Finite Group Databasebeta

← #86749

Subgroups — #86749

Order 384.

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
1C3×D4×Q8C211yesmaximal, characteristic, complemented
2#5817C211yesmaximal, characteristic, complemented
3#5817C211yesmaximal, characteristic, complemented
4#5812C211yesmaximal, characteristic, complemented
5C2×Q8×Dic3C211yesmaximal, characteristic, complemented
6#5732C213yesmaximal, complemented
7#5731C213yesmaximal, complemented
8#5643C213yesmaximal, complemented
9#5639C213yesmaximal, complemented
10#5635C213yesmaximal, complemented
11#5624C213yesmaximal, complemented
12#5574C211yesmaximal, characteristic, complemented
13#5569C211yesmaximal, characteristic, complemented
14#5565C213yesmaximal, complemented
15#5538C213yesmaximal, complemented
16#3516—31nomaximal, Sylow
17C22×C3×Q8C2211yescharacteristic
18C22×C3×Q8C2211yescharacteristic
19C2×#239C2211yescharacteristic
20C3×C4⋊Q8C2213yes—
21C3×C22⋊Q8C2213yes—
22C3×C22⋊Q8C2213yes—
23C3×C4×Q8C2211yescharacteristic
24C3×C4×D4C2213yes—
25#947C2213yes—
26#947C2213yes—
27#946C2213yes—
28#946C2213yes—
29Q8×Dic3C2213yes—
30Q8×Dic3C2213yes—
31Q8×Dic3C2213yes—
32Q8×Dic3C2213yes—
33Q8×Dic3C2211yescharacteristic
34Q8×Dic3C2211yescharacteristic
35Q8×Dic3C2211yescharacteristic
36#939C2213yes—
37#935C2211yescharacteristic
38#930C2213yes—
39#930C2213yes—
40C4×#67C2213yes—
41C4×#67C2213yes—
42#926C2213yes—
43#926C2213yes—
44C2×C4⋊Dic3C2213yes—
45C2×C4×Dic3C2213yes—
46#898C2216yes—
47#898C2216yes—
48#898C2213yes—
49#897C2216yes—
50#893C2213yes—
51#892C2216yes—
52D3×C4⋊C4C2213yes—
53#890C2213yes—
54#889C2216yes—
55#889C2213yes—
56#888C2213yes—
57#886C2213yes—
58#885C2213yes—
59#883C2216yes—
60#67⋊C4C2216yes—
61#879C2213yes—
62#878C2213yes—
63C4×D12C2213yes—
64#872C2213yes—
65#870C2213yes—
66C4×Dic6C2213yes—
67#557—31no—
68#556—33no—
69#554—33no—
70#553—33no—
71#552—33no—
72D4×Q8D311yescharacteristic, complemented
73#548—31no—
74#548—31no—
75#542—33no—
76#541—33no—
77#529—33no—
78#529—33no—
79#520—31no—
80#519—31no—
81C2×C4×Q8—31no—
82C2×C3×Q8—24no—
83C2×C3×Q8—24no—
84C2×C3×Q8C2313yes—
85C2×C3×Q8C2313yes—
86C2×C3×Q8C2311yescharacteristic
87C2×C3×D4C2311yescharacteristic
88C22×C3×C4C2313yes—
89C22×C3×C4C2313yes—
90C2×#67C2313yes—
91C2×#67C2313yes—
92C22×Dic3C2311yescharacteristic
93C22×Dic3C2313yes—
94#239—24no—
95C2×D12C2313yes—
96C2×C4×D3C2313yes—
97C2×C4×D3C2316yes—
98C2×Dic6C2313yes—
99C3×C4⋊C4C2313yes—
100C3×C4⋊C4C2316yes—
101C3×C4⋊C4C2313yes—
102C3×C22⋊C4C2313yes—
103C3×C22⋊C4C2313yes—
104C3×C42C2313yes—
105#217C2311yescharacteristic
106#217C2311yescharacteristic
107#217C2313yes—
108#217C2311yescharacteristic
109(C2×D3)⋊C4C2313yes—
110(C2×D3)⋊C4C2313yes—
111(C2×D3)⋊C4C2316yes—
112(C2×D3)⋊C4C2316yes—
113(C2×D3)⋊C4C2313yes—
114(C2×D3)⋊C4C2313yes—
115C4⋊Dic3C2313yes—
116C4⋊Dic3C2313yes—
117C4⋊Dic3C2313yes—
118C4⋊Dic3C2313yes—
119C4⋊Dic3C2313yes—
120C4⋊Dic3C2316yes—
121C4⋊Dic3C2313yes—
122Dic3⋊C4C2311yescharacteristic
123Dic3⋊C4C2313yes—
124Dic3⋊C4C2316yes—
125Dic3⋊C4C2311yescharacteristic
126Dic3⋊C4C2313yes—
127Dic3⋊C4C2313yes—
128Dic3⋊C4C2313yes—
129C4×Dic3C2313yes—
130C4×Dic3C2313yes—
131C4×Dic3C2313yes—
132C4×Dic3C2313yes—
