Finite Group Databasebeta

← #46822774

Subgroups — #46822774

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#31771295C211yesmaximal, characteristic, complemented
2#31771264C211yesmaximal, characteristic
3#31770960C211yesmaximal, characteristic, complemented
4#31770947C211yesmaximal, characteristic, complemented
5#31770919C211yesmaximal, characteristic, complemented
6#31770913C211yesmaximal, characteristic, complemented
7#31770846C211yesmaximal, characteristic, complemented
8#31770834C211yesmaximal, characteristic, complemented
9#31770828C211yesmaximal, characteristic, complemented
10#31770769C211yesmaximal, characteristic, complemented
11#31770763C211yesmaximal, characteristic, complemented
12C4×Dic1076C211yesmaximal, characteristic, complemented
13#31770602C211yesmaximal, characteristic, complemented
14C2×#22575378C211yesmaximal, characteristic, complemented
15C8×D4×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C22×Dic538C2211yescharacteristic
18C2×Dic1076C2211yescharacteristic
19C2×Dic1076C2211yescharacteristic
20C2×#16864391C2211yescharacteristic
21#22575446—21no—
22#22575445C2211yescharacteristic
23#22575443—21no—
24#22575441C2211yescharacteristic
25#22575439—21no—
26#22575434—21no—
27#22575432C2211yescharacteristic
28#22575432C2211yescharacteristic
29#22575432C2211yescharacteristic
30#22575431—21no—
31#22575427C2211yescharacteristic
32#22575425—21no—
33C4×Dic538C2211yescharacteristic
34C4×Dic538C2211yescharacteristic
35#22575413—21no—
36#22575412C2211yescharacteristic
37#22575409—21no—
38C2×C4⋊Dic269C2211yescharacteristic
39#22575387C2211yescharacteristic
40#22575387C2211yescharacteristic
41#22575385C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575378C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575378C2211yescharacteristic
46#22575378C2211yescharacteristic
47#22575378C2211yescharacteristic
48#22575378C2211yescharacteristic
49#22575375C2211yescharacteristic
50#22575375C2211yescharacteristic
51#22575375C2211yescharacteristic
52C22×C8×C269C2211yescharacteristic
53C22×C8×C269C2211yescharacteristic
54C4×D4×C269C2211yescharacteristic
55C4⋊C8×C269C2211yescharacteristic
56C22⋊C8×C269C2211yescharacteristic
57C22⋊C8×C269C2211yescharacteristic
58C4×C8×C269C2211yescharacteristic
59#16864402—22no—
60#16864402—41no—
61C2×Dic538—22no—
62C2×Dic538—21no—
63C2×Dic538—41no—
64C2×Dic538C2311yescharacteristic
65C2×Dic538C2311yescharacteristic
66C2×Dic538C2311yescharacteristic
67C2×D1076C2311yescharacteristic
68C2×C22⋊D269—21no—
69C2×C22⋊D269—21no—
70C22×Dic269—21no—
71C22×Dic269—21no—
72C2×C4×D269—21no—
73Dic1076—22no—
74Dic1076—41no—
75#16864391—41no—
76C4⋊Dic269—21no—
77C4⋊Dic269C2311yescharacteristic
78C4⋊Dic269C2311yescharacteristic
79C4⋊Dic269C2311yescharacteristic
80C4⋊Dic269C2311yescharacteristic
81#16864381—21no—
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85#16864381—21no—
86#16864381—21no—
87#16864381—21no—
88C22⋊Dic269—21no—
89C22⋊Dic269—21no—
90C22⋊Dic269—21no—
91C22⋊Dic269—21no—
92#16864379—21no—
93#16864379—21no—
