Finite Group Databasebeta

← #47982139

Subgroups — #47982139

Order 35456.

238 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 51 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#31800631C211yesmaximal, characteristic
2#31800158C211yesmaximal, characteristic
3#31799921C211yesmaximal, characteristic
4#31799740C211yesmaximal, characteristic
5#31799739C211yesmaximal, characteristic
6#31799727C211yesmaximal, characteristic
7#451×C277C211yesmaximal, characteristic
8C2×#17984553—21no—
9#22579879—21no—
10#22579878—21no—
11#22579870—21no—
12#22579870—21no—
13#22579859C2211yescharacteristic
14#22579857—21no—
15#22579836—21no—
16C2×#17984542—21no—
17C2×#17984542C2211yescharacteristic
18#22579804—21no—
19C22⋊#14555660C2211yescharacteristic
20#22579787—21no—
21#22579787C2211yescharacteristic
22C22×Q8×C277C2211yescharacteristic
23C2×Q16×C277—21no—
24C22⋊Q8×C277C2211yescharacteristic
25#103×C277—21no—
26C22⋊C8×C277C2211yescharacteristic
27C2×Dic554—21no—
28C2×Dic554D411yescharacteristic
29C22×Dic277—21no—
30C22×Dic277D411yescharacteristic
31C22×Dic277D411yescharacteristic
32#17984553—42no—
33C2×#14555660—21no—
34C4⋊Dic277—21no—
35C4⋊Dic277D411yescharacteristic
36#17984542—21no—
37#17984542—21no—
38#17984542—21no—
39#17984542—21no—
40#17984542—21no—
41#17984542—21no—
42#17984542—21no—
43#17984542—42no—
44C22⋊Dic277—21no—
45C4×Dic277—21no—
46C4×Dic277—21no—
47C2×Q8×C277—21no—
48C2×Q8×C277—21no—
49C2×Q8×C277—42no—
50C2×Q8×C277D411yescharacteristic
51C22×C4×C277—21no—
52C22×C4×C277C2311yescharacteristic
53Q16×C277—42no—
54C2×C8×C277—21no—
55C4⋊C4×C277—21no—
56C4⋊C4×C277D411yescharacteristic
57C22⋊C4×C277—21no—
58Dic554—41no—
59Dic554—81no—
60C2×Dic277—21no—
61C2×Dic277—21no—
62C2×Dic277—22no—
63C2×Dic277—21no—
64C2×Dic277—21no—
65C2×Dic277—21no—
66C2×Dic277—41no—
67C2×Dic277—41no—
68C2×Dic277—41no—
69C2×Dic277Q1612yescomplemented
70#14555660—41no—
71C23×C277C2×D411yescharacteristic
72Q8×C277—22no—
73Q8×C277—22no—
74Q8×C277—41no—
75Q8×C277—41no—
76Q8×C277—41no—
77C2×C4×C277—22no—
78C2×C4×C277—21no—
79C2×C4×C277—21no—
80C2×C4×C277—41no—
81C2×C4×C277—41no—
82C2×C4×C277—41no—
83C2×C4×C277C2×D411yescharacteristic
84C2×C4×C277C2×D411yescharacteristic
85C8×C277—41no—
86C22×C277—21no—
87C22×C277—21no—
88C22×C277#12011yescharacteristic
89C22×C277C2×Q1611yescharacteristic
90C22×C277#13711yescharacteristic
91C4×C277—21no—
92C4×C277—21no—
93C4×C277—41no—
94C4×C277—42no—
95C4×C277—41no—
96Dic277—22no—
97Dic277—42no—
98Dic277—41no—
99Dic277—41no—
100Dic277—41no—
101C2×C277—21no—
102C2×C277—21no—
103C2×C277#45111yescharacteristic
104C2×C277#45611yescharacteristic
105C2×C277B(4,𝔽2)11yescharacteristic
106C277#160511yescharacteristic, complemented, Sylow
107#1605—2771nomaximal, Sylow
108#544—2771no—
109#451—2771no—
110#451D27711yescharacteristic
111#395—2771no—
112#328—2771no—
113#328—2771no—
114#324—2771no—
115C22×Q8C2×D27711yescharacteristic
116C2×Q16—21no—
117C2×Q16—5541no—
118C4⋊Q8—5541no—
119C4⋊Q8—5541no—
120#125—5541no—
121#125—5541no—
122C22⋊Q8—2771no—
123C22⋊Q8—5541no—
124C22⋊Q8C2×D27711yescharacteristic
125#117—5541no—
126C2×C4⋊C4—2771no—
127C2×C4⋊C4—5541no—
128#103—21no—
129#103—5541no—
130C22⋊C8—2771no—
131C22⋊C8C2×D27711yescharacteristic
132#95—2771no—
133#95—5541no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—42no—
137C2×Q8—2771no—
138C2×Q8—5541no—
139C2×Q8C22⋊D27711yescharacteristic
140C22×C4—21no—
141C22×C4—2771no—
142C22×C4—2771no—
143C22×C4—5541no—
144C22×C4C22×D27711yescharacteristic
145Q16—42no—
146Q16—11082no—
147C2×C8—21no—
148C2×C8—5541no—
149C4⋊C4—21no—
150C4⋊C4—2771no—
151C4⋊C4—5541no—
152C4⋊C4—5541no—
153C4⋊C4—5541no—
154C4⋊C4—5541no—
155C4⋊C4—5541no—
156C4⋊C4—5541no—
157C4⋊C4—5541no—
158C4⋊C4—5541no—
159C4⋊C4—11082no—
160C4⋊C4C22⋊D27711yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—5541no—
163C42—5541no—
164C42—5541no—
165C23D4×D27711yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—41no—
171Q8—11081no—
172Q8—22161no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—2772no—
180C2×C4—5541no—
181C2×C4—5541no—
182C2×C4—5542no—
183C2×C4—5541no—
184C2×C4—5541no—
185C2×C4—5541no—
186C2×C4—11081no—
187C2×C4—11081no—
188C2×C4—11081no—
189C2×C4D4×D27711yescharacteristic
190C2×C4C2×C22⋊D27711yescharacteristic
191C8—41no—
192C8—11081no—
193C22—21no—
194C22—21no—
195C22#2257984811yescharacteristic
196C22Q16×D27711yescharacteristic
197C22#2257991211yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—42no—
202C4—41no—
203C4—5542no—
204C4—11082no—
205C4—11081no—
206C4—11081no—
207C4—11081no—
208C2—21no—
209C2—21no—
210C2#3180015611yescharacteristic
211C2#3180018311yescharacteristic
212C2#3180018811yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#451×C277C2
socleC22×C277#120
prime radicalC23×C277C2×D4
hypercenter#451D277
hypocenterC277#1605
LCSG ▷ C22×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
69. C2×Dic277Q16semidirect
106. C277#1605semidirect

Maximal subgroups

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

subgroupindex
#318006312
#318001582
#317999212
#317997402
#317997392
#317997272
#451×C2772
#1605277