Finite Group Databasebeta

← #46821099

Subgroups — #46821099

Order 34432.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771217C211yesmaximal, characteristic, complemented
2#31770940C211yesmaximal, characteristic, complemented
3#31770935C211yesmaximal, characteristic, complemented
4#31770912C211yesmaximal, characteristic, complemented
5#31770905C211yesmaximal, characteristic, complemented
6#31770815C211yesmaximal, characteristic, complemented
7#31770810C211yesmaximal, characteristic, complemented
8#31770767C211yesmaximal, characteristic
9#31770767C211yesmaximal, characteristic
10#31770710C211yesmaximal, characteristic, complemented
11#31770705C211yesmaximal, characteristic, complemented
12C4×#16864392C211yesmaximal, characteristic, complemented
13C4×#16864390C211yesmaximal, characteristic, complemented
14#31770666C211yesmaximal, characteristic, complemented
15#520×C269C211yesmaximal, characteristic
16C2×#16864392C2211yescharacteristic
17C2×#16864392C2211yescharacteristic
18C2×#16864390C2211yescharacteristic
19C2×#16864390C2211yescharacteristic
20#22575453C2211yescharacteristic
21#22575446—21no—
22#22575446—21no—
23#22575445C2211yescharacteristic
24#22575443—21no—
25#22575443—21no—
26#22575432C2211yescharacteristic
27#22575432C2211yescharacteristic
28C4×Dic538C2211yescharacteristic
29C4×Dic538C2211yescharacteristic
30#22575386C2211yescharacteristic
31#22575386C2211yescharacteristic
32#22575384C2211yescharacteristic
33#22575384C2211yescharacteristic
34C4⋊#14524130C2211yescharacteristic
35C4⋊#14524130C2211yescharacteristic
36#22575377C2211yescharacteristic
37#22575377C2211yescharacteristic
38#22575376C2211yescharacteristic
39#22575376C2211yescharacteristic
40#22575376C2211yescharacteristic
41#22575376C2211yescharacteristic
42#22575374C2211yescharacteristic
43#22575374C2211yescharacteristic
44C22⋊#14524130C2211yescharacteristic
45C22⋊#14524130C2211yescharacteristic
46#22575364C2211yescharacteristic
47C4×#14524130C2211yescharacteristic
48C2×#41×C269C2211yescharacteristic
49C4×Q8×C269C2211yescharacteristic
50C4×Q8×C269C2211yescharacteristic
51C4×D4×C269—21no—
52C4×D4×C269—21no—
53C4×D4×C269C2211yescharacteristic
54C4×D4×C269C2211yescharacteristic
55#117×C269—21no—
56#117×C269C2211yescharacteristic
57C2×C4⋊C4×C269—21no—
58C2×C4⋊C4×C269C2211yescharacteristic
59C2×Dic538C2311yescharacteristic
60C2×Dic538C2311yescharacteristic
61#16864392—22no—
62#16864392—22no—
63#16864390—22no—
64#16864390—22no—
65C2×#14524130C2311yescharacteristic
66C2×#14524130C2311yescharacteristic
67C2×#14524130C2311yescharacteristic
68C2×#14524130C2311yescharacteristic
69C4⋊Dic269—21no—
70C4⋊Dic269—21no—
71C4⋊Dic269C2311yescharacteristic
72C4⋊Dic269C2311yescharacteristic
73#16864381—21no—
74#16864381—21no—
75#16864381—21no—
76#16864381—21no—
77#16864381—21no—
78#16864381—21no—
79C22⋊Dic269—21no—
80C22⋊Dic269—21no—
81C4×Dic269—21no—
82C4×Dic269—21no—
83#41×C269—22no—
84#41×C269—22no—
85C2×Q8×C269C2311yescharacteristic
