Finite Group Databasebeta

← #47982147

Subgroups — #47982147

Order 35456.

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

normal subgroups only

This group has 260 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#31800157C211yesmaximal, characteristic, complemented
2#31800140C211yesmaximal, characteristic, complemented
3#31799914C211yesmaximal, characteristic, complemented
4#31799739C211yesmaximal, characteristic, complemented
5#31799736C211yesmaximal, characteristic, complemented
6#31799726C211yesmaximal, characteristic, complemented
7#538×C277C211yesmaximal, characteristic
8C22×Dic554C2211yescharacteristic
9C2×#17984553—21no—
10C2×#17984551—21no—
11C2×C22⋊Dic277—21no—
12#22579803—21no—
13#22579803—21no—
14C22⋊#14555660C2211yescharacteristic
15C22⋊#14555660C2211yescharacteristic
16#22579787—21no—
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
27C2×Dic554—21no—
28C2×Dic554—21no—
29C2×Dic554—42no—
30C22×Dic277—21no—
31C22×Dic277—21no—
32#17984553—42no—
33#17984551—42no—
34C2×#14555660—21no—
35C2×#14555660—21no—
36C22⋊Dic277—42no—
37C24×C277D411yescharacteristic
38C2×Q8×C277D411yescharacteristic
39C2×D4×C277—21no—
40C2×D4×C277—21no—
41C2×D4×C277—21no—
42C2×D4×C277D411yescharacteristic
43C22×C4×C277—21no—
44C22×C4×C277D411yescharacteristic
45C22×C4×C277C2311yescharacteristic
46C4⋊C4×C277—21no—
47C4⋊C4×C277—21no—
48C4⋊C4×C277D411yescharacteristic
49C4⋊C4×C277D411yescharacteristic
50C22⋊C4×C277—21no—
51C22⋊C4×C277—21no—
52C22⋊C4×C277—21no—
53C22⋊C4×C277—21no—
54C22⋊C4×C277—21no—
55C22⋊C4×C277—21no—
56C22⋊C4×C277—21no—
57C42×C277—21no—
58Dic554—22no—
59Dic554—22no—
60Dic554—41no—
61Dic554—41no—
62C2×Dic277—22no—
63C2×Dic277—41no—
64C2×Dic277—41no—
65C2×Dic277—41no—
66C2×Dic277—41no—
67C2×Dic277—41no—
68#14555660—41no—
69#14555660—41no—
70C23×C277—21no—
71C23×C277—21no—
72C23×C277—21no—
73C23×C277—21no—
74C23×C277—41no—
75C23×C277—41no—
76C23×C277C2×D411yescharacteristic
77Q8×C277—41no—
78D4×C277—41no—
79D4×C277—41no—
80D4×C277—41no—
81D4×C277—81no—
82D4×C277—81no—
83C2×C4×C277—21no—
84C2×C4×C277—21no—
85C2×C4×C277—21no—
86C2×C4×C277—21no—
87C2×C4×C277—41no—
88C2×C4×C277—41no—
89C2×C4×C277—81no—
90C2×C4×C277C2×D411yescharacteristic
91C2×C4×C277C2×D411yescharacteristic
92C22×C277—21no—
93C22×C277—21no—
94C22×C277—42no—
95C22×C277—41no—
96C22×C277—41no—
97C22×C277—41no—
98C22×C277—41no—
99C22×C277—41no—
100C22×C277—41no—
101C22×C277—81no—
102C22×C277#12011yescharacteristic
103C22×C277#13511yescharacteristic
104C22×C277#13711yescharacteristic
105C4×C277—21no—
106C4×C277—21no—
107C4×C277—41no—
108C4×C277—41no—
109C4×C277—41no—
110C4×C277—41no—
111Dic277—42no—
112Dic277—81no—
113C2×C277—21no—
114C2×C277—21no—
115C2×C277—81no—
116C2×C277—81no—
117C2×C277#45211yescharacteristic
118C2×C277#45511yescharacteristic
119C2×C277B(4,𝔽2)11yescharacteristic
120C277#160611yescharacteristic, complemented, Sylow
121#1606—2771nomaximal, Sylow
122#538D27711yescharacteristic
123#451—2771no—
124#448—2771no—
125#393—2771no—
126#328—2771no—
127#327—2771no—
128#323—2771no—
129C22×Q8—2771no—
130C2×Q16—5541no—
131C2×SD16—5541no—
132#126—21no—
133#124—21no—
134#123—21no—
135C22⋊Q8C2×D27711yescharacteristic
136#121—21no—
137#121C2×D27711yescharacteristic
138#120—21no—
139C4×D4—21no—
140C2×C22⋊C4—5541no—
141C2×C22⋊C4C2×D27711yescharacteristic
142#103—5541no—
143#103—5541no—
144C22⋊C8—2771no—
145C22⋊C8—2771no—
146#95—2771no—
147#95—5541no—
148C24C22⋊D27711yescharacteristic
149C2×Q8—5541no—
150C2×Q8—5541no—
151C2×Q8—11082no—
152C2×Q8C22⋊D27711yescharacteristic
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—21no—
156C2×D4C22⋊D27711yescharacteristic
157C22×C4—21no—
158C22×C4—5541no—
159C22×C4—5541no—
160C22×C4C22⋊D27711yescharacteristic
161C22×C4C22×D27711yescharacteristic
162Q16—11082no—
163SD16—11082no—
164C2×C8—5541no—
165C2×C8—5541no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4C22⋊D27711yescharacteristic
169C4⋊C4C22⋊D27711yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—21no—
173C22⋊C4—21no—
174C22⋊C4—21no—
175C22⋊C4—21no—
176C22⋊C4—21no—
177C22⋊C4—11082no—
178C42—21no—
179C23—21no—
180C23—21no—
181C23—21no—
182C23—21no—
183C23—41no—
184C23—41no—
185C23C2×C22⋊D27711yescharacteristic
186Q8—41no—
187Q8—5542no—
188Q8—5542no—
189Q8—11081no—
190Q8—11081no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—81no—
195D4—81no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—81no—
203C2×C4—5542no—
204C2×C4—11081no—
205C2×C4—11081no—
206C2×C4—11081no—
207C2×C4—11081no—
208C2×C4—11081no—
209C2×C4C2×C22⋊D27711yescharacteristic
210C2×C4C2×C22⋊D27711yescharacteristic
211C8—11081no—
212C8—11081no—
213C22—21no—
214C22—21no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—81no—
223C22#2257984911yescharacteristic
224C22#2257990011yescharacteristic
225C22#2257991011yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—41no—
230C4—41no—
231C4—41no—
232C4—11082no—
233C4—22161no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—81no—
238C2#3180016411yescharacteristic
239C2#3180018011yescharacteristic
240C2#3180018911yescharacteristic
subgroupG/H
centerC22#22579849
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting, prime radical#538×C277C2
socleC22×C277#120
hypercenter#538D277
hypocenterC277#1606
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. #31800157C2semidirect
2. #31800140C2semidirect
3. #31799914C2semidirect
4. #31799739C2semidirect
5. #31799736C2semidirect
6. #31799726C2semidirect
120. C277#1606semidirect

Maximal subgroups

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

subgroupindex
#318001572
#318001402
#317999142
#317997392
#317997362
#317997262
#538×C2772
#1606277