Finite Group Databasebeta

← #47981799

Subgroups — #47981799

Order 35456.

200 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 65 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#31800536C211yesmaximal, characteristic
2#31800059C211yesmaximal, characteristic, complemented
3#31799743C212yesmaximal, complemented
4#31799741C212yesmaximal, complemented
5#432×C277C211yesmaximal, characteristic, complemented
6#22579874—21no—
7#22579872C2211yescharacteristic
8#22579868C2211yescharacteristic
9#22579863—21no—
10#22579859C411yescharacteristic
11#22579854C411yescharacteristic
12C4×Dic554C411yescharacteristic
13C4×D1108C411yescharacteristic
14C4×C22⋊D277—21no—
15#22579837—21no—
16C4⋊#14555660—21no—
17C22⋊#14555660—21no—
18#22579791C2212yes—
19C2×C42×C277C2211yescharacteristic
20C4⋊C8×C277—21no—
21C22⋊C8×C277—21no—
22#97×C277C2212yes—
23C2×Dic554C2×C411yescharacteristic
24C2×D1108C2×C411yescharacteristic
25C2×C22⋊D277—21no—
26C2×C4×D277—21no—
27C2×#14555660—22no—
28C4⋊Dic277C2×C411yescharacteristic
29C4⋊Dic277C2×C411yescharacteristic
30#17984542—21no—
31#17984542—21no—
32#17984542—21no—
33#17984542—21no—
34C22⋊Dic277—21no—
35#17984540—21no—
36#17984540—21no—
37#17984540—21no—
38#17984540—21no—
39C4×Dic277—21no—
40C22×C4×C277C2×C411yescharacteristic
41C22×C4×C277D411yescharacteristic
42C22×C4×C277D411yescharacteristic
43C2×C8×C277—22no—
44C42×C277C2×C411yescharacteristic
45C42×C277D411yescharacteristic
46C42×C277D411yescharacteristic
47C42×C277C2311yescharacteristic
48C22×D277—21no—
49Dic554—41no—
50D1108—41no—
51C22⋊D277—42no—
52C2×Dic277—21no—
53C2×Dic277—21no—
54C2×Dic277—21no—
55C4×D277—42no—
56#14555660—42no—
57C23×C277C22⋊C411yescharacteristic
58C2×C4×C277—41no—
59C2×C4×C277—41no—
60C2×C4×C277—41no—
61C2×C4×C277C22⋊C411yescharacteristic
62C2×C4×C277C22⋊C411yescharacteristic
63C2×C4×C277C22⋊C411yescharacteristic
64C2×C4×C277C22×C411yescharacteristic
65C2×C4×C277C2×D411yescharacteristic
66C2×C4×C277C2×D411yescharacteristic
67C8×C277—42no—
68C22×C277—21no—
69C22×C277—21no—
70C22×C277—21no—
71C22×C277C2×C22⋊C411yescharacteristic
72C2×D277—41no—
73C2×D277—41no—
74C2×D277—41no—
75C4×C277—21no—
76C4×C277—21no—
77C4×C277—21no—
78C4×C277—21no—
79C4×C277—21no—
80C4×C277—21no—
81Dic277—41no—
82Dic277—41no—
83Dic277—41no—
84C2×C277—41no—
85C2×C277#41311yescharacteristic
86C2×C277#42111yescharacteristic
87C2×C277#42111yescharacteristic
88D277—81no—
89C277#153511yescharacteristic, complemented, Sylow
90#1535—2771nomaximal, Sylow
91#529—2771no—
92#432—2771no—
93#432D27711yescharacteristic, complemented
94#330—2772no—
95#329—2772no—
96#126—5541no—
97#125—2771no—
98#124—2771no—
99#123—5541no—
100C22⋊Q8—2771no—
101#121—2771no—
102C4×Q8—2771no—
103C4×D4—2771no—
104C4×D4—5541no—
105#117—5541no—
106C2×C42C2×D27711yescharacteristic
107C4⋊C8—21no—
108C4⋊C8—5541no—
109C22⋊C8—21no—
110C22⋊C8—5541no—
111#97—2772no—
112#97C2×D27712yes—
113C2×Q8—2771no—
114C2×D4—2771no—
115C2×D4—5541no—
116C22×C4—5541no—
117C22×C4C4×D27711yescharacteristic
118C22×C4C22⋊D27711yescharacteristic
119C22×C4D110811yescharacteristic
120C2×C8—22no—
121C2×C8—5542no—
122C4⋊C4—2771no—
123C4⋊C4—2771no—
124C4⋊C4—5541no—
125C4⋊C4—5541no—
126C4⋊C4—5541no—
127C4⋊C4—5541no—
128C22⋊C4—5541no—
129C22⋊C4—5541no—
130C22⋊C4—5541no—
131C22⋊C4—5541no—
132C22⋊C4—5541no—
133C42—5541no—
134C42C4×D27711yescharacteristic
135C42C22⋊D27711yescharacteristic
136C42D110811yescharacteristic
137C42C22×D27711yescharacteristic
138C23—5541no—
139C23#1798454011yescharacteristic
140Q8—11081no—
141D4—11081no—
142D4—11082no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—5541no—
147C2×C4—5541no—
148C2×C4—5541no—
149C2×C4—11082no—
150C2×C4#1798454011yescharacteristic
151C2×C4#1798454011yescharacteristic
152C2×C4#1798454011yescharacteristic
153C2×C4C2×C4×D27711yescharacteristic
154C2×C4C2×C22⋊D27711yescharacteristic
155C2×C4C2×D110811yescharacteristic
156C8—42no—
157C8—11082no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—11081no—
162C22—11081no—
163C22—11081no—
164C22C2×#1798454011yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—11081no—
172C4—11081no—
173C4—11081no—
174C2—41no—
175C2—22161no—
176C2#3179998411yescharacteristic
177C2#3180001811yescharacteristic
178C2#3180002011yescharacteristic
subgroupG/H
centerC22C2×#17984540
commutatorC2×C4×C277C22×C4
FrattiniC42C22×D277
Fitting#432×C277C2
socleC22×C277C2×C22⋊C4
prime radical#22579854C4
cosocleC42×C277C23
hypercenter#432D277
hypocenterC277#1535
LCSG ▷ C2×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #31800059C2semidirect
3. #31799743C2semidirect
4. #31799741C2semidirect
5. #432×C277C2semidirect
89. C277#1535semidirect
93. #432D277semidirect

Maximal subgroups

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

subgroupindex
#318005362
#318000592
#317997432
#317997412
#432×C2772
#1535277