Finite Group Databasebeta

← #1614×C277 #47979003

Subgroups — #1614×C277 #47979003

Order 35456.

236 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 68 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#543×C277C211yesmaximal, characteristic
2#484×C277C212yesmaximal, complemented
3#399×C277C211yesmaximal, characteristic
4#328×C277C212yesmaximal, complemented
5#323×C277C211yesmaximal, characteristic
6C22⋊Q8×C277—22no—
7C22⋊Q8×C277—21no—
8C22⋊Q8×C277—22no—
9C22⋊Q8×C277C2212yes—
10C2×C4⋊C4×C277—21no—
11C2×C4⋊C4×C277C2211yescharacteristic
12C2×C22⋊C4×C277—21no—
13C2×C22⋊C4×C277—21no—
14C2×C22⋊C4×C277C2211yescharacteristic
15#107×C277—22no—
16#103×C277—22no—
17C22⋊C8×C277C2212yes—
18#95×C277C2211yescharacteristic
19C24×C277D411yescharacteristic
20C2×Q8×C277—21no—
21C2×Q8×C277D412yes—
22C22×C4×C277—21no—
23C22×C4×C277—21no—
24C22×C4×C277—21no—
25C22×C4×C277—21no—
26C22×C4×C277D411yescharacteristic
27C22×C4×C277C2311yescharacteristic
28C2×C8×C277—22no—
29C4⋊C4×C277—21no—
30C4⋊C4×C277—22no—
31C4⋊C4×C277—22no—
32C4⋊C4×C277—22no—
33C4⋊C4×C277—42no—
34C4⋊C4×C277D412yes—
35C22⋊C4×C277—22no—
36C22⋊C4×C277—22no—
37C22⋊C4×C277—22no—
38C22⋊C4×C277—42no—
39C23×C277—21no—
40C23×C277—21no—
41C23×C277—41no—
42C23×C277—41no—
43C23×C277Q1612yes—
44C23×C277C2×D411yescharacteristic
45Q8×C277—42no—
46Q8×C277—81no—
47C2×C4×C277—22no—
48C2×C4×C277—22no—
49C2×C4×C277—21no—
50C2×C4×C277—22no—
51C2×C4×C277—41no—
52C2×C4×C277—41no—
53C2×C4×C277—41no—
54C2×C4×C277—41no—
55C2×C4×C277—41no—
56C2×C4×C277—41no—
57C2×C4×C277—41no—
58C2×C4×C277—81no—
59C2×C4×C277—81no—
60C2×C4×C277C2×D412yes—
61C8×C277—42no—
62C22×C277—21no—
63C22×C277—21no—
64C22×C277—22no—
65C22×C277—42no—
66C22×C277—41no—
67C22×C277—41no—
68C22×C277—81no—
69C22×C277#12011yescharacteristic
70C22×C277C2×Q1611yescharacteristic
71C22×C277#13711yescharacteristic
72C4×C277—22no—
73C4×C277—42no—
74C4×C277—41no—
75C4×C277—42no—
76C4×C277—42no—
77C4×C277—81no—
78C2×C277—21no—
79C2×C277—21no—
80C2×C277—42no—
81C2×C277#45111yescharacteristic
82C2×C277#45311yescharacteristic
83C2×C277#45811yescharacteristic
84C277#161411yescharacteristic, direct product factor, Sylow
85#1614C27711yesmaximal, characteristic, direct product factor, Sylow
86#543C2×C27711yescharacteristic
87#484C2×C27712yescomplemented
88#399C2×C27711yescharacteristic
89#328C2×C27712yescomplemented
90#323C2×C27711yescharacteristic
91C22⋊Q8—22no—
92C22⋊Q8—21no—
93C22⋊Q8—22no—
94C22⋊Q8C22×C27712yes—
95C2×C4⋊C4—21no—
96C2×C4⋊C4C22×C27711yescharacteristic
97C2×C22⋊C4—21no—
98C2×C22⋊C4—21no—
99C2×C22⋊C4C22×C27711yescharacteristic
100#107—22no—
101#103—22no—
102C22⋊C8C22×C27712yes—
103#95C22×C27711yescharacteristic
104C24D4×C27711yescharacteristic
105C2×Q8—21no—
106C2×Q8D4×C27712yes—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4D4×C27711yescharacteristic
112C22×C4C23×C27711yescharacteristic
113C2×C8—22no—
114C4⋊C4—21no—
115C4⋊C4—22no—
116C4⋊C4—22no—
117C4⋊C4—22no—
118C4⋊C4—42no—
119C4⋊C4D4×C27712yes—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C22⋊C4—22no—
123C22⋊C4—42no—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23Q16×C27712yes—
129C23C2×D4×C27711yescharacteristic
130Q8—42no—
131Q8—81no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—81no—
144C2×C4—81no—
145C2×C4C2×D4×C27712yes—
146C8—42no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#120×C27711yescharacteristic
155C22C2×Q16×C27711yescharacteristic
156C22#137×C27711yescharacteristic
157C4—22no—
158C4—42no—
159C4—41no—
160C4—42no—
161C4—42no—
162C4—81no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#451×C27711yescharacteristic
167C2#453×C27711yescharacteristic
168C2#458×C27711yescharacteristic
subgroupG/H
center, socleC22×C277#120
commutator, Frattini, cosocleC22×C4C23×C277
prime radicalC24×C277D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C277 ◁ C22×C4×C277 ◁ G

Complements

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

NH ≅ G/Ntype
2. #484×C277C2semidirect
4. #328×C277C2semidirect
84. C277#1614direct (N × H)
85. #1614C277direct (N × H)
87. #484C2×C277semidirect
89. #328C2×C277semidirect

Maximal subgroups

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

subgroupindex
#543×C2772
#484×C2772
#399×C2772
#328×C2772
#323×C2772
#1614277