Finite Group Databasebeta

← #47983186

Subgroups — #47983186

Order 35456.

312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31800470C211yesmaximal, characteristic
2#31800025C211yesmaximal, characteristic, complemented
3C2×#22579808C211yesmaximal, characteristic
4C2×#22579806C211yesmaximal, characteristic
5C4×#17984542C211yesmaximal, characteristic, complemented
6#31799761C211yesmaximal, characteristic, complemented
7#339×C277C211yesmaximal, characteristic, complemented
8C2×#17984563C2211yescharacteristic
9C2×#17984547C2211yescharacteristic
10#22579845C411yescharacteristic, complemented
11#22579845C411yescharacteristic, complemented
12#22579842C411yescharacteristic, complemented
13#22579842C411yescharacteristic, complemented
14#22579840—21no—
15#22579840—21no—
16#22579837—21no—
17C2×#17984542—21no—
18C2×C4×Dic277C2211yescharacteristic
19C2×C4×Dic277C2211yescharacteristic
20C42×D277—21no—
21#22579809—21no—
22#22579809—21no—
23#22579808—22no—
24#22579806—22no—
25#22579787—21no—
26C2×M16×C277C2211yescharacteristic
27#117×C277C2211yescharacteristic
28C2×C42×C277C2211yescharacteristic
29#17984563—21no—
30#17984563—21no—
31#17984563D412yes—
32#17984563Q812yes—
33C2×Dic554C2×C411yescharacteristic
34C2×D1108C2×C411yescharacteristic
35C2×C22⋊D277—21no—
36C22×Dic277—21no—
37C22×Dic277D411yescharacteristic
38C22×Dic277D411yescharacteristic
39C2×C4×D277—21no—
40C2×C4×D277—21no—
41C2×C4×D277—21no—
42#17984547—21no—
43#17984547—21no—
44C2×#14555660—21no—
45#17984542—24no—
46#17984542—21no—
47#17984542—21no—
48#17984540—21no—
49#17984540—21no—
50C4×Dic277—21no—
51C4×Dic277—21no—
52C4×Dic277—21no—
53C4×Dic277—21no—
54C4×Dic277C2×C411yescharacteristic
55C4×Dic277C2×C411yescharacteristic
56C4×Dic277D411yescharacteristic
57C4×Dic277D411yescharacteristic
58C22×C4×C277—21no—
59C22×C4×C277C2311yescharacteristic
60M16×C277—21no—
61M16×C277—21no—
62C2×C8×C277—21no—
63C4⋊C4×C277C2×C411yescharacteristic
64C4⋊C4×C277C2×C411yescharacteristic
65C22⋊C4×C277—21no—
66C42×C277—21no—
67C42×C277—21no—
68C42×C277—21no—
69C22×D277—21no—
70Dic554—21no—
71Dic554C4⋊C412yescomplemented
72D1108—21no—
73D1108C4⋊C412yescomplemented
74C22⋊D277—22no—
75C22⋊D277—22no—
76C2×Dic277—21no—
77C2×Dic277—22no—
78C2×Dic277—22no—
79C2×Dic277—41no—
80C2×Dic277—41no—
81C2×Dic277—41no—
82C2×Dic277C22⋊C411yescharacteristic
83C2×Dic277C22⋊C411yescharacteristic
84C2×Dic277C22⋊C411yescharacteristic
85C2×Dic277C22⋊C411yescharacteristic
86C4×D277—22no—
87C4×D277—22no—
88C4×D277—42no—
89C4×D277—42no—
90#14555660—41no—
91C23×C277C2×D411yescharacteristic
92C2×C4×C277—22no—
93C2×C4×C277—21no—
94C2×C4×C277—21no—
95C2×C4×C277—41no—
96C2×C4×C277—41no—
97C2×C4×C277C22×C411yescharacteristic
98C2×C4×C277C2×D411yescharacteristic
99C2×C4×C277C2×D411yescharacteristic
100C2×C4×C277C2×Q811yescharacteristic
101C2×C4×C277#4111yescharacteristic
102C2×C4×C277#4111yescharacteristic
103C8×C277—41no—
104C22×C277—21no—
105C22×C277—21no—
106C22×C277C2×C22⋊C411yescharacteristic
107C22×C277#12111yescharacteristic
108C22×C277C22⋊Q811yescharacteristic
109C2×D277—22no—
110C2×D277—41no—
111C2×D277—41no—
112C4×C277—42no—
113C4×C277—41no—
114C4×C277—41no—
115C4×C277C2×C4⋊C411yescharacteristic
116C4×C277#11711yescharacteristic
117C4×C277#12111yescharacteristic
118C4×C277C22⋊Q811yescharacteristic
119Dic277—22no—
120Dic277—21no—
121Dic277—21no—
122Dic277—21no—
123Dic277—42no—
124Dic277#10412yescomplemented
125C2×C277—21no—
126C2×C277—21no—
127C2×C277#38011yescharacteristic
