Finite Group Databasebeta

← #47983130

Subgroups — #47983130

Order 35456.

548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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#31800838C211yesmaximal, characteristic
2#31800018C212yesmaximal, complemented
3#31799999C212yesmaximal, complemented
4#31799976C211yesmaximal, characteristic, complemented
5#408×C277C211yesmaximal, characteristic, complemented
6#22579928C412yescomplemented
7#22579927—22no—
8#22579926—22no—
9#22579925—22no—
10#22579925C412yescomplemented
11C2×#17984563—22no—
12C2×#17984563C2212yes—
13#41×D277—24no—
14#22579839C2212yescomplemented
15#22579806—24no—
16#22579805—22no—
17#22579802—22no—
18#22579795—22no—
19C2×#41×C277C2211yescharacteristic
20C2×M16×C277C2211yescharacteristic, complemented
21C22×C8×C277C2211yescharacteristic, complemented
22C22⋊C8×C277—22no—
23#17984564—24no—
24#17984563—24no—
25#17984563—24no—
26#17984563—24no—
27#17984563—22no—
28#17984563—22no—
29#17984563C2×C414yes—
30#17984563D414yes—
31#17984562—28no—
32#17984562—24no—
33C2×Dic554—22no—
34C2×Dic554D412yes—
35Q8×D277—24no—
36C2×D1108—22no—
37C2×D1108D412yes—
38C2×C22⋊D277—24no—
39C2×C22⋊D277—22no—
40D4×D277—28no—
41D4×D277—24no—
42C2×C4×D277—24no—
43C2×C4×D277—22no—
44C4⋊Dic277—22no—
45C22⋊Dic277—22no—
46C4×Dic277—22no—
47#41×C277—22no—
48#41×C277—22no—
49C2×Q8×C277C2×C411yescharacteristic
50C2×D4×C277C2×C411yescharacteristic
51C2×D4×C277D412yes—
52C22×C4×C277D412yes—
53C22×C4×C277C2311yescharacteristic
54M16×C277—22no—
55C2×C8×C277—21no—
56C2×C8×C277—21no—
57C2×C8×C277—22no—
58C22×D277—24no—
59C22×D277—22no—
60Dic554—24no—
61Dic554—22no—
62Dic554C22⋊C414yes—
63D1108—24no—
64D1108—22no—
65D1108C22⋊C414yes—
66C22⋊D277—28no—
67C22⋊D277—24no—
68C22⋊D277—24no—
69C2×Dic277—24no—
70C2×Dic277—22no—
71C2×Dic277—42no—
72C4×D277—28no—
73C4×D277—24no—
74C4×D277—24no—
75C23×C277C22⋊C412yes—
76C23×C277C2×D411yescharacteristic
77Q8×C277—22no—
78D4×C277—24no—
79D4×C277—22no—
80C2×C4×C277—22no—
81C2×C4×C277—22no—
82C2×C4×C277C22⋊C412yes—
83C2×C4×C277C22×C411yescharacteristic
84C2×C4×C277C2×D412yes—
85C2×C4×C277C2×D412yes—
86C2×C4×C277C2×D411yescharacteristic
87C8×C277—41no—
88C8×C277—41no—
89C22×C277—22no—
90C22×C277—41no—
91C22×C277—42no—
92C22×C277C2×C22⋊C411yescharacteristic
93C22×C277#12012yes—
94C2×D277—24no—
95C2×D277—82no—
96C2×D277—84no—
97C4×C277—22no—
98C4×C277C2×C22⋊C412yes—
99C4×C277#12011yescharacteristic
100C4×C277#12011yescharacteristic
101Dic277—24no—
102Dic277—82no—
103C2×C277—22no—
104C2×C277—21no—
105C2×C277—42no—
106C2×C277#37911yescharacteristic
107D277—44no—
108C277#179411yescharacteristic, complemented, Sylow
109#1794—2771nomaximal, Sylow
110#585—2771no—
111#421—2772no—
112#416—2772no—
113#410—2771no—
