Finite Group Databasebeta

← #28404568

Subgroups — #28404568

Order 14464.

1012 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299324C211yesmaximal, characteristic, complemented
2#20299322C213yesmaximal, complemented
3#20299306C213yesmaximal, complemented
4#20299294C213yesmaximal, complemented
5#20299282C213yesmaximal, complemented
6#20299259C211yesmaximal, characteristic, complemented
7#20299259C211yesmaximal, characteristic, complemented
8#20299221C213yesmaximal, complemented
9#20299209C213yesmaximal, complemented
10#20299134C213yesmaximal, complemented
11#20299128C213yesmaximal, complemented
12#20299080C211yesmaximal, characteristic, complemented
13#20299076C211yesmaximal, characteristic, complemented
14C2×Q8×Dic113C211yesmaximal, characteristic, complemented
15D4×Q8×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17#16813621C2213yes—
18#16813617C2216yes—
19#16813617C2213yes—
20#16813617C2216yes—
21#16813615C2213yes—
22#16813614C2213yes—
23#16813613C2213yes—
24#16813612C2216yes—
25#16813612C2213yes—
26#16813611C2213yes—
27#16813611C2213yes—
28#16813608C2213yes—
29#16813606C2213yes—
30#16813604C2216yes—
31#16813603C2211yescharacteristic
32#16813602C2216yes—
33#16813599C2213yes—
34#16813598C2213yes—
35#16813598C2213yes—
36#16813596C2213yes—
37#16813596C2213yes—
38#16813594C2213yes—
39Q8×Dic113C2213yes—
40Q8×Dic113C2213yes—
41Q8×Dic113C2211yescharacteristic
42Q8×Dic113C2211yescharacteristic
43Q8×Dic113C2213yes—
44Q8×Dic113C2211yescharacteristic
45Q8×Dic113C2213yes—
46C4×Dic226C2213yes—
47C4×D452C2213yes—
48#16813584C2213yes—
49C4×C22⋊D113C2213yes—
50C4×C22⋊D113C2213yes—
51#16813582C2216yes—
52#16813581C2213yes—
53#16813581C2213yes—
54#16813580C2216yes—
55#16813579C2213yes—
56C2×C4⋊Dic113C2213yes—
57C4⋊C4×D113C2213yes—
58C2×C4×Dic113C2213yes—
59C22×Q8×C113C2211yescharacteristic
60C22×Q8×C113C2211yescharacteristic
61C4⋊Q8×C113C2213yes—
62C22⋊Q8×C113C2213yes—
63C22⋊Q8×C113C2213yes—
64C4×Q8×C113C2211yescharacteristic
65C4×D4×C113C2213yes—
66#14268648—24no—
67C2×Dic226C2313yes—
68C2×D452C2313yes—
69C2×C22⋊D113C2313yes—
70C2×C22⋊D113C2313yes—
71C22×Dic113C2311yescharacteristic
72C22×Dic113C2313yes—
73C2×C4×D113C2313yes—
74C2×C4×D113C2316yes—
75C4⋊Dic113C2313yes—
76C4⋊Dic113C2313yes—
77C4⋊Dic113C2316yes—
78C4⋊Dic113C2313yes—
79C4⋊Dic113C2313yes—
80C4⋊Dic113C2313yes—
81C4⋊Dic113C2313yes—
82#14268626C2313yes—
83#14268626C2311yescharacteristic
84#14268626C2316yes—
85#14268626C2313yes—
86#14268626C2313yes—
87#14268626C2311yescharacteristic
88#14268626C2313yes—
89C22⋊Dic113C2313yes—
90C22⋊Dic113C2311yescharacteristic
91C22⋊Dic113C2311yescharacteristic
92C22⋊Dic113C2311yescharacteristic
93#14268624C2313yes—
94#14268624C2313yes—
95#14268624C2313yes—
96#14268624C2316yes—
97#14268624C2316yes—
98#14268624C2313yes—
99C4×Dic113C2313yes—
100C4×Dic113C2313yes—
101C4×Dic113C2313yes—
102C4×Dic113C2313yes—
103C4×Dic113C2316yes—
