Finite Group Databasebeta

← #28402908

Subgroups — #28402908

Order 14464.

398 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299303C211yesmaximal, characteristic, complemented
2#20299267C211yesmaximal, characteristic
3#20298943C211yesmaximal, characteristic, complemented
4#20298911C211yesmaximal, characteristic, complemented
5#20298910C211yesmaximal, characteristic, complemented
6#20298891C211yesmaximal, characteristic, complemented
7#20298844C211yesmaximal, characteristic, complemented
8#20298843C211yesmaximal, characteristic, complemented
9#20298797C211yesmaximal, characteristic, complemented
10#20298763C211yesmaximal, characteristic, complemented
11#20298760C211yesmaximal, characteristic, complemented
12#20298690C211yesmaximal, characteristic, complemented
13#20298674C211yesmaximal, characteristic, complemented
14#20298598C211yesmaximal, characteristic, complemented
15#417×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18C2×#14268636C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813618—21no—
23#16813618C2211yescharacteristic
24#16813612—21no—
25#16813602C2211yescharacteristic
26#16813601—21no—
27#16813601C2211yescharacteristic
28#16813600—21no—
29#16813596—21no—
30#16813596C2211yescharacteristic
31#16813593—21no—
32#16813593C2211yescharacteristic
33Q8×Dic113C2211yescharacteristic
34#16813587C2211yescharacteristic
35C4×C22⋊D113—21no—
36C4×C22⋊D113—21no—
37C4×C22⋊D113C2211yescharacteristic
38C4⋊C4×D113C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C2×M16×C113C2211yescharacteristic
54C2×C4⋊C4×C113C2211yescharacteristic
55#103×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268648—22no—
60#14268648—41no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63C2×D452—21no—
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113D411yescharacteristic
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113C2311yescharacteristic
73#14268637—22no—
74#14268636—41no—
75#14268635—41no—
76#14268630—41no—
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C4⋊Dic113—21no—
80C4⋊Dic113—21no—
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626D411yescharacteristic
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113D411yescharacteristic
91#14268624—21no—
92#14268624—21no—
93#14268624D411yescharacteristic
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97#41×C113—22no—
98#41×C113—41no—
99C2×Q8×C113C2311yescharacteristic
100C2×D4×C113—21no—
101C2×D4×C113C2311yescharacteristic
102C22×C4×C113—21no—
103C22×C4×C113—21no—
104C22×C4×C113C2311yescharacteristic
105M16×C113—41no—
106C2×C8×C113C2311yescharacteristic
107C2×C8×C113C2311yescharacteristic
108C4⋊C4×C113—21no—
109C4⋊C4×C113C2311yescharacteristic
110C4⋊C4×C113C2311yescharacteristic
111C23×C113—21no—
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114C22×D113C2×D411yescharacteristic
115Q8×C113—21no—
116Q8×C113#4112yes—
117D4×C113—21no—
118D4×C113—21no—
119D4×C113—42no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—42no—
126C2×C4×C113—81no—
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2411yescharacteristic
129C22⋊D113—22no—
130C22⋊D113—42no—
131C22⋊D113—81no—
132C22⋊D113—81no—
133C22⋊D113—81no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139C2×Dic113C2×D411yescharacteristic
140D452—21no—
141D452—21no—
142D452—42no—
143C4×D113—21no—
144C4×D113—21no—
145C4×D113—42no—
146C4×D113—81no—
147Dic226—21no—
148Dic226—21no—
149Dic226—81no—
150C8×C113—21no—
151C8×C113—21no—
152#11744751—21no—
153#11744751—21no—
154C22×C113—21no—
155C22×C113—21no—
156C22×C113—21no—
157C22×C113—41no—
158C22×C113—41no—
159C22×C113—41no—
160C22×C113C22×D411yescharacteristic
161C2×D113—21no—
162C2×D113—21no—
163C2×D113—21no—
164C2×D113—41no—
165C2×D113—41no—
166C2×D113—41no—
167C4×C113—22no—
168C4×C113—21no—
169C4×C113—41no—
170C4×C113—41no—
171C4×C113C2×#4111yescharacteristic
172C4×C113H(5,𝔽2)11yescharacteristic
173Dic113—21no—
174Dic113—21no—
175Dic113—41no—
176Dic113—41no—
177Dic113—41no—
178Dic113#13712yes—
179C2×C113—41no—
180C2×C113—81no—
181C2×C113#54611yescharacteristic
182C2×C113C2×#13711yescharacteristic
183C2×C113#57611yescharacteristic
184D113—41no—
185D113—81no—
186#3333—1131nomaximal, Sylow
