Finite Group Databasebeta

← #28402445

Subgroups — #28402445

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#20299306C211yesmaximal, characteristic
2#20299261C211yesmaximal, characteristic
3#20298947C211yesmaximal, characteristic, complemented
4#20298935C211yesmaximal, characteristic, complemented
5#20298931C211yesmaximal, characteristic, complemented
6#20298892C211yesmaximal, characteristic, complemented
7#20298838C211yesmaximal, characteristic, complemented
8#20298806C211yesmaximal, characteristic, complemented
9#20298753C211yesmaximal, characteristic, complemented
10#20298752C211yesmaximal, characteristic, complemented
11#20298690C211yesmaximal, characteristic, complemented
12C8×C22⋊D113C211yesmaximal, characteristic
13C2×#16813547C211yesmaximal, characteristic, complemented
14#103×D113C211yesmaximal, characteristic, complemented
15#467×C113C211yesmaximal, characteristic, complemented
16C22×Dic226C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268637C2211yescharacteristic
20C2×C8×D113C2211yescharacteristic
21#16813621—21no—
22#16813621C2211yescharacteristic
23#16813620C2211yescharacteristic
24#16813612—21no—
25#16813602—21no—
26#16813602C2211yescharacteristic
27#16813600—21no—
28#16813599—21no—
29#16813599—21no—
30#16813598C2211yescharacteristic
31Q8×Dic113C2211yescharacteristic
32#16813587C2211yescharacteristic
33C4×C22⋊D113C2211yescharacteristic
34#16813582—21no—
35#16813582—21no—
36C2×C4⋊Dic113C2211yescharacteristic
37C4⋊C4×D113C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813551C2211yescharacteristic
41#16813547C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813545C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×Q16×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54C22⋊Q8×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#107×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59C2×Dic226—22no—
60C2×Dic226—21no—
61C2×Dic226—21no—
62C2×Dic226—21no—
63C2×Dic226—41no—
64C2×Dic226C2311yescharacteristic
65C2×Dic226C2311yescharacteristic
66Q8×D113—22no—
67Q8×D113—41no—
68C2×C22⋊D113D411yescharacteristic
69C22×Dic113—21no—
70C22×Dic113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113C2311yescharacteristic
74#14268637—22no—
75#14268637—41no—
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C8×D113—41no—
79C4⋊Dic113—21no—
80C4⋊Dic113—21no—
81C4⋊Dic113—21no—
82C4⋊Dic113C2311yescharacteristic
83C4⋊Dic113C2311yescharacteristic
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89#14268626—21no—
90#14268626D411yescharacteristic
91C22⋊Dic113D411yescharacteristic
92#14268624—21no—
93#14268624—21no—
94#14268624D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113—21no—
97C4×Dic113C2311yescharacteristic
98C2×Q8×C113C2311yescharacteristic
99C2×Q8×C113C2311yescharacteristic
100C22×C4×C113C2311yescharacteristic
101Q16×C113—41no—
102C2×C8×C113—41no—
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C4⋊C4×C113—21no—
106C4⋊C4×C113—21no—
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
110C22⋊C4×C113—21no—
111C23×C113C2×D411yescharacteristic
112C22×D113C2×D411yescharacteristic
113Q8×C113—21no—
114Q8×C113—21no—
115Q8×C113—21no—
116Q8×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—21no—
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2411yescharacteristic
125C22⋊D113Q1614yescomplemented
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—42no—
131C2×Dic113—81no—
132C2×Dic113C2×D411yescharacteristic
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135C4×D113—21no—
136C4×D113—21no—
137C4×D113—42no—
138C4×D113—81no—
139Dic226—21no—
140Dic226—21no—
141Dic226—21no—
142Dic226—42no—
143Dic226—42no—
144Dic226—81no—
145Dic226#4112yes—
146C8×C113—21no—
147C8×C113—21no—
148#11744751—21no—
149#11744751—21no—
150C22×C113—21no—
151C22×C113—21no—
152C22×C113C2×Q1612yes—
153C22×C113C22×D411yescharacteristic
154C2×D113—21no—
155C2×D113—21no—
156C2×D113C2×Q1612yes—
157C4×C113—21no—
158C4×C113—41no—
159C4×C113—41no—
160C4×C113—41no—
161C4×C113—41no—
162C4×C113C2×#4111yescharacteristic
163C4×C113H(5,𝔽2)11yescharacteristic
164Dic113—22no—
165Dic113—21no—
166Dic113—21no—
167Dic113—41no—
168Dic113—41no—
