Finite Group Databasebeta

← #28399452

Subgroups — #28399452

Order 14464.

484 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813643C211yesmaximal, characteristic
2#20299080C211yesmaximal, characteristic, complemented
3#20299077C211yesmaximal, characteristic, complemented
4#20298708C211yesmaximal, characteristic, complemented
5#20298707C211yesmaximal, characteristic, complemented
6#20298703C211yesmaximal, characteristic, complemented
7#20298702C211yesmaximal, characteristic, complemented
8C4×#14268636C211yesmaximal, characteristic, complemented
9SD16×Dic113C211yesmaximal, characteristic, complemented
10#20298685C211yesmaximal, characteristic, complemented
11#106×D113C211yesmaximal, characteristic, complemented
12#20298598C211yesmaximal, characteristic, complemented
13#20298596C211yesmaximal, characteristic, complemented
14#20298552C211yesmaximal, characteristic, complemented
15C4×SD16×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18#16813643C418yescomplemented
19C2×#14268637C2211yescharacteristic
20C2×#14268636C2211yescharacteristic
21C2×#14268632C2211yescharacteristic
22C2×#14268630C2211yescharacteristic
23C2×C8×D113C2211yescharacteristic
24Q8×Dic113C2211yescharacteristic
25C4×Dic226C2211yescharacteristic
26#16813587C2211yescharacteristic
27C4×D452—21no—
28C4×D452C2211yescharacteristic
29D4×Dic113C2211yescharacteristic
30#16813584—21no—
31#16813584C2211yescharacteristic
32C4×C22⋊D113—21no—
33#16813582—21no—
34#16813579—21no—
35#16813579C2211yescharacteristic
36#16813578—21no—
37C2×#14268626—21no—
38C4⋊C4×D113—21no—
39C4⋊C4×D113C2211yescharacteristic
40C4⋊C4×D113C2211yescharacteristic
41#16813554C2211yescharacteristic
42#16813553C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813533C2211yescharacteristic
51#16813532C2211yescharacteristic
52C8×Dic113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54C4×Q8×C113C2211yescharacteristic
55C4×D4×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C4×C8×C113C2211yescharacteristic
60#14268648—22no—
61#14268648C2×C414yescomplemented
62#14268646—22no—
63#14268646C2×C414yescomplemented
64C2×Dic226C2311yescharacteristic
65C2×D452—21no—
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C22×Dic113—21no—
69C22×Dic113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113—21no—
74C2×C4×D113—21no—
75C2×C4×D113C2311yescharacteristic
76#14268637C2×C414yescomplemented
77#14268636C2×C414yescomplemented
78#14268632C2×C414yescomplemented
79#14268630—22no—
80C2×#11744751C2311yescharacteristic
81C2×#11744751C2311yescharacteristic
82C8×D113C2×C414yescomplemented
83C4⋊Dic113—21no—
84C4⋊Dic113C2311yescharacteristic
85C4⋊Dic113C2311yescharacteristic
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89#14268626—21no—
90#14268626D411yescharacteristic
91#14268626D411yescharacteristic
92C22⋊Dic113—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624D411yescharacteristic
96#14268624D411yescharacteristic
97C4×Dic113—21no—
98C4×Dic113—21no—
99C4×Dic113—21no—
100C4×Dic113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C2×D4×C113C2311yescharacteristic
103C22×C4×C113—21no—
104SD16×C113C2×C414yescomplemented
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113—21no—
108C4⋊C4×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C42×C113—21no—
112C42×C113C2311yescharacteristic
113C23×C113—21no—
114C22×D113—21no—
115C22×D113C2×D411yescharacteristic
116Q8×C113—21no—
117Q8×C113C22×C412yes—
118D4×C113—21no—
119D4×C113C22×C412yes—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—81no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2411yescharacteristic
127C22⋊D113—24no—
128C2×Dic113—21no—
129C2×Dic113—24no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—81no—
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135C2×Dic113C2×D411yescharacteristic
136D452—24no—
137D452—21no—
138D452C22×C412yes—
139C4×D113—24no—
140C4×D113—81no—
141C4×D113—81no—
142C4×D113—81no—
143C4×D113—81no—
144C4×D113C22×C412yes—
145C4×D113#4112yes—
146Dic226—21no—
147Dic226C22×C412yes—
148C8×C113—21no—
149C8×C113C22×C412yes—
150#11744751—21no—
151#11744751C22×C412yes—
152C22×C113—22no—
153C22×C113—41no—
154C22×C113—41no—
155C22×C113C22×D411yescharacteristic
156C2×D113—21no—
157C2×D113—21no—
158C2×D113—22no—
159C2×D113—41no—
160C2×D113—41no—
161C2×D113C4×D412yes—
162C4×C113—22no—
163C4×C113—21no—
164C4×C113—21no—
165C4×C113—41no—
166C4×C113—41no—
167C4×C113C23×C411yescharacteristic
168C4×C113C2×#4111yescharacteristic
169Dic113—22no—
170Dic113—21no—
171Dic113—21no—
172Dic113—41no—
173Dic113—41no—
174Dic113C4×D412yes—
175C2×C113—42no—
176C2×C113C2×C4×D411yescharacteristic
177C2×C113#57711yescharacteristic
