Finite Group Databasebeta

← #47985666

Subgroups — #47985666

Order 35456.

1224 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 249 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
1C24×Dic277C211yesmaximal, characteristic, complemented
2C2×#22579849C211yesmaximal, characteristic
3C2×#22579840C213yesmaximal, complemented
4#31799879C213yesmaximal, complemented
5#31799874C213yesmaximal, complemented
6C22⋊C4×Dic277C213yesmaximal, complemented
7#379×C277C211yesmaximal, characteristic, complemented
8C22×C22⋊D277C2213yes—
9C23×Dic277—212no—
10C23×Dic277C2213yes—
11C23×Dic277C2213yes—
12C22×C4×D277C2211yescharacteristic, complemented
13#22579849C418yescomplemented
14#22579840—212no—
15C2×#17984542C2213yescomplemented
16C2×C22⋊Dic277C2213yes—
17C2×#17984540C2213yescomplemented
18C2×C4×Dic277C2213yescomplemented
19#22579787C2216yescomplemented
20C25×C277C2211yescharacteristic
21C2×C22⋊C4×C277C2213yes—
22C2×C22⋊C4×C277C2213yes—
23C23×D277C2311yescharacteristic
24C2×C22⋊D277—26no—
25C2×C22⋊D277—26no—
26C2×C22⋊D277C2×C4112yescomplemented
27C22×Dic277—232no—
28C22×Dic277—212no—
29C22×Dic277—212no—
30C22×Dic277—26no—
31C22×Dic277D4112yescomplemented
32C22×Dic277C2313yes—
33C22×Dic277C2313yes—
34C22×Dic277C2311yescharacteristic
35C2×C4×D277—26no—
36#17984542—26no—
37C22⋊Dic277C2×C4112yescomplemented
38#17984540—26no—
39C4×Dic277—26no—
40C24×C277—26no—
41C24×C277—26no—
42C24×C277C2×C414yescomplemented
43C24×C277C2313yes—
44C22×C4×C277C2313yes—
45C22×C4×C277C2311yescharacteristic
46C22⋊C4×C277—26no—
47C22⋊C4×C277—26no—
48C22×D277—23no—
49C22×D277—23no—
50C22×D277C22×C412yescomplemented
51C22⋊D277—224no—
52C2×Dic277—224no—
53C2×Dic277—23no—
54C2×Dic277—26no—
55C2×Dic277—23no—
56C2×Dic277—224no—
57C2×Dic277C22×C416yescomplemented
58C2×Dic277C2×D416yes—
59C2×Dic277C2×D416yes—
60C4×D277—44no—
61C23×C277—224no—
62C23×C277—28no—
63C23×C277—224no—
64C23×C277—26no—
65C23×C277—26no—
66C23×C277C22×C416yes—
67C23×C277C2×D416yes—
68C23×C277#4116yes—
69C23×C277C2411yescharacteristic
70C2×C4×C277—23no—
71C2×C4×C277—23no—
72C2×C4×C277—26no—
73C22×C277—232no—
74C22×C277—212no—
75C22×C277—26no—
76C22×C277—26no—
77C22×C277—212no—
78C22×C277C4×D4112yescomplemented
79C22×C277C23×C411yescharacteristic
80C22×C277C22×D413yes—
81C22×C277C2×#4113yes—
82C2×D277—26no—
83C2×D277—41no—
84C2×D277—43no—
85C4×C277—41no—
86C4×C277—43no—
87Dic277—26no—
88Dic277—26no—
89Dic277#12014yescomplemented
90C2×C277—212no—
91C2×C277C2×C4×D413yes—
92C2×C277C2×#12011yescharacteristic
93C2×C277#52513yes—
94D277—42no—
95C277C4×#12011yescharacteristic, complemented, Sylow
96C4×#120—2771nomaximal, Sylow
97C24×C4—2771no—
98C2×#120—2771no—
99C2×C4×D4—2773no—
100#386—2773no—
101#385—2773no—
102#379D27711yescharacteristic, complemented
