Finite Group Databasebeta

← #28404191

Subgroups — #28404191

Order 14464.

1094 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299324C211yesmaximal, characteristic, complemented
2#20299320C213yesmaximal, complemented
3#20299289C213yesmaximal, complemented
4#20299283C213yesmaximal, complemented
5Q8×C22⋊D113C211yesmaximal, characteristic, complemented
6#20299260C211yesmaximal, characteristic, complemented
7#20299259C211yesmaximal, characteristic, complemented
8#20299249C213yesmaximal, complemented
9#20299152C213yesmaximal, complemented
10#20299135C213yesmaximal, complemented
11#20299132C213yesmaximal, complemented
12C4×#14268648C211yesmaximal, characteristic, complemented
13C4×#14268647C213yesmaximal, complemented
14C4×Q8×D113C211yesmaximal, characteristic, complemented
15C2×C4×Q8×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268647C2213yes—
18C2×Q8×D113C2211yescharacteristic
19#16813621C2213yes—
20#16813620C2213yes—
21#16813617C2216yes—
22#16813616C2216yes—
23#16813614C2213yes—
24#16813613C2213yes—
25#16813612C2216yes—
26#16813611C2213yes—
27#16813610C2213yes—
28#16813607C2216yes—
29#16813605C2216yes—
30#16813602C2213yes—
31#16813601C2213yes—
32#16813600C2216yes—
33#16813598C2213yes—
34#16813598C2213yes—
35#16813597C2213yes—
36#16813596C2213yes—
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⋊D113C2211yescharacteristic
49C4×C22⋊D113C2213yes—
50C4×C22⋊D113C2213yes—
51#16813581C2213yes—
52#16813580C2213yes—
53#16813579C2213yes—
54#16813579C2213yes—
55#16813579C2216yes—
56C4⋊C4×D113C2213yes—
57C42×D113C2213yes—
58C42×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—
67#14268647—212no—
68C2×Dic226C2313yes—
69C2×Dic226C2313yes—
70Q8×D113—24no—
71C2×D452C2313yes—
72C2×D452C2313yes—
73C2×C22⋊D113C2313yes—
74C2×C22⋊D113C2311yescharacteristic
75C2×C4×D113C2311yescharacteristic
76C2×C4×D113C2313yes—
77C2×C4×D113C2313yes—
78C2×C4×D113C2313yes—
79C2×C4×D113C2313yes—
80C2×C4×D113C2313yes—
81C4⋊Dic113C2313yes—
82C4⋊Dic113C2313yes—
83C4⋊Dic113C2313yes—
84C4⋊Dic113C2313yes—
85#14268626C2316yes—
86#14268626C2311yescharacteristic
87#14268626C2313yes—
88#14268626C2313yes—
89#14268626C2313yes—
90#14268626C2316yes—
91#14268626C2316yes—
92C22⋊Dic113C2311yescharacteristic
93C22⋊Dic113C2313yes—
94#14268624C2311yescharacteristic
95#14268624C2313yes—
96#14268624C2313yes—
97#14268624C2313yes—
98#14268624C2316yes—
99#14268624C2316yes—
100#14268624C2316yes—
101C4×Dic113C2311yescharacteristic
102C4×Dic113C2313yes—
103C4×Dic113C2313yes—
104C4×Dic113C2313yes—
105C4×Dic113C2313yes—
106C4×Dic113C2313yes—
107C2×Q8×C113—24no—
108C2×Q8×C113C2313yes—
109C2×Q8×C113C2311yescharacteristic
110C22×C4×C113C2313yes—
111C22×C4×C113C2311yescharacteristic
112C22×C4×C113C2313yes—
113C4⋊C4×C113C2313yes—
114C4⋊C4×C113C2313yes—
115C4⋊C4×C113C2316yes—
116C42×C113C2313yes—
117C42×C113C2313yes—
118C42×C113C2313yes—
119C42×C113C2313yes—
