Finite Group Databasebeta

← #47986440

Subgroups — #47986440

Order 35456.

528 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C2×#22579845C211yesmaximal, characteristic, complemented
2C2×#22579838C211yesmaximal, characteristic
3#31799937C211yesmaximal, characteristic
4#31799936C212yesmaximal, complemented
5#31799926C212yesmaximal
6#31799922C211yesmaximal, characteristic, complemented
7#31799915C211yesmaximal, characteristic
8#31799853C211yesmaximal, characteristic, complemented
9#31799853C212yesmaximal, complemented
10#31799849C212yesmaximal
11#400×C277C211yesmaximal, characteristic, complemented
12C22×Dic554C2211yescharacteristic
13C22×C4×D277C2211yescharacteristic
14#22579845—24no—
15#22579838—24no—
16C2×C4⋊Dic277C2211yescharacteristic
17C2×#17984542C2212yes—
18C2×#17984542C2212yes—
19C2×#17984542C2212yes—
20C2×#17984542C2212yes—
21C2×#17984540C2212yes—
22C2×#17984540C2212yes—
23C2×#17984540C2211yescharacteristic
24C2×#17984540C2211yescharacteristic
25C2×C4×Dic277C2212yes—
26C2×C4×Dic277C2212yes—
27C2×C4×Dic277C2211yescharacteristic
28C2×C4×Dic277C2211yescharacteristic
29#22579787C2212yes—
30#22579787C2212yes—
31#22579787C2211yescharacteristic
32C2×C4⋊C4×C277C2211yescharacteristic
33C2×C4⋊C4×C277C2211yescharacteristic
34#95×C277C2212yes—
35#95×C277C2211yescharacteristic
36#95×C277C2212yes—
37C23×D277C2311yescharacteristic
38C2×Dic554—24no—
39C2×Dic554—22no—
40C22×Dic277C2311yescharacteristic
41C22×Dic277C2311yescharacteristic
42C22×Dic277C2312yes—
43C22×Dic277C2312yes—
44C22×Dic277C2311yescharacteristic
45C2×C4×D277—22no—
46C2×C4×D277—22no—
47C2×C4×D277Q814yescomplemented
48C4⋊Dic277—22no—
49#17984542—24no—
50#17984542—24no—
51#17984542—24no—
52#17984542—24no—
53#17984540—22no—
54#17984540—24no—
55#17984540—24no—
56#17984540—22no—
57C4×Dic277—22no—
58C4×Dic277—24no—
59C4×Dic277—24no—
60C4×Dic277D414yes—
61C22×C4×C277C2312yes—
62C22×C4×C277C2311yescharacteristic
63C22×C4×C277C2312yes—
64C22×C4×C277C2311yescharacteristic
65C22×C4×C277C2311yescharacteristic
66C4⋊C4×C277—22no—
67C4⋊C4×C277—22no—
68C22×D277—21no—
69C22×D277—22no—
70C22×D277—22no—
71C22×D277—21no—
72C22×D277C2×Q812yes—
73Dic554—28no—
74C2×Dic277—22no—
75C2×Dic277—22no—
76C2×Dic277—22no—
77C2×Dic277—22no—
78C2×Dic277—22no—
79C2×Dic277—21no—
80C2×Dic277—22no—
81C2×Dic277C2×D412yes—
82C2×Dic277C2×D412yes—
83C2×Dic277C2×Q812yes—
84C2×Dic277#4114yes—
85C2×Dic277#4114yes—
86C2×Dic277#4112yes—
87C4×D277—28no—
88C23×C277C2411yescharacteristic
89C2×C4×C277—21no—
90C2×C4×C277—21no—
91C2×C4×C277—22no—
92C2×C4×C277—21no—
93C2×C4×C277—22no—
94C2×C4×C277—22no—
95C2×C4×C277—22no—
96C2×C4×C277—22no—
97C2×C4×C277—22no—
98C2×C4×C277—22no—
99C2×C4×C277—22no—
100C2×C4×C277C2×D412yes—
101C2×C4×C277C2×Q812yes—
102C22×C277C22×D411yescharacteristic
103C22×C277C22×Q811yescharacteristic
104C22×C277C2×#4111yescharacteristic
105C22×C277C2×#4112yes—
106C22×C277C2×#4112yes—
107C2×D277—22no—
108C2×D277—24no—
109C2×D277—41no—
110C2×D277—42no—
111C2×D277—41no—
112C4×C277—22no—
113C4×C277—22no—
114C4×C277—41no—
115C4×C277—42no—
116C4×C277—42no—
117Dic277—24no—
118Dic277—24no—
119Dic277—22no—
120Dic277—41no—
121Dic277C22⋊Q814yes—
122C2×C277C2×C22⋊Q811yescharacteristic
