Finite Group Databasebeta

← #46821013

Subgroups — #46821013

Order 34432.

380 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771159C211yesmaximal, characteristic
2C4×Q8×D269C211yesmaximal, characteristic
3#31770937C211yesmaximal, characteristic
4#31770934C211yesmaximal, characteristic
5#31770889C211yesmaximal, characteristic, complemented
6#31770888C211yesmaximal, characteristic, complemented
7#31770814C211yesmaximal, characteristic, complemented
8#31770813C211yesmaximal, characteristic, complemented
9#31770762C211yesmaximal, characteristic
10#31770759C211yesmaximal, characteristic
11#31770713C211yesmaximal, characteristic, complemented
12#31770710C211yesmaximal, characteristic, complemented
13#31770710C211yesmaximal, characteristic, complemented
14#31770660C211yesmaximal, characteristic
15#441×C269C211yesmaximal, characteristic, complemented
16C2×Q8×D269C2211yescharacteristic
17C2×Dic1076C2211yescharacteristic
18C2×#16864392C2211yescharacteristic
19C2×#16864392C2211yescharacteristic
20#22575452C2211yescharacteristic
21#22575451C2211yescharacteristic
22#22575443—21no—
23#22575433C2211yescharacteristic
24#22575431—21no—
25#22575429C2211yescharacteristic
26Q8×Dic269C2211yescharacteristic
27C4×Dic538—21no—
28C4×Dic538—21no—
29C4×Dic538C2211yescharacteristic
30C4×Dic538C2211yescharacteristic
31#22575418—21no—
32#22575418C2211yescharacteristic
33#22575410—21no—
34C4⋊C4×D269—21no—
35C4⋊C4×D269C2211yescharacteristic
36C42×D269—21no—
37C42×D269C2211yescharacteristic
38#22575385C2211yescharacteristic
39#22575384C2211yescharacteristic
40#22575384C2211yescharacteristic
41#22575382C2211yescharacteristic
42#22575382C2211yescharacteristic
43#22575378C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575377C2211yescharacteristic
46#22575377C2211yescharacteristic
47#22575376C2211yescharacteristic
48#22575376C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575365C2211yescharacteristic
51#22575364C2211yescharacteristic
52C2×Q16×C269C2211yescharacteristic
53C4×Q8×C269C2211yescharacteristic
54C4×Q8×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56#103×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#97×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538—21no—
61C2×Dic538C2311yescharacteristic
62C2×Dic538C2311yescharacteristic
63Q8×D269—22no—
64Q8×D269—22no—
65C2×C4×D269—21no—
66C2×C4×D269—21no—
67C2×C4×D269D411yescharacteristic
68C2×C4×D269D411yescharacteristic
69C2×C4×D269C2311yescharacteristic
70Dic1076—22no—
71#16864392—22no—
72#16864392—22no—
73C2×#14524130C2311yescharacteristic
74C2×#14524130C2311yescharacteristic
75C4⋊Dic269—21no—
76C4⋊Dic269—21no—
77C4⋊Dic269C2311yescharacteristic
78C4⋊Dic269C2311yescharacteristic
79#16864381—21no—
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85#16864381—21no—
86#16864381—21no—
87#16864379—21no—
88#16864379—21no—
89C4×Dic269—21no—
90C4×Dic269—21no—
91C4×Dic269—21no—
92C4×Dic269—21no—
93C4×Dic269D411yescharacteristic
94C4×Dic269D411yescharacteristic
95C4×Dic269C2311yescharacteristic
96C2×Q8×C269C2311yescharacteristic
97C2×Q8×C269C2311yescharacteristic
98Q16×C269—22no—
99C2×C8×C269C2311yescharacteristic
100C2×C8×C269C2311yescharacteristic
101C4⋊C4×C269—21no—
102C4⋊C4×C269—21no—
103C4⋊C4×C269C2311yescharacteristic
104C4⋊C4×C269C2311yescharacteristic
105C42×C269—21no—
106C42×C269—21no—
107C42×C269C2311yescharacteristic
108C22×D269C2×D411yescharacteristic
109Dic538—24no—
110Dic538—21no—
111Dic538—21no—
112Dic538—21no—
113Dic538—42no—
114Dic538#4112yes—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269—21no—
118C2×Dic269—21no—
119C2×Dic269C2×D411yescharacteristic
120C2×Dic269C2×D411yescharacteristic
121C2×Dic269C2×D411yescharacteristic
122C4×D269—24no—
123C4×D269—22no—
124C4×D269—21no—
125C4×D269—21no—
126C4×D269—22no—
127C4×D269—42no—
128#14524130—21no—
129#14524130—21no—
130Q8×C269—21no—
131Q8×C269—21no—
132Q8×C269—21no—
133Q8×C269#4112yes—
134C2×C4×C269—21no—
135C2×C4×C269—21no—
136C2×C4×C269—21no—
137C2×C4×C269—21no—
138C2×C4×C269C2×D411yescharacteristic
139C2×C4×C269C2×D411yescharacteristic
140C2×C4×C269C2411yescharacteristic
141C8×C269—21no—
142C8×C269—21no—
143C22×C269C22×D411yescharacteristic
144C2×D269—21no—
