Finite Group Databasebeta

← #28390546

Subgroups — #28390546

Order 14464.

536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16813670C211yesmaximal, characteristic
2#20298616C211yesmaximal, characteristic, complemented
3#20298614C211yesmaximal, characteristic, complemented
4#20298607C211yesmaximal, characteristic, complemented
5#20298580C211yesmaximal, characteristic, complemented
6#20298571C211yesmaximal, characteristic, complemented
7#419×C113C211yesmaximal, characteristic, complemented
8#16813670—22no—
9#16813670—22no—
10#16813670—22no—
11#16813670—22no—
12C2×#14268648—21no—
13C2×#14268648C412yescomplemented
14C2×#14268647—22no—
15C2×#14268647C2211yescharacteristic
16C2×#14268647C2211yescharacteristic
17C2×Q8×D113—21no—
18C2×Q8×D113C412yescomplemented
19C2×#14268631C2211yescharacteristic
20#16813581C2211yescharacteristic
21#16813550—22no—
22#16813548—22no—
23#16813546—22no—
24#16813540—21no—
25#16813538—21no—
26#16813536—22no—
27C22×Q8×C113C2211yescharacteristic
28C2×M16×C113C2211yescharacteristic
29#117×C113C2211yescharacteristic
30#103×C113—22no—
31#14268648—24no—
32#14268648—24no—
33#14268648—24no—
34#14268648—24no—
35#14268647—28no—
36#14268647—28no—
37#14268647—21no—
38#14268647—21no—
39#14268647—21no—
40#14268647—21no—
41#14268647—21no—
42#14268647—21no—
43#14268647D412yes—
44#14268647D412yes—
45C2×Dic226—22no—
46C2×Dic226C2×C411yescharacteristic
47C2×Dic226D411yescharacteristic
48Q8×D113—24no—
49Q8×D113—24no—
50Q8×D113—24no—
51Q8×D113—24no—
52C2×D452—22no—
53C2×D452C2×C411yescharacteristic
54C2×D452D411yescharacteristic
55C2×C22⋊D113—21no—
56C2×C22⋊D113D412yes—
57C2×C4×D113—22no—
58C2×C4×D113—21no—
59C2×C4×D113—22no—
60C2×C4×D113C2×C412yes—
61#14268631—21no—
62#14268631—21no—
63C2×#11744751—21no—
64C4⋊Dic113—21no—
65C22⋊Dic113—21no—
66C4×Dic113—21no—
67C2×Q8×C113—21no—
68C2×Q8×C113—21no—
69C2×Q8×C113—21no—
70C2×Q8×C113C2×C412yes—
71C2×Q8×C113D412yes—
72C2×Q8×C113D412yes—
73C22×C4×C113—21no—
74C22×C4×C113C2311yescharacteristic
75M16×C113—21no—
76M16×C113—21no—
77C2×C8×C113—21no—
78C4⋊C4×C113—21no—
79C22⋊C4×C113—21no—
80C42×C113—21no—
81C23×C113C2×D411yescharacteristic
82C22×D113—21no—
83C22×D113C22⋊C412yes—
84Q8×C113—22no—
85Q8×C113—22no—
86Q8×C113—22no—
87Q8×C113C22⋊C414yes—
88C2×C4×C113—22no—
89C2×C4×C113—22no—
90C2×C4×C113—22no—
91C2×C4×C113—41no—
92C2×C4×C113C22×C411yescharacteristic
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2×D411yescharacteristic
96C2×C4×C113C2×D411yescharacteristic
97C2×C4×C113C2×D411yescharacteristic
98C22⋊D113—22no—
99C22⋊D113—22no—
100C22⋊D113—22no—
101C22⋊D113—22no—
102C2×Dic113—21no—
103C2×Dic113—41no—
104C2×Dic113C22⋊C412yes—
105D452—28no—
106D452—21no—
107D452—21no—
108D452—21no—
109D452C22⋊C412yes—
110C4×D113—28no—
111C4×D113—28no—
112C4×D113—22no—
113C4×D113—22no—
114C4×D113—22no—
115C4×D113—22no—
116Dic226—28no—
117Dic226—21no—
118Dic226—21no—
119Dic226—21no—
120Dic226C22⋊C412yes—
121C8×C113—41no—
122#11744751—41no—
123C22×C113—41no—
124C22×C113C2×C22⋊C411yescharacteristic
125C22×C113#12011yescharacteristic
126C22×C113#12011yescharacteristic
127C2×D113—22no—
128C2×D113—22no—
129C2×D113—42no—
130C2×D113—42no—
131C4×C113—24no—
132C4×C113—81no—
133C4×C113C2×C22⋊C411yescharacteristic
134C4×C113C2×C22⋊C411yescharacteristic
135C4×C113#12011yescharacteristic
136C4×C113#12011yescharacteristic
137Dic113—22no—
138Dic113—22no—
139Dic113—81no—
140C2×C113—21no—
141C2×C113—21no—
142C2×C113—21no—
