Finite Group Databasebeta

← #47982302

Subgroups — #47982302

Order 35456.

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

normal subgroups only

This group has 214 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#31800713C211yesmaximal, characteristic
2#31800381C211yesmaximal, characteristic, complemented
3#31800298C211yesmaximal, characteristic, complemented
4#31800293C211yesmaximal, characteristic
5#31799732C211yesmaximal, characteristic, complemented
6#31799729C211yesmaximal, characteristic
7#333×C277C211yesmaximal, characteristic, complemented
8C2×#17984553—22no—
9#22579880C2211yescharacteristic
10#22579871—21no—
11#22579860—21no—
12#22579856—22no—
13C4×Dic554C2211yescharacteristic
14C4×D1108C2211yescharacteristic
15#22579842—21no—
16C4⋊C4×D277—21no—
17#22579814—21no—
18#22579812—21no—
19#22579805—21no—
20#22579802—21no—
21C4×#14555660C2211yescharacteristic
22C4⋊Q8×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4⋊C8×C277C2211yescharacteristic
25C2×Dic554—21no—
26C2×Dic554D411yescharacteristic
27C2×D1108D411yescharacteristic
28C2×C4×D277—22no—
29C2×C4×D277—21no—
30#17984553—44no—
31C2×#14555660—21no—
32C4⋊Dic277—22no—
33C4⋊Dic277—21no—
34C4⋊Dic277—21no—
35C4⋊Dic277D411yescharacteristic
36C4⋊Dic277D411yescharacteristic
37#17984542—22no—
38#17984542—21no—
39#17984540—22no—
40#17984540—21no—
41C4×Dic277—21no—
42C2×Q8×C277D412yes—
43C2×C8×C277—21no—
44C2×C8×C277—21no—
45C4⋊C4×C277—21no—
46C4⋊C4×C277—21no—
47C42×C277C2311yescharacteristic
48C22×D277—21no—
49Dic554—21no—
50Dic554—21no—
51Dic554—42no—
52D1108—21no—
53D1108Q1612yescomplemented
54C2×Dic277—21no—
55C2×Dic277—21no—
56C2×Dic277—21no—
57C2×Dic277—41no—
58C4×D277—41no—
59C4×D277—41no—
60C4×D277—82no—
61#14555660—22no—
62Q8×C277—42no—
63C2×C4×C277—22no—
64C2×C4×C277C2×D411yescharacteristic
65C2×C4×C277C2×D411yescharacteristic
66C2×C4×C277C2×D411yescharacteristic
67C8×C277—41no—
68C8×C277—41no—
69C22×C277#12011yescharacteristic
70C2×D277—22no—
71C2×D277—41no—
72C2×D277—41no—
73C4×C277—21no—
74C4×C277—42no—
75C4×C277C2×Q1611yescharacteristic
76C4×C277#13511yescharacteristic
77C4×C277#13711yescharacteristic
78C4×C277#13711yescharacteristic
79Dic277—41no—
80Dic277—41no—
81Dic277—41no—
82Dic277—81no—
83C2×C277#45111yescharacteristic
84C2×C277#45211yescharacteristic
85C2×C277#45311yescharacteristic
86D277—42no—
87C277#163211yescharacteristic, complemented, Sylow
88#1632—2771nomaximal, Sylow
89#554—2771no—
90#494—2771no—
91#477—2771no—
92#476—2771no—
93#333D27711yescharacteristic, complemented
94Q8⋊C8—2771no—
95D4⋊C8—2771no—
96C2×Q16—5542no—
97C4⋊Q8—2771no—
98C4⋊Q8C2×D27711yescharacteristic
99#125—5541no—
100C22⋊Q8—5541no—
101C22⋊Q8—5542no—
102C4×Q8—2771no—
103C4×D4—2771no—
104C4×D4—5541no—
105C2×C4⋊C4—5541no—
106#107—5541no—
107#106—5541no—
108C4⋊C8C2×D27711yescharacteristic
109C4⋊C8C2×D27711yescharacteristic
110#103—5541no—
111#102—5541no—
112C4×C8—2771no—
113C2×Q8—2771no—
114C2×Q8—5541no—
115C2×Q8D110812yes—
116C2×D4—2771no—
117C22×C4—5542no—
118C22×C4—5541no—
119Q16—11084no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—5541no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—2771no—
126C4⋊C4—2771no—
127C4⋊C4—5542no—
128C4⋊C4—5542no—
129C4⋊C4—5541no—
130C4⋊C4—5541no—
131C4⋊C4—5541no—
132C22⋊C4—5542no—
133C22⋊C4—5541no—
134C42—5541no—
135C42C22×D27711yescharacteristic
136C23—5541no—
137Q8—42no—
138Q8—5541no—
139Q8—5541no—
140Q8—11082no—
141D4—2772no—
142D4—5541no—
143C2×C4—22no—
144C2×C4—5541no—
145C2×C4—5541no—
146C2×C4—5541no—
147C2×C4—11081no—
148C2×C4—11081no—
149C2×C4—11081no—
150C2×C4—22162no—
151C2×C4D4×D27711yescharacteristic
152C2×C4D4×D27711yescharacteristic
153C2×C4C2×D110811yescharacteristic
154C8—41no—
155C8—41no—
156C8—5542no—
157C22—5542no—
158C22—11081no—
159C22—11081no—
160C22#2257985011yescharacteristic
161C4—21no—
162C4—42no—
163C4—11081no—
164C4—11081no—
165C4—11081no—
166C4—22161no—
167C4Q16×D27711yescharacteristic
168C4#2257990111yescharacteristic
169C4#2257990911yescharacteristic
170C4#2257991211yescharacteristic
171C2—11082no—
172C2#3180015911yescharacteristic
173C2#3180016711yescharacteristic
174C2#3180017211yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#333×C277C2
socleC22×C277#120
prime radicalC2×D1108D4
hypercenter#333D277
hypocenterC277#1632
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #31800381C2semidirect
3. #31800298C2semidirect
5. #31799732C2semidirect
7. #333×C277C2semidirect
53. D1108Q16semidirect
87. C277#1632semidirect
93. #333D277semidirect

Maximal subgroups

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

subgroupindex
#318007132
#318003812
#318002982
#318002932
#317997322
#317997292
#333×C2772
#1632277