Finite Group Databasebeta

← #46822933

Subgroups — #46822933

Order 34432.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771293C211yesmaximal, characteristic
2Q8×D1076C211yesmaximal, characteristic
3#31770975C211yesmaximal, characteristic, complemented
4#31770948C211yesmaximal, characteristic, complemented
5#31770937C211yesmaximal, characteristic, complemented
6#31770864C211yesmaximal, characteristic, complemented
7#31770847C211yesmaximal, characteristic, complemented
8#31770816C211yesmaximal, characteristic, complemented
9#31770762C211yesmaximal, characteristic, complemented
10#31770762C211yesmaximal, characteristic, complemented
11#31770710C211yesmaximal, characteristic, complemented
12#31770675C211yesmaximal, characteristic
13#31770612C211yesmaximal, characteristic, complemented
14#103×D269C211yesmaximal, characteristic, complemented
15#479×C269C211yesmaximal, characteristic, complemented
16C2×Q8×D269C2211yescharacteristic
17C2×Q8×D269C2211yescharacteristic
18C2×Dic1076C2211yescharacteristic
19C2×Dic1076C2211yescharacteristic
20C2×#16864392C2211yescharacteristic
21C2×#16864385C2211yescharacteristic
22C2×C8×D269C2211yescharacteristic
23#22575453—21no—
24#22575453C2211yescharacteristic
25#22575448—21no—
26#22575444—21no—
27#22575438—21no—
28#22575433—21no—
29#22575433—21no—
30#22575433C2211yescharacteristic
31#22575433C2211yescharacteristic
32#22575433C2211yescharacteristic
33#22575433C2211yescharacteristic
34C4×Dic538C2211yescharacteristic
35C4×D1076—21no—
36C4×D1076C2211yescharacteristic
37#22575411—21no—
38#22575411C2211yescharacteristic
39C4⋊C4×D269C2211yescharacteristic
40#22575384C2211yescharacteristic
41#22575378C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575377C2211yescharacteristic
44#22575376C2211yescharacteristic
45#22575376C2211yescharacteristic
46#22575376C2211yescharacteristic
47#22575376C2211yescharacteristic
48#22575376C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575365C2211yescharacteristic
51#22575364C2211yescharacteristic
52#125×C269C2211yescharacteristic
53C4×Q8×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#103×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538—21no—
61C2×Dic538C2311yescharacteristic
62C2×Dic538C2311yescharacteristic
63C2×Dic538C2311yescharacteristic
64Q8×D269—22no—
65Q8×D269—22no—
66Q8×D269—41no—
67Q8×D269—41no—
68C2×D1076D411yescharacteristic
69C2×C4×D269—21no—
70C2×C4×D269—21no—
71C2×C4×D269—21no—
72C2×C4×D269C2311yescharacteristic
73C2×C4×D269C2311yescharacteristic
74Dic1076—41no—
75Dic1076—41no—
76#16864392—22no—
77#16864385—41no—
78C2×#14524130C2311yescharacteristic
79C2×#14524130C2311yescharacteristic
80C8×D269—41no—
81C4⋊Dic269—21no—
82C4⋊Dic269—21no—
83C4⋊Dic269—21no—
84C4⋊Dic269—21no—
85C4⋊Dic269—21no—
86C4⋊Dic269—21no—
87C4⋊Dic269D411yescharacteristic
88C4⋊Dic269C2311yescharacteristic
89#16864381—21no—
90#16864381—21no—
91#16864379—21no—
92#16864379—21no—
93#16864379—21no—
