Finite Group Databasebeta

← #28400830

Subgroups — #28400830

Order 14464.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299078C211yesmaximal, characteristic, complemented
2#20298931C211yesmaximal, characteristic, complemented
3#20298909C211yesmaximal, characteristic, complemented
4#20298890C211yesmaximal, characteristic, complemented
5#20298875C211yesmaximal, characteristic, complemented
6#20298817C211yesmaximal, characteristic, complemented
7#20298810C211yesmaximal, characteristic, complemented
8#20298758C211yesmaximal, characteristic, complemented
9#20298741C211yesmaximal, characteristic
10#20298698C211yesmaximal, characteristic, complemented
11#20298696C211yesmaximal, characteristic, complemented
12C4×#14268637C211yesmaximal, characteristic, complemented
13C4×#14268632C211yesmaximal, characteristic, complemented
14#20298659C211yesmaximal, characteristic, complemented
15#542×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268634C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21C4×Dic226C2211yescharacteristic
22C4×Dic226C2211yescharacteristic
23C4×D452C2211yescharacteristic
24C4×D452C2211yescharacteristic
25#16813582—21no—
26#16813582—21no—
27#16813580—21no—
28C2×C4⋊Dic113C2211yescharacteristic
29C4⋊C4×D113—21no—
30#16813555C2211yescharacteristic
31#16813555C2211yescharacteristic
32#16813555C2211yescharacteristic
33#16813555C2211yescharacteristic
34C4⋊#11744751C2211yescharacteristic
35C4⋊#11744751C2211yescharacteristic
36#16813546C2211yescharacteristic
37#16813546C2211yescharacteristic
38#16813545C2211yescharacteristic
39#16813545C2211yescharacteristic
40#16813543C2211yescharacteristic
41#16813543C2211yescharacteristic
42#16813542C2211yescharacteristic
43#16813542C2211yescharacteristic
44C22⋊#11744751C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46#16813533C2211yescharacteristic
47C4×#11744751C2211yescharacteristic
48C4⋊Q8×C113C2211yescharacteristic
49#126×C113—21no—
50#124×C113—21no—
51#124×C113C2211yescharacteristic
52#123×C113—21no—
53C22⋊Q8×C113—21no—
54C22⋊Q8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56C4×Q8×C113C2211yescharacteristic
57C4×D4×C113C2211yescharacteristic
58#117×C113C2211yescharacteristic
59#14268647—22no—
60#14268647—22no—
61C2×Dic226C2311yescharacteristic
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C22×Dic113—21no—
65C2×C4×D113—21no—
66C2×C4×D113—21no—
67C2×C4×D113—21no—
68#14268637—22no—
69#14268635—22no—
70#14268634—22no—
71#14268632—22no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C2×#11744751C2311yescharacteristic
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81#14268624—21no—
82#14268624—21no—
83C4×Dic113—21no—
84C4×Dic113—21no—
85C2×Q8×C113—21no—
86C2×Q8×C113C2311yescharacteristic
87C2×D4×C113—21no—
88C2×D4×C113C2311yescharacteristic
89C22×C4×C113—21no—
90C22×C4×C113C2311yescharacteristic
91C4⋊C4×C113—21no—
92C4⋊C4×C113—21no—
93C4⋊C4×C113—21no—
94C4⋊C4×C113D411yescharacteristic
95C4⋊C4×C113D411yescharacteristic
96C4⋊C4×C113C2311yescharacteristic
97C4⋊C4×C113C2311yescharacteristic
98C22⋊C4×C113—21no—
99C22⋊C4×C113—21no—
100C22⋊C4×C113—21no—
101C22⋊C4×C113—21no—
102C22⋊C4×C113—21no—
103C22⋊C4×C113D411yescharacteristic
104C22⋊C4×C113D411yescharacteristic
105C42×C113—21no—
106C42×C113C2311yescharacteristic
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C23×C113C2×D411yescharacteristic
110C22×D113—21no—
111Q8×C113—21no—
112Q8×C113—21no—
113Q8×C113—81no—
114D4×C113—21no—
115D4×C113—21no—
116D4×C113—81no—
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×C113C2×D411yescharacteristic
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2411yescharacteristic
129C22⋊D113—24no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—81no—
134D452—21no—
135D452#4112yes—
136C4×D113—24no—
137C4×D113—81no—
138C4×D113—81no—
139Dic226—21no—
140Dic226#4112yes—
141#11744751—21no—
142#11744751—21no—
143#11744751—21no—
144#11744751—21no—
145C22×C113—21no—
146C22×C113—21no—
147C22×C113—21no—
148C22×C113—41no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113C22×D411yescharacteristic
152C2×D113—22no—
153C2×D113—41no—
154C2×D113—41no—
155C4×C113—21no—
156C4×C113—21no—
157C4×C113—21no—
158C4×C113—21no—
159C4×C113—21no—
160C4×C113—41no—
161C4×C113—41no—
162C4×C113—41no—
163C4×C113C2×#4111yescharacteristic
164C4×C113C2×#4111yescharacteristic
