Finite Group Databasebeta

← #46822798

Subgroups — #46822798

Order 34432.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771323C211yesmaximal, characteristic, complemented
2#31771254C211yesmaximal, characteristic
3#31770954C211yesmaximal, characteristic, complemented
4#31770946C211yesmaximal, characteristic, complemented
5#31770945C211yesmaximal, characteristic, complemented
6#31770883C211yesmaximal, characteristic, complemented
7#31770846C211yesmaximal, characteristic, complemented
8#31770845C211yesmaximal, characteristic, complemented
9#31770814C211yesmaximal, characteristic, complemented
10#31770768C211yesmaximal, characteristic, complemented
11#31770767C211yesmaximal, characteristic, complemented
12#31770696C211yesmaximal, characteristic, complemented
13C8×C22⋊D269C211yesmaximal, characteristic, complemented
14#31770598C211yesmaximal, characteristic, complemented
15#416×C269C211yesmaximal, characteristic, complemented
16C2×#16864401C2211yescharacteristic
17C2×Dic1076C2211yescharacteristic
18C2×#16864392C2211yescharacteristic
19C2×#16864390C2211yescharacteristic
20C2×C8×D269C2211yescharacteristic
21#22575452C2211yescharacteristic
22#22575451C2211yescharacteristic
23#22575447—21no—
24#22575446—21no—
25#22575439—21no—
26#22575436—21no—
27#22575434—21no—
28#22575433C2211yescharacteristic
29#22575432C2211yescharacteristic
30#22575432C2211yescharacteristic
31#22575429C2211yescharacteristic
32#22575425—21no—
33C4×Dic538—21no—
34#22575418C2211yescharacteristic
35D4×Dic269C2211yescharacteristic
36C4×C22⋊D269C2211yescharacteristic
37#22575411C2211yescharacteristic
38C2×#16864381—21no—
39#22575387C2211yescharacteristic
40#22575386C2211yescharacteristic
41#22575384C2211yescharacteristic
42#22575382C2211yescharacteristic
43#22575378C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575377C2211yescharacteristic
46#22575376C2211yescharacteristic
47#22575376C2211yescharacteristic
48#22575374C2211yescharacteristic
49C22⋊#14524130C2211yescharacteristic
50#22575365C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C2×#41×C269C2211yescharacteristic
53C22×C8×C269C2211yescharacteristic
54#117×C269C2211yescharacteristic
55#103×C269C2211yescharacteristic
56#103×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59#16864401—22no—
60#16864401—41no—
61C2×Dic538—21no—
62C2×Dic538C2311yescharacteristic
63C2×Dic538C2311yescharacteristic
64C2×C22⋊D269—21no—
65C2×C22⋊D269D411yescharacteristic
66C22×Dic269—21no—
67C22×Dic269—21no—
68C2×C4×D269C2311yescharacteristic
69Dic1076—41no—
70#16864392—41no—
71#16864390—22no—
72C2×#14524130C2311yescharacteristic
73C2×#14524130C2311yescharacteristic
74C8×D269—41no—
75C4⋊Dic269—21no—
76C4⋊Dic269C2311yescharacteristic
77C4⋊Dic269C2311yescharacteristic
78#16864381—21no—
79#16864381—21no—
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85#16864381D411yescharacteristic
86C22⋊Dic269—21no—
87C22⋊Dic269—21no—
88C22⋊Dic269—21no—
89C22⋊Dic269D411yescharacteristic
90#16864379—21no—
91#16864379—21no—
92#16864379—21no—
