Finite Group Databasebeta

← #399×D277 #47986413

Subgroups — #399×D277 #47986413

Order 35456.

908 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 203 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
1C2×C4⋊C4×D277C213yesmaximal, complemented
2C2×C22⋊C4×D277C213yesmaximal
3#31799939C211yesmaximal, characteristic, complemented
4#31799938C213yesmaximal, complemented
5#31799937C213yesmaximal, complemented
6#95×D277C211yesmaximal, characteristic, complemented
7#399×C277C211yesmaximal, characteristic, complemented
8C24×D277C2211yescharacteristic
9C22×C4×D277C2213yes—
10C22×C4×D277C2213yes—
11C2×C4⋊Dic277C2213yescomplemented
12C2×#17984542C2216yescomplemented
13C4⋊C4×D277—212no—
14C2×C22⋊Dic277C2213yes—
15C2×#17984540C2213yes—
16C2×#17984540C2213yes—
17C22⋊C4×D277—212no—
18#22579787C2213yescomplemented
19C2×C4⋊C4×C277C2213yescomplemented
20C2×C22⋊C4×C277C2213yes—
21#95×C277C2211yescharacteristic, complemented
22C23×D277—26no—
23C23×D277—26no—
24C23×D277Q814yes—
25C23×D277C2311yescharacteristic
26C23×D277C2311yescharacteristic
27C22×Dic277C2313yes—
28C22×Dic277C2313yes—
29C2×C4×D277—212no—
30C2×C4×D277—26no—
31C2×C4×D277—212no—
32C2×C4×D277D4112yes—
33C4⋊Dic277—26no—
34#17984542—212no—
35C22⋊Dic277—26no—
36#17984540—26no—
37#17984540—26no—
38C24×C277C2311yescharacteristic
39C22×C4×C277C2313yes—
40C22×C4×C277C2313yes—
41C4⋊C4×C277—26no—
42C22⋊C4×C277—26no—
43C22×D277—23no—
44C22×D277—23no—
45C22×D277—224no—
46C22×D277—412no—
47C22×D277—44no—
48C22×D277C2×D416yes—
49C22×D277C2×Q812yes—
50C22×D277C2×Q812yes—
51C22×D277#4116yes—
52C2×Dic277—26no—
53C2×Dic277—23no—
54C2×Dic277—26no—
55C2×Dic277C2×D416yes—
56C4×D277—224no—
57C4×D277—412no—
58C23×C277—23no—
59C23×C277—23no—
60C23×C277C2×Q812yes—
61C23×C277C2411yescharacteristic
62C2×C4×C277—26no—
63C2×C4×C277—23no—
64C2×C4×C277—26no—
65C2×C4×C277C2×D416yes—
66C22×C277—26no—
67C22×C277—43no—
68C22×C277—41no—
69C22×C277C22×D413yes—
70C22×C277C22×Q811yescharacteristic
71C22×C277C2×#4113yes—
72C2×D277—26no—
73C2×D277—43no—
74C2×D277—41no—
75C2×D277—416no—
76C2×D277C22⋊Q8112yes—
77C2×D277#123112yes—
78C2×D277#12714yes—
79C4×C277—26no—
80C4×C277—43no—
81Dic277—26no—
82Dic277—43no—
83C2×C277—42no—
84C2×C277C2×C22⋊Q813yes—
85C2×C277C2×#12313yes—
86C2×C277C2×#12711yescharacteristic
87D277—42no—
88D277#39918yesdirect product factor
89C277C2×#39911yescharacteristic, complemented, Sylow
90C2×#399—2771nomaximal, Sylow
91C22×C4⋊C4—2773no—
92C22×C22⋊C4—2773no—
93#399—2773no—
94#399—2773no—
95#399—2771no—
96#399D27711yescharacteristic, direct product factor
97C2×#95—2771no—
98C25—2771no—
99C23×C4—2773no—
100C23×C4—2773no—
101C2×C4⋊C4—2776no—
102C2×C4⋊C4—2773no—
103C2×C4⋊C4—55412no—
104C2×C4⋊C4C2×D27713yescomplemented
105C2×C22⋊C4—2773no—
106C2×C22⋊C4—2773no—
107C2×C22⋊C4—2773no—
108C2×C22⋊C4—55412no—
109C2×C22⋊C4C2×D27713yes—
110#95—2773no—
111#95C2×D27711yescharacteristic, complemented
112C24—2771no—
113C24—2774no—
114C24—2771no—
115C24—5546no—
116C24—5546no—
117C24C22×D27711yescharacteristic
118C22×C4—2773no—
119C22×C4—27712no—
120C22×C4—2773no—
121C22×C4—55412no—
122C22×C4—5546no—
123C22×C4—55412no—
124C22×C4C22×D27713yes—
125C22×C4C22×D27713yes—
126C4⋊C4—26no—
127C4⋊C4—55412no—
128C4⋊C4—5546no—
129C22⋊C4—26no—
130C22⋊C4—5546no—
131C22⋊C4—5546no—
132C22⋊C4—5546no—
133C23—23no—
134C23—23no—
135C23—2776no—
136C23—2772no—
137C23—2776no—
138C23—2772no—
139C23—55424no—
140C23—5543no—
141C23—5543no—
142C23—110812no—
143C23—11084no—
144C23Q8×D27712yes—
145C23C23×D27711yescharacteristic
146C2×C4—26no—
147C2×C4—23no—
148C2×C4—26no—
149C2×C4—2776no—
150C2×C4—55424no—
151C2×C4—5546no—
152C2×C4—5543no—
153C2×C4—5546no—
154C2×C4—110812no—
155C2×C4D4×D27716yes—
156C22—26no—
157C22—43no—
158C22—41no—
159C22—27712no—
160C22—27712no—
161C22—2774no—
162C22—5546no—
163C22—110816no—
164C22—11083no—
165C22—11081no—
166C22C2×D4×D27713yes—
167C22C2×Q8×D27711yescharacteristic
168C22#41×D27713yes—
169C4—26no—
170C4—43no—
171C4—5546no—
172C4—11083no—
173C2—42no—
174C2—2778no—
175C2—11082no—
176C2C22⋊Q8×D27713yes—
177C2#123×D27713yes—
178C2#127×D27711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D277
commutator, socle, cosocleC23×C277C24
Fitting#399×C277C2
prime radicalC24×D277C22
hypercenter#399D277
hypocenterC277C2×#399
LCSG ▷ C23×C277 ▷ C277
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D277C2semidirect
3. #31799939C2semidirect
4. #31799938C2semidirect
5. #31799937C2semidirect
6. #95×D277C2semidirect
7. #399×C277C2semidirect
11. C2×C4⋊Dic277C22semidirect
12. C2×#17984542C22semidirect
18. #22579787C22semidirect
19. C2×C4⋊C4×C277C22semidirect
21. #95×C277C22semidirect
88. D277#399direct (N × H)
89. C277C2×#399semidirect
96. #399D277direct (N × H)
104. C2×C4⋊C4C2×D277semidirect
111. #95C2×D277semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D2772
C2×C22⋊C4×D2772
#317999392
#317999382
#317999372
#95×D2772
#399×C2772
C2×#399277