169Dic113—41no—
170Dic113C2×Q1612yes—
171C2×C113—22no—
172C2×C113#54611yescharacteristic
173C2×C113C22×Q1611yescharacteristic
174C2×C113#57711yescharacteristic
175D113—22no—
176#3299—1131nomaximal, Sylow
177C113#329911yescharacteristic, complemented, Sylow
178#554—1131no—
179D4×Q8—1131no—
180#487—1131no—
181#484—1131no—
182#484—1131no—
183#477—1131no—
184#467—1131no—
185#467D11311yescharacteristic, complemented
186#462—1131no—
187#451—1131no—
188#451—1131no—
189C4×Q16—1131no—
190C8×D4—1131no—
191C2×#103—1131no—
192C2×#103—1131no—
193C22×Q8—1131no—
194C22×Q8—1131no—
195C2×Q16—1131no—
196C2×Q16—1131no—
197C2×Q16C2×D11311yescharacteristic
198C22×C8—1131no—
199C22×C8C2×D11311yescharacteristic
200C4⋊Q8—1131no—
201C4⋊Q8—1131no—
202C4⋊Q8—2261no—
203#125—2261no—
204C22⋊Q8—1131no—
205C22⋊Q8—1131no—
206C22⋊Q8—2261no—
207C22⋊Q8—2261no—
208C22⋊Q8—2261no—
209C22⋊Q8—2261no—
210C22⋊Q8C2×D11311yescharacteristic
211C22⋊Q8C2×D11311yescharacteristic
212C4×Q8—1131no—
213C4×Q8—1131no—
214C4×D4—1131no—
215C4×D4—2261no—
216C4×D4—2261no—
217C2×C4⋊C4—1131no—
218C2×C4⋊C4—1131no—
219#107—1131no—
220#107—1131no—
221#107C2×D11311yescharacteristic
222C4⋊C8—1131no—
223#103—1131no—
224#103—1131no—
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#103C2×D11311yescharacteristic
232#103C2×D11311yescharacteristic
233C22⋊C8—1131no—
234C22⋊C8—1131no—
235C4×C8—1131no—
236C2×Q8—1131no—
237C2×Q8—1131no—
238C2×Q8—4521no—
239C2×Q8—4521no—
240C2×Q8—2261no—
241C2×Q8—2261no—
242C2×Q8—2262no—
243C2×Q8—2262no—
244C2×Q8—2261no—
245C2×Q8C22×D11311yescharacteristic
246C2×Q8C22×D11311yescharacteristic
247C2×D4—1131no—
248C22×C4—1131no—
249C22×C4—2261no—
250C22×C4—2261no—
251C22×C4—2261no—
252C22×C4—2261no—
253C22×C4C22×D11311yescharacteristic
254Q16—41no—
255Q16—4521no—
256Q16—2262no—
257C2×C8—41no—
258C2×C8—1131no—
259C2×C8—1131no—
260C2×C8—4521no—
261C2×C8C22×D11311yescharacteristic
262C2×C8C22×D11311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—1131no—
266C4⋊C4—1131no—
267C4⋊C4—1131no—
268C4⋊C4—2261no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4—2261no—
276C4⋊C4—2261no—
277C4⋊C4C22×D11311yescharacteristic
278C4⋊C4C22×D11311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—1131no—
282C22⋊C4—1131no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C42—1131no—
286C42—2261no—
287C42—2261no—
288C23—1131no—
289C23D4×D11311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294Q8—1132no—
295Q8—9041no—
296Q8—4522no—
297Q8—4522no—
298Q8—2261no—
299Q8—2261no—
300Q8—2261no—
301D4—1134no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—1131no—
309C2×C4—1131no—
310C2×C4—1131no—
311C2×C4—9041no—
312C2×C4—9041no—
313C2×C4—4522no—
314C2×C4—4522no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4D4×D11311yescharacteristic
322C2×C4C23×D11311yescharacteristic
323C8—21no—
324C8—21no—
325C8—2261no—
326C8—2261no—
327C22—21no—
328C22—21no—
329C22—1132no—
330C22—2261no—
331C22—2261no—
332C22Q16×D11312yes—
333C22C2×D4×D11311yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—1132no—
340C4—4521no—
341C4—4521no—
342C4—4521no—
343C4—2261no—
344C4—2261no—
345C4—2262no—
346C4#41×D11311yescharacteristic
347C4#1681366711yescharacteristic
348C2—22no—
349C2—2262no—
350C2#2029923711yescharacteristic
351C2C2×Q16×D11311yescharacteristic
352C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#467×C113C2
socleC22×C113C22×D4
prime radicalC2×C22⋊D113D4
hypercenter#467D113
hypocenterC113#3299
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
3. #20298947C2semidirect
4. #20298935C2semidirect
5. #20298931C2semidirect
6. #20298892C2semidirect
7. #20298838C2semidirect
8. #20298806C2semidirect
9. #20298753C2semidirect
10. #20298752C2semidirect
11. #20298690C2semidirect
13. C2×#16813547C2semidirect
14. #103×D113C2semidirect
15. #467×C113C2semidirect
125. C22⋊D113Q16semidirect
177. C113#3299semidirect
185. #467D113semidirect

Maximal subgroups

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

subgroupindex
#202993062
#202992612
#202989472
#202989352
#202989312
#202988922
#202988382
#202988062
#202987532
#202987522
#202986902
C8×C22⋊D1132
C2×#168135472
#103×D1132
#467×C1132
#3299113