145C2×D269—21no—
146C2×D269#13712yes—
147C4×C269—22no—
148C4×C269—21no—
149C4×C269—21no—
150C4×C269—41no—
151C4×C269—41no—
152C4×C269—41no—
153C4×C269C2×#4111yescharacteristic
154C4×C269C2×#4111yescharacteristic
155Dic269—22no—
156Dic269—21no—
157Dic269—21no—
158Dic269—41no—
159Dic269—41no—
160Dic269—41no—
161Dic269#13712yes—
162C2×C269#52511yescharacteristic
163C2×C269C2×#13711yescharacteristic
164C2×C269C2×#13711yescharacteristic
165D269—22no—
166C269#311311yescharacteristic, complemented, Sylow
167#3113—2691nomaximal, Sylow
168#533—2691no—
169C2×C4×Q8—2691no—
170#483—2691no—
171#483—2691no—
172#475—2691no—
173#475—2691no—
174#462—2691no—
175#462—2691no—
176#451—2691no—
177#451—2691no—
178#441—2691no—
179#441—2691no—
180#441—2691no—
181#441D26911yescharacteristic, complemented
182#432—2691no—
183C22×Q8—2691no—
184C2×Q16—2691no—
185C2×Q16—2691no—
186C2×Q16—2691no—
187C2×Q16C2×D26911yescharacteristic
188C4⋊Q8—2691no—
189C4⋊Q8—2691no—
190#125—5381no—
191C22⋊Q8—2691no—
192C22⋊Q8—2691no—
193C22⋊Q8—5381no—
194C4×Q8—2691no—
195C4×Q8—2691no—
196C4×Q8—2691no—
197C4×Q8—2691no—
198C4×Q8—5381no—
199C4×Q8—5381no—
200C4×Q8—5381no—
201C4×Q8C2×D26911yescharacteristic
202C4×Q8C2×D26911yescharacteristic
203#117—5381no—
204C2×C4⋊C4—2691no—
205C2×C4⋊C4—5381no—
206C2×C42—2691no—
207C2×C42—5381no—
208#106—2691no—
209#106—2691no—
210#106—2691no—
211#106C2×D26911yescharacteristic
212C4⋊C8—2691no—
213C4⋊C8—2691no—
214#103—2691no—
215#103—2691no—
216#103—2691no—
217#103—2691no—
218#103—2691no—
219#103—2691no—
220#103C2×D26911yescharacteristic
221#103C2×D26911yescharacteristic
222C22⋊C8—2691no—
223C22⋊C8—2691no—
224#97—2691no—
225#97C2×D26911yescharacteristic
226C2×Q8—2691no—
227C2×Q8—2691no—
228C2×Q8—5381no—
229C2×Q8—5381no—
230C2×Q8—5382no—
231C2×Q8—5382no—
232C2×Q8C22×D26911yescharacteristic
233C2×Q8C22×D26911yescharacteristic
234C22×C4—2691no—
235C22×C4—2691no—
236C22×C4—2691no—
237C22×C4—5381no—
238C22×C4—5381no—
239Q16—22no—
240Q16—5382no—
241Q16—5382no—
242Q16—5382no—
243C2×C8—2691no—
244C2×C8—2691no—
245C2×C8C22×D26911yescharacteristic
246C2×C8C22×D26911yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—2691no—
250C4⋊C4—2691no—
251C4⋊C4—5381no—
252C4⋊C4—5381no—
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
263C22⋊C4—5381no—
264C22⋊C4—5381no—
265C42—21no—
266C42—21no—
267C42—2691no—
268C42—2691no—
269C42—2691no—
270C42—5381no—
271C42—5381no—
272C42—5381no—
273C42—5381no—
274C42C22×D26911yescharacteristic
275C23—2691no—
276Q8—21no—
277Q8—21no—
278Q8—21no—
279Q8—2692no—
280Q8—5384no—
281Q8—5381no—
282Q8—5381no—
283Q8—5381no—
284Q8—10762no—
285Q8#1686440212yes—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—2691no—
291C2×C4—2691no—
292C2×C4—2691no—
293C2×C4—5382no—
294C2×C4—5382no—
295C2×C4—5384no—
296C2×C4—5381no—
297C2×C4—5381no—
298C2×C4—5381no—
299C2×C4—5381no—
300C2×C4—5381no—
301C2×C4—5381no—
302C2×C4—10762no—
303C2×C4D4×D26911yescharacteristic
304C2×C4D4×D26911yescharacteristic
305C2×C4C23×D26911yescharacteristic
306C8—21no—
307C8—21no—
308C8—5381no—
309C8—5381no—
310C22—2692no—
311C22—5381no—
312C22—5381no—
313C22C2×D4×D26911yescharacteristic
314C4—21no—
315C4—21no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—2692no—
321C4—5381no—
322C4—5381no—
323C4—5382no—
324C4—10761no—
325C4—10761no—
326C4—10761no—
327C4#41×D26911yescharacteristic
328C4C2×#1686440211yescharacteristic
329C2—5382no—
330C2#3177111411yescharacteristic
331C2#137×D26911yescharacteristic
332C2#137×D26911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#441×C269C2
socleC22×C269C22×D4
prime radicalC22×D269C2×D4
hypercenter#441D269
hypocenterC269#3113
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
5. #31770889C2semidirect
6. #31770888C2semidirect
7. #31770814C2semidirect
8. #31770813C2semidirect
11. #31770713C2semidirect
12. #31770710C2semidirect
13. #31770710C2semidirect
15. #441×C269C2semidirect
166. C269#3113semidirect
181. #441D269semidirect

Maximal subgroups

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

subgroupindex
#317711592
C4×Q8×D2692
#317709372
#317709342
#317708892
#317708882
#317708142
#317708132
#317707622
#317707592
#317707132
#317707102
#317706602
#441×C2692
#3113269