94#16864379—21no—
95C4×Dic269—21no—
96C4×Dic269—21no—
97C4×Dic269—21no—
98C2×D4×C269D411yescharacteristic
99C22×C4×C269C2311yescharacteristic
100C22×C4×C269C2311yescharacteristic
101C2×C8×C269—41no—
102C2×C8×C269—41no—
103C2×C8×C269C2311yescharacteristic
104C2×C8×C269C2311yescharacteristic
105C2×C8×C269C2311yescharacteristic
106C2×C8×C269C2311yescharacteristic
107C4⋊C4×C269D411yescharacteristic
108C22⋊C4×C269D411yescharacteristic
109C22⋊C4×C269D411yescharacteristic
110C42×C269C2311yescharacteristic
111C22×D269—21no—
112Dic538—21no—
113Dic538—21no—
114Dic538—21no—
115Dic538—21no—
116Dic538—21no—
117Dic538—42no—
118Dic538#4112yes—
119D1076—21no—
120D1076—21no—
121C22⋊D269—42no—
122C22⋊D269—42no—
123C2×Dic269—21no—
124C2×Dic269—21no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C2×Dic269—21no—
128C2×Dic269—21no—
129C2×Dic269—21no—
130C2×Dic269—42no—
131C2×Dic269—42no—
132C4×D269—42no—
133C23×C269C2×D411yescharacteristic
134C23×C269C2×D411yescharacteristic
135D4×C269—22no—
136C2×C4×C269—21no—
137C2×C4×C269—21no—
138C2×C4×C269—21no—
139C2×C4×C269—21no—
140C2×C4×C269C2×D411yescharacteristic
141C2×C4×C269C2×D411yescharacteristic
142C2×C4×C269C2×D411yescharacteristic
143C2×C4×C269C2×D411yescharacteristic
144C2×C4×C269C2411yescharacteristic
145C8×C269—21no—
146C8×C269—21no—
147C8×C269—21no—
148C8×C269—21no—
149C22×C269—21no—
150C22×C269—21no—
151C22×C269—21no—
152C22×C269—21no—
153C22×C269—21no—
154C22×C269#13512yes—
155C22×C269C22×D411yescharacteristic
156C2×D269—41no—
157C2×D269—41no—
158C2×D269—41no—
159C4×C269—21no—
160C4×C269—21no—
161C4×C269—21no—
162C4×C269—21no—
163C4×C269C2×#4111yescharacteristic
164C4×C269H(5,𝔽2)11yescharacteristic
165Dic269—22no—
166Dic269—41no—
167Dic269—41no—
168Dic269—41no—
169Dic269—41no—
170Dic269—41no—
171Dic269—41no—
172C2×C269—22no—
173C2×C269—41no—
174C2×C269#54611yescharacteristic
175C2×C269C2×#13511yescharacteristic
176C2×C269#57811yescharacteristic
177D269—81no—
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#452—2691no—
190#451—2691no—
191C4×Q16—2691no—
192C8×D4D26911yescharacteristic, complemented
193#416—2691no—
194C2×#103—2691no—
195C2×#41—2691no—
196C22×Q8—2691no—
197C2×Q16—2691no—
198C2×Q16—2691no—
199C2×SD16—2691no—
200C22×C8C2×D26911yescharacteristic
201C22×C8C2×D26911yescharacteristic
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—2691no—
211C22⋊Q8—5381no—
212#121—2691no—
213#121—5381no—
214C4×Q8—2691no—
215C4×Q8—2691no—
216C4×D4—5381no—
217C4×D4C2×D26911yescharacteristic
218#117—2691no—
219#117—5381no—
220C2×C4⋊C4—2691no—
221#107—2691no—
222#107—2691no—
223#106—2691no—
224C4⋊C8C2×D26911yescharacteristic
225#103—2691no—
226#103—2691no—
227#103—2691no—
228#103—2691no—
229#103—2691no—
230#103—2691no—
231#103—2691no—
232#102—2691no—
233#102—2691no—
234#102—2691no—
235C22⋊C8C2×D26911yescharacteristic
236C22⋊C8C2×D26911yescharacteristic
237C4×C8C2×D26911yescharacteristic
238#41—5382no—
239#41—10761no—
240C2×Q8—2691no—
241C2×Q8—2691no—
242C2×Q8—2691no—
243C2×Q8—5382no—
244C2×Q8—5381no—
