46821251

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#31771235C211yesmaximal, characteristic, complemented
2#31771180C211yesmaximal, characteristic
3#31770972C211yesmaximal, characteristic, complemented
4#31770966C211yesmaximal, characteristic, complemented
5#31770965C211yesmaximal, characteristic, complemented
6#31770962C211yesmaximal, characteristic, complemented
7#31770961C211yesmaximal, characteristic, complemented
8#31770955C211yesmaximal, characteristic, complemented
9#31770954C211yesmaximal, characteristic, complemented
10#31770612C211yesmaximal, characteristic, complemented
11#31770605C211yesmaximal, characteristic
12#31770600C211yesmaximal, characteristic
13#103×D269C211yesmaximal, characteristic, complemented
14#31770562C211yesmaximal, characteristic, complemented
15#491×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic
17C2×Q8×D269C2211yescharacteristic
18C2×#16864385C2211yescharacteristic
19C2×C8×D269C2211yescharacteristic
20#22575453C2211yescharacteristic
21#22575452—21no—
22#22575452C2211yescharacteristic
23#22575451C2211yescharacteristic
24#22575444C2211yescharacteristic
25#22575443—21no—
26#22575442C2211yescharacteristic
27#22575441C2211yescharacteristic
28#22575438—21no—
29#22575438—21no—
30#22575433—21no—
31#22575431—21no—
32#22575431—21no—
33#22575431—21no—
34#22575411C2211yescharacteristic
35#22575410C2211yescharacteristic
36C4⋊C4×D269C2211yescharacteristic
37#22575378C2211yescharacteristic
38#22575378C2211yescharacteristic
39#22575377C2211yescharacteristic
40#22575377C2211yescharacteristic
41#22575377C2211yescharacteristic
42#22575377C2211yescharacteristic
43#22575376C2211yescharacteristic
44#22575376C2211yescharacteristic
45#22575375C2211yescharacteristic
46#22575375C2211yescharacteristic
47#22575373C2211yescharacteristic
48#22575373C2211yescharacteristic
49#22575363C2211yescharacteristic
50C4×#14524130C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C4⋊Q8×C269C2211yescharacteristic
53#125×C269C2211yescharacteristic
54#103×C269C2211yescharacteristic
55#103×C269C2211yescharacteristic
56#103×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#97×C269C2211yescharacteristic
59#16864403—22no—
60#16864403—22no—
61C2×Dic538—21no—
62C2×Dic538—21no—
63C2×Dic538—21no—
64C2×Dic538C2311yescharacteristic
65Q8×D269—22no—
66Q8×D269—22no—
67C2×D1076—21no—
68C2×D1076C2311yescharacteristic
69C2×C4×D269—21no—
70C2×C4×D269—21no—
71C2×C4×D269—21no—
72C2×C4×D269C2311yescharacteristic
73#16864385—22no—
74C2×#14524130C2311yescharacteristic
75C2×#14524130C2311yescharacteristic
76C8×D269—22no—
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#16864381D411yescharacteristic
87#16864381D411yescharacteristic
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92#16864379—21no—
93#16864379D411yescharacteristic
94#16864379D411yescharacteristic
95C4×Dic269—21no—
96C4×Dic269C2311yescharacteristic
97C2×Q8×C269C2311yescharacteristic
98C2×Q8×C269C2311yescharacteristic
99C2×C8×C269C2311yescharacteristic
100C2×C8×C269C2311yescharacteristic
101C4⋊C4×C269—21no—
102C4⋊C4×C269—21no—
103C4⋊C4×C269—21no—
104C4⋊C4×C269—21no—
105C4⋊C4×C269C2311yescharacteristic
106C4⋊C4×C269C2311yescharacteristic
107C42×C269C2311yescharacteristic
108C22×D269—21no—
109C22×D269C2×D411yescharacteristic
110Dic538—21no—
111Dic538—21no—
112Dic538—42no—
113Dic538—81no—
114Dic538—81no—
115D1076—21no—
116D1076—21no—
117D1076—42no—
118C2×Dic269—21no—
119C2×Dic269—21no—
120C2×Dic269—21no—
121C2×Dic269C2×D411yescharacteristic
122C2×Dic269C2×D411yescharacteristic
123C2×Dic269C2×D411yescharacteristic
124C4×D269—42no—
125C4×D269—42no—
126C4×D269—81no—
127C4×D269#4112yes—
128C4×D269#4112yes—
