Finite Group Databasebeta

← #47982233

Subgroups — #47982233

Order 35456.

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

normal subgroups only

This group has 278 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, complemented
2#31800378C211yesmaximal, characteristic, complemented
3#31800203C211yesmaximal, characteristic, complemented
4#31800198C211yesmaximal, characteristic, complemented
5#31799732C211yesmaximal, characteristic, complemented
6#31799729C211yesmaximal, characteristic, complemented
7#331×C277C211yesmaximal, characteristic, complemented
8C2×#17984562—21no—
9C2×#17984552—21no—
10C2×D2216—21no—
11C2×#17984548—22no—
12#22579877C2211yescharacteristic
13#22579876—21no—
14#22579852—22no—
15#22579851—21no—
16C4×Dic554C2211yescharacteristic
17C4×D1108C2211yescharacteristic
18D4×Dic277—21no—
19#22579802—21no—
20#22579802—21no—
21C4×#14555660C2211yescharacteristic
22#127×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4⋊C8×C277C2211yescharacteristic
25#17984562—42no—
26#17984562—42no—
27C2×Dic554D411yescharacteristic
28C2×D1108—21no—
29C2×D1108—21no—
30C2×D1108—21no—
31C2×D1108D411yescharacteristic
32C2×C22⋊D277—22no—
33C2×C22⋊D277—22no—
34C22×Dic277—22no—
35C2×C4×D277—21no—
36#17984552—42no—
37D2216—42no—
38#17984548—44no—
39C2×#14555660—21no—
40C4⋊Dic277D411yescharacteristic
41C4⋊Dic277D411yescharacteristic
42#17984542—21no—
43C22⋊Dic277—22no—
44#17984540—21no—
45C4×Dic277—21no—
46C2×D4×C277—21no—
47C2×D4×C277—21no—
48C2×D4×C277D412yes—
49C2×C8×C277—21no—
50C2×C8×C277—21no—
51C42×C277C2311yescharacteristic
52C22×D277—21no—
53C22×D277—41no—
54Dic554—21no—
55Dic554D812yescomplemented
56D1108—21no—
57D1108—21no—
58D1108—42no—
59D1108—41no—
60D1108—41no—
61D1108—41no—
62D1108—41no—
63C22⋊D277—44no—
64C22⋊D277—82no—
65C2×Dic277—21no—
66C2×Dic277—21no—
67C2×Dic277—21no—
68C2×Dic277—44no—
69C4×D277—41no—
70C4×D277—41no—
71#14555660—22no—
72C23×C277—22no—
73D4×C277—42no—
74D4×C277—41no—
75D4×C277—41no—
76D4×C277—41no—
77D4×C277—41no—
78C2×C4×C277C2×D411yescharacteristic
79C2×C4×C277C2×D411yescharacteristic
80C2×C4×C277C2×D411yescharacteristic
81C8×C277—41no—
82C8×C277—41no—
83C22×C277—42no—
84C22×C277—42no—
85C22×C277—42no—
86C22×C277#12011yescharacteristic
87C2×D277—41no—
88C2×D277—41no—
89C2×D277—41no—
90C2×D277—81no—
91C2×D277—81no—
92C2×D277—81no—
93C4×C277—21no—
94C4×C277C2×D811yescharacteristic
95C4×C277#13511yescharacteristic
96C4×C277AGL(1,ℤ/8)11yescharacteristic
97C4×C277AGL(1,ℤ/8)11yescharacteristic
98Dic277—22no—
99Dic277—41no—
100Dic277—41no—
101C2×C277—82no—
102C2×C277#44711yescharacteristic
103C2×C277#44911yescharacteristic
104C2×C277#45311yescharacteristic
105D277—81no—
106D277—161no—
107C277#162111yescharacteristic, complemented, Sylow
108#1621—2771nomaximal, Sylow
109#550—2771no—
110#493—2771no—
111#460—2771no—
112#459—2771no—
113#331D27711yescharacteristic, complemented
114Q8⋊C8—2771no—
115D4⋊C8—2771no—
116C2×#41—5541no—
117C2×SD16—5541no—
118C2×D8—5541no—
119C2×D8—5542no—
120#127—2771no—
121#127—5541no—
122#127C2×D27711yescharacteristic
123#121—5541no—
124#121—5542no—
125C4×Q8—2771no—
126C4×D4—2771no—
127C4×D4—5541no—
128C4⋊C8C2×D27711yescharacteristic
129C4⋊C8C2×D27711yescharacteristic
130#102—5541no—
131#102—5541no—
132C4×C8—2771no—
133#41—11082no—
134#41—11082no—
135C2×Q8—2771no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—2771no—
139C2×D4—5542no—
140C2×D4—5542no—
141C2×D4—5541no—
142C2×D4—5541no—
143C2×D4—5541no—
144C2×D4D110812yes—
145C22×C4—5542no—
146C22×C4—5541no—
147SD16—11082no—
148D8—11082no—
149D8—11084no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—5541no—
153C4⋊C4—2771no—
154C4⋊C4—2771no—
155C4⋊C4—5541no—
156C22⋊C4—5542no—
157C22⋊C4—5541no—
158C42—5541no—
159C42C22×D27711yescharacteristic
160C23—22no—
161C23—5541no—
162C23—11081no—
163Q8—2772no—
164Q8—5541no—
165D4—42no—
166D4—41no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—5541no—
171D4—5541no—
172D4—11082no—
173D4—11084no—
174D4—11081no—
175D4—11081no—
176D4—11081no—
177D4—11081no—
178D4—22162no—
179C2×C4—5541no—
180C2×C4—5541no—
181C2×C4—5541no—
182C2×C4—11084no—
183C2×C4—11081no—
184C2×C4—11081no—
185C2×C4D4×D27711yescharacteristic
186C2×C4D4×D27711yescharacteristic
187C2×C4C2×D110811yescharacteristic
188C8—41no—
189C8—41no—
190C8—5542no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—11081no—
195C22—11081no—
196C22—11081no—
197C22—22161no—
198C22—22161no—
199C22—22161no—
200C22#2257985011yescharacteristic
201C4—21no—
202C4—5542no—
203C4—11081no—
204C4—11081no—
205C4D8×D27711yescharacteristic
206C4#2257990111yescharacteristic
207C4#2257990411yescharacteristic
208C4#2257990711yescharacteristic
209C2—82no—
210C2—44321no—
211C2—22161no—
212C2#3180013711yescharacteristic
213C2#3180014811yescharacteristic
214C2#3180017211yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#331×C277C2
socleC22×C277#120
hypercenter#331D277
hypocenterC277#1621
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #31800672C2semidirect
2. #31800378C2semidirect
3. #31800203C2semidirect
4. #31800198C2semidirect
5. #31799732C2semidirect
6. #31799729C2semidirect
7. #331×C277C2semidirect
55. Dic554D8semidirect
107. C277#1621semidirect
113. #331D277semidirect

Maximal subgroups

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

subgroupindex
#318006722
#318003782
#318002032
#318001982
#317997322
#317997292
#331×C2772
#1621277