178C2×C113#57711yescharacteristic
179D113—22no—
180D113—42no—
181#2952—1131nomaximal, Sylow
182C113#295211yescharacteristic, complemented, Sylow
183C2×#135—1131no—
184#520—1131no—
185#520—1131no—
186#442—1131no—
187#442—1131no—
188#441—1131no—
189#441—1131no—
190C4×SD16—1131no—
191C4×SD16—1131no—
192C4×SD16—1131no—
193C4×SD16D11311yescharacteristic, complemented
194C2×#106—1131no—
195#417—1131no—
196#417—1131no—
197#405—1131no—
198C2×#41—1131no—
199C2×#41—1131no—
200#135—1138no—
201C2×Q16—1131no—
202C2×SD16—1131no—
203C2×SD16C2×D11311yescharacteristic
204C2×D8—1131no—
205C2×M16—1131no—
206C22×C8—1131no—
207C4×Q8—1131no—
208C4×Q8—1131no—
209C4×Q8—1131no—
210C4×Q8C2×D11311yescharacteristic
211C4×D4—1131no—
212C4×D4—1131no—
213C4×D4—1131no—
214C4×D4—2261no—
215C4×D4—2261no—
216C4×D4—2261no—
217C4×D4—2261no—
218C4×D4C2×D11311yescharacteristic
219#117—1131no—
220#117—2261no—
221#117—2261no—
222C2×C4⋊C4—1131no—
223C2×C4⋊C4—1131no—
224C2×C4⋊C4—2261no—
225C2×C4⋊C4—2261no—
226#106—1131no—
227#106—1131no—
228#106—1131no—
229#106C2×D11311yescharacteristic
230#103—1131no—
231#103—1131no—
232#103—1131no—
233#103C2×D11311yescharacteristic
234#102—1131no—
235#102—1131no—
236#102—1131no—
237#102C2×D11311yescharacteristic
238#97—1131no—
239#97—1131no—
240C4×C8—1131no—
241C4×C8C2×D11311yescharacteristic
242#41—1134no—
243#41—1134no—
244#41—2262no—
245#41—2262no—
246C2×Q8—1131no—
247C2×Q8C22×D11311yescharacteristic
248C2×D4—1131no—
249C2×D4—2261no—
250C2×D4—2261no—
251C2×D4C22×D11311yescharacteristic
252C22×C4—21no—
253C22×C4—1131no—
254C22×C4—2261no—
255C22×C4—2261no—
256C22×C4—2261no—
257C22×C4—2261no—
258C22×C4—2261no—
259C22×C4—2261no—
260C22×C4—2261no—
261Q16—1134no—
262SD16—1134no—
263SD16C4×D11314yescomplemented
264D8—1134no—
265M16—2262no—
266C2×C8—1131no—
267C2×C8—1134no—
268C2×C8—1131no—
269C2×C8C22×D11311yescharacteristic
270C2×C8C22×D11311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—1131no—
273C4⋊C4—1131no—
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—2261no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4C22×D11311yescharacteristic
282C4⋊C4C22×D11311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—1131no—
285C22⋊C4—1131no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C42—21no—
290C42—1131no—
291C42—2261no—
292C42—2261no—
293C42—2261no—
294C42C22×D11311yescharacteristic
295C23—21no—
296C23—1131no—
297C23—2261no—
298Q8—21no—
299Q8—1132no—
300Q8—2261no—
301Q8C2×C4×D11312yes—
302D4—21no—
303D4—1132no—
304D4—2264no—
305D4—2264no—
306D4—2261no—
307D4C2×C4×D11312yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—1131no—
313C2×C4—1132no—
314C2×C4—1132no—
315C2×C4—1131no—
316C2×C4—1131no—
317C2×C4—9041no—
318C2×C4—9041no—
319C2×C4—9041no—
320C2×C4—9041no—
321C2×C4—9041no—
322C2×C4—2264no—
323C2×C4—2264no—
324C2×C4—2261no—
325C2×C4—2261no—
326C2×C4—2261no—
327C2×C4D4×D11311yescharacteristic
328C2×C4D4×D11311yescharacteristic
329C2×C4C23×D11311yescharacteristic
330C8—21no—
331C8—1132no—
332C8—2261no—
333C8C2×C4×D11312yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—1132no—
338C22—4521no—
339C22—4521no—
340C22—2262no—
341C22—2261no—
342C22—2261no—
343C22C2×D4×D11311yescharacteristic
344C4—22no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—1132no—
350C4—4521no—
351C4—4521no—
352C4—2262no—
353C4—2261no—
354C4—2261no—
355C4C22×C4×D11311yescharacteristic
356C4#41×D11311yescharacteristic
357C2—42no—
358C2—4522no—
359C2—2262no—
360C2C4×D4×D11311yescharacteristic
361C2#2029940411yescharacteristic
362C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
FittingC4×SD16×C113C2
socleC22×C113C22×D4
prime radicalC2×#16813643C2
cosocleC2×C4×C113C24
hypercenterC4×SD16D113
hypocenterC113#2952
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #20299080C2semidirect
3. #20299077C2semidirect
4. #20298708C2semidirect
5. #20298707C2semidirect
6. #20298703C2semidirect
7. #20298702C2semidirect
8. C4×#14268636C2semidirect
9. SD16×Dic113C2semidirect
10. #20298685C2semidirect
11. #106×D113C2semidirect
12. #20298598C2semidirect
13. #20298596C2semidirect
14. #20298552C2semidirect
15. C4×SD16×C113C2semidirect
18. #16813643C4semidirect
61. #14268648C2×C4semidirect
63. #14268646C2×C4semidirect
76. #14268637C2×C4semidirect
77. #14268636C2×C4semidirect
78. #14268632C2×C4semidirect
82. C8×D113C2×C4semidirect
104. SD16×C113C2×C4semidirect
182. C113#2952semidirect
193. C4×SD16D113semidirect
263. SD16C4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136432
#202990802
#202990772
#202987082
#202987072
#202987032
#202987022
C4×#142686362
SD16×Dic1132
#202986852
#106×D1132
#202985982
#202985962
#202985522
C4×SD16×C1132
#2952113