86C2×D4×C269—21no—
87C2×D4×C269C2311yescharacteristic
88C22×C4×C269—21no—
89C22×C4×C269—21no—
90C22×C4×C269—21no—
91C22×C4×C269—21no—
92C22×C4×C269C2311yescharacteristic
93C4⋊C4×C269—21no—
94C4⋊C4×C269—21no—
95C4⋊C4×C269—21no—
96C4⋊C4×C269D411yescharacteristic
97C4⋊C4×C269D411yescharacteristic
98C4⋊C4×C269C2311yescharacteristic
99C4⋊C4×C269C2311yescharacteristic
100C22⋊C4×C269—21no—
101C22⋊C4×C269—21no—
102C22⋊C4×C269D411yescharacteristic
103C22⋊C4×C269D411yescharacteristic
104C42×C269—21no—
105C42×C269—21no—
106C42×C269C2311yescharacteristic
107C42×C269C2311yescharacteristic
108Dic538—21no—
109Dic538—21no—
110Dic538—21no—
111Dic538—21no—
112C2×Dic269—21no—
113C2×Dic269—21no—
114C2×Dic269—21no—
115C2×Dic269—21no—
116#14524130—21no—
117#14524130—21no—
118#14524130—21no—
119#14524130—21no—
120C23×C269—21no—
121C23×C269C2×D411yescharacteristic
122Q8×C269—21no—
123Q8×C269#4112yes—
124D4×C269—24no—
125D4×C269—21no—
126D4×C269#4112yes—
127C2×C4×C269—24no—
128C2×C4×C269—21no—
129C2×C4×C269—21no—
130C2×C4×C269—21no—
131C2×C4×C269—21no—
132C2×C4×C269—21no—
133C2×C4×C269—81no—
134C2×C4×C269—81no—
135C2×C4×C269—81no—
136C2×C4×C269C2×D411yescharacteristic
137C2×C4×C269C2×D411yescharacteristic
138C2×C4×C269C2×D411yescharacteristic
139C2×C4×C269C2×D411yescharacteristic
140C2×C4×C269C2×D411yescharacteristic
141C2×C4×C269C2411yescharacteristic
142C22×C269—21no—
143C22×C269—22no—
144C22×C269—21no—
145C22×C269—21no—
146C22×C269—41no—
147C22×C269—41no—
148C22×C269C22×D411yescharacteristic
149C4×C269—21no—
150C4×C269—22no—
151C4×C269—21no—
152C4×C269—21no—
153C4×C269—21no—
154C4×C269—21no—
155C4×C269—41no—
156C4×C269—41no—
157C4×C269C2×#4111yescharacteristic
158C4×C269C2×#4111yescharacteristic
159Dic269—41no—
160Dic269—41no—
161Dic269—41no—
162Dic269—41no—
163C2×C269—41no—
164C2×C269—42no—
165C2×C269#52511yescharacteristic
166C2×C269#57711yescharacteristic
167C2×C269#57811yescharacteristic
168C269#312011yescharacteristic, complemented, Sylow
169#3120—2691nomaximal, Sylow
170#541—2691no—
171#520D26911yescharacteristic
172#484—2691no—
173#483—2691no—
174#479—2691no—
175#478—2691no—
176#462—2691no—
177#461—2691no—
178#452—2691no—
179#452—2691no—
180#441—2691no—
181#440—2691no—
182C4×Q16—2691no—
183C4×SD16—2691no—
184#433—2691no—
185C2×#41C2×D26911yescharacteristic
186C2×Q16—2691no—
187C2×Q16—2691no—
188C2×SD16—2691no—
189C2×SD16—2691no—
190C4⋊Q8—2691no—
191#126—5381no—
192#126—5381no—
193#125—2691no—
194#125—5381no—
195#125—5381no—
196C22⋊Q8—2691no—
197C22⋊Q8—2691no—
198C4×Q8—2691no—
199C4×Q8—2691no—
200C4×Q8C2×D26911yescharacteristic
201C4×Q8C2×D26911yescharacteristic
202C4×D4—21no—
203C4×D4—21no—
204C4×D4C2×D26911yescharacteristic
205C4×D4C2×D26911yescharacteristic
206#117—21no—
207#117C2×D26911yescharacteristic
208C2×C4⋊C4—21no—
209C2×C4⋊C4C2×D26911yescharacteristic
210#107—2691no—
211#107—2691no—
212#106—2691no—
213#106—2691no—
214C4⋊C8—2691no—
215C4⋊C8—2691no—
216#103—2691no—
217#103—2691no—
