Finite Group Databasebeta

← #28406416

Subgroups — #28406416

Order 14464.

618 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 88 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×#16813687C212yesmaximal, complemented
2C2×#16813686C212yesmaximal, complemented
3#20299569C211yesmaximal, characteristic, complemented
4C4×C22⋊#90673C211yesmaximal, characteristic, complemented
5C2×#41×D113C211yesmaximal, characteristic
6C2×#14268657C2212yescomplemented
7C2×C22⋊#90673—21no—
8C2×C4×#90673C2212yescomplemented
9#16813687—24no—
10#16813686—24no—
11#16813679—21no—
12C22⋊#11744753—21no—
13(C2×#90673)⋊C4—21no—
14C2×#14268648C2211yescharacteristic
15C2×#14268647—21no—
16C2×#14268647C411yescharacteristic, complemented
17C2×#14268646—21no—
18C2×#14268646C2211yescharacteristic
19#41×D113—24no—
20#41×D113—24no—
21C2×Q8×D113C411yescharacteristic, complemented
22C2×D4×D113—21no—
23C2×D4×D113C411yescharacteristic, complemented
24C22×C4×D113—21no—
25C22×C4×D113C2211yescharacteristic
26C2×#41×C113C411yescharacteristic, complemented
27C22×#90673—22no—
28#14268657—22no—
29#14268657—22no—
30C2×#11744753—22no—
31C22⋊#90673—24no—
32C4×#90673—22no—
33C4×#90673—22no—
34C23×D113—21no—
35C23×D113D411yescharacteristic
36#14268648—22no—
37#14268648D414yes—
38#14268647—28no—
39#14268647—22no—
40#14268647—22no—
41#14268646—28no—
42#14268646—22no—
43#14268646D414yes—
44C2×Dic226—21no—
45C2×Dic226C2×C411yescharacteristic
46Q8×D113—22no—
47Q8×D113—22no—
48C2×D452—21no—
49C2×D452C2×C411yescharacteristic
50C2×C22⋊D113—21no—
51C2×C22⋊D113—21no—
52C2×C22⋊D113—21no—
53D4×D113—28no—
54D4×D113—22no—
55D4×D113—22no—
56C22×Dic113—21no—
57C22×Dic113D411yescharacteristic
58C2×C4×D113—28no—
59C2×C4×D113—21no—
60C2×C4×D113—21no—
61C2×C4×D113—21no—
62C2×C4×D113—22no—
63C2×C4×D113—22no—
64C2×C4×D113C2×C411yescharacteristic
65C2×C4×D113D411yescharacteristic
66C2×C4×D113D411yescharacteristic
67C2×C4×D113C2311yescharacteristic
68#41×C113—22no—
69#41×C113—22no—
70C2×Q8×C113C2×C411yescharacteristic
71C2×D4×C113—21no—
72C2×D4×C113C2×C411yescharacteristic
73C22×C4×C113—21no—
74C22×C4×C113C2×C411yescharacteristic
75C23×C113—21no—
76C23×C113C22⋊C411yescharacteristic
77C22×D113—24no—
78C22×D113—21no—
79C22×D113—22no—
80C22×D113—22no—
81C22×D113—41no—
82C22×D113—42no—
83C22×D113—42no—
84C22×D113C22⋊C411yescharacteristic
85C22×D113C2×D411yescharacteristic
86C2×#90673—24no—
87C2×#90673—42no—
88C2×#90673—42no—
89Q8×C113—21no—
90Q8×C113C22⋊C412yescomplemented
91D4×C113—24no—
92D4×C113—21no—
93D4×C113C22⋊C412yescomplemented
94C2×C4×C113—24no—
95C2×C4×C113—21no—
96C2×C4×C113—21no—
97C2×C4×C113—21no—
98C2×C4×C113C22⋊C411yescharacteristic
99C2×C4×C113C22×C411yescharacteristic
100C22⋊D113—24no—
101C22⋊D113—24no—
102C22⋊D113—24no—
103C2×Dic113—21no—
104C2×Dic113—24no—
105C2×Dic113—22no—
106C2×Dic113C22⋊C411yescharacteristic
107C2×Dic113C2×D411yescharacteristic
108D452—24no—
109D452—21no—
110D452C22⋊C412yescomplemented
111C4×D113—24no—
112C4×D113—24no—
113C4×D113—22no—
114C4×D113—21no—
115C4×D113—21no—
116C4×D113—22no—
117C4×D113—24no—
118C4×D113C2×D412yes—
119C4×D113C2×D412yes—
120Dic226—24no—
121Dic226—21no—
122Dic226C22⋊C412yescomplemented
123#11744753—42no—
124C22×C113—21no—
125C22×C113—22no—
126C22×C113—21no—
127C22×C113—21no—
128C22×C113—41no—
129C22×C113—41no—
130C22×C113C2×C22⋊C411yescharacteristic
131C2×D113—21no—
132C2×D113—21no—
133C2×D113—21no—
134C2×D113—21no—
135C2×D113—22no—
136C2×D113—44no—
137C2×D113—48no—
138C2×D113—41no—
139C2×D113—41no—
140C2×D113#10412yescomplemented
141C2×D113#12012yes—
142#90673—44no—
143C4×C113—22no—
144C4×C113—21no—
145C4×C113C2×C22⋊C411yescharacteristic
146C4×C113C2×C22⋊C411yescharacteristic
147Dic113—21no—
148Dic113—22no—
149Dic113#12012yes—
150C2×C113—41no—
151C2×C113—42no—
152C2×C113#37911yescharacteristic
153C2×C113C2×#10411yescharacteristic
154C2×C113#42111yescharacteristic
