Finite Group Databasebeta

← #353×D271 #46838020

Subgroups — #353×D271 #46838020

Order 34688.

368 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 57 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#127×D271C211yesmaximal, characteristic
2#99×D271C212yesmaximal, complemented
3#31773690C211yesmaximal, characteristic, complemented
4#31773689C212yesmaximal, complemented
5#353×C271C211yesmaximal, characteristic, complemented
6C2×D4×D271—22no—
7C2×D4×D271C411yescharacteristic, complemented
8C2×D4×D271C2211yescharacteristic
9#22576157C411yescharacteristic, complemented
10#22576156—22no—
11#22576156C411yescharacteristic, complemented
12#22576156C2211yescharacteristic
13C22⋊C4×D271—22no—
14C42×D271C411yescharacteristic, complemented
15#22576075C2212yescomplemented
16#22576074—22no—
17#127×C271C2211yescharacteristic
18#99×C271C2212yescomplemented
19C23×D271—21no—
20C23×D271D412yes—
21C2×D1084—22no—
22C2×D1084C2×C411yescharacteristic
23C2×D1084C2×C411yescharacteristic, complemented
24C2×C22⋊D271—22no—
25C2×C22⋊D271—21no—
26C2×C22⋊D271—22no—
27C2×C22⋊D271D412yes—
28D4×D271—41no—
29D4×D271—41no—
30D4×D271—41no—
31D4×D271—41no—
32D4×D271—48no—
33C2×C4×D271—21no—
34C2×C4×D271—42no—
35C2×C4×D271C2×C411yescharacteristic
36C22⋊Dic271—22no—
37(C2×D271)⋊C4—42no—
38C4×Dic271—21no—
39C4×Dic271C2×C411yescharacteristic, complemented
40C2×D4×C271—22no—
41C2×D4×C271C2×C411yescharacteristic, complemented
42C2×D4×C271C2311yescharacteristic
43C22⋊C4×C271—22no—
44C42×C271C2×C411yescharacteristic, complemented
45C22×D271—22no—
46C22×D271—22no—
47C22×D271—21no—
48C22×D271—44no—
49C22×D271—44no—
50C22×D271—41no—
51C22×D271—41no—
52C22×D271C22⋊C411yescharacteristic
53C22×D271C22⋊C412yes—
54D1084—41no—
55D1084—41no—
56D1084—44no—
57C22⋊D271—42no—
58C22⋊D271—44no—
59C22⋊D271—44no—
60C22⋊D271—42no—
61C2×Dic271—21no—
62C2×Dic271—42no—
63C2×Dic271C22⋊C411yescharacteristic
64C4×D271—24no—
65C4×D271—21no—
66C4×D271—21no—
67C4×D271—84no—
68C23×C271—21no—
69C23×C271C2×D412yes—
70D4×C271—41no—
71D4×C271—41no—
72D4×C271—44no—
73C2×C4×C271—21no—
74C2×C4×C271—42no—
75C2×C4×C271C22×C411yescharacteristic
76C22×C271—22no—
77C22×C271—42no—
78C22×C271—42no—
79C22×C271—41no—
80C22×C271C2×C22⋊C411yescharacteristic
81C2×D271—22no—
82C2×D271—22no—
83C2×D271—44no—
84C2×D271—42no—
85C2×D271—42no—
86C2×D271—41no—
87C2×D271—82no—
88C2×D271—82no—
89C2×D271—82no—
90C2×D271#9911yescharacteristic
91C2×D271#9911yescharacteristic
92C4×C271—22no—
93C4×C271—21no—
94C4×C271—82no—
95Dic271—22no—
96Dic271—21no—
97Dic271—82no—
98C2×C271—21no—
99C2×C271—42no—
100C2×C271—81no—
101C2×C271C2×#9911yescharacteristic
102D271—21no—
103D271—42no—
104D271—81no—
105D271#35312yesdirect product factor
106C271C2×#35311yescharacteristic, complemented, Sylow
107C2×#353—2711nomaximal, Sylow
108C2×#127—2711no—
109C2×#99—2712no—
