Finite Group Databasebeta

← #47982269

Subgroups — #47982269

Order 35456.

250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic554C211yesmaximal, characteristic, complemented
2#31800348C211yesmaximal, characteristic, complemented
3#31800199C211yesmaximal, characteristic, complemented
4#31799747C211yesmaximal, characteristic, complemented
5#31799732C211yesmaximal, characteristic, complemented
6D4⋊#14555660C211yesmaximal, characteristic, complemented
7#459×C277C211yesmaximal, characteristic
8C22×Dic554—21no—
9C2×#17984551—21no—
10#22579880C2211yescharacteristic
11#22579879—21no—
12#22579859—21no—
13#22579857—22no—
14C4×Dic554C2211yescharacteristic
15D4×Dic277—21no—
16C4⋊#14555660C2211yescharacteristic
17#22579801—22no—
18#22579801—21no—
19C4×#14555660C2211yescharacteristic
20C2×D8×C277—21no—
21#127×C277C2211yescharacteristic
22C4×D4×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24#102×C277—21no—
25C2×Dic554—22no—
26C2×Dic554—21no—
27C2×Dic554—42no—
28C2×Dic554—42no—
29C2×Dic554D411yescharacteristic
30C22×Dic277—22no—
31#17984551—42no—
32C2×#14555660—21no—
33C2×#14555660—21no—
34C4⋊Dic277—21no—
35C4⋊Dic277D411yescharacteristic
36C4⋊Dic277D412yes—
37#17984542—22no—
38#17984542—21no—
39C22⋊Dic277—22no—
40C4×Dic277—21no—
41C2×D4×C277—21no—
42C2×D4×C277—21no—
43C2×D4×C277—21no—
44C2×D4×C277D411yescharacteristic
45C22×C4×C277—21no—
46D8×C277—42no—
47C2×C8×C277—21no—
48C4⋊C4×C277D411yescharacteristic
49C22⋊C4×C277—21no—
50C42×C277C2311yescharacteristic
51Dic554—21no—
52Dic554—44no—
53Dic554—41no—
54Dic554—41no—
55Dic554D812yescomplemented
56C2×Dic277—21no—
57C2×Dic277—21no—
58C2×Dic277—22no—
59C2×Dic277—44no—
60#14555660—41no—
61#14555660—41no—
62C23×C277—21no—
63C23×C277—41no—
64D4×C277—21no—
65D4×C277—42no—
66D4×C277—41no—
67D4×C277—41no—
68D4×C277—41no—
69D4×C277—41no—
70D4×C277SD1612yescomplemented
71C2×C4×C277—21no—
72C2×C4×C277—41no—
73C2×C4×C277—41no—
74C2×C4×C277C2×D411yescharacteristic
75C2×C4×C277C2×D411yescharacteristic
76C2×C4×C277C2×D411yescharacteristic
77C8×C277—41no—
78C22×C277—22no—
79C22×C277—41no—
80C22×C277—41no—
81C22×C277—81no—
82C22×C277—81no—
83C22×C277—81no—
84C22×C277#12011yescharacteristic
85C4×C277—21no—
86C4×C277—41no—
87C4×C277C2×D811yescharacteristic
88C4×C277C2×SD1611yescharacteristic
89C4×C277AGL(1,ℤ/8)11yescharacteristic
90C4×C277#13711yescharacteristic
91Dic277—22no—
92Dic277—42no—
93Dic277—41no—
94C2×C277—42no—
95C2×C277—161no—
96C2×C277#44711yescharacteristic
97C2×C277#44811yescharacteristic
98C2×C277#45411yescharacteristic
99C277#162711yescharacteristic, complemented, Sylow
100#1627—2771nomaximal, Sylow
101D4×Q8—2771no—
102#486—2771no—
103#460—2771no—
104#459D27711yescharacteristic
105#332—2771no—
106Q8⋊C8—2771no—
107D4⋊C8—2771no—
108C22×Q8—5541no—
109C2×SD16—5541no—
110C2×D8—21no—
111C4⋊Q8—2771no—
112C4⋊Q8—5541no—
113#127C2×D27711yescharacteristic
114C22⋊Q8—5542no—
115C22⋊Q8—5541no—
116C4×Q8—2771no—
117C4×D4—5541no—
118C4×D4C2×D27711yescharacteristic
119C4⋊C8—2771no—
120C4⋊C8C2×D27711yescharacteristic
121#102—21no—
122#102—5541no—
123#102—5542no—
124C4×C8—2771no—
125C2×Q8—2771no—
126C2×Q8—5542no—
127C2×Q8—5541no—
128C2×Q8—11082no—
129C2×Q8—11082no—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4C22⋊D27711yescharacteristic
134C22×C4—21no—
135C22×C4—5542no—
136SD16—11082no—
137D8—42no—
138C2×C8—21no—
139C2×C8—5541no—
140C2×C8—5541no—
141C4⋊C4—2771no—
142C4⋊C4—2772no—
143C4⋊C4—5542no—
144C4⋊C4—5541no—
145C4⋊C4—5541no—
146C4⋊C4C22⋊D27711yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—5542no—
149C42—5541no—
150C42C22×D27711yescharacteristic
151C23—21no—
152C23—41no—
153Q8—2772no—
154Q8—5541no—
155Q8—11084no—
156Q8—11081no—
157Q8—11081no—
158D4—21no—
159D4—42no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—41no—
164D4#1798455112yescomplemented
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—5541no—
169C2×C4—5541no—
170C2×C4—5542no—
171C2×C4—11084no—
172C2×C4D4×D27711yescharacteristic
173C2×C4D4×D27711yescharacteristic
174C2×C4C2×C22⋊D27711yescharacteristic
175C8—41no—
176C8—11081no—
177C8—11081no—
178C22—22no—
179C22—41no—
180C22—41no—
181C22—81no—
182C22—81no—
183C22—81no—
184C22#2257984811yescharacteristic
185C4—21no—
186C4—41no—
187C4—5542no—
188C4—11082no—
189C4—11081no—
190C4D8×D27711yescharacteristic
191C4C2×#1798455111yescharacteristic
192C4#2257990411yescharacteristic
193C4#2257991011yescharacteristic
194C2—42no—
195C2—161no—
196C2#3180013411yescharacteristic
197C2#3180014011yescharacteristic
198C2#3180017311yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting, prime radical#459×C277C2
socleC22×C277#120
hypercenter#459D277
hypocenterC277#1627
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. D4×Dic554C2semidirect
2. #31800348C2semidirect
3. #31800199C2semidirect
4. #31799747C2semidirect
5. #31799732C2semidirect
6. D4⋊#14555660C2semidirect
55. Dic554D8semidirect
70. D4×C277SD16semidirect
99. C277#1627semidirect
164. D4#17984551semidirect

Maximal subgroups

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

subgroupindex
D4×Dic5542
#318003482
#318001992
#317997472
#317997322
D4⋊#145556602
#459×C2772
#1627277