Finite Group Databasebeta

← #46835430

Subgroups — #46835430

Order 34688.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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#31774567C211yesmaximal, characteristic, complemented
2#31774273C211yesmaximal, characteristic, complemented
3#31774098C211yesmaximal, characteristic, complemented
4#31774093C211yesmaximal, characteristic, complemented
5#31773627C211yesmaximal, characteristic, complemented
6#31773624C211yesmaximal, characteristic, complemented
7#331×C271C211yesmaximal, characteristic, complemented
8C2×#16864653—21no—
9C2×#16864643—21no—
10C2×D2168—21no—
11C2×#16864639—22no—
12#22576157C2211yescharacteristic
13#22576156—21no—
14#22576132—22no—
15#22576131—21no—
16C4×Dic542C2211yescharacteristic
17C4×D1084C2211yescharacteristic
18D4×Dic271—21no—
19#22576082—21no—
20#22576082—21no—
21C4×C271⋊C8C2211yescharacteristic
22#127×C271C2211yescharacteristic
23C4⋊C8×C271C2211yescharacteristic
24C4⋊C8×C271C2211yescharacteristic
25#16864653—42no—
26#16864653—42no—
27C2×Dic542D411yescharacteristic
28C2×D1084—21no—
29C2×D1084—21no—
30C2×D1084—21no—
31C2×D1084D411yescharacteristic
32C2×C22⋊D271—22no—
33C2×C22⋊D271—22no—
34C22×Dic271—22no—
35C2×C4×D271—21no—
36#16864643—42no—
37D2168—42no—
38#16864639—44no—
39C2×C271⋊C8—21no—
40C4⋊Dic271D411yescharacteristic
41C4⋊Dic271D411yescharacteristic
42Dic271⋊C4—21no—
43C22⋊Dic271—22no—
44(C2×D271)⋊C4—21no—
45C4×Dic271—21no—
46C2×D4×C271—21no—
47C2×D4×C271—21no—
48C2×D4×C271D412yes—
49C2×C8×C271—21no—
50C2×C8×C271—21no—
51C42×C271C2311yescharacteristic
52C22×D271—21no—
53C22×D271—41no—
54Dic542—21no—
55Dic542D812yescomplemented
56D1084—21no—
57D1084—21no—
58D1084—42no—
59D1084—41no—
60D1084—41no—
61D1084—41no—
62D1084—41no—
63C22⋊D271—44no—
64C22⋊D271—82no—
65C2×Dic271—21no—
66C2×Dic271—21no—
67C2×Dic271—21no—
68C2×Dic271—44no—
69C4×D271—41no—
70C4×D271—41no—
71C271⋊C8—22no—
72C23×C271—22no—
73D4×C271—42no—
74D4×C271—41no—
75D4×C271—41no—
76D4×C271—41no—
77D4×C271—41no—
78C2×C4×C271C2×D411yescharacteristic
79C2×C4×C271C2×D411yescharacteristic
80C2×C4×C271C2×D411yescharacteristic
81C8×C271—41no—
82C8×C271—41no—
83C22×C271—42no—
84C22×C271—42no—
85C22×C271—42no—
86C22×C271#12011yescharacteristic
87C2×D271—41no—
88C2×D271—41no—
89C2×D271—41no—
90C2×D271—81no—
91C2×D271—81no—
92C2×D271—81no—
93C4×C271—21no—
94C4×C271C2×D811yescharacteristic
95C4×C271#13511yescharacteristic
96C4×C271AGL(1,ℤ/8)11yescharacteristic
97C4×C271AGL(1,ℤ/8)11yescharacteristic
98Dic271—22no—
99Dic271—41no—
100Dic271—41no—
101C2×C271—82no—
102C2×C271#44711yescharacteristic
103C2×C271#44911yescharacteristic
104C2×C271#45311yescharacteristic
105D271—81no—
106D271—161no—
107C271#162111yescharacteristic, complemented, Sylow
108#1621—2711nomaximal, Sylow
109#550—2711no—
110#493—2711no—
111#460—2711no—
112#459—2711no—
113#331D27111yescharacteristic, complemented
114Q8⋊C8—2711no—
115D4⋊C8—2711no—
116C2×#41—5421no—
117C2×SD16—5421no—
118C2×D8—5421no—
119C2×D8—5422no—
120#127—2711no—
121#127—5421no—
122#127C2×D27111yescharacteristic
123#121—5421no—
124#121—5422no—
125C4×Q8—2711no—
126C4×D4—2711no—
127C4×D4—5421no—
128C4⋊C8C2×D27111yescharacteristic
129C4⋊C8C2×D27111yescharacteristic
130#102—5421no—
131#102—5421no—
132C4×C8—2711no—
133#41—10842no—
134#41—10842no—
135C2×Q8—2711no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—2711no—
139C2×D4—5422no—
140C2×D4—5422no—
141C2×D4—5421no—
142C2×D4—5421no—
143C2×D4—5421no—
144C2×D4D108412yes—
145C22×C4—5422no—
146C22×C4—5421no—
147SD16—10842no—
148D8—10842no—
149D8—10844no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—5421no—
153C4⋊C4—2711no—
154C4⋊C4—2711no—
155C4⋊C4—5421no—
156C22⋊C4—5422no—
157C22⋊C4—5421no—
158C42—5421no—
159C42C22×D27111yescharacteristic
160C23—22no—
161C23—5421no—
162C23—10841no—
163Q8—2712no—
164Q8—5421no—
165D4—42no—
166D4—41no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—5421no—
171D4—5421no—
172D4—10842no—
173D4—10844no—
174D4—10841no—
175D4—10841no—
176D4—10841no—
177D4—10841no—
178D4—21682no—
179C2×C4—5421no—
180C2×C4—5421no—
181C2×C4—5421no—
182C2×C4—10844no—
183C2×C4—10841no—
184C2×C4—10841no—
185C2×C4D4×D27111yescharacteristic
186C2×C4D4×D27111yescharacteristic
187C2×C4C2×D108411yescharacteristic
188C8—41no—
189C8—41no—
190C8—5422no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—10841no—
195C22—10841no—
196C22—10841no—
197C22—21681no—
198C22—21681no—
199C22—21681no—
200C22#2257613011yescharacteristic
201C4—21no—
202C4—5422no—
203C4—10841no—
204C4—10841no—
205C4D8×D27111yescharacteristic
206C4#2257618111yescharacteristic
207C4#2257618411yescharacteristic
208C4#2257618711yescharacteristic
209C2—82no—
210C2—21681no—
211C2—43361no—
212C2#3177403211yescharacteristic
213C2#3177404311yescharacteristic
214C2#3177406711yescharacteristic
subgroupG/H
centerC22#22576130
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
Fitting#331×C271C2
socleC22×C271#120
hypercenter#331D271
hypocenterC271#1621
LCSG ▷ C42×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #31774567C2semidirect
2. #31774273C2semidirect
3. #31774098C2semidirect
4. #31774093C2semidirect
5. #31773627C2semidirect
6. #31773624C2semidirect
7. #331×C271C2semidirect
55. Dic542D8semidirect
107. C271#1621semidirect
113. #331D271semidirect

Maximal subgroups

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

subgroupindex
#317745672
#317742732
#317740982
#317740932
#317736272
#317736242
#331×C2712
#1621271