Finite Group Databasebeta

← #28404172

Subgroups — #28404172

Order 14464.

1112 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299331C213yesmaximal, complemented
2#20299324C211yesmaximal, characteristic, complemented
3#20299316C213yesmaximal, complemented
4#20299298C213yesmaximal, complemented
5#20299292C213yesmaximal, complemented
6#20299267C211yesmaximal, characteristic, complemented
7#20299260C211yesmaximal, characteristic, complemented
8#20299255C211yesmaximal, characteristic, complemented
9#20299145C213yesmaximal, complemented
10#20299132C213yesmaximal, complemented
11#20299130C213yesmaximal, complemented
12C4×#14268648C211yesmaximal, characteristic, complemented
13C4×#14268647C213yesmaximal, complemented
14C4×Q8×D113C211yesmaximal, characteristic, complemented
15C4×#41×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268647C2213yes—
18C2×Q8×D113C2211yescharacteristic
19#16813621C2213yes—
20#16813618C2213yes—
21#16813616C2216yes—
22#16813615C2216yes—
23#16813614C2213yes—
24#16813613C2213yes—
25#16813610C2213yes—
26#16813609C2213yes—
27#16813608C2216yes—
28#16813605C2216yes—
29#16813604C2216yes—
30#16813602C2213yes—
31#16813601C2213yes—
32#16813597C2213yes—
33#16813596C2213yes—
34#16813595C2216yes—
35#16813593C2213yes—
36#16813593C2213yes—
37Q8×Dic113C2211yescharacteristic
38Q8×Dic113C2211yescharacteristic
39C4×Dic226C2213yes—
40C4×Dic226C2213yes—
41C4×Dic226C2213yes—
42#16813587C2213yes—
43C4×D452C2213yes—
44C4×D452C2213yes—
45C4×D452C2213yes—
46#16813584C2213yes—
47C4×C22⋊D113C2213yes—
48C4×C22⋊D113C2213yes—
49C4×C22⋊D113C2213yes—
50C4×C22⋊D113C2213yes—
51C4×C22⋊D113C2216yes—
52#16813581C2213yes—
53#16813580C2213yes—
54#16813579C2211yescharacteristic
55#16813579C2213yes—
56C4⋊C4×D113C2213yes—
57C42×D113C2213yes—
58C42×D113C2213yes—
59C2×#41×C113C2211yescharacteristic
60C4×Q8×C113C2211yescharacteristic
61C4×Q8×C113C2211yescharacteristic
62C4×D4×C113C2213yes—
63C4×D4×C113C2213yes—
64#117×C113C2213yes—
65C2×C42×C113C2213yes—
66#14268648—24no—
67#14268647—212no—
68C2×Dic226C2313yes—
69C2×Dic226C2313yes—
70Q8×D113—24no—
71C2×D452C2313yes—
72C2×D452C2313yes—
73C2×C22⋊D113C2313yes—
74C2×C22⋊D113C2313yes—
75C2×C22⋊D113C2316yes—
76C2×C4×D113C2313yes—
77C2×C4×D113C2313yes—
78C2×C4×D113C2313yes—
79C2×C4×D113C2313yes—
80C2×C4×D113C2313yes—
81C2×C4×D113C2311yescharacteristic
82C4⋊Dic113C2313yes—
83C4⋊Dic113C2313yes—
84C4⋊Dic113C2313yes—
85C4⋊Dic113C2313yes—
86#14268626C2316yes—
87#14268626C2311yescharacteristic
88#14268626C2311yescharacteristic
89#14268626C2313yes—
90#14268626C2313yes—
91#14268626C2316yes—
92C22⋊Dic113C2313yes—
93C22⋊Dic113C2313yes—
94C22⋊Dic113C2316yes—
95#14268624C2311yescharacteristic
96#14268624C2311yescharacteristic
97#14268624C2313yes—
98#14268624C2313yes—
99#14268624C2316yes—
100#14268624C2316yes—
101C4×Dic113C2311yescharacteristic
102C4×Dic113C2313yes—
103C4×Dic113C2313yes—
104C4×Dic113C2313yes—
105C4×Dic113C2313yes—
106C4×Dic113C2313yes—
107#41×C113—24no—
108C2×Q8×C113C2311yescharacteristic
109C2×D4×C113C2313yes—
