Finite Group Databasebeta

← #47983687

Subgroups — #47983687

Order 35456.

312 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 85 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#31800769C211yesmaximal, characteristic
2#31800573C211yesmaximal, characteristic
3#31800010C212yesmaximal, complemented
4#31799758C212yesmaximal, complemented
5#410×C277C211yesmaximal, characteristic
6C22×Dic554C2211yescharacteristic
7#22579887—24no—
8C2×#17984547—22no—
9C2×#17984547C2212yes—
10#22579878C412yescomplemented
11#22579867C412yescomplemented
12#22579861—22no—
13#22579859—22no—
14#22579839C2211yescharacteristic
15#22579803—24no—
16C2×#41×C277C2211yescharacteristic
17#117×C277C2212yes—
18#99×C277—22no—
19C2×Dic554—21no—
20C2×Dic554—22no—
21C2×Dic554—22no—
22C2×Dic554C2×C412yes—
23C22×Dic277—21no—
24#17984547—24no—
25#17984547—22no—
26#17984547—22no—
27C2×#14555660—24no—
28C2×#14555660D414yes—
29C4⋊Dic277—21no—
30#17984542—24no—
31C22⋊Dic277—24no—
32C22⋊Dic277—21no—
33C4×Dic277C2×C412yes—
34#41×C277—22no—
35#41×C277—22no—
36C2×Q8×C277C2×C411yescharacteristic
37C2×D4×C277C2×C411yescharacteristic
38C2×D4×C277D412yes—
39C22×C4×C277D412yes—
40C22×C4×C277C2311yescharacteristic
41C4⋊C4×C277—22no—
42C22⋊C4×C277—22no—
43C42×C277—22no—
44Dic554—24no—
45Dic554—41no—
46Dic554—41no—
47C2×Dic277—22no—
48C2×Dic277—22no—
49C2×Dic277—42no—
50#14555660—24no—
51C23×C277C22⋊C412yes—
52C23×C277C2×D411yescharacteristic
53Q8×C277—22no—
54D4×C277—24no—
55D4×C277—22no—
56C2×C4×C277—22no—
57C2×C4×C277—22no—
58C2×C4×C277—42no—
59C2×C4×C277C22⋊C412yes—
60C2×C4×C277C22×C411yescharacteristic
61C2×C4×C277C2×D412yes—
62C2×C4×C277C2×D411yescharacteristic
63C2×C4×C277#4112yes—
64C22×C277—22no—
65C22×C277—41no—
66C22×C277—42no—
67C22×C277C2×C22⋊C411yescharacteristic
68C22×C277#12112yes—
69C4×C277—22no—
70C4×C277—82no—
71C4×C277C4×D412yes—
72C4×C277#12011yescharacteristic
73C4×C277#12311yescharacteristic
74Dic277—42no—
75Dic277—42no—
76C2×C277—21no—
77C2×C277—22no—
78C2×C277—42no—
79C2×C277#38611yescharacteristic
80C277#190911yescharacteristic, complemented, Sylow
81#1909—2771nomaximal, Sylow
82#568—2771no—
83#536—2771no—
84#419—2772no—
85#410D27711yescharacteristic
86H(3,ℤ/4)—2772no—
87C2×#41C2×D27711yescharacteristic
88C22×Q8—2771no—
89#131—5544no—
90C2×M16—2772no—
91C2×M16—5542no—
92C4⋊Q8—2772no—
93#124—2772no—
94#123—5542no—
95C22⋊Q8—5542no—
96#117—2771no—
97#117C2×D27712yes—
98#103—5544no—
99#99—22no—
100#41—22no—
101#41—22no—
102C2×Q8—2772no—
103C2×Q8—5541no—
104C2×Q8—5542no—
105C2×Q8—5542no—
106C2×Q8C4×D27711yescharacteristic
107C2×D4C4×D27711yescharacteristic
108C2×D4C22⋊D27712yes—
109C22×C4—5541no—
110C22×C4D110812yes—
111C22×C4C22×D27711yescharacteristic
112M16—5544no—
113M16—5542no—
114M16—5542no—
115C2×C8—2774no—
116C2×C8—5544no—
117C4⋊C4—22no—
118C4⋊C4—5544no—
119C4⋊C4—5541no—
120C22⋊C4—22no—
121C22⋊C4—5544no—
122C22⋊C4—5541no—
123C42—22no—
124C42—2772no—
125C23#1798454012yes—
126C23C2×C22⋊D27711yescharacteristic
127Q8—22no—
128Q8—5544no—
129Q8—11081no—
130Q8—11081no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—5542no—
137C2×C4—5542no—
138C2×C4—11082no—
139C2×C4#1798454012yes—
140C2×C4C2×C4×D27711yescharacteristic
141C2×C4D4×D27712yes—
142C2×C4C2×D110811yescharacteristic
143C2×C4#1798456212yes—
144C8—5544no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×#1798454011yescharacteristic
149C22#2257985212yes—
150C4—22no—
151C4—82no—
152C4—11082no—
153C4—11082no—
154C4#2257984012yes—
155C4#2257985011yescharacteristic
156C4#2257986411yescharacteristic
157C2—22no—
158C2—21no—
159C2—42no—
160C2#3179987911yescharacteristic
subgroupG/H
centerC2#31799879
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
Fitting#410×C277C2
socleC2×C277#386
prime radicalC2×#41×C277C22
cosocleC22×C4×C277C23
hypercenter#410D277
hypocenterC277#1909
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #31800010C2semidirect
4. #31799758C2semidirect
10. #22579878C4semidirect
11. #22579867C4semidirect
80. C277#1909semidirect

Maximal subgroups

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

subgroupindex
#318007692
#318005732
#318000102
#317997582
#410×C2772
#1909277