129#14524130—21no—
130#14524130—21no—
131Q8×C269—21no—
132Q8×C269—21no—
133Q8×C269—21no—
134Q8×C269—21no—
135C2×C4×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×C269C22×D411yescharacteristic
145C2×D269—21no—
146C2×D269—21no—
147C2×D269—41no—
148C2×D269—41no—
149C2×D269—41no—
150C2×D269#12412yes—
151C4×C269—21no—
152C4×C269—21no—
153C4×C269—41no—
154C4×C269—41no—
155C4×C269—41no—
156C4×C269—41no—
157C4×C269C2×#4111yescharacteristic
158C4×C269C2×#4111yescharacteristic
159Dic269—21no—
160Dic269—21no—
161Dic269—41no—
162Dic269—41no—
163Dic269—41no—
164Dic269#12412yes—
165C2×C269C2×#12411yescharacteristic
166C2×C269#57711yescharacteristic
167C2×C269#57811yescharacteristic
168D269—22no—
169D269—81no—
170C269#313711yescharacteristic, complemented, Sylow
171#3137—2691nomaximal, Sylow
172#544—2691no—
173#536—2691no—
174#491—2691no—
175#491D26911yescharacteristic, complemented
176#489—2691no—
177#489—2691no—
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—5381no—
198#125C2×D26911yescharacteristic
199#124—2691no—
200#124—2691no—
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#103C2×D26911yescharacteristic
219#103C2×D26911yescharacteristic
220#103C2×D26911yescharacteristic
221#103C2×D26911yescharacteristic
222#102—2691no—
223#102—2691no—
224#102—2691no—
225#102—2691no—
226#97—2691no—
227#97C2×D26911yescharacteristic
228C4×C8—2691no—
229C4×C8—2691no—
230#41—5382no—
231#41—5382no—
232C2×Q8—2691no—
233C2×Q8—5381no—
234C2×Q8—5381no—
235C2×Q8—5382no—
236C2×Q8—5382no—
237C2×Q8—5381no—
238C2×Q8C22×D26911yescharacteristic
239C2×Q8C22×D26911yescharacteristic
240C2×D4—2691no—
241C2×D4—5381no—
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—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—2691no—
257C4⋊C4—2691no—
258C4⋊C4—2691no—
259C4⋊C4—2691no—
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—2691no—
270C22⋊C4—2691no—
271C22⋊C4—5381no—
272C22⋊C4—5381no—
273C22⋊C4—5381no—
274C22⋊C4—5381no—
275C22⋊C4—5381no—
276C42—2691no—
277C42—5381no—
278C42C22×D26911yescharacteristic
279C23—2691no—
280C23—5381no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—21no—
285Q8—5381no—
286Q8—5381no—
287Q8—10762no—
288Q8—21521no—
289Q8—21521no—
290D4—5381no—
291D4—5381no—
292D4—10762no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—2691no—
298C2×C4—2692no—
299C2×C4—2692no—
300C2×C4—2691no—
301C2×C4—2691no—
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—2692no—
316C22—5381no—
317C22—5381no—
318C22—10761no—
319C22—10761no—
320C22—10761no—
321C22C2×D4×D26911yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—2692no—
329C4—5381no—
330C4—5381no—
331C4—10761no—
332C4—10761no—
333C4—10761no—
334C4#41×D26911yescharacteristic
335C4#41×D26911yescharacteristic
336C2—5382no—
337C2—21521no—
338C2#124×D26911yescharacteristic
339C2#3177141411yescharacteristic
340C2#3177142111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#491×C269C2
socleC22×C269C22×D4
prime radicalC2×#16864403C22
hypercenter#491D269
hypocenterC269#3137
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #31771235C2semidirect
3. #31770972C2semidirect
4. #31770966C2semidirect
5. #31770965C2semidirect
6. #31770962C2semidirect
7. #31770961C2semidirect
8. #31770955C2semidirect
9. #31770954C2semidirect
10. #31770612C2semidirect
13. #103×D269C2semidirect
14. #31770562C2semidirect
15. #491×C269C2semidirect
170. C269#3137semidirect
175. #491D269semidirect

Maximal subgroups

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

subgroupindex
#317712352
#317711802
#317709722
#317709662
#317709652
#317709622
#317709612
#317709552
#317709542
#317706122
#317706052
#317706002
#103×D2692
#317705622
#491×C2692
#3137269