Finite Group Databasebeta

← #47982165

Subgroups — #47982165

Order 35456.

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

normal subgroups only

This group has 216 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#31800597C211yesmaximal, characteristic
2#31800333C211yesmaximal, characteristic, complemented
3#31800313C211yesmaximal, characteristic
4#31799934C211yesmaximal, characteristic, complemented
5#31799738C211yesmaximal, characteristic, complemented
6#31799727C211yesmaximal, characteristic, complemented
7#327×C277C211yesmaximal, characteristic
8#22579873—21no—
9#22579870—21no—
10#22579861—21no—
11#22579861—21no—
12#22579859C2211yescharacteristic
13#22579857—21no—
14D4×Dic277—21no—
15C2×C4⋊Dic277—21no—
16C2×C4⋊Dic277C2211yescharacteristic
17C2×#17984542C2211yescharacteristic
18#22579813—21no—
19#22579812—21no—
20#22579805—21no—
21#22579801—21no—
22C22⋊#14555660C2211yescharacteristic
23#22579787—21no—
24#121×C277C2211yescharacteristic
25C22⋊C8×C277C2211yescharacteristic
26#95×C277C2211yescharacteristic
27C2×Dic554D411yescharacteristic
28C22×Dic277—21no—
29C22×Dic277—21no—
30C22×Dic277D411yescharacteristic
31C22×Dic277D411yescharacteristic
32C2×#14555660—21no—
33C4⋊Dic277—21no—
34C4⋊Dic277—21no—
35C4⋊Dic277—21no—
36C4⋊Dic277—42no—
37C4⋊Dic277D411yescharacteristic
38#17984542—21no—
39#17984542—21no—
40#17984542—21no—
41#17984542—21no—
42#17984542—21no—
43C22⋊Dic277—21no—
44C22⋊Dic277—21no—
45C22⋊Dic277—21no—
46C22⋊Dic277—21no—
47C4×Dic277—21no—
48C2×D4×C277—21no—
49C2×D4×C277D411yescharacteristic
50C22×C4×C277—21no—
51C22×C4×C277C2311yescharacteristic
52C2×C8×C277—21no—
53C4⋊C4×C277D411yescharacteristic
54C22⋊C4×C277—21no—
55Dic554—41no—
56C2×Dic277—21no—
57C2×Dic277—21no—
58C2×Dic277—21no—
59C2×Dic277—21no—
60C2×Dic277—21no—
61C2×Dic277—21no—
62C2×Dic277—41no—
63C2×Dic277—41no—
64C2×Dic277—41no—
65C2×Dic277—41no—
66C2×Dic277—81no—
67#14555660—41no—
68C23×C277—21no—
69C23×C277C2×D411yescharacteristic
70D4×C277—41no—
71D4×C277—41no—
72D4×C277—41no—
73C2×C4×C277—22no—
74C2×C4×C277—21no—
75C2×C4×C277—41no—
76C2×C4×C277—41no—
77C2×C4×C277—41no—
78C2×C4×C277C2×D411yescharacteristic
79C2×C4×C277C2×D411yescharacteristic
80C8×C277—41no—
81C22×C277—21no—
82C22×C277—21no—
83C22×C277—41no—
84C22×C277—41no—
85C22×C277—41no—
86C22×C277#12011yescharacteristic
87C22×C277#13511yescharacteristic
88C22×C277AGL(1,ℤ/8)11yescharacteristic
89C4×C277—21no—
90C4×C277—21no—
91C4×C277—42no—
92C4×C277—41no—
93Dic277—41no—
94Dic277—41no—
95Dic277—41no—
96Dic277—41no—
97Dic277—81no—
98C2×C277—21no—
99C2×C277—21no—
100C2×C277—81no—
101C2×C277#44911yescharacteristic
102C2×C277#45611yescharacteristic
103C2×C277#45811yescharacteristic
104C277#160911yescharacteristic, complemented, Sylow
105#1609—2771nomaximal, Sylow
106#539—2771no—
107#483—2771no—
108#480—2771no—
109#398—2771no—
110#328—2771no—
111#327D27711yescharacteristic
112#324—2771no—
113#126—5541no—
114#125—5541no—
115#123—5541no—
116#123—5541no—
117C22⋊Q8—2771no—
118C22⋊Q8—5541no—
119#121C2×D27711yescharacteristic
120C4×D4—5541no—
121C2×C4⋊C4—2771no—
122C2×C4⋊C4—2771no—
123C2×C4⋊C4—5541no—
124#107—5541no—
125#106—5541no—
126#103—5541no—
127#102—5541no—
128C22⋊C8—2771no—
129C22⋊C8C2×D27711yescharacteristic
130#95—5541no—
131#95C2×D27711yescharacteristic
132C2×Q8—2771no—
133C2×D4—21no—
134C2×D4D110811yescharacteristic
135C22×C4—21no—
136C22×C4—2771no—
137C22×C4—2771no—
138C22×C4—5541no—
139C22×C4—5541no—
140C22×C4C22×D27711yescharacteristic
141C2×C8—21no—
142C2×C8—5541no—
143C4⋊C4—2771no—
144C4⋊C4—5541no—
145C4⋊C4—5541no—
146C4⋊C4—5541no—
147C4⋊C4—5541no—
148C4⋊C4—5541no—
149C4⋊C4—5541no—
150C4⋊C4—5541no—
151C4⋊C4—5541no—
152C4⋊C4—11082no—
153C4⋊C4D110811yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—5541no—
156C22⋊C4—5541no—
157C22⋊C4—5541no—
158C22⋊C4—5541no—
159C42—5541no—
160C23—21no—
161C23D4×D27711yescharacteristic
162Q8—11081no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—5541no—
172C2×C4—5541no—
173C2×C4—5541no—
174C2×C4—5541no—
175C2×C4—5541no—
176C2×C4—5541no—
177C2×C4—11081no—
178C2×C4—11081no—
179C2×C4—11081no—
180C2×C4—11081no—
181C2×C4—22161no—
182C2×C4D4×D27711yescharacteristic
183C2×C4C2×D110811yescharacteristic
184C8—41no—
185C8—11081no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#2257985011yescharacteristic
192C22#2257990111yescharacteristic
193C22#2257990411yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—11081no—
199C4—11081no—
200C4—11081no—
201C4—11081no—
202C4—22161no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#3180014811yescharacteristic
207C2#3180018611yescharacteristic
208C2#3180019311yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#327×C277C2
socleC22×C277#120
prime radical#121×C277C22
hypercenter#327D277
hypocenterC277#1609
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. #31800333C2semidirect
4. #31799934C2semidirect
5. #31799738C2semidirect
6. #31799727C2semidirect
104. C277#1609semidirect

Maximal subgroups

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

subgroupindex
#318005972
#318003332
#318003132
#317999342
#317997382
#317997272
#327×C2772
#1609277