Finite Group Databasebeta

← #28402432

Subgroups — #28402432

Order 14464.

420 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C22⋊D113C211yesmaximal, characteristic, complemented
2#20299248C211yesmaximal, characteristic
3#20298947C211yesmaximal, characteristic, complemented
4#20298929C211yesmaximal, characteristic, complemented
5#20298927C211yesmaximal, characteristic, complemented
6#20298881C211yesmaximal, characteristic, complemented
7#20298825C211yesmaximal, characteristic, complemented
8#20298824C211yesmaximal, characteristic, complemented
9#20298801C211yesmaximal, characteristic, complemented
10#20298735C211yesmaximal, characteristic, complemented
11SD16×Dic113C211yesmaximal, characteristic, complemented
12#20298661C211yesmaximal, characteristic, complemented
13C2×#16813546C211yesmaximal, characteristic, complemented
14#103×D113C211yesmaximal, characteristic, complemented
15#448×C113C211yesmaximal, characteristic, complemented
16C2×#14268646—21no—
17C2×Q8×D113C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C22×#11744751C2211yescharacteristic
20C2×C8×D113C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813620—21no—
23#16813620C2211yescharacteristic
24#16813604—21no—
25#16813603—21no—
26#16813601—21no—
27#16813601C2211yescharacteristic
28#16813599—21no—
29#16813598—21no—
30#16813598C2211yescharacteristic
31#16813593C2211yescharacteristic
32Q8×Dic113C2211yescharacteristic
33D4×Dic113C2211yescharacteristic
34C4×C22⋊D113—21no—
35C4×C22⋊D113C2211yescharacteristic
36C2×C4⋊Dic113C2211yescharacteristic
37C4⋊C4×D113C2211yescharacteristic
38#16813554C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813546C2211yescharacteristic
48#16813545C2211yescharacteristic
49#16813543C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C22×Q8×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268646—44no—
60C2×Dic226—21no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63Q8×D113—22no—
64Q8×D113—41no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113D411yescharacteristic
67C22×Dic113—21no—
68C22×Dic113—21no—
69C2×C4×D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113C2311yescharacteristic
72#14268635—41no—
73C2×#11744751—41no—
74C2×#11744751C2311yescharacteristic
75C2×#11744751C2311yescharacteristic
76C8×D113—41no—
77C4⋊Dic113—21no—
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—
88#14268626D411yescharacteristic
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113—21no—
92C22⋊Dic113D411yescharacteristic
93#14268624—21no—
94#14268624D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113—21no—
98C2×Q8×C113—22no—
99C2×Q8×C113—41no—
100C2×Q8×C113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C2×D4×C113—21no—
103C2×D4×C113C2311yescharacteristic
104C22×C4×C113—21no—
105C22×C4×C113C2311yescharacteristic
106SD16×C113—22no—
107SD16×C113—41no—
108C2×C8×C113C2311yescharacteristic
109C2×C8×C113C2311yescharacteristic
110C4⋊C4×C113C2311yescharacteristic
111C22⋊C4×C113—21no—
112C23×C113—21no—
113C23×C113C2×D411yescharacteristic
114C22×D113C2×D411yescharacteristic
115Q8×C113—21no—
116Q8×C113—21no—
117Q8×C113—21no—
118Q8×C113—42no—
119Q8×C113#4112yescomplemented
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
131C22⋊D113—42no—
132C22⋊D113SD1614yescomplemented
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—42no—
138C2×Dic113—42no—
139C2×Dic113C2×D411yescharacteristic
140C2×Dic113C2×D411yescharacteristic
141C2×Dic113C2×D411yescharacteristic
142C4×D113—21no—
143C4×D113—21no—
144C4×D113—42no—
145C4×D113—42no—
146Dic226—21no—
147Dic226—21no—
148Dic226—42no—
149Dic226—42no—
150C8×C113—21no—
151C8×C113—21no—
152#11744751—21no—
153#11744751—21no—
154C22×C113—21no—
155C22×C113—21no—
156C22×C113—41no—
157C22×C113—41no—
158C22×C113—41no—
159C22×C113C2×SD1612yes—
160C22×C113C22×D411yescharacteristic
161C2×D113—21no—
162C2×D113—21no—
163C2×D113C2×SD1612yes—
164C4×C113—22no—
165C4×C113—21no—
166C4×C113—41no—
167C4×C113—41no—
168C4×C113C2×#4111yescharacteristic
169C4×C113H(5,𝔽2)11yescharacteristic
170Dic113—21no—
171Dic113—21no—
172Dic113—41no—
173Dic113—41no—
174Dic113—41no—
175Dic113—41no—
176Dic113C2×SD1612yes—
177C2×C113—22no—
178C2×C113—81no—
179C2×C113#54611yescharacteristic
180C2×C113C22×SD1611yescharacteristic
181C2×C113#57811yescharacteristic