104C4×Dic113C2313yes—
105C2×Q8×C113—24no—
106C2×Q8×C113—24no—
107C2×Q8×C113C2313yes—
108C2×Q8×C113C2313yes—
109C2×Q8×C113C2311yescharacteristic
110C2×D4×C113C2311yescharacteristic
111C22×C4×C113C2313yes—
112C22×C4×C113C2313yes—
113C4⋊C4×C113C2313yes—
114C4⋊C4×C113C2316yes—
115C4⋊C4×C113C2313yes—
116C22⋊C4×C113C2313yes—
117C22⋊C4×C113C2313yes—
118C42×C113C2313yes—
119C23×C113C2411yescharacteristic
120C23×C113C2411yescharacteristic
121C22×D113C2413yes—
122Q8×C113—26no—
123Q8×C113—26no—
124Q8×C113#4114yes—
125D4×C113—22no—
126C2×C4×C113—26no—
127C2×C4×C113—26no—
128C2×C4×C113C2411yescharacteristic
129C2×C4×C113C2413yes—
130C2×C4×C113C2413yes—
131C2×C4×C113C2413yes—
132C2×C4×C113C2413yes—
133C22⋊D113—26no—
134C22⋊D113—43no—
135C2×Dic113—22no—
136C2×Dic113—43no—
137C2×Dic113C2411yescharacteristic
138C2×Dic113C2411yescharacteristic
139C2×Dic113C2413yes—
140C2×Dic113C2411yescharacteristic
141C2×Dic113C2413yes—
142C2×Dic113C2413yes—
143C2×Dic113C2411yescharacteristic
144D452—26no—
145C4×D113—26no—
146C4×D113—46no—
147Dic226—43no—
148C22×C113—21no—
149C22×C113—21no—
150C22×C113—21no—
151C22×C113—21no—
152C22×C113—21no—
153C22×C1132−1+412yes—
154C22×C113C2511yescharacteristic
155C2×D113—23no—
156C2×D113—23no—
157C2×D113—23no—
158C4×C113—23no—
159C4×C113—23no—
160C4×C113—21no—
161C4×C113—23no—
162C4×C113C2×#4116yes—
163Dic113—21no—
164Dic113—21no—
165Dic113—21no—
166Dic113—23no—
167Dic113—21no—
168Dic113—23no—
169Dic113—23no—
170C2×C113—22no—
171C2×C113—41no—
172C2×C113C22×#4111yescharacteristic
173C2×C113C2×2−1+411yescharacteristic
174C2×C113#58511yescharacteristic
175D113—43no—
176#3516—1131nomaximal, Sylow
177C113#351611yescharacteristic, complemented, Sylow
178#557—1131no—
179#556—1133no—
180#554—1133no—
181#553—1133no—
182#552—1133no—
183D4×Q8D11311yescharacteristic, complemented
184#548—1131no—
185#548—1131no—
186#542—1133no—
187#541—1133no—
188#529—1133no—
189#529—1133no—
190#520—1131no—
191#519—1131no—
192C2×C4×Q8—1131no—
193C2×#41—1131no—
194C22×Q8C2×D11311yescharacteristic
195C22×Q8C2×D11311yescharacteristic
196C4⋊Q8—1133no—
197C4⋊Q8C2×D11313yes—
198#126—1136no—
199#126—1133no—
200#126—1136no—
201#126—1133no—
202#125—1133no—
203#125—1133no—
204#125—1136no—
205#125—1133no—
206#124—1133no—
207#124—1133no—
208#124—1133no—
209#123—1131no—
210#123—1133no—
211#123—1136no—
212C22⋊Q8—1133no—
213C22⋊Q8—1133no—
214C22⋊Q8—1136no—
215C22⋊Q8—1133no—
216C22⋊Q8C2×D11313yes—
217C22⋊Q8C2×D11313yes—
218#121—1133no—
219#121—1133no—
220#121—1133no—
221C4×Q8—1131no—
222C4×Q8—1133no—
223C4×Q8—1131no—
224C4×Q8—1133no—
225C4×Q8—1133no—
226C4×Q8—1131no—
227C4×Q8—1133no—
228C4×Q8—1133no—
229C4×Q8C2×D11311yescharacteristic
230C4×D4—1133no—
231C4×D4—1133no—
232C4×D4—1133no—
233C4×D4—1136no—
234C4×D4—1133no—
235C4×D4C2×D11313yes—
236#117—1133no—
237#117—1133no—
238#117—1136no—
239#117—1133no—
240C2×C4⋊C4—1133no—
241C2×C4⋊C4—1133no—
242C2×C42—1133no—
