Finite Group Databasebeta

← #47981800

Subgroups — #47981800

Order 35456.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#31800551C211yesmaximal, characteristic
2#31800057C212yesmaximal, complemented
3#31799742C211yesmaximal, characteristic, complemented
4#31799741C212yesmaximal, complemented
5#329×C277C211yesmaximal, characteristic, complemented
6C2×#17984564C411yescharacteristic
7C2×#17984562C411yescharacteristic
8#22579878C411yescharacteristic
9#22579876C411yescharacteristic
10#22579868C2211yescharacteristic
11#22579853—22no—
12#22579840—22no—
13C42×D277C2211yescharacteristic
14#22579809—22no—
15#22579792—22no—
16#22579791C2212yes—
17#124×C277C2211yescharacteristic
18#97×C277C2212yes—
19#17984564—42no—
20#17984562—42no—
21C2×Dic554C2×C411yescharacteristic
22C2×D1108—21no—
23C2×D1108C2×C411yescharacteristic
24C2×C22⋊D277—21no—
25C2×C22⋊D277—22no—
26C22×Dic277—21no—
27C2×C4×D277—21no—
28C2×C4×D277C2×C411yescharacteristic
29C2×C4×D277D412yes—
30C2×#14555660—22no—
31#17984542—22no—
32#17984540—22no—
33C4×Dic277C2×C411yescharacteristic
34C4×Dic277D412yes—
35C2×Q8×C277C2×C411yescharacteristic
36C2×D4×C277C2×C411yescharacteristic
37C2×C8×C277—22no—
38C22⋊C4×C277—22no—
39C42×C277C2311yescharacteristic
40C22×D277—21no—
41C22×D277C22⋊C411yescharacteristic
42Dic554—41no—
43D1108—41no—
44D1108—42no—
45C22⋊D277—44no—
46C22⋊D277—42no—
47C2×Dic277—21no—
48C2×Dic277—42no—
49C2×Dic277C22⋊C412yes—
50C2×Dic277C22⋊C411yescharacteristic
51C4×D277—22no—
52C4×D277—42no—
53C4×D277—42no—
54#14555660—42no—
55C23×C277—21no—
56Q8×C277—41no—
57D4×C277—41no—
58C2×C4×C277—21no—
59C2×C4×C277C22×C411yescharacteristic
60C2×C4×C277C2×D412yes—
61C8×C277—42no—
62C22×C277—41no—
63C22×C277—42no—
64C22×C277C2×C22⋊C411yescharacteristic
65C2×D277—21no—
66C2×D277—22no—
67C2×D277—41no—
68C2×D277—42no—
69C4×C277—21no—
70C4×C277—22no—
71C4×C277—41no—
72Dic277—22no—
73Dic277—41no—
74Dic277#10012yes—
75C2×C277—81no—
76C2×C277C2×#10011yescharacteristic
77C2×C277#42112yes—
78D277—41no—
79D277—81no—
80C277#153611yescharacteristic, complemented, Sylow
81#1536—2771nomaximal, Sylow
82#532—2771no—
83#432—2772no—
84#329—2771no—
85#329—2772no—
86#329D27711yescharacteristic, complemented
87C2×#41—2771no—
88C2×#41—2771no—
89C4⋊Q8—2771no—
90#127—2771no—
91#124—2771no—
92#124C2×D27711yescharacteristic
93#121—5542no—
94C4×D4—5542no—
95C2×C42—2771no—
96C4⋊C8—5542no—
97C22⋊C8—5542no—
98#97—2772no—
99#97C2×D27712yes—
100#41—11082no—
101#41—11082no—
102C2×Q8—2771no—
103C2×Q8C4×D27711yescharacteristic
104C2×D4—2771no—
105C2×D4—5541no—
106C2×D4—5542no—
107C2×D4—5541no—
108C2×D4C4×D27711yescharacteristic
109C22×C4—2771no—
110C22×C4—2772no—
111C22×C4—5541no—
112C22×C4—5541no—
113C2×C8—22no—
114C2×C8—5542no—
115C4⋊C4—5542no—
116C22⋊C4—22no—
117C22⋊C4—5542no—
118C42—2771no—
119C42—2772no—
120C42C22×D27711yescharacteristic
121C23—21no—
122C23—2771no—
123C23—5541no—
124Q8—41no—
125Q8—11081no—
126D4—41no—
127D4—11081no—
128D4—11082no—
129D4—11084no—
130D4—11082no—
131C2×C4—21no—
132C2×C4—2771no—
133C2×C4—2772no—
134C2×C4—5542no—
135C2×C4—5541no—
136C2×C4—11082no—
137C2×C4—11082no—
138C2×C4—11082no—
139C2×C4C2×C4×D27711yescharacteristic
140C2×C4D4×D27712yes—
141C8—42no—
142C8—11082no—
143C22—41no—
144C22—42no—
145C22—5541no—
146C22—5542no—
147C22—11081no—
148C22—11082no—
149C22C22⋊C4×D27711yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—2772no—
154C4—5542no—
155C4—11081no—
156C2—81no—
157C2—11081no—
158C2—22161no—
159C2#100×D27711yescharacteristic
160C2#3180001712yes—
subgroupG/H
centerC22C22⋊C4×D277
commutatorC2×C4×C277C22×C4
FrattiniC42C22×D277
Fitting#329×C277C2
socleC22×C277C2×C22⋊C4
prime radical#31800551C2
cosocleC42×C277C23
hypercenter#329D277
hypocenterC277#1536
LCSG ▷ C2×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31800057C2semidirect
3. #31799742C2semidirect
4. #31799741C2semidirect
5. #329×C277C2semidirect
80. C277#1536semidirect
86. #329D277semidirect

Maximal subgroups

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

subgroupindex
#318005512
#318000572
#317997422
#317997412
#329×C2772
#1536277