94#16864379—21no—
95#16864379—21no—
96#16864379D411yescharacteristic
97#16864379D411yescharacteristic
98C4×Dic269—21no—
99C4×Dic269—21no—
100C2×Q8×C269C2311yescharacteristic
101C2×C8×C269C2311yescharacteristic
102C2×C8×C269C2311yescharacteristic
103C4⋊C4×C269—21no—
104C4⋊C4×C269—21no—
105C4⋊C4×C269—21no—
106C4⋊C4×C269C2311yescharacteristic
107C4⋊C4×C269C2311yescharacteristic
108C4⋊C4×C269C2311yescharacteristic
109C42×C269—21no—
110C42×C269C2311yescharacteristic
111C22×D269C2×D411yescharacteristic
112C22×D269C2×D411yescharacteristic
113Dic538—21no—
114Dic538—21no—
115Dic538—21no—
116Dic538—21no—
117Dic538—21no—
118Dic538—21no—
119Dic538—42no—
120Dic538—42no—
121D1076—22no—
122C2×Dic269—21no—
123C2×Dic269—21no—
124C2×Dic269—21no—
125C2×Dic269—21no—
126C2×Dic269C2×D411yescharacteristic
127C2×Dic269C2×D411yescharacteristic
128C4×D269—21no—
129C4×D269—21no—
130C4×D269—21no—
131C4×D269—21no—
132C4×D269—42no—
133C4×D269—42no—
134C4×D269—42no—
135#14524130—21no—
136#14524130—21no—
137Q8×C269—21no—
138Q8×C269#4112yes—
139C2×C4×C269—21no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269C2×D411yescharacteristic
144C2×C4×C269C2×D411yescharacteristic
145C2×C4×C269C2411yescharacteristic
146C8×C269—21no—
147C8×C269—21no—
148C22×C269C22×D411yescharacteristic
149C2×D269—21no—
150C2×D269—21no—
151C2×D269—21no—
152C2×D269—21no—
153C2×D269—21no—
154C2×D269#13712yes—
155C4×C269—22no—
156C4×C269—21no—
157C4×C269—21no—
158C4×C269—41no—
159C4×C269—41no—
160C4×C269—41no—
161C4×C269C2×#4111yescharacteristic
162C4×C269H(5,𝔽2)11yescharacteristic
163Dic269—21no—
164Dic269—21no—
165Dic269—41no—
166Dic269—41no—
167Dic269—41no—
168Dic269—41no—
169C2×C269#54611yescharacteristic
170C2×C269C2×#13711yescharacteristic
171C2×C269#57811yescharacteristic
172D269—22no—
173D269—41no—
174C269#331211yescharacteristic, complemented, Sylow
175#3312—2691nomaximal, Sylow
176#552—2691no—
177D4×Q8—2691no—
178#491—2691no—
179#485—2691no—
180#483—2691no—
181#479D26911yescharacteristic, complemented
182#470—2691no—
183#467—2691no—
184#462—2691no—
185#451—2691no—
186#451—2691no—
187#441—2691no—
188#435—2691no—
189#419—2691no—
190C2×#103—2691no—
191C22×Q8—2691no—
192C22×Q8—2691no—
193C2×Q16—2691no—
194C2×Q16—2691no—
195C2×Q16—2691no—
196C2×M16—2691no—
197C22×C8—2691no—
198C4⋊Q8—2691no—
199C4⋊Q8—5381no—
200#126—5381no—
201#125—5381no—
202#125C2×D26911yescharacteristic
203#123—5381no—
204C22⋊Q8—2691no—
205C22⋊Q8—2691no—
206C22⋊Q8—2691no—
207C22⋊Q8—2691no—
208C22⋊Q8—5381no—
209C22⋊Q8—5381no—
210C4×Q8—2691no—
211C4×Q8C2×D26911yescharacteristic
212C4×D4—2691no—
213C4×D4—5381no—
214#117—2691no—
215#117—5381no—
216C2×C4⋊C4—2691no—
217#107C2×D26911yescharacteristic
218#106—2691no—
219#106C2×D26911yescharacteristic
220C4⋊C8C2×D26911yescharacteristic
221#103—2691no—
222#103—2691no—
223#103—2691no—
224#103—2691no—
225#103—2691no—
226#103—2691no—
227#103—2691no—
228#103—2691no—
229#103C2×D26911yescharacteristic
230#103C2×D26911yescharacteristic
