Finite Group Databasebeta

← #47984855

Subgroups — #47984855

Order 35456.

230 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 55 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#31800577C211yesmaximal, characteristic
2#101×D277C212yesmaximal, complemented
3#31799801C211yesmaximal, characteristic, complemented
4#31799798C212yesmaximal, complemented
5#356×C277C211yesmaximal, characteristic, complemented
6C2×#17984564C411yescharacteristic
7C2×Q8×D277C2211yescharacteristic
8M16×D277—22no—
9#22579878C411yescharacteristic
10#22579869C2211yescharacteristic
11#22579868C411yescharacteristic
12#22579865—22no—
13#22579858—22no—
14#22579837C411yescharacteristic
15#22579799C2212yes—
16#22579798—22no—
17C4⋊Q8×C277C2211yescharacteristic
18#101×C277C2212yes—
19#17984564—42no—
20C2×Dic554C2×C411yescharacteristic
21C2×Dic554D412yes—
22Q8×D277—42no—
23C2×D1108—21no—
24C2×D1108C2×C411yescharacteristic
25C2×C4×D277—21no—
26C2×C4×D277C2×C411yescharacteristic
27C2×C4×D277D412yes—
28#17984547—22no—
29#17984546—42no—
30C8×D277—42no—
31#17984542—21no—
32#17984542—22no—
33#17984540—21no—
34#17984540—22no—
35#17984540—22no—
36C4×Dic277C2×C411yescharacteristic
37C2×Q8×C277C2×C411yescharacteristic
38C2×Q8×C277C2311yescharacteristic
39M16×C277—22no—
40C4⋊C4×C277—22no—
41C42×C277C2×C411yescharacteristic
42C22×D277—21no—
43C22×D277C22⋊C411yescharacteristic
44Dic554—41no—
45Dic554—42no—
46D1108—41no—
47D1108—42no—
48C2×Dic277—21no—
49C2×Dic277C22⋊C412yes—
50C2×Dic277C22⋊C411yescharacteristic
51C4×D277—22no—
52C4×D277—22no—
53C4×D277—22no—
54C4×D277—42no—
55#14555660—42no—
56Q8×C277—41no—
57Q8×C277—41no—
58C2×C4×C277—21no—
59C2×C4×C277—21no—
60C2×C4×C277C22×C411yescharacteristic
61C2×C4×C277C2×D412yes—
62C8×C277—42no—
63C22×C277C2×C22⋊C411yescharacteristic
64C2×D277—41no—
65C2×D277—42no—
66C2×D277—41no—
67C2×D277#9912yes—
68C4×C277—22no—
69C4×C277—21no—
70C4×C277—41no—
71C4×C277—41no—
72Dic277—21no—
73Dic277—22no—
74Dic277—41no—
75C2×C277—21no—
76C2×C277C2×#9911yescharacteristic
77D277—22no—
78D277—81no—
79C277#213311yescharacteristic, complemented, Sylow
80#2133—2771nomaximal, Sylow
81#536—2771no—
82C2×#101—2772no—
83#356—2771no—
84#356D27711yescharacteristic, complemented
85#355—2772no—
86C2×#41—2771no—
87C22×Q8—2771no—
88C2×M16—5542no—
89C4⋊Q8—2771no—
90C4⋊Q8C2×D27711yescharacteristic
91#124—2771no—
92#124—2771no—
93#123—5542no—
94C22⋊Q8—5542no—
95#117—2771no—
96#101—2772no—
97#101—5542no—
98#101C2×D27712yes—
99#41—11082no—
100C2×Q8—2771no—
101C2×Q8—2772no—
102C2×Q8—11082no—
103C2×Q8C4×D27711yescharacteristic
104C2×Q8C22×D27711yescharacteristic
105C2×D4—2771no—
106C2×D4—5541no—
107C22×C4—2771no—
108C22×C4—2772no—
109C22×C4—5541no—
110M16—22no—
111M16—5542no—
112M16—11082no—
113C2×C8—11082no—
114C4⋊C4—22no—
115C4⋊C4—5541no—
116C4⋊C4—5542no—
117C22⋊C4—5542no—
118C22⋊C4—5541no—
119C22⋊C4—5542no—
120C42—2771no—
121C42C4×D27711yescharacteristic
122C23—2771no—
123C23—5541no—
124Q8—41no—
125Q8—41no—
126Q8—11082no—
127Q8—11081no—
128D4—11081no—
129D4—11082no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—2772no—
133C2×C4—2771no—
134C2×C4—5542no—
135C2×C4—5542no—
136C2×C4—5542no—
137C2×C4—5541no—
138C2×C4—11082no—
139C2×C4C2×C4×D27711yescharacteristic
140C2×C4D4×D27712yes—
141C8—42no—
142C8—11082no—
143C22—2772no—
144C22—11081no—
145C22—11082no—
146C22—11081no—
147C22C22⋊C4×D27711yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—5541no—
153C4—5542no—
154C4—11081no—
155C2—21no—
156C2—5542no—
157C2—22161no—
158C2#99×D27711yescharacteristic
subgroupG/H
centerC2#99×D277
commutatorC2×C4×C277C22×C4
FrattiniC2×Q8C22×D277
Fitting#356×C277C2
socleC2×C277C2×#99
prime radicalC2×#17984564C4
cosocleC2×Q8×C277C23
hypercenter#356D277
hypocenterC277#2133
LCSG ▷ C2×C4×C277 ▷ C22×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #101×D277C2semidirect
3. #31799801C2semidirect
4. #31799798C2semidirect
5. #356×C277C2semidirect
79. C277#2133semidirect
84. #356D277semidirect

Maximal subgroups

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

subgroupindex
#318005772
#101×D2772
#317998012
#317997982
#356×C2772
#2133277