Finite Group Databasebeta

← #28403038

Subgroups — #28403038

Order 14464.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299252C211yesmaximal, characteristic, complemented
2#20299008C211yesmaximal, characteristic, complemented
3#20298922C211yesmaximal, characteristic, complemented
4#20298916C211yesmaximal, characteristic, complemented
5#20298914C211yesmaximal, characteristic, complemented
6#20298909C211yesmaximal, characteristic, complemented
7#20298895C211yesmaximal, characteristic, complemented
8#20298888C211yesmaximal, characteristic, complemented
9#20298849C211yesmaximal, characteristic, complemented
10#20298832C211yesmaximal, characteristic, complemented
11#20298708C211yesmaximal, characteristic, complemented
12#20298670C211yesmaximal, characteristic, complemented
13#20298641C211yesmaximal, characteristic, complemented
14C2×#16813553C211yesmaximal, characteristic, complemented
15#553×C113C211yesmaximal, characteristic, complemented
16C2×#14268646—21no—
17C2×#14268632C2211yescharacteristic
18C2×#14268631C2211yescharacteristic
19C22×#11744751C2211yescharacteristic
20#16813622C2211yescharacteristic
21#16813606—21no—
22#16813606—21no—
23#16813602—21no—
24#16813596C2211yescharacteristic
25#16813596C2211yescharacteristic
26C4×D452C2211yescharacteristic
27C2×C4⋊Dic113C2211yescharacteristic
28C2×C4⋊Dic113C2211yescharacteristic
29#16813555C2211yescharacteristic
30#16813555C2211yescharacteristic
31#16813555C2211yescharacteristic
32#16813553C2211yescharacteristic
33#16813553C2211yescharacteristic
34#16813553C2211yescharacteristic
35#16813553C2211yescharacteristic
36#16813553C2211yescharacteristic
37#16813553C2211yescharacteristic
38C4⋊#11744751C2211yescharacteristic
39#16813543C2211yescharacteristic
40#16813543C2211yescharacteristic
41#16813543C2211yescharacteristic
42#16813542C2211yescharacteristic
43#16813542C2211yescharacteristic
44#16813542C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46C22⋊#11744751C2211yescharacteristic
47#16813533C2211yescharacteristic
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#14268646—44no—
60C2×Dic226—21no—
61C2×D452C2311yescharacteristic
62C2×C22⋊D113—21no—
63C2×C22⋊D113—21no—
64C22×Dic113—21no—
65C22×Dic113—21no—
66C2×C4×D113—21no—
67#14268632—22no—
68#14268631—22no—
69C2×#11744751—22no—
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80#14268624—21no—
81#14268624—21no—
82#14268624—21no—
83C2×D4×C113—21no—
84C2×D4×C113—21no—
85C2×D4×C113D411yescharacteristic
86C2×D4×C113C2311yescharacteristic
87C22×C4×C113—21no—
88C22×C4×C113—21no—
89C22×C4×C113C2311yescharacteristic
90C22×C4×C113C2311yescharacteristic
91C4⋊C4×C113—21no—
92C4⋊C4×C113—21no—
93C4⋊C4×C113—21no—
94C4⋊C4×C113D411yescharacteristic
95C4⋊C4×C113C2311yescharacteristic
96C4⋊C4×C113C2311yescharacteristic
97C4⋊C4×C113C2311yescharacteristic
98C22⋊C4×C113—21no—
99C22⋊C4×C113—21no—
100C22⋊C4×C113—21no—
101C22⋊C4×C113—21no—
102C22⋊C4×C113D411yescharacteristic
103C22⋊C4×C113D411yescharacteristic
104C42×C113—21no—
105C42×C113C2311yescharacteristic
106C23×C113—21no—
107C23×C113C2×D411yescharacteristic
108C23×C113C2×D411yescharacteristic
109C22×D113—21no—
110D4×C113—22no—
111D4×C113—21no—
112D4×C113—21no—
113D4×C113—42no—
114D4×C113—81no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—81no—
123C2×C4×C113—81no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2411yescharacteristic
129C22⋊D113—42no—
130C22⋊D113—42no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—42no—
135C2×Dic113—42no—
136D452—21no—
137D452—21no—
138C4×D113—42no—
139Dic226—42no—
140#11744751—21no—
141#11744751—21no—
142#11744751—21no—
143#11744751#4112yescomplemented
144C22×C113—21no—
145C22×C113—21no—
146C22×C113—21no—
147C22×C113—21no—
148C22×C113—21no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113—41no—
152C22×C113AGL(1,ℤ/8)12yes—
153C22×C113C22×D411yescharacteristic
154C2×D113—41no—
155C2×D113—41no—
156C2×D113—41no—
157C4×C113—21no—
158C4×C113—21no—
159C4×C113—21no—
160C4×C113—21no—
161C4×C113—41no—
162C4×C113—41no—
163C4×C113—41no—
164C4×C113C2×#4111yescharacteristic
165C4×C1132−1+411yescharacteristic
166Dic113—41no—
167Dic113—41no—
168Dic113—41no—
169C2×C113—22no—
170C2×C113—41no—
171C2×C113—81no—
172C2×C113#54711yescharacteristic
