Finite Group Databasebeta

← #47982268

Subgroups — #47982268

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
1Q8×D1108C211yesmaximal, characteristic, complemented
2#31800348C211yesmaximal, characteristic, complemented
3#31800194C211yesmaximal, characteristic
4#31799749C211yesmaximal, characteristic, complemented
5Q8⋊#14555660C211yesmaximal, characteristic, complemented
6#31799729C211yesmaximal, characteristic, complemented
7#460×C277C211yesmaximal, characteristic, complemented
8C2×Q8×D277—21no—
9C2×#17984548—21no—
10#22579880—21no—
11#22579880C2211yescharacteristic
12#22579860—22no—
13#22579860—21no—
14C4×D1108—21no—
15C4×D1108C2211yescharacteristic
16C4⋊#14555660C2211yescharacteristic
17#22579801—22no—
18#22579801—21no—
19C4×#14555660C2211yescharacteristic
20C2×SD16×C277—21no—
21#127×C277C2211yescharacteristic
22C4×Q8×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24#102×C277—21no—
25C2×Dic554—22no—
26C2×Dic554—21no—
27Q8×D277—42no—
28Q8×D277—42no—
29C2×D1108D411yescharacteristic
30C2×C4×D277—22no—
31C2×C4×D277—21no—
32#17984548—42no—
33C2×#14555660—21no—
34C2×#14555660—21no—
35C4⋊Dic277—22no—
36C4⋊Dic277—21no—
37C4⋊Dic277D411yescharacteristic
38C4⋊Dic277D412yes—
39#17984540—22no—
40#17984540—21no—
41C2×Q8×C277D411yescharacteristic
42C2×D4×C277—21no—
43C2×D4×C277—21no—
44C2×D4×C277—21no—
45SD16×C277—42no—
46C2×C8×C277—21no—
47C4⋊C4×C277—21no—
48C4⋊C4×C277D411yescharacteristic
49C42×C277—21no—
50C42×C277C2311yescharacteristic
51C22×D277—21no—
52Dic554—44no—
53Dic554—41no—
54Dic554—41no—
55D1108—21no—
56D1108SD1612yescomplemented
57C2×Dic277—22no—
58C2×Dic277—21no—
59C4×D277—44no—
60C4×D277—41no—
61C4×D277—41no—
62#14555660—41no—
63#14555660—41no—
64C23×C277—41no—
65Q8×C277—21no—
66Q8×C277D812yescomplemented
67D4×C277—42no—
68D4×C277—41no—
69D4×C277—41no—
70D4×C277—41no—
71D4×C277—41no—
72C2×C4×C277—21no—
73C2×C4×C277—21no—
74C2×C4×C277C2×D411yescharacteristic
75C2×C4×C277C2×D411yescharacteristic
76C2×C4×C277C2×D411yescharacteristic
77C8×C277—41no—
78C22×C277—81no—
79C22×C277—81no—
80C22×C277—81no—
81C22×C277#12011yescharacteristic
82C2×D277—22no—
83C2×D277—41no—
84C2×D277—41no—
85C4×C277—22no—
86C4×C277—21no—
87C4×C277—41no—
88C4×C277C2×D811yescharacteristic
89C4×C277C2×SD1611yescharacteristic
90C4×C277AGL(1,ℤ/8)11yescharacteristic
91C4×C277#13711yescharacteristic
92Dic277—42no—
93Dic277—41no—
94C2×C277—161no—
95C2×C277#44711yescharacteristic
96C2×C277#44811yescharacteristic
97C2×C277#45411yescharacteristic
98D277—42no—
99C277#162711yescharacteristic, complemented, Sylow
100#1627—2771nomaximal, Sylow
101D4×Q8—2771no—
102#486—2771no—
103#460D27711yescharacteristic, complemented
104#459—2771no—
105#332—2771no—
106Q8⋊C8—2771no—
107D4⋊C8—2771no—
108C22×Q8—5541no—
109C2×SD16—21no—
110C2×D8—5541no—
111C4⋊Q8—2771no—
112C4⋊Q8—5541no—
113#127C2×D27711yescharacteristic
114C22⋊Q8—5542no—
115C22⋊Q8—5541no—
116C4×Q8C2×D27711yescharacteristic
117C4×D4—2771no—
118C4×D4—5541no—
119C4⋊C8—2771no—
120C4⋊C8C2×D27711yescharacteristic
121#102—21no—
122#102—5541no—
123#102—5542no—
124C4×C8—2771no—
125C2×Q8—5542no—
126C2×Q8—5541no—
127C2×Q8—11082no—
128C2×Q8—11082no—
129C2×Q8C22⋊D27711yescharacteristic
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—2771no—
134C22×C4—5542no—
135C22×C4—5541no—
136SD16—42no—
137D8—11082no—
138C2×C8—21no—
139C2×C8—5541no—
140C2×C8—5541no—
141C4⋊C4—21no—
142C4⋊C4—2771no—
143C4⋊C4—2772no—
144C4⋊C4—5542no—
145C4⋊C4—5541no—
146C4⋊C4C22⋊D27711yescharacteristic
147C22⋊C4—5542no—
148C22⋊C4—5541no—
149C42—21no—
150C42C22×D27711yescharacteristic
151C23—41no—
152C23—5541no—
153Q8—21no—
154Q8—11084no—
155Q8—11081no—
156Q8—11081no—
157Q8#1798454812yescomplemented
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—2772no—
164D4—5541no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—5542no—
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—81no—
179C22—81no—
180C22—81no—
181C22—5542no—
182C22—11081no—
183C22—11081no—
184C22#2257984811yescharacteristic
185C4—22no—
186C4—21no—
187C4—41no—
188C4—11082no—
189C4—11081no—
190C4C2×#1798454811yescharacteristic
191C4SD16×D27711yescharacteristic
192C4#2257990511yescharacteristic
193C4#2257990911yescharacteristic
194C2—161no—
195C2—11082no—
196C2#3180013511yescharacteristic
197C2#3180013911yescharacteristic
198C2#3180017311yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#460×C277C2
socleC22×C277#120
prime radical#31800194C2
hypercenter#460D277
hypocenterC277#1627
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. Q8×D1108C2semidirect
2. #31800348C2semidirect
4. #31799749C2semidirect
5. Q8⋊#14555660C2semidirect
6. #31799729C2semidirect
7. #460×C277C2semidirect
56. D1108SD16semidirect
66. Q8×C277D8semidirect
99. C277#1627semidirect
103. #460D277semidirect
157. Q8#17984548semidirect

Maximal subgroups

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

subgroupindex
Q8×D11082
#318003482
#318001942
#317997492
Q8⋊#145556602
#317997292
#460×C2772
#1627277