Finite Group Databasebeta

← #47982492

Subgroups — #47982492

Order 35456.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#31800746C211yesmaximal, characteristic
2#31800371C211yesmaximal, characteristic, complemented
3#31800362C211yesmaximal, characteristic, complemented
4#31800361C211yesmaximal, characteristic, complemented
5#31799743C211yesmaximal, characteristic, complemented
6#31799741C211yesmaximal, characteristic, complemented
7#329×C277C211yesmaximal, characteristic, complemented
8#22579880C2211yescharacteristic
9#22579872C2211yescharacteristic
10#22579868C2211yescharacteristic
11#22579864—21no—
12#22579862—21no—
13#22579857—21no—
14#22579856—21no—
15#22579853—21no—
16#22579852—21no—
17#22579805—21no—
18#22579805—21no—
19#22579805—21no—
20#22579804—21no—
21#22579802—21no—
22#22579801—21no—
23#22579791C2211yescharacteristic
24#124×C277C2211yescharacteristic
25#97×C277C2211yescharacteristic
26#97×C277C2211yescharacteristic
27C2×Dic554—21no—
28C2×Dic554D411yescharacteristic
29C2×D1108D411yescharacteristic
30C2×C22⋊D277—21no—
31C2×C22⋊D277—21no—
32C22×Dic277—21no—
33C2×C4×D277—21no—
34C2×#14555660—21no—
35C4⋊Dic277—21no—
36C4⋊Dic277—21no—
37C4⋊Dic277—21no—
38C4⋊Dic277D411yescharacteristic
39C4⋊Dic277D411yescharacteristic
40#17984542—21no—
41#17984542—21no—
42#17984542—21no—
43C22⋊Dic277—21no—
44#17984540—21no—
45#17984540—21no—
46#17984540—21no—
47C2×Q8×C277D411yescharacteristic
48C2×D4×C277D411yescharacteristic
49C2×C8×C277—21no—
50C2×C8×C277—21no—
51C22⋊C4×C277—21no—
52C22⋊C4×C277—21no—
53C42×C277C2311yescharacteristic
54C22×D277—21no—
55Dic554—41no—
56Dic554—42no—
57D1108—41no—
58C22⋊D277—81no—
59C22⋊D277—81no—
60C2×Dic277—21no—
61C2×Dic277—21no—
62C2×Dic277—21no—
63C2×Dic277—41no—
64C2×Dic277—81no—
65C4×D277—81no—
66#14555660—41no—
67C23×C277—21no—
68Q8×C277—41no—
69D4×C277—41no—
70C2×C4×C277—21no—
71C2×C4×C277C2×D411yescharacteristic
72C2×C4×C277C2×D411yescharacteristic
73C2×C4×C277C2×D411yescharacteristic
74C8×C277—41no—
75C8×C277—41no—
76C22×C277—41no—
77C22×C277—41no—
78C22×C277—41no—
79C22×C277#12011yescharacteristic
80C2×D277—41no—
81C2×D277—41no—
82C2×D277—41no—
83C4×C277—21no—
84C4×C277—21no—
85C4×C277—21no—
86C4×C277—41no—
87Dic277—41no—
88Dic277—41no—
89Dic277—41no—
90Dic277—81no—
91C2×C277—81no—
92C2×C277#45411yescharacteristic
93C2×C277#45511yescharacteristic
94C2×C277#45511yescharacteristic
95D277—81no—
96C277#166211yescharacteristic, complemented, Sylow
97#1662—2771nomaximal, Sylow
98#562—2771no—
99#491—2771no—
100#489—2771no—
101#489—2771no—
102#330—2771no—
103#329—2771no—
104#329D27711yescharacteristic, complemented
105C4⋊Q8—2771no—
106#125—2771no—
107#124—2771no—
108#124C2×D27711yescharacteristic
109#123—5541no—
110#123—5541no—
111C22⋊Q8—5541no—
112C22⋊Q8—5541no—
113#121—5541no—
114#121—5541no—
115#103—5541no—
116#103—5541no—
117#103—5541no—
118#103—5541no—
119#102—5541no—
120#102—5541no—
121#97—2771no—
122#97C2×D27711yescharacteristic
123#97C2×D27711yescharacteristic
124C2×Q8—2771no—
125C2×Q8—5541no—
126C2×Q8D110811yescharacteristic
127C2×D4—2771no—
128C2×D4—5541no—
129C2×D4—5541no—
130C2×D4D110811yescharacteristic
131C22×C4—5541no—
132C22×C4—5541no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—5541no—
136C4⋊C4—2771no—
137C4⋊C4—2771no—
138C4⋊C4—5541no—
139C4⋊C4—5541no—
140C4⋊C4—5541no—
141C4⋊C4—5541no—
142C4⋊C4—5541no—
143C4⋊C4—5541no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—5541no—
147C22⋊C4—5541no—
148C22⋊C4—5541no—
149C22⋊C4—5541no—
150C42C22×D27711yescharacteristic
151C23—21no—
152C23—5541no—
153Q8—41no—
154Q8—11081no—
155Q8—11082no—
156D4—41no—
157D4—11081no—
158D4—22161no—
159D4—22161no—
160C2×C4—21no—
161C2×C4—5541no—
162C2×C4—5541no—
163C2×C4—5541no—
164C2×C4—11081no—
165C2×C4—22161no—
166C2×C4—22161no—
167C2×C4D4×D27711yescharacteristic
168C2×C4D4×D27711yescharacteristic
169C2×C4C2×D110811yescharacteristic
170C8—41no—
171C8—41no—
172C8—11081no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—11081no—
177C22—11081no—
178C22—11081no—
179C22#2257985011yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—11081no—
185C4—11081no—
186C4—11081no—
187C4—22161no—
188C2—81no—
189C2—22161no—
190C2#3180017611yescharacteristic
191C2#3180018111yescharacteristic
192C2#3180018211yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#329×C277C2
socleC22×C277#120
prime radical#31800746C2
hypercenter#329D277
hypocenterC277#1662
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31800371C2semidirect
3. #31800362C2semidirect
4. #31800361C2semidirect
5. #31799743C2semidirect
6. #31799741C2semidirect
7. #329×C277C2semidirect
96. C277#1662semidirect
104. #329D277semidirect

Maximal subgroups

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

subgroupindex
#318007462
#318003712
#318003622
#318003612
#317997432
#317997412
#329×C2772
#1662277