114#408D27711yescharacteristic, complemented
1152−1+4—2772no—
1162−1+4—5542no—
117H(5,𝔽2)—2772no—
118H(5,𝔽2)—5542no—
119H(5,𝔽2)—5542no—
120C2×#41—2772no—
121C2×#41—5544no—
122C2×#41—5542no—
123C2×#41C2×D27711yescharacteristic
124C2×M16C2×D27711yescharacteristic, complemented
125C22×C8C2×D27711yescharacteristic, complemented
126#117—2772no—
127#104—5544no—
128#103—5542no—
129#102—5542no—
130#99—5542no—
131C22⋊C8—22no—
132#41—22no—
133#41—22no—
134#41—2774no—
135#41—2774no—
136#41—5544no—
137#41—5544no—
138#41—5544no—
139#41—5548no—
140#41—5544no—
141#41—5544no—
142#41—5542no—
143#41—5542no—
144C2×Q8—2772no—
145C2×Q8—5542no—
146C2×Q8—5544no—
147C2×Q8C4×D27711yescharacteristic
148C2×D4—2772no—
149C2×D4—5542no—
150C2×D4—5544no—
151C2×D4—5548no—
152C2×D4—5544no—
153C2×D4—5542no—
154C2×D4C4×D27711yescharacteristic
155C2×D4D110812yes—
156C22×C4—5544no—
157C22×C4—5542no—
158C22×C4C22⋊D27712yes—
159C22×C4C22×D27711yescharacteristic
160M16—22no—
161C2×C8—22no—
162C2×C8—21no—
163C2×C8—21no—
164C4⋊C4—5542no—
165C22⋊C4—5542no—
166C42—5542no—
167C23—5544no—
168C23—5542no—
169C23#1798454012yes—
170C23C2×D110811yescharacteristic
171Q8—22no—
172Q8—2774no—
173Q8—5544no—
174Q8—5542no—
175D4—24no—
176D4—22no—
177D4—2774no—
178D4—5544no—
179D4—5548no—
180D4—5544no—
181D4—5544no—
182D4—5542no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—5548no—
186C2×C4—5544no—
187C2×C4—5542no—
188C2×C4—5544no—
189C2×C4—5544no—
190C2×C4—11082no—
191C2×C4#1798454012yes—
192C2×C4C2×C4×D27711yescharacteristic
193C2×C4D4×D27712yes—
194C2×C4D4×D27712yes—
195C2×C4C2×C22⋊D27711yescharacteristic
196C8—41no—
197C8—41no—
198C22—22no—
199C22—41no—
200C22—42no—
201C22—5544no—
202C22—22162no—
203C22—22164no—
204C22C2×#1798454011yescharacteristic
205C22#2257985012yes—
206C4—22no—
207C4—5544no—
208C4—22162no—
209C4C22⋊C4×D27712yes—
210C4#2257984811yescharacteristic
211C4#2257984811yescharacteristic
212C2—22no—
213C2—21no—
214C2—42no—
215C2—11084no—
216C2#3179985711yescharacteristic
subgroupG/H
centerC4#22579848
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
Fitting#408×C277C2
socleC2×C277#379
prime radical#31800838C2
cosocleC22×C4×C277C23
hypercenter#408D277
hypocenterC277#1794
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #31800018C2semidirect
3. #31799999C2semidirect
4. #31799976C2semidirect
5. #408×C277C2semidirect
6. #22579928C4semidirect
10. #22579925C4semidirect
14. #22579839C22semidirect
20. C2×M16×C277C22semidirect
21. C22×C8×C277C22semidirect
108. C277#1794semidirect
114. #408D277semidirect
124. C2×M16C2×D277semidirect
125. C22×C8C2×D277semidirect

Maximal subgroups

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

subgroupindex
#318008382
#318000182
#317999992
#317999762
#408×C2772
#1794277