Finite Group Databasebeta

← #28391614

Subgroups — #28391614

Order 14464.

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

normal subgroups only

This group has 406 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
1C2×#16813648C211yesmaximal, characteristic, complemented
2#20299176C211yesmaximal, characteristic, complemented
3C2×#16813549C211yesmaximal, characteristic, complemented
4C2×#16813548C211yesmaximal, characteristic, complemented
5#20298501C211yesmaximal, characteristic, complemented
6#20298366C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C113C211yesmaximal, characteristic, complemented
8C2×#14268647C2211yescharacteristic
9#16813648—22no—
10#16813648—22no—
11C2×#14268635—21no—
12C2×#14268632—21no—
13C2×#14268631C2211yescharacteristic
14#16813601—21no—
15#16813598—21no—
16#16813596—21no—
17#16813594—22no—
18#16813593—21no—
19C2×C4⋊Dic113C2211yescharacteristic
20C2×C22⋊Dic113—22no—
21C2×C4×Dic113C2211yescharacteristic
22#16813549—22no—
23#16813548—22no—
24C2×#41×C113C2211yescharacteristic
25C22×D4×C113C2211yescharacteristic
26AGL(1,ℤ/8)×C113—22no—
27AGL(1,ℤ/8)×C113—22no—
28C2×SD16×C113—21no—
29C2×D8×C113—21no—
30C2×M16×C113C2211yescharacteristic
31#14268647—21no—
32#14268647—21no—
33#14268647—21no—
34#14268647—21no—
35C2×Dic226D411yescharacteristic
36C2×D452D411yescharacteristic
37C2×C22⋊D113—21no—
38C2×C22⋊D113—22no—
39C22×Dic113—21no—
40C22×Dic113D412yes—
41C2×C4×D113—21no—
42#14268635—24no—
43#14268632—24no—
44#14268631—21no—
45#14268631D412yescomplemented
46C2×#11744751—21no—
47C4⋊Dic113—21no—
48C4⋊Dic113—21no—
49#14268626—22no—
50C22⋊Dic113—22no—
51C22⋊Dic113—44no—
52#14268624—22no—
53C4×Dic113—21no—
54C4×Dic113—21no—
55C24×C113—21no—
56#41×C113—21no—
57#41×C113—21no—
58#41×C113—21no—
59#41×C113—21no—
60C2×Q8×C113D411yescharacteristic
61C2×D4×C113—21no—
62C2×D4×C113—21no—
63C2×D4×C113—21no—
64C2×D4×C113—21no—
65C2×D4×C113—21no—
66C2×D4×C113—21no—
67C2×D4×C113D411yescharacteristic
68C2×D4×C113D412yescomplemented
69C22×C4×C113—21no—
70C22×C4×C113C2311yescharacteristic
71SD16×C113—24no—
72D8×C113—24no—
73M16×C113—21no—
74M16×C113D412yescomplemented
75C2×C8×C113—21no—
76C23×C113—21no—
77C23×C113—22no—
78C23×C113—42no—
79C23×C113—42no—
80C23×C113—41no—
81C23×C113—41no—
82C23×C113C2×D411yescharacteristic
83C22×D113—21no—
84Q8×C113—21no—
85Q8×C113—21no—
86D4×C113—21no—
87D4×C113—22no—
88D4×C113—22no—
89D4×C113—21no—
90D4×C113—41no—
91D4×C113—41no—
92D4×C113—41no—
93D4×C113—41no—
94C2×C4×C113—21no—
95C2×C4×C113—41no—
96C2×C4×C113—41no—
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2×D411yescharacteristic
99C2×C4×C113C2×D411yescharacteristic
100C2×C4×C113C2×D411yescharacteristic
101C2×C4×C113C2×D411yescharacteristic
102C2×C4×C113#4111yescharacteristic
103C22⋊D113—41no—
104C22⋊D113—41no—
105C22⋊D113—82no—
106C2×Dic113—22no—
107C2×Dic113—22no—
108C2×Dic113—21no—
109C2×Dic113—41no—
110C2×Dic113—41no—
111C2×Dic113—42no—
112D452—21no—
113D452—21no—
114C4×D113—41no—
115C4×D113—41no—
116Dic226—21no—
117Dic226—21no—
118C8×C113—22no—
119#11744751—22no—
120C22×C113—21no—
121C22×C113—21no—
122C22×C113—44no—
123C22×C113—41no—
124C22×C113—42no—
125C22×C113—41no—
126C22×C113—41no—
127C22×C113—82no—
128C22×C113—81no—
129C22×C113—81no—
130C22×C113#12011yescharacteristic
131C22×C113#12111yescharacteristic
132C22×C113#12711yescharacteristic
133C2×D113—41no—
134C2×D113—41no—
135C2×D113—41no—
136C4×C113—41no—
137C4×C113#12011yescharacteristic
138C4×C113#12011yescharacteristic
139C4×C113#12111yescharacteristic
140C4×C113#12111yescharacteristic
141Dic113—42no—
142Dic113—41no—
143Dic113—42no—
144C2×C113—21no—
145C2×C113—21no—
146C2×C113—81no—
147C2×C113—82no—
148C2×C113#39211yescharacteristic
