Finite Group Databasebeta

← #47982183

Subgroups — #47982183

Order 35456.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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#31800590C211yesmaximal, characteristic
2#31800333C211yesmaximal, characteristic, complemented
3#31800316C211yesmaximal, characteristic, complemented
4#31799927C211yesmaximal, characteristic, complemented
5#31799740C211yesmaximal, characteristic, complemented
6#31799737C211yesmaximal, characteristic, complemented
7#323×C277C211yesmaximal, characteristic, complemented
8#22579873—21no—
9#22579866—21no—
10#22579862—21no—
11#22579859C2211yescharacteristic
12#22579854C2211yescharacteristic
13#22579853—21no—
14#22579849—21no—
15C4×C22⋊D277—21no—
16C2×C4⋊Dic277C2211yescharacteristic
17C2×C22⋊Dic277—21no—
18#22579814—21no—
19#22579812—21no—
20#22579805—21no—
21#22579802—21no—
22#22579787—21no—
23#22579787C2211yescharacteristic
24C2×C22⋊C4×C277C2211yescharacteristic
25C22⋊C8×C277C2211yescharacteristic
26C22⋊C8×C277C2211yescharacteristic
27C2×Dic554D411yescharacteristic
28C2×D1108D411yescharacteristic
29C2×C22⋊D277—21no—
30C2×C22⋊D277—21no—
31C2×C22⋊D277—21no—
32C22×Dic277—21no—
33C22×Dic277—21no—
34C2×C4×D277—21no—
35C4⋊Dic277—21no—
36C4⋊Dic277—21no—
37C4⋊Dic277D411yescharacteristic
38C4⋊Dic277D411yescharacteristic
39#17984542—21no—
40#17984542—21no—
41C22⋊Dic277—21no—
42C22⋊Dic277—21no—
43C22⋊Dic277—21no—
44C22⋊Dic277—42no—
45#17984540—21no—
46#17984540—21no—
47C4×Dic277—21no—
48C24×C277D411yescharacteristic
49C22×C4×C277D411yescharacteristic
50C22×C4×C277C2311yescharacteristic
51C2×C8×C277—21no—
52C2×C8×C277—21no—
53C22⋊C4×C277—21no—
54C22⋊C4×C277—21no—
55C22×D277—21no—
56Dic554—41no—
57D1108—41no—
58C22⋊D277—41no—
59C22⋊D277—41no—
60C22⋊D277—81no—
61C22⋊D277—81no—
62C2×Dic277—21no—
63C2×Dic277—21no—
64C2×Dic277—21no—
65C2×Dic277—41no—
66C2×Dic277—41no—
67C2×Dic277—41no—
68C2×Dic277—41no—
69C2×Dic277—41no—
70C2×Dic277—41no—
71C4×D277—81no—
72C23×C277—21no—
73C23×C277—21no—
74C23×C277—21no—
75C23×C277—41no—
76C23×C277—41no—
77C23×C277C2×D411yescharacteristic
78C2×C4×C277—21no—
79C2×C4×C277—41no—
80C2×C4×C277—41no—
81C2×C4×C277C2×D411yescharacteristic
82C2×C4×C277C2×D411yescharacteristic
83C8×C277—41no—
84C8×C277—41no—
85C22×C277—21no—
86C22×C277—21no—
87C22×C277—42no—
88C22×C277—41no—
89C22×C277—41no—
90C22×C277—41no—
91C22×C277—81no—
92C22×C277#12011yescharacteristic
93C22×C277#13511yescharacteristic
94C22×C277AGL(1,ℤ/8)11yescharacteristic
95C2×D277—41no—
96C2×D277—41no—
97C2×D277—41no—
98C4×C277—21no—
99C4×C277—21no—
100C4×C277—41no—
101Dic277—41no—
102Dic277—41no—
103Dic277—41no—
104Dic277—81no—
105Dic277—81no—
106C2×C277—21no—
107C2×C277—21no—
108C2×C277—81no—
109C2×C277#44911yescharacteristic
110C2×C277#45511yescharacteristic
111C2×C277#45811yescharacteristic
112D277—81no—
113C277#161211yescharacteristic, complemented, Sylow
114#1612—2771nomaximal, Sylow
115#538—2771no—
116#483—2771no—
117#480—2771no—
118#397—2771no—
119#328—2771no—
120#327—2771no—
121#323D27711yescharacteristic, complemented
122#126—5541no—
123#124—5541no—
124#123—5541no—
125C22⋊Q8—2771no—
126#121—2771no—
127#121—5541no—
128#120—5541no—
129C4×D4—5541no—
130C2×C4⋊C4—2771no—
131C2×C22⋊C4—5541no—
132C2×C22⋊C4C2×D27711yescharacteristic
133#107—5541no—
134#106—5541no—
135#103—5541no—
136#102—5541no—
137C22⋊C8C2×D27711yescharacteristic
138C22⋊C8C2×D27711yescharacteristic
139#95—2771no—
140#95—5541no—
141C24D110811yescharacteristic
142C2×Q8—2771no—
143C2×D4—2771no—
144C2×D4—5541no—
145C2×D4—5541no—
146C2×D4—5541no—
147C22×C4—5541no—
148C22×C4—5541no—
149C22×C4—5541no—
150C22×C4D110811yescharacteristic
151C22×C4C22×D27711yescharacteristic
152C2×C8—21no—
153C2×C8—21no—
154C4⋊C4—2771no—
155C4⋊C4—2771no—
156C4⋊C4—5541no—
157C4⋊C4—5541no—
158C4⋊C4—5541no—
159C4⋊C4—5541no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—5541no—
163C22⋊C4—5541no—
164C22⋊C4—5541no—
165C22⋊C4—5541no—
166C22⋊C4—5541no—
167C22⋊C4—11082no—
168C42—5541no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—5541no—
175C23C2×D110811yescharacteristic
176Q8—11081no—
177D4—11081no—
178D4—11081no—
179D4—11081no—
180D4—22161no—
181D4—22161no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—5541no—
186C2×C4—5541no—
187C2×C4—5541no—
188C2×C4—11081no—
189C2×C4—11081no—
190C2×C4—11081no—
191C2×C4—11081no—
192C2×C4—11081no—
193C2×C4—11081no—
194C2×C4—22161no—
195C2×C4D4×D27711yescharacteristic
196C2×C4D4×D27711yescharacteristic
197C8—41no—
198C8—41no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—11081no—
207C22—11081no—
208C22—11081no—
209C22#2257985011yescharacteristic
210C22#2257990211yescharacteristic
211C22#2257990811yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—11081no—
216C4—11081no—
217C4—11081no—
218C4—22161no—
219C4—22161no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—22161no—
224C2#3180014911yescharacteristic
225C2#3180018211yescharacteristic
226C2#3180019311yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#323×C277C2
socleC22×C277#120
prime radical#31800590C2
hypercenter#323D277
hypocenterC277#1612
LCSG ▷ C22×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #31800333C2semidirect
3. #31800316C2semidirect
4. #31799927C2semidirect
5. #31799740C2semidirect
6. #31799737C2semidirect
7. #323×C277C2semidirect
113. C277#1612semidirect
121. #323D277semidirect

Maximal subgroups

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

subgroupindex
#318005902
#318003332
#318003162
#317999272
#317997402
#317997372
#323×C2772
#1612277