110#353—2711no—
111#353—2712no—
112#353D27111yescharacteristic, direct product factor
113C22×D4—2711no—
114C22×D4—2711no—
115C22×D4—5422no—
116#127—2711no—
117#127—2711no—
118#127—2711no—
119#127—5422no—
120#127C2×D27111yescharacteristic
121C2×C22⋊C4—5422no—
122C2×C42—2711no—
123#99—2712no—
124#99—5422no—
125#99C2×D27112yescomplemented
126C24—2712no—
127C24—5421no—
128C2×D4—22no—
129C2×D4—2712no—
130C2×D4—2711no—
131C2×D4—2711no—
132C2×D4—5422no—
133C2×D4—5421no—
134C2×D4—5422no—
135C2×D4—5422no—
136C2×D4—10841no—
137C2×D4—10841no—
138C2×D4—10841no—
139C2×D4—10841no—
140C2×D4—10848no—
141C2×D4C4×D27111yescharacteristic, complemented
142C2×D4C22×D27111yescharacteristic
143C22×C4—2711no—
144C22×C4—5421no—
145C22×C4—10842no—
146C22⋊C4—22no—
147C22⋊C4—5422no—
148C22⋊C4—10842no—
149C42—2711no—
150C42—5421no—
151C42C4×D27111yescharacteristic, complemented
152C23—21no—
153C23—2711no—
154C23—2712no—
155C23—5422no—
156C23—5422no—
157C23—5421no—
158C23—10841no—
159C23—10841no—
160C23—10844no—
161C23—10844no—
162C23D4×D27112yes—
163D4—41no—
164D4—41no—
165D4—44no—
166D4—10841no—
167D4—10841no—
168D4—10844no—
169D4—10842no—
170D4—10844no—
171D4—10844no—
172D4—10842no—
173C2×C4—21no—
174C2×C4—42no—
175C2×C4—2711no—
176C2×C4—5421no—
177C2×C4—5421no—
178C2×C4—5424no—
179C2×C4—5421no—
180C2×C4—10842no—
181C2×C4—21684no—
182C2×C4C2×C4×D27111yescharacteristic
183C22—22no—
184C22—42no—
185C22—42no—
186C22—41no—
187C22—2711no—
188C22—2711no—
189C22—5422no—
190C22—5422no—
191C22—10842no—
192C22—10842no—
193C22—10844no—
194C22—10841no—
195C22—21682no—
196C22—21682no—
197C22—21682no—
198C22C22⋊C4×D27111yescharacteristic
199C4—22no—
200C4—21no—
201C4—82no—
202C4—5422no—
203C4—5421no—
204C4—21682no—
205C2—21no—
206C2—42no—
207C2—81no—
208C2—2712no—
209C2—5421no—
210C2—10842no—
211C2—21681no—
212C2#99×D27111yescharacteristic
subgroupG/H
centerC2#99×D271
commutatorC2×C4×C271C22×C4
FrattiniC2×D4C22×D271
Fitting#353×C271C2
socleC2×C271C2×#99
prime radical#127×D271C2
cosocleC2×D4×C271C23
hypercenter#353D271
hypocenterC271C2×#353
LCSG ▷ C2×C4×C271 ▷ C22×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #99×D271C2semidirect
3. #31773690C2semidirect
4. #31773689C2semidirect
5. #353×C271C2semidirect
7. C2×D4×D271C4semidirect
9. #22576157C4semidirect
11. #22576156C4semidirect
14. C42×D271C4semidirect
15. #22576075C22semidirect
18. #99×C271C22semidirect
23. C2×D1084C2×C4semidirect
39. C4×Dic271C2×C4semidirect
41. C2×D4×C271C2×C4semidirect
44. C42×C271C2×C4semidirect
105. D271#353direct (N × H)
106. C271C2×#353semidirect
112. #353D271direct (N × H)
125. #99C2×D271semidirect
141. C2×D4C4×D271semidirect
151. C42C4×D271semidirect

Maximal subgroups

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

subgroupindex
#127×D2712
#99×D2712
#317736902
#317736892
#353×C2712
C2×#353271