Finite Group Databasebeta

← #47981664

Subgroups — #47981664

Order 35456.

240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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#31800052C211yesmaximal, characteristic
3#31799853C211yesmaximal, 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×#17984542—21no—
18C2×C4×Dic277—21no—
19C2×C4×Dic277C2211yescharacteristic
20#22579809—21no—
21C22⋊#14555660C2211yescharacteristic
22C8×Dic277—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—24no—
36#17984542—21no—
37#17984542—21no—
38#17984542—21no—
39#17984542—21no—
40#17984542—21no—
41C22⋊Dic277—21no—
42C4×Dic277—21no—
43C4×Dic277—21no—
44C4×Dic277—42no—
45C4×Dic277C2×C411yescharacteristic
46C4×Dic277C2×C411yescharacteristic
47C4×Dic277D411yescharacteristic
48C4×Dic277D411yescharacteristic
49C2×Q8×C277C2×C411yescharacteristic
50C22×C4×C277—21no—
51C22×C4×C277C2311yescharacteristic
52C2×C8×C277—21no—
53C4⋊C4×C277—21no—
54C4⋊C4×C277C2×C411yescharacteristic
55C22⋊C4×C277—21no—
56Dic554—42no—
57Dic554—41no—
58C2×Dic277—22no—
59C2×Dic277—22no—
60C2×Dic277—21no—
61C2×Dic277—21no—
62C2×Dic277—41no—
63C2×Dic277—41no—
64C2×Dic277C22⋊C411yescharacteristic
65C2×Dic277C22⋊C411yescharacteristic
66C2×Dic277C22⋊C411yescharacteristic
67C2×Dic277C22⋊C411yescharacteristic
68C2×Dic277SD1612yes—
69C2×Dic277Q1612yes—
70#14555660—41no—
71C23×C277C2×D411yescharacteristic
72Q8×C277—41no—
73C2×C4×C277—22no—
74C2×C4×C277—21no—
75C2×C4×C277—21no—
76C2×C4×C277—41no—
77C2×C4×C277—41no—
78C2×C4×C277—41no—
79C2×C4×C277C22×C411yescharacteristic
80C2×C4×C277C2×D411yescharacteristic
81C8×C277—41no—
82C22×C277—21no—
83C22×C277—21no—
84C22×C277C2×C22⋊C411yescharacteristic
85C22×C277C2×SD1611yescharacteristic
86C22×C277C2×Q1611yescharacteristic
87C4×C277—21no—
88C4×C277—21no—
89C4×C277—42no—
90C4×C277—41no—
91C4×C277—41no—
92Dic277—21no—
93Dic277—42no—
94Dic277—41no—
95Dic277—41no—
96Dic277#10312yes—
97Dic277#10312yes—
98Dic277#10412yes—
99C2×C277—21no—
100C2×C277—21no—
101C2×C277#41011yescharacteristic
102C2×C277C2×#10311yescharacteristic
103C2×C277C2×#10411yescharacteristic
104C277#150311yescharacteristic, complemented, Sylow
105#1503—2771nomaximal, Sylow
106#533—2771no—
107#431—2771no—
108C4×C4⋊C4—2771no—
109#328—2771no—
110#328—2771no—
111#328—2771no—
112#328D27711yescharacteristic
113C4⋊Q8—2771no—
114C4⋊Q8—2771no—
115#125—5541no—
116C22⋊Q8—2771no—
117C22⋊Q8—5541no—
118C22⋊Q8C2×D27711yescharacteristic
119C4×Q8—2771no—
120C4×Q8—2771no—
121C4×Q8—5541no—
122#117—5541no—
123C2×C4⋊C4—5541no—
124C2×C42—2771no—
125C2×C42—5541no—
126C4⋊C8—5541no—
127C22⋊C8—2771no—
128C22⋊C8C2×D27711yescharacteristic
129C4×C8—5541no—
130#95—2771no—
131#95C2×D27711yescharacteristic
132C2×Q8—2771no—
133C2×Q8—5541no—
134C2×Q8C4×D27711yescharacteristic
135C22×C4—21no—
136C22×C4—2771no—
137C22×C4—2771no—
138C22×C4—5541no—
139C22×C4C22×D27711yescharacteristic
140C2×C8—21no—
141C2×C8—5541no—
142C4⋊C4—21no—
143C4⋊C4—2771no—
144C4⋊C4—5541no—
145C4⋊C4—5541no—
146C4⋊C4—5541no—
147C4⋊C4—5541no—
148C4⋊C4—5541no—
149C4⋊C4—5544no—
150C4⋊C4—5541no—
151C4⋊C4C4×D27711yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—5541no—
154C42—2771no—
155C42—2771no—
156C42—2771no—
157C42—2771no—
158C42—5541no—
159C42—5541no—
160C42—11082no—
161C23D4×D27711yescharacteristic
162Q8—41no—
163Q8—11081no—
164Q8—11082no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—2771no—
172C2×C4—2771no—
173C2×C4—2771no—
174C2×C4—2772no—
175C2×C4—2772no—
176C2×C4—2771no—
177C2×C4—5542no—
178C2×C4—5542no—
179C2×C4—5541no—
180C2×C4—5541no—
181C2×C4—11081no—
182C2×C4—11081no—
183C2×C4C2×C4×D27711yescharacteristic
184C2×C4D4×D27711yescharacteristic
185C8—41no—
186C8—11081no—
187C22—21no—
188C22—21no—
189C22C22⋊C4×D27711yescharacteristic
190C22SD16×D27711yescharacteristic
191C22Q16×D27711yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—41no—
196C4—41no—
197C4—2772no—
198C4—2772no—
199C4—2772no—
200C4—5541no—
201C4—11082no—
202C4—11081no—
203C4—11081no—
204C2—21no—
205C2—21no—
206C2#3179997411yescharacteristic
207C2#103×D27711yescharacteristic
208C2#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#1503
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
104. C277#1503semidirect

Maximal subgroups

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

subgroupindex
#318005542
#318000522
#317998532
#317997402
#317997392
#317997382
#328×C2772
#1503277