93#16864379D411yescharacteristic
94C4×Dic269—21no—
95C4×Dic269—21no—
96C4×Dic269C2311yescharacteristic
97#41×C269—22no—
98#41×C269—41no—
99C2×Q8×C269C2311yescharacteristic
100C2×D4×C269—21no—
101C2×D4×C269C2311yescharacteristic
102C22×C4×C269—21no—
103C22×C4×C269C2311yescharacteristic
104C2×C8×C269—41no—
105C2×C8×C269C2311yescharacteristic
106C2×C8×C269C2311yescharacteristic
107C4⋊C4×C269C2311yescharacteristic
108C4⋊C4×C269C2311yescharacteristic
109C22⋊C4×C269—21no—
110C42×C269—21no—
111C22×D269C2×D411yescharacteristic
112Dic538—21no—
113Dic538—21no—
114Dic538—21no—
115Dic538—21no—
116Dic538—42no—
117C22⋊D269—22no—
118C22⋊D269—42no—
119C2×Dic269—21no—
120C2×Dic269—21no—
121C2×Dic269—21no—
122C2×Dic269—21no—
123C2×Dic269—42no—
124C2×Dic269—42no—
125C2×Dic269C2×D411yescharacteristic
126C2×Dic269C2×D411yescharacteristic
127C2×Dic269C2×D411yescharacteristic
128C4×D269—21no—
129C4×D269—21no—
130#14524130—21no—
131#14524130—21no—
132C23×C269—21no—
133C23×C269C2×D411yescharacteristic
134Q8×C269—21no—
135Q8×C269—21no—
136D4×C269—21no—
137D4×C269—42no—
138D4×C269#4112yes—
139C2×C4×C269—21no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269—42no—
145C2×C4×C269C2×D411yescharacteristic
146C2×C4×C269C2411yescharacteristic
147C8×C269—21no—
148C8×C269—21no—
149C22×C269—21no—
150C22×C269—22no—
151C22×C269—21no—
152C22×C269—21no—
153C22×C269—41no—
154C22×C269—41no—
155C22×C269C22×D411yescharacteristic
156C2×D269—21no—
157C2×D269—21no—
158C2×D269—21no—
159C4×C269—21no—
160C4×C269—41no—
161C4×C269—41no—
162C4×C269—41no—
163C4×C269C2×#4111yescharacteristic
164C4×C269H(5,𝔽2)11yescharacteristic
165Dic269—21no—
166Dic269—21no—
167Dic269—41no—
168Dic269—41no—
169Dic269—41no—
170Dic269—41no—
171Dic269#13512yes—
172C2×C269—41no—
173C2×C269—42no—
174C2×C269#54611yescharacteristic
175C2×C269C2×#13511yescharacteristic
176C2×C269#57811yescharacteristic
177D269—41no—
178C269#330211yescharacteristic, complemented, Sylow
179#3302—2691nomaximal, Sylow
180#556—2691no—
181#547—2691no—
182#487—2691no—
183#485—2691no—
184#485—2691no—
185#474—2691no—
186#467—2691no—
187#467—2691no—
188#462—2691no—
189#452—2691no—
190#452—2691no—
191C4×SD16—2691no—
192C8×D4—2691no—
193#416—2691no—
194#416D26911yescharacteristic, complemented
195C2×#41—2691no—
196C2×#41C2×D26911yescharacteristic
197C2×Q16—2691no—
198C2×Q16—2691no—
199C2×SD16—2691no—
200C22×C8—2691no—
201C22×C8C2×D26911yescharacteristic
202C4⋊Q8—2691no—
203C4⋊Q8—2691no—
204#126—5381no—
205#126—5381no—
206#124—5381no—
207#123—5381no—
208#123—5381no—
209C22⋊Q8—2691no—
210C22⋊Q8—2691no—
211C22⋊Q8—2691no—
212C22⋊Q8—2691no—
213#121—5381no—
214C4×Q8—2691no—
215C4×Q8—5381no—
216C4×D4—2691no—
217C4×D4—2691no—
218#117—2691no—
219#117C2×D26911yescharacteristic
220C2×C4⋊C4—5381no—
221#107—2691no—
222#107—2691no—
223#106—2691no—
224C4⋊C8—2691no—
225#103—2691no—
226#103—2691no—
227#103—2691no—
228#103—2691no—
229#103—2691no—
230#103C2×D26911yescharacteristic
231#103C2×D26911yescharacteristic
232#102—2691no—
233#102C2×D26911yescharacteristic
234#102C2×D26911yescharacteristic
