Finite Group Databasebeta

← #47983761

Subgroups — #47983761

Order 35456.

230 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 99 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#31799901C211yesmaximal, characteristic
2C4⋊C4×Dic277C211yesmaximal, characteristic
3#31799765C211yesmaximal, characteristic
4#31799764C211yesmaximal, characteristic
5#31799764C211yesmaximal, characteristic
6#31799756C211yesmaximal, characteristic
7C2×#107×C277C211yesmaximal, characteristic
8C22×#14555660C2211yescharacteristic
9C2×C4⋊Dic277—21no—
10C2×C4⋊Dic277C2211yescharacteristic
11C2×C4⋊Dic277C2211yescharacteristic
12C2×C4×Dic277—21no—
13C2×C4×Dic277C2211yescharacteristic
14#22579787—21no—
15#22579787—21no—
16C22×C8×C277C2211yescharacteristic
17C2×C4⋊C4×C277C2211yescharacteristic
18C2×C4⋊C4×C277C2211yescharacteristic
19#107×C277C414yescomplemented
20C22×Dic277—21no—
21C22×Dic277—21no—
22C22×Dic277D411yescharacteristic
23C22×Dic277D411yescharacteristic
24C2×#14555660—21no—
25C2×#14555660—21no—
26C2×#14555660—21no—
27C4⋊Dic277—21no—
28C4⋊Dic277—21no—
29C4⋊Dic277—21no—
30C4⋊Dic277—42no—
31C4⋊Dic277Q812yes—
32C4×Dic277—21no—
33C4×Dic277—21no—
34C4×Dic277—42no—
35C22×C4×C277—21no—
36C22×C4×C277—21no—
37C22×C4×C277C2311yescharacteristic
38C2×C8×C277—21no—
39C2×C8×C277—21no—
40C2×C8×C277C2×C412yes—
41C4⋊C4×C277—21no—
42C4⋊C4×C277—21no—
43C4⋊C4×C277C2×C412yes—
44C4⋊C4×C277C2×C412yes—
45C2×Dic277—21no—
46C2×Dic277—21no—
47C2×Dic277—22no—
48C2×Dic277—21no—
49C2×Dic277—21no—
50C2×Dic277—21no—
51C2×Dic277—41no—
52C2×Dic277—41no—
53C2×Dic277—41no—
54C2×Dic277—41no—
55C2×Dic277—41no—
56C2×Dic277Q1612yes—
57#14555660—41no—
58C23×C277C2×D411yescharacteristic
59C2×C4×C277—22no—
60C2×C4×C277—22no—
61C2×C4×C277—41no—
62C2×C4×C277—41no—
63C2×C4×C277—41no—
64C2×C4×C277—41no—
65C2×C4×C277C22×C411yescharacteristic
66C2×C4×C277C2×Q811yescharacteristic
67C2×C4×C277#4111yescharacteristic
68C2×C4×C277#4111yescharacteristic
69C2×C4×C277#4111yescharacteristic
70C2×C4×C277#4111yescharacteristic
71C8×C277—22no—
72C22×C277C4×D411yescharacteristic
73C22×C277C22⋊Q811yescharacteristic
74C22×C277#12311yescharacteristic
75C22×C277C2×Q1611yescharacteristic
76C22×C277#13511yescharacteristic
77C22×C277AGL(1,ℤ/8)11yescharacteristic
78C22×C277AGL(1,ℤ/8)11yescharacteristic
79C4×C277—42no—
80C4×C277—42no—
81C4×C277#11711yescharacteristic
82C4×C277C4×Q811yescharacteristic
83C4×C277#12511yescharacteristic
84C4×C277#12611yescharacteristic
85Dic277—22no—
86Dic277—42no—
87Dic277—41no—
88Dic277—81no—
89C2×C277#38711yescharacteristic
90C2×C277C4×Q1611yescharacteristic
91C2×C277#44211yescharacteristic
92C2×C277#47711yescharacteristic
93C2×C277#47811yescharacteristic
94C2×C277#48211yescharacteristic
95C2×C277#48411yescharacteristic
96C277#192111yescharacteristic, complemented, Sylow
97#1921—2771nomaximal, Sylow
98C2×#107D27711yescharacteristic
99#389—2771no—
100C4×C4⋊C4—2771no—
101#340—2771no—
102#340—2771no—
103#340—2771no—
104#336—2771no—
105C22×C8—2771no—
106C22×C8C2×D27711yescharacteristic
107C2×C4⋊C4—2771no—
108C2×C4⋊C4—2771no—
109C2×C4⋊C4—5541no—
110C2×C4⋊C4C2×D27711yescharacteristic
111C2×C4⋊C4C2×D27711yescharacteristic
112C2×C42—2771no—
113C2×C42—5541no—
114#107Dic27714yescomplemented
115#95—5541no—
116#95—5541no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—2771no—
120C22×C4—2771no—
121C22×C4—5541no—
122C22×C4—5541no—
123C22×C4C22×D27711yescharacteristic
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—5541no—
127C2×C8—5541no—
128C2×C8—5541no—
129C2×C8C2×Dic27712yes—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—2772no—
133C4⋊C4—5541no—
134C4⋊C4—5541no—
135C4⋊C4—5541no—
136C4⋊C4—11082no—
137C4⋊C4C2×Dic27712yes—
138C4⋊C4C2×Dic27712yes—
139C42—5541no—
140C42—5541no—
141C42—11082no—
142C23D4×D27711yescharacteristic
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—2772no—
150C2×C4—5541no—
151C2×C4—5541no—
152C2×C4—5542no—
153C2×C4—5541no—
154C2×C4—5541no—
155C2×C4—5541no—
156C2×C4—11081no—
157C2×C4—11081no—
158C2×C4—11081no—
159C2×C4—11081no—
160C2×C4—11081no—
161C2×C4C22×Dic27711yescharacteristic
162C2×C4Q8×D27711yescharacteristic
163C2×C4#1798456211yescharacteristic
164C2×C4#1798456311yescharacteristic
165C2×C4#1798456311yescharacteristic
166C2×C4#1798456411yescharacteristic
167C8—22no—
168C8—11081no—
169C22D4×Dic27711yescharacteristic
170C22#2257985811yescharacteristic
171C22#2257986511yescharacteristic
172C22Q16×D27711yescharacteristic
173C22#2257990311yescharacteristic
174C22#2257990411yescharacteristic
175C22#2257990411yescharacteristic
176C4—42no—
177C4—42no—
178C4—5542no—
179C4—11081no—
180C4—11082no—
181C4—22161no—
182C4#2257983911yescharacteristic
183C4Q8×Dic27711yescharacteristic
184C4#2257987011yescharacteristic
185C4#2257987511yescharacteristic
186C2#3179988811yescharacteristic
187C2Q16×Dic27711yescharacteristic
188C2#3180011411yescharacteristic
189C2#3180029611yescharacteristic
190C2#3180030511yescharacteristic
191C2#3180032911yescharacteristic
192C2#3180033911yescharacteristic
subgroupG/H
centerC23D4×D277
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
FittingC2×#107×C277C2
socle, prime radicalC23×C277C2×D4
cosocleC22×C4×C277C23
hypercenterC2×#107D277
hypocenterC277#1921
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
19. #107×C277C4semidirect
96. C277#1921semidirect
114. #107Dic277semidirect

Maximal subgroups

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

subgroupindex
#317999012
C4⋊C4×Dic2772
#317997652
#317997642
#317997562
C2×#107×C2772
#1921277