Finite Group Databasebeta

← #47984332

Subgroups — #47984332

Order 35456.

466 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 67 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#31800628C211yesmaximal, characteristic, complemented
2#31799857C212yesmaximal
3#31799857C211yesmaximal, characteristic
4#31799768C212yesmaximal, complemented
5#342×C277C211yesmaximal, characteristic, complemented
6C24×D277C2211yescharacteristic
7#22579859—22no—
8#22579857—24no—
9C2×C22⋊Dic277C2211yescharacteristic
10C2×C22⋊Dic277C2212yes—
11C2×#17984540—24no—
12C2×#17984540—22no—
13C2×C22⋊C4×C277C2212yes—
14C2×C22⋊C4×C277C2211yescharacteristic
15C23×D277—22no—
16C23×D277—21no—
17C23×D277—21no—
18C23×D277—22no—
19C23×D277—44no—
20C23×D277Q812yescomplemented
21C2×Dic554—22no—
22C22×Dic277—21no—
23C22×Dic277D414yes—
24C4⋊Dic277—22no—
25#17984542—24no—
26C22⋊Dic277—22no—
27C22⋊Dic277—22no—
28C22⋊Dic277—22no—
29#17984540—44no—
30#17984540—48no—
31C24×C277C2311yescharacteristic
32C22×C4×C277—22no—
33C22×C4×C277D412yes—
34C22⋊C4×C277—22no—
35C22⋊C4×C277—22no—
36C22⋊C4×C277—22no—
37C22×D277—28no—
38C22×D277—24no—
39C22×D277—24no—
40C22×D277—22no—
41C22×D277—44no—
42C22×D277—44no—
43C22×D277—48no—
44C22×D277—44no—
45C22×D277—42no—
46C22×D277—41no—
47C22×D277—42no—
48C22×D277—41no—
49Dic554—82no—
50C2×Dic277—24no—
51C2×Dic277—44no—
52C2×Dic277—42no—
53C2×Dic277—41no—
54C23×C277—42no—
55C23×C277C2×D412yes—
56C23×C277C2×D411yescharacteristic
57C23×C277C2×Q811yescharacteristic
58C23×C277#4111yescharacteristic
59C23×C277#4112yes—
60C2×C4×C277—22no—
61C2×C4×C277—42no—
62C2×C4×C277—44no—
63C2×C4×C277—42no—
64C22×C277—24no—
65C22×C277—22no—
66C22×C277—41no—
67C22×C277—41no—
68C22×C277—42no—
69C22×C277#12011yescharacteristic
70C22×C277C22⋊Q812yes—
71C22×C277C22⋊Q811yescharacteristic
72C22×C277#12412yes—
73C22×C277#12411yescharacteristic
74C2×D277—28no—
75C2×D277—24no—
76C2×D277—44no—
77C2×D277—48no—
78C2×D277—44no—
79C2×D277—42no—
80C2×D277—42no—
81C2×D277—44no—
82C4×C277—42no—
83C4×C277—82no—
84Dic277—44no—
85Dic277—81no—
86C2×C277—21no—
87C2×C277—22no—
88C2×C277—22no—
89C2×C277—21no—
90C2×C277#39311yescharacteristic
91C2×C277B(4,𝔽2)12yes—
92D277—44no—
93C277#202911yescharacteristic, complemented, Sylow
94#2029—2771nomaximal, Sylow
95#543—2771no—
96#379—2772no—
97#379—2771no—
98#342—2772no—
99#342D27711yescharacteristic, complemented
100C25—2771no—
101C22⋊Q8—5544no—
102C22⋊Q8—5542no—
103C2×C22⋊C4—2772no—
104C2×C22⋊C4—2771no—
105C2×C22⋊C4—5544no—
106C2×C22⋊C4—5542no—
107C2×C22⋊C4C2×D27712yes—
108C2×C22⋊C4C2×D27711yescharacteristic
109C24—2772no—
110C24—5542no—
111C24—5541no—
112C24—5541no—
113C24—5542no—
114C24—11084no—
115C24C22×D27711yescharacteristic
116C2×Q8—5542no—
117C22×C4—22no—
118C22×C4—2774no—
119C22×C4—5541no—
120C22×C4D110812yes—
121C4⋊C4—5544no—
122C4⋊C4—5542no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—5542no—
127C22⋊C4—5542no—
128C22⋊C4—5542no—
129C22⋊C4—11084no—
130C22⋊C4—11088no—
131C23—42no—
132C23—5548no—
133C23—5544no—
134C23—5544no—
135C23—5542no—
136C23—11084no—
137C23—11082no—
138C23—11084no—
139C23—11084no—
140C23—11088no—
141C23—11081no—
142C23—11082no—
143C23—11081no—
144C23D4×D27712yes—
145C23C2×D110811yescharacteristic
146C23Q8×D27711yescharacteristic
147C23#1798456211yescharacteristic
148C23#1798456312yes—
149Q8—22162no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—42no—
154C2×C4—5544no—
155C2×C4—11084no—
156C2×C4—11082no—
157C2×C4—11081no—
158C22—24no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22—42no—
163C22—5548no—
164C22—5544no—
165C22—11088no—
166C22—11084no—
167C22—11084no—
168C22—11082no—
169C22—11082no—
170C22—11084no—
171C22#2257985011yescharacteristic
172C22#2257985812yes—
173C22#2257986011yescharacteristic
174C22#2257986612yes—
175C22#2257986811yescharacteristic
176C4—42no—
177C4—82no—
178C4—11084no—
179C4—22161no—
180C2—22no—
181C2—21no—
182C2—22no—
183C2—21no—
184C2—11084no—
185C2#3179991511yescharacteristic
186C2#3180019012yes—
subgroupG/H
centerC22#22579850
commutator, cosocleC24×C277C23
FrattiniC24C22×D277
Fitting#342×C277C2
socleC22×C277#120
prime radicalC24×D277C22
hypercenter#342D277
hypocenterC277#2029
LCSG ▷ C24×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #31800628C2semidirect
4. #31799768C2semidirect
5. #342×C277C2semidirect
20. C23×D277Q8semidirect
93. C277#2029semidirect
99. #342D277semidirect

Maximal subgroups

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

subgroupindex
#318006282
#317998572
#317997682
#342×C2772
#2029277