Finite Group Databasebeta

← #28401455

Subgroups — #28401455

Order 14464.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299176C211yesmaximal, characteristic
2#20299171C211yesmaximal, characteristic, complemented
3#20298938C211yesmaximal, characteristic, complemented
4#20298934C211yesmaximal, characteristic, complemented
5#20298926C211yesmaximal, characteristic, complemented
6#20298920C211yesmaximal, characteristic, complemented
7#20298855C211yesmaximal, characteristic, complemented
8#20298841C211yesmaximal, characteristic, complemented
9#20298836C211yesmaximal, characteristic, complemented
10#20298826C211yesmaximal, characteristic, complemented
11#20298760C211yesmaximal, characteristic, complemented
12#20298752C211yesmaximal, characteristic, complemented
13#20298735C211yesmaximal, characteristic, complemented
14#20298563C211yesmaximal, characteristic, complemented
15#452×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21C2×C8×D113C2211yescharacteristic
22#16813621—21no—
23#16813608—21no—
24#16813607—21no—
25#16813604—21no—
26#16813602C2211yescharacteristic
27#16813601—21no—
28#16813601C2211yescharacteristic
29#16813598C2211yescharacteristic
30#16813598C2211yescharacteristic
31#16813598C2211yescharacteristic
32#16813596—21no—
33#16813594—21no—
34#16813594—21no—
35#16813593C2211yescharacteristic
36#16813593C2211yescharacteristic
37#16813580C2211yescharacteristic
38C2×C4⋊Dic113C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813556C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813553C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813546C2211yescharacteristic
48#16813543C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813534C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C2×Q16×C113C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×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⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113D411yescharacteristic
70C2×C22⋊D113D411yescharacteristic
71C22×Dic113—21no—
72C2×C4×D113—21no—
73C2×C4×D113C2311yescharacteristic
74C2×C4×D113C2311yescharacteristic
75#14268637—41no—
76#14268635—41no—
77#14268630—41no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C8×D113—41no—
81C4⋊Dic113—21no—
82C4⋊Dic113—21no—
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85C4⋊Dic113C2311yescharacteristic
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89#14268626—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113—21no—
92C22⋊Dic113—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98C4×Dic113—21no—
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
116C22×D113C2×D411yescharacteristic
117C22×D113C2×D411yescharacteristic
118Q8×C113—21no—
119Q8×C113—21no—
120Q8×C113—21no—
121Q8×C113—21no—
122D4×C113—21no—
123D4×C113—21no—
124D4×C113—42no—
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—
135C22⋊D113—81no—
136C22⋊D113—81no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113—81no—
142C2×Dic113C2×D411yescharacteristic
143C2×Dic113C2×D411yescharacteristic
144D452—41no—
145C4×D113—21no—
146C4×D113—21no—
147C4×D113—21no—
148C4×D113—21no—
149C4×D113—42no—
150Dic226—21no—
151Dic226—21no—
152Dic226—41no—
153Dic226—42no—
154C8×C113—21no—
155C8×C113—21no—
156#11744751—21no—
157#11744751—21no—
158C22×C113—21no—
159C22×C113—21no—
160C22×C113—21no—
161C22×C113—41no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113C22×D411yescharacteristic
165C2×D113—21no—
166C2×D113—21no—
167C2×D113—21no—
168C2×D113—21no—
169C2×D113—21no—
170C2×D113—21no—
171C4×C113—21no—
172C4×C113—41no—
173C4×C113—41no—
174C4×C113—41no—
175C4×C113H(5,𝔽2)11yescharacteristic
176C4×C113H(5,𝔽2)11yescharacteristic
177Dic113—21no—
178Dic113—21no—
179Dic113—41no—
180Dic113—41no—
181Dic113—41no—
182Dic113—41no—
183C2×C113—41no—
184C2×C113—81no—
185C2×C113#53411yescharacteristic
186C2×C113#57711yescharacteristic
187C2×C113#57811yescharacteristic
188D113—41no—
189D113—41no—
190#3201—1131nomaximal, Sylow
191C113#320111yescharacteristic, complemented, Sylow
192#537—1131no—
193#536—1131no—
194#485—1131no—
195#484—1131no—
196#483—1131no—
