Finite Group Databasebeta

← #47982236

Subgroups — #47982236

Order 35456.

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

normal subgroups only

This group has 236 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, complemented
2#31800199C211yesmaximal, characteristic, complemented
3#31800194C211yesmaximal, characteristic
4#31799751C211yesmaximal, characteristic, complemented
5#31799734C211yesmaximal, characteristic, complemented
6#31799731C211yesmaximal, characteristic, complemented
7#492×C277C211yesmaximal, characteristic, complemented
8C2×#17984551—21no—
9C2×#17984548—21no—
10#22579871—21no—
11#22579860—21no—
12#22579856—22no—
13C4×Dic554C2211yescharacteristic
14C4×D1108C2211yescharacteristic
15#22579842—21no—
16C4⋊C4×D277—21no—
17C4⋊#14555660C2211yescharacteristic
18C4⋊#14555660C2211yescharacteristic
19#22579801—21no—
20#22579801—21no—
21C2×SD16×C277—22no—
22C4⋊Q8×C277C2211yescharacteristic
23#127×C277C2211yescharacteristic
24C4×C8×C277C2211yescharacteristic
25C2×Dic554D411yescharacteristic
26C2×D1108D411yescharacteristic
27C2×C4×D277—22no—
28C2×C4×D277—21no—
29#17984551—42no—
30#17984548—42no—
31C2×#14555660—21no—
32C2×#14555660—21no—
33C4⋊Dic277—22no—
34C4⋊Dic277D411yescharacteristic
35C4⋊Dic277D411yescharacteristic
36#17984542—22no—
37#17984542—21no—
38#17984540—22no—
39#17984540—21no—
40C4×Dic277—21no—
41C2×Q8×C277D412yes—
42C2×D4×C277—21no—
43C2×D4×C277—21no—
44C2×D4×C277—21no—
45SD16×C277—44no—
46C2×C8×C277—21no—
47C4⋊C4×C277—21no—
48C4⋊C4×C277—21no—
49C42×C277C2311yescharacteristic
50C22×D277—21no—
51Dic554—21no—
52Dic554—21no—
53D1108—21no—
54D1108SD1612yescomplemented
55C2×Dic277—21no—
56C2×Dic277—21no—
57C2×Dic277—21no—
58C4×D277—41no—
59C4×D277—41no—
60C4×D277—82no—
61#14555660—41no—
62#14555660—41no—
63C23×C277—41no—
64Q8×C277—42no—
65D4×C277—42no—
66D4×C277—41no—
67D4×C277—41no—
68D4×C277—41no—
69D4×C277—41no—
70C2×C4×C277—22no—
71C2×C4×C277C2×D411yescharacteristic
72C2×C4×C277C2×D411yescharacteristic
73C2×C4×C277C2×D411yescharacteristic
74C8×C277—22no—
75C22×C277—81no—
76C22×C277—81no—
77C22×C277—81no—
78C22×C277#12011yescharacteristic
79C2×D277—22no—
80C2×D277—41no—
81C2×D277—41no—
82C4×C277—21no—
83C4×C277—42no—
84C4×C277C2×SD1611yescharacteristic
85C4×C277#13511yescharacteristic
86C4×C277AGL(1,ℤ/8)11yescharacteristic
87C4×C277#13711yescharacteristic
88Dic277—41no—
89Dic277—41no—
90Dic277—41no—
91C2×C277—161no—
92C2×C277#44811yescharacteristic
93C2×C277#44911yescharacteristic
94C2×C277#45311yescharacteristic
95D277—42no—
96C277#162211yescharacteristic, complemented, Sylow
97#1622—2771nomaximal, Sylow
98#554—2771no—
99#492D27711yescharacteristic, complemented
100#460—2771no—
101#459—2771no—
102#333—2771no—
103Q8⋊C8—2771no—
104D4⋊C8—2771no—
105C2×SD16—22no—
106C2×SD16—5541no—
107C2×D8—5541no—
108C4⋊Q8C2×D27711yescharacteristic
109#127C2×D27711yescharacteristic
110#125—5541no—
111C22⋊Q8—5541no—
112C22⋊Q8—5542no—
113C4×Q8—2771no—
114C4×D4—2771no—
115C4×D4—5541no—
116C2×C4⋊C4—5541no—
117C4⋊C8—2771no—
118C4⋊C8—2771no—
119#102—5541no—
120#102—5541no—
121C4×C8C2×D27711yescharacteristic
122C2×Q8—2771no—
123C2×Q8C22⋊D27712yes—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—2771no—
128C22×C4—5542no—
129C22×C4—5541no—
130SD16—44no—
131SD16—11082no—
132D8—11082no—
133C2×C8—21no—
134C2×C8—5541no—
135C2×C8—5541no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—2771no—
139C4⋊C4—2771no—
140C4⋊C4—5542no—
141C4⋊C4—5542no—
142C4⋊C4—5541no—
143C22⋊C4—5542no—
144C22⋊C4—5541no—
145C42—5541no—
146C42C22×D27711yescharacteristic
147C23—41no—
148C23—5541no—
149Q8—42no—
150Q8—5541no—
151Q8—5541no—
152D4—42no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—2772no—
158D4—5541no—
159C2×C4—22no—
160C2×C4—5541no—
161C2×C4—5541no—
162C2×C4—5541no—
163C2×C4—11081no—
164C2×C4—11081no—
165C2×C4—22162no—
166C2×C4D4×D27711yescharacteristic
167C2×C4D4×D27711yescharacteristic
168C2×C4C2×C22⋊D27711yescharacteristic
169C8—22no—
170C8—11081no—
171C8—11081no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—5542no—
176C22—11081no—
177C22—11081no—
178C22#2257984811yescharacteristic
179C4—21no—
180C4—42no—
181C4—11081no—
182C4—11081no—
183C4—11081no—
184C4SD16×D27711yescharacteristic
185C4#2257990111yescharacteristic
186C4#2257990711yescharacteristic
187C4#2257990911yescharacteristic
188C2—161no—
189C2—11082no—
190C2#3180013911yescharacteristic
191C2#3180014611yescharacteristic
192C2#3180016911yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#492×C277C2
socleC22×C277#120
prime radical#31800194C2
hypercenter#492D277
hypocenterC277#1622
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #31800713C2semidirect
2. #31800199C2semidirect
4. #31799751C2semidirect
5. #31799734C2semidirect
6. #31799731C2semidirect
7. #492×C277C2semidirect
54. D1108SD16semidirect
96. C277#1622semidirect
99. #492D277semidirect

Maximal subgroups

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

subgroupindex
#318007132
#318001992
#318001942
#317997512
#317997342
#317997312
#492×C2772
#1622277