Finite Group Databasebeta

← #46822767

Subgroups — #46822767

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#31771265C211yesmaximal, characteristic
3#31770961C211yesmaximal, characteristic, complemented
4#31770943C211yesmaximal, characteristic, complemented
5#31770920C211yesmaximal, characteristic, complemented
6#31770911C211yesmaximal, characteristic, complemented
7#31770837C211yesmaximal, characteristic, complemented
8#31770829C211yesmaximal, characteristic, complemented
9#31770765C211yesmaximal, characteristic, complemented
10#31770759C211yesmaximal, characteristic, complemented
11#31770697C211yesmaximal, characteristic, complemented
12C8×C22⋊D269C211yesmaximal, characteristic, complemented
13#31770602C211yesmaximal, characteristic, complemented
14#103×D269C211yesmaximal, characteristic, complemented
15#467×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C2×Q8×D269C2211yescharacteristic
18C2×#16864392C2211yescharacteristic
19C2×#16864389C2211yescharacteristic
20C2×C8×D269C2211yescharacteristic
21#22575446—21no—
22#22575444C2211yescharacteristic
23#22575443—21no—
24#22575442C2211yescharacteristic
25#22575439—21no—
26#22575435—21no—
27#22575431—21no—
28#22575429C2211yescharacteristic
29#22575428C2211yescharacteristic
30#22575426—21no—
31Q8×Dic269C2211yescharacteristic
32#22575418C2211yescharacteristic
33#22575415—21no—
34C4×C22⋊D269C2211yescharacteristic
35#22575412C2211yescharacteristic
36#22575411—21no—
37C4⋊C4×D269C2211yescharacteristic
38#22575386C2211yescharacteristic
39#22575384C2211yescharacteristic
40#22575382C2211yescharacteristic
41#22575378C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575377C2211yescharacteristic
44#22575377C2211yescharacteristic
45#22575376C2211yescharacteristic
46#22575375C2211yescharacteristic
47#22575375C2211yescharacteristic
48#22575373C2211yescharacteristic
49C22⋊#14524130C2211yescharacteristic
50#22575365C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C2×Q16×C269C2211yescharacteristic
53C22×C8×C269C2211yescharacteristic
54C22⋊Q8×C269C2211yescharacteristic
55C22⋊Q8×C269C2211yescharacteristic
56#107×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#103×C269C2211yescharacteristic
59#16864402—22no—
60#16864402—41no—
61C2×Dic538—21no—
62C2×Dic538C2311yescharacteristic
63Q8×D269—22no—
64Q8×D269—41no—
65C2×D1076—21no—
66C2×D1076C2311yescharacteristic
67C2×C22⋊D269—21no—
68C2×C22⋊D269D411yescharacteristic
69C2×C4×D269—21no—
70C2×C4×D269—21no—
71C2×C4×D269—21no—
72C2×C4×D269C2311yescharacteristic
73#16864392—22no—
74#16864389—41no—
75C2×#14524130C2311yescharacteristic
76C2×#14524130C2311yescharacteristic
77C8×D269—41no—
78C4⋊Dic269—21no—
79C4⋊Dic269—21no—
80C4⋊Dic269C2311yescharacteristic
81C4⋊Dic269C2311yescharacteristic
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85#16864381—21no—
86#16864381D411yescharacteristic
87C22⋊Dic269—21no—
88C22⋊Dic269D411yescharacteristic
89#16864379—21no—
90#16864379—21no—
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—
102C2×C8×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×D269—21no—
112C22×D269C2×D411yescharacteristic
113Dic538—21no—
114Dic538—42no—
115Dic538#4112yes—
116D1076—21no—
117D1076—21no—
118D1076—42no—
119C22⋊D269—22no—
120C22⋊D269—42no—
121C2×Dic269—21no—
122C2×Dic269—21no—
123C2×Dic269—21no—
124C2×Dic269C2×D411yescharacteristic
125C2×Dic269C2×D411yescharacteristic
126C2×Dic269C2×D411yescharacteristic
127C4×D269—21no—
128C4×D269—21no—
129C4×D269—42no—
130C4×D269—42no—
131C4×D269—42no—
132#14524130—21no—
133#14524130—21no—
134C23×C269C2×D411yescharacteristic
135Q8×C269—21no—
136Q8×C269—21no—
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—21no—
155C2×D269—41no—
156C2×D269—41no—
157C2×D269—41no—
158C2×D269#13512yes—
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—22no—
168Dic269—21no—
169Dic269—21no—
170Dic269—41no—
171Dic269—41no—
172C2×C269—41no—
173C2×C269#54611yescharacteristic
174C2×C269C2×#13511yescharacteristic
175C2×C269#57811yescharacteristic
176D269—22no—
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#467D26911yescharacteristic, complemented
187#465—2691no—
188#464—2691no—
189#452—2691no—
190#451—2691no—
191C4×Q16—2691no—
192C8×D4—2691no—
193#416—2691no—
194C2×#103—2691no—
195C2×#41—2691no—
196C22×Q8—2691no—
197C2×Q16—2691no—
198C2×Q16C2×D26911yescharacteristic
199C2×SD16—2691no—
200C22×C8—2691no—
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—5381no—
210C22⋊Q8C2×D26911yescharacteristic
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#107C2×D26911yescharacteristic
223#106—2691no—
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⋊C8—2691no—
237C4×C8—2691no—
238#41—5382no—
239#41—10761no—
240C2×Q8—2691no—
241C2×Q8—5381no—
242C2×Q8—5382no—
243C2×Q8—10761no—
244C2×Q8C22×D26911yescharacteristic
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—41no—
256Q16—5382no—
257SD16—10761no—
258C2×C8—41no—
259C2×C8—2691no—
260C2×C8—2691no—
261C2×C8—10761no—
262C2×C8C22×D26911yescharacteristic
263C2×C8C22×D26911yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
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⋊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—2691no—
287C42—5381no—
288C42—5381no—
289C42—5381no—
290C23—2691no—
291C23—5381no—
292C23D4×D26911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—2692no—
298Q8—5381no—
299Q8—10762no—
300D4—5382no—
301D4—5381no—
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—2692no—
332C22—5381no—
333C22—5381no—
334C22—10761no—
335C22—10761no—
336C22—10761no—
337C22C2×D4×D26911yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—5381no—
344C4—5381no—
345C4—5382no—
346C4—5381no—
347C4—10761no—
348C4—10761no—
349C4#41×D26911yescharacteristic
350C4#2257549811yescharacteristic
351C2—41no—
352C2—5382no—
353C2—21521no—
354C2#3177124411yescharacteristic
355C2#135×D26911yescharacteristic
356C2#3177141811yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#467×C269C2
socleC22×C269C22×D4
prime radical#31771265C2
hypercenter#467D269
hypocenterC269#3300
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #31771289C2semidirect
3. #31770961C2semidirect
4. #31770943C2semidirect
5. #31770920C2semidirect
6. #31770911C2semidirect
7. #31770837C2semidirect
8. #31770829C2semidirect
9. #31770765C2semidirect
10. #31770759C2semidirect
11. #31770697C2semidirect
12. C8×C22⋊D269C2semidirect
13. #31770602C2semidirect
14. #103×D269C2semidirect
15. #467×C269C2semidirect
178. C269#3300semidirect
186. #467D269semidirect

Maximal subgroups

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

subgroupindex
#317712892
#317712652
#317709612
#317709432
#317709202
#317709112
#317708372
#317708292
#317707652
#317707592
#317706972
C8×C22⋊D2692
#317706022
#103×D2692
#467×C2692
#3300269