123C2×C277#52511yescharacteristic
124C2×C277#52912yes—
125C2×C277#53211yescharacteristic
126C2×C277#53312yes—
127D277—42no—
128C277#239611yescharacteristic, complemented, Sylow
129#2396—2771nomaximal, Sylow
130C2×C4×Q8—2771no—
131C2×#117—2771no—
132#400D27711yescharacteristic, complemented
133#399—2771no—
134#398—2772no—
135#396—2772no—
136#395—2771no—
137#393—2771no—
138C4×C4⋊C4—2772no—
139C4×C4⋊C4—2771no—
140C4×C22⋊C4—2772no—
141C22×Q8—2771no—
142C23×C4—2771no—
143C4×Q8—5544no—
144#117—5544no—
145C2×C4⋊C4—2771no—
146C2×C4⋊C4—2772no—
147C2×C4⋊C4—2772no—
148C2×C4⋊C4—2772no—
149C2×C4⋊C4—2772no—
150C2×C4⋊C4C2×D27711yescharacteristic
151C2×C4⋊C4C2×D27711yescharacteristic
152C2×C22⋊C4—2771no—
153C2×C22⋊C4—2771no—
154C2×C22⋊C4—2772no—
155C2×C22⋊C4—2772no—
156C2×C42—2771no—
157C2×C42—2771no—
158C2×C42—2772no—
159C2×C42—2772no—
160#95—2772no—
161#95—2772no—
162#95—2771no—
163#95C2×D27712yes—
164#95C2×D27711yescharacteristic
165#95C2×D27712yes—
166C24—2771no—
167C2×Q8—5544no—
168C2×Q8—5542no—
169C22×C4—2771no—
170C22×C4—2772no—
171C22×C4—2772no—
172C22×C4—2771no—
173C22×C4—2774no—
174C22×C4—2771no—
175C22×C4—5542no—
176C22×C4—5542no—
177C22×C4C22×D27712yes—
178C22×C4C22×D27711yescharacteristic
179C22×C4C22×D27712yes—
180C22×C4C22×D27711yescharacteristic
181C22×C4C22×D27711yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—5544no—
185C4⋊C4—5544no—
186C4⋊C4—5544no—
187C4⋊C4—5544no—
188C4⋊C4—5542no—
189C22⋊C4—5544no—
190C22⋊C4—5544no—
191C22⋊C4—5542no—
192C22⋊C4—5542no—
193C42—2774no—
194C42—5544no—
195C42—5542no—
196C42—5544no—
197C23—2772no—
198C23—5541no—
199C23—5542no—
200C23—5542no—
201C23—5541no—
202C23C23×D27711yescharacteristic
203Q8—5548no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—2772no—
216C2×C4—2772no—
217C2×C4—2772no—
218C2×C4—2772no—
219C2×C4—2774no—
220C2×C4—2774no—
221C2×C4—5548no—
222C2×C4—5542no—
223C2×C4—5542no—
224C2×C4—5542no—
225C2×C4—5542no—
226C2×C4—5542no—
227C2×C4—5541no—
228C2×C4—5542no—
229C2×C4D4×D27712yes—
230C2×C4Q8×D27712yes—
231C22—5542no—
232C22—5544no—
233C22—11081no—
234C22—11082no—
235C22—11081no—
236C22C2×D4×D27711yescharacteristic
237C22C2×Q8×D27711yescharacteristic
238C22#41×D27711yescharacteristic
239C22#41×D27712yes—
240C22#41×D27712yes—
241C4—22no—
242C4—22no—
243C4—41no—
244C4—42no—
245C4—42no—
246C4—2774no—
247C4—5544no—
248C4—5544no—
249C4—5542no—
250C4—11081no—
251C2—11082no—
252C2C22⋊Q8×D27711yescharacteristic
253C2#3180051011yescharacteristic
254C2#3180053512yes—
255C2#3180055111yescharacteristic
256C2#3180055812yes—
subgroupG/H
center, FrattiniC23C23×D277
commutator, socle, cosocleC23×C277C24
Fitting#400×C277C2
prime radicalC23×D277C23
hypercenter#400D277
hypocenterC277#2396
LCSG ▷ C23×C277 ▷ C277
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#22579845C2semidirect
4. #31799936C2semidirect
6. #31799922C2semidirect
8. #31799853C2semidirect
9. #31799853C2semidirect
11. #400×C277C2semidirect
47. C2×C4×D277Q8semidirect
128. C277#2396semidirect
132. #400D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225798452
C2×#225798382
#317999372
#317999362
#317999262
#317999222
#317999152
#317998532
#317998492
#400×C2772
#2396277