Finite Group Databasebeta

← #28401467

Subgroups — #28401467

Order 14464.

378 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#20299172C211yesmaximal, characteristic
2#20299171C211yesmaximal, characteristic
3#20298940C211yesmaximal, characteristic, complemented
4#20298938C211yesmaximal, characteristic, complemented
5#20298937C211yesmaximal, characteristic, complemented
6#20298936C211yesmaximal, characteristic, complemented
7#20298855C211yesmaximal, characteristic, complemented
8#20298853C211yesmaximal, characteristic, complemented
9#20298838C211yesmaximal, characteristic, complemented
10#20298836C211yesmaximal, characteristic, complemented
11#20298754C211yesmaximal, characteristic, complemented
12#20298752C211yesmaximal, characteristic, complemented
13#20298752C211yesmaximal, characteristic, complemented
14#20298563C211yesmaximal, characteristic
15#451×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268637C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21C2×C8×D113C2211yescharacteristic
22#16813621—21no—
23#16813620—21no—
24#16813611—21no—
25#16813608—21no—
26#16813607—21no—
27#16813605—21no—
28#16813605—21no—
29#16813604—21no—
30#16813602C2211yescharacteristic
31#16813601C2211yescharacteristic
32#16813598C2211yescharacteristic
33#16813598C2211yescharacteristic
34#16813598C2211yescharacteristic
35#16813598C2211yescharacteristic
36#16813598C2211yescharacteristic
37#16813581C2211yescharacteristic
38#16813580C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813554C2211yescharacteristic
42#16813553C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813546C2211yescharacteristic
48#16813546C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813534C2211yescharacteristic
52C22×Q8×C113C2211yescharacteristic
53C2×Q16×C113C2211yescharacteristic
54C2×Q16×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268647—41no—
60#14268647—41no—
61C2×Dic226—21no—
62C2×Dic226D411yescharacteristic
63C2×Dic226C2311yescharacteristic
64Q8×D113—41no—
65Q8×D113—41no—
66C2×D452D411yescharacteristic
67C2×C22⋊D113D411yescharacteristic
68C2×C22⋊D113D411yescharacteristic
69C2×C4×D113—21no—
70C2×C4×D113C2311yescharacteristic
71C2×C4×D113C2311yescharacteristic
72#14268637—41no—
73#14268637—41no—
74#14268630—41no—
75C2×#11744751C2311yescharacteristic
76C2×#11744751C2311yescharacteristic
77C8×D113—41no—
78C4⋊Dic113—21no—
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97C4×Dic113—21no—
98C4×Dic113—21no—
99C2×Q8×C113—21no—
100C2×Q8×C113—41no—
101C2×Q8×C113—41no—
102C2×Q8×C113C2311yescharacteristic
103C2×Q8×C113C2311yescharacteristic
104C2×Q8×C113C2311yescharacteristic
105C22×C4×C113—21no—
106C22×C4×C113C2311yescharacteristic
107Q16×C113—41no—
108Q16×C113—41no—
109C2×C8×C113C2311yescharacteristic
110C2×C8×C113C2311yescharacteristic
111C4⋊C4×C113—21no—
112C4⋊C4×C113C2311yescharacteristic
113C22⋊C4×C113—21no—
114C23×C113C2×D411yescharacteristic
115C22×D113C2×D411yescharacteristic
116C22×D113C2×D411yescharacteristic
117Q8×C113—21no—
118Q8×C113—21no—
119Q8×C113—21no—
120Q8×C113—21no—
121Q8×C113—21no—
122Q8×C113—21no—
123Q8×C113—42no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—42no—
131C2×C4×C113C2×D411yescharacteristic
132C2×C4×C113C2411yescharacteristic
133C22⋊D113—41no—
134C22⋊D113—41no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113C2×D411yescharacteristic
140C2×Dic113C2×D411yescharacteristic
141D452—41no—
142C4×D113—21no—
143C4×D113—21no—
144C4×D113—21no—
145C4×D113—21no—
146C4×D113—42no—
147Dic226—21no—
148Dic226—21no—
149Dic226—41no—
150Dic226—42no—
151C8×C113—21no—
152C8×C113—21no—
153#11744751—21no—
154#11744751—21no—
155C22×C113—21no—
156C22×C113—21no—
157C22×C113—21no—
158C22×C113C22×D411yescharacteristic
159C2×D113—21no—
160C2×D113—21no—
161C2×D113—21no—
162C2×D113—21no—
163C2×D113—21no—
164C2×D113—21no—
165C4×C113—21no—
166C4×C113—41no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113—41no—
170C4×C113H(5,𝔽2)11yescharacteristic
171C4×C113H(5,𝔽2)11yescharacteristic
172Dic113—21no—
173Dic113—21no—
174Dic113—41no—
175Dic113—41no—
176Dic113—41no—
177Dic113—41no—
178C2×C113—41no—
179C2×C113#53411yescharacteristic
180C2×C113#57811yescharacteristic
