Finite Group Databasebeta

← #46822800

Subgroups — #46822800

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#31771257C211yesmaximal, characteristic
3#31770954C211yesmaximal, characteristic, complemented
4#31770949C211yesmaximal, characteristic, complemented
5#31770884C211yesmaximal, characteristic, complemented
6#31770847C211yesmaximal, characteristic, complemented
7#31770844C211yesmaximal, characteristic, complemented
8#31770814C211yesmaximal, characteristic, complemented
9#31770770C211yesmaximal, characteristic, complemented
10#31770769C211yesmaximal, characteristic, complemented
11#31770692C211yesmaximal, characteristic, complemented
12#31770668C211yesmaximal, characteristic, complemented
13#31770600C211yesmaximal, characteristic, complemented
14#31770599C211yesmaximal, characteristic, complemented
15#485×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic
17C2×#16864402C2211yescharacteristic
18C2×Dic1076C2211yescharacteristic
19C2×#16864392C2211yescharacteristic
20C2×#16864391C2211yescharacteristic
21C22×#14524130C2211yescharacteristic
22C2×C8×D269C2211yescharacteristic
23#22575452C2211yescharacteristic
24#22575451C2211yescharacteristic
25#22575447—21no—
26#22575446—21no—
27#22575439—21no—
28#22575438—21no—
29#22575435—21no—
30#22575433C2211yescharacteristic
31#22575433C2211yescharacteristic
32#22575432C2211yescharacteristic
33#22575426—21no—
34C4×Dic538—21no—
35#22575418C2211yescharacteristic
36#22575415C2211yescharacteristic
37C4×C22⋊D269C2211yescharacteristic
38#22575411C2211yescharacteristic
39C4⋊C4×D269—21no—
40#22575386C2211yescharacteristic
41#22575382C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575377C2211yescharacteristic
44#22575376C2211yescharacteristic
45#22575376C2211yescharacteristic
46#22575376C2211yescharacteristic
47#22575375C2211yescharacteristic
48#22575373C2211yescharacteristic
49#22575373C2211yescharacteristic
50#22575365C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C22⋊Q8×C269C2211yescharacteristic
53#117×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56#103×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58C22⋊C8×C269C2211yescharacteristic
59#16864403—22no—
60#16864403—41no—
61#16864402—22no—
62#16864402—41no—
63C2×Dic538—21no—
64C2×Dic538C2311yescharacteristic
65C2×Dic538C2311yescharacteristic
66C2×D1076—21no—
67C2×D1076C2311yescharacteristic
68C2×C22⋊D269—21no—
69C2×C22⋊D269D411yescharacteristic
70C2×C4×D269—21no—
71C2×C4×D269—21no—
72C2×C4×D269—21no—
73C2×C4×D269C2311yescharacteristic
74Dic1076—41no—
75#16864392—41no—
76#16864391—22no—
77C2×#14524130—41no—
78C2×#14524130C2311yescharacteristic
79C2×#14524130C2311yescharacteristic
80C8×D269—41no—
81C4⋊Dic269—21no—
82C4⋊Dic269—21no—
83C4⋊Dic269C2311yescharacteristic
84#16864381—21no—
85#16864381—21no—
86#16864381—21no—
87#16864381—21no—
88#16864381—21no—
89#16864381D411yescharacteristic
90C22⋊Dic269—21no—
91C22⋊Dic269D411yescharacteristic
92#16864379—21no—
93#16864379—21no—
94#16864379—21no—
95#16864379—21no—
96#16864379D411yescharacteristic
97C4×Dic269—21no—
98C4×Dic269—21no—
99C4×Dic269C2311yescharacteristic
100C2×Q8×C269C2311yescharacteristic
101C22×C4×C269C2311yescharacteristic
102C2×C8×C269C2311yescharacteristic
103C2×C8×C269C2311yescharacteristic
104C4⋊C4×C269—21no—
105C4⋊C4×C269C2311yescharacteristic
106C4⋊C4×C269C2311yescharacteristic
107C4⋊C4×C269C2311yescharacteristic
108C22⋊C4×C269—21no—
109C22⋊C4×C269—21no—
110C42×C269—21no—
111C22×D269—21no—
112C22×D269C2×D411yescharacteristic
113Dic538—21no—
114Dic538—21no—
115Dic538—21no—
116Dic538—21no—
117Dic538—42no—
118D1076—21no—
119D1076—42no—
120D1076#4112yes—
121C22⋊D269—22no—
122C22⋊D269—42no—
123C2×Dic269—21no—
124C2×Dic269—21no—
125C2×Dic269—21no—
126C2×Dic269C2×D411yescharacteristic
127C2×Dic269C2×D411yescharacteristic
128C2×Dic269C2×D411yescharacteristic
129C4×D269—21no—
130C4×D269—21no—
131C4×D269—42no—
132C4×D269—42no—
133C4×D269—42no—
134#14524130—21no—
135#14524130—21no—
136C23×C269C2×D411yescharacteristic
137Q8×C269—21no—
138Q8×C269—21no—
139C2×C4×C269—21no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269C2×D411yescharacteristic
