Finite Group Databasebeta

← #46822931

Subgroups — #46822931

Order 34432.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771289C211yesmaximal, characteristic
2#31771268C211yesmaximal, characteristic
3#31770972C211yesmaximal, characteristic, complemented
4#31770943C211yesmaximal, characteristic, complemented
5#31770937C211yesmaximal, characteristic, complemented
6#31770915C211yesmaximal, characteristic, complemented
7#31770845C211yesmaximal, characteristic, complemented
8#31770813C211yesmaximal, characteristic, complemented
9#31770760C211yesmaximal, characteristic, complemented
10#31770759C211yesmaximal, characteristic, complemented
11#31770709C211yesmaximal, characteristic, complemented
12#31770674C211yesmaximal, characteristic
13#31770615C211yesmaximal, characteristic, complemented
14#103×D269C211yesmaximal, characteristic, complemented
15#470×C269C211yesmaximal, characteristic, complemented
16C22×Dic538C2211yescharacteristic
17C2×Q8×D269C2211yescharacteristic
18C2×#16864392C2211yescharacteristic
19C2×#16864392C2211yescharacteristic
20C2×C8×D269C2211yescharacteristic
21#22575452—21no—
22#22575451C2211yescharacteristic
23#22575446—21no—
24#22575444C2211yescharacteristic
25#22575443—21no—
26#22575435—21no—
27#22575433C2211yescharacteristic
28#22575431—21no—
29#22575430—21no—
30#22575429C2211yescharacteristic
31Q8×Dic269C2211yescharacteristic
32#22575418C2211yescharacteristic
33C4×C22⋊D269C2211yescharacteristic
34#22575413—21no—
35#22575412C2211yescharacteristic
36#22575411—21no—
37C4⋊C4×D269C2211yescharacteristic
38#22575386C2211yescharacteristic
39#22575384C2211yescharacteristic
40#22575382C2211yescharacteristic
41#22575378C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575378C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575377C2211yescharacteristic
46#22575377C2211yescharacteristic
47#22575376C2211yescharacteristic
48#22575376C2211yescharacteristic
49C22⋊#14524130C2211yescharacteristic
50#22575365C2211yescharacteristic
51#22575363C2211yescharacteristic
52C2×Q16×C269C2211yescharacteristic
53C2×M16×C269C2211yescharacteristic
54C22⋊Q8×C269C2211yescharacteristic
55C22⋊Q8×C269C2211yescharacteristic
56#106×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#103×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538—22no—
61C2×Dic538—21no—
62C2×Dic538—41no—
63C2×Dic538C2311yescharacteristic
64C2×Dic538C2311yescharacteristic
65Q8×D269—22no—
66Q8×D269—41no—
67C2×C22⋊D269D411yescharacteristic
68C22×Dic269—21no—
69C2×C4×D269—21no—
70C2×C4×D269—21no—
71C2×C4×D269C2311yescharacteristic
72#16864392—22no—
73#16864392—41no—
74C2×#14524130C2311yescharacteristic
75C2×#14524130C2311yescharacteristic
76C8×D269—41no—
77C4⋊Dic269—21no—
78C4⋊Dic269—21no—
79C4⋊Dic269—21no—
80C4⋊Dic269C2311yescharacteristic
81C4⋊Dic269C2311yescharacteristic
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85#16864381—21no—
86#16864381—21no—
87#16864381—21no—
88#16864381D411yescharacteristic
89C22⋊Dic269—21no—