155D113—22no—
156D113—22no—
157D113—42no—
158#1789—1131nomaximal, Sylow
159C113#178911yescharacteristic, complemented, Sylow
160C22×#41—1131no—
161C2×#104—1132no—
162C2×#104—1132no—
163#407—1131no—
164C4×C22⋊C4—1131no—
165C2×#41—1131no—
166C2×#41—1131no—
167C2×#41—1131no—
168C2×#41—2261no—
169C2×#41—2261no—
170C2×#41—2264no—
171C2×#41—2264no—
172C2×#41#9067311yescharacteristic, complemented
173C22×Q8—1131no—
174C22×D4—1131no—
175C22×D4—2261no—
176C23×C4—1131no—
177C23×C4—2261no—
178C2×M16—1132no—
179C2×C22⋊C4—2261no—
180C2×C42—1132no—
181#104—2264no—
182#104—2264no—
183C22⋊C8—2261no—
184C22⋊C8—2261no—
185#95—2261no—
186C24—1131no—
187C24—2261no—
188#41—22no—
189#41—22no—
190#41—1134no—
191#41—1134no—
192#41—2262no—
193#41—2262no—
194#41—2268no—
195#41—2262no—
196#41—2262no—
197#41—2268no—
198C2×Q8—1131no—
199C2×Q8—2261no—
200C2×Q8—2262no—
201C2×Q8—2262no—
202C2×Q8C2×#9067311yescharacteristic
203C2×D4—21no—
204C2×D4—1131no—
205C2×D4—2261no—
206C2×D4—2261no—
207C2×D4—2262no—
208C2×D4—2268no—
209C2×D4—2261no—
210C2×D4—2261no—
211C2×D4—2262no—
212C2×D4C2×#9067311yescharacteristic
213C22×C4—21no—
214C22×C4—1131no—
215C22×C4—1131no—
216C22×C4—1131no—
217C22×C4—1131no—
218C22×C4—1131no—
219C22×C4—2262no—
220C22×C4—2262no—
221C22×C4—2261no—
222C22×C4—2261no—
223C22×C4—2268no—
224C22×C4—2261no—
225C22×C4—2262no—
226C22×C4—2261no—
227C22×C4C2×#9067311yescharacteristic
228M16—2262no—
229M16—2262no—
230C2×C8—2262no—
231C22⋊C4—2264no—
232C42—2262no—
233C42—2262no—
234C23—21no—
235C23—1131no—
236C23—1131no—
237C23—4521no—
238C23—4522no—
239C23—4522no—
240C23—2262no—
241C23—2262no—
242C23—2264no—
243C23—2261no—
244C23C22⋊#9067311yescharacteristic
245Q8—21no—
246Q8—1132no—
247Q8—2264no—
248Q8—2261no—
249Q8C22⋊#9067312yescomplemented
250D4—24no—
251D4—21no—
252D4—1132no—
253D4—2264no—
254D4—2264no—
255D4—2264no—
256D4—2264no—
257D4—2261no—
258D4C22⋊#9067312yescomplemented
259C2×C4—24no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—1131no—
264C2×C4—1132no—
265C2×C4—1132no—
266C2×C4—1131no—
267C2×C4—4522no—
268C2×C4—4522no—
269C2×C4—2262no—
270C2×C4—2264no—
271C2×C4—2262no—
272C2×C4—2264no—
273C2×C4—2264no—
274C2×C4—2262no—
275C2×C4—2264no—
276C2×C4—2264no—
277C2×C4—2261no—
278C2×C4—2261no—
279C2×C4—2261no—
280C2×C4C22⋊#9067311yescharacteristic
281C2×C4C22×#9067311yescharacteristic
282C8—4522no—
283C22—21no—
284C22—22no—
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—1132no—
290C22—1132no—
291C22—4528no—
292C22—4524no—
293C22—4521no—
294C22—4521no—
295C22—2262no—
296C22—2261no—
297C22—2261no—
298C22—2261no—
299C22—2261no—
300C22C2×C22⋊#9067311yescharacteristic
301C4—21no—
302C4—22no—
303C4—1132no—
304C4—4524no—
305C4—2261no—
306C4—2262no—
307C4C2×C22⋊#9067311yescharacteristic
308C4C2×C22⋊#9067311yescharacteristic
309C2—41no—
310C2—42no—
311C2—4522no—
312C2—2262no—
313C2—2262no—
314C2#2029953911yescharacteristic
315C2D113⋊#10411yescharacteristic
316C2#2029959511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC2×#41×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC2×#41×D113C2
cosocleC2×C4×D113C23
hypercenterC2×#41#90673
hypocenterC113#1789
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#16813687C2semidirect
2. C2×#16813686C2semidirect
3. #20299569C2semidirect
4. C4×C22⋊#90673C2semidirect
6. C2×#14268657C22semidirect
8. C2×C4×#90673C22semidirect
16. C2×#14268647C4semidirect
21. C2×Q8×D113C4semidirect
23. C2×D4×D113C4semidirect
26. C2×#41×C113C4semidirect
90. Q8×C113C22⋊C4semidirect
93. D4×C113C22⋊C4semidirect
110. D452C22⋊C4semidirect
122. Dic226C22⋊C4semidirect
140. C2×D113#104semidirect
159. C113#1789semidirect
172. C2×#41#90673semidirect
249. Q8C22⋊#90673semidirect
258. D4C22⋊#90673semidirect

Maximal subgroups

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

subgroupindex
C2×#168136872
C2×#168136862
#202995692
C4×C22⋊#906732
C2×#41×D1132
#1789113