218#103—2691no—
219#103—2691no—
220#103—2691no—
221#103—2691no—
222#102—2691no—
223#102—2691no—
224C22⋊C8—2691no—
225C22⋊C8—2691no—
226#97—2691no—
227C4×C8—2691no—
228#41—22no—
229#41—22no—
230C2×Q8—2691no—
231C2×Q8—2691no—
232C2×Q8C22×D26911yescharacteristic
233C2×D4—21no—
234C2×D4C22×D26911yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4C22×D26911yescharacteristic
240Q16—5382no—
241Q16—5382no—
242SD16—5382no—
243SD16—5382no—
244C2×C8—2691no—
245C2×C8—2691no—
246C2×C8—2691no—
247C2×C8—2691no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—2691no—
252C4⋊C4—2691no—
253C4⋊C4—5381no—
254C4⋊C4—5381no—
255C4⋊C4—5381no—
256C4⋊C4—5381no—
257C4⋊C4—5381no—
258C4⋊C4—5381no—
259C4⋊C4—5381no—
260C4⋊C4—5381no—
261C4⋊C4C22⋊D26911yescharacteristic
262C4⋊C4C22⋊D26911yescharacteristic
263C4⋊C4C22×D26911yescharacteristic
264C4⋊C4C22×D26911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—5381no—
268C22⋊C4—5381no—
269C22⋊C4C22⋊D26911yescharacteristic
270C22⋊C4C22⋊D26911yescharacteristic
271C42—21no—
272C42—21no—
273C42—5381no—
274C42—5381no—
275C42C22×D26911yescharacteristic
276C42C22×D26911yescharacteristic
277C23—21no—
278C23C2×C22⋊D26911yescharacteristic
279Q8—21no—
280Q8—5381no—
281Q8—5381no—
282Q8—5381no—
283Q8—5381no—
284Q8#1686440212yes—
285D4—24no—
286D4—21no—
287D4#1686440212yes—
288C2×C4—24no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—5381no—
298C2×C4—5381no—
299C2×C4—5381no—
300C2×C4—5381no—
301C2×C4C2×C22⋊D26911yescharacteristic
302C2×C4C2×C22⋊D26911yescharacteristic
303C2×C4C2×C22⋊D26911yescharacteristic
304C2×C4C2×C22⋊D26911yescharacteristic
305C2×C4C2×C22⋊D26911yescharacteristic
306C2×C4C23×D26911yescharacteristic
307C8—5381no—
308C8—5381no—
309C8—5381no—
310C8—5381no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—41no—
316C22—41no—
317C22C22×C22⋊D26911yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—22no—
324C4—41no—
325C4—41no—
326C4—10761no—
327C4—10761no—
328C4—10761no—
329C4—10761no—
330C4C2×#1686440211yescharacteristic
331C4C2×#1686440211yescharacteristic
332C2—41no—
333C2—42no—
334C2#3177111611yescharacteristic
335C2#3177141611yescharacteristic
336C2#3177142011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#520×C269C2
socleC22×C269C22×D4
prime radicalC2×#41×C269C22
hypercenter#520D269
hypocenterC269#3120
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #31771217C2semidirect
2. #31770940C2semidirect
3. #31770935C2semidirect
4. #31770912C2semidirect
5. #31770905C2semidirect
6. #31770815C2semidirect
7. #31770810C2semidirect
10. #31770710C2semidirect
11. #31770705C2semidirect
12. C4×#16864392C2semidirect
13. C4×#16864390C2semidirect
14. #31770666C2semidirect
168. C269#3120semidirect

Maximal subgroups

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

subgroupindex
#317712172
#317709402
#317709352
#317709122
#317709052
#317708152
#317708102
#317707672
#317707102
#317707052
C4×#168643922
C4×#168643902
#317706662
#520×C2692
#3120269