187C113#333311yescharacteristic, complemented, Sylow
188#554—1131no—
189#550—1131no—
190#486—1131no—
191#480—1131no—
192#480—1131no—
193#477—1131no—
194#468—1131no—
195#468—1131no—
196#460—1131no—
197#452—1131no—
198#452—1131no—
199C4×Q16—1131no—
200#436—1131no—
201#417—1131no—
202#417D11311yescharacteristic, complemented
203C2×#41—1131no—
204C2×#41C2×D11311yescharacteristic
205C2×Q16—1131no—
206C2×SD16—1131no—
207C2×SD16—1131no—
208C2×M16—1131no—
209C2×M16C2×D11311yescharacteristic
210C4⋊Q8—1131no—
211#127—1131no—
212#127—2261no—
213#125—2261no—
214C22⋊Q8—1131no—
215C22⋊Q8—1131no—
216C22⋊Q8—2261no—
217C22⋊Q8—2261no—
218#121—1131no—
219#121—1131no—
220#121—2261no—
221#121—2261no—
222C4×Q8—1131no—
223C4×Q8—1131no—
224C4×D4—1131no—
225C4×D4—2261no—
226C4×D4—2261no—
227C2×C4⋊C4—1131no—
228C2×C4⋊C4C2×D11311yescharacteristic
229#107—1131no—
230#107—1131no—
231#107—1131no—
232C4⋊C8—1131no—
233#103—1131no—
234#103—1131no—
235#103C2×D11311yescharacteristic
236#103C2×D11311yescharacteristic
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#102—1131no—
241#102C2×D11311yescharacteristic
242#102C2×D11311yescharacteristic
243C22⋊C8—1131no—
244C22⋊C8—1131no—
245C4×C8—1131no—
246#41—22no—
247#41—41no—
248#41—4521no—
249#41—2262no—
250C2×Q8—1131no—
251C2×Q8—2261no—
252C2×Q8C22×D11311yescharacteristic
253C2×D4—21no—
254C2×D4—1131no—
255C2×D4—1131no—
256C2×D4—2261no—
257C2×D4—2261no—
258C2×D4—2261no—
259C2×D4—2261no—
260C2×D4—2261no—
261C2×D4C22×D11311yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—1131no—
265C22×C4—2261no—
266C22×C4—2261no—
267C22×C4C22×D11311yescharacteristic
268Q16—2262no—
269SD16—4521no—
270SD16—4521no—
271M16—41no—
272M16—4521no—
273C2×C8—1131no—
274C2×C8—1131no—
275C2×C8C22×D11311yescharacteristic
276C2×C8C22×D11311yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—1131no—
279C4⋊C4—1131no—
280C4⋊C4—1131no—
281C4⋊C4—2261no—
282C4⋊C4—2261no—
283C4⋊C4—2261no—
284C4⋊C4—2261no—
285C4⋊C4—2261no—
286C4⋊C4—2261no—
287C4⋊C4C22×D11311yescharacteristic
288C4⋊C4C22×D11311yescharacteristic
289C22⋊C4—1131no—
290C22⋊C4—1131no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C22⋊C4—2261no—
295C42—1131no—
296C42—2261no—
297C42—2261no—
298C23—21no—
299C23—1131no—
300C23—2261no—
301C23D4×D11311yescharacteristic
302Q8—21no—
303Q8—9041no—
304Q8—2261no—
305Q8—2261no—
306Q8#1426864712yes—
307D4—21no—
308D4—21no—
309D4—42no—
310D4—9041no—
311D4—9041no—
312D4—9041no—
313D4—4522no—
314D4—4522no—
315D4—2262no—
316D4—2261no—
317D4—2261no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—81no—
325C2×C4—1131no—
326C2×C4—1131no—
327C2×C4—1131no—
328C2×C4—9041no—
329C2×C4—4522no—
330C2×C4—2261no—
331C2×C4—2261no—
332C2×C4—2261no—
333C2×C4—2261no—
334C2×C4—2261no—
335C2×C4D4×D11311yescharacteristic
336C2×C4C23×D11311yescharacteristic
337C8—21no—
338C8—21no—
339C8—2261no—
340C8—2261no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—4521no—
348C22—4521no—
349C22—4521no—
350C22—2261no—
351C22—2261no—
352C22—2261no—
353C22C2×D4×D11311yescharacteristic
354C4—21no—
355C4—22no—
356C4—41no—
357C4—41no—
358C4—1132no—
359C4—4521no—
360C4—4521no—
361C4—4521no—
362C4—2261no—
363C4—2261no—
364C4C2×#1426864711yescharacteristic
365C4#1681366711yescharacteristic
366C2—41no—
367C2—81no—
368C2—9041no—
369C2—4521no—
370C2#2029923811yescharacteristic
371C2#137×D11311yescharacteristic
372C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#417×C113C2
socleC22×C113C22×D4
prime radical#20299267C2
hypercenter#417D113
hypocenterC113#3333
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #20299303C2semidirect
3. #20298943C2semidirect
4. #20298911C2semidirect
5. #20298910C2semidirect
6. #20298891C2semidirect
7. #20298844C2semidirect
8. #20298843C2semidirect
9. #20298797C2semidirect
10. #20298763C2semidirect
11. #20298760C2semidirect
12. #20298690C2semidirect
13. #20298674C2semidirect
14. #20298598C2semidirect
15. #417×C113C2semidirect
187. C113#3333semidirect
202. #417D113semidirect

Maximal subgroups

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

subgroupindex
#202993032
#202992672
#202989432
#202989112
#202989102
#202988912
#202988442
#202988432
#202987972
#202987632
#202987602
#202986902
#202986742
#202985982
#417×C1132
#3333113