Finite Group Databasebeta

← #28402319

Subgroups — #28402319

Order 14464.

472 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14268637C211yesmaximal, characteristic, complemented
2C2×Q16×D113C211yesmaximal, characteristic, complemented
3Q8×C22⋊D113C211yesmaximal, characteristic
4#20299261C211yesmaximal, characteristic
5#20298976C211yesmaximal, characteristic, complemented
6#20298838C211yesmaximal, characteristic, complemented
7#20298837C211yesmaximal, characteristic, complemented
8#20298807C211yesmaximal, characteristic, complemented
9#20298806C211yesmaximal, characteristic, complemented
10#20298756C211yesmaximal, characteristic, complemented
11#20298755C211yesmaximal, characteristic, complemented
12#20298752C211yesmaximal, characteristic, complemented
13#20298690C211yesmaximal, characteristic, complemented
14#20298661C211yesmaximal, characteristic
15#451×C113C211yesmaximal, characteristic, complemented
16C22×Dic226C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×Q8×D113C2211yescharacteristic
19C2×Dic452C2211yescharacteristic
20C2×Dic452C2211yescharacteristic
21C2×#14268637—24no—
22C2×#14268637C2211yescharacteristic
23C2×#14268637C2211yescharacteristic
24C2×#14268637C2211yescharacteristic
25C2×#14268637C2211yescharacteristic
26C2×#14268637C2211yescharacteristic
27Q16×D113—24no—
28C22×#11744751C2211yescharacteristic
29C2×C8×D113C2211yescharacteristic
30#16813621—21no—
31#16813620—21no—
32#16813620C2211yescharacteristic
33#16813620C2211yescharacteristic
34#16813602C2211yescharacteristic
35#16813601—21no—
36#16813601C2211yescharacteristic
37#16813600—21no—
38#16813599—21no—
39#16813598—21no—
40#16813598C2211yescharacteristic
41Q8×Dic113C2211yescharacteristic
42#16813587C2211yescharacteristic
43C4×C22⋊D113—21no—
44C4×C22⋊D113C2211yescharacteristic
45#16813582—21no—
46#16813555C2211yescharacteristic
47#16813551C2211yescharacteristic
48#16813547C2211yescharacteristic
49#16813547C2211yescharacteristic
50#16813546C2211yescharacteristic
51#16813545C2211yescharacteristic
52#16813534C2211yescharacteristic
53C8×Dic113C2211yescharacteristic
54C22×Q8×C113C2211yescharacteristic
55C2×Q16×C113C2211yescharacteristic
56C2×Q16×C113C2211yescharacteristic
57C22⋊Q8×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59#103×C113C2211yescharacteristic
60C22⋊C8×C113C2211yescharacteristic
61C2×Dic226—22no—
62C2×Dic226—21no—
63C2×Dic226—21no—
64C2×Dic226—21no—
65C2×Dic226—41no—
66C2×Dic226C2311yescharacteristic
67C2×Dic226C2311yescharacteristic
68C2×Dic226C2311yescharacteristic
69Q8×D113—22no—
70Q8×D113—22no—
71Q8×D113—41no—
72Q8×D113—41no—
73C2×C22⋊D113D411yescharacteristic
74C22×Dic113—21no—
75C2×C4×D113—21no—
76C2×C4×D113—21no—
77C2×C4×D113C2311yescharacteristic
78Dic452—22no—
79Dic452—41no—
80#14268637—22no—
81#14268637—22no—
82#14268637—22no—
83#14268637—22no—
84#14268637D414yescomplemented
85C2×#11744751—22no—
86C2×#11744751C2311yescharacteristic
87C2×#11744751C2311yescharacteristic
88C8×D113—22no—
89C4⋊Dic113—21no—
90C4⋊Dic113—21no—
91C4⋊Dic113C2311yescharacteristic
92#14268626—21no—
93#14268626—21no—
94#14268626—21no—
95#14268626—21no—
96#14268626—21no—
97#14268626—21no—
98#14268626—21no—
99#14268626D411yescharacteristic
100C22⋊Dic113—21no—
101C22⋊Dic113D411yescharacteristic
102#14268624—21no—
103#14268624—21no—