103C4×C22⋊C4—2773no—
104C25C2×D27711yescharacteristic
105C22×D4—2773no—
106C23×C4—2773no—
107C23×C4—2773no—
108C23×C4—2771no—
109C23×C4—55412no—
110#120—2778no—
111C4×D4—55412no—
112C2×C4⋊C4—2773no—
113C2×C22⋊C4—2773no—
114C2×C22⋊C4—2773no—
115C2×C22⋊C4C2×D27713yes—
116C2×C22⋊C4C2×D27713yes—
117C2×C42—2773no—
118#95—2776no—
119C24—26no—
120C24—26no—
121C24—2771no—
122C24C4×D27714yescomplemented
123C24C22×D27713yes—
124C2×D4—27712no—
125C2×D4—5546no—
126C2×D4—5546no—
127C22×C4—2771no—
128C22×C4—27712no—
129C22×C4—2773no—
130C22×C4—2773no—
131C22×C4—5546no—
132C22×C4—55412no—
133C22×C4—55412no—
134C22×C4—55432no—
135C22×C4—5546no—
136C22×C4C22×D27713yes—
137C22×C4C22×D27711yescharacteristic
138C4⋊C4—5546no—
139C22⋊C4—26no—
140C22⋊C4—26no—
141C22⋊C4—27712no—
142C22⋊C4—5546no—
143C42—5546no—
144C23—28no—
145C23—224no—
146C23—224no—
147C23—26no—
148C23—26no—
149C23—2772no—
150C23—5543no—
151C23—5543no—
152C23C2×C4×D27716yes—
153C23D4×D27716yes—
154C23#1798456216yes—
155C23C23×D27711yescharacteristic
156D4—55424no—
157C2×C4—23no—
158C2×C4—23no—
159C2×C4—26no—
160C2×C4—2776no—
161C2×C4—2776no—
162C2×C4—2776no—
163C2×C4—55424no—
164C2×C4—55424no—
165C2×C4—5543no—
166C2×C4—5546no—
167C2×C4—5543no—
168C2×C4—11084no—
169C22—232no—
170C22—212no—
171C22—26no—
172C22—26no—
173C22—212no—
174C22—5546no—
175C22—11081no—
176C22—11083no—
177C22#22579840112yescomplemented
178C22C22×C4×D27711yescharacteristic
179C22C2×D4×D27713yes—
180C22C2×#1798456213yes—
181C4—41no—
182C4—43no—
183C4—2774no—
184C4—5546no—
185C4—5546no—
186C2—212no—
187C2—11082no—
188C2C2×#2257984013yes—
189C2#120×D27711yescharacteristic
190C2#3180050813yes—
subgroupG/H
center, FrattiniC23C23×D277
commutatorC22×C277C23×C4
Fitting#379×C277C2
socle, cosocleC23×C277C24
prime radicalC2×#22579849C2
hypercenter#379D277
hypocenterC277C4×#120
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C24×Dic277C2semidirect
3. C2×#22579840C2semidirect
4. #31799879C2semidirect
5. #31799874C2semidirect
6. C22⋊C4×Dic277C2semidirect
7. #379×C277C2semidirect
12. C22×C4×D277C22semidirect
13. #22579849C4semidirect
15. C2×#17984542C22semidirect
17. C2×#17984540C22semidirect
18. C2×C4×Dic277C22semidirect
19. #22579787C22semidirect
26. C2×C22⋊D277C2×C4semidirect
31. C22×Dic277D4semidirect
37. C22⋊Dic277C2×C4semidirect
42. C24×C277C2×C4semidirect
50. C22×D277C22×C4semidirect
57. C2×Dic277C22×C4semidirect
78. C22×C277C4×D4semidirect
89. Dic277#120semidirect
95. C277C4×#120semidirect
102. #379D277semidirect
122. C24C4×D277semidirect
177. C22#22579840semidirect

Maximal subgroups

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

subgroupindex
C24×Dic2772
C2×#225798492
C2×#225798402
#317998792
#317998742
C22⋊C4×Dic2772
#379×C2772
C4×#120277