Finite Group Databasebeta

← #47986431

Subgroups — #47986431

Order 35456.

560 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 147 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×#22579842C211yesmaximal, characteristic
2C2×#22579838C211yesmaximal, characteristic, complemented
3#31799941C211yesmaximal, characteristic, complemented
4#31799939C211yesmaximal, characteristic, complemented
5#31799929C212yesmaximal, complemented
6#31799928C211yesmaximal, characteristic, complemented
7#31799919C212yesmaximal
8C4⋊C4×Dic277C212yesmaximal, complemented
9#31799849C212yesmaximal, complemented
10#31799849C211yesmaximal, characteristic, complemented
11#398×C277C211yesmaximal, characteristic, complemented
12C22×D1108C2211yescharacteristic
13C22×C4×D277C2211yescharacteristic
14C22×C4×D277C2211yescharacteristic
15#22579842—24no—
16#22579838—24no—
17C2×C4⋊Dic277C2212yes—
18C2×C4⋊Dic277C2211yescharacteristic
19C2×#17984540C2212yes—
20C2×#17984540C2212yes—
21C2×#17984540C2212yes—
22C2×#17984540C2212yes—
23C2×#17984540C2211yescharacteristic
24C2×#17984540C2211yescharacteristic
25C2×C4×Dic277C2212yes—
26C2×C4×Dic277C2212yes—
27C2×C4×Dic277C2211yescharacteristic
28#22579787C2211yescharacteristic
29#22579787C2212yes—
30#22579787C2212yes—
31#22579787C2212yes—
32C2×C4⋊C4×C277C2212yes—
33C2×C4⋊C4×C277C2211yescharacteristic
34C2×C4⋊C4×C277C2211yescharacteristic
35#95×C277C2212yes—
36#95×C277C2211yescharacteristic
37C23×D277C2311yescharacteristic
38C23×D277C2311yescharacteristic
39C2×D1108—22no—
40C2×D1108—22no—
41C2×D1108—22no—
42C22×Dic277C2312yes—
43C22×Dic277C2311yescharacteristic
44C22×Dic277C2312yes—
45C22×Dic277C2311yescharacteristic
46C2×C4×D277—24no—
47C2×C4×D277—22no—
48C2×C4×D277—24no—
49C2×C4×D277D414yes—
50C4⋊Dic277—22no—
51C4⋊Dic277—24no—
52#17984540—24no—
53#17984540—22no—
54#17984540—24no—
55#17984540—22no—
56#17984540—24no—
57#17984540—24no—
58C4×Dic277—24no—
59C4×Dic277—22no—
60C4×Dic277—24no—
61C22×C4×C277C2311yescharacteristic
62C22×C4×C277C2312yes—
63C22×C4×C277C2311yescharacteristic
64C22×C4×C277C2312yes—
65C22×C4×C277C2311yescharacteristic
66C4⋊C4×C277—22no—
67C4⋊C4×C277—22no—
68C4⋊C4×C277—24no—
69C22×D277—21no—
70C22×D277—22no—
71C22×D277—22no—
72C22×D277—22no—
73C22×D277—22no—
74C22×D277—21no—
75C22×D277—21no—
76C22×D277—21no—
77C22×D277C2×D412yes—
78C22×D277#4112yes—
79D1108—28no—
80C2×Dic277—21no—
81C2×Dic277—22no—
82C2×Dic277—22no—
83C2×Dic277—22no—
84C2×Dic277—22no—
85C2×Dic277—22no—
86C2×Dic277—22no—
87C2×Dic277—22no—
88C2×Dic277C2×D412yes—
89C2×Dic277#4114yes—
90C4×D277—28no—
91C4×D277—44no—
92C23×C277C2411yescharacteristic
93C2×C4×C277—21no—
94C2×C4×C277—22no—
95C2×C4×C277—22no—
96C2×C4×C277—22no—
97C2×C4×C277—21no—
98C2×C4×C277—22no—
99C2×C4×C277—21no—
100C2×C4×C277—22no—
101C2×C4×C277—22no—
102C2×C4×C277—22no—
103C2×C4×C277C2×D412yes—
104C2×C4×C277#4112yes—
105C2×C4×C277#4114yes—
106C22×C277C22×D411yescharacteristic
107C22×C277C2×#4112yes—
108C22×C277C2×#4111yescharacteristic
109C22×C277C2×#4111yescharacteristic
110C22×C277C2×#4112yes—
111C2×D277—22no—
112C2×D277—22no—
113C2×D277—22no—
114C2×D277—24no—
115C2×D277—22no—
116C2×D277—41no—
117C2×D277—42no—
118C2×D277—42no—
119C2×D277—42no—
120C2×D277—41no—
121C4×C277—22no—
122C4×C277—22no—
123C4×C277—24no—
124C4×C277—41no—
125C4×C277—42no—
126Dic277—42no—
127Dic277—41no—
128Dic277—42no—
