Finite Group Databasebeta

← #46836958

Subgroups — #46836958

Order 34688.

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#31773796C211yesmaximal, characteristic
2C4⋊C4×Dic271C211yesmaximal, characteristic
3#31773660C211yesmaximal, characteristic
4#31773659C211yesmaximal, characteristic
5#31773659C211yesmaximal, characteristic
6#31773651C211yesmaximal, characteristic
7C2×#107×C271C211yesmaximal, characteristic
8C22×C271⋊C8C2211yescharacteristic
9C2×C4⋊Dic271—21no—
10C2×C4⋊Dic271C2211yescharacteristic
11C2×C4⋊Dic271C2211yescharacteristic
12C2×C4×Dic271—21no—
13C2×C4×Dic271C2211yescharacteristic
14C271⋊#95—21no—
15C271⋊#95—21no—
16C22×C8×C271C2211yescharacteristic
17C2×C4⋊C4×C271C2211yescharacteristic
18C2×C4⋊C4×C271C2211yescharacteristic
19#107×C271C414yescomplemented
20C22×Dic271—21no—
21C22×Dic271—21no—
22C22×Dic271D411yescharacteristic
23C22×Dic271D411yescharacteristic
24C2×C271⋊C8—21no—
25C2×C271⋊C8—21no—
26C2×C271⋊C8—21no—
27C4⋊Dic271—21no—
28C4⋊Dic271—21no—
29C4⋊Dic271—21no—
30C4⋊Dic271—42no—
31C4⋊Dic271Q812yes—
32C4×Dic271—21no—
33C4×Dic271—21no—
34C4×Dic271—42no—
35C22×C4×C271—21no—
36C22×C4×C271—21no—
37C22×C4×C271C2311yescharacteristic
38C2×C8×C271—21no—
39C2×C8×C271—21no—
40C2×C8×C271C2×C412yes—
41C4⋊C4×C271—21no—
42C4⋊C4×C271—21no—
43C4⋊C4×C271C2×C412yes—
44C4⋊C4×C271C2×C412yes—
45C2×Dic271—21no—
46C2×Dic271—21no—
47C2×Dic271—22no—
48C2×Dic271—21no—
49C2×Dic271—21no—
50C2×Dic271—21no—
51C2×Dic271—41no—
52C2×Dic271—41no—
53C2×Dic271—41no—
54C2×Dic271—41no—
55C2×Dic271—41no—
56C2×Dic271Q1612yes—
57C271⋊C8—41no—
58C23×C271C2×D411yescharacteristic
59C2×C4×C271—22no—
60C2×C4×C271—22no—
61C2×C4×C271—41no—
62C2×C4×C271—41no—
63C2×C4×C271—41no—
64C2×C4×C271—41no—
65C2×C4×C271C22×C411yescharacteristic
66C2×C4×C271C2×Q811yescharacteristic
67C2×C4×C271#4111yescharacteristic
68C2×C4×C271#4111yescharacteristic
69C2×C4×C271#4111yescharacteristic
70C2×C4×C271#4111yescharacteristic
71C8×C271—22no—
72C22×C271C4×D411yescharacteristic
73C22×C271C22⋊Q811yescharacteristic
74C22×C271#12311yescharacteristic
75C22×C271C2×Q1611yescharacteristic
76C22×C271#13511yescharacteristic
77C22×C271AGL(1,ℤ/8)11yescharacteristic
78C22×C271AGL(1,ℤ/8)11yescharacteristic
79C4×C271—42no—
80C4×C271—42no—
81C4×C271#11711yescharacteristic
82C4×C271C4×Q811yescharacteristic
83C4×C271#12511yescharacteristic
84C4×C271#12611yescharacteristic
85Dic271—22no—
86Dic271—42no—
87Dic271—41no—
88Dic271—81no—
89C2×C271#38711yescharacteristic
90C2×C271C4×Q1611yescharacteristic
91C2×C271#44211yescharacteristic
92C2×C271#47711yescharacteristic
93C2×C271#47811yescharacteristic
94C2×C271#48211yescharacteristic
95C2×C271#48411yescharacteristic
96C271#192111yescharacteristic, complemented, Sylow
97#1921—2711nomaximal, Sylow
98C2×#107D27111yescharacteristic
99#389—2711no—
100C4×C4⋊C4—2711no—
101#340—2711no—
102#340—2711no—
103#340—2711no—
104#336—2711no—
105C22×C8—2711no—
106C22×C8C2×D27111yescharacteristic
107C2×C4⋊C4—2711no—
108C2×C4⋊C4—2711no—
109C2×C4⋊C4—5421no—
110C2×C4⋊C4C2×D27111yescharacteristic
111C2×C4⋊C4C2×D27111yescharacteristic
112C2×C42—2711no—
113C2×C42—5421no—
114#107Dic27114yescomplemented
115#95—5421no—
116#95—5421no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—2711no—
120C22×C4—2711no—
121C22×C4—5421no—
122C22×C4—5421no—
123C22×C4C22×D27111yescharacteristic
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—5421no—
127C2×C8—5421no—
128C2×C8—5421no—
129C2×C8C2×Dic27112yes—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—2712no—
133C4⋊C4—5421no—
134C4⋊C4—5421no—
135C4⋊C4—5421no—
136C4⋊C4—10842no—
137C4⋊C4C2×Dic27112yes—
138C4⋊C4C2×Dic27112yes—
139C42—5421no—
140C42—5421no—
141C42—10842no—
142C23D4×D27111yescharacteristic
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—2712no—
150C2×C4—5421no—
151C2×C4—5421no—
152C2×C4—5422no—
153C2×C4—5421no—
154C2×C4—5421no—
155C2×C4—5421no—
156C2×C4—10841no—
157C2×C4—10841no—
158C2×C4—10841no—
159C2×C4—10841no—
160C2×C4—10841no—
161C2×C4C22×Dic27111yescharacteristic
162C2×C4Q8×D27111yescharacteristic
163C2×C4#1686465311yescharacteristic
164C2×C4#1686465411yescharacteristic
165C2×C4#1686465411yescharacteristic
166C2×C4#1686465511yescharacteristic
167C8—22no—
168C8—10841no—
169C22D4×Dic27111yescharacteristic
170C22#2257613811yescharacteristic
171C22#2257614511yescharacteristic
172C22Q16×D27111yescharacteristic
173C22#2257618311yescharacteristic
174C22#2257618411yescharacteristic
175C22#2257618411yescharacteristic
176C4—42no—
177C4—42no—
178C4—5422no—
179C4—10841no—
180C4—10842no—
181C4—21681no—
182C4#2257611911yescharacteristic
183C4Q8×Dic27111yescharacteristic
184C4#2257615011yescharacteristic
185C4#2257615511yescharacteristic
186C2#3177378311yescharacteristic
187C2Q16×Dic27111yescharacteristic
188C2#3177400911yescharacteristic
189C2#3177419111yescharacteristic
190C2#3177420011yescharacteristic
191C2#3177422411yescharacteristic
192C2#3177423411yescharacteristic
subgroupG/H
centerC23D4×D271
commutatorC2×C4×C271C22×C4
FrattiniC22×C4C22×D271
FittingC2×#107×C271C2
socle, prime radicalC23×C271C2×D4
cosocleC22×C4×C271C23
hypercenterC2×#107D271
hypocenterC271#1921
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
19. #107×C271C4semidirect
96. C271#1921semidirect
114. #107Dic271semidirect

Maximal subgroups

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

subgroupindex
#317737962
C4⋊C4×Dic2712
#317736602
#317736592
#317736512
C2×#107×C2712
#1921271