149C2×C113#45311yescharacteristic
150C2×C113#45411yescharacteristic
151D113—81no—
152#2006—1131nomaximal, Sylow
153C113#200611yescharacteristic, complemented, Sylow
154C2×AGL(1,ℤ/8)—1131no—
155C2×AGL(1,ℤ/8)D11311yescharacteristic, complemented
156#537—1131no—
157C2×#104—1131no—
158C2×#104—1131no—
159#390—1131no—
160#343—1131no—
161C2×#41—1131no—
162C2×#41C2×D11311yescharacteristic
163C22×D4C2×D11311yescharacteristic
164AGL(1,ℤ/8)—22no—
165AGL(1,ℤ/8)—22no—
166AGL(1,ℤ/8)—2262no—
167AGL(1,ℤ/8)—2262no—
168C2×SD16—21no—
169C2×SD16—2261no—
170C2×D8—21no—
171C2×D8—2261no—
172C2×M16—1131no—
173C2×M16C2×D11311yescharacteristic
174C22⋊Q8—2261no—
175C22⋊Q8—2261no—
176#121—2261no—
177#121—2262no—
178#121—2261no—
179C2×C4⋊C4—1131no—
180C2×C22⋊C4—2262no—
181C2×C42—1131no—
182#104—2262no—
183#104—2262no—
184C24—21no—
185#41—21no—
186#41—21no—
187#41—21no—
188#41—21no—
189#41—2261no—
190#41—2261no—
191#41—2261no—
192#41—2261no—
193C2×Q8—1131no—
194C2×Q8C22⋊D11311yescharacteristic
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—1131no—
202C2×D4—2262no—
203C2×D4—2261no—
204C2×D4C22⋊D11311yescharacteristic
205C2×D4C22⋊D11312yescomplemented
206C22×C4—21no—
207C22×C4—1132no—
208C22×C4—2261no—
209C22×C4—2261no—
210C22×C4C22×D11311yescharacteristic
211SD16—24no—
212SD16—2264no—
213D8—24no—
214D8—2264no—
215M16—21no—
216M16—1132no—
217M16—2261no—
218M16C22⋊D11312yescomplemented
219C2×C8—21no—
220C2×C8—2261no—
221C4⋊C4—2262no—
222C4⋊C4—2261no—
223C4⋊C4—2261no—
224C22⋊C4—4524no—
225C22⋊C4—2262no—
226C22⋊C4—2262no—
227C42—2261no—
228C42—2261no—
229C23—21no—
230C23—22no—
231C23—42no—
232C23—42no—
233C23—41no—
234C23—41no—
235C23—2261no—
236C23D4×D11311yescharacteristic
237Q8—21no—
238Q8—21no—
239Q8—2261no—
240Q8—2261no—
241D4—22no—
242D4—21no—
243D4—22no—
244D4—21no—
245D4—41no—
246D4—41no—
247D4—41no—
248D4—41no—
249D4—9042no—
250D4—4521no—
251D4—4521no—
252D4—2261no—
253D4—2261no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—4521no—
258C2×C4—4521no—
259C2×C4—4521no—
260C2×C4—4521no—
261C2×C4—4522no—
262C2×C4—2262no—
263C2×C4—2262no—
264C2×C4—2261no—
265C2×C4D4×D11311yescharacteristic
266C2×C4D4×D11311yescharacteristic
267C2×C4C2×C22⋊D11311yescharacteristic
268C2×C4C2×C22⋊D11311yescharacteristic
269C2×C4C2×C22⋊D11311yescharacteristic
270C2×C4#1426864611yescharacteristic
271C8—22no—
272C8—2262no—
273C22—21no—
274C22—21no—
275C22—44no—
276C22—41no—
277C22—42no—
278C22—41no—
279C22—41no—
280C22—82no—
281C22—81no—
282C22—81no—
283C22—4521no—
284C22—4521no—
285C22—4521no—
286C22#1681359011yescharacteristic
287C22#1681359411yescharacteristic
288C22#1681361811yescharacteristic
289C4—41no—
290C4—4522no—
291C4—4521no—
292C4—4522no—
293C4#1681359011yescharacteristic
294C4#1681359111yescharacteristic
295C4#1681359311yescharacteristic
296C4#1681359411yescharacteristic
297C2—21no—
298C2—21no—
299C2—82no—
300C2—81no—
301C2—9041no—
302C2#2029850611yescharacteristic
303C2#2029876411yescharacteristic
304C2#2029876911yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
FittingC2×AGL(1,ℤ/8)×C113C2
socleC22×C113#120
hypercenterC2×AGL(1,ℤ/8)D113
hypocenterC113#2006
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#16813648C2semidirect
2. #20299176C2semidirect
3. C2×#16813549C2semidirect
4. C2×#16813548C2semidirect
5. #20298501C2semidirect
6. #20298366C2semidirect
7. C2×AGL(1,ℤ/8)×C113C2semidirect
45. #14268631D4semidirect
68. C2×D4×C113D4semidirect
74. M16×C113D4semidirect
153. C113#2006semidirect
155. C2×AGL(1,ℤ/8)D113semidirect
205. C2×D4C22⋊D113semidirect
218. M16C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136482
#202991762
C2×#168135492
C2×#168135482
#202985012
#202983662
C2×AGL(1,ℤ/8)×C1132
#2006113