Finite Group Databasebeta

← #47986429

Subgroups — #47986429

Order 35456.

560 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 143 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×#22579840C211yesmaximal, characteristic
2C2×#22579838C211yesmaximal, characteristic, complemented
3#31799942C211yesmaximal, characteristic, complemented
4#31799938C211yesmaximal, characteristic, complemented
5#31799933C211yesmaximal, characteristic, complemented
6#31799931C212yesmaximal, complemented
7#31799917C212yesmaximal
8#31799853C212yesmaximal, complemented
9C22⋊C4×Dic277C212yesmaximal, complemented
10#31799849C211yesmaximal, characteristic, complemented
11#397×C277C211yesmaximal, characteristic, complemented
12C22×C22⋊D277C2211yescharacteristic
13C23×Dic277C2211yescharacteristic
14C22×C4×D277C2211yescharacteristic
15#22579840—24no—
16#22579838—24no—
17C2×C4⋊Dic277C2211yescharacteristic
18C2×#17984542C2212yes—
19C2×#17984542C2212yes—
20C2×#17984542C2211yescharacteristic
21C2×C22⋊Dic277C2212yes—
22C2×#17984540C2212yes—
23C2×#17984540C2212yes—
24C2×#17984540C2211yescharacteristic
25C2×C4×Dic277C2212yes—
26C2×C4×Dic277C2212yes—
27C2×C4×Dic277C2211yescharacteristic
28#22579787C2211yescharacteristic
29#22579787C2212yes—
30#22579787C2212yes—
31#22579787C2212yes—
32C2×C4⋊C4×C277C2211yescharacteristic
33C2×C22⋊C4×C277C2212yes—
34C2×C22⋊C4×C277C2211yescharacteristic
35#95×C277C2211yescharacteristic
36#95×C277C2212yes—
37C23×D277C2311yescharacteristic
38C2×C22⋊D277—22no—
39C2×C22⋊D277—22no—
40C2×C22⋊D277—22no—
41C22×Dic277—22no—
42C22×Dic277—24no—
43C22×Dic277C2311yescharacteristic
44C22×Dic277C2312yes—
45C22×Dic277C2312yes—
46C22×Dic277C2311yescharacteristic
47C22×Dic277C2311yescharacteristic
48C2×C4×D277—24no—
49C2×C4×D277D414yes—
50C4⋊Dic277—22no—
51#17984542—24no—
52#17984542—24no—
53#17984542—22no—
54C22⋊Dic277—24no—
55#17984540—24no—
56#17984540—22no—
57#17984540—24no—
58C4×Dic277—24no—
59C4×Dic277—22no—
60C4×Dic277—24no—
61C24×C277C2311yescharacteristic
62C22×C4×C277C2312yes—
63C22×C4×C277C2311yescharacteristic
64C22×C4×C277C2312yes—
65C22×C4×C277C2311yescharacteristic
66C4⋊C4×C277—22no—
67C22⋊C4×C277—24no—
68C22⋊C4×C277—22no—
69C22×D277—22no—
70C22×D277—22no—
71C22×D277—21no—
72C22×D277—21no—
73C22×D277C2×D412yes—
74C22⋊D277—28no—
75C2×Dic277—21no—
76C2×Dic277—22no—
77C2×Dic277—22no—
78C2×Dic277—21no—
79C2×Dic277—22no—
80C2×Dic277—21no—
81C2×Dic277—22no—
82C2×Dic277—22no—
83C2×Dic277—22no—
84C2×Dic277—44no—
85C2×Dic277C2×D412yes—
86C2×Dic277#4114yes—
87C2×Dic277#4112yes—
88C2×Dic277#4114yes—
89C4×D277—28no—
90C23×C277—21no—
91C23×C277—22no—
92C23×C277—22no—
93C23×C277—21no—
94C23×C277#4112yes—
95C23×C277C2411yescharacteristic
96C2×C4×C277—22no—
97C2×C4×C277—21no—
98C2×C4×C277—22no—
99C2×C4×C277—22no—
100C2×C4×C277—22no—
101C2×C4×C277—22no—
102C2×C4×C277—22no—
103C2×C4×C277—22no—
104C2×C4×C277—22no—
105C2×C4×C277C2×D412yes—
106C22×C277—22no—
107C22×C277—24no—
108C22×C277—41no—
109C22×C277—42no—
110C22×C277—41no—
111C22×C277C22×D411yescharacteristic
112C22×C277C2×#4112yes—
113C22×C277C2×#4111yescharacteristic
114C22×C277C2×#4112yes—
115C22×C277C2×#4111yescharacteristic
116C2×D277—22no—
117C2×D277—22no—
118C2×D277—22no—
119C2×D277—42no—
120C2×D277—42no—
121C4×C277—22no—
122C4×C277—42no—
123C4×C277—42no—
124C4×C277—41no—
125Dic277—22no—
126Dic277—24no—
127Dic277—41no—
128Dic277—42no—
129Dic277#12314yes—
130C2×C277—42no—