146C2×C4×C269C2411yescharacteristic
147C8×C269—21no—
148C8×C269—21no—
149C22×C269—21no—
150C22×C269—21no—
151C22×C269—21no—
152C22×C269C22×D411yescharacteristic
153C2×D269—21no—
154C2×D269—22no—
155C2×D269—21no—
156C2×D269—21no—
157C2×D269—41no—
158C2×D269—41no—
159C4×C269—21no—
160C4×C269—41no—
161C4×C269—41no—
162C4×C269—41no—
163C4×C269—41no—
164C4×C269C2×#4111yescharacteristic
165C4×C269H(5,𝔽2)11yescharacteristic
166Dic269—21no—
167Dic269—21no—
168Dic269—41no—
169Dic269—41no—
170Dic269—41no—
171Dic269#13512yes—
172C2×C269—41no—
173C2×C269#54611yescharacteristic
174C2×C269C2×#13511yescharacteristic
175C2×C269#57811yescharacteristic
176D269—41no—
177D269—42no—
178C269#330211yescharacteristic, complemented, Sylow
179#3302—2691nomaximal, Sylow
180#556—2691no—
181#547—2691no—
182#487—2691no—
183#485—2691no—
184#485D26911yescharacteristic, complemented
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#416—2691no—
195C2×#41—2691no—
196C2×#41—2691no—
197C2×Q16—2691no—
198C2×Q16—2691no—
199C2×SD16—2691no—
200C22×C8—2691no—
201C22×C8—2691no—
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⋊Q8C2×D26911yescharacteristic
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#107C2×D26911yescharacteristic
223#106C2×D26911yescharacteristic
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#102—2691no—
234#102—2691no—
235C22⋊C8—2691no—
236C22⋊C8C2×D26911yescharacteristic
237C4×C8—2691no—
238#41—5382no—
239#41—5382no—
240#41—10761no—
241#41—10761no—
242C2×Q8—2691no—
243C2×Q8—2691no—
244C2×Q8—5381no—
245C2×Q8C22×D26911yescharacteristic
246C2×D4—2691no—
247C2×D4—2691no—
248C2×D4—5381no—
249C2×D4—5381no—
250C22×C4—2691no—
251C22×C4—5381no—
252C22×C4—5381no—
253C22×C4—5381no—
254C22×C4C22×D26911yescharacteristic
255Q16—10761no—
256Q16—10761no—
257SD16—5382no—
258C2×C8—2691no—
259C2×C8—2691no—
260C2×C8—10761no—
261C2×C8—10761no—
262C2×C8C22×D26911yescharacteristic
263C2×C8C22×D26911yescharacteristic
264C4⋊C4—21no—
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⋊C4C22×D26911yescharacteristic
275C4⋊C4C22×D26911yescharacteristic
276C4⋊C4C22×D26911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2691no—
280C22⋊C4—2691no—
281C22⋊C4—5381no—
282C22⋊C4—5381no—
283C22⋊C4—5381no—
284C22⋊C4—5381no—
285C22⋊C4—5381no—
286C42—21no—
287C42—2691no—
288C42—5381no—
289C42—5381no—
290C23—2691no—
291C23—5381no—
292C23D4×D26911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—5381no—
296Q8—5381no—
297Q8—5381no—
298Q8—5381no—
299Q8—10762no—
300D4—2692no—
301D4—5382no—
302D4—5381no—
303D4—10762no—
304D4—10762no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
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—10762no—
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—21no—
331C22—5381no—
332C22—5381no—
333C22—5382no—
334C22—5381no—
335C22—10761no—
336C22—10761no—
337C22C2×D4×D26911yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—2692no—
344C4—5381no—
345C4—5381no—
346C4—10761no—
347C4—10761no—
348C4—10761no—
349C4#41×D26911yescharacteristic
350C4#2257549911yescharacteristic
351C2—41no—
352C2—10761no—
353C2—10762no—
354C2#3177124711yescharacteristic
355C2#135×D26911yescharacteristic
356C2#3177142111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#485×C269C2
socleC22×C269C22×D4
prime radical#31771257C2
hypercenter#485D269
hypocenterC269#3302
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #31771323C2semidirect
3. #31770954C2semidirect
4. #31770949C2semidirect
5. #31770884C2semidirect
6. #31770847C2semidirect
7. #31770844C2semidirect
8. #31770814C2semidirect
9. #31770770C2semidirect
10. #31770769C2semidirect
11. #31770692C2semidirect
12. #31770668C2semidirect
13. #31770600C2semidirect
14. #31770599C2semidirect
15. #485×C269C2semidirect
178. C269#3302semidirect
184. #485D269semidirect

Maximal subgroups

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

subgroupindex
#317713232
#317712572
#317709542
#317709492
#317708842
#317708472
#317708442
#317708142
#317707702
#317707692
#317706922
#317706682
#317706002
#317705992
#485×C2692
#3302269