104#14268624D411yescharacteristic
105C4×Dic113—21no—
106C4×Dic113—21no—
107C4×Dic113C2311yescharacteristic
108C2×Q8×C113—21no—
109C2×Q8×C113—22no—
110C2×Q8×C113—41no—
111C2×Q8×C113C2311yescharacteristic
112C2×Q8×C113C2311yescharacteristic
113C2×Q8×C113C2311yescharacteristic
114C22×C4×C113—21no—
115C22×C4×C113C2311yescharacteristic
116Q16×C113—22no—
117Q16×C113—41no—
118C2×C8×C113C2311yescharacteristic
119C2×C8×C113C2311yescharacteristic
120C4⋊C4×C113—21no—
121C4⋊C4×C113C2311yescharacteristic
122C22⋊C4×C113—21no—
123C23×C113C2×D411yescharacteristic
124C22×D113C2×D411yescharacteristic
125Q8×C113—21no—
126Q8×C113—21no—
127Q8×C113—21no—
128Q8×C113—21no—
129Q8×C113—21no—
130Q8×C113—42no—
131Q8×C113C2×D412yes—
132C2×C4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113—42no—
139C2×C4×C113C2×D411yescharacteristic
140C2×C4×C113C2411yescharacteristic
141C22⋊D113Q1614yescomplemented
142C2×Dic113—21no—
143C2×Dic113—21no—
144C2×Dic113—21no—
145C2×Dic113—21no—
146C2×Dic113—42no—
147C2×Dic113C2×D411yescharacteristic
148C2×Dic113C2×D411yescharacteristic
149C2×Dic113C2×D411yescharacteristic
150C4×D113—21no—
151C4×D113—21no—
152C4×D113—42no—
153C4×D113—42no—
154Dic226—21no—
155Dic226—21no—
156Dic226—21no—
157Dic226—21no—
158Dic226—21no—
159Dic226—42no—
160Dic226—42no—
161Dic226—42no—
162Dic226C2×D412yes—
163C8×C113—21no—
164C8×C113—21no—
165#11744751—21no—
166#11744751C2×D412yes—
167C22×C113—21no—
168C22×C113—21no—
169C22×C113C2×Q1612yescomplemented
170C22×C113C22×D411yescharacteristic
171C2×D113—21no—
172C2×D113—21no—
173C2×D113C2×Q1612yescomplemented
174C4×C113—21no—
175C4×C113—22no—
176C4×C113—41no—
177C4×C113—41no—
178C4×C113—41no—
179C4×C113C22×D411yescharacteristic
180C4×C113H(5,𝔽2)11yescharacteristic
181Dic113—22no—
182Dic113—21no—
183Dic113—21no—
184Dic113—41no—
185Dic113—41no—
186Dic113—41no—
187Dic113C2×Q1612yescomplemented
188C2×C113—22no—
189C2×C113D4211yescharacteristic
190C2×C113C22×Q1611yescharacteristic
191C2×C113#57811yescharacteristic
192D113—22no—
193D4×Q16—1131nomaximal, Sylow
194C113D4×Q1611yescharacteristic, complemented, Sylow
195C22×Q16—1131no—
196C22×Q16—1131no—
197D4×Q8—1131no—
198D4×Q8—1131no—
199#494—1131no—
200#467—1131no—
201#467—1131no—
202#462—1131no—
203#462—1131no—
204#451—1131no—
205#451—1131no—
206#451—1131no—
207#451D11311yescharacteristic, complemented
208C4×Q16—1131no—
209C8×D4—1131no—
210C22×Q8—1131no—
211C22×Q8—1131no—
212C22×Q8—1131no—
213C22×Q8C2×D11311yescharacteristic
214C2×Q16—1131no—
215C2×Q16—1131no—
216C2×Q16—1131no—
217C2×Q16—1131no—
218C2×Q16—1131no—
219C2×Q16—1131no—
220C2×Q16—1131no—
221C2×Q16—2264no—
222C2×Q16—2264no—
223C2×Q16C2×D11311yescharacteristic
224C2×Q16C2×D11311yescharacteristic
225C22×C8—1131no—
226C22×C8—1131no—
227C4⋊Q8—1131no—
228C4⋊Q8—1131no—
229C4⋊Q8—2261no—
230C4⋊Q8—2261no—
231C22⋊Q8—1131no—
232C22⋊Q8—1131no—
233C22⋊Q8—1131no—
234C22⋊Q8—2261no—
235C22⋊Q8—2261no—
236C22⋊Q8—2261no—
237C22⋊Q8—2261no—
238C22⋊Q8C2×D11311yescharacteristic
239C4×Q8—1131no—
240C4×Q8—1131no—
241C4×D4—1131no—
242C4×D4—2261no—
243C4×D4—2261no—
244#107—1131no—
245C4⋊C8—1131no—
246#103—1131no—
247#103—1131no—
248#103—1131no—
249#103—1131no—
250#103C2×D11311yescharacteristic
251#103C2×D11311yescharacteristic
252C22⋊C8—1131no—
253C22⋊C8C2×D11311yescharacteristic
254C4×C8—1131no—
255C2×Q8—21no—
