Finite Group Databasebeta

← #47982295

Subgroups — #47982295

Order 35456.

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

normal subgroups only

This group has 256 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#31800672C211yesmaximal, characteristic
2#31800374C211yesmaximal, characteristic, complemented
3#31800298C211yesmaximal, characteristic, complemented
4#31800293C211yesmaximal, characteristic, complemented
5#31799732C211yesmaximal, characteristic, complemented
6#31799729C211yesmaximal, characteristic, complemented
7#331×C277C211yesmaximal, characteristic, complemented
8C2×#17984562—21no—
9C2×#17984551—22no—
10#22579880C2211yescharacteristic
11#22579876—21no—
12#22579852—22no—
13#22579851—21no—
14C4×Dic554C2211yescharacteristic
15C4×D1108C2211yescharacteristic
16D4×Dic277—21no—
17#22579814—21no—
18#22579812—21no—
19#22579805—21no—
20#22579802—21no—
21C4×#14555660C2211yescharacteristic
22#127×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4⋊C8×C277C2211yescharacteristic
25#17984562—42no—
26#17984562—42no—
27C2×Dic554—21no—
28C2×Dic554D411yescharacteristic
29C2×D1108D411yescharacteristic
30C2×C22⋊D277—22no—
31C2×C22⋊D277—22no—
32C22×Dic277—22no—
33C2×C4×D277—21no—
34#17984551—44no—
35C2×#14555660—21no—
36C4⋊Dic277—21no—
37C4⋊Dic277—21no—
38C4⋊Dic277D411yescharacteristic
39C4⋊Dic277D411yescharacteristic
40#17984542—21no—
41C22⋊Dic277—22no—
42#17984540—21no—
43C4×Dic277—21no—
44C2×D4×C277—21no—
45C2×D4×C277—21no—
46C2×D4×C277D412yes—
47C2×C8×C277—21no—
48C2×C8×C277—21no—
49C42×C277C2311yescharacteristic
50C22×D277—21no—
51Dic554—21no—
52Dic554—42no—
53Dic554SD1612yescomplemented
54D1108—21no—
55D1108—21no—
56C22⋊D277—44no—
57C22⋊D277—82no—
58C2×Dic277—21no—
59C2×Dic277—21no—
60C2×Dic277—21no—
61C2×Dic277—44no—
62C2×Dic277—41no—
63C4×D277—41no—
64C4×D277—41no—
65#14555660—22no—
66C23×C277—22no—
67D4×C277—42no—
68D4×C277—41no—
69D4×C277—41no—
70D4×C277—41no—
71D4×C277—41no—
72C2×C4×C277C2×D411yescharacteristic
73C2×C4×C277C2×D411yescharacteristic
74C2×C4×C277C2×D411yescharacteristic
75C8×C277—41no—
76C8×C277—41no—
77C22×C277—42no—
78C22×C277—42no—
79C22×C277—42no—
80C22×C277#12011yescharacteristic
81C2×D277—41no—
82C2×D277—41no—
83C2×D277—41no—
84C4×C277—21no—
85C4×C277C2×SD1611yescharacteristic
86C4×C277#13511yescharacteristic
87C4×C277AGL(1,ℤ/8)11yescharacteristic
88C4×C277#13711yescharacteristic
89Dic277—22no—
90Dic277—41no—
91Dic277—41no—
92Dic277—81no—
93C2×C277—82no—
94C2×C277#45011yescharacteristic
95C2×C277#45211yescharacteristic
96C2×C277#45311yescharacteristic
97D277—81no—
98C277#163111yescharacteristic, complemented, Sylow
99#1631—2771nomaximal, Sylow
100#550—2771no—
101#492—2771no—
102#477—2771no—
103#476—2771no—
104#331D27711yescharacteristic, complemented
105Q8⋊C8—2771no—
106D4⋊C8—2771no—
107C2×#41—5541no—
108C2×SD16—5542no—
109C4⋊Q8—2771no—
110#127—5541no—
111#127C2×D27711yescharacteristic
112#121—5541no—
113#121—5542no—
114C4×Q8—2771no—
115C4×D4—2771no—
116C4×D4—5541no—
117#107—5541no—
118#106—5541no—
119C4⋊C8C2×D27711yescharacteristic
120C4⋊C8C2×D27711yescharacteristic
121#103—5541no—
122#102—5541no—
123C4×C8—2771no—
124#41—11082no—
125#41—11082no—
126C2×Q8—2771no—
127C2×Q8—5541no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—2771no—
131C2×D4—5542no—
132C2×D4—5542no—
133C2×D4D110812yes—
134C22×C4—5542no—
135C22×C4—5541no—
136SD16—11084no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—5541no—
140C4⋊C4—2771no—
141C4⋊C4—2771no—
142C4⋊C4—5541no—
143C4⋊C4—5541no—
144C4⋊C4—5541no—
145C22⋊C4—5542no—
146C22⋊C4—5541no—
147C42—5541no—
148C42C22×D27711yescharacteristic
149C23—22no—
150C23—5541no—
151Q8—2772no—
152Q8—5541no—
153Q8—11082no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—5541no—
160D4—5541no—
161D4—11084no—
162D4—22162no—
163C2×C4—5541no—
164C2×C4—5541no—
165C2×C4—5541no—
166C2×C4—11084no—
167C2×C4—11081no—
168C2×C4—11081no—
169C2×C4—11081no—
170C2×C4D4×D27711yescharacteristic
171C2×C4D4×D27711yescharacteristic
172C2×C4C2×D110811yescharacteristic
173C8—41no—
174C8—41no—
175C8—5542no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—11081no—
180C22—11081no—
181C22—11081no—
182C22#2257985011yescharacteristic
183C4—21no—
184C4—5542no—
185C4—11081no—
186C4—11081no—
187C4—22161no—
188C4SD16×D27711yescharacteristic
189C4#2257989911yescharacteristic
190C4#2257990411yescharacteristic
191C4#2257990911yescharacteristic
192C2—82no—
193C2—22161no—
194C2#3180015411yescharacteristic
195C2#3180016511yescharacteristic
196C2#3180017211yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#331×C277C2
socleC22×C277#120
prime radical#31800672C2
hypercenter#331D277
hypocenterC277#1631
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #31800374C2semidirect
3. #31800298C2semidirect
4. #31800293C2semidirect
5. #31799732C2semidirect
6. #31799729C2semidirect
7. #331×C277C2semidirect
53. Dic554SD16semidirect
98. C277#1631semidirect
104. #331D277semidirect

Maximal subgroups

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

subgroupindex
#318006722
#318003742
#318002982
#318002932
#317997322
#317997292
#331×C2772
#1631277