Finite Group Databasebeta

← #28404567

Subgroups — #28404567

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#20299320C213yesmaximal, complemented
3#20299303C213yesmaximal, complemented
4#20299296C213yesmaximal, complemented
5#20299289C213yesmaximal, complemented
6Q8×C22⋊D113C211yesmaximal, characteristic, complemented
7#20299260C211yesmaximal, characteristic, complemented
8#20299259C211yesmaximal, characteristic, complemented
9#20299220C213yesmaximal, complemented
10#20299206C213yesmaximal, complemented
11#20299132C213yesmaximal, complemented
12#20299132C213yesmaximal, complemented
13#20299080C211yesmaximal, characteristic, complemented
14#20299074C211yesmaximal, characteristic, complemented
15C2×C4×Q8×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18#16813621C2213yes—
19#16813620C2213yes—
20#16813617C2216yes—
21#16813616C2213yes—
22#16813616C2213yes—
23#16813616C2216yes—
24#16813614C2213yes—
25#16813614C2213yes—
26#16813613C2213yes—
27#16813612C2216yes—
28#16813611C2213yes—
29#16813610C2213yes—
30#16813610C2213yes—
31#16813607C2216yes—
32#16813605C2211yescharacteristic
33#16813605C2213yes—
34#16813602C2213yes—
35#16813601C2213yes—
36#16813601C2213yes—
37#16813600C2216yes—
38#16813598C2213yes—
39#16813598C2213yes—
40#16813597C2213yes—
41#16813596C2213yes—
42#16813596C2213yes—
43Q8×Dic113C2211yescharacteristic
44Q8×Dic113C2211yescharacteristic
45C4×Dic226C2213yes—
46C4×Dic226C2213yes—
47#16813587C2213yes—
48C4×D452C2213yes—
49C4×D452C2213yes—
50#16813584C2213yes—
51C4×C22⋊D113C2216yes—
52C4×C22⋊D113C2213yes—
53C4×C22⋊D113C2213yes—
54#16813580C2213yes—
55#16813579C2216yes—
56#16813579C2213yes—
57#16813579C2213yes—
58C4⋊C4×D113C2213yes—
59C22×Q8×C113C2211yescharacteristic
60C4×Q8×C113C2213yes—
61C4×Q8×C113C2211yescharacteristic
62C4×Q8×C113C2211yescharacteristic
63C4×Q8×C113C2213yes—
64C2×C4⋊C4×C113C2213yes—
65C2×C42×C113C2213yes—
66#14268648—24no—
67C2×Dic226C2313yes—
68C2×Dic226C2313yes—
69Q8×D113—24no—
70C2×D452C2313yes—
71C2×D452C2313yes—
72C2×C22⋊D113C2313yes—
73C2×C22⋊D113C2311yescharacteristic
74C2×C4×D113C2313yes—
75C2×C4×D113C2313yes—
76C2×C4×D113C2316yes—
77C4⋊Dic113C2313yes—
78C4⋊Dic113C2313yes—
79C4⋊Dic113C2313yes—
80C4⋊Dic113C2313yes—
81#14268626C2313yes—
82#14268626C2311yescharacteristic
83#14268626C2313yes—
84#14268626C2313yes—
85#14268626C2313yes—
86#14268626C2316yes—
87#14268626C2313yes—
88#14268626C2316yes—
89#14268626C2313yes—
90#14268626C2311yescharacteristic
91C22⋊Dic113C2311yescharacteristic
92C22⋊Dic113C2313yes—
93#14268624C2311yescharacteristic
94#14268624C2313yes—
95#14268624C2313yes—
96#14268624C2313yes—
97#14268624C2313yes—
98#14268624C2316yes—
99#14268624C2316yes—
100#14268624C2313yes—
101#14268624C2313yes—
102#14268624C2311yescharacteristic