173C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
174C2×C113#57711yescharacteristic
175D113—81no—
176#3345—1131nomaximal, Sylow
177C113#334511yescharacteristic, complemented, Sylow
178#553D11311yescharacteristic, complemented
179#547—1131no—
180#501—1131no—
181#482—1131no—
182#481—1131no—
183#481—1131no—
184#480—1131no—
185#478—1131no—
186#476—1131no—
187#469—1131no—
188#466—1131no—
189#442—1131no—
190#435—1131no—
191#428—1131no—
192C2×#106—1131no—
193C2×#41—2261no—
194C2×D8—1131no—
195C2×M16—1131no—
196C22×C8—1131no—
197C4⋊Q8—1131no—
198#126—21no—
199#125C2×D11311yescharacteristic
200#123—21no—
201#123—2261no—
202#123—2261no—
203C22⋊Q8—2261no—
204#121—21no—
205#121—1131no—
206#121—1131no—
207#121C2×D11311yescharacteristic
208#121C2×D11311yescharacteristic
209C4×D4—21no—
210C4×D4—1131no—
211C4×D4C2×D11311yescharacteristic
212C4×D4C2×D11311yescharacteristic
213#117C2×D11311yescharacteristic
214C2×C4⋊C4—1131no—
215C2×C4⋊C4—1131no—
216C2×C4⋊C4C2×D11311yescharacteristic
217#107—1131no—
218#107—1131no—
219#107—1131no—
220#106—1131no—
221#106—1131no—
222#106—1131no—
223#106—1131no—
224#106—1131no—
225#106—1131no—
226C4⋊C8—1131no—
227#102—1131no—
228#102—1131no—
229#102—1131no—
230#102—1131no—
231#102—1131no—
232#102—1131no—
233C22⋊C8—1131no—
234C22⋊C8—1131no—
235#97—1131no—
236#41—4524no—
237C2×Q8—2261no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—1131no—
241C2×D4—2261no—
242C2×D4—2261no—
243C2×D4C22⋊D11311yescharacteristic
244C2×D4C22×D11311yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—2261no—
248C22×C4—2261no—
249C22×C4—2261no—
250C22×C4C22×D11311yescharacteristic
251C22×C4C22×D11311yescharacteristic
252D8—2262no—
253M16—2262no—
254C2×C8—1131no—
255C2×C8—1131no—
256C2×C8—1131no—
257C2×C8—1131no—
258C2×C8—2262no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—1131no—
263C4⋊C4—1131no—
264C4⋊C4—1131no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4C22⋊D11311yescharacteristic
269C4⋊C4C22×D11311yescharacteristic
270C4⋊C4C22×D11311yescharacteristic
271C4⋊C4C22×D11311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—2261no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4C22⋊D11311yescharacteristic
280C22⋊C4C22⋊D11311yescharacteristic
281C42—21no—
282C42C22×D11311yescharacteristic
283C23—21no—
284C23—2261no—
285C23C2×C22⋊D11311yescharacteristic
286C23C2×C22⋊D11311yescharacteristic
287Q8—4522no—
288D4—22no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—81no—
293D4—4522no—
294D4—4522no—
295D4—2261no—
296D4—2261no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—4522no—
307C2×C4—4522no—
308C2×C4—4522no—
309C2×C4—2261no—
310C2×C4—2261no—
311C2×C4—2261no—
312C2×C4C2×C22⋊D11311yescharacteristic
313C2×C4C2×C22⋊D11311yescharacteristic
314C2×C4C2×C22⋊D11311yescharacteristic
315C2×C4C2×C22⋊D11311yescharacteristic
316C2×C4C23×D11311yescharacteristic
317C8—1132no—
318C8—2261no—
319C8—2261no—
320C8—2261no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—4521no—
330C22—4521no—
331C22—4521no—
332C22#1681364712yes—
333C22C22×C22⋊D11311yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—4521no—
342C4—4521no—
343C4—4521no—
344C4#41×D11311yescharacteristic
345C4#1681366911yescharacteristic
346C2—22no—
347C2—41no—
348C2—81no—
349C2—9041no—
350C2#2029924711yescharacteristic
351C2C2×#1681364711yescharacteristic
352C2#2029940911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#553×C113C2
socleC22×C113C22×D4
hypercenter#553D113
hypocenterC113#3345
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. #20299252C2semidirect
2. #20299008C2semidirect
3. #20298922C2semidirect
4. #20298916C2semidirect
5. #20298914C2semidirect
6. #20298909C2semidirect
7. #20298895C2semidirect
8. #20298888C2semidirect
9. #20298849C2semidirect
10. #20298832C2semidirect
11. #20298708C2semidirect
12. #20298670C2semidirect
13. #20298641C2semidirect
14. C2×#16813553C2semidirect
15. #553×C113C2semidirect
143. #11744751#41semidirect
177. C113#3345semidirect
178. #553D113semidirect

Maximal subgroups

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

subgroupindex
#202992522
#202990082
#202989222
#202989162
#202989142
#202989092
#202988952
#202988882
#202988492
#202988322
#202987082
#202986702
#202986412
C2×#168135532
#553×C1132
#3345113