Finite Group Databasebeta

← #46838047

Subgroups — #46838047

Order 34688.

250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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#31774443C211yesmaximal, characteristic
2#31773881C211yesmaximal, characteristic, complemented
3#31773695C212yesmaximal, complemented
4#31773693C212yesmaximal, complemented
5#413×C271C211yesmaximal, characteristic, complemented
6C2×#16864654C411yescharacteristic
7C2×#16864638—21no—
8#22576158C2211yescharacteristic
9#22576156C411yescharacteristic
10#22576149C2211yescharacteristic
11#22576147C411yescharacteristic
12#22576132—21no—
13#22576132—21no—
14C4×C22⋊D271—21no—
15C4×C22⋊D271—21no—
16C2×C4×Dic271C411yescharacteristic
17#22576079C2212yes—
18#22576077—21no—
19C2×#41×C271C2211yescharacteristic
20C2×M16×C271—21no—
21#101×C271C2212yes—
22#100×C271—21no—
23#16864654—41no—
24#16864654—41no—
25C2×Dic542C2×C411yescharacteristic
26C2×D1084C2×C411yescharacteristic
27C2×C22⋊D271—21no—
28C2×C22⋊D271—21no—
29C2×C22⋊D271—21no—
30C22×Dic271—21no—
31C2×C4×D271—21no—
32#16864638—22no—
33#16864638—41no—
34C2×C271⋊C8—41no—
35Dic271⋊C4—21no—
36Dic271⋊C4—21no—
37C22⋊Dic271—21no—
38C22⋊Dic271—21no—
39(C2×D271)⋊C4—21no—
40(C2×D271)⋊C4—21no—
41C4×Dic271—21no—
42C4×Dic271C2×C411yescharacteristic
43C4×Dic271C2×C411yescharacteristic
44#41×C271—41no—
45#41×C271—41no—
46C2×Q8×C271C2311yescharacteristic
47C2×D4×C271C2×C411yescharacteristic
48C2×D4×C271D411yescharacteristic
49C2×D4×C271D411yescharacteristic
50C22×C4×C271C2×C411yescharacteristic
51C22×C4×C271D411yescharacteristic
52C22×C4×C271D411yescharacteristic
53M16×C271—22no—
54M16×C271—41no—
55C2×C8×C271—41no—
56C22×D271—21no—
57Dic542—41no—
58D1084—41no—
59C22⋊D271—42no—
60C22⋊D271—42no—
61C22⋊D271—42no—
62C2×Dic271—21no—
63C2×Dic271—21no—
64C2×Dic271—21no—
65C2×Dic271—42no—
66C4×D271—41no—
67C4×D271—41no—
68C271⋊C8—42no—
69C23×C271C22⋊C411yescharacteristic
70C23×C271C22⋊C411yescharacteristic
71C23×C271C22⋊C411yescharacteristic
72Q8×C271—41no—
73D4×C271—41no—
74D4×C271—41no—
75D4×C271—41no—
76C2×C4×C271—21no—
77C2×C4×C271—21no—
78C2×C4×C271—21no—
79C2×C4×C271—21no—
80C2×C4×C271—21no—
81C2×C4×C271—21no—
82C2×C4×C271C22⋊C411yescharacteristic
83C2×C4×C271C22×C411yescharacteristic
84C2×C4×C271C2×D411yescharacteristic
85C2×C4×C271C2×D411yescharacteristic
86C8×C271—42no—
87C22×C271—21no—
88C22×C271—21no—
89C22×C271—21no—
90C22×C271—41no—
91C22×C271—41no—
92C22×C271—41no—
93C22×C271C2×C22⋊C411yescharacteristic
94C2×D271—41no—
95C2×D271—41no—
96C2×D271—41no—
97C4×C271—21no—
98C4×C271—21no—
99C4×C271—21no—
100C4×C271#9911yescharacteristic
101C4×C271#9911yescharacteristic
102Dic271—22no—
103Dic271—41no—
104Dic271—41no—
105C2×C271—21no—
106C2×C271—41no—
107C2×C271—41no—
108C2×C271—41no—