256C2×Q8—22no—
257C2×Q8—41no—
258C2×Q8—1131no—
259C2×Q8—1131no—
260C2×Q8—1131no—
261C2×Q8—4521no—
262C2×Q8—4521no—
263C2×Q8—4521no—
264C2×Q8—2261no—
265C2×Q8—2261no—
266C2×Q8—2262no—
267C2×Q8—2262no—
268C2×Q8—2262no—
269C2×Q8—2261no—
270C2×Q8C22×D11311yescharacteristic
271C2×Q8C22×D11311yescharacteristic
272C2×Q8C22×D11311yescharacteristic
273C2×D4—1131no—
274C22×C4—21no—
275C22×C4—1131no—
276C22×C4—2261no—
277C22×C4—2261no—
278C22×C4—2261no—
279C22×C4C22×D11311yescharacteristic
280Q16—22no—
281Q16—41no—
282Q16—1134no—
283Q16—4521no—
284Q16—2262no—
285Q16—2262no—
286Q16—2262no—
287Q16—2262no—
288Q16—2262no—
289C2×C8—1131no—
290C2×C8—1131no—
291C2×C8—2262no—
292C2×C8—2262no—
293C2×C8C22×D11311yescharacteristic
294C2×C8C22×D11311yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—1131no—
297C4⋊C4—1131no—
298C4⋊C4—2261no—
299C4⋊C4—2261no—
300C4⋊C4—2261no—
301C4⋊C4—2261no—
302C4⋊C4—2261no—
303C4⋊C4—2261no—
304C4⋊C4—2261no—
305C4⋊C4—2261no—
306C4⋊C4—2261no—
307C4⋊C4C22×D11311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—1131no—
310C22⋊C4—1131no—
311C22⋊C4—2261no—
312C22⋊C4—2261no—
313C22⋊C4—2261no—
314C42—1131no—
315C42—2261no—
316C42—2261no—
317C23—1131no—
318C23D4×D11311yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—42no—
325Q8—1132no—
326Q8—4522no—
327Q8—4522no—
328Q8—4522no—
329Q8—2261no—
330Q8—2261no—
331Q8—2261no—
332Q8—2261no—
333Q8—2261no—
334Q8D4×D11312yes—
335D4—1134no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—1131no—
344C2×C4—1131no—
345C2×C4—1131no—
346C2×C4—4522no—
347C2×C4—4522no—
348C2×C4—4522no—
349C2×C4—2261no—
350C2×C4—2261no—
351C2×C4—2261no—
352C2×C4—2261no—
353C2×C4—2261no—
354C2×C4—2261no—
355C2×C4D4×D11311yescharacteristic
356C2×C4C23×D11311yescharacteristic
357C8—21no—
358C8—21no—
359C8—1132no—
360C8—2261no—
361C22—21no—
362C22—21no—
363C22—1132no—
364C22—2261no—
365C22—2261no—
366C22Q16×D11312yescomplemented
367C22C2×D4×D11311yescharacteristic
368C4—21no—
369C4—22no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—1132no—
374C4—4521no—
375C4—4521no—
376C4—4521no—
377C4—2261no—
378C4—2261no—
379C4—2262no—
380C4C2×D4×D11311yescharacteristic
381C4#1681366711yescharacteristic
382C2—22no—
383C2—2262no—
384C2#2029923011yescharacteristic
385C2C2×Q16×D11311yescharacteristic
386C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#451×C113C2
socleC22×C113C22×D4
prime radicalC2×C22⋊D113D4
hypercenter#451D113
hypocenterC113D4×Q16
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
1. C22×#14268637C2semidirect
2. C2×Q16×D113C2semidirect
5. #20298976C2semidirect
6. #20298838C2semidirect
7. #20298837C2semidirect
8. #20298807C2semidirect
9. #20298806C2semidirect
10. #20298756C2semidirect
11. #20298755C2semidirect
12. #20298752C2semidirect
13. #20298690C2semidirect
15. #451×C113C2semidirect
84. #14268637D4semidirect
141. C22⋊D113Q16semidirect
169. C22×C113C2×Q16semidirect
173. C2×D113C2×Q16semidirect
187. Dic113C2×Q16semidirect
194. C113D4×Q16semidirect
207. #451D113semidirect
366. C22Q16×D113semidirect

Maximal subgroups

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

subgroupindex
C22×#142686372
C2×Q16×D1132
Q8×C22⋊D1132
#202992612
#202989762
#202988382
#202988372
#202988072
#202988062
#202987562
#202987552
#202987522
#202986902
#202986612
#451×C1132
D4×Q16113