143C2×C113#37911yescharacteristic
144D113—42no—
145D113—42no—
146#1796—1131nomaximal, Sylow
147C113#179611yescharacteristic, complemented, Sylow
148C2×2−1+4—1131no—
149#421—1131no—
150#421—1131no—
151#419—1131no—
152#419D11311yescharacteristic, complemented
153#413—1131no—
154#410—1131no—
1552−1+4—2262no—
1562−1+4—2262no—
1572−1+4—2262no—
1582−1+4—2262no—
159C2×#41—1131no—
160C2×#41—1132no—
161C2×#41—1131no—
162C2×#41—2262no—
163C2×#41—2261no—
164C22×Q8—1132no—
165C22×Q8—2261no—
166C22×Q8C2×D11311yescharacteristic
167C2×M16—1131no—
168C2×M16C2×D11311yescharacteristic
169#117—1131no—
170#117C2×D11311yescharacteristic
171#104—2262no—
172#104—2262no—
173#103—22no—
174#103—2262no—
175#101—2261no—
176#100—2261no—
177#99—2262no—
178#41—1132no—
179#41—1132no—
180#41—2268no—
181#41—2268no—
182#41—2264no—
183#41—2264no—
184#41—2264no—
185#41—2264no—
186#41—2261no—
187#41—2261no—
188#41—2261no—
189#41—2261no—
190#41—2261no—
191#41—2261no—
192C2×Q8—21no—
193C2×Q8—21no—
194C2×Q8—21no—
195C2×Q8—1131no—
196C2×Q8—1131no—
197C2×Q8—2262no—
198C2×Q8—2264no—
199C2×Q8—2264no—
200C2×Q8—2264no—
201C2×Q8—2264no—
202C2×Q8C4×D11312yes—
203C2×Q8D45212yes—
204C2×Q8C22⋊D11312yes—
205C2×D4—1132no—
206C2×D4—1131no—
207C2×D4—1131no—
208C2×D4—2262no—
209C2×D4—2261no—
210C22×C4—21no—
211C22×C4—1132no—
212C22×C4—2262no—
213C22×C4—2262no—
214C22×C4—2261no—
215C22×C4C22×D11311yescharacteristic
216M16—21no—
217M16—21no—
218M16—2261no—
219M16—2261no—
220C2×C8—21no—
221C2×C8—2261no—
222C4⋊C4—21no—
223C4⋊C4—2261no—
224C22⋊C4—21no—
225C22⋊C4—2261no—
226C42—21no—
227C42—2261no—
228C23—1132no—
229C23—2261no—
230C23D4×D11311yescharacteristic
231Q8—22no—
232Q8—22no—
233Q8—22no—
234Q8—1132no—
235Q8—2268no—
236Q8—2261no—
237Q8—2261no—
238Q8—2261no—
239Q8#1426862414yes—
240D4—1132no—
241D4—2268no—
242D4—2262no—
243D4—2262no—
244D4—2262no—
245D4—2262no—
246D4—2261no—
247D4—2261no—
248D4—2261no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—1132no—
254C2×C4—4521no—
255C2×C4—2268no—
256C2×C4—2268no—
257C2×C4—2261no—
258C2×C4—2262no—
259C2×C4—2262no—
260C2×C4—2262no—
261C2×C4—2262no—
262C2×C4C2×C4×D11311yescharacteristic
263C2×C4D4×D11311yescharacteristic
264C2×C4D4×D11311yescharacteristic
265C2×C4D4×D11311yescharacteristic
266C2×C4C2×C22⋊D11311yescharacteristic
267C2×C4C2×D45211yescharacteristic
268C8—41no—
269C8—4521no—
270C22—41no—
271C22—4522no—
272C22—4522no—
273C22—2262no—
274C22—2262no—
275C22C22⋊C4×D11311yescharacteristic
276C22#1681359011yescharacteristic
277C22#1681359211yescharacteristic
278C4—24no—
279C4—81no—
280C4—9041no—
281C4—2262no—
282C4—2262no—
283C4C22⋊C4×D11311yescharacteristic
284C4C2×#1426862411yescharacteristic
285C4#1681359011yescharacteristic
286C4#1681359211yescharacteristic
287C2—21no—
288C2—21no—
289C2—21no—
290C2—4522no—
291C2—4522no—
292C2#2029845311yescharacteristic
subgroupG/H
centerC2#20298453
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#419×C113C2
socleC2×C113#379
prime radicalC2×#16813670C2
cosocleC22×C4×C113C23
hypercenter#419D113
hypocenterC113#1796
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. #20298616C2semidirect
3. #20298614C2semidirect
4. #20298607C2semidirect
5. #20298580C2semidirect
6. #20298571C2semidirect
7. #419×C113C2semidirect
13. C2×#14268648C4semidirect
18. C2×Q8×D113C4semidirect
147. C113#1796semidirect
152. #419D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136702
#202986162
#202986142
#202986072
#202985802
#202985712
#419×C1132
#1796113