Finite Group Databasebeta

← #28391702

Subgroups — #28391702

Order 14464.

430 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 75 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#20299157C211yesmaximal, characteristic
2C2×#16813605C211yesmaximal, characteristic, complemented
3C2×#16813537C211yesmaximal, characteristic, complemented
4C2×#16813536C211yesmaximal, characteristic, complemented
5#20298461C211yesmaximal, characteristic, complemented
6#20298364C211yesmaximal, characteristic, complemented
7C2×#123×C113C211yesmaximal, characteristic, complemented
8C22×C22⋊D113C2211yescharacteristic
9#16813605—22no—
10#16813605—21no—
11#16813605—22no—
12#16813603—21no—
13#16813594—22no—
14#16813591—21no—
15#16813590—21no—
16C2×#14268626—21no—
17C2×C22⋊Dic113C2211yescharacteristic
18C2×C22⋊Dic113C2211yescharacteristic
19C2×C22⋊Dic113C2211yescharacteristic
20C2×#14268624—21no—
21#16813537—22no—
22#16813536—22no—
23#16813529—22no—
24C22×D4×C113C2211yescharacteristic
25C23×C4×C113C2211yescharacteristic
26#123×C113—22no—
27#123×C113—22no—
28C2×C4⋊C4×C113—21no—
29C2×C22⋊C4×C113—21no—
30C2×C22⋊C4×C113C2211yescharacteristic
31C23×D113D411yescharacteristic
32C2×C22⋊D113—21no—
33C2×C22⋊D113—21no—
34C2×C22⋊D113—21no—
35C2×C22⋊D113—21no—
36C2×C22⋊D113—21no—
37C2×C22⋊D113—21no—
38C2×C22⋊D113—22no—
39C22×Dic113—21no—
40C22×Dic113—21no—
41C22×Dic113D411yescharacteristic
42C22×Dic113D412yes—
43#14268626—24no—
44#14268626—22no—
45C22⋊Dic113—22no—
46C22⋊Dic113—21no—
47C22⋊Dic113—21no—
48C22⋊Dic113—21no—
49C22⋊Dic113—21no—
50C22⋊Dic113—21no—
51C22⋊Dic113D412yescomplemented
52#14268624—24no—
53#14268624—22no—
54C24×C113D411yescharacteristic
55C24×C113C2311yescharacteristic
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×C113—21no—
63C22×C4×C113—21no—
64C22×C4×C113—21no—
65C22×C4×C113—21no—
66C22×C4×C113—21no—
67C22×C4×C113—21no—
68C22×C4×C113—21no—
69C22×C4×C113D411yescharacteristic
70C22×C4×C113D412yescomplemented
71C4⋊C4×C113—24no—
72C22⋊C4×C113—24no—
73C22⋊C4×C113—21no—
74C22⋊C4×C113D412yescomplemented
75C23×C113—21no—
76C23×C113—21no—
77C23×C113—21no—
78C23×C113—42no—
79C23×C113—42no—
80C23×C113C2×D411yescharacteristic
81C23×C113C2×D411yescharacteristic
82C23×C113C2×D411yescharacteristic
83C23×C113C2×D411yescharacteristic
84C23×C113C2×D411yescharacteristic
85C23×C113C2×D411yescharacteristic
86C23×C113#4111yescharacteristic
87C22×D113—21no—
88C22×D113—21no—
89C22×D113—21no—
90C22×D113—42no—
91D4×C113—41no—
92D4×C113—41no—
93D4×C113—41no—
94D4×C113—41no—
95C2×C4×C113—22no—
96C2×C4×C113—22no—
97C2×C4×C113—21no—
98C2×C4×C113—22no—
99C2×C4×C113—21no—
100C2×C4×C113—22no—
101C2×C4×C113—21no—
102C2×C4×C113—42no—
103C2×C4×C113—41no—
104C2×C4×C113—41no—
105C2×C4×C113—41no—
106C2×C4×C113—41no—
107C22⋊D113—41no—
108C22⋊D113—41no—
109C22⋊D113—41no—
110C22⋊D113—41no—
111C22⋊D113—82no—
112C2×Dic113—22no—
113C2×Dic113—22no—
114C2×Dic113—21no—
115C2×Dic113—21no—
116C2×Dic113—21no—
117C2×Dic113—42no—
118C2×Dic113—42no—
119C2×Dic113—42no—
120C2×Dic113—41no—
121C22×C113—22no—
122C22×C113—22no—
123C22×C113—22no—
124C22×C113—41no—
125C22×C113—41no—
126C22×C113—41no—
127C22×C113—41no—
128C22×C113—42no—
129C22×C113—41no—
130C22×C113—42no—
131C22×C113—81no—
132C22×C113#12011yescharacteristic
133C22×C113#12011yescharacteristic
134C22×C113#12011yescharacteristic
135C22×C113#12111yescharacteristic
136C22×C113#12111yescharacteristic
137C22×C113#12111yescharacteristic
138C22×C113#12711yescharacteristic
139C2×D113—42no—
140C2×D113—41no—
141C2×D113—42no—
142C2×D113—81no—
143C4×C113—42no—
144C4×C113—42no—
145C4×C113—41no—
146Dic113—42no—
147Dic113—41no—
148Dic113—42no—
149Dic113—81no—
150C2×C113—21no—
151C2×C113—21no—
152C2×C113—21no—
153C2×C113—21no—
154C2×C113—21no—
