Finite Group Databasebeta

← #47982210

Subgroups — #47982210

Order 35456.

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

normal subgroups only

This group has 202 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#31800338C211yesmaximal, characteristic
3#31800335C211yesmaximal, characteristic
4#31799942C211yesmaximal, characteristic
5#31799738C211yesmaximal, characteristic
6#31799727C211yesmaximal, characteristic
7#328×C277C211yesmaximal, characteristic
8#22579879—21no—
9#22579878—21no—
10#22579870—21no—
11#22579870—21no—
12#22579859C2211yescharacteristic
13#22579857—21no—
14#22579836—21no—
15C2×C4⋊Dic277C2211yescharacteristic
16C2×#17984542C2211yescharacteristic
17#22579814—21no—
18#22579813—21no—
19#22579805—21no—
20#22579804—21no—
21C22⋊#14555660C2211yescharacteristic
22#22579787—21no—
23#22579787—21no—
24C22⋊Q8×C277C2211yescharacteristic
25C22⋊C8×C277C2211yescharacteristic
26#95×C277C2211yescharacteristic
27C2×Dic554—21no—
28C2×Dic554D411yescharacteristic
29C22×Dic277—21no—
30C22×Dic277D411yescharacteristic
31C22×Dic277D411yescharacteristic
32C2×#14555660—21no—
33C4⋊Dic277—21no—
34C4⋊Dic277—21no—
35C4⋊Dic277—21no—
36C4⋊Dic277D411yescharacteristic
37#17984542—21no—
38#17984542—21no—
39#17984542—21no—
40#17984542—21no—
41#17984542—21no—
42#17984542—21no—
43#17984542—21no—
44C22⋊Dic277—21no—
45C4×Dic277—21no—
46C4×Dic277—21no—
47C2×Q8×C277D411yescharacteristic
48C22×C4×C277—21no—
49C22×C4×C277C2311yescharacteristic
50C2×C8×C277—21no—
51C4⋊C4×C277—21no—
52C4⋊C4×C277D411yescharacteristic
53C22⋊C4×C277—21no—
54Dic554—41no—
55Dic554—81no—
56C2×Dic277—21no—
57C2×Dic277—21no—
58C2×Dic277—21no—
59C2×Dic277—21no—
60C2×Dic277—21no—
61C2×Dic277—41no—
62C2×Dic277—42no—
63C2×Dic277—41no—
64C2×Dic277Q1612yes—
65#14555660—41no—
66C23×C277C2×D411yescharacteristic
67Q8×C277—41no—
68C2×C4×C277—21no—
69C2×C4×C277—21no—
70C2×C4×C277—41no—
71C2×C4×C277—41no—
72C2×C4×C277—41no—
73C2×C4×C277—41no—
74C2×C4×C277C2×D411yescharacteristic
75C2×C4×C277C2×D411yescharacteristic
76C8×C277—41no—
77C22×C277—21no—
78C22×C277—21no—
79C22×C277#12011yescharacteristic
80C22×C277C2×Q1611yescharacteristic
81C22×C277#13711yescharacteristic
82C4×C277—21no—
83C4×C277—21no—
84C4×C277—41no—
85C4×C277—41no—
86C4×C277—81no—
87Dic277—22no—
88Dic277—41no—
89Dic277—41no—
90Dic277—41no—
91Dic277—81no—
92C2×C277—21no—
93C2×C277—21no—
94C2×C277#45111yescharacteristic
95C2×C277#45411yescharacteristic
96C2×C277#45811yescharacteristic
97C277#161711yescharacteristic, complemented, Sylow
98#1617—2771nomaximal, Sylow
99#544—2771no—
100#484—2771no—
101#484—2771no—
102#400—2771no—
103#328—2771no—
104#328D27711yescharacteristic
105#324—2771no—
106C4⋊Q8—5541no—
107C4⋊Q8—5541no—
108#125—5541no—
109#125—5541no—
110C22⋊Q8—2771no—
111C22⋊Q8—5541no—
112C22⋊Q8C2×D27711yescharacteristic
113#117—5541no—
114C2×C4⋊C4—2771no—
115C2×C4⋊C4—2771no—
116#107—5541no—
117#107—5541no—
118#103—5541no—
119#103—5541no—
120C22⋊C8—2771no—
121C22⋊C8C2×D27711yescharacteristic
122#95—5541no—
123#95—5541no—
124#95C2×D27711yescharacteristic
125C2×Q8—2771no—
126C2×Q8—5541no—
127C2×Q8D110811yescharacteristic
128C22×C4—21no—
129C22×C4—2771no—
130C22×C4—2771no—
131C22×C4—5541no—
132C22×C4C22×D27711yescharacteristic
133C2×C8—21no—
134C2×C8—5541no—
135C4⋊C4—21no—
136C4⋊C4—2771no—
137C4⋊C4—5541no—
138C4⋊C4—5541no—
139C4⋊C4—5541no—
140C4⋊C4—5541no—
141C4⋊C4—5541no—
142C4⋊C4—5541no—
143C4⋊C4—5541no—
144C4⋊C4—5541no—
145C4⋊C4—5541no—
146C4⋊C4—5541no—
147C4⋊C4D110811yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—5541no—
150C42—5541no—
151C42—5541no—
152C23D4×D27711yescharacteristic
153Q8—41no—
154Q8—11081no—
155Q8—22161no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—2772no—
163C2×C4—5541no—
164C2×C4—5541no—
165C2×C4—5541no—
166C2×C4—5541no—
167C2×C4—5541no—
168C2×C4—11081no—
169C2×C4—11082no—
170C2×C4—11081no—
171C2×C4D4×D27711yescharacteristic
172C2×C4C2×D110811yescharacteristic
173C8—41no—
174C8—11081no—
175C22—21no—
176C22—21no—
177C22#2257985011yescharacteristic
178C22Q16×D27711yescharacteristic
179C22#2257990911yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—5542no—
186C4—11081no—
187C4—11081no—
188C4—11081no—
189C4—22161no—
190C2—21no—
191C2—21no—
192C2#3180015911yescharacteristic
193C2#3180017611yescharacteristic
194C2#3180019311yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#328×C277C2
socleC22×C277#120
prime radicalC23×C277C2×D4
hypercenter#328D277
hypocenterC277#1617
LCSG ▷ C22×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
97. C277#1617semidirect

Maximal subgroups

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

subgroupindex
#318006312
#318003382
#318003352
#317999422
#317997382
#317997272
#328×C2772
#1617277