Finite Group Databasebeta

← #47982267

Subgroups — #47982267

Order 35456.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#31800667C211yesmaximal, characteristic, complemented
2#31800199C211yesmaximal, characteristic, complemented
3#31800194C211yesmaximal, characteristic
4#31799748C211yesmaximal, characteristic, complemented
5#31799734C211yesmaximal, characteristic, complemented
6#31799731C211yesmaximal, characteristic, complemented
7#486×C277C211yesmaximal, characteristic, complemented
8C2×Q8×D277—21no—
9C2×#17984551—21no—
10C2×#17984548—21no—
11#22579879—21no—
12#22579858—22no—
13#22579856—21no—
14C4×Dic554C2211yescharacteristic
15C4×D1108C2211yescharacteristic
16#22579842—21no—
17C4⋊#14555660C2211yescharacteristic
18C4⋊#14555660C2211yescharacteristic
19#22579801—21no—
20#22579801—21no—
21C4⋊Q8×C277C2211yescharacteristic
22#127×C277C2211yescharacteristic
23#102×C277—22no—
24C4×C8×C277C2211yescharacteristic
25C2×Dic554—22no—
26C2×Dic554D411yescharacteristic
27Q8×D277—42no—
28Q8×D277—42no—
29C2×D1108D411yescharacteristic
30C2×C4×D277—22no—
31C2×C4×D277—21no—
32#17984551—42no—
33#17984548—42no—
34C2×#14555660—21no—
35C2×#14555660—21no—
36C4⋊Dic277D411yescharacteristic
37C4⋊Dic277D411yescharacteristic
38#17984542—22no—
39#17984542—21no—
40#17984540—22no—
41#17984540—21no—
42C4×Dic277—21no—
43C2×Q8×C277—21no—
44C2×D4×C277—21no—
45C2×D4×C277—21no—
46C2×D4×C277—21no—
47C2×C8×C277—21no—
48C4⋊C4×C277—21no—
49C4⋊C4×C277D412yes—
50C42×C277C2311yescharacteristic
51C22×D277—21no—
52Dic554—21no—
53Dic554—44no—
54Dic554D812yescomplemented
55D1108—21no—
56D1108SD1612yescomplemented
57C2×Dic277—21no—
58C2×Dic277—21no—
59C2×Dic277—21no—
60C4×D277—44no—
61C4×D277—41no—
62C4×D277—41no—
63#14555660—41no—
64#14555660—41no—
65C23×C277—41no—
66Q8×C277—41no—
67Q8×C277—41no—
68D4×C277—42no—
69D4×C277—41no—
70D4×C277—41no—
71D4×C277—41no—
72D4×C277—41no—
73C2×C4×C277—22no—
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—21no—
86C4×C277—42no—
87C4×C277C2×D811yescharacteristic
88C4×C277C2×SD1611yescharacteristic
89C4×C277AGL(1,ℤ/8)11yescharacteristic
90C4×C277#13711yescharacteristic
91Dic277—22no—
92Dic277—41no—
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#486D27711yescharacteristic, complemented
103#460—2771no—
104#459—2771no—
105#332—2771no—
106Q8⋊C8—2771no—
107D4⋊C8—2771no—
108C22×Q8—5541no—
109C2×SD16—5541no—
110C2×D8—5541no—
111C4⋊Q8—5541no—
112C4⋊Q8C2×D27711yescharacteristic
113#127C2×D27711yescharacteristic
114C22⋊Q8—5541no—
115C22⋊Q8—5542no—
116C4×Q8—2771no—
117C4×D4—2771no—
118C4×D4—5541no—
119C4⋊C8—2771no—
120C4⋊C8—2771no—
121#102—22no—
122#102—5541no—
123#102—5541no—
124C4×C8C2×D27711yescharacteristic
125C2×Q8—21no—
126C2×Q8—2771no—
127C2×Q8—5542no—
128C2×Q8—11082no—
129C2×Q8—11082no—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—2771no—
134C22×C4—5542no—
135C22×C4—5541no—
136SD16—11082no—
137D8—11082no—
138C2×C8—21no—
139C2×C8—5541no—
140C2×C8—5541no—
141C4⋊C4—21no—
142C4⋊C4—2771no—
143C4⋊C4—2771no—
144C4⋊C4—5542no—
145C4⋊C4—5541no—
146C4⋊C4C22⋊D27712yes—
147C22⋊C4—5542no—
148C22⋊C4—5541no—
149C42—5541no—
150C42C22×D27711yescharacteristic
151C23—41no—
152C23—5541no—
153Q8—41no—
154Q8—41no—
155Q8—2772no—
156Q8—5541no—
157Q8—11084no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—2772no—
164D4—5541no—
165C2×C4—22no—
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—81no—
179C22—81no—
180C22—81no—
181C22—5542no—
182C22—11081no—
183C22—11081no—
184C22#2257984811yescharacteristic
185C4—21no—
186C4—42no—
187C4—5542no—
188C4—11081no—
189C4—11081no—
190C4D8×D27711yescharacteristic
191C4SD16×D27711yescharacteristic
192C4#2257990411yescharacteristic
193C4#2257990911yescharacteristic
194C2—161no—
195C2—11082no—
196C2#3180013411yescharacteristic
197C2#3180013911yescharacteristic
198C2#3180017411yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#486×C277C2
socleC22×C277#120
prime radical#31800194C2
hypercenter#486D277
hypocenterC277#1627
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #31800667C2semidirect
2. #31800199C2semidirect
4. #31799748C2semidirect
5. #31799734C2semidirect
6. #31799731C2semidirect
7. #486×C277C2semidirect
54. Dic554D8semidirect
56. D1108SD16semidirect
99. C277#1627semidirect
102. #486D277semidirect

Maximal subgroups

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

subgroupindex
#318006672
#318001992
#318001942
#317997482
#317997342
#317997312
#486×C2772
#1627277