Finite Group Databasebeta

← #28402821

Subgroups — #28402821

Order 14464.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299257C211yesmaximal, characteristic, complemented
2#20298955C211yesmaximal, characteristic, complemented
3#20298928C211yesmaximal, characteristic, complemented
4#20298922C211yesmaximal, characteristic, complemented
5#20298902C211yesmaximal, characteristic, complemented
6#20298849C211yesmaximal, characteristic, complemented
7#20298842C211yesmaximal, characteristic, complemented
8#20298813C211yesmaximal, characteristic, complemented
9#20298741C211yesmaximal, characteristic, complemented
10#20298736C211yesmaximal, characteristic, complemented
11C4×#14268635C211yesmaximal, characteristic, complemented
12#20298676C211yesmaximal, characteristic, complemented
13#20298606C211yesmaximal, characteristic, complemented
14#20298597C211yesmaximal, characteristic, complemented
15#553×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C22×Dic226C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21C2×#14268631C2211yescharacteristic
22C2×#14268631C2211yescharacteristic
23#16813610C2211yescharacteristic
24#16813608—21no—
25#16813601C2211yescharacteristic
26#16813600—21no—
27#16813596C2211yescharacteristic
28#16813594—21no—
29C4×Dic226C2211yescharacteristic
30#16813582—21no—
31#16813555C2211yescharacteristic
32#16813553C2211yescharacteristic
33#16813553C2211yescharacteristic
34C4⋊#11744751C2211yescharacteristic
35#16813545C2211yescharacteristic
36#16813545C2211yescharacteristic
37#16813545C2211yescharacteristic
38#16813545C2211yescharacteristic
39#16813545C2211yescharacteristic
40#16813545C2211yescharacteristic
41#16813543C2211yescharacteristic
42#16813542C2211yescharacteristic
43#16813542C2211yescharacteristic
44#16813542C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46C22⋊#11744751C2211yescharacteristic
47C4×#11744751C2211yescharacteristic
48#126×C113—21no—
49#125×C113C2211yescharacteristic
50#123×C113—21no—
51#121×C113—21no—
52#121×C113C2211yescharacteristic
53#121×C113C2211yescharacteristic
54C4×D4×C113—21no—
55C4×D4×C113C2211yescharacteristic
56C4×D4×C113C2211yescharacteristic
57#117×C113C2211yescharacteristic
58C2×C4⋊C4×C113C2211yescharacteristic
59#14268647—22no—
60#14268647—41no—
61C2×Dic226—22no—
62C2×Dic226—21no—
63C2×Dic226—41no—
64C2×Dic226C2311yescharacteristic
65C2×Dic226C2311yescharacteristic
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C22×Dic113—21no—
70C2×C4×D113—21no—
71#14268635—22no—
72#14268635—41no—
73#14268632—41no—
74#14268631—41no—
75#14268631—41no—
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81#14268626—21no—
82#14268626—21no—
83C22⋊Dic113—21no—
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87C4×Dic113—21no—
88C2×D4×C113—21no—
89C2×D4×C113—21no—
90C2×D4×C113D411yescharacteristic
91C2×D4×C113C2311yescharacteristic
92C22×C4×C113—21no—
93C22×C4×C113—21no—
94C22×C4×C113C2311yescharacteristic
95C22×C4×C113C2311yescharacteristic
96C4⋊C4×C113—21no—
97C4⋊C4×C113—21no—
98C4⋊C4×C113—21no—
99C4⋊C4×C113D411yescharacteristic
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C22⋊C4×C113—21no—
104C22⋊C4×C113—21no—
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C22⋊C4×C113D411yescharacteristic
108C22⋊C4×C113D411yescharacteristic
109C42×C113—21no—
110C42×C113C2311yescharacteristic
111C23×C113—21no—
112C23×C113C2×D411yescharacteristic
113C23×C113C2×D411yescharacteristic
114C22×D113—21no—
115D4×C113—21no—
116D4×C113—21no—
117D4×C113—41no—
118D4×C113—42no—
119D4×C113—81no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—81no—
128C2×C4×C113—81no—
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2×D411yescharacteristic
131C2×C4×C113C2×D411yescharacteristic
132C2×C4×C113C2×D411yescharacteristic
133C2×C4×C113C2411yescharacteristic
134C22⋊D113—42no—
135C22⋊D113—42no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113—42no—
140D452—21no—
141D452—21no—
142C4×D113—42no—
143Dic226—21no—
144Dic226—21no—
145Dic226—21no—
146Dic226—42no—
147Dic226#4112yes—
148#11744751—21no—
149#11744751—21no—
150#11744751—21no—
151#11744751—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113—21no—
156C22×C113—21no—
157C22×C113—21no—
158C22×C113—41no—
159C22×C113—41no—
160C22×C113—41no—
161C22×C113C22×D411yescharacteristic
162C2×D113—41no—
163C2×D113—41no—
164C2×D113—41no—
165C4×C113—21no—
166C4×C113—21no—
167C4×C113—21no—
168C4×C113—21no—
169C4×C113—41no—
170C4×C113—41no—
