Finite Group Databasebeta

← #47982113

Subgroups — #47982113

Order 35456.

320 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 53 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#31800152C211yesmaximal, characteristic, complemented
2#31800135C211yesmaximal, characteristic, complemented
3#31799911C211yesmaximal, characteristic, complemented
4#31799739C211yesmaximal, characteristic, complemented
5#31799736C211yesmaximal, characteristic, complemented
6#31799726C211yesmaximal, characteristic, complemented
7#538×C277C211yesmaximal, characteristic, complemented
8C22×D1108C2211yescharacteristic
9C22×C22⋊D277—21no—
10C2×#17984550—21no—
11C2×#17984548—21no—
12C2×#17984540—21no—
13#22579800—21no—
14#22579800—21no—
15C22⋊#14555660C2211yescharacteristic
16C22⋊#14555660C2211yescharacteristic
17#22579787C2211yescharacteristic
18#126×C277—21no—
19#124×C277—21no—
20#123×C277—21no—
21C22⋊Q8×C277C2211yescharacteristic
22#121×C277—21no—
23#121×C277C2211yescharacteristic
24#120×C277—21no—
25C4×D4×C277—21no—
26C2×C22⋊C4×C277C2211yescharacteristic
27C23×D277—21no—
28C2×D1108—21no—
29C2×D1108—21no—
30C2×D1108—42no—
31C2×C22⋊D277—42no—
32C2×C22⋊D277—42no—
33C2×C22⋊D277—42no—
34C22×Dic277—21no—
35#17984550—42no—
36#17984548—42no—
37C2×#14555660—21no—
38C2×#14555660—21no—
39#17984540—42no—
40C24×C277D411yescharacteristic
41C2×Q8×C277D411yescharacteristic, complemented
42C2×D4×C277—21no—
43C2×D4×C277—21no—
44C2×D4×C277—21no—
45C2×D4×C277D411yescharacteristic, complemented
46C22×C4×C277—21no—
47C22×C4×C277D411yescharacteristic
48C22×C4×C277C2311yescharacteristic
49C4⋊C4×C277—21no—
50C4⋊C4×C277—21no—
51C4⋊C4×C277D411yescharacteristic, complemented
52C4⋊C4×C277D411yescharacteristic, complemented
53C22⋊C4×C277—21no—
54C22⋊C4×C277—21no—
55C22⋊C4×C277—21no—
56C22⋊C4×C277—21no—
57C22⋊C4×C277—21no—
58C22⋊C4×C277—21no—
59C22⋊C4×C277—21no—
60C42×C277—21no—
61C22×D277—22no—
62C22×D277—41no—
63C22×D277—41no—
64C22×D277—41no—
65C22×D277—41no—
66C22×D277—41no—
67C22×D277—41no—
68D1108—22no—
69D1108—22no—
70D1108—41no—
71D1108—41no—
72C22⋊D277—48no—
73C2×Dic277—22no—
74C2×Dic277—41no—
75C2×Dic277—41no—
76#14555660—41no—
77#14555660—41no—
78C23×C277—21no—
79C23×C277—21no—
80C23×C277—21no—
81C23×C277—21no—
82C23×C277—41no—
83C23×C277—41no—
84C23×C277C2×D411yescharacteristic
85Q8×C277—41no—
86D4×C277—41no—
87D4×C277—41no—
88D4×C277—41no—
89D4×C277—81no—
90D4×C277—81no—
91C2×C4×C277—21no—
92C2×C4×C277—21no—
93C2×C4×C277—21no—
94C2×C4×C277—21no—
95C2×C4×C277—41no—
96C2×C4×C277—41no—
97C2×C4×C277—81no—
98C2×C4×C277C2×D411yescharacteristic
99C2×C4×C277C2×D411yescharacteristic
100C22×C277—21no—
101C22×C277—21no—
102C22×C277—42no—
103C22×C277—41no—
104C22×C277—41no—
105C22×C277—41no—
106C22×C277—41no—
107C22×C277—41no—
108C22×C277—41no—
109C22×C277—81no—
110C22×C277#12011yescharacteristic
111C22×C277#13511yescharacteristic
112C22×C277AGL(1,ℤ/8)11yescharacteristic
113C2×D277—42no—
114C2×D277—42no—
115C2×D277—42no—
116C2×D277—81no—
117C2×D277—81no—
118C2×D277—81no—
119C2×D277—81no—
120C4×C277—21no—
121C4×C277—21no—
122C4×C277—41no—
123C4×C277—41no—
124C4×C277—41no—
125C4×C277—41no—
126Dic277—42no—
127C2×C277—21no—
128C2×C277—21no—
129C2×C277—81no—
130C2×C277—81no—
131C2×C277#44911yescharacteristic
132C2×C277#45311yescharacteristic
133C2×C277B(4,𝔽2)11yescharacteristic
134D277—82no—
135C277#160011yescharacteristic, complemented, Sylow
