Finite Group Databasebeta

← #28391605

Subgroups — #28391605

Order 14464.

394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#16813655C211yesmaximal, characteristic, complemented
2#20299165C211yesmaximal, characteristic
3C2×#16813609C211yesmaximal, characteristic, complemented
4C2×#16813548C211yesmaximal, characteristic, complemented
5#20298608C211yesmaximal, characteristic, complemented
6#20298359C211yesmaximal, characteristic, complemented
7C2×#100×C113C211yesmaximal, characteristic, complemented
8C2×#14268647C2211yescharacteristic
9C22×Dic226C2211yescharacteristic
10#16813655—22no—
11#16813655—22no—
12C2×Dic452—21no—
13C2×#14268636—21no—
14#16813618—21no—
15#16813609—21no—
16#16813609—22no—
17#16813609—22no—
18#16813593—22no—
19#16813591—22no—
20#16813581C2211yescharacteristic
21C2×C22⋊Dic113—22no—
22C2×C4×Dic113C2211yescharacteristic
23#16813548—22no—
24#16813547—22no—
25C22×D4×C113C2211yescharacteristic
26C2×M16×C113C2211yescharacteristic
27C2×M16×C113C2211yescharacteristic
28#100×C113—22no—
29#14268647—21no—
30#14268647—21no—
31#14268647—21no—
32#14268647—21no—
33C2×Dic226—21no—
34C2×Dic226—21no—
35C2×Dic226—21no—
36C2×Dic226—21no—
37C2×Dic226—21no—
38C2×Dic226D411yescharacteristic
39C2×Dic226D412yescomplemented
40C2×D452D411yescharacteristic
41C2×C22⋊D113—21no—
42C2×C22⋊D113—24no—
43C22×Dic113—21no—
44C22×Dic113—21no—
45C2×C4×D113—21no—
46Dic452—24no—
47#14268636—24no—
48C4⋊Dic113D412yes—
49C22⋊Dic113—28no—
50C22⋊Dic113—24no—
51C22⋊Dic113—21no—
52C4×Dic113—21no—
53C4×Dic113—21no—
54C4×Dic113D412yescomplemented
55C24×C113D412yes—
56C2×D4×C113—21no—
57C2×D4×C113—21no—
58C2×D4×C113—21no—
59C2×D4×C113—21no—
60C2×D4×C113—21no—
61C2×D4×C113—21no—
62C22×C4×C113C2311yescharacteristic
63M16×C113—21no—
64M16×C113—21no—
65M16×C113—21no—
66M16×C113D412yescomplemented
67C2×C8×C113—21no—
68C2×C8×C113—21no—
69C23×C113—22no—
70C23×C113—22no—
71C23×C113—22no—
72C23×C113—44no—
73C23×C113C2×D411yescharacteristic
74C22×D113—21no—
75D4×C113—41no—
76D4×C113—41no—
77D4×C113—41no—
78D4×C113—41no—
79C2×C4×C113C2×D411yescharacteristic
80C2×C4×C113C2×D411yescharacteristic
81C2×C4×C113C2×D411yescharacteristic
82C2×C4×C113C2×D411yescharacteristic
83C2×C4×C113C2×D411yescharacteristic
84C2×C4×C113#4111yescharacteristic
85C22⋊D113—41no—
86C22⋊D113—41no—
87C22⋊D113—84no—
88C2×Dic113—22no—
89C2×Dic113—22no—
90C2×Dic113—21no—
91C2×Dic113—22no—
92C2×Dic113—42no—
93C2×Dic113—41no—
94C2×Dic113—41no—
95D452—21no—
96D452—21no—
97C4×D113—41no—
98C4×D113—41no—
99Dic226—22no—
100Dic226—21no—
101Dic226—22no—
102Dic226—21no—
103Dic226—41no—
104Dic226—41no—
105C8×C113—22no—
106C8×C113—41no—
107C22×C113—22no—
108C22×C113—44no—
109C22×C113—42no—
110C22×C113—44no—
111C22×C113—82no—
112C22×C113#12011yescharacteristic
113C22×C113#12011yescharacteristic
114C22×C113#12111yescharacteristic
115C2×D113—41no—
116C2×D113—42no—
117C4×C113#12011yescharacteristic
118C4×C113#12111yescharacteristic
119C4×C113#12111yescharacteristic
120C4×C113#12711yescharacteristic
121Dic113—42no—
122Dic113—42no—
123Dic113—41no—
124Dic113—42no—
125C2×C113—21no—
126C2×C113—21no—
127C2×C113—82no—
128C2×C113#39211yescharacteristic
129C2×C113#45512yes—