110C22×C4×C113C2313yes—
111C22×C4×C113C2313yes—
112C22×C4×C113C2313yes—
113C4⋊C4×C113C2313yes—
114C4⋊C4×C113C2313yes—
115C22⋊C4×C113C2316yes—
116C42×C113C2313yes—
117C42×C113C2311yescharacteristic
118C42×C113C2313yes—
119C42×C113C2313yes—
120C23×C113C2413yes—
121C22×D113C2413yes—
122C22×D113C2411yescharacteristic
123Q8×C113#4114yescomplemented
124D4×C113—26no—
125C2×C4×C113—26no—
126C2×C4×C113—26no—
127C2×C4×C113—43no—
128C2×C4×C113C2411yescharacteristic
129C2×C4×C113C2411yescharacteristic
130C2×C4×C113C2413yes—
131C2×C4×C113C2413yes—
132C2×C4×C113C2413yes—
133C2×C4×C113C2411yescharacteristic
134C22⋊D113—26no—
135C22⋊D113—26no—
136C22⋊D113—46no—
137C2×Dic113C2411yescharacteristic
138C2×Dic113C2411yescharacteristic
139C2×Dic113C2413yes—
140C2×Dic113C2413yes—
141C2×Dic113C2413yes—
142C2×Dic113C2411yescharacteristic
143D452—26no—
144D452—26no—
145C4×D113—26no—
146C4×D113—26no—
147C4×D113—26no—
148C4×D113—43no—
149C4×D113—43no—
150C4×D113#4114yescomplemented
151Dic226—26no—
152Dic226—26no—
153C22×C113—23no—
154C22×C113—23no—
155C22×C113—23no—
156C22×C113C2511yescharacteristic
157C2×D113—21no—
158C2×D113—21no—
159C2×D113—23no—
160C2×D113—23no—
161C2×D113—23no—
162C2×D113C2×#4112yes—
163C4×C113—23no—
164C4×C113—21no—
165C4×C113—23no—
166C4×C113—21no—
167C4×C113C2×#4112yes—
168C4×C113C2×#4116yes—
169Dic113—23no—
170Dic113—23no—
171Dic113—21no—
172Dic113—21no—
173Dic113—23no—
174Dic113C2×#4112yes—
175C2×C113—43no—
176C2×C113C22×#4111yescharacteristic
177C2×C113C22×#4111yescharacteristic
178C2×C113#58511yescharacteristic
179D113—22no—
180D113—43no—
181#3480—1131nomaximal, Sylow
182C113#348011yescharacteristic, complemented, Sylow
183#559—1133no—
184#557—1131no—
185#556—1133no—
186#553—1133no—
187#553—1133no—
188#550—1131no—
189#548—1131no—
190#548—1131no—
191#532—1133no—
192#529—1133no—
193#529—1133no—
194C4×#41—1131no—
195C4×#41—1133no—
196C4×#41D11311yescharacteristic, complemented
197C2×C4×Q8—1131no—
198C2×#41—1131no—
199C2×#41—1133no—
200C2×#41C2×D11311yescharacteristic
201C22×Q8—1131no—
202C4⋊Q8—1133no—
203#127—1133no—
204#126—1136no—
205#126—1136no—
206#125—1133no—
207#125—1133no—
208#124—1133no—
209#124—1136no—
210#124—1133no—
211#123—1136no—
212#123—1136no—
213C22⋊Q8—1133no—
214C22⋊Q8—1133no—
215#121—1133no—
216#121—1133no—
217#121—1133no—
218#121—1133no—
219#121—1136no—
220C4×Q8—1131no—
221C4×Q8—1131no—
222C4×Q8—1133no—
223C4×Q8—1133no—
224C4×Q8—1133no—
225C4×Q8—1133no—
226C4×Q8C2×D11311yescharacteristic
227C4×Q8C2×D11311yescharacteristic
228C4×D4—1133no—
229C4×D4—1133no—
230C4×D4—1133no—
231C4×D4—1133no—
232C4×D4—1136no—
233C4×D4—1133no—
234C4×D4—1133no—
235C4×D4—1133no—
236C4×D4—1133no—
237C4×D4C2×D11313yes—
238C4×D4C2×D11313yes—
239#117—1133no—
240#117—1133no—
241#117—1131no—
242#117—1133no—
243#117C2×D11313yes—
244C2×C4⋊C4—1133no—
245C2×C42—1133no—
246C2×C42—1133no—
247C2×C42C2×D11313yes—
248#41—24no—
249#41—22612no—
250#41—2264no—
251C2×Q8—1133no—
252C2×Q8—1133no—
253C2×Q8—2264no—
254C2×Q8C22×D11311yescharacteristic