90C22⋊Dic269D411yescharacteristic
91#16864379—21no—
92#16864379—21no—
93#16864379D411yescharacteristic
94C4×Dic269—21no—
95C4×Dic269—21no—
96C4×Dic269—21no—
97C4×Dic269C2311yescharacteristic
98C2×Q8×C269C2311yescharacteristic
99C2×Q8×C269C2311yescharacteristic
100C22×C4×C269C2311yescharacteristic
101Q16×C269—41no—
102M16×C269—41no—
103C2×C8×C269C2311yescharacteristic
104C2×C8×C269C2311yescharacteristic
105C4⋊C4×C269—21no—
106C4⋊C4×C269—21no—
107C4⋊C4×C269C2311yescharacteristic
108C4⋊C4×C269C2311yescharacteristic
109C22⋊C4×C269—21no—
110C22⋊C4×C269—21no—
111C22×D269C2×D411yescharacteristic
112Dic538—21no—
113Dic538—21no—
114Dic538—21no—
115Dic538—42no—
116Dic538—42no—
117Dic538#4112yes—
118C22⋊D269—22no—
119C2×Dic269—21no—
120C2×Dic269—21no—
121C2×Dic269—21no—
122C2×Dic269—21no—
123C2×Dic269—42no—
124C2×Dic269C2×D411yescharacteristic
125C2×Dic269C2×D411yescharacteristic
126C2×Dic269C2×D411yescharacteristic
127C4×D269—21no—
128C4×D269—21no—
129C4×D269—42no—
130C4×D269—42no—
131#14524130—21no—
132#14524130—21no—
133C23×C269C2×D411yescharacteristic
134Q8×C269—21no—
135Q8×C269—21no—
136Q8×C269—21no—
137Q8×C269—21no—
138C2×C4×C269—21no—
139C2×C4×C269—21no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269C2×D411yescharacteristic
145C2×C4×C269C2411yescharacteristic
146C8×C269—21no—
147C8×C269—21no—
148C22×C269—21no—
149C22×C269—21no—
150C22×C269—21no—
151C22×C269C22×D411yescharacteristic
152C2×D269—21no—
153C2×D269—21no—
154C2×D269#13712yes—
155C4×C269—21no—
156C4×C269—41no—
157C4×C269—41no—
158C4×C269—41no—
159C4×C269—41no—
160C4×C269C2×#4111yescharacteristic
161C4×C269H(5,𝔽2)11yescharacteristic
162Dic269—21no—
163Dic269—22no—
164Dic269—21no—
165Dic269—21no—
166Dic269—41no—
167Dic269—41no—
168Dic269—41no—
169C2×C269—41no—
170C2×C269#54611yescharacteristic
171C2×C269C2×#13711yescharacteristic
172C2×C269#57811yescharacteristic
173D269—22no—
174C269#331211yescharacteristic, complemented, Sylow
175#3312—2691nomaximal, Sylow
176#552—2691no—
177D4×Q8—2691no—
178#491—2691no—
179#485—2691no—
180#483—2691no—
181#479—2691no—
182#470D26911yescharacteristic, complemented
183#467—2691no—
184#462—2691no—
185#451—2691no—
186#451—2691no—
187#441—2691no—
188#435—2691no—
189#419—2691no—
190C2×#103—2691no—
191C22×Q8—2691no—
192C22×Q8—2691no—
193C2×Q16—2691no—
194C2×Q16—2691no—
195C2×Q16C2×D26911yescharacteristic
196C2×M16C2×D26911yescharacteristic
197C22×C8—2691no—
198C4⋊Q8—2691no—
199C4⋊Q8—5381no—
200#126—5381no—
201#125—2691no—
202#125—5381no—
203#123—5381no—
204C22⋊Q8—2691no—
205C22⋊Q8—2691no—
206C22⋊Q8—5381no—
207C22⋊Q8—5381no—
208C22⋊Q8C2×D26911yescharacteristic
209C22⋊Q8C2×D26911yescharacteristic
210C4×Q8—2691no—
211C4×Q8—2691no—
212C4×D4—2691no—
213C4×D4—5381no—
214#117—2691no—
215#117—5381no—
216C2×C4⋊C4—2691no—
217#107—2691no—
218#106—2691no—
219#106C2×D26911yescharacteristic
220C4⋊C8—2691no—
221#103—2691no—
222#103—2691no—
223#103—2691no—
224#103—2691no—
225#103—2691no—
226#103—2691no—
227#103—2691no—
228#103—2691no—
