Finite Group Databasebeta

← #47983120

Subgroups — #47983120

Order 35456.

620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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×#22579925C211yesmaximal, characteristic
2C2×#22579808C212yesmaximal, complemented
3#31800001C212yesmaximal, complemented
4C2×#22579797C211yesmaximal, characteristic, complemented
5#390×C277C211yesmaximal, characteristic, complemented
6#22579925—24no—
7#22579925—22no—
8#22579925C414yescomplemented
9C2×#17984563C2212yes—
10C2×#17984562—22no—
11C22×C22⋊D277—22no—
12C2×D4×D277—22no—
13C2×#17984547C2212yescomplemented
14#22579808—24no—
15#22579803—22no—
16#22579800—22no—
17#22579797—22no—
18C22×D4×C277C2211yescharacteristic
19C2×C4⋊C4×C277C2211yescharacteristic, complemented
20C2×C22⋊C4×C277—22no—
21C2×C42×C277C2211yescharacteristic, complemented
22C23×D277—22no—
23#17984563—22no—
24#17984563—22no—
25#17984563C2×C414yes—
26#17984563D414yes—
27#17984562—28no—
28#17984562—28no—
29C2×Dic554D412yes—
30C2×D1108D412yes—
31C2×C22⋊D277—24no—
32C2×C22⋊D277—28no—
33C2×C22⋊D277—28no—
34C2×C22⋊D277—22no—
35D4×D277—28no—
36D4×D277—28no—
37C22×Dic277—22no—
38C2×C4×D277—22no—
39#17984547—22no—
40#17984547—22no—
41C2×#14555660—22no—
42C24×C277D412yes—
43C2×D4×C277—22no—
44C2×D4×C277—22no—
45C2×D4×C277C2×C412yes—
46C2×D4×C277D412yes—
47C22×C4×C277—21no—
48C22×C4×C277—21no—
49C22×C4×C277C2311yescharacteristic
50C4⋊C4×C277—22no—
51C22⋊C4×C277—44no—
52C42×C277—22no—
53C22×D277—22no—
54C22×D277—28no—
55C22×D277—82no—
56C22×D277—82no—
57Dic554—22no—
58Dic554C22⋊C414yescomplemented
59D1108—22no—
60D1108C22⋊C414yescomplemented
61C22⋊D277—216no—
62C22⋊D277—24no—
63C22⋊D277—24no—
64C2×Dic277—28no—
65C2×Dic277—22no—
66C4×D277—24no—
67C4×D277—24no—
68#14555660—42no—
69C23×C277—22no—
70C23×C277—22no—
71C23×C277—42no—
72C23×C277—42no—
73C23×C277C22⋊C414yes—
74C23×C277C2×D411yescharacteristic
75D4×C277—24no—
76D4×C277—24no—
77C2×C4×C277—22no—
78C2×C4×C277—41no—
79C2×C4×C277—41no—
80C2×C4×C277—42no—
81C2×C4×C277—41no—
82C2×C4×C277C22×C411yescharacteristic
83C2×C4×C277C2×D412yes—
84C2×C4×C277C2×D412yes—
85C2×C4×C277C2×D411yescharacteristic
86C22×C277—21no—
87C22×C277—21no—
88C22×C277—24no—
89C22×C277—44no—
90C22×C277—42no—
91C22×C277—42no—
92C22×C277—82no—
93C22×C277C2×C22⋊C411yescharacteristic
94C22×C277#12011yescharacteristic
95C22×C277#12011yescharacteristic
96C2×D277—24no—
97C2×D277—42no—
98C2×D277—42no—
99C2×D277—88no—
100C4×C277—42no—
101C4×C277—81no—
102C4×C277C2×C22⋊C412yes—
103C4×C277#12012yes—
104Dic277—24no—
105C2×C277—21no—
106C2×C277—21no—
107C2×C277—44no—
108C2×C277#37911yescharacteristic
109C2×C277#45311yescharacteristic
110C2×C277#45511yescharacteristic
111D277—44no—
112C277#179211yescharacteristic, complemented, Sylow
113#1792—2771nomaximal, Sylow
114C2×H(5,𝔽2)—2771no—
115C2×#104—2772no—