235C22⋊C8—2691no—
236C22⋊C8—2691no—
237C4×C8—2691no—
238#41—22no—
239#41—41no—
240#41—5382no—
241#41—10761no—
242C2×Q8—2691no—
243C2×Q8—2691no—
244C2×Q8—5381no—
245C2×Q8C22×D26911yescharacteristic
246C2×D4—21no—
247C2×D4—2691no—
248C2×D4—5381no—
249C2×D4C22×D26911yescharacteristic
250C22×C4—21no—
251C22×C4—2691no—
252C22×C4—5381no—
253C22×C4—5381no—
254C22×C4C22×D26911yescharacteristic
255Q16—10761no—
256Q16—10761no—
257SD16—5382no—
258C2×C8—41no—
259C2×C8—2691no—
260C2×C8—2691no—
261C2×C8—10761no—
262C2×C8C22×D26911yescharacteristic
263C2×C8C22×D26911yescharacteristic
264C4⋊C4—2691no—
265C4⋊C4—2691no—
266C4⋊C4—2691no—
267C4⋊C4—5381no—
268C4⋊C4—5381no—
269C4⋊C4—5381no—
270C4⋊C4—5381no—
271C4⋊C4—5381no—
272C4⋊C4—5381no—
273C4⋊C4—5381no—
274C4⋊C4—5381no—
275C4⋊C4C22×D26911yescharacteristic
276C4⋊C4C22×D26911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2691no—
279C22⋊C4—2691no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C22⋊C4—5381no—
283C22⋊C4—5381no—
284C22⋊C4—5381no—
285C22⋊C4—5381no—
286C42—21no—
287C42—2691no—
288C42—5381no—
289C42—5381no—
290C23—21no—
291C23—2691no—
292C23D4×D26911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—5381no—
296Q8—5381no—
297Q8—5381no—
298Q8—5381no—
299Q8—10762no—
300D4—21no—
301D4—42no—
302D4—5382no—
303D4—10762no—
304D4#1686440212yes—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—2691no—
312C2×C4—2691no—
313C2×C4—2691no—
314C2×C4—5381no—
315C2×C4—5381no—
316C2×C4—5381no—
317C2×C4—5381no—
318C2×C4—5381no—
319C2×C4—5381no—
320C2×C4—10762no—
321C2×C4—10762no—
322C2×C4D4×D26911yescharacteristic
323C2×C4C23×D26911yescharacteristic
324C8—21no—
325C8—21no—
326C8—5381no—
327C8—5381no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—5381no—
335C22—5381no—
336C22—5381no—
337C22C2×D4×D26911yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—2692no—
343C4—5381no—
344C4—5381no—
345C4—10761no—
346C4—10761no—
347C4—10761no—
348C4—10761no—
349C4C2×#1686440211yescharacteristic
350C4#2257549811yescharacteristic
351C2—41no—
352C2—42no—
353C2—10761no—
354C2#3177124511yescharacteristic
355C2#135×D26911yescharacteristic
356C2#3177141911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#416×C269C2
socleC22×C269C22×D4
prime radical#31771254C2
hypercenter#416D269
hypocenterC269#3302
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #31771323C2semidirect
3. #31770954C2semidirect
4. #31770946C2semidirect
5. #31770945C2semidirect
6. #31770883C2semidirect
7. #31770846C2semidirect
8. #31770845C2semidirect
9. #31770814C2semidirect
10. #31770768C2semidirect
11. #31770767C2semidirect
12. #31770696C2semidirect
13. C8×C22⋊D269C2semidirect
14. #31770598C2semidirect
15. #416×C269C2semidirect
178. C269#3302semidirect
194. #416D269semidirect

Maximal subgroups

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

subgroupindex
#317713232
#317712542
#317709542
#317709462
#317709452
#317708832
#317708462
#317708452
#317708142
#317707682
#317707672
#317706962
C8×C22⋊D2692
#317705982
#416×C2692
#3302269