Finite Group Databasebeta

← #46822765

Subgroups — #46822765

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#31771289C211yesmaximal, characteristic, complemented
2#31771262C211yesmaximal, characteristic
3#31770958C211yesmaximal, characteristic, complemented
4#31770947C211yesmaximal, characteristic, complemented
5#31770917C211yesmaximal, characteristic, complemented
6#31770910C211yesmaximal, characteristic, complemented
7#31770844C211yesmaximal, characteristic, complemented
8#31770831C211yesmaximal, characteristic, complemented
9#31770825C211yesmaximal, characteristic, complemented
10#31770759C211yesmaximal, characteristic, complemented
11Q16×Dic269C211yesmaximal, characteristic, complemented
12#31770668C211yesmaximal, characteristic, complemented
13#31770601C211yesmaximal, characteristic, complemented
14#103×D269C211yesmaximal, characteristic, complemented
15#452×C269C211yesmaximal, characteristic, complemented
16C2×Q8×D269C2211yescharacteristic
17C2×#16864392C2211yescharacteristic
18C22×#14524130C2211yescharacteristic
19C2×C8×D269C2211yescharacteristic
20#22575446—21no—
21#22575444C2211yescharacteristic
22#22575443—21no—
23#22575440—21no—
24#22575440C2211yescharacteristic
25#22575435—21no—
26#22575432—21no—
27#22575432C2211yescharacteristic
28#22575429C2211yescharacteristic
29#22575424—21no—
30#22575424C2211yescharacteristic
31Q8×Dic269C2211yescharacteristic
32Q8×Dic269C2211yescharacteristic
33C4×C22⋊D269—21no—
34C4×C22⋊D269C2211yescharacteristic
35#22575412C2211yescharacteristic
36#22575411—21no—
37C4⋊C4×D269C2211yescharacteristic
38#22575387C2211yescharacteristic
39#22575386C2211yescharacteristic
40#22575385C2211yescharacteristic
41#22575382C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575378C2211yescharacteristic
44#22575377C2211yescharacteristic
45#22575377C2211yescharacteristic
46#22575377C2211yescharacteristic
47#22575376C2211yescharacteristic
48#22575374C2211yescharacteristic
49#22575374C2211yescharacteristic
50#22575365C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C2×#41×C269C2211yescharacteristic
53C2×Q16×C269C2211yescharacteristic
54C2×SD16×C269C2211yescharacteristic
55C22⋊Q8×C269C2211yescharacteristic
56#103×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58C22⋊C8×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538C2311yescharacteristic
61Q8×D269—22no—
62Q8×D269—41no—
63C2×C22⋊D269—21no—
64C2×C22⋊D269D411yescharacteristic
65C2×C4×D269—21no—
66C2×C4×D269—21no—
67C2×C4×D269C2311yescharacteristic
68#16864392—41no—
69C2×#14524130—41no—
70C2×#14524130C2311yescharacteristic
71C2×#14524130C2311yescharacteristic
72C8×D269—41no—
73C4⋊Dic269—21no—
74C4⋊Dic269—21no—
75C4⋊Dic269—21no—
76C4⋊Dic269C2311yescharacteristic
77C4⋊Dic269C2311yescharacteristic
78C4⋊Dic269C2311yescharacteristic
79#16864381—21no—
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83#16864381D411yescharacteristic
84C22⋊Dic269—21no—
85C22⋊Dic269—21no—
86C22⋊Dic269—21no—
87C22⋊Dic269—21no—
88C22⋊Dic269—21no—
89C22⋊Dic269D411yescharacteristic
90#16864379—21no—
91#16864379D411yescharacteristic
92C4×Dic269—21no—
93C4×Dic269—21no—
94C4×Dic269—21no—
95C4×Dic269C2311yescharacteristic
96#41×C269—22no—
97#41×C269—41no—
98C2×Q8×C269C2311yescharacteristic
99C2×Q8×C269C2311yescharacteristic
100C2×D4×C269—21no—
101C2×D4×C269C2311yescharacteristic
102C22×C4×C269—21no—
103C22×C4×C269C2311yescharacteristic
104Q16×C269—22no—
105SD16×C269—41no—
106C2×C8×C269C2311yescharacteristic
107C2×C8×C269C2311yescharacteristic
108C4⋊C4×C269—21no—
109C4⋊C4×C269C2311yescharacteristic
110C22⋊C4×C269—21no—
111C22×D269C2×D411yescharacteristic
112Dic538—21no—
113Dic538—21no—
114Dic538—42no—
115C22⋊D269—22no—
116C22⋊D269—42no—
117C2×Dic269—21no—
118C2×Dic269—21no—
119C2×Dic269—21no—
120C2×Dic269—21no—
121C2×Dic269C2×D411yescharacteristic
122C2×Dic269C2×D411yescharacteristic
123C2×Dic269C2×D411yescharacteristic
124C4×D269—21no—
125C4×D269—21no—
126C4×D269—42no—
127C4×D269—42no—
128#14524130—21no—
129#14524130—21no—
130C23×C269—21no—
131C23×C269C2×D411yescharacteristic