103C4×Dic113C2316yes—
104C4×Dic113C2313yes—
105C4×Dic113C2313yes—
106C2×Q8×C113—24no—
107C2×Q8×C113C2313yes—
108C2×Q8×C113C2311yescharacteristic
109C22×C4×C113C2313yes—
110C22×C4×C113C2311yescharacteristic
111C22×C4×C113C2313yes—
112C4⋊C4×C113C2313yes—
113C4⋊C4×C113C2313yes—
114C4⋊C4×C113C2316yes—
115C42×C113C2313yes—
116C42×C113C2313yes—
117C42×C113C2313yes—
118C42×C113C2313yes—
119C23×C113C2411yescharacteristic
120C22×D113C2411yescharacteristic
121C22×D113C2413yes—
122Q8×C113—26no—
123Q8×C113#4114yes—
124C2×C4×C113—22no—
125C2×C4×C113—26no—
126C2×C4×C113—43no—
127C2×C4×C113C2411yescharacteristic
128C2×C4×C113C2411yescharacteristic
129C2×C4×C113C2413yes—
130C2×C4×C113C2413yes—
131C2×C4×C113C2413yes—
132C2×C4×C113C2413yes—
133C22⋊D113—26no—
134C22⋊D113—22no—
135C2×Dic113C2411yescharacteristic
136C2×Dic113C2413yes—
137C2×Dic113C2411yescharacteristic
138C2×Dic113C2413yes—
139C2×Dic113C2413yes—
140C2×Dic113C2411yescharacteristic
141D452—26no—
142D452—43no—
143C4×D113—26no—
144C4×D113—26no—
145C4×D113—46no—
146Dic226—26no—
147Dic226—43no—
148C22×C113—21no—
149C22×C113—21no—
150C22×C1132−1+412yes—
151C22×C113C2511yescharacteristic
152C2×D113—21no—
153C2×D113—23no—
154C2×D113—21no—
155C2×D113—23no—
156C2×D113—23no—
157C2×D113—21no—
158C4×C113—23no—
159C4×C113—21no—
160C4×C113—21no—
161C4×C113—23no—
162C4×C113—23no—
163C4×C113C2×#4116yes—
164Dic113—23no—
165Dic113—21no—
166Dic113—23no—
167Dic113—21no—
168Dic113—21no—
169Dic113—23no—
170C2×C113—22no—
171C2×C113C22×#4111yescharacteristic
172C2×C113C2×2−1+411yescharacteristic
173C2×C113#58511yescharacteristic
174D113—41no—
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×Q8—1131no—
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×Q8D11311yescharacteristic, complemented
193C2×#41—1131no—
194C22×Q8—1131no—
195C22×Q8C2×D11311yescharacteristic
196C4⋊Q8—1133no—
197C4⋊Q8—1133no—
198#126—1136no—
199#126—1136no—
200#126—1133no—
201#126—1133no—
202#125—1136no—
203#125—1133no—
204#125—1133no—
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—1133no—
215C22⋊Q8—1133no—
216C22⋊Q8—1133no—
217C22⋊Q8—1136no—
218#121—1133no—
219#121—1133no—
220#121—1133no—
221C4×Q8—1131no—
222C4×Q8—1131no—
223C4×Q8—1133no—
224C4×Q8—1133no—
225C4×Q8—1133no—
226C4×Q8C2×D11311yescharacteristic
227C4×Q8C2×D11313yes—
228C4×Q8C2×D11311yescharacteristic
229C4×Q8C2×D11313yes—
230C4×D4—1133no—
231C4×D4—1133no—
232C4×D4—1136no—
233C4×D4—1133no—
234C4×D4—1133no—
235C4×D4—1133no—
236#117—1133no—
237#117—1133no—
238#117—1133no—
239#117—1136no—
240C2×C4⋊C4—1133no—
241C2×C4⋊C4C2×D11313yes—
242C2×C42C2×D11313yes—
243#41—2264no—
244C2×Q8—24no—
245C2×Q8—1133no—
246C2×Q8—1133no—
247C2×Q8—2264no—
248C2×Q8C22×D11313yes—
249C2×Q8C22×D11311yescharacteristic
250C2×D4—1133no—
251C2×D4—1131no—
252C2×D4—1133no—
