Finite Group Databasebeta

← #354×D271 #46838023

Subgroups — #354×D271 #46838023

Order 34688.

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

normal subgroups only

This group has 284 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#124×D271C211yesmaximal, characteristic
2#99×D271C212yesmaximal
3#31773692C211yesmaximal, characteristic, complemented
4#31773691C212yesmaximal, complemented
5#354×C271C211yesmaximal, characteristic, complemented
6C2×Q8×D271C411yescharacteristic, complemented
7C2×D4×D271C2211yescharacteristic
8#22576149C411yescharacteristic, complemented
9#22576148C411yescharacteristic, complemented
10#22576147C2211yescharacteristic
11#22576146—22no—
12C22⋊C4×D271—22no—
13C22⋊C4×D271—22no—
14C42×D271C411yescharacteristic, complemented
15#22576075C2212yes—
16#22576074—22no—
17#124×C271C2211yescharacteristic
18#99×C271C2212yes—
19C23×D271D412yes—
20C2×Dic542—21no—
21C2×Dic542C2×C411yescharacteristic, complemented
22Q8×D271—41no—
23Q8×D271—41no—
24C2×D1084C2×C411yescharacteristic
25C2×C22⋊D271D412yes—
26D4×D271—41no—
27D4×D271—41no—
28C2×C4×D271—21no—
29C2×C4×D271—21no—
30C2×C4×D271—42no—
31C2×C4×D271C2×C411yescharacteristic
32C22⋊Dic271—22no—
33C22⋊Dic271—22no—
34(C2×D271)⋊C4—22no—
35(C2×D271)⋊C4—22no—
36(C2×D271)⋊C4—42no—
37C4×Dic271—21no—
38C4×Dic271C2×C411yescharacteristic, complemented
39C2×Q8×C271C2×C411yescharacteristic, complemented
40C2×D4×C271C2311yescharacteristic
41C22⋊C4×C271—22no—
42C22⋊C4×C271—22no—
43C42×C271C2×C411yescharacteristic, complemented
44C22×D271—22no—
45C22×D271—22no—
46C22×D271—44no—
47C22×D271C22⋊C411yescharacteristic
48C22×D271C22⋊C412yes—
49Dic542—42no—
50Dic542—41no—
51D1084—41no—
52C22⋊D271—42no—
53C2×Dic271—21no—
54C2×Dic271—21no—
55C2×Dic271—42no—
56C2×Dic271C22⋊C411yescharacteristic
57C4×D271—21no—
58C4×D271—21no—
59C4×D271—42no—
60C4×D271—41no—
61C4×D271—41no—
62C4×D271—84no—
63C23×C271C2×D412yes—
64Q8×C271—41no—
65D4×C271—41no—
66C2×C4×C271—21no—
67C2×C4×C271—21no—
68C2×C4×C271—42no—
69C2×C4×C271C22×C411yescharacteristic
70C22×C271—22no—
71C22×C271—42no—
72C22×C271C2×C22⋊C411yescharacteristic
73C2×D271—22no—
74C2×D271—22no—
75C2×D271—44no—
76C2×D271—42no—
77C2×D271—82no—
78C2×D271#9911yescharacteristic
79C2×D271#9911yescharacteristic
80C4×C271—21no—
81C4×C271—41no—
82C4×C271—41no—
83C4×C271—82no—
84Dic271—21no—
85Dic271—41no—
86Dic271—41no—
87Dic271—82no—
88C2×C271—21no—
89C2×C271—42no—
90C2×C271C2×#9911yescharacteristic
91D271—21no—
92D271—42no—
93D271#35412yesdirect product factor
94C271C2×#35411yescharacteristic, complemented, Sylow
95C2×#354—2711nomaximal, Sylow
96C2×#124—2711no—
97C2×#99—2712no—
98#354—2711no—
99#354—2712no—
100#354D27111yescharacteristic, direct product factor
101C22×Q8—2711no—
102C22×D4—2711no—
103#124—2711no—
104#124—2711no—
105#124—2711no—
106#124—5422no—
107#124C2×D27111yescharacteristic
108C2×C22⋊C4—5422no—
109C2×C22⋊C4—5422no—
110C2×C42—2711no—
111#99—2712no—
112#99—5422no—
113#99C2×D27112yes—
114C24—2712no—
115C2×Q8—2711no—
116C2×Q8—5421no—
117C2×Q8—10841no—
118C2×Q8—10841no—
119C2×Q8C4×D27111yescharacteristic, complemented
120C2×D4—2712no—
121C2×D4—2711no—
122C2×D4—10841no—
123C2×D4—10841no—
124C2×D4C22×D27111yescharacteristic
125C22×C4—2711no—
126C22×C4—5421no—
127C22×C4—5421no—
128C22×C4—10842no—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C22⋊C4—5422no—
132C22⋊C4—5422no—
133C22⋊C4—5422no—
134C22⋊C4—5422no—
135C22⋊C4—10842no—
136C42—2711no—
137C42—5421no—
138C42C4×D27111yescharacteristic, complemented
139C23—2711no—
140C23—2712no—
141C23—5422no—
142C23—5422no—
143C23—10844no—
144C23D4×D27112yes—
145Q8—41no—
146Q8—10841no—
147Q8—10842no—
148D4—41no—
149D4—10841no—
150D4—10842no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—42no—
154C2×C4—2711no—
155C2×C4—5421no—
156C2×C4—5421no—
157C2×C4—5421no—
158C2×C4—5421no—
159C2×C4—10841no—
160C2×C4—10841no—
161C2×C4—10842no—
162C2×C4—10842no—
163C2×C4—21684no—
164C2×C4C2×C4×D27111yescharacteristic
165C22—22no—
166C22—42no—
167C22—2711no—
168C22—2711no—
169C22—5422no—
170C22—5422no—
171C22—10842no—
172C22—10844no—
173C22—21682no—
174C22C22⋊C4×D27111yescharacteristic
175C4—21no—
176C4—41no—
177C4—41no—
178C4—82no—
179C4—5421no—
180C4—10841no—
181C4—10841no—
182C4—21682no—
183C2—21no—
184C2—42no—
185C2—2712no—
186C2—5421no—
187C2—10842no—
188C2#99×D27111yescharacteristic
subgroupG/H
centerC2#99×D271
commutatorC2×C4×C271C22×C4
FrattiniC2×D4C22×D271
Fitting#354×C271C2
socleC2×C271C2×#99
prime radicalC2×D4×D271C22
cosocleC2×D4×C271C23
hypercenter#354D271
hypocenterC271C2×#354
LCSG ▷ C2×C4×C271 ▷ C22×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #31773692C2semidirect
4. #31773691C2semidirect
5. #354×C271C2semidirect
6. C2×Q8×D271C4semidirect
8. #22576149C4semidirect
9. #22576148C4semidirect
14. C42×D271C4semidirect
21. C2×Dic542C2×C4semidirect
38. C4×Dic271C2×C4semidirect
39. C2×Q8×C271C2×C4semidirect
43. C42×C271C2×C4semidirect
93. D271#354direct (N × H)
94. C271C2×#354semidirect
100. #354D271direct (N × H)
119. C2×Q8C4×D271semidirect
138. C42C4×D271semidirect

Maximal subgroups

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

subgroupindex
#124×D2712
#99×D2712
#317736922
#317736912
#354×C2712
C2×#354271