Finite Group Databasebeta

← #47983569

Subgroups — #47983569

Order 35456.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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×#22579868C211yesmaximal, characteristic
2#31800479C211yesmaximal, characteristic, complemented
3#31800008C211yesmaximal, characteristic
4#31800006C211yesmaximal, characteristic
5C2×#22579798C211yesmaximal, characteristic, complemented
6#31799762C211yesmaximal, characteristic, complemented
7#339×C277C211yesmaximal, characteristic, complemented
8C22×Dic554C2211yescharacteristic
9C22×D1108C2211yescharacteristic
10C2×#17984547C2211yescharacteristic
11#22579868—22no—
12#22579868C414yescomplemented
13C4×Dic554—22no—
14#22579845—22no—
15#22579839C2211yescharacteristic
16#22579836—22no—
17C2×#17984540—22no—
18#22579802—22no—
19#22579800—22no—
20#22579798—22no—
21C2×M16×C277C2211yescharacteristic
22#117×C277C2211yescharacteristic
23C2×C42×C277C2211yescharacteristic
24C23×D277—21no—
25C2×Dic554—21no—
26C2×Dic554—21no—
27C2×Dic554—21no—
28C2×Dic554—21no—
29C2×Dic554C2×C412yes—
30C2×Dic554D412yes—
31C2×D1108—21no—
32C2×D1108—21no—
33C2×D1108—21no—
34C2×D1108—21no—
35C2×D1108—21no—
36C2×D1108C2×C412yes—
37C22×Dic277D412yes—
38#17984547—21no—
39#17984547—21no—
40C2×#14555660—21no—
41C4⋊Dic277D412yes—
42#17984542—24no—
43C22⋊Dic277—21no—
44#17984540—28no—
45C4×Dic277—24no—
46C4×Dic277—21no—
47C22×C4×C277—21no—
48C22×C4×C277C2311yescharacteristic
49M16×C277—21no—
50M16×C277—21no—
51C2×C8×C277—21no—
52C4⋊C4×C277D412yes—
53C22⋊C4×C277—21no—
54C42×C277—21no—
55C42×C277—21no—
56C42×C277C2×C412yes—
57C22×D277—22no—
58C22×D277—44no—
59C22×D277—41no—
60C22×D277—41no—
61Dic554—22no—
62Dic554—22no—
63Dic554—22no—
64Dic554—22no—
65D1108—22no—
66D1108—22no—
67D1108—41no—
68D1108—41no—
69C2×Dic277—22no—
70C2×Dic277—22no—
71C2×Dic277—22no—
72C2×Dic277C22⋊C414yes—
73#14555660—41no—
74C23×C277C2×D411yescharacteristic
75C2×C4×C277—22no—
76C2×C4×C277—22no—
77C2×C4×C277—42no—
78C2×C4×C277C22×C411yescharacteristic
79C2×C4×C277C2×D411yescharacteristic
80C2×C4×C277C2×D411yescharacteristic
81C2×C4×C277C2×D411yescharacteristic
82C2×C4×C277#4111yescharacteristic
83C2×C4×C277#4111yescharacteristic
84C8×C277—41no—
85C22×C277—22no—
86C22×C277C2×C22⋊C411yescharacteristic
87C22×C277#12011yescharacteristic
88C22×C277#12311yescharacteristic
89C2×D277—44no—
90C2×D277—42no—
91C2×D277—82no—
92C2×D277—82no—
93C4×C277—42no—
94C4×C277—42no—
95C4×C277C4×D411yescharacteristic
96C4×C277C4×D411yescharacteristic
97C4×C277#12111yescharacteristic
98C4×C277#12111yescharacteristic
99Dic277—24no—
100Dic277—42no—
101C2×C277—21no—
102C2×C277—21no—
103C2×C277#38611yescharacteristic
104C2×C277#45412yes—
105D277—82no—
106C277#188811yescharacteristic, complemented, Sylow
107#1888—2771nomaximal, Sylow
108C2×#124—2771no—
109#519—2771no—
110#418—2771no—
111#418—2771no—
112C2×#101—2771no—
113#339—2771no—
114#339D27711yescharacteristic, complemented
115C22×Q8—2771no—
116C22×D4—2771no—
117C2×M16—2771no—
118C2×M16C2×D27711yescharacteristic
119#124—2774no—
120#124—5542no—
121C4×Q8—5542no—
122C4×Q8—5542no—
123#117—2771no—
124#117—5542no—
125#117C2×D27711yescharacteristic
126C2×C22⋊C4—5542no—
127C2×C42C2×D27711yescharacteristic
128#102—5542no—
129#102—5542no—
130#101—5542no—
131C24—5541no—
132C2×Q8—2772no—
133C2×Q8—2772no—
134C2×Q8—5541no—
135C2×Q8—5541no—
136C2×Q8—5541no—
137C2×Q8—5541no—
138C2×D4—2772no—
139C2×D4—5541no—
140C2×D4—5541no—
141C2×D4—5541no—
142C2×D4—5541no—
143C2×D4—5541no—
144C22×C4—21no—
145C22×C4—2772no—
146C22×C4C22×D27711yescharacteristic
147M16—21no—
148M16—21no—
149M16—5541no—
150M16—5541no—
151C2×C8—21no—
152C2×C8—5541no—
153C4⋊C4—2772no—
154C4⋊C4—5544no—
155C4⋊C4D110812yes—
156C22⋊C4—21no—
157C22⋊C4—5548no—
158C22⋊C4—5541no—
159C42—21no—
160C42—21no—
161C42—5544no—
162C42—5541no—
163C42C4×D27712yes—
164C23—5542no—
165C23—11084no—
166C23—11081no—
167C23—11081no—
168C23D4×D27711yescharacteristic
169Q8—5542no—
170Q8—5542no—
171Q8—5542no—
172Q8—5542no—
173D4—5542no—
174D4—5542no—
175D4—11081no—
176D4—11081no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—2774no—
181C2×C4—5542no—
182C2×C4—5542no—
183C2×C4—5542no—
184C2×C4C2×C4×D27711yescharacteristic
185C2×C4D4×D27711yescharacteristic
186C2×C4D4×D27711yescharacteristic
187C2×C4C2×D110811yescharacteristic
188C2×C4#1798456311yescharacteristic
189C2×C4#1798456411yescharacteristic
190C8—41no—
191C8—11081no—
192C22—22no—
193C22—11084no—
194C22—11082no—
195C22—22162no—
196C22—22162no—
197C22C22⋊C4×D27711yescharacteristic
198C22#2257985011yescharacteristic
199C22#2257986511yescharacteristic
200C4—42no—
201C4—42no—
202C4—5544no—
203C4—11082no—
204C4#2257984211yescharacteristic
205C4C4×D110811yescharacteristic
206C4#2257985311yescharacteristic
207C4#2257985511yescharacteristic
208C2—21no—
209C2—21no—
210C2—22162no—
211C2#3179988011yescharacteristic
212C2#3180017612yes—
subgroupG/H
centerC22#22579850
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
Fitting#339×C277C2
socleC22×C277#120
prime radicalC22×D1108C22
cosocleC22×C4×C277C23
hypercenter#339D277
hypocenterC277#1888
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #31800479C2semidirect
5. C2×#22579798C2semidirect
6. #31799762C2semidirect
7. #339×C277C2semidirect
12. #22579868C4semidirect
106. C277#1888semidirect
114. #339D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225798682
#318004792
#318000082
#318000062
C2×#225797982
#317997622
#339×C2772
#1888277