130D113—81no—
131#2004—1131nomaximal, Sylow
132C113#200411yescharacteristic, complemented, Sylow
133C2×#137—1131no—
134#535—1131no—
135C2×#124—1131no—
136C2×#104—1131no—
137#419—1131no—
138C2×#100D11311yescharacteristic, complemented
139#339—1131no—
140C2×#41—1131no—
141C22×Q8—1131no—
142C22×D4C2×D11311yescharacteristic
143#137—2262no—
144#137—2262no—
145C2×Q16—2261no—
146C2×SD16—2261no—
147C2×M16C2×D11311yescharacteristic
148C2×M16C2×D11311yescharacteristic
149#127—2261no—
150#124—2262no—
151#124—2262no—
152#124—2261no—
153#121—2262no—
154#120—2262no—
155#117—1131no—
156C2×C22⋊C4—2262no—
157C2×C42—1131no—
158#104—2262no—
159#103—2262no—
160#100—22no—
161C24D45212yes—
162#41—2261no—
163#41—2261no—
164#41—2261no—
165#41—2261no—
166C2×Q8—1131no—
167C2×Q8—1132no—
168C2×Q8—2261no—
169C2×Q8—2261no—
170C2×Q8—2261no—
171C2×Q8—2261no—
172C2×Q8—2261no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—1131no—
180C2×D4—2264no—
181C2×D4—2261no—
182C22×C4—2261no—
183C22×C4—2261no—
184C22×C4—2261no—
185C22×C4C22×D11311yescharacteristic
186Q16—2264no—
187SD16—2264no—
188M16—21no—
189M16—21no—
190M16—21no—
191M16C22⋊D11312yescomplemented
192C2×C8—21no—
193C2×C8—21no—
194C4⋊C4—1132no—
195C22⋊C4—2268no—
196C22⋊C4—2264no—
197C22⋊C4—2261no—
198C42—1132no—
199C42—2261no—
200C42—2261no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—44no—
205C23—2261no—
206C23C2×D45211yescharacteristic
207Q8—4521no—
208Q8—4521no—
209Q8—2262no—
210Q8—2261no—
211Q8—2262no—
212Q8—2261no—
213D4—41no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—9044no—
218D4—4521no—
219D4—4521no—
220D4—2261no—
221D4—2261no—
222C2×C4—4522no—
223C2×C4—4521no—
224C2×C4—4521no—
225C2×C4—4521no—
226C2×C4—4521no—
227C2×C4—2262no—
228C2×C4—2262no—
229C2×C4—2262no—
230C2×C4—2261no—
231C2×C4D4×D11311yescharacteristic
232C2×C4D4×D11311yescharacteristic
233C2×C4D4×D11311yescharacteristic
234C2×C4D4×D11311yescharacteristic
235C2×C4C2×C22⋊D11311yescharacteristic
236C2×C4#1426864711yescharacteristic
237C8—22no—
238C8—41no—
239C22—22no—
240C22—44no—
241C22—42no—
242C22—44no—
243C22—82no—
244C22—4521no—
245C22—4522no—
246C22#1681359211yescharacteristic
247C22#1681359211yescharacteristic
248C22#1681359611yescharacteristic
249C4—4522no—
250C4—4521no—
251C4—4522no—
252C4—4522no—
253C4#1681359011yescharacteristic
254C4#1681359511yescharacteristic
255C4#1681359511yescharacteristic
256C4#1681361811yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—9041no—
261C2#2029850711yescharacteristic
262C2#2029877812yes—
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
FittingC2×#100×C113C2
socleC22×C113#120
prime radical#20299165C2
hypercenterC2×#100D113
hypocenterC113#2004
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#16813655C2semidirect
3. C2×#16813609C2semidirect
4. C2×#16813548C2semidirect
5. #20298608C2semidirect
6. #20298359C2semidirect
7. C2×#100×C113C2semidirect
39. C2×Dic226D4semidirect
54. C4×Dic113D4semidirect
66. M16×C113D4semidirect
132. C113#2004semidirect
138. C2×#100D113semidirect
191. M16C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136552
#202991652
C2×#168136092
C2×#168135482
#202986082
#202983592
C2×#100×C1132
#2004113