229#103C2×D26911yescharacteristic
230#103C2×D26911yescharacteristic
231C22⋊C8—2691no—
232C22⋊C8—2691no—
233#97—2691no—
234C2×Q8—2691no—
235C2×Q8—2691no—
236C2×Q8—5381no—
237C2×Q8—5382no—
238C2×Q8—5381no—
239C2×Q8—5382no—
240C2×Q8—10761no—
241C2×Q8—10761no—
242C2×Q8C22×D26911yescharacteristic
243C2×Q8C22×D26911yescharacteristic
244C2×D4—2691no—
245C22×C4—2691no—
246C22×C4—5381no—
247C22×C4—5381no—
248C22×C4—5381no—
249C22×C4C22×D26911yescharacteristic
250Q16—41no—
251Q16—5382no—
252Q16—10761no—
253M16—41no—
254C2×C8—2691no—
255C2×C8—2691no—
256C2×C8—10761no—
257C2×C8C22×D26911yescharacteristic
258C2×C8C22×D26911yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—2691no—
262C4⋊C4—2691no—
263C4⋊C4—2691no—
264C4⋊C4—5381no—
265C4⋊C4—5381no—
266C4⋊C4—5381no—
267C4⋊C4—5381no—
268C4⋊C4—5381no—
269C4⋊C4—5381no—
270C4⋊C4—5381no—
271C4⋊C4—5381no—
272C4⋊C4—5381no—
273C4⋊C4C22×D26911yescharacteristic
274C4⋊C4C22×D26911yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—2691no—
278C22⋊C4—2691no—
279C22⋊C4—5381no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C42—2691no—
283C42—5381no—
284C42—5381no—
285C42—5381no—
286C23—2691no—
287C23D4×D26911yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—2692no—
293Q8—5381no—
294Q8—5381no—
295Q8—5381no—
296Q8—10762no—
297Q8—10762no—
298D4—5382no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—2691no—
306C2×C4—2691no—
307C2×C4—2691no—
308C2×C4—5381no—
309C2×C4—5381no—
310C2×C4—5381no—
311C2×C4—5381no—
312C2×C4—5381no—
313C2×C4—5381no—
314C2×C4—10762no—
315C2×C4—10762no—
316C2×C4—10762no—
317C2×C4D4×D26911yescharacteristic
318C2×C4C23×D26911yescharacteristic
319C8—21no—
320C8—21no—
321C8—5381no—
322C8—5381no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—2692no—
327C22—5381no—
328C22—5381no—
329C22C2×D4×D26911yescharacteristic
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—5381no—
336C4—5381no—
337C4—5381no—
338C4—5382no—
339C4—10761no—
340C4—10761no—
341C4—10761no—
342C4#41×D26911yescharacteristic
343C4#2257549811yescharacteristic
344C2—41no—
345C2—5382no—
346C2#3177124411yescharacteristic
347C2#137×D26911yescharacteristic
348C2#3177142111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#470×C269C2
socleC22×C269C22×D4
prime radicalC2×C22⋊D269D4
hypercenter#470D269
hypocenterC269#3312
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
3. #31770972C2semidirect
4. #31770943C2semidirect
5. #31770937C2semidirect
6. #31770915C2semidirect
7. #31770845C2semidirect
8. #31770813C2semidirect
9. #31770760C2semidirect
10. #31770759C2semidirect
11. #31770709C2semidirect
13. #31770615C2semidirect
14. #103×D269C2semidirect
15. #470×C269C2semidirect
174. C269#3312semidirect
182. #470D269semidirect

Maximal subgroups

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

subgroupindex
#317712892
#317712682
#317709722
#317709432
#317709372
#317709152
#317708452
#317708132
#317707602
#317707592
#317707092
#317706742
#317706152
#103×D2692
#470×C2692
#3312269