Finite Group Databasebeta

← #28401029

Subgroups — #28401029

Order 14464.

552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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
2C2×#16813653C211yesmaximal, characteristic, complemented
3C2×#16813652C211yesmaximal, characteristic, complemented
4#20299144C211yesmaximal, characteristic
5C2×#16813620C211yesmaximal, characteristic, complemented
6#20298991C212yesmaximal, complemented
7#20298989C212yesmaximal, complemented
8#20298976C212yesmaximal, complemented
9#20298969C212yesmaximal, complemented
10M16×Dic113C211yesmaximal, characteristic, complemented
11C2×#137×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C22×Dic226C2211yescharacteristic
14#16813655—24no—
15#16813653—24no—
16#16813652—24no—
17C2×Dic452C2212yes—
18C2×#14268637C2212yes—
19C2×#14268637C2212yes—
20C2×#14268636C2212yes—
21C2×#14268635C2212yes—
22C2×#14268634C2212yes—
23C2×#14268631C2211yescharacteristic
24#16813620—22no—
25#16813620C2212yes—
26#16813620C2212yes—
27#16813620C2211yescharacteristic
28#16813618C2211yescharacteristic
29#16813611C2211yescharacteristic
30#16813609C2211yescharacteristic
31#16813594—22no—
32C4×C22⋊D113—22no—
33C2×#14268626—22no—
34C2×C4×Dic113C2211yescharacteristic
35#16813532C2212yes—
36C8×Dic113C2212yes—
37C2×#41×C113C2211yescharacteristic
38C22×Q8×C113C2211yescharacteristic
39#137×C113—24no—
40C2×Q16×C113C2212yes—
41C2×SD16×C113C2212yes—
42C2×M16×C113C2211yescharacteristic
43#14268647—22no—
44#14268647—22no—
45C2×Dic226—22no—
46C2×Dic226—22no—
47C2×Dic226—21no—
48C2×Dic226C2311yescharacteristic
49C2×Dic226C2312yes—
50C2×D452C2311yescharacteristic
51C2×C22⋊D113—21no—
52C2×C22⋊D113—22no—
53C22×Dic113—21no—
54C22×Dic113D412yes—
55C2×C4×D113—21no—
56Dic452—24no—
57#14268637—24no—
58#14268637—24no—
59#14268636—24no—
60#14268635—24no—
61#14268634—24no—
62#14268631D414yescomplemented
63C2×#11744751C2312yes—
64#14268626—24no—
65#14268626—24no—
66#14268626—22no—
67C22⋊Dic113—22no—
68#14268624—22no—
69C4×Dic113D412yes—
70C4×Dic113C2311yescharacteristic
71C4×Dic113C2311yescharacteristic
72#41×C113—22no—
73#41×C113—22no—
74C2×Q8×C113—21no—
75C2×Q8×C113—22no—
76C2×Q8×C113—22no—
77C2×Q8×C113C2311yescharacteristic
78C2×Q8×C113C2312yes—
79C2×D4×C113—21no—
80C2×D4×C113C2311yescharacteristic
81C22×C4×C113—21no—
82C22×C4×C113—21no—
83C22×C4×C113C2311yescharacteristic
84Q16×C113—24no—
85SD16×C113—24no—
86M16×C113D414yescomplemented
87C2×C8×C113C2312yes—
88C23×C113—21no—
89C23×C113C2×D411yescharacteristic
90C22×D113—21no—
91Q8×C113—22no—
92Q8×C113—21no—
93Q8×C113—22no—
94Q8×C113—21no—
95Q8×C113—42no—
96D4×C113—21no—
97D4×C113—21no—
98D4×C113—42no—
99C2×C4×C113—21no—
100C2×C4×C113—22no—
101C2×C4×C113—42no—
102C2×C4×C113—42no—
103C2×C4×C113C2×D411yescharacteristic
104C2×C4×C113C2×D412yes—
105C2×C4×C113C2×D412yes—
106C2×C4×C113C2411yescharacteristic
107C22⋊D113—42no—
108C22⋊D113—44no—
109C2×Dic113—24no—
110C2×Dic113—21no—
111C2×Dic113—22no—
112C2×Dic113—42no—
113C2×Dic113C2×D412yes—
114C2×Dic113C2×D412yes—
115D452—21no—
116D452—21no—
117C4×D113—42no—
118Dic226—22no—
119Dic226—22no—
120Dic226—21no—
121Dic226—21no—
122Dic226—42no—
123C8×C113C2×D414yes—
124#11744751C2×D414yes—
125C22×C113—22no—
126C22×C113—41no—
127C22×C113—42no—
128C22×C113#12712yes—
129C22×C113C22×D411yescharacteristic
130C2×D113—41no—
131C2×D113—42no—
132C4×C113—41no—
133C4×C113—42no—
134C4×C113#12712yes—
135C4×C113C22×D411yescharacteristic
136C4×C113C22×D411yescharacteristic
137Dic113—22no—
138Dic113—42no—
139Dic113—41no—
140Dic113#13714yescomplemented
141C2×C113—22no—
142C2×C113—81no—
143C2×C113C2×#12711yescharacteristic