245C2×Q8—10761no—
246C2×D4—2691no—
247C2×D4—5381no—
248C2×D4—5381no—
249C2×D4D107611yescharacteristic
250C22×C4—5381no—
251C22×C4—5381no—
252C22×C4—5381no—
253C22×C4C22×D26911yescharacteristic
254C22×C4C22×D26911yescharacteristic
255Q16—5382no—
256Q16—10761no—
257SD16—10761no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8C22×D26911yescharacteristic
261C2×C8C22×D26911yescharacteristic
262C2×C8C22×D26911yescharacteristic
263C2×C8C22×D26911yescharacteristic
264C4⋊C4—2691no—
265C4⋊C4—2691no—
266C4⋊C4—2691no—
267C4⋊C4—2691no—
268C4⋊C4—5381no—
269C4⋊C4—5381no—
270C4⋊C4—5381no—
271C4⋊C4—5381no—
272C4⋊C4—5381no—
273C4⋊C4—5381no—
274C4⋊C4—5381no—
275C4⋊C4—5381no—
276C4⋊C4D107611yescharacteristic
277C22⋊C4—5381no—
278C22⋊C4—5381no—
279C22⋊C4—5381no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C22⋊C4—5381no—
283C22⋊C4—5381no—
284C22⋊C4D107611yescharacteristic
285C22⋊C4D107611yescharacteristic
286C42—5381no—
287C42—5381no—
288C42—5381no—
289C42C22×D26911yescharacteristic
290C23—5381no—
291C23C2×D107611yescharacteristic
292C23C2×D107611yescharacteristic
293Q8—2692no—
294Q8—5381no—
295Q8—5381no—
296Q8—5381no—
297Q8—5381no—
298Q8—5381no—
299Q8—10762no—
300D4—22no—
301D4—5381no—
302D4—5381no—
303D4—10762no—
304D4—10762no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—5381no—
310C2×C4—5381no—
311C2×C4—5381no—
312C2×C4—5381no—
313C2×C4—5381no—
314C2×C4—5381no—
315C2×C4—5381no—
316C2×C4—10762no—
317C2×C4—10762no—
318C2×C4—10762no—
319C2×C4C2×D107611yescharacteristic
320C2×C4C2×D107611yescharacteristic
321C2×C4C2×D107611yescharacteristic
322C2×C4C2×D107611yescharacteristic
323C2×C4C23×D26911yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—10761no—
334C22—10761no—
335C22—10761no—
336C22#2257547512yes—
337C22C22×D107611yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—5382no—
343C4—10761no—
344C4—10761no—
345C4—10761no—
346C4—10761no—
347C4—10761no—
348C4—10761no—
349C4#41×D26911yescharacteristic
350C4#2257549811yescharacteristic
351C2—22no—
352C2—41no—
353C2—21521no—
354C2#3177125011yescharacteristic
355C2C2×#2257547511yescharacteristic
356C2#3177142211yescharacteristic
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC8×D4×C269C2
socleC22×C269C22×D4
prime radical#31771264C2
hypercenterC8×D4D269
hypocenterC269#3300
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #31771295C2semidirect
3. #31770960C2semidirect
4. #31770947C2semidirect
5. #31770919C2semidirect
6. #31770913C2semidirect
7. #31770846C2semidirect
8. #31770834C2semidirect
9. #31770828C2semidirect
10. #31770769C2semidirect
11. #31770763C2semidirect
12. C4×Dic1076C2semidirect
13. #31770602C2semidirect
14. C2×#22575378C2semidirect
15. C8×D4×C269C2semidirect
178. C269#3300semidirect
192. C8×D4D269semidirect

Maximal subgroups

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

subgroupindex
#317712952
#317712642
#317709602
#317709472
#317709192
#317709132
#317708462
#317708342
#317708282
#317707692
#317707632
C4×Dic10762
#317706022
C2×#225753782
C8×D4×C2692
#3300269