171C4×C113—41no—
172C4×C113C2×#4111yescharacteristic
173C4×C113H(5,𝔽2)11yescharacteristic
174Dic113—22no—
175Dic113—41no—
176Dic113—41no—
177C2×C113—41no—
178C2×C113—41no—
179C2×C113—81no—
180C2×C113#54611yescharacteristic
181C2×C113#57511yescharacteristic
182C2×C113#57711yescharacteristic
183D113—81no—
184#3326—1131nomaximal, Sylow
185C113#332611yescharacteristic, complemented, Sylow
186#553D11311yescharacteristic, complemented
187#548—1131no—
188#488—1131no—
189#483—1131no—
190#482—1131no—
191#479—1131no—
192#469—1131no—
193#468—1131no—
194#463—1131no—
195#449—1131no—
196#448—1131no—
197C4×SD16—1131no—
198#436—1131no—
199#419—1131no—
200#417—1131no—
201C2×#41—1131no—
202C22×Q8—1131no—
203C2×SD16—1131no—
204C2×SD16—1131no—
205C2×D8—1131no—
206C2×M16—1131no—
207C2×M16—1131no—
208#126—21no—
209#125C2×D11311yescharacteristic
210#124—1131no—
211#124—2261no—
212#123—21no—
213C22⋊Q8—1131no—
214C22⋊Q8—2261no—
215#121—21no—
216#121—1131no—
217#121—2261no—
218#121C2×D11311yescharacteristic
219#121C2×D11311yescharacteristic
220C4×Q8—1131no—
221C4×D4—21no—
222C4×D4—2261no—
223C4×D4C2×D11311yescharacteristic
224C4×D4C2×D11311yescharacteristic
225#117C2×D11311yescharacteristic
226C2×C4⋊C4C2×D11311yescharacteristic
227#107—1131no—
228#106—1131no—
229#106—1131no—
230C4⋊C8—1131no—
231#103—1131no—
232#103—1131no—
233#103—1131no—
234#103—1131no—
235#103—1131no—
236#103—1131no—
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#102—1131no—
241C22⋊C8—1131no—
242C22⋊C8—1131no—
243C4×C8—1131no—
244#41—4521no—
245#41—2262no—
246C2×Q8—1131no—
247C2×Q8—1131no—
248C2×Q8—4521no—
249C2×Q8—2262no—
250C2×Q8—2261no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—1131no—
254C2×D4—2261no—
255C2×D4—2261no—
256C2×D4C22⋊D11311yescharacteristic
257C2×D4C22×D11311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—2261no—
261C22×C4—2261no—
262C22×C4C22×D11311yescharacteristic
263C22×C4C22×D11311yescharacteristic
264SD16—4521no—
265SD16—2262no—
266D8—4521no—
267M16—4521no—
268M16—4521no—
269C2×C8—1131no—
270C2×C8—1131no—
271C2×C8—1131no—
272C2×C8—1131no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—1131no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4C22⋊D11311yescharacteristic
280C4⋊C4C22×D11311yescharacteristic
281C4⋊C4C22×D11311yescharacteristic
282C4⋊C4C22×D11311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4C22⋊D11311yescharacteristic
292C22⋊C4C22⋊D11311yescharacteristic
293C42—21no—
294C42—2261no—
295C42C22×D11311yescharacteristic
296C23—21no—
297C23—2261no—
298C23C2×C22⋊D11311yescharacteristic
299C23C2×C22⋊D11311yescharacteristic
300Q8—1132no—
301Q8—4522no—
302Q8—2261no—
303Q8—2261no—
304Q8—2261no—
305D4—21no—
306D4—21no—
307D4—41no—
308D4—42no—
309D4—81no—
310D4—4522no—
311D4—4522no—
312D4—2261no—
313D4—2261no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—4522no—
324C2×C4—4522no—
325C2×C4—2261no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4C2×C22⋊D11311yescharacteristic
329C2×C4C2×C22⋊D11311yescharacteristic
330C2×C4C2×C22⋊D11311yescharacteristic
331C2×C4C2×C22⋊D11311yescharacteristic
332C2×C4C23×D11311yescharacteristic
333C8—2261no—
334C8—2261no—
335C8—2261no—
336C8—2261no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—4521no—
347C22—4521no—
348C22—4521no—
349C22C22×C22⋊D11311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—4521no—
358C4—4521no—
359C4—2262no—
360C4#41×D11311yescharacteristic
361C4#1681366811yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—9041no—
366C2#2029923611yescharacteristic
367C2#2029939611yescharacteristic
368C2#2029940911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#553×C113C2
socleC22×C113C22×D4
hypercenter#553D113
hypocenterC113#3326
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #20299257C2semidirect
2. #20298955C2semidirect
3. #20298928C2semidirect
4. #20298922C2semidirect
5. #20298902C2semidirect
6. #20298849C2semidirect
7. #20298842C2semidirect
8. #20298813C2semidirect
9. #20298741C2semidirect
10. #20298736C2semidirect
11. C4×#14268635C2semidirect
12. #20298676C2semidirect
13. #20298606C2semidirect
14. #20298597C2semidirect
15. #553×C113C2semidirect
185. C113#3326semidirect
186. #553D113semidirect

Maximal subgroups

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

subgroupindex
#202992572
#202989552
#202989282
#202989222
#202989022
#202988492
#202988422
#202988132
#202987412
#202987362
C4×#142686352
#202986762
#202986062
#202985972
#553×C1132
#3326113