109C2×C271C2×#9911yescharacteristic
110D271—81no—
111C271#213211yescharacteristic, complemented, Sylow
112#2132—2711nomaximal, Sylow
113#532—2711no—
114#413—2711no—
115#413D27111yescharacteristic, complemented
116#356—2712no—
117#355—2712no—
118C2×#41—2711no—
119C2×#41C2×D27111yescharacteristic
120C2×M16—21no—
121C2×M16—5421no—
122C4⋊Q8—2711no—
123#127—2711no—
124#124—2711no—
125#124—2711no—
126#121—5421no—
127#121—5421no—
128C4×D4—5421no—
129C4×D4—5421no—
130C2×C42—2711no—
131#101—2712no—
132#101C2×D27112yes—
133#100—21no—
134#100—5421no—
135#41—41no—
136#41—41no—
137#41—10841no—
138#41—10841no—
139C2×Q8—2711no—
140C2×Q8C22×D27111yescharacteristic
141C2×D4—2711no—
142C2×D4—5421no—
143C2×D4—5421no—
144C2×D4—5421no—
145C2×D4C4×D27111yescharacteristic
146C2×D4C22⋊D27111yescharacteristic
147C2×D4D108411yescharacteristic
148C22×C4—5421no—
149C22×C4—5421no—
150C22×C4C4×D27111yescharacteristic
151C22×C4C22⋊D27111yescharacteristic
152C22×C4D108411yescharacteristic
153M16—22no—
154M16—41no—
155M16—5422no—
156M16—10841no—
157C2×C8—41no—
158C2×C8—10841no—
159C4⋊C4—5421no—
160C4⋊C4—5421no—
161C22⋊C4—5421no—
162C22⋊C4—5421no—
163C22⋊C4—5421no—
164C22⋊C4—5421no—
165C42—2711no—
166C42—2711no—
167C42—5421no—
168C23—5421no—
169C23(C2×D271)⋊C411yescharacteristic
170C23(C2×D271)⋊C411yescharacteristic
171C23(C2×D271)⋊C411yescharacteristic
172Q8—41no—
173Q8—10841no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—10841no—
178D4—10842no—
179D4—10842no—
180D4—10842no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—5421no—
188C2×C4—5421no—
189C2×C4—5421no—
190C2×C4—10842no—
191C2×C4—10841no—
192C2×C4—10841no—
193C2×C4(C2×D271)⋊C411yescharacteristic
194C2×C4C2×C4×D27111yescharacteristic
195C2×C4C2×C22⋊D27111yescharacteristic
196C2×C4C2×D108411yescharacteristic
197C8—42no—
198C8—10842no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—10841no—
206C22—10841no—
207C22—10841no—
208C22C2×(C2×D271)⋊C411yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—5422no—
213C4—10841no—
214C4—10841no—
215C4#2257607411yescharacteristic
216C4#2257607411yescharacteristic
217C2—21no—
218C2—41no—
219C2—41no—
220C2—41no—
221C2—21681no—
222C2C2×#2257607411yescharacteristic
subgroupG/H
centerC4#22576074
commutatorC2×C4×C271C22×C4
FrattiniC2×Q8C22×D271
Fitting#413×C271C2
socleC2×C271C2×#99
prime radical#31774443C2
cosocleC2×Q8×C271C23
hypercenter#413D271
hypocenterC271#2132
LCSG ▷ C2×C4×C271 ▷ C22×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #31773881C2semidirect
3. #31773695C2semidirect
4. #31773693C2semidirect
5. #413×C271C2semidirect
111. C271#2132semidirect
115. #413D271semidirect

Maximal subgroups

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

subgroupindex
#317744432
#317738812
#317736952
#317736932
#413×C2712
#2132271