255C2×D4—1136no—
256C2×D4—1133no—
257C2×D4—1133no—
258C2×D4—1133no—
259C2×D4—1133no—
260C2×D4C22×D11313yes—
261C22×C4—1131no—
262C22×C4—1133no—
263C22×C4—1133no—
264C22×C4—1133no—
265C22×C4—1133no—
266C22×C4—1133no—
267C22×C4C22×D11313yes—
268C22×C4C22×D11313yes—
269C22×C4C22×D11313yes—
270C4⋊C4—1133no—
271C4⋊C4—1136no—
272C4⋊C4—1131no—
273C4⋊C4—1131no—
274C4⋊C4—1133no—
275C4⋊C4—1133no—
276C4⋊C4—1133no—
277C4⋊C4—1133no—
278C4⋊C4—1133no—
279C4⋊C4—1136no—
280C4⋊C4C22×D11313yes—
281C4⋊C4C22×D11313yes—
282C22⋊C4—1133no—
283C22⋊C4—1133no—
284C22⋊C4—1136no—
285C22⋊C4—1131no—
286C22⋊C4—1131no—
287C22⋊C4—1133no—
288C22⋊C4—1136no—
289C22⋊C4—1133no—
290C22⋊C4—1136no—
291C22⋊C4C22×D11316yes—
292C42—1133no—
293C42—1133no—
294C42—1133no—
295C42—1133no—
296C42—1131no—
297C42—1133no—
298C42C22×D11313yes—
299C42C22×D11313yes—
300C42C22×D11313yes—
301C42C22×D11311yescharacteristic
302C23—1131no—
303C23—1133no—
304C23C23×D11313yes—
305Q8—2266no—
306Q8—2266no—
307Q8#1426864714yescomplemented
308D4—26no—
309D4—4526no—
310D4—2266no—
311D4—2266no—
312D4—2266no—
313D4—2266no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—43no—
317C2×C4—1131no—
318C2×C4—1134no—
319C2×C4—1131no—
320C2×C4—1131no—
321C2×C4—1133no—
322C2×C4—1133no—
323C2×C4—1133no—
324C2×C4—4523no—
325C2×C4—4523no—
326C2×C4—2266no—
327C2×C4—2266no—
328C2×C4—2266no—
329C2×C4C23×D11313yes—
330C2×C4C23×D11311yescharacteristic
331C2×C4C23×D11311yescharacteristic
332C2×C4C23×D11313yes—
333C2×C4C23×D11313yes—
334C2×C4C23×D11311yescharacteristic
335C22—23no—
336C22—23no—
337C22—23no—
338C22—1132no—
339C22—2263no—
340C22—2263no—
341C22—2263no—
342C22—2261no—
343C22—2261no—
344C22C24×D11311yescharacteristic
345C4—23no—
346C4—21no—
347C4—21no—
348C4—23no—
349C4—1132no—
350C4—2263no—
351C4—2261no—
352C4—2263no—
353C4—2261no—
354C4—2263no—
355C4#41×D11312yes—
356C4C2×#1426864716yes—
357C2—43no—
358C2—4523no—
359C2—2262no—
360C2C2×#41×D11311yescharacteristic
361C2C22×#1426864711yescharacteristic
362C2#2029943411yescharacteristic
subgroupG/H
centerC2×C4C23×D113
commutator, socle, cosocleC22×C113C25
FrattiniC22C24×D113
FittingC4×#41×C113C2
hypercenterC4×#41D113
hypocenterC113#3480
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #20299331C2semidirect
2. #20299324C2semidirect
3. #20299316C2semidirect
4. #20299298C2semidirect
5. #20299292C2semidirect
6. #20299267C2semidirect
7. #20299260C2semidirect
8. #20299255C2semidirect
9. #20299145C2semidirect
10. #20299132C2semidirect
11. #20299130C2semidirect
12. C4×#14268648C2semidirect
13. C4×#14268647C2semidirect
14. C4×Q8×D113C2semidirect
15. C4×#41×C113C2semidirect
123. Q8×C113#41semidirect
150. C4×D113#41semidirect
182. C113#3480semidirect
196. C4×#41D113semidirect
307. Q8#14268647semidirect

Maximal subgroups

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

subgroupindex
#202993312
#202993242
#202993162
#202992982
#202992922
#202992672
#202992602
#202992552
#202991452
#202991322
#202991302
C4×#142686482
C4×#142686472
C4×Q8×D1132
C4×#41×C1132
#3480113