Finite Group Databasebeta

← #47982275

Subgroups — #47982275

Order 35456.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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#31800722C211yesmaximal, characteristic, complemented
2#31800348C211yesmaximal, characteristic, complemented
3#31800199C211yesmaximal, characteristic, complemented
4#31799749C211yesmaximal, characteristic, complemented
5#31799732C211yesmaximal, characteristic, complemented
6D4⋊#14555660C211yesmaximal, characteristic, complemented
7#459×C277C211yesmaximal, characteristic
8C2×#17984551—21no—
9#22579880C2211yescharacteristic
10#22579873—22no—
11#22579867—21no—
12#22579859—21no—
13C4×Dic554C2211yescharacteristic
14#22579845—21no—
15#22579839—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—21no—
26C2×Dic554D411yescharacteristic
27#17984551—42no—
28C2×#14555660—21no—
29C2×#14555660—21no—
30C4⋊Dic277—21no—
31C4⋊Dic277D411yescharacteristic
32C4⋊Dic277D412yes—
33#17984542—22no—
34#17984542—21no—
35C22⋊Dic277—22no—
36C22⋊Dic277—22no—
37C4×Dic277—22no—
38C4×Dic277—21no—
39C2×D4×C277—21no—
40C2×D4×C277—21no—
41C2×D4×C277—21no—
42C2×D4×C277D411yescharacteristic
43C22×C4×C277—21no—
44D8×C277—42no—
45C2×C8×C277—21no—
46C4⋊C4×C277D411yescharacteristic
47C22⋊C4×C277—21no—
48C42×C277C2311yescharacteristic
49Dic554—21no—
50Dic554—21no—
51Dic554—41no—
52Dic554—41no—
53C2×Dic277—21no—
54C2×Dic277—21no—
55C2×Dic277—22no—
56#14555660—41no—
57#14555660—41no—
58C23×C277—21no—
59C23×C277—41no—
60D4×C277—21no—
61D4×C277—21no—
62D4×C277—42no—
63D4×C277—41no—
64D4×C277—41no—
65D4×C277—41no—
66D4×C277—41no—
67C2×C4×C277—21no—
68C2×C4×C277—41no—
69C2×C4×C277—41no—
70C2×C4×C277C2×D411yescharacteristic
71C2×C4×C277C2×D411yescharacteristic
72C2×C4×C277C2×D411yescharacteristic
73C8×C277—41no—
74C22×C277—41no—
75C22×C277—41no—
76C22×C277—41no—
77C22×C277—81no—
78C22×C277—81no—
79C22×C277—81no—
80C22×C277#12011yescharacteristic
81C4×C277—21no—
82C4×C277—41no—
83C4×C277#13511yescharacteristic
84C4×C277#13511yescharacteristic
85C4×C277AGL(1,ℤ/8)11yescharacteristic
86C4×C277AGL(1,ℤ/8)11yescharacteristic
87Dic277—41no—
88Dic277—42no—
89Dic277—41no—
90C2×C277—81no—
91C2×C277—161no—
92C2×C277#44911yescharacteristic
93C2×C277#44911yescharacteristic
94C2×C277#45411yescharacteristic
95C277#162811yescharacteristic, complemented, Sylow
96#1628—2771nomaximal, Sylow
97#556—2771no—
98#486—2771no—
99#460—2771no—
100#459D27711yescharacteristic
101#332—2771no—
102Q8⋊C8—2771no—
103D4⋊C8—2771no—
104C2×SD16—5541no—
105C2×D8—21no—
106C4⋊Q8—2771no—
107#127C2×D27711yescharacteristic
108#126—5542no—
109#124—5541no—
110C22⋊Q8—5541no—
111C4×Q8—2771no—
112C4×Q8—5541no—
113C4×D4C2×D27711yescharacteristic
114#117—5541no—
115C4⋊C8—2771no—
116C4⋊C8C2×D27711yescharacteristic
117#102—21no—
118#102—5541no—
119#102—5542no—
120C4×C8—2771no—
121C2×Q8—2771no—
122C2×Q8—5541no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4C22⋊D27711yescharacteristic
127C22×C4—21no—
128SD16—11082no—
129D8—42no—
130C2×C8—21no—
131C2×C8—5541no—
132C2×C8—5541no—
133C4⋊C4—2771no—
134C4⋊C4—2772no—
135C4⋊C4—5542no—
136C4⋊C4—5541no—
137C4⋊C4—5541no—
138C4⋊C4C22⋊D27711yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—5542no—
141C22⋊C4—5542no—
142C42—5542no—
143C42—5541no—
144C42C22×D27711yescharacteristic
145C23—21no—
146C23—41no—
147Q8—5541no—
148Q8—5541no—
149Q8—11081no—
150Q8—11081no—
151D4—21no—
152D4—21no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—5541no—
162C2×C4—5542no—
163C2×C4—5541no—
164C2×C4D4×D27711yescharacteristic
165C2×C4D4×D27711yescharacteristic
166C2×C4C2×C22⋊D27711yescharacteristic
167C8—41no—
168C8—11081no—
169C8—11081no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—81no—
174C22—81no—
175C22—81no—
176C22#2257984811yescharacteristic
177C4—21no—
178C4—41no—
179C4—11081no—
180C4—11082no—
181C4—11081no—
182C4#2257989911yescharacteristic
183C4#2257990011yescharacteristic
184C4#2257990411yescharacteristic
185C4#2257990611yescharacteristic
186C2—81no—
187C2—161no—
188C2#3180014411yescharacteristic
189C2#3180014511yescharacteristic
190C2#3180017311yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting, prime radical#459×C277C2
socleC22×C277#120
hypercenter#459D277
hypocenterC277#1628
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. #31800722C2semidirect
2. #31800348C2semidirect
3. #31800199C2semidirect
4. #31799749C2semidirect
5. #31799732C2semidirect
6. D4⋊#14555660C2semidirect
95. C277#1628semidirect

Maximal subgroups

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

subgroupindex
#318007222
#318003482
#318001992
#317997492
#317997322
D4⋊#145556602
#459×C2772
#1628277