144C2×C113C2×#13712yes—
145D113—81no—
146#3152—1131nomaximal, Sylow
147C113#315211yescharacteristic, complemented, Sylow
148C2×#137—1131no—
149C2×#137—1131no—
150C2×#137—1131no—
151C2×#137D11311yescharacteristic, complemented
152#532—1131no—
153C2×C4⋊Q8—1131no—
154#497—1132no—
155#497—1132no—
156#494—1132no—
157#492—1132no—
158C4×M16—1131no—
159C2×#41—1131no—
160C2×#41C2×D11311yescharacteristic
161C22×Q8—1131no—
162C22×Q8C2×D11311yescharacteristic
163#137—24no—
164#137—2264no—
165#137—2264no—
166#137—2264no—
167C2×Q16—1132no—
168C2×Q16—1132no—
169C2×Q16—1132no—
170C2×Q16C2×D11312yes—
171C2×SD16—1132no—
172C2×SD16—1132no—
173C2×SD16—1132no—
174C2×SD16C2×D11312yes—
175C2×M16—1131no—
176C2×M16C2×D11311yescharacteristic
177C4⋊Q8—1132no—
178C4⋊Q8—1132no—
179C4⋊Q8—1131no—
180C4⋊Q8—2262no—
181#127—1131no—
182#124—1131no—
183#124—1131no—
184#121—2262no—
185C4×D4—2262no—
186C2×C4⋊C4—2262no—
187C2×C42—1131no—
188#97—1132no—
189C4×C8—1132no—
190#41—22no—
191#41—22no—
192#41—2262no—
193#41—2262no—
194C2×Q8—21no—
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—1131no—
198C2×Q8—1132no—
199C2×Q8—2262no—
200C2×Q8—2262no—
201C2×Q8—2261no—
202C2×Q8C22×D11311yescharacteristic
203C2×Q8C22×D11312yes—
204C2×D4—21no—
205C2×D4—1131no—
206C2×D4—2262no—
207C2×D4—2261no—
208C2×D4C22×D11311yescharacteristic
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—1132no—
212C22×C4—2261no—
213C22×C4—2261no—
214C22×C4C22×D11311yescharacteristic
215Q16—24no—
216Q16—2264no—
217Q16—2264no—
218Q16—2264no—
219SD16—24no—
220SD16—2264no—
221SD16—2264no—
222SD16—2264no—
223M16—1134no—
224M16C22⋊D11314yescomplemented
225C2×C8—1132no—
226C2×C8C22×D11312yes—
227C4⋊C4—2264no—
228C4⋊C4—2264no—
229C4⋊C4—2262no—
230C22⋊C4—2262no—
231C22⋊C4—2262no—
232C42—1132no—
233C42—1131no—
234C42—1131no—
235C23—21no—
236C23—2261no—
237C23D4×D11311yescharacteristic
238Q8—22no—
239Q8—21no—
240Q8—22no—
241Q8—21no—
242Q8—42no—
243Q8—4522no—
244Q8—2262no—
245Q8—2261no—
246Q8—2262no—
247Q8—2261no—
248D4—21no—
249D4—21no—
250D4—42no—
251D4—4524no—
252D4—4522no—
253D4—2261no—
254D4—2261no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—1132no—
260C2×C4—1132no—
261C2×C4—4522no—
262C2×C4—4522no—
263C2×C4—2264no—
264C2×C4—2261no—
265C2×C4—2262no—
266C2×C4D4×D11311yescharacteristic
267C2×C4D4×D11312yes—
268C2×C4C2×C22⋊D11312yes—
269C2×C4C23×D11311yescharacteristic
270C8—1134no—
271C8C2×C22⋊D11314yes—
272C22—22no—
273C22—42no—
274C22—41no—
275C22—4522no—
276C22—4521no—
277C22#1681361812yes—
278C22C2×D4×D11311yescharacteristic
279C4—41no—
280C4—42no—
281C4—1134no—
282C4—4521no—
283C4—4522no—
284C4—2262no—
285C4#1681361812yes—
286C4C2×D4×D11311yescharacteristic
287C4C22×C22⋊D11311yescharacteristic
288C2—22no—
289C2—81no—
290C2—9041no—
291C2C2×#1681361811yescharacteristic
292C2#137×D11312yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#137×C113C2
socleC22×C113C22×D4
prime radical#20299144C2
hypercenterC2×#137D113
hypocenterC113#3152
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#16813655C2semidirect
2. C2×#16813653C2semidirect
3. C2×#16813652C2semidirect
5. C2×#16813620C2semidirect
6. #20298991C2semidirect
7. #20298989C2semidirect
8. #20298976C2semidirect
9. #20298969C2semidirect
10. M16×Dic113C2semidirect
11. C2×#137×C113C2semidirect
62. #14268631D4semidirect
86. M16×C113D4semidirect
140. Dic113#137semidirect
147. C113#3152semidirect
151. C2×#137D113semidirect
224. M16C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136552
C2×#168136532
C2×#168136522
#202991442
C2×#168136202
#202989912
#202989892
#202989762
#202989692
M16×Dic1132
C2×#137×C1132
#3152113