136#1600—2771nomaximal, Sylow
137#538D27711yescharacteristic, complemented
138#450—2771no—
139#447—2771no—
140#392—2771no—
141#328—2771no—
142#327—2771no—
143#323—2771no—
144C22×D4—2771no—
145C22×D4—5541no—
146C2×SD16—5541no—
147C2×D8—5541no—
148#126—21no—
149#124—21no—
150#123—21no—
151C22⋊Q8C2×D27711yescharacteristic
152#121—21no—
153#121C2×D27711yescharacteristic
154#120—21no—
155C4×D4—21no—
156C2×C22⋊C4—5541no—
157C2×C22⋊C4C2×D27711yescharacteristic
158#102—5541no—
159#102—5541no—
160C22⋊C8—2771no—
161C22⋊C8—2771no—
162#95—2771no—
163C24—5541no—
164C24C22⋊D27711yescharacteristic
165C2×Q8C22⋊D27711yescharacteristic, complemented
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—5541no—
170C2×D4—5541no—
171C2×D4—11082no—
172C2×D4—11082no—
173C2×D4—11082no—
174C2×D4—11082no—
175C2×D4C22⋊D27711yescharacteristic, complemented
176C22×C4—21no—
177C22×C4—5541no—
178C22×C4C22⋊D27711yescharacteristic
179C22×C4C22×D27711yescharacteristic
180SD16—11082no—
181D8—11082no—
182C2×C8—5541no—
183C2×C8—5541no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4C22⋊D27711yescharacteristic, complemented
187C4⋊C4C22⋊D27711yescharacteristic, complemented
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—21no—
191C22⋊C4—21no—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—11082no—
196C42—21no—
197C23—21no—
198C23—21no—
199C23—21no—
200C23—21no—
201C23—41no—
202C23—41no—
203C23—5542no—
204C23—11081no—
205C23—11081no—
206C23—11081no—
207C23—11081no—
208C23—11081no—
209C23—11081no—
210C23C2×C22⋊D27711yescharacteristic
211Q8—41no—
212D4—41no—
213D4—41no—
214D4—41no—
215D4—81no—
216D4—81no—
217D4—5542no—
218D4—5542no—
219D4—11081no—
220D4—11081no—
221D4—11088no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—81no—
229C2×C4—5542no—
230C2×C4—11081no—
231C2×C4—11081no—
232C2×C4C2×C22⋊D27711yescharacteristic
233C2×C4C2×C22⋊D27711yescharacteristic
234C8—11081no—
235C8—11081no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—81no—
246C22—11082no—
247C22—11082no—
248C22—11082no—
249C22—22161no—
250C22—22161no—
251C22—22161no—
252C22—22161no—
253C22#2257984911yescharacteristic
254C22#2257990011yescharacteristic
255C22#2257990511yescharacteristic
256C4—21no—
257C4—21no—
258C4—41no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4—11082no—
263C2—21no—
264C2—21no—
265C2—81no—
266C2—81no—
267C2—22162no—
268C2#3180014711yescharacteristic
269C2#3180017011yescharacteristic
270C2#3180018911yescharacteristic
subgroupG/H
centerC22#22579849
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#538×C277C2
socleC22×C277#120
hypercenter#538D277
hypocenterC277#1600
LCSG ▷ C22×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #538

Complements

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

NH ≅ G/Ntype
1. #31800152C2semidirect
2. #31800135C2semidirect
3. #31799911C2semidirect
4. #31799739C2semidirect
5. #31799736C2semidirect
6. #31799726C2semidirect
7. #538×C277C2semidirect
41. C2×Q8×C277D4semidirect
45. C2×D4×C277D4semidirect
51. C4⋊C4×C277D4semidirect
52. C4⋊C4×C277D4semidirect
135. C277#1600semidirect
137. #538D277semidirect
165. C2×Q8C22⋊D277semidirect
175. C2×D4C22⋊D277semidirect
186. C4⋊C4C22⋊D277semidirect
187. C4⋊C4C22⋊D277semidirect

Maximal subgroups

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

subgroupindex
#318001522
#318001352
#317999112
#317997392
#317997362
#317997262
#538×C2772
#1600277