Finite Group Databasebeta

← #47981677

Subgroups — #47981677

Order 35456.

228 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 63 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#31800554C211yesmaximal, characteristic
2#31800056C211yesmaximal, characteristic
3#31799847C211yesmaximal, characteristic
4#31799740C211yesmaximal, characteristic
5#31799739C211yesmaximal, characteristic
6#31799738C211yesmaximal, characteristic
7#328×C277C211yesmaximal, characteristic
8#22579879C411yescharacteristic, complemented
9#22579878C411yescharacteristic, complemented
10#22579870—21no—
11#22579859C2211yescharacteristic
12#22579857—21no—
13Q8×Dic277C411yescharacteristic, complemented
14#22579845—21no—
15#22579845C411yescharacteristic, complemented
16#22579836—21no—
17C2×C4×Dic277—21no—
18C2×C4×Dic277C2211yescharacteristic
19#22579809—21no—
20C22⋊#14555660C2211yescharacteristic
21#22579790—21no—
22#22579787—21no—
23#22579787C2211yescharacteristic
24C22⋊Q8×C277C2211yescharacteristic
25C22⋊C8×C277C2211yescharacteristic
26#95×C277C2211yescharacteristic
27C2×Dic554—21no—
28C2×Dic554C2×C411yescharacteristic
29C22×Dic277—21no—
30C22×Dic277D411yescharacteristic
31C22×Dic277D411yescharacteristic
32C2×#14555660—21no—
33C4⋊Dic277—21no—
34C4⋊Dic277C2×C411yescharacteristic
35#17984542—21no—
36#17984542—21no—
37#17984542—21no—
38#17984542—21no—
39#17984542—21no—
40C22⋊Dic277—21no—
41C4×Dic277—24no—
42C4×Dic277—21no—
43C4×Dic277—21no—
44C4×Dic277C2×C411yescharacteristic
45C4×Dic277C2×C411yescharacteristic
46C4×Dic277D411yescharacteristic
47C4×Dic277D411yescharacteristic
48C2×Q8×C277C2×C411yescharacteristic
49C22×C4×C277—21no—
50C22×C4×C277C2311yescharacteristic
51C2×C8×C277—21no—
52C4⋊C4×C277—21no—
53C4⋊C4×C277C2×C411yescharacteristic
54C22⋊C4×C277—21no—
55Dic554—42no—
56Dic554—41no—
57C2×Dic277—21no—
58C2×Dic277—21no—
59C2×Dic277—22no—
60C2×Dic277—22no—
61C2×Dic277—21no—
62C2×Dic277—21no—
63C2×Dic277—41no—
64C2×Dic277—41no—
65C2×Dic277C22⋊C411yescharacteristic
66C2×Dic277C22⋊C411yescharacteristic
67C2×Dic277C22⋊C411yescharacteristic
68C2×Dic277C22⋊C411yescharacteristic
69#14555660—41no—
70C23×C277C2×D411yescharacteristic
71Q8×C277—41no—
72C2×C4×C277—22no—
73C2×C4×C277—21no—
74C2×C4×C277—21no—
75C2×C4×C277—41no—
76C2×C4×C277—41no—
77C2×C4×C277—41no—
78C2×C4×C277C22×C411yescharacteristic
79C2×C4×C277C2×D411yescharacteristic
80C8×C277—41no—
81C22×C277—21no—
82C22×C277—21no—
83C22×C277C2×C22⋊C411yescharacteristic
84C22×C277#13711yescharacteristic
85C22×C277#13711yescharacteristic
86C4×C277—21no—
87C4×C277—21no—
88C4×C277—42no—
89C4×C277—41no—
90C4×C277—41no—
91Dic277—21no—
92Dic277—21no—
93Dic277—21no—
94Dic277—42no—
95Dic277—41no—
96Dic277—41no—
97Dic277#10412yes—
98C2×C277—21no—
99C2×C277—21no—
100C2×C277#41011yescharacteristic
101C2×C277#41911yescharacteristic
102C2×C277C2×#10411yescharacteristic
103C277#150611yescharacteristic, complemented, Sylow
104#1506—2771nomaximal, Sylow
105#533—2771no—
106#432—2771no—
107#376—2771no—
108#328—2771no—
109#328—2771no—
110#328—2771no—
111#328D27711yescharacteristic
112C4⋊Q8—2771no—
113C4⋊Q8—2771no—
114#125—5541no—
115C22⋊Q8—2771no—
116C22⋊Q8—5541no—
117C22⋊Q8C2×D27711yescharacteristic
118C4×Q8—2771no—
119C4×Q8—2771no—
120C4×Q8—5541no—
121#117—5541no—
122C2×C42—2771no—
123C2×C42—5541no—
124C4⋊C8—5541no—
125C22⋊C8—2771no—
126C22⋊C8C2×D27711yescharacteristic
127#97—5541no—
128#95—2771no—
129#95—5541no—
130#95C2×D27711yescharacteristic
131C2×Q8—2771no—
132C2×Q8—5541no—
133C2×Q8C4×D27711yescharacteristic
134C22×C4—21no—
135C22×C4—2771no—
136C22×C4—2771no—
137C22×C4—5541no—
138C22×C4C22×D27711yescharacteristic
139C2×C8—21no—
140C2×C8—5541no—
141C4⋊C4—21no—
142C4⋊C4—2771no—
143C4⋊C4—5541no—
144C4⋊C4—5541no—
145C4⋊C4—5541no—
146C4⋊C4—5541no—
147C4⋊C4—5541no—
148C4⋊C4—5541no—
149C4⋊C4C4×D27711yescharacteristic
150C22⋊C4—21no—
151C22⋊C4—5541no—
152C42—2771no—
153C42—2771no—
154C42—2771no—
155C42—2771no—
156C42—5541no—
157C42—5541no—
158C42—5544no—
159C23D4×D27711yescharacteristic
160Q8—41no—
161Q8—11081no—
162Q8—11082no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—2771no—
170C2×C4—2771no—
171C2×C4—2771no—
172C2×C4—2771no—
173C2×C4—5542no—
174C2×C4—5541no—
175C2×C4—5541no—
176C2×C4—5542no—
177C2×C4—5541no—
178C2×C4—5541no—
179C2×C4—11081no—
180C2×C4—11081no—
181C2×C4C2×C4×D27711yescharacteristic
182C2×C4D4×D27711yescharacteristic
183C8—41no—
184C8—11081no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D27711yescharacteristic
188C22#2257990911yescharacteristic
189C22#2257991211yescharacteristic
190C4—21no—
191C4—21no—
192C4—42no—
193C4—41no—
194C4—41no—
195C4—2772no—
196C4—5541no—
197C4—5541no—
198C4—5541no—
199C4—11082no—
200C4—11081no—
201C4—11081no—
202C2—21no—
203C2—21no—
204C2#3179997411yescharacteristic
205C2#3180000911yescharacteristic
206C2#104×D27711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D277
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
Fitting#328×C277C2
socleC22×C277C2×C22⋊C4
prime radicalC23×C277C2×D4
cosocleC22×C4×C277C23
hypercenter#328D277
hypocenterC277#1506
LCSG ▷ C2×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #22579879C4semidirect
9. #22579878C4semidirect
13. Q8×Dic277C4semidirect
15. #22579845C4semidirect
103. C277#1506semidirect

Maximal subgroups

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

subgroupindex
#318005542
#318000562
#317998472
#317997402
#317997392
#317997382
#328×C2772
#1506277