132Q8×C269—21no—
133Q8×C269—21no—
134Q8×C269—21no—
135Q8×C269#4112yes—
136D4×C269—21no—
137D4×C269—21no—
138D4×C269—42no—
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—21no—
151C22×C269—21no—
152C22×C269—41no—
153C22×C269—41no—
154C22×C269—41no—
155C22×C269C22×D411yescharacteristic
156C2×D269—21no—
157C2×D269—21no—
158C2×D269#13512yes—
159C4×C269—21no—
160C4×C269—22no—
161C4×C269—41no—
162C4×C269—41no—
163C4×C269C2×#4111yescharacteristic
164C4×C269H(5,𝔽2)11yescharacteristic
165Dic269—21no—
166Dic269—21no—
167Dic269—21no—
168Dic269—41no—
169Dic269—41no—
170Dic269—41no—
171Dic269—41no—
172C2×C269—41no—
173C2×C269—81no—
174C2×C269#54611yescharacteristic
175C2×C269C2×#13511yescharacteristic
176C2×C269#57811yescharacteristic
177D269—22no—
178C269#330011yescharacteristic, complemented, Sylow
179#3300—2691nomaximal, Sylow
180#552—2691no—
181#548—2691no—
182#488—2691no—
183#485—2691no—
184#480—2691no—
185#479—2691no—
186#467—2691no—
187#465—2691no—
188#464—2691no—
189#452D26911yescharacteristic, complemented
190#451—2691no—
191C4×Q16—2691no—
192C8×D4—2691no—
193#416—2691no—
194C2×#103—2691no—
195C2×#41C2×D26911yescharacteristic
196C22×Q8—2691no—
197C2×Q16—2691no—
198C2×Q16C2×D26911yescharacteristic
199C2×SD16C2×D26911yescharacteristic
200C22×C8—2691no—
201C22×C8—2691no—
202#126—5381no—
203#125—2691no—
204#125—5381no—
205#124—2691no—
206#124—5381no—
207#123—5381no—
208C22⋊Q8—2691no—
209C22⋊Q8—2691no—
210C22⋊Q8—5381no—
211C22⋊Q8C2×D26911yescharacteristic
212#121—2691no—
213#121—5381no—
214C4×Q8—2691no—
215C4×Q8—2691no—
216C4×D4—2691no—
217C4×D4—5381no—
218#117—2691no—
219#117—5381no—
220C2×C4⋊C4—2691no—
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#103—2691no—
231#103C2×D26911yescharacteristic
232#102—2691no—
233#102—2691no—
234#102C2×D26911yescharacteristic
235C22⋊C8—2691no—
236C22⋊C8C2×D26911yescharacteristic
237C4×C8—2691no—
238#41—22no—
239#41—41no—
240C2×Q8—2691no—
241C2×Q8—5381no—
242C2×Q8—5382no—
243C2×Q8—10761no—
244C2×Q8C22×D26911yescharacteristic
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—22no—
256Q16—10761no—
257SD16—41no—
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—2691no—
268C4⋊C4—2691no—
269C4⋊C4—5381no—
270C4⋊C4—5381no—
271C4⋊C4—5381no—
272C4⋊C4—5381no—
273C4⋊C4—5381no—
274C4⋊C4—5381no—
275C4⋊C4—5381no—
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—2691no—
287C42—5381no—
288C42—5381no—
289C42—5381no—
290C23—21no—
291C23—2691no—
292C23D4×D26911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—5381no—
297Q8—5381no—
298Q8—10762no—
299Q8#1686440112yes—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—5382no—
304D4—10762no—
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—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—2692no—
335C22—5381no—
336C22—5381no—
337C22C2×D4×D26911yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—5381no—
343C4—5381no—
344C4—5381no—
345C4—10761no—
346C4—10761no—
347C4—10761no—
348C4—10761no—
349C4C2×#1686440111yescharacteristic
350C4#2257549811yescharacteristic
351C2—41no—
352C2—81no—
353C2—5382no—
354C2#3177124211yescharacteristic
355C2#135×D26911yescharacteristic
356C2#3177142111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#452×C269C2
socleC22×C269C22×D4
prime radical#31771262C2
hypercenter#452D269
hypocenterC269#3300
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #31771289C2semidirect
3. #31770958C2semidirect
4. #31770947C2semidirect
5. #31770917C2semidirect
6. #31770910C2semidirect
7. #31770844C2semidirect
8. #31770831C2semidirect
9. #31770825C2semidirect
10. #31770759C2semidirect
11. Q16×Dic269C2semidirect
12. #31770668C2semidirect
13. #31770601C2semidirect
14. #103×D269C2semidirect
15. #452×C269C2semidirect
178. C269#3300semidirect
189. #452D269semidirect

Maximal subgroups

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

subgroupindex
#317712892
#317712622
#317709582
#317709472
#317709172
#317709102
#317708442
#317708312
#317708252
#317707592
Q16×Dic2692
#317706682
#317706012
#103×D2692
#452×C2692
#3300269