243#41—2264no—
244C2×Q8—24no—
245C2×Q8—24no—
246C2×Q8—1133no—
247C2×Q8C22×D11313yes—
248C2×Q8C22×D11313yes—
249C2×Q8C22×D11311yescharacteristic
250C2×D4—1133no—
251C2×D4—1133no—
252C2×D4—1133no—
253C2×D4C22×D11311yescharacteristic
254C22×C4—1133no—
255C22×C4—1131no—
256C22×C4—1136no—
257C22×C4—1133no—
258C22×C4C22×D11313yes—
259C22×C4C22×D11313yes—
260C4⋊C4—1133no—
261C4⋊C4—1133no—
262C4⋊C4—1133no—
263C4⋊C4—1136no—
264C4⋊C4—1131no—
265C4⋊C4—1133no—
266C4⋊C4—1133no—
267C4⋊C4—1133no—
268C4⋊C4—1133no—
269C4⋊C4—1133no—
270C4⋊C4—1133no—
271C4⋊C4—1136no—
272C4⋊C4—1131no—
273C4⋊C4—1133no—
274C4⋊C4C22×D11313yes—
275C4⋊C4C22×D11316yes—
276C4⋊C4C22×D11313yes—
277C22⋊C4—1133no—
278C22⋊C4—1131no—
279C22⋊C4—1131no—
280C22⋊C4—1131no—
281C22⋊C4—1133no—
282C22⋊C4—1133no—
283C22⋊C4—1133no—
284C22⋊C4—1136no—
285C22⋊C4—1136no—
286C22⋊C4—1133no—
287C22⋊C4C22×D11313yes—
288C22⋊C4C22×D11313yes—
289C42—1133no—
290C42—1133no—
291C42—1133no—
292C42—1133no—
293C42—1136no—
294C42—1133no—
295C42C22×D11313yes—
296C23—1133no—
297C23C23×D11311yescharacteristic
298C23C23×D11311yescharacteristic
299Q8—26no—
300Q8—26no—
301Q8—4523no—
302Q8#1426864614yes—
303D4—22no—
304D4—4523no—
305D4—2266no—
306D4—2266no—
307C2×C4—26no—
308C2×C4—26no—
309C2×C4—1131no—
310C2×C4—1131no—
311C2×C4—1133no—
312C2×C4—1131no—
313C2×C4—1133no—
314C2×C4—1133no—
315C2×C4—1131no—
316C2×C4—4526no—
317C2×C4—4523no—
318C2×C4—2262no—
319C2×C4—2266no—
320C2×C4C23×D11313yes—
321C2×C4C23×D11313yes—
322C2×C4C23×D11311yescharacteristic
323C2×C4C23×D11313yes—
324C2×C4C23×D11313yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—2263no—
331C22—2263no—
332C22—2263no—
333C22#1681367012yes—
334C22C24×D11311yescharacteristic
335C4—23no—
336C4—23no—
337C4—21no—
338C4—23no—
339C4—2261no—
340C4—2261no—
341C4—2261no—
342C4—2263no—
343C4—2263no—
344C4—2263no—
345C4—2261no—
346C4C2×#1426864616yes—
347C2—22no—
348C2—41no—
349C2—4523no—
350C2C22×#1426864611yescharacteristic
351C2C2×#1681367011yescharacteristic
352C2#2029943511yescharacteristic
subgroupG/H
center, FrattiniC22C24×D113
commutator, socle, cosocleC22×C113C25
FittingD4×Q8×C113C2
hypercenterD4×Q8D113
hypocenterC113#3516
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. #20299324C2semidirect
2. #20299322C2semidirect
3. #20299306C2semidirect
4. #20299294C2semidirect
5. #20299282C2semidirect
6. #20299259C2semidirect
7. #20299259C2semidirect
8. #20299221C2semidirect
9. #20299209C2semidirect
10. #20299134C2semidirect
11. #20299128C2semidirect
12. #20299080C2semidirect
13. #20299076C2semidirect
14. C2×Q8×Dic113C2semidirect
15. D4×Q8×C113C2semidirect
177. C113#3516semidirect
183. D4×Q8D113semidirect

Maximal subgroups

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

subgroupindex
#202993242
#202993222
#202993062
#202992942
#202992822
#202992592
#202992212
#202992092
#202991342
#202991282
#202990802
#202990762
C2×Q8×Dic1132
D4×Q8×C1132
#3516113