129Dic277#12314yes—
130C2×C277C2×#12311yescharacteristic
131C2×C277#52511yescharacteristic
132C2×C277#52912yes—
133C2×C277#52912yes—
134C2×C277#53211yescharacteristic
135D277—42no—
136D277—42no—
137C277#239511yescharacteristic, complemented, Sylow
138#2395—2771nomaximal, Sylow
139C2×C4×D4—2771no—
140C2×#117—2771no—
141#400—2771no—
142#399—2771no—
143#398D27711yescharacteristic, complemented
144#397—2771no—
145#397—2772no—
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—2772no—
157C2×C4⋊C4C2×D27711yescharacteristic
158C2×C4⋊C4C2×D27711yescharacteristic
159C2×C4⋊C4C2×D27712yes—
160C2×C22⋊C4—2772no—
161C2×C22⋊C4—2771no—
162C2×C22⋊C4—2771no—
163C2×C22⋊C4—2772no—
164C2×C22⋊C4—2772no—
165C2×C22⋊C4—2772no—
166C2×C42—2772no—
167C2×C42—2771no—
168C2×C42—2772no—
169#95—2771no—
170#95—2772no—
171#95—2772no—
172#95—2772no—
173#95C2×D27712yes—
174#95C2×D27711yescharacteristic
175C24—2771no—
176C24—2771no—
177C2×D4—5542no—
178C2×D4—5542no—
179C2×D4—5542no—
180C22×C4—2771no—
181C22×C4—2774no—
182C22×C4—2772no—
183C22×C4—2771no—
184C22×C4—2772no—
185C22×C4—5544no—
186C22×C4—5542no—
187C22×C4—5544no—
188C22×C4C22×D27711yescharacteristic
189C22×C4C22×D27712yes—
190C22×C4C22×D27711yescharacteristic
191C22×C4C22×D27711yescharacteristic
192C22×C4C22×D27712yes—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—24no—
196C4⋊C4—5542no—
197C4⋊C4—5544no—
198C22⋊C4—5544no—
199C22⋊C4—5544no—
200C22⋊C4—5542no—
201C22⋊C4—5542no—
202C22⋊C4—5544no—
203C22⋊C4—5544no—
204C42—5544no—
205C42—5544no—
206C42—5542no—
207C23—2772no—
208C23—2772no—
209C23—5541no—
210C23—5542no—
211C23—5542no—
212C23—5541no—
213C23—5541no—
214C23—5541no—
215C23—5542no—
216C23—5542no—
217C23C23×D27711yescharacteristic
218D4—5548no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—2772no—
230C2×C4—2774no—
231C2×C4—5548no—
232C2×C4—5541no—
233C2×C4—5542no—
234C2×C4—5542no—
235C2×C4—5542no—
236C2×C4—5542no—
237C2×C4—5542no—
238C2×C4—5542no—
239C2×C4—5542no—
240C2×C4—11084no—
241C2×C4D4×D27712yes—
242C2×C4#1798456212yes—
243C2×C4#1798456414yes—
244C22—5542no—
245C22—5542no—
246C22—5542no—
247C22—5544no—
248C22—5542no—
249C22—11081no—
250C22—11082no—
251C22—11082no—
252C22—11082no—
253C22—11081no—
254C22C2×D4×D27711yescharacteristic
255C22#41×D27712yes—
256C22#41×D27711yescharacteristic
257C22C2×#1798456211yescharacteristic
258C22C2×#1798456412yes—
259C4—22no—
260C4—22no—
261C4—24no—
262C4—41no—
263C4—42no—
264C4—2774no—
265C4—11082no—
266C4—11081no—
267C4—11082no—
268C2—11082no—
269C2—11082no—
270C2#123×D27711yescharacteristic
271C2#3180051211yescharacteristic
272C2#3180053712yes—
273C2#3180053812yes—
274C2#3180055311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D277
commutator, socle, cosocleC23×C277C24
Fitting#398×C277C2
prime radicalC22×D1108C22
hypercenter#398D277
hypocenterC277#2395
LCSG ▷ C23×C277 ▷ C277
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#22579838C2semidirect
3. #31799941C2semidirect
4. #31799939C2semidirect
5. #31799929C2semidirect
6. #31799928C2semidirect
8. C4⋊C4×Dic277C2semidirect
9. #31799849C2semidirect
10. #31799849C2semidirect
11. #398×C277C2semidirect
137. C277#2395semidirect
143. #398D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225798422
C2×#225798382
#317999412
#317999392
#317999292
#317999282
#317999192
C4⋊C4×Dic2772
#317998492
#398×C2772
#2395277