181C2×C113#57811yescharacteristic
182D113—41no—
183D113—41no—
184#3202—1131nomaximal, Sylow
185C113#320211yescharacteristic, complemented, Sylow
186#536—1131no—
187#536—1131no—
188#485—1131no—
189#485—1131no—
190#485—1131no—
191#485—1131no—
192#470—1131no—
193#470—1131no—
194#467—1131no—
195#467—1131no—
196#451—1131no—
197#451—1131no—
198#451—1131no—
199#451D11311yescharacteristic, complemented
200#408—1131no—
201C2×#41—1131no—
202C22×Q8—1131no—
203C22×Q8C2×D11311yescharacteristic
204C2×Q16—1131no—
205C2×Q16—1131no—
206C2×Q16C2×D11311yescharacteristic
207C2×Q16C2×D11311yescharacteristic
208C2×M16—1131no—
209C22×C8—1131no—
210C4⋊Q8—2261no—
211C4⋊Q8—2261no—
212#124—2261no—
213#124—2261no—
214#123—2261no—
215#123—2261no—
216#123—2261no—
217#123—2261no—
218C22⋊Q8—1131no—
219C22⋊Q8—1131no—
220C22⋊Q8—1131no—
221C22⋊Q8—1131no—
222C22⋊Q8—1131no—
223C22⋊Q8—1131no—
224C22⋊Q8—1131no—
225C22⋊Q8C2×D11311yescharacteristic
226#117—1131no—
227#117—1131no—
228#107—1131no—
229#107—1131no—
230#106—1131no—
231#106—1131no—
232#103—1131no—
233#103—1131no—
234#103—1131no—
235#103—1131no—
236#103—1131no—
237#103—1131no—
238#103C2×D11311yescharacteristic
239#103C2×D11311yescharacteristic
240C22⋊C8—1131no—
241C22⋊C8—1131no—
242C22⋊C8—1131no—
243C22⋊C8C2×D11311yescharacteristic
244#41—4521no—
245#41—4521no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—1131no—
250C2×Q8—1131no—
251C2×Q8—4521no—
252C2×Q8—4521no—
253C2×Q8—2261no—
254C2×Q8C22×D11311yescharacteristic
255C2×Q8C22×D11311yescharacteristic
256C2×Q8C22×D11311yescharacteristic
257C2×D4—1131no—
258C2×D4—1131no—
259C2×D4—1131no—
260C22×C4—21no—
261C22×C4—1131no—
262C22×C4—1131no—
263C22×C4—2261no—
264C22×C4C22×D11311yescharacteristic
265Q16—41no—
266Q16—41no—
267Q16—4521no—
268Q16—4521no—
269M16—4521no—
270C2×C8—1131no—
271C2×C8—1131no—
272C2×C8—4521no—
273C2×C8C22×D11311yescharacteristic
274C2×C8C22×D11311yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—1131no—
277C4⋊C4—1131no—
278C4⋊C4—1131no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4—2261no—
282C4⋊C4—2261no—
283C4⋊C4—2261no—
284C4⋊C4—2261no—
285C4⋊C4—2261no—
286C4⋊C4C22×D11311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C22⋊C4—2261no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C42—2261no—
298C42—2261no—
299C23—1131no—
300C23—1131no—
301C23D4×D11311yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—42no—
309Q8—4521no—
310Q8—4522no—
311Q8—2261no—
312Q8—2261no—
313D4—4521no—
314D4—4521no—
315D4—4521no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—1131no—
324C2×C4—1131no—
325C2×C4—4522no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4—2261no—
329C2×C4—2261no—
330C2×C4—2261no—
331C2×C4—2261no—
332C2×C4—2261no—
333C2×C4—2261no—
334C2×C4D4×D11311yescharacteristic
335C2×C4C23×D11311yescharacteristic
336C8—21no—
337C8—21no—
338C8—2261no—
339C8—2261no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—2261no—
344C22—2261no—
345C22—2261no—
346C22—2261no—
347C22—2261no—
348C22—2261no—
349C22C2×D4×D11311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—4521no—
356C4—4521no—
357C4—4521no—
358C4—4521no—
359C4—2261no—
360C4—2261no—
361C4#1681366711yescharacteristic
362C4#1681366711yescharacteristic
363C2—41no—
364C2—4521no—
365C2—4521no—
366C2#2029915811yescharacteristic
367C2#2029941111yescharacteristic
368C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#451×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268647C22
hypercenter#451D113
hypocenterC113#3202
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #20298940C2semidirect
4. #20298938C2semidirect
5. #20298937C2semidirect
6. #20298936C2semidirect
7. #20298855C2semidirect
8. #20298853C2semidirect
9. #20298838C2semidirect
10. #20298836C2semidirect
11. #20298754C2semidirect
12. #20298752C2semidirect
13. #20298752C2semidirect
15. #451×C113C2semidirect
185. C113#3202semidirect
199. #451D113semidirect

Maximal subgroups

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

subgroupindex
#202991722
#202991712
#202989402
#202989382
#202989372
#202989362
#202988552
#202988532
#202988382
#202988362
#202987542
#202987522
#202985632
#451×C1132
#3202113