155C2×C113—21no—
156C2×C113—81no—
157C2×C113#39211yescharacteristic
158C2×C113#45812yes—
159D113—81no—
160#2022—1131nomaximal, Sylow
161C113#202211yescharacteristic, complemented, Sylow
162#534—1131no—
163C2×#123—1131no—
164C2×#123D11311yescharacteristic, complemented
165C2×#99—1131no—
166C2×#99—1131no—
167#381—1131no—
168#342—1131no—
169C22×D4—1131no—
170C22×D4C2×D11311yescharacteristic
171C23×C4C2×D11311yescharacteristic
172#123—22no—
173#123—22no—
174#123—2262no—
175#123—2261no—
176#123—2261no—
177#123—2262no—
178#121—2262no—
179#120—2261no—
180#120—2261no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—2261no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—1131no—
185C2×C22⋊C4—1131no—
186C2×C22⋊C4—1131no—
187C2×C22⋊C4—2261no—
188C2×C22⋊C4C2×D11311yescharacteristic
189#99—2262no—
190#99—2262no—
191#95—2262no—
192C24—1131no—
193C24C22⋊D11311yescharacteristic
194C24C22×D11311yescharacteristic
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—2262no—
202C2×D4—2261no—
203C2×D4—2261no—
204C2×D4—2261no—
205C2×D4—2261no—
206C2×D4—2261no—
207C2×D4—2261no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—1132no—
216C22×C4—1131no—
217C22×C4—2261no—
218C22×C4—2261no—
219C22×C4C22⋊D11311yescharacteristic
220C22×C4C22⋊D11312yescomplemented
221C4⋊C4—24no—
222C4⋊C4—2264no—
223C4⋊C4—2262no—
224C22⋊C4—24no—
225C22⋊C4—21no—
226C22⋊C4—1132no—
227C22⋊C4—2264no—
228C22⋊C4—2262no—
229C22⋊C4—2261no—
230C22⋊C4—2261no—
231C22⋊C4—2262no—
232C22⋊C4—2261no—
233C22⋊C4—2261no—
234C22⋊C4—2261no—
235C22⋊C4C22⋊D11312yescomplemented
236C23—21no—
237C23—21no—
238C23—21no—
239C23—42no—
240C23—42no—
241C23—4522no—
242C23—2261no—
243C23—2261no—
244C23—2261no—
245C23D4×D11311yescharacteristic
246C23D4×D11311yescharacteristic
247C23D4×D11311yescharacteristic
248C23C2×C22⋊D11311yescharacteristic
249C23C2×C22⋊D11311yescharacteristic
250C23C2×C22⋊D11311yescharacteristic
251C23#1426864611yescharacteristic
252D4—41no—
253D4—41no—
254D4—41no—
255D4—41no—
256D4—9042no—
257D4—4521no—
258D4—4521no—
259D4—4521no—
260D4—4521no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—4522no—
274C2×C4—4521no—
275C2×C4—4522no—
276C2×C4—4522no—
277C2×C4—2262no—
278C2×C4—2261no—
279C2×C4—2262no—
280C2×C4—2261no—
281C2×C4—2261no—
282C22—22no—
283C22—22no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—41no—
291C22—42no—
292C22—81no—
293C22—9041no—
294C22—4522no—
295C22—4521no—
296C22—4522no—
297C22#1681359011yescharacteristic
298C22#1681359011yescharacteristic
299C22#1681359111yescharacteristic
300C22#1681359311yescharacteristic
301C22#1681359411yescharacteristic
302C22#1681359411yescharacteristic
303C22#1681361811yescharacteristic
304C4—42no—
305C4—42no—
306C4—41no—
307C4—9041no—
308C4—4522no—
309C4—4521no—
310C4—4522no—
311C2—21no—
312C2—21no—
313C2—21no—
314C2—21no—
315C2—21no—
316C2—21no—
317C2—81no—
318C2—9041no—
319C2#2029850611yescharacteristic
320C2#2029878712yes—
subgroupG/H
centerC22#16813590
commutator, cosocleC24×C113C23
FrattiniC24C22×D113
FittingC2×#123×C113C2
socleC22×C113#120
prime radical#20299157C2
hypercenterC2×#123D113
hypocenterC113#2022
LCSG ▷ C24×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C24 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×#16813605C2semidirect
3. C2×#16813537C2semidirect
4. C2×#16813536C2semidirect
5. #20298461C2semidirect
6. #20298364C2semidirect
7. C2×#123×C113C2semidirect
51. C22⋊Dic113D4semidirect
70. C22×C4×C113D4semidirect
74. C22⋊C4×C113D4semidirect
161. C113#2022semidirect
164. C2×#123D113semidirect
220. C22×C4C22⋊D113semidirect
235. C22⋊C4C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
#202991572
C2×#168136052
C2×#168135372
C2×#168135362
#202984612
#202983642
C2×#123×C1132
#2022113