Finite Group Databasebeta

← #355×D271 #46838040

Subgroups — #355×D271 #46838040

Order 34688.

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

normal subgroups only

This group has 260 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#101×D271C212yesmaximal, complemented
3#31773694C211yesmaximal, characteristic, complemented
4#31773693C212yesmaximal, complemented
5#355×C271C211yesmaximal, characteristic, complemented
6C2×Q8×D271C2211yescharacteristic
7C2×D4×D271C411yescharacteristic
8M16×D271—22no—
9#22576149C2211yescharacteristic
10#22576148C411yescharacteristic
11#22576147C411yescharacteristic
12#22576146—22no—
13C22⋊C4×D271—22no—
14C42×D271C411yescharacteristic
15#22576079C2212yescomplemented
16#22576078—22no—
17#124×C271C2211yescharacteristic
18#101×C271C2212yescomplemented
19C23×D271—21no—
20C2×Dic542C2×C411yescharacteristic
21C2×Dic542D412yes—
22Q8×D271—41no—
23Q8×D271—41no—
24C2×D1084C2×C411yescharacteristic
25C2×C22⋊D271—21no—
26D4×D271—41no—
27D4×D271—41no—
28C2×C4×D271—21no—
29C2×C4×D271C2×C411yescharacteristic
30C2×C4×D271D412yes—
31#16864638—22no—
32#16864637—42no—
33C8×D271—42no—
34C22⋊Dic271—22no—
35(C2×D271)⋊C4—22no—
36(C2×D271)⋊C4—22no—
37C4×Dic271—21no—
38C4×Dic271C2×C411yescharacteristic
39C2×Q8×C271C2311yescharacteristic
40C2×D4×C271C2×C411yescharacteristic
41M16×C271—22no—
42C22⋊C4×C271—22no—
43C42×C271C2×C411yescharacteristic
44C22×D271—21no—
45C22×D271—44no—
46C22×D271—41no—
47C22×D271—41no—
48C22×D271C22⋊C411yescharacteristic
49Dic542—41no—
50Dic542—42no—
51D1084—41no—
52C22⋊D271—42no—
53C2×Dic271—21no—
54C2×Dic271C22⋊C411yescharacteristic
55C2×Dic271C22⋊C412yes—
56C4×D271—22no—
57C4×D271—22no—
58C4×D271—21no—
59C4×D271—21no—
60C4×D271—42no—
61C271⋊C8—42no—
62C23×C271—21no—
63Q8×C271—41no—
64D4×C271—41no—
65C2×C4×C271—21no—
66C2×C4×C271C22×C411yescharacteristic
67C2×C4×C271C2×D412yes—
68C8×C271—42no—
69C22×C271—42no—
70C22×C271—41no—
71C22×C271C2×C22⋊C411yescharacteristic
72C2×D271—22no—
73C2×D271—42no—
74C2×D271—41no—
75C2×D271—82no—
76C2×D271—82no—
77C2×D271#9911yescharacteristic
78C2×D271#9911yescharacteristic
79C4×C271—22no—
80C4×C271—21no—
81C4×C271—41no—
82Dic271—21no—
83Dic271—22no—
84Dic271—41no—
85C2×C271—21no—
86C2×C271—81no—
87C2×C271C2×#9911yescharacteristic
88D271—21no—
89D271—81no—
90D271#35512yesdirect product factor
91C271C2×#35511yescharacteristic, complemented, Sylow
92C2×#355—2711nomaximal, Sylow
93C2×#124—2711no—
94C2×#101—2712no—
95#355—2711no—
96#355—2712no—
97#355D27111yescharacteristic, direct product factor
98C22×Q8—2711no—
99C22×D4—2711no—
100C2×M16—5422no—
101#124—2711no—
102#124—2711no—
103#124—2711no—
104#124—5422no—
105#124C2×D27111yescharacteristic
106C2×C22⋊C4—5422no—
107C2×C42—2711no—
108#101—2712no—
109#101—5422no—
110#101C2×D27112yescomplemented
111C24—5421no—
112C2×Q8—2711no—
113C2×Q8—2712no—
114C2×Q8—10841no—
115C2×Q8—10841no—
116C2×Q8C22×D27111yescharacteristic
117C2×D4—2711no—
118C2×D4—5421no—
119C2×D4—10841no—
120C2×D4—10841no—
121C2×D4C4×D27111yescharacteristic
122C22×C4—2711no—
123C22×C4—2712no—
124C22×C4—5421no—
125M16—22no—
126M16—5422no—
127M16—10842no—
128C2×C8—10842no—
129C22⋊C4—22no—
130C22⋊C4—5422no—
131C22⋊C4—5422no—
132C22⋊C4—5422no—
133C42—2711no—
134C42—5421no—
135C42C4×D27111yescharacteristic
136C23—21no—
137C23—2711no—
138C23—5421no—
139C23—10841no—
140C23—10841no—
141C23—10844no—
142Q8—41no—
143Q8—10842no—
144Q8—10841no—
145D4—41no—
146D4—10841no—
147D4—10842no—
148C2×C4—21no—
149C2×C4—2711no—
150C2×C4—2712no—
151C2×C4—5422no—
152C2×C4—5422no—
153C2×C4—5421no—
154C2×C4—5421no—
155C2×C4—5421no—
156C2×C4—10842no—
157C2×C4C2×C4×D27111yescharacteristic
158C2×C4D4×D27112yes—
159C8—42no—
160C8—10842no—
161C22—42no—
162C22—41no—
163C22—2711no—
164C22—2711no—
165C22—5422no—
166C22—10842no—
167C22—10841no—
168C22—21682no—
169C22—21682no—
170C22C22⋊C4×D27111yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—5421no—
175C4—5422no—
176C4—10841no—
177C2—21no—
178C2—81no—
179C2—2712no—
180C2—5421no—
181C2—21681no—
182C2#99×D27111yescharacteristic
subgroupG/H
centerC2#99×D271
commutatorC2×C4×C271C22×C4
FrattiniC2×Q8C22×D271
Fitting#355×C271C2
socleC2×C271C2×#99
prime radicalC2×D4×D271C4
cosocleC2×Q8×C271C23
hypercenter#355D271
hypocenterC271C2×#355
LCSG ▷ C2×C4×C271 ▷ C22×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D271C2semidirect
3. #31773694C2semidirect
4. #31773693C2semidirect
5. #355×C271C2semidirect
15. #22576079C22semidirect
18. #101×C271C22semidirect
90. D271#355direct (N × H)
91. C271C2×#355semidirect
97. #355D271direct (N × H)
110. #101C2×D271semidirect

Maximal subgroups

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

subgroupindex
#124×D2712
#101×D2712
#317736942
#317736932
#355×C2712
C2×#355271