Finite Group Databasebeta

← #47983269

Subgroups — #47983269

Order 35456.

262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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#31800470C211yesmaximal, characteristic
2#31799984C211yesmaximal, characteristic
3#31799975C211yesmaximal, characteristic
4#31799763C211yesmaximal, characteristic, complemented
5#31799761C211yesmaximal, characteristic, complemented
6#31799758C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C277C211yesmaximal, characteristic, complemented
8C2×#17984563C2211yescharacteristic
9C2×#17984547C2211yescharacteristic
10#22579845—21no—
11#22579842—21no—
12#22579840—22no—
13#22579839C2211yescharacteristic
14#22579837C412yescomplemented
15C2×C4×Dic277C2211yescharacteristic
16C42×D277C412yescomplemented
17#22579798—21no—
18#22579796—21no—
19#22579794—22no—
20C2×M16×C277C2211yescharacteristic
21#117×C277C2211yescharacteristic
22#117×C277C2211yescharacteristic
23#17984563—21no—
24#17984563—21no—
25#17984563—21no—
26#17984563—21no—
27C2×Dic554D411yescharacteristic
28C2×D1108D411yescharacteristic
29C2×C22⋊D277D412yes—
30C22×Dic277—21no—
31C2×C4×D277—22no—
32C2×C4×D277C2×C412yes—
33#17984547—21no—
34#17984547—21no—
35C2×#14555660—21no—
36C4⋊Dic277—21no—
37#17984542—22no—
38C22⋊Dic277—21no—
39#17984540—22no—
40C4×Dic277—22no—
41C4×Dic277—21no—
42C4×Dic277—21no—
43C4×Dic277C2×C411yescharacteristic
44C4×Dic277C2×C411yescharacteristic
45C22×C4×C277C2311yescharacteristic
46M16×C277—21no—
47M16×C277—21no—
48C2×C8×C277—21no—
49C4⋊C4×C277—21no—
50C4⋊C4×C277—21no—
51C22⋊C4×C277—21no—
52C22⋊C4×C277—21no—
53C42×C277—21no—
54C42×C277C2×C412yes—
55C22×D277C22⋊C412yes—
56Dic554—21no—
57Dic554—21no—
58D1108—21no—
59D1108—21no—
60C22⋊D277—22no—
61C22⋊D277—22no—
62C2×Dic277—21no—
63C2×Dic277—21no—
64C2×Dic277—42no—
65C2×Dic277—41no—
66C2×Dic277C22⋊C412yes—
67C4×D277—22no—
68C4×D277—22no—
69C4×D277—44no—
70#14555660—41no—
71C23×C277C2×D411yescharacteristic
72C2×C4×C277—22no—
73C2×C4×C277—41no—
74C2×C4×C277C22×C411yescharacteristic
75C2×C4×C277C2×D411yescharacteristic
76C2×C4×C277#4111yescharacteristic
77C2×C4×C277#4111yescharacteristic
78C2×C4×C277#4111yescharacteristic
79C2×C4×C277#4111yescharacteristic
80C8×C277—41no—
81C22×C277—41no—
82C22×C277C2×C22⋊C411yescharacteristic
83C22×C277#12311yescharacteristic
84C22×C277#12311yescharacteristic
85C2×D277—22no—
86C2×D277—42no—
87C4×C277—42no—
88C4×C277—81no—
89C4×C277#11711yescharacteristic
90C4×C277#11711yescharacteristic
91C4×C277#12311yescharacteristic
92C4×C277#12311yescharacteristic
93Dic277—22no—
94Dic277—22no—
95Dic277—41no—
96Dic277—81no—
97C2×C277—21no—
98C2×C277—21no—
99C2×C277—21no—
100C2×C277#38111yescharacteristic
101D277—42no—
102C277#182711yescharacteristic, complemented, Sylow
103#1827—2771nomaximal, Sylow
104C4×#41—2771no—
105#413—2771no—
106#410—2771no—
107#339—2771no—
108#339—2771no—
109H(3,ℤ/4)—2771no—
110H(3,ℤ/4)D27711yescharacteristic, complemented
111C2×#41—2771no—
112C2×M16—2771no—
113C2×M16C2×D27711yescharacteristic
114C4×Q8—5541no—
115C4×D4—5542no—
116C4×D4—5541no—
117#117—2772no—
118#117—2771no—
119#117C2×D27711yescharacteristic
120#117C2×D27711yescharacteristic
121C2×C42—2771no—
122C2×C42—2772no—
123#101—5541no—
124#100—5541no—
125#99—5542no—
126#41—5541no—
127#41—5541no—
128#41—5541no—
129#41—5541no—
130C2×Q8—2771no—
131C2×D4—2772no—
132C2×D4—2771no—
133C22×C4—2772no—
134C22×C4—5542no—
135C22×C4—5541no—
136C22×C4C22×D27711yescharacteristic
137M16—21no—
138M16—21no—
139M16—5541no—
140M16—5541no—
141C2×C8—21no—
142C2×C8—5541no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—5542no—
146C4⋊C4—5541no—
147C22⋊C4—21no—
148C22⋊C4—21no—
149C22⋊C4—5542no—
150C22⋊C4—5541no—
151C42—21no—
152C42—2771no—
153C42—2771no—
154C42—5542no—
155C42—5541no—
156C42—5541no—
157C42C4×D27712yes—
158C23—2772no—
159C23D4×D27711yescharacteristic
160Q8—5541no—
161Q8—5541no—
162D4—5542no—
163D4—5542no—
164D4—5541no—
165D4—5541no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—2772no—
169C2×C4—5541no—
170C2×C4—5542no—
171C2×C4—5542no—
172C2×C4—5541no—
173C2×C4—11084no—
174C2×C4—11082no—
175C2×C4—11081no—
176C2×C4C2×C4×D27711yescharacteristic
177C2×C4D4×D27711yescharacteristic
178C2×C4#1798456211yescharacteristic
179C2×C4#1798456311yescharacteristic
180C2×C4#1798456311yescharacteristic
181C2×C4#1798456411yescharacteristic
182C8—41no—
183C8—11081no—
184C22—41no—
185C22—5542no—
186C22—11082no—
187C22C22⋊C4×D27711yescharacteristic
188C22#2257986211yescharacteristic
189C22#2257986511yescharacteristic
190C4—42no—
191C4—81no—
192C4—5542no—
193C4—5542no—
194C4—11081no—
195C4—22161no—
196C4#2257983711yescharacteristic
197C4#2257983811yescharacteristic
198C4#2257986211yescharacteristic
199C4#2257986511yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—11082no—
204C2#3179986411yescharacteristic
subgroupG/H
centerC4#22579837
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
FittingH(3,ℤ/4)×C277C2
socleC2×C277#381
prime radicalC2×#17984563C22
cosocleC22×C4×C277C23
hypercenterH(3,ℤ/4)D277
hypocenterC277#1827
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C4 ◁ #117 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #31799763C2semidirect
5. #31799761C2semidirect
6. #31799758C2semidirect
7. H(3,ℤ/4)×C277C2semidirect
14. #22579837C4semidirect
16. C42×D277C4semidirect
102. C277#1827semidirect
110. H(3,ℤ/4)D277semidirect

Maximal subgroups

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

subgroupindex
#318004702
#317999842
#317999752
#317997632
#317997612
#317997582
H(3,ℤ/4)×C2772
#1827277