Finite Group Databasebeta

← #47982171

Subgroups — #47982171

Order 35456.

254 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 51 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#31800579C211yesmaximal, characteristic
2#31800316C211yesmaximal, characteristic, complemented
3#31800313C211yesmaximal, characteristic, complemented
4#31799934C211yesmaximal, characteristic, complemented
5#31799735C211yesmaximal, characteristic, complemented
6#31799727C211yesmaximal, characteristic, complemented
7#327×C277C211yesmaximal, characteristic, complemented
8C2×#17984562—21no—
9#22579858—21no—
10#22579857—21no—
11#22579854C2211yescharacteristic
12#22579853—21no—
13#22579852—21no—
14#22579852—21no—
15C2×C4⋊Dic277—21no—
16C2×C4⋊Dic277C2211yescharacteristic
17C2×#17984542C2211yescharacteristic
18#22579814—21no—
19#22579813—21no—
20#22579802—21no—
21#22579801—21no—
22C22⋊#14555660C2211yescharacteristic
23#22579787—21no—
24#121×C277C2211yescharacteristic
25C22⋊C8×C277C2211yescharacteristic
26#95×C277C2211yescharacteristic
27#17984562—42no—
28#17984562—42no—
29C2×Dic554—21no—
30C2×D1108D411yescharacteristic
31C2×C22⋊D277—21no—
32C2×C22⋊D277—21no—
33C2×C22⋊D277—21no—
34C22×Dic277—21no—
35C22×Dic277—21no—
36C22×Dic277D411yescharacteristic
37C22×Dic277D411yescharacteristic
38C2×C4×D277—21no—
39C2×#14555660—21no—
40C4⋊Dic277—21no—
41C4⋊Dic277—21no—
42C4⋊Dic277—42no—
43C4⋊Dic277D411yescharacteristic
44#17984542—21no—
45#17984542—21no—
46#17984542—21no—
47C22⋊Dic277—21no—
48#17984540—21no—
49#17984540—21no—
50C2×D4×C277—21no—
51C2×D4×C277D411yescharacteristic
52C22×C4×C277—21no—
53C22×C4×C277C2311yescharacteristic
54C2×C8×C277—21no—
55C4⋊C4×C277D411yescharacteristic
56C22⋊C4×C277—21no—
57C22×D277—21no—
58Dic554—42no—
59D1108—41no—
60C22⋊D277—42no—
61C22⋊D277—41no—
62C22⋊D277—41no—
63C22⋊D277—81no—
64C2×Dic277—21no—
65C2×Dic277—21no—
66C2×Dic277—21no—
67C2×Dic277—21no—
68C2×Dic277—42no—
69C2×Dic277—41no—
70C2×Dic277—41no—
71C2×Dic277—41no—
72C2×Dic277—41no—
73C2×Dic277D812yes—
74C4×D277—42no—
75#14555660—41no—
76C23×C277—21no—
77C23×C277C2×D411yescharacteristic
78D4×C277—41no—
79D4×C277—41no—
80D4×C277—41no—
81C2×C4×C277—22no—
82C2×C4×C277—21no—
83C2×C4×C277—41no—
84C2×C4×C277—41no—
85C2×C4×C277—41no—
86C2×C4×C277C2×D411yescharacteristic
87C2×C4×C277C2×D411yescharacteristic
88C8×C277—41no—
89C22×C277—21no—
90C22×C277—21no—
91C22×C277—41no—
92C22×C277—41no—
93C22×C277—41no—
94C22×C277#12011yescharacteristic
95C22×C277C2×D811yescharacteristic
96C22×C277AGL(1,ℤ/8)11yescharacteristic
97C2×D277—41no—
98C2×D277—41no—
99C2×D277—41no—
100C4×C277—21no—
101C4×C277—21no—
102C4×C277—42no—
103C4×C277—41no—
104Dic277—22no—
105Dic277—41no—
106Dic277—41no—
107Dic277—81no—
108C2×C277—21no—
109C2×C277—21no—
110C2×C277—81no—
111C2×C277#44711yescharacteristic
112C2×C277#45611yescharacteristic
113C2×C277#45811yescharacteristic
114D277—81no—
115C277#161011yescharacteristic, complemented, Sylow
116#1610—2771nomaximal, Sylow
117#537—2771no—
118#480—2771no—
119#480—2771no—
120#398—2771no—
121#327—2771no—
122#327D27711yescharacteristic, complemented
123#324—2771no—
124C2×#41—5541no—
125C22⋊Q8—5541no—
126C22⋊Q8—5541no—
127#121—2771no—
128#121—5541no—
129#121—5541no—
130#121—5541no—
131#121C2×D27711yescharacteristic
132C2×C4⋊C4—2771no—
133C2×C4⋊C4—2771no—
134C2×C4⋊C4—5541no—
135#107—5541no—
136#107—5541no—
137#102—5541no—
138#102—5541no—
139C22⋊C8—2771no—
140C22⋊C8C2×D27711yescharacteristic
141#95—5541no—
142#95C2×D27711yescharacteristic
143#41—11082no—
144#41—11082no—
145C2×Q8—5541no—
146C2×D4—21no—
147C2×D4—2771no—
148C2×D4—5541no—
149C2×D4—5541no—
150C2×D4—5541no—
151C2×D4D110811yescharacteristic
152C22×C4—21no—
153C22×C4—2771no—
154C22×C4—2771no—
155C22×C4—5541no—
156C22×C4—5541no—
157C22×C4—5541no—
158C22×C4C22×D27711yescharacteristic
159C2×C8—21no—
160C2×C8—5541no—
161C4⋊C4—2771no—
162C4⋊C4—5541no—
163C4⋊C4—5541no—
164C4⋊C4—5541no—
165C4⋊C4—5541no—
166C4⋊C4—5541no—
167C4⋊C4—11082no—
168C4⋊C4D110811yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—5541no—
171C22⋊C4—5541no—
172C22⋊C4—5541no—
173C23—21no—
174C23—5541no—
175C23D4×D27711yescharacteristic
176Q8—11082no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—11081no—
181D4—11082no—
182D4—11081no—
183D4—11081no—
184D4—22161no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—2772no—
191C2×C4—5541no—
192C2×C4—5541no—
193C2×C4—5541no—
194C2×C4—5541no—
195C2×C4—11082no—
196C2×C4—11082no—
197C2×C4—11081no—
198C2×C4—11081no—
199C2×C4—11081no—
200C2×C4—11081no—
201C2×C4D4×D27711yescharacteristic
202C2×C4C2×D110811yescharacteristic
203C8—41no—
204C8—11081no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—11081no—
211C22—11081no—
212C22—11081no—
213C22#2257985011yescharacteristic
214C22D8×D27711yescharacteristic
215C22#2257990711yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—41no—
220C4—5542no—
221C4—11081no—
222C4—11081no—
223C4—22161no—
224C2—21no—
225C2—21no—
226C2—81no—
227C2—22161no—
228C2#3180013711yescharacteristic
229C2#3180018611yescharacteristic
230C2#3180019311yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#327×C277C2
socleC22×C277#120
prime radical#31800579C2
hypercenter#327D277
hypocenterC277#1610
LCSG ▷ C22×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #31800316C2semidirect
3. #31800313C2semidirect
4. #31799934C2semidirect
5. #31799735C2semidirect
6. #31799727C2semidirect
7. #327×C277C2semidirect
115. C277#1610semidirect
122. #327D277semidirect

Maximal subgroups

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

subgroupindex
#318005792
#318003162
#318003132
#317999342
#317997352
#317997272
#327×C2772
#1610277