182D113—22no—
183#3298—1131nomaximal, Sylow
184C113#329811yescharacteristic, complemented, Sylow
185D4×Q8—1131no—
186#547—1131no—
187#487—1131no—
188#483—1131no—
189#483—1131no—
190#475—1131no—
191#465—1131no—
192#465—1131no—
193#461—1131no—
194#448—1131no—
195#448D11311yescharacteristic, complemented
196C4×SD16—1131no—
197C8×D4—1131no—
198C2×#103—1131no—
199C2×#103—1131no—
200C2×#41—2261no—
201C22×Q8—1131no—
202C22×Q8C2×D11311yescharacteristic
203C2×SD16—1131no—
204C2×SD16C2×D11311yescharacteristic
205C2×SD16C2×D11311yescharacteristic
206C22×C8—1131no—
207C22×C8—1131no—
208C4⋊Q8—1131no—
209C4⋊Q8—1131no—
210C4⋊Q8—2261no—
211#123—2261no—
212#123—2261no—
213C22⋊Q8—1131no—
214C22⋊Q8—1131no—
215C22⋊Q8—2261no—
216C22⋊Q8—2261no—
217C22⋊Q8—2261no—
218#121—1131no—
219#121C2×D11311yescharacteristic
220C4×Q8—1131no—
221C4×D4—1131no—
222C4×D4—1131no—
223C4×D4—2261no—
224C2×C4⋊C4—1131no—
225C2×C4⋊C4—1131no—
226#106—1131no—
227#106—1131no—
228#106—1131no—
229C4⋊C8—1131no—
230#103—1131no—
231#103—1131no—
232#103—1131no—
233#103—1131no—
234#103—1131no—
235#103—1131no—
236#103—1131no—
237#103C2×D11311yescharacteristic
238#103C2×D11311yescharacteristic
239#102—1131no—
240C22⋊C8—1131no—
241C22⋊C8C2×D11311yescharacteristic
242C4×C8—1131no—
243#41—4524no—
244C2×Q8—21no—
245C2×Q8—22no—
246C2×Q8—41no—
247C2×Q8—1131no—
248C2×Q8—4521no—
249C2×Q8—2261no—
250C2×Q8—2261no—
251C2×Q8—2262no—
252C2×Q8C22×D11311yescharacteristic
253C2×Q8C22×D11311yescharacteristic
254C2×D4—21no—
255C2×D4—1131no—
256C2×D4—2261no—
257C2×D4C22×D11311yescharacteristic
258C22×C4—21no—
259C22×C4—1131no—
260C22×C4—2261no—
261C22×C4—2261no—
262C22×C4—2261no—
263C22×C4—2261no—
264C22×C4C22×D11311yescharacteristic
265SD16—22no—
266SD16—41no—
267SD16—4521no—
268C2×C8—1131no—
269C2×C8—1131no—
270C2×C8—4521no—
271C2×C8—4521no—
272C2×C8C22×D11311yescharacteristic
273C2×C8C22×D11311yescharacteristic
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—1131no—
277C4⋊C4—1131no—
278C4⋊C4—2261no—
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—1131no—
289C22⋊C4—1131no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C42—1131no—
295C42—2261no—
296C23—21no—
297C23—1131no—
298C23D4×D11311yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—21no—
302Q8—42no—
303Q8—4522no—
304Q8—4522no—
305Q8—2261no—
306Q8—2261no—
307Q8#1426864612yescomplemented
308D4—21no—
309D4—21no—
310D4—42no—
311D4—1134no—
312D4—4522no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—1131no—
320C2×C4—1131no—
321C2×C4—1131no—
322C2×C4—4522no—
323C2×C4—4522no—
324C2×C4—4522no—
325C2×C4—4522no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4—2261no—
329C2×C4—2261no—
330C2×C4—2261no—
331C2×C4—2261no—
332C2×C4D4×D11311yescharacteristic
333C2×C4C23×D11311yescharacteristic
334C8—21no—
335C8—21no—
336C8—2261no—
337C8—2261no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—1132no—
344C22—2261no—
345C22—2261no—
346C22SD16×D11312yes—
347C22C2×D4×D11311yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—41no—
352C4—1132no—
353C4—4521no—
354C4—4521no—
355C4—4521no—
356C4—4521no—
357C4—2261no—
358C4—2261no—
359C4C2×#1426864611yescharacteristic
360C4#1681366711yescharacteristic
361C2—22no—
362C2—81no—
363C2—2262no—
364C2#2029923511yescharacteristic
365C2C2×SD16×D11311yescharacteristic
366C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#448×C113C2
socleC22×C113C22×D4
prime radical#20299248C2
hypercenter#448D113
hypocenterC113#3298
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. Q8×C22⋊D113C2semidirect
3. #20298947C2semidirect
4. #20298929C2semidirect
5. #20298927C2semidirect
6. #20298881C2semidirect
7. #20298825C2semidirect
8. #20298824C2semidirect
9. #20298801C2semidirect
10. #20298735C2semidirect
11. SD16×Dic113C2semidirect
12. #20298661C2semidirect
13. C2×#16813546C2semidirect
14. #103×D113C2semidirect
15. #448×C113C2semidirect
119. Q8×C113#41semidirect
132. C22⋊D113SD16semidirect
184. C113#3298semidirect
195. #448D113semidirect
307. Q8#14268646semidirect

Maximal subgroups

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

subgroupindex
Q8×C22⋊D1132
#202992482
#202989472
#202989292
#202989272
#202988812
#202988252
#202988242
#202988012
#202987352
SD16×Dic1132
#202986612
C2×#168135462
#103×D1132
#448×C1132
#3298113