128C2×C277C2×#10411yescharacteristic
129C2×C277#42111yescharacteristic
130D277—42no—
131C277#180611yescharacteristic, complemented, Sylow
132#1806—2771nomaximal, Sylow
133C4×#41—2771no—
134#423—2771no—
135C2×#104—2771no—
136C2×#104—2771no—
137C4×C4⋊C4—2771no—
138#339—2771no—
139#339D27711yescharacteristic, complemented
140C2×#41—2771no—
141C2×M16—2771no—
142C2×M16C2×D27711yescharacteristic
143C4×Q8—2771no—
144C4×Q8—2771no—
145C4×D4—2771no—
146C4×D4—2771no—
147C4×D4—5541no—
148C4×D4—5541no—
149#117—5541no—
150#117C2×D27711yescharacteristic
151C2×C4⋊C4—5541no—
152C2×C42—2771no—
153C2×C42—2771no—
154C2×C42—5541no—
155C2×C42C2×D27711yescharacteristic
156C4⋊C8—5541no—
157C4⋊C8—5541no—
158#104—5542no—
159#104—5542no—
160#95—5541no—
161#41—2772no—
162#41—2772no—
163#41—5541no—
164#41—5541no—
165C2×Q8—2771no—
166C2×D4—2771no—
167C2×D4—5541no—
168C22×C4—21no—
169C22×C4—2771no—
170C22×C4—2771no—
171C22×C4—5541no—
172C22×C4—5541no—
173C22×C4—5541no—
174C22×C4—5541no—
175C22×C4C22×D27711yescharacteristic
176M16—21no—
177M16—21no—
178M16—5541no—
179M16—5541no—
180C2×C8—21no—
181C2×C8—5541no—
182C4⋊C4—5541no—
183C4⋊C4—5541no—
184C4⋊C4—5544no—
185C4⋊C4C4×D27711yescharacteristic
186C4⋊C4C4×D27711yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—5541no—
189C22⋊C4—5541no—
190C42—21no—
191C42—21no—
192C42—21no—
193C42—2771no—
194C42—2771no—
195C42—2771no—
196C42—2771no—
197C42—5541no—
198C42—5541no—
199C42—5541no—
200C42—5541no—
201C23—5541no—
202C23D4×D27711yescharacteristic
203Q8—2772no—
204Q8—5541no—
205D4—2772no—
206D4—5542no—
207D4—5542no—
208D4—5541no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—2771no—
215C2×C4—2771no—
216C2×C4—2771no—
217C2×C4—2771no—
218C2×C4—5542no—
219C2×C4—5541no—
220C2×C4—5542no—
221C2×C4—5542no—
222C2×C4—5542no—
223C2×C4—11082no—
224C2×C4—11082no—
225C2×C4—11081no—
226C2×C4—11081no—
227C2×C4—11081no—
228C2×C4C2×C4×D27711yescharacteristic
229C2×C4D4×D27711yescharacteristic
230C2×C4D4×D27711yescharacteristic
231C2×C4Q8×D27711yescharacteristic
232C2×C4#1798456311yescharacteristic
233C2×C4#1798456311yescharacteristic
234C8—41no—
235C8—11081no—
236C22—21no—
237C22—21no—
238C22—5542no—
239C22—11081no—
240C22—11081no—
241C22C22⋊C4×D27711yescharacteristic
242C22#2257985311yescharacteristic
243C22#2257985811yescharacteristic
244C4—42no—
245C4—41no—
246C4—41no—
247C4—2772no—
248C4—5542no—
249C4—5541no—
250C4—5541no—
251C4—5541no—
252C4—11082no—
253C4C4⋊C4×D27711yescharacteristic
254C4#2257983711yescharacteristic
255C4#2257985311yescharacteristic
256C4#2257985811yescharacteristic
257C2—21no—
258C2—21no—
259C2—11082no—
260C2#3179986111yescharacteristic
261C2#104×D27711yescharacteristic
262C2#3180001711yescharacteristic
subgroupG/H
centerC2×C4D4×D277
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
Fitting#339×C277C2
socleC22×C277C2×C22⋊C4
prime radicalC2×#17984563C22
cosocleC22×C4×C277C23
hypercenter#339D277
hypocenterC277#1806
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #31800025C2semidirect
5. C4×#17984542C2semidirect
6. #31799761C2semidirect
7. #339×C277C2semidirect
10. #22579845C4semidirect
11. #22579845C4semidirect
12. #22579842C4semidirect
13. #22579842C4semidirect
71. Dic554C4⋊C4semidirect
73. D1108C4⋊C4semidirect
124. Dic277#104semidirect
131. C277#1806semidirect
139. #339D277semidirect

Maximal subgroups

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

subgroupindex
#318004702
#318000252
C2×#225798082
C2×#225798062
C4×#179845422
#317997612
#339×C2772
#1806277