231C22⋊C8—2691no—
232C22⋊C8—2691no—
233#97—2691no—
234C2×Q8—2691no—
235C2×Q8—2691no—
236C2×Q8—2691no—
237C2×Q8—5381no—
238C2×Q8—5381no—
239C2×Q8—5382no—
240C2×Q8—5382no—
241C2×Q8—10761no—
242C2×Q8—10761no—
243C2×Q8C22×D26911yescharacteristic
244C2×D4—2691no—
245C22×C4—2691no—
246C22×C4—2691no—
247C22×C4—5381no—
248C22×C4—5381no—
249C22×C4—5381no—
250Q16—5382no—
251Q16—10761no—
252Q16—10761no—
253M16—10761no—
254C2×C8—2691no—
255C2×C8—2691no—
256C2×C8—10761no—
257C2×C8C22×D26911yescharacteristic
258C2×C8C22×D26911yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—2691no—
263C4⋊C4—2691no—
264C4⋊C4—5381no—
265C4⋊C4—5381no—
266C4⋊C4—5381no—
267C4⋊C4—5381no—
268C4⋊C4—5381no—
269C4⋊C4—5381no—
270C4⋊C4—5381no—
271C4⋊C4—5381no—
272C4⋊C4C22×D26911yescharacteristic
273C4⋊C4C22×D26911yescharacteristic
274C4⋊C4C22×D26911yescharacteristic
275C22⋊C4—2691no—
276C22⋊C4—2691no—
277C22⋊C4—5381no—
278C22⋊C4—5381no—
279C22⋊C4—5381no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C42—21no—
283C42—5381no—
284C42—5381no—
285C42C22×D26911yescharacteristic
286C23—2691no—
287C23—2691no—
288Q8—21no—
289Q8—5381no—
290Q8—5381no—
291Q8—5381no—
292Q8—5381no—
293Q8—5381no—
294Q8—5381no—
295Q8—10762no—
296Q8—10762no—
297Q8#1686440312yes—
298D4—5382no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—2691no—
304C2×C4—2691no—
305C2×C4—5381no—
306C2×C4—5381no—
307C2×C4—5381no—
308C2×C4—5381no—
309C2×C4—5381no—
310C2×C4—5381no—
311C2×C4—5381no—
312C2×C4—5381no—
313C2×C4—10762no—
314C2×C4—10762no—
315C2×C4—10762no—
316C2×C4D4×D26911yescharacteristic
317C2×C4D4×D26911yescharacteristic
318C2×C4C23×D26911yescharacteristic
319C8—21no—
320C8—21no—
321C8—5381no—
322C8—5381no—
323C22—2692no—
324C22—5381no—
325C22—5381no—
326C22—5381no—
327C22—5381no—
328C22—5381no—
329C22C2×D4×D26911yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—5381no—
337C4—5381no—
338C4—10761no—
339C4—10761no—
340C4—10761no—
341C4—10761no—
342C4C2×#1686440311yescharacteristic
343C4#2257549911yescharacteristic
344C2—5382no—
345C2—10761no—
346C2#3177124611yescharacteristic
347C2#137×D26911yescharacteristic
348C2#3177141911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#479×C269C2
socleC22×C269C22×D4
prime radicalC2×D1076D4
hypercenter#479D269
hypocenterC269#3312
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
3. #31770975C2semidirect
4. #31770948C2semidirect
5. #31770937C2semidirect
6. #31770864C2semidirect
7. #31770847C2semidirect
8. #31770816C2semidirect
9. #31770762C2semidirect
10. #31770762C2semidirect
11. #31770710C2semidirect
13. #31770612C2semidirect
14. #103×D269C2semidirect
15. #479×C269C2semidirect
174. C269#3312semidirect
181. #479D269semidirect

Maximal subgroups

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

subgroupindex
#317712932
Q8×D10762
#317709752
#317709482
#317709372
#317708642
#317708472
#317708162
#317707622
#317707102
#317706752
#317706122
#103×D2692
#479×C2692
#3312269