Finite Group Databasebeta

← #28401655

Subgroups — #28401655

Order 14464.

364 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299208C211yesmaximal, characteristic, complemented
2#20299169C211yesmaximal, characteristic
3#20298989C211yesmaximal, characteristic, complemented
4#20298976C211yesmaximal, characteristic, complemented
5#20298965C211yesmaximal, characteristic, complemented
6#20298951C211yesmaximal, characteristic, complemented
7#20298819C211yesmaximal, characteristic, complemented
8#20298818C211yesmaximal, characteristic, complemented
9#20298807C211yesmaximal, characteristic, complemented
10#20298806C211yesmaximal, characteristic, complemented
11#20298760C211yesmaximal, characteristic
12#20298756C211yesmaximal, characteristic, complemented
13#20298753C211yesmaximal, characteristic, complemented
14#20298656C211yesmaximal, characteristic, complemented
15#452×C113C211yesmaximal, characteristic
16C22×Dic226C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×Dic452C2211yescharacteristic
19C2×#14268637C2211yescharacteristic
20C2×#14268637C2211yescharacteristic
21C2×#14268637C2211yescharacteristic
22C2×#14268635C2211yescharacteristic
23#16813620C2211yescharacteristic
24#16813620C2211yescharacteristic
25#16813620C2211yescharacteristic
26#16813615—21no—
27#16813615—21no—
28#16813613—21no—
29#16813613C2211yescharacteristic
30#16813612—21no—
31#16813609C2211yescharacteristic
32#16813609C2211yescharacteristic
33#16813603—21no—
34#16813603—21no—
35#16813601—21no—
36#16813601—21no—
37#16813601C2211yescharacteristic
38Q8×Dic113C2211yescharacteristic
39#16813587C2211yescharacteristic
40#16813581C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813543C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C2×Q16×C113C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226—41no—
61C2×Dic226—41no—
62C2×Dic226C2311yescharacteristic
63C2×Dic226C2311yescharacteristic
64C2×Dic226C2311yescharacteristic
65C22×Dic113—21no—
66Dic452—41no—
67Dic452—41no—
68#14268637—41no—
69#14268637—41no—
70#14268637—41no—
71#14268635—41no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113D411yescharacteristic
77C4⋊Dic113D411yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113—21no—
92C22⋊Dic113—21no—
93C22⋊Dic113D411yescharacteristic
94C22⋊Dic113D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113—21no—
97C4×Dic113C2311yescharacteristic
98C4×Dic113C2311yescharacteristic
99#41×C113—41no—
100#41×C113—41no—
101C2×Q8×C113C2311yescharacteristic
102C2×Q8×C113C2311yescharacteristic
103C2×D4×C113—21no—
104C2×D4×C113C2311yescharacteristic
105C22×C4×C113—21no—
106C22×C4×C113C2311yescharacteristic
107Q16×C113—41no—
108SD16×C113—41no—
109C2×C8×C113C2311yescharacteristic
110C2×C8×C113C2311yescharacteristic
111C4⋊C4×C113—21no—
112C4⋊C4×C113C2311yescharacteristic
113C22⋊C4×C113—21no—
114C23×C113—21no—
115C23×C113C2×D411yescharacteristic
116Q8×C113—21no—
117Q8×C113—21no—
118Q8×C113—21no—
119Q8×C113—21no—
120D4×C113—21no—
121D4×C113—21no—
122D4×C113—42no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—42no—
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2411yescharacteristic
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—42no—
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139C2×Dic113C2×D411yescharacteristic
140Dic226—21no—
141Dic226—21no—
142Dic226—21no—
143Dic226—21no—
144Dic226—21no—
145Dic226—21no—
146Dic226—42no—
147C8×C113—21no—
148C8×C113—21no—
149#11744751—21no—
150#11744751—21no—
151C22×C113—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—41no—
155C22×C113—41no—
156C22×C113—41no—
157C22×C113C22×D411yescharacteristic
158C4×C113—21no—
159C4×C113—41no—
160C4×C113—41no—
161C4×C113—41no—
162C4×C113H(5,𝔽2)11yescharacteristic
163C4×C113H(5,𝔽2)11yescharacteristic
164Dic113—21no—
165Dic113—21no—
166Dic113—21no—
167Dic113—21no—
168Dic113—41no—
169Dic113—41no—
170Dic113—41no—