116#417—2772no—
117C2×#100—2771no—
118#390D27711yescharacteristic, complemented
119H(5,𝔽2)—2774no—
120H(5,𝔽2)—5544no—
121H(5,𝔽2)—5542no—
122C2×#41—2772no—
123C2×#41—5542no—
124C22×D4—5542no—
125C22×D4—5542no—
126C22×D4C2×D27711yescharacteristic
127C2×M16—2772no—
128C2×C4⋊C4C2×D27711yescharacteristic, complemented
129C2×C22⋊C4—22no—
130C2×C42C2×D27711yescharacteristic, complemented
131#104—5544no—
132#103—5542no—
133#102—5542no—
134#100—5542no—
135C24—5542no—
136C24C22⋊D27712yes—
137#41—2774no—
138#41—2774no—
139#41—5548no—
140#41—5548no—
141#41—5542no—
142#41—5542no—
143C2×Q8—2772no—
144C2×D4—22no—
145C2×D4—22no—
146C2×D4—2772no—
147C2×D4—5548no—
148C2×D4—5548no—
149C2×D4—5544no—
150C2×D4—5548no—
151C2×D4—5548no—
152C2×D4—5542no—
153C2×D4C4×D27712yes—
154C2×D4D110812yes—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—5542no—
158C22×C4—5542no—
159C22×C4C22×D27711yescharacteristic
160M16—5542no—
161M16—5542no—
162C2×C8—5542no—
163C4⋊C4—22no—
164C22⋊C4—44no—
165C42—22no—
166C23—22no—
167C23—22no—
168C23—42no—
169C23—42no—
170C23—5548no—
171C23—5542no—
172C23—22162no—
173C23—22162no—
174C23#1798454014yes—
175C23C2×C22⋊D27711yescharacteristic
176Q8—2774no—
177Q8—5542no—
178D4—24no—
179D4—24no—
180D4—2774no—
181D4—55416no—
182D4—5544no—
183D4—5544no—
184D4—5542no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—41no—
190C2×C4—5548no—
191C2×C4—5542no—
192C2×C4—5544no—
193C2×C4—5544no—
194C2×C4C2×C4×D27711yescharacteristic
195C2×C4D4×D27712yes—
196C2×C4D4×D27712yes—
197C2×C4C2×D110811yescharacteristic
198C8—11082no—
199C22—21no—
200C22—21no—
201C22—24no—
202C22—44no—
203C22—42no—
204C22—42no—
205C22—82no—
206C22—5544no—
207C22—11082no—
208C22—11082no—
209C22—22168no—
210C22C2×#1798454011yescharacteristic
211C22#2257984811yescharacteristic
212C22#2257984811yescharacteristic
213C4—42no—
214C4—81no—
215C4—5544no—
216C4C22⋊C4×D27712yes—
217C4#2257985012yes—
218C2—21no—
219C2—21no—
220C2—44no—
221C2—11084no—
222C2#3179985711yescharacteristic
223C2#3180016911yescharacteristic
224C2#3180017911yescharacteristic
subgroupG/H
centerC22#22579848
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
Fitting#390×C277C2
socleC22×C277#120
prime radicalC2×#22579925C2
cosocleC22×C4×C277C23
hypercenter#390D277
hypocenterC277#1792
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#22579808C2semidirect
3. #31800001C2semidirect
4. C2×#22579797C2semidirect
5. #390×C277C2semidirect
8. #22579925C4semidirect
13. C2×#17984547C22semidirect
19. C2×C4⋊C4×C277C22semidirect
21. C2×C42×C277C22semidirect
58. Dic554C22⋊C4semidirect
60. D1108C22⋊C4semidirect
112. C277#1792semidirect
118. #390D277semidirect
128. C2×C4⋊C4C2×D277semidirect
130. C2×C42C2×D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225799252
C2×#225798082
#318000012
C2×#225797972
#390×C2772
#1792277