120C23×C113C2411yescharacteristic
121C22×D113C2413yes—
122C22×D113C2411yescharacteristic
123Q8×C113—26no—
124Q8×C113#4114yescomplemented
125C2×C4×C113—26no—
126C2×C4×C113—26no—
127C2×C4×C113—22no—
128C2×C4×C113C2411yescharacteristic
129C2×C4×C113C2413yes—
130C2×C4×C113C2413yes—
131C2×C4×C113C2413yes—
132C2×C4×C113C2413yes—
133C2×C4×C113C2411yescharacteristic
134C22⋊D113—26no—
135C22⋊D113#4114yescomplemented
136C2×Dic113C2411yescharacteristic
137C2×Dic113C2411yescharacteristic
138C2×Dic113C2413yes—
139C2×Dic113C2413yes—
140C2×Dic113C2413yes—
141C2×Dic113C2411yescharacteristic
142D452—26no—
143D452—26no—
144C4×D113—26no—
145C4×D113—26no—
146C4×D113—26no—
147C4×D113—22no—
148C4×D113—26no—
149C4×D113—26no—
150Dic226—26no—
151Dic226—26no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113C2×#4112yes—
155C22×C113C2511yescharacteristic
156C2×D113—21no—
157C2×D113—21no—
158C2×D113—23no—
159C2×D113—23no—
160C2×D113—23no—
161C2×D113C2×#4112yes—
162C4×C113—23no—
163C4×C113—23no—
164C4×C113—23no—
165C4×C113—21no—
166C4×C113C2×#4116yes—
167C4×C1132−1+412yes—
168Dic113—23no—
169Dic113—23no—
170Dic113—21no—
171Dic113—21no—
172Dic113—23no—
173Dic113C2×#4112yes—
174C2×C113—22no—
175C2×C113C22×#4111yescharacteristic
176C2×C113C22×#4111yescharacteristic
177C2×C113C2×2−1+411yescharacteristic
178D113—22no—
179D113—43no—
180#3482—1131nomaximal, Sylow
181C113#348211yescharacteristic, complemented, Sylow
182#557—1131no—
183#556—1133no—
184#552—1133no—
185#552—1133no—
186D4×Q8—1131no—
187#548—1131no—
188#548—1131no—
189#547—1133no—
190#533—1133no—
191#529—1133no—
192#529—1133no—
193C4×#41—1131no—
194C4×#41—1133no—
195C2×C4×Q8—1131no—
196C2×C4×Q8D11311yescharacteristic, complemented
197C2×#41—1131no—
198C2×#41—1133no—
199C22×Q8—1131no—
200C22×Q8C2×D11311yescharacteristic
201C4⋊Q8—1133no—
202C4⋊Q8—1133no—
203#126—1136no—
204#126—1136no—
205#125—1133no—
206#125—1136no—
207#125—1133no—
208#124—1133no—
209#124—1133no—
210#123—1136no—
211#123—1136no—
212C22⋊Q8—1133no—
213C22⋊Q8—1133no—
214C22⋊Q8—1133no—
215C22⋊Q8—1136no—
216C22⋊Q8—1133no—
217#121—1133no—
218#121—1133no—
219C4×Q8—1131no—
220C4×Q8—1131no—
221C4×Q8—1133no—
222C4×Q8—1133no—
223C4×Q8—1133no—
224C4×Q8—1133no—
225C4×Q8C2×D11311yescharacteristic
226C4×Q8C2×D11313yes—
227C4×Q8C2×D11311yescharacteristic
228C4×Q8C2×D11313yes—
229C4×D4—1131no—
230C4×D4—1133no—
231C4×D4—1133no—
232C4×D4—1133no—
233C4×D4—1133no—
234C4×D4—1133no—
235C4×D4—1133no—
236C4×D4—1133no—
237#117—1133no—
238#117—1133no—
239#117—1133no—
240#117—1133no—
241#117—1136no—
242C2×C4⋊C4—1133no—
243C2×C4⋊C4C2×D11313yes—
244C2×C42—1133no—
245C2×C42—1133no—
246C2×C42C2×D11313yes—
247#41—22612no—
248#41—2264no—
249C2×Q8—24no—
250C2×Q8—1133no—
251C2×Q8—1133no—
252C2×Q8—2264no—
253C2×Q8C22×D11313yes—
254C2×Q8C22×D11311yescharacteristic
255C2×D4—1131no—
256C2×D4—1133no—
257C2×D4—1133no—
258C2×D4—1133no—
259C22×C4—1133no—
260C22×C4—1133no—
