Finite Group Databasebeta

← #47984861

Subgroups — #47984861

Order 35456.

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

normal subgroups only

This group has 230 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#31800573C211yesmaximal, characteristic
2#31799986C211yesmaximal, characteristic
3#31799800C214yesmaximal, complemented
4#413×C277C211yesmaximal, characteristic
5C22×Dic554C411yescharacteristic
6C2×#17984547—21no—
7#22579878C2212yes—
8#22579867C412yes—
9#22579861—21no—
10#22579861—21no—
11#22579859—21no—
12#22579859—21no—
13#22579839C411yescharacteristic
14#22579799C2212yes—
15#22579797—21no—
16C2×#41×C277C2211yescharacteristic
17C2×M16×C277—21no—
18#101×C277C2212yes—
19#100×C277—21no—
20C2×Dic554—21no—
21C2×Dic554—41no—
22C2×Dic554—41no—
23C2×Dic554C2×C412yes—
24C22×Dic277—21no—
25#17984547—22no—
26#17984547—41no—
27C2×#14555660—41no—
28C4⋊Dic277—21no—
29#17984542—22no—
30#17984542—22no—
31C22⋊Dic277—21no—
32C22⋊Dic277—22no—
33C22⋊Dic277—22no—
34C4×Dic277C2×C412yes—
35#41×C277—41no—
36#41×C277—41no—
37C2×Q8×C277C2311yescharacteristic
38C2×D4×C277C2×C411yescharacteristic
39C2×D4×C277D411yescharacteristic
40C2×D4×C277D411yescharacteristic
41C22×C4×C277C2×C411yescharacteristic
42C22×C4×C277D411yescharacteristic
43C22×C4×C277D411yescharacteristic
44M16×C277—22no—
45M16×C277—41no—
46C2×C8×C277—41no—
47Dic554—41no—
48Dic554—41no—
49Dic554—42no—
50C2×Dic277—22no—
51C2×Dic277—22no—
52C2×Dic277—42no—
53#14555660—42no—
54C23×C277C22⋊C411yescharacteristic
55C23×C277C22⋊C411yescharacteristic
56C23×C277C22⋊C411yescharacteristic
57Q8×C277—41no—
58D4×C277—41no—
59D4×C277—41no—
60D4×C277—41no—
61C2×C4×C277—21no—
62C2×C4×C277—21no—
63C2×C4×C277—21no—
64C2×C4×C277—21no—
65C2×C4×C277—21no—
66C2×C4×C277—21no—
67C2×C4×C277C22⋊C411yescharacteristic
68C2×C4×C277C22×C411yescharacteristic
69C2×C4×C277C2×D411yescharacteristic
70C2×C4×C277C2×D411yescharacteristic
71C8×C277—42no—
72C22×C277—21no—
73C22×C277—21no—
74C22×C277—21no—
75C22×C277—41no—
76C22×C277—41no—
77C22×C277—41no—
78C22×C277C2×C22⋊C411yescharacteristic
79C4×C277—21no—
80C4×C277—21no—
81C4×C277—21no—
82C4×C277#9911yescharacteristic
83C4×C277#9911yescharacteristic
84Dic277—42no—
85Dic277—42no—
86C2×C277—21no—
87C2×C277—41no—
88C2×C277—41no—
89C2×C277—41no—
90C2×C277C2×#9911yescharacteristic
91C277#213511yescharacteristic, complemented, Sylow
92#2135—2771nomaximal, Sylow
93#536—2771no—
94#413—2771no—
95#413D27711yescharacteristic
96#356—2774no—
97C2×#41C2×D27711yescharacteristic
98C22×Q8—2771no—
99C2×M16—21no—
100C2×M16—5541no—
101C4⋊Q8—2772no—
102#124—2772no—
103#123—5541no—
104#123—5541no—
105C22⋊Q8—5541no—
106C22⋊Q8—5541no—
107#117—2771no—
108#101—2772no—
109#101C2×D27712yes—
110#100—21no—
111#100—5541no—
112#41—41no—
113#41—41no—
114C2×Q8—2772no—
115C2×Q8—5541no—
116C2×Q8—11081no—
117C2×Q8—11081no—
118C2×Q8C22×D27711yescharacteristic
119C2×D4C4×D27711yescharacteristic
120C2×D4C22⋊D27711yescharacteristic
121C2×D4D110811yescharacteristic
122C22×C4—5541no—
123C22×C4C4×D27711yescharacteristic
124C22×C4C22⋊D27711yescharacteristic
125C22×C4D110811yescharacteristic
126M16—22no—
127M16—41no—
128M16—5542no—
129M16—11081no—
130C2×C8—41no—
131C2×C8—11081no—
132C4⋊C4—5541no—
133C4⋊C4—5542no—
134C4⋊C4—5542no—
135C22⋊C4—5541no—
136C22⋊C4—5542no—
137C22⋊C4—5542no—
138C42—2772no—
139C23#1798454011yescharacteristic
140C23#1798454011yescharacteristic
141C23#1798454011yescharacteristic
142Q8—41no—
143Q8—11082no—
144Q8—11081no—
145Q8—11081no—
146D4—41no—
147D4—41no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—5542no—
156C2×C4—5542no—
157C2×C4—11082no—
158C2×C4#1798454011yescharacteristic
159C2×C4C2×C4×D27711yescharacteristic
160C2×C4C2×C22⋊D27711yescharacteristic
161C2×C4C2×D110811yescharacteristic
162C8—42no—
163C8—11082no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22C2×#1798454011yescharacteristic
171C4—21no—
172C4—21no—
173C4—21no—
174C4—11082no—
175C4—11082no—
176C4#2257979411yescharacteristic
177C4#2257979411yescharacteristic
178C2—21no—
179C2—41no—
180C2—41no—
181C2—41no—
182C2C2×#2257979411yescharacteristic
subgroupG/H
centerC2C2×#22579794
commutatorC2×C4×C277C22×C4
FrattiniC2×Q8C22×D277
Fitting#413×C277C2
socleC2×C277C2×#99
prime radicalC2×#41×C277C22
cosocleC2×Q8×C277C23
hypercenter#413D277
hypocenterC277#2135
LCSG ▷ C2×C4×C277 ▷ C22×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #31799800C2semidirect
91. C277#2135semidirect

Maximal subgroups

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

subgroupindex
#318005732
#317999862
#317998002
#413×C2772
#2135277