Finite Group Databasebeta

← #47982357

Subgroups — #47982357

Order 35456.

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

normal subgroups only

This group has 250 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#31800279C211yesmaximal, characteristic, complemented
3#31800209C211yesmaximal, characteristic, complemented
4#31799746C211yesmaximal, characteristic, complemented
5#31799734C211yesmaximal, characteristic, complemented
6#31799731C211yesmaximal, characteristic, complemented
7#486×C277C211yesmaximal, characteristic, complemented
8C2×#17984562—21no—
9C2×#17984553—21no—
10#22579876—21no—
11#22579852—22no—
12#22579851—21no—
13C4×Dic554C2211yescharacteristic
14C4×D1108C2211yescharacteristic
15D4×Dic277—21no—
16#22579813—21no—
17C4⋊#14555660C2211yescharacteristic
18C4⋊#14555660C2211yescharacteristic
19#22579804—21no—
20#22579800—21no—
21C4⋊Q8×C277C2211yescharacteristic
22#127×C277C2211yescharacteristic
23#102×C277—22no—
24C4×C8×C277C2211yescharacteristic
25#17984562—42no—
26#17984562—42no—
27C2×Dic554D411yescharacteristic
28C2×D1108D411yescharacteristic
29C2×C22⋊D277—22no—
30C2×C22⋊D277—22no—
31C22×Dic277—22no—
32C2×C4×D277—21no—
33#17984553—42no—
34C2×#14555660—21no—
35C2×#14555660—21no—
36C4⋊Dic277D411yescharacteristic
37C4⋊Dic277D411yescharacteristic
38#17984542—21no—
39C22⋊Dic277—22no—
40#17984540—21no—
41C4×Dic277—21no—
42C2×Q8×C277—21no—
43C2×D4×C277—21no—
44C2×D4×C277—21no—
45C2×D4×C277D412yes—
46C2×C8×C277—21no—
47C4⋊C4×C277—21no—
48C4⋊C4×C277—21no—
49C42×C277C2311yescharacteristic
50C22×D277—21no—
51Dic554—21no—
52Dic554D812yes—
53D1108—21no—
54D1108—21no—
55C22⋊D277—44no—
56C22⋊D277—82no—
57C2×Dic277—21no—
58C2×Dic277—21no—
59C2×Dic277—21no—
60C2×Dic277—44no—
61C4×D277—41no—
62C4×D277—41no—
63#14555660—41no—
64#14555660—41no—
65C23×C277—22no—
66Q8×C277—41no—
67Q8×C277—41no—
68D4×C277—42no—
69D4×C277—41no—
70D4×C277—41no—
71D4×C277—41no—
72D4×C277—41no—
73C2×C4×C277—41no—
74C2×C4×C277C2×D411yescharacteristic
75C2×C4×C277C2×D411yescharacteristic
76C2×C4×C277C2×D411yescharacteristic
77C8×C277—41no—
78C22×C277—42no—
79C22×C277—42no—
80C22×C277—42no—
81C22×C277#12011yescharacteristic
82C2×D277—41no—
83C2×D277—41no—
84C2×D277—41no—
85C4×C277—21no—
86C4×C277—81no—
87C4×C277C2×D811yescharacteristic
88C4×C277#13511yescharacteristic
89C4×C277AGL(1,ℤ/8)11yescharacteristic
90C4×C277#13711yescharacteristic
91Dic277—22no—
92Dic277—41no—
93Dic277—41no—
94C2×C277—82no—
95C2×C277#44711yescharacteristic
96C2×C277#45211yescharacteristic
97C2×C277#45511yescharacteristic
98D277—81no—
99C277#164111yescharacteristic, complemented, Sylow
100#1641—2771nomaximal, Sylow
101#550—2771no—
102#486D27711yescharacteristic, complemented
103#474—2771no—
104#462—2771no—
105#331—2771no—
106Q8⋊C8—2771no—
107D4⋊C8—2771no—
108C2×#41—5541no—
109C2×Q16—5541no—
110C4⋊Q8C2×D27711yescharacteristic
111#127—5541no—
112#127C2×D27711yescharacteristic
113#121—5541no—
114#121—5542no—
115C4×Q8—2771no—
116C4×D4—2771no—
117C4×D4—5541no—
118#107—5541no—
119C4⋊C8—2771no—
120C4⋊C8—2771no—
121#103—5541no—
122#102—22no—
123#102—5541no—
124C4×C8C2×D27711yescharacteristic
125#41—11082no—
126#41—11082no—
127C2×Q8—21no—
128C2×Q8—2771no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—2771no—
132C2×D4—5542no—
133C2×D4—5542no—
134C2×D4C22⋊D27712yes—
135C22×C4—5542no—
136C22×C4—5541no—
137Q16—11082no—
138C2×C8—21no—
139C2×C8—5541no—
140C2×C8—5541no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2771no—
144C4⋊C4—2771no—
145C4⋊C4—5541no—
146C22⋊C4—5542no—
147C22⋊C4—5541no—
148C42—5541no—
149C42C22×D27711yescharacteristic
150C23—22no—
151C23—5541no—
152Q8—41no—
153Q8—41no—
154Q8—2772no—
155Q8—5541no—
156D4—42no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—5541no—
162D4—5541no—
163D4—11084no—
164D4—22162no—
165C2×C4—41no—
166C2×C4—5541no—
167C2×C4—5541no—
168C2×C4—5541no—
169C2×C4—11084no—
170C2×C4—11081no—
171C2×C4—11081no—
172C2×C4D4×D27711yescharacteristic
173C2×C4D4×D27711yescharacteristic
174C2×C4C2×C22⋊D27711yescharacteristic
175C8—41no—
176C8—11081no—
177C8—11081no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—11081no—
182C22—11081no—
183C22—11081no—
184C22#2257984811yescharacteristic
185C4—21no—
186C4—81no—
187C4—5542no—
188C4—11081no—
189C4—11081no—
190C4D8×D27711yescharacteristic
191C4#2257990111yescharacteristic
192C4#2257990411yescharacteristic
193C4#2257990911yescharacteristic
194C2—82no—
195C2—22161no—
196C2#3180013411yescharacteristic
197C2#3180016111yescharacteristic
198C2#3180017911yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#486×C277C2
socleC22×C277#120
prime radical#31800672C2
hypercenter#486D277
hypocenterC277#1641
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #31800279C2semidirect
3. #31800209C2semidirect
4. #31799746C2semidirect
5. #31799734C2semidirect
6. #31799731C2semidirect
7. #486×C277C2semidirect
99. C277#1641semidirect
102. #486D277semidirect

Maximal subgroups

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

subgroupindex
#318006722
#318002792
#318002092
#317997462
#317997342
#317997312
#486×C2772
#1641277