197#482—1131no—
198#470—1131no—
199#468—1131no—
200#467—1131no—
201#465—1131no—
202#452—1131no—
203#452D11311yescharacteristic, complemented
204#451—1131no—
205#448—1131no—
206#408—1131no—
207C2×#41—1131no—
208C2×#41C2×D11311yescharacteristic
209C22×Q8—1131no—
210C2×Q16—1131no—
211C2×Q16C2×D11311yescharacteristic
212C2×SD16—1131no—
213C2×SD16C2×D11311yescharacteristic
214C2×M16—1131no—
215C22×C8—1131no—
216C4⋊Q8—2261no—
217#124—2261no—
218#123—2261no—
219#123—2261no—
220C22⋊Q8—1131no—
221C22⋊Q8—1131no—
222C22⋊Q8—1131no—
223C22⋊Q8—1131no—
224C22⋊Q8—1131no—
225C22⋊Q8—2261no—
226C22⋊Q8C2×D11311yescharacteristic
227#121—1131no—
228#121—1131no—
229#121—2261no—
230#121—2261no—
231#121—2261no—
232#117—1131no—
233C2×C4⋊C4—1131no—
234#107—1131no—
235#107—1131no—
236#106—1131no—
237#106—1131no—
238#103—1131no—
239#103—1131no—
240#103—1131no—
241#103—1131no—
242#103—1131no—
243#103C2×D11311yescharacteristic
244#102—1131no—
245#102C2×D11311yescharacteristic
246C22⋊C8—1131no—
247C22⋊C8—1131no—
248C22⋊C8—1131no—
249C22⋊C8C2×D11311yescharacteristic
250#41—41no—
251#41—41no—
252#41—4521no—
253#41—4521no—
254C2×Q8—1131no—
255C2×Q8—1131no—
256C2×Q8—4521no—
257C2×Q8—4521no—
258C2×Q8—2261no—
259C2×Q8C22×D11311yescharacteristic
260C2×Q8C22×D11311yescharacteristic
261C2×D4—21no—
262C2×D4—1131no—
263C2×D4—1131no—
264C2×D4—1131no—
265C2×D4—2261no—
266C2×D4—2261no—
267C2×D4C22×D11311yescharacteristic
268C22×C4—21no—
269C22×C4—1131no—
270C22×C4—1131no—
271C22×C4—2261no—
272C22×C4—2261no—
273C22×C4C22×D11311yescharacteristic
274Q16—41no—
275Q16—4521no—
276SD16—41no—
277SD16—4521no—
278M16—4521no—
279C2×C8—1131no—
280C2×C8—1131no—
281C2×C8—4521no—
282C2×C8C22×D11311yescharacteristic
283C2×C8C22×D11311yescharacteristic
284C4⋊C4—21no—
285C4⋊C4—1131no—
286C4⋊C4—1131no—
287C4⋊C4—1131no—
288C4⋊C4—2261no—
289C4⋊C4—2261no—
290C4⋊C4—2261no—
291C4⋊C4—2261no—
292C4⋊C4—2261no—
293C4⋊C4—2261no—
294C4⋊C4C22×D11311yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C22⋊C4—2261no—
300C22⋊C4—2261no—
301C22⋊C4—2261no—
302C22⋊C4—2261no—
303C22⋊C4—2261no—
304C42—2261no—
305C23—21no—
306C23—1131no—
307C23—1131no—
308C23D4×D11311yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—4521no—
314Q8—4522no—
315Q8—2261no—
316Q8—2261no—
317D4—21no—
318D4—21no—
319D4—42no—
320D4—9041no—
321D4—9041no—
322D4—4521no—
323D4—4521no—
324D4—4521no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—1131no—
332C2×C4—1131no—
333C2×C4—9041no—
334C2×C4—4522no—
335C2×C4—2261no—
336C2×C4—2261no—
337C2×C4—2261no—
338C2×C4—2261no—
339C2×C4—2261no—
340C2×C4—2261no—
341C2×C4—2261no—
342C2×C4—2261no—
343C2×C4D4×D11311yescharacteristic
344C2×C4C23×D11311yescharacteristic
345C8—21no—
346C8—21no—
347C8—2261no—
348C8—2261no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—2261no—
356C22—2261no—
357C22—2261no—
358C22—2261no—
359C22—2261no—
360C22—2261no—
361C22C2×D4×D11311yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—4521no—
367C4—4521no—
368C4—4521no—
369C4—4521no—
370C4—2261no—
371C4—2261no—
372C4#1681366711yescharacteristic
373C4#1681366711yescharacteristic
374C2—41no—
375C2—81no—
376C2—4521no—
377C2—4521no—
378C2#2029915811yescharacteristic
379C2#2029940711yescharacteristic
380C2#2029941211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#452×C113C2
socleC22×C113C22×D4
prime radical#20299176C2
hypercenter#452D113
hypocenterC113#3201
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
2. #20299171C2semidirect
3. #20298938C2semidirect
4. #20298934C2semidirect
5. #20298926C2semidirect
6. #20298920C2semidirect
7. #20298855C2semidirect
8. #20298841C2semidirect
9. #20298836C2semidirect
10. #20298826C2semidirect
11. #20298760C2semidirect
12. #20298752C2semidirect
13. #20298735C2semidirect
14. #20298563C2semidirect
15. #452×C113C2semidirect
191. C113#3201semidirect
203. #452D113semidirect

Maximal subgroups

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

subgroupindex
#202991762
#202991712
#202989382
#202989342
#202989262
#202989202
#202988552
#202988412
#202988362
#202988262
#202987602
#202987522
#202987352
#202985632
#452×C1132
#3201113