261C22×C4—1133no—
262C22×C4—1133no—
263C22×C4—1131no—
264C22×C4—1133no—
265C22×C4C22×D11313yes—
266C22×C4C22×D11313yes—
267C22×C4C22×D11311yescharacteristic
268C4⋊C4—1133no—
269C4⋊C4—1136no—
270C4⋊C4—1131no—
271C4⋊C4—1133no—
272C4⋊C4—1133no—
273C4⋊C4—1133no—
274C4⋊C4—1133no—
275C4⋊C4—1133no—
276C4⋊C4—1133no—
277C4⋊C4—1136no—
278C4⋊C4—1136no—
279C4⋊C4C22×D11313yes—
280C4⋊C4C22×D11313yes—
281C4⋊C4C22×D11316yes—
282C22⋊C4—1131no—
283C22⋊C4—1133no—
284C22⋊C4—1131no—
285C22⋊C4—1133no—
286C22⋊C4—1136no—
287C22⋊C4—1133no—
288C22⋊C4—1133no—
289C22⋊C4—1136no—
290C22⋊C4—1136no—
291C42—1133no—
292C42—1133no—
293C42—1133no—
294C42—1133no—
295C42—1131no—
296C42—1133no—
297C42C22×D11313yes—
298C42C22×D11313yes—
299C42C22×D11313yes—
300C42C22×D11313yes—
301C23—1131no—
302C23—1133no—
303C23C23×D11311yescharacteristic
304Q8—26no—
305Q8—2266no—
306Q8—2266no—
307Q8#1426864714yescomplemented
308D4—1134no—
309D4—2266no—
310D4—2266no—
311D4—2266no—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—22no—
315C2×C4—1131no—
316C2×C4—1131no—
317C2×C4—1131no—
318C2×C4—1133no—
319C2×C4—1133no—
320C2×C4—1133no—
321C2×C4—2266no—
322C2×C4—2266no—
323C2×C4—2266no—
324C2×C4—2266no—
325C2×C4—2266no—
326C2×C4—2262no—
327C2×C4C23×D11313yes—
328C2×C4C23×D11311yescharacteristic
329C2×C4C23×D11313yes—
330C2×C4C23×D11313yes—
331C2×C4C23×D11313yes—
332C2×C4C23×D11311yescharacteristic
333C22—21no—
334C22—21no—
335C22—1132no—
336C22—2263no—
337C22—2263no—
338C22—2263no—
339C22—2261no—
340C22—2261no—
341C22#41×D11312yes—
342C22C24×D11311yescharacteristic
343C4—23no—
344C4—23no—
345C4—23no—
346C4—21no—
347C4—1132no—
348C4—2263no—
349C4—2261no—
350C4—2263no—
351C4—2261no—
352C4—2263no—
353C4C2×#1426864716yes—
354C4#1681367012yes—
355C2—22no—
356C2—4523no—
357C2—2262no—
358C2C2×#41×D11311yescharacteristic
359C2C22×#1426864711yescharacteristic
360C2C2×#1681367011yescharacteristic
subgroupG/H
centerC2×C4C23×D113
commutator, socle, cosocleC22×C113C25
FrattiniC22C24×D113
FittingC2×C4×Q8×C113C2
hypercenterC2×C4×Q8D113
hypocenterC113#3482
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #20299324C2semidirect
2. #20299320C2semidirect
3. #20299289C2semidirect
4. #20299283C2semidirect
5. Q8×C22⋊D113C2semidirect
6. #20299260C2semidirect
7. #20299259C2semidirect
8. #20299249C2semidirect
9. #20299152C2semidirect
10. #20299135C2semidirect
11. #20299132C2semidirect
12. C4×#14268648C2semidirect
13. C4×#14268647C2semidirect
14. C4×Q8×D113C2semidirect
15. C2×C4×Q8×C113C2semidirect
124. Q8×C113#41semidirect
135. C22⋊D113#41semidirect
181. C113#3482semidirect
196. C2×C4×Q8D113semidirect
307. Q8#14268647semidirect

Maximal subgroups

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

subgroupindex
#202993242
#202993202
#202992892
#202992832
Q8×C22⋊D1132
#202992602
#202992592
#202992492
#202991522
#202991352
#202991322
C4×#142686482
C4×#142686472
C4×Q8×D1132
C2×C4×Q8×C1132
#3482113