131C2×C277C2×#12311yescharacteristic
132C2×C277#52511yescharacteristic
133C2×C277#52912yes—
134C2×C277#52912yes—
135C2×C277#53211yescharacteristic
136D277—42no—
137C277#239511yescharacteristic, complemented, Sylow
138#2395—2771nomaximal, Sylow
139C2×C4×D4—2771no—
140C2×#117—2771no—
141#400—2771no—
142#399—2771no—
143#398—2771no—
144#397—2772no—
145#397D27711yescharacteristic, complemented
146#394—2772no—
147C4×C4⋊C4—2772no—
148C4×C22⋊C4—2772no—
149C4×C22⋊C4—2771no—
150C22×D4—2771no—
151C23×C4—2771no—
152C23×C4—2771no—
153C4×D4—5544no—
154#117—5544no—
155C2×C4⋊C4—2771no—
156C2×C4⋊C4—2771no—
157C2×C4⋊C4—2772no—
158C2×C4⋊C4—2772no—
159C2×C4⋊C4C2×D27711yescharacteristic
160C2×C22⋊C4—2772no—
161C2×C22⋊C4—2772no—
162C2×C22⋊C4—2771no—
163C2×C22⋊C4—2772no—
164C2×C22⋊C4C2×D27711yescharacteristic
165C2×C22⋊C4C2×D27712yes—
166C2×C42—2772no—
167C2×C42—2771no—
168C2×C42—2772no—
169#95—2772no—
170#95—2772no—
171#95—2771no—
172#95—2772no—
173#95C2×D27711yescharacteristic
174#95C2×D27712yes—
175C24—2771no—
176C24C22×D27711yescharacteristic
177C2×D4—5542no—
178C2×D4—5542no—
179C2×D4—5542no—
180C22×C4—2771no—
181C22×C4—2772no—
182C22×C4—2771no—
183C22×C4—2774no—
184C22×C4—2771no—
185C22×C4—2772no—
186C22×C4—5544no—
187C22×C4—5542no—
188C22×C4—5544no—
189C22×C4C22×D27712yes—
190C22×C4C22×D27712yes—
191C22×C4C22×D27711yescharacteristic
192C22×C4C22×D27711yescharacteristic
193C4⋊C4—22no—
194C4⋊C4—5544no—
195C4⋊C4—5544no—
196C4⋊C4—5542no—
197C4⋊C4—5542no—
198C22⋊C4—24no—
199C22⋊C4—22no—
200C22⋊C4—5544no—
201C22⋊C4—5544no—
202C22⋊C4—5542no—
203C22⋊C4—5544no—
204C42—5544no—
205C42—5544no—
206C42—5542no—
207C23—21no—
208C23—22no—
209C23—22no—
210C23—21no—
211C23—2772no—
212C23—5542no—
213C23—5542no—
214C23—5541no—
215C23—5541no—
216C23#1798456212yes—
217C23C23×D27711yescharacteristic
218D4—5548no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—2772no—
229C2×C4—2774no—
230C2×C4—2774no—
231C2×C4—2772no—
232C2×C4—5548no—
233C2×C4—5541no—
234C2×C4—5542no—
235C2×C4—5542no—
236C2×C4—5541no—
237C2×C4—5542no—
238C2×C4—5541no—
239C2×C4—5542no—
240C2×C4—5542no—
241C2×C4—5542no—
242C2×C4—11084no—
243C2×C4D4×D27712yes—
244C22—22no—
245C22—24no—
246C22—41no—
247C22—42no—
248C22—41no—
249C22—5542no—
250C22—5542no—
251C22—5542no—
252C22—11082no—
253C22—11082no—
254C22C2×D4×D27711yescharacteristic
255C22#41×D27712yes—
256C22#41×D27711yescharacteristic
257C22#41×D27712yes—
258C22C2×#1798456211yescharacteristic
259C4—22no—
260C4—42no—
261C4—42no—
262C4—41no—
263C4—2774no—
264C4—5542no—
265C4—5544no—
266C4—11081no—
267C4—11082no—
268C2—42no—
269C2—11082no—
270C2#123×D27711yescharacteristic
271C2#3180051211yescharacteristic
272C2#3180052912yes—
273C2#3180053512yes—
274C2#3180055111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D277
commutator, socle, cosocleC23×C277C24
Fitting#397×C277C2
prime radicalC22×C22⋊D277C22
hypercenter#397D277
hypocenterC277#2395
LCSG ▷ C23×C277 ▷ C277
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#22579838C2semidirect
3. #31799942C2semidirect
4. #31799938C2semidirect
5. #31799933C2semidirect
6. #31799931C2semidirect
8. #31799853C2semidirect
9. C22⋊C4×Dic277C2semidirect
10. #31799849C2semidirect
11. #397×C277C2semidirect
137. C277#2395semidirect
145. #397D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225798402
C2×#225798382
#317999422
#317999382
#317999332
#317999312
#317999172
#317998532
C22⋊C4×Dic2772
#317998492
#397×C2772
#2395277