253C2×D4—1133no—
254C22×C4—1136no—
255C22×C4—1133no—
256C22×C4—1133no—
257C22×C4C22×D11311yescharacteristic
258C22×C4C22×D11313yes—
259C22×C4C22×D11313yes—
260C4⋊C4—1133no—
261C4⋊C4—1133no—
262C4⋊C4—1131no—
263C4⋊C4—1133no—
264C4⋊C4—1133no—
265C4⋊C4—1133no—
266C4⋊C4—1133no—
267C4⋊C4—1136no—
268C4⋊C4—1133no—
269C4⋊C4—1133no—
270C4⋊C4—1136no—
271C4⋊C4—1133no—
272C4⋊C4—1131no—
273C4⋊C4—1133no—
274C4⋊C4C22×D11313yes—
275C4⋊C4C22×D11313yes—
276C4⋊C4C22×D11316yes—
277C22⋊C4—1131no—
278C22⋊C4—1133no—
279C22⋊C4—1133no—
280C22⋊C4—1131no—
281C22⋊C4—1133no—
282C22⋊C4—1133no—
283C22⋊C4—1133no—
284C22⋊C4—1136no—
285C22⋊C4—1131no—
286C22⋊C4—1136no—
287C22⋊C4—1133no—
288C22⋊C4—1133no—
289C42—1136no—
290C42—1133no—
291C42—1133no—
292C42C22×D11313yes—
293C42C22×D11313yes—
294C42C22×D11313yes—
295C42C22×D11313yes—
296C23—1131no—
297C23—1133no—
298C23C23×D11311yescharacteristic
299Q8—26no—
300Q8—4523no—
301Q8—2266no—
302Q8#1426864714yes—
303D4—4523no—
304D4—2266no—
305D4—2262no—
306D4—2266no—
307C2×C4—22no—
308C2×C4—26no—
309C2×C4—43no—
310C2×C4—1131no—
311C2×C4—1133no—
312C2×C4—1131no—
313C2×C4—1133no—
314C2×C4—1133no—
315C2×C4—1131no—
316C2×C4—4526no—
317C2×C4—2266no—
318C2×C4—2266no—
319C2×C4C23×D11313yes—
320C2×C4C23×D11311yescharacteristic
321C2×C4C23×D11311yescharacteristic
322C2×C4C23×D11313yes—
323C2×C4C23×D11313yes—
324C2×C4C23×D11313yes—
325C22—21no—
326C22—21no—
327C22—2261no—
328C22—2263no—
329C22—2261no—
330C22—2263no—
331C22—2263no—
332C22—2261no—
333C22#1681367012yes—
334C22C24×D11311yescharacteristic
335C4—23no—
336C4—21no—
337C4—21no—
338C4—23no—
339C4—23no—
340C4—2261no—
341C4—2263no—
342C4—2263no—
343C4—2261no—
344C4—2263no—
345C4—2261no—
346C4C2×#1426864716yes—
347C2—22no—
348C2—4521no—
349C2—4523no—
350C2C22×#1426864711yescharacteristic
351C2C2×#1681367011yescharacteristic
352C2#2029943411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D113
commutator, socle, cosocleC22×C113C25
FittingC2×C4×Q8×C113C2
hypercenterC2×C4×Q8D113
hypocenterC113#3516
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #20299324C2semidirect
2. #20299320C2semidirect
3. #20299303C2semidirect
4. #20299296C2semidirect
5. #20299289C2semidirect
6. Q8×C22⋊D113C2semidirect
7. #20299260C2semidirect
8. #20299259C2semidirect
9. #20299220C2semidirect
10. #20299206C2semidirect
11. #20299132C2semidirect
12. #20299132C2semidirect
13. #20299080C2semidirect
14. #20299074C2semidirect
15. C2×C4×Q8×C113C2semidirect
177. C113#3516semidirect
192. C2×C4×Q8D113semidirect

Maximal subgroups

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

subgroupindex
#202993242
#202993202
#202993032
#202992962
#202992892
Q8×C22⋊D1132
#202992602
#202992592
#202992202
#202992062
#202991322
#202990802
#202990742
C2×C4×Q8×C1132
#3516113