171Dic113—41no—
172C2×C113—41no—
173C2×C113—81no—
174C2×C113#53511yescharacteristic
175C2×C113#57811yescharacteristic
176C2×C113#57811yescharacteristic
177#3223—1131nomaximal, Sylow
178C113#322311yescharacteristic, complemented, Sylow
179#541—1131no—
180#536—1131no—
181#497—1131no—
182#494—1131no—
183#491—1131no—
184#488—1131no—
185#464—1131no—
186#464—1131no—
187#462—1131no—
188#462—1131no—
189#452—1131no—
190#452D11311yescharacteristic
191#451—1131no—
192#451—1131no—
193#433—1131no—
194C2×#41C2×D11311yescharacteristic
195C22×Q8—1131no—
196C2×Q16—1131no—
197C2×Q16—1131no—
198C2×Q16—1131no—
199C2×Q16—1131no—
200C2×Q16—1131no—
201C2×Q16C2×D11311yescharacteristic
202C2×SD16—1131no—
203C2×SD16C2×D11311yescharacteristic
204C4⋊Q8—1131no—
205C4⋊Q8—1131no—
206C4⋊Q8—1131no—
207#126—2261no—
208#126—2261no—
209#125—1131no—
210#125—2261no—
211#125—2261no—
212#124—1131no—
213#124—1131no—
214#123—2261no—
215#123—2261no—
216C22⋊Q8—1131no—
217C22⋊Q8—2261no—
218C22⋊Q8—2261no—
219C22⋊Q8C2×D11311yescharacteristic
220C4×Q8—1131no—
221C4×Q8—1131no—
222#117—1131no—
223C4⋊C8—1131no—
224C4⋊C8—1131no—
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103C2×D11311yescharacteristic
231#102—1131no—
232#102C2×D11311yescharacteristic
233C22⋊C8—1131no—
234C22⋊C8C2×D11311yescharacteristic
235#97—1131no—
236C4×C8—1131no—
237#41—41no—
238#41—41no—
239C2×Q8—1131no—
240C2×Q8—1131no—
241C2×Q8—1131no—
242C2×Q8—4521no—
243C2×Q8—4521no—
244C2×Q8—2261no—
245C2×Q8C22×D11311yescharacteristic
246C2×Q8C22×D11311yescharacteristic
247C2×D4—21no—
248C2×D4C22×D11311yescharacteristic
249C22×C4—21no—
250C22×C4—2261no—
251C22×C4C22×D11311yescharacteristic
252Q16—41no—
253Q16—4521no—
254Q16—4521no—
255Q16—4521no—
256Q16—4521no—
257Q16—4521no—
258SD16—41no—
259SD16—4521no—
260C2×C8—1131no—
261C2×C8—1131no—
262C2×C8C22×D11311yescharacteristic
263C2×C8C22×D11311yescharacteristic
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⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4C22×D11311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—1131no—
282C22⋊C4—1131no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C42—1131no—
289C42—1131no—
290C42—2261no—
291C42—2261no—
292C23—21no—
293C23D4×D11311yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—4522no—
299Q8—2261no—
300Q8—2261no—
301Q8—2261no—
302Q8—2261no—
303Q8—2261no—
304Q8—2261no—
305D4—21no—
306D4—21no—
307D4—42no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—1131no—
315C2×C4—1131no—
316C2×C4—1131no—
317C2×C4—1131no—
318C2×C4—4522no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4D4×D11311yescharacteristic
324C2×C4C23×D11311yescharacteristic
325C8—21no—
326C8—21no—
327C8—2261no—
328C8—2261no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22C2×D4×D11311yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—4521no—
341C4—4521no—
342C4—4521no—
343C4—4521no—
344C4—2261no—
345C4—2261no—
346C4—2261no—
347C4—2261no—
348C4#1681366711yescharacteristic
349C4#1681366711yescharacteristic
350C2—41no—
351C2—81no—
352C2#2029916311yescharacteristic
353C2#2029941211yescharacteristic
354C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#452×C113C2
socleC22×C113C22×D4
prime radicalC2×#41×C113C22
hypercenter#452D113
hypocenterC113#3223
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #20299208C2semidirect
3. #20298989C2semidirect
4. #20298976C2semidirect
5. #20298965C2semidirect
6. #20298951C2semidirect
7. #20298819C2semidirect
8. #20298818C2semidirect
9. #20298807C2semidirect
10. #20298806C2semidirect
12. #20298756C2semidirect
13. #20298753C2semidirect
14. #20298656C2semidirect
178. C113#3223semidirect

Maximal subgroups

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

subgroupindex
#202992082
#202991692
#202989892
#202989762
#202989652
#202989512
#202988192
#202988182
#202988072
#202988062
#202987602
#202987562
#202987532
#202986562
#452×C1132
#3223113