165Dic113—22no—
166Dic113—41no—
167Dic113—41no—
168C2×C113—41no—
169C2×C113—81no—
170C2×C113#52511yescharacteristic
171C2×C113#57611yescharacteristic
172C2×C113#57811yescharacteristic
173D113—42no—
174#3124—1131nomaximal, Sylow
175C113#312411yescharacteristic, complemented, Sylow
176#542D11311yescharacteristic, complemented
177#520—1131no—
178#484—1131no—
179#480—1131no—
180#477—1131no—
181#474—1131no—
182#464—1131no—
183#463—1131no—
184#452—1131no—
185#449—1131no—
186#440—1131no—
187#440—1131no—
188C4×Q16—1131no—
189C4×D8—1131no—
190#433—1131no—
191C2×#41—1131no—
192C2×Q16—1131no—
193C2×SD16—1131no—
194C2×SD16—1131no—
195C2×D8—1131no—
196C4⋊Q8C2×D11311yescharacteristic
197#126—21no—
198#124—21no—
199#124C2×D11311yescharacteristic
200#123—21no—
201C22⋊Q8—21no—
202C22⋊Q8C2×D11311yescharacteristic
203#121C2×D11311yescharacteristic
204C4×Q8—1131no—
205C4×Q8—1131no—
206C4×Q8C2×D11311yescharacteristic
207C4×D4—1131no—
208C4×D4—1131no—
209C4×D4—2261no—
210C4×D4—2261no—
211C4×D4C2×D11311yescharacteristic
212#117—2261no—
213#117C2×D11311yescharacteristic
214C2×C4⋊C4—1131no—
215C2×C4⋊C4—2261no—
216#107—1131no—
217#107—1131no—
218#107—1131no—
219#107—1131no—
220C4⋊C8—1131no—
221C4⋊C8—1131no—
222#103—1131no—
223#103—1131no—
224#103—1131no—
225#103—1131no—
226#102—1131no—
227#102—1131no—
228#102—1131no—
229#102—1131no—
230C22⋊C8—1131no—
231C22⋊C8—1131no—
232#97—1131no—
233C4×C8—1131no—
234#41—2262no—
235#41—2262no—
236C2×Q8—21no—
237C2×Q8—1131no—
238C2×Q8C22×D11311yescharacteristic
239C2×D4—21no—
240C2×D4—1131no—
241C2×D4—2261no—
242C2×D4C22×D11311yescharacteristic
243C22×C4—21no—
244C22×C4—2261no—
245C22×C4—2261no—
246C22×C4—2261no—
247C22×C4—2261no—
248C22×C4C22×D11311yescharacteristic
249Q16—2262no—
250SD16—2262no—
251SD16—2262no—
252D8—2262no—
253C2×C8—1131no—
254C2×C8—1131no—
255C2×C8—1131no—
256C2×C8—1131no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—1131no—
261C4⋊C4—1131no—
262C4⋊C4—2261no—
263C4⋊C4—2261no—
264C4⋊C4—2261no—
265C4⋊C4C22⋊D11311yescharacteristic
266C4⋊C4C22⋊D11311yescharacteristic
267C4⋊C4C22×D11311yescharacteristic
268C4⋊C4C22×D11311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4C22⋊D11311yescharacteristic
277C22⋊C4C22⋊D11311yescharacteristic
278C42—21no—
279C42—2261no—
280C42—2261no—
281C42C22×D11311yescharacteristic
282C42C22×D11311yescharacteristic
283C23—21no—
284C23—2261no—
285C23C2×C22⋊D11311yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—81no—
289Q8—1132no—
290Q8—2261no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—1132no—
295D4—2264no—
296D4—2261no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—9041no—
304C2×C4—9041no—
305C2×C4—9041no—
306C2×C4—2264no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4—2261no—
310C2×C4C2×C22⋊D11311yescharacteristic
311C2×C4C2×C22⋊D11311yescharacteristic
312C2×C4C2×C22⋊D11311yescharacteristic
313C2×C4C2×C22⋊D11311yescharacteristic
314C2×C4C2×C22⋊D11311yescharacteristic
315C2×C4C23×D11311yescharacteristic
316C8—2261no—
317C8—2261no—
318C8—2261no—
319C8—2261no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—4521no—
327C22—4521no—
328C22—2262no—
329C22C22×C22⋊D11311yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—4521no—
339C4—4521no—
340C4—2262no—
341C4#41×D11311yescharacteristic
342C4#41×D11311yescharacteristic
343C2—41no—
344C2—81no—
345C2—4522no—
346C2#2029910511yescharacteristic
347C2#2029940111yescharacteristic
348C2#2029941311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#542×C113C2
socleC22×C113C22×D4
prime radical#20298741C2
hypercenter#542D113
hypocenterC113#3124
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #20299078C2semidirect
2. #20298931C2semidirect
3. #20298909C2semidirect
4. #20298890C2semidirect
5. #20298875C2semidirect
6. #20298817C2semidirect
7. #20298810C2semidirect
8. #20298758C2semidirect
10. #20298698C2semidirect
11. #20298696C2semidirect
12. C4×#14268637C2semidirect
13. C4×#14268632C2semidirect
14. #20298659C2semidirect
15. #542×C113C2semidirect
175. C113#3124semidirect
176. #542D113semidirect

Maximal subgroups

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

subgroupindex
#202990782
#202989312
#202989092
#202988902
#202988752
#202988172
#202988102
#202987582
#202987412
#202986982
#202986962
C4×#142686372
C4×#142686322
#202986592
#542×C1132
#3124113