133C4×Dic3C2316yes—
134C4×Dic3C2313yes—
135C2×#41—31no—
136C22×Q8C2×D311yescharacteristic
137C22×Q8C2×D311yescharacteristic
138C4⋊Q8—33no—
139C4⋊Q8C2×D313yes—
140#126—36no—
141#126—33no—
142#126—36no—
143#126—33no—
144#125—33no—
145#125—33no—
146#125—36no—
147#125—33no—
148#124—33no—
149#124—33no—
150#124—33no—
151#123—31no—
152#123—33no—
153#123—36no—
154C22⋊Q8—33no—
155C22⋊Q8—33no—
156C22⋊Q8—36no—
157C22⋊Q8—33no—
158C22⋊Q8C2×D313yes—
159C22⋊Q8C2×D313yes—
160#121—33no—
161#121—33no—
162#121—33no—
163C4×Q8—31no—
164C4×Q8—33no—
165C4×Q8—31no—
166C4×Q8—33no—
167C4×Q8—33no—
168C4×Q8—31no—
169C4×Q8—33no—
170C4×Q8—33no—
171C4×Q8C2×D311yescharacteristic
172C4×D4—33no—
173C4×D4—33no—
174C4×D4—33no—
175C4×D4—36no—
176C4×D4—33no—
177C4×D4C2×D313yes—
178#117—33no—
179#117—33no—
180#117—36no—
181#117—33no—
182C2×C4⋊C4—33no—
183C2×C4⋊C4—33no—
184C2×C42—33no—
185C23×C3C2411yescharacteristic
186C23×C3C2411yescharacteristic
187C22×D3C2413yes—
188C3×Q8—26no—
189C3×Q8—26no—
190C3×Q8#4114yes—
191C3×D4—22no—
192C2×C3×C4—26no—
193C2×C3×C4—26no—
194C2×C3×C4C2413yes—
195C2×C3×C4C2413yes—
196C2×C3×C4C2411yescharacteristic
197C2×C3×C4C2413yes—
198C2×C3×C4C2413yes—
199#67—26no—
200#67—43no—
201C2×Dic3—22no—
202C2×Dic3—43no—
203C2×Dic3C2411yescharacteristic
204C2×Dic3C2411yescharacteristic
205C2×Dic3C2413yes—
206C2×Dic3C2413yes—
207C2×Dic3C2411yescharacteristic
208C2×Dic3C2413yes—
209C2×Dic3C2411yescharacteristic
210D12—26no—
211C4×D3—26no—
212C4×D3—46no—
213Dic6—43no—
214#41—64no—
215C2×Q8—24no—
216C2×Q8—24no—
217C2×Q8—33no—
218C2×Q8C22×D313yes—
219C2×Q8C22×D313yes—
220C2×Q8C22×D311yescharacteristic
221C2×D4—33no—
222C2×D4—33no—
223C2×D4—33no—
224C2×D4C22×D311yescharacteristic
225C22×C4—31no—
226C22×C4—33no—
227C22×C4—33no—
228C22×C4—36no—
229C22×C4C22×D313yes—
230C22×C4C22×D313yes—
231C4⋊C4—33no—
232C4⋊C4—33no—
233C4⋊C4—33no—
234C4⋊C4—36no—
235C4⋊C4—31no—
236C4⋊C4—33no—
237C4⋊C4—33no—
238C4⋊C4—33no—
239C4⋊C4—33no—
240C4⋊C4—33no—
241C4⋊C4—33no—
242C4⋊C4—36no—
243C4⋊C4—31no—
244C4⋊C4—33no—
245C4⋊C4C22×D313yes—
246C4⋊C4C22×D316yes—
247C4⋊C4C22×D313yes—
248C22⋊C4—33no—
249C22⋊C4—31no—
250C22⋊C4—31no—
251C22⋊C4—31no—
252C22⋊C4—33no—
253C22⋊C4—33no—
254C22⋊C4—33no—
255C22⋊C4—36no—
256C22⋊C4—36no—
257C22⋊C4—33no—
258C22⋊C4C22×D313yes—
259C22⋊C4C22×D313yes—
260C42—33no—
261C42—33no—
262C42—33no—
263C42—33no—
264C42—36no—
265C42—33no—
266C42C22×D313yes—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C32−1+412yes—
273C22×C3C2511yescharacteristic
274C2×D3—23no—
275C2×D3—23no—
276C2×D3—23no—
277C3×C4—23no—
278C3×C4—23no—
279C3×C4—21no—
280C3×C4—23no—
281C3×C4C2×#4116yes—
282Dic3—21no—
283Dic3—21no—
284Dic3—21no—
285Dic3—23no—
286Dic3—21no—
287Dic3—23no—
288Dic3—23no—
289C23—33no—
290C23C23×D311yescharacteristic
291C23C23×D311yescharacteristic
292Q8—26no—
293Q8—26no—
294Q8—123no—
295Q8#23714yes—
296D4—22no—
297D4—66no—
298D4—66no—
299D4—123no—
300C2×C4—26no—
301C2×C4—26no—
302C2×C4—31no—
303C2×C4—31no—
304C2×C4—33no—
305C2×C4—31no—
306C2×C4—33no—
307C2×C4—33no—
308C2×C4—31no—
309C2×C4—62no—
310C2×C4—66no—
311C2×C4—126no—
312C2×C4—123no—
313C2×C4C23×D313yes—
314C2×C4C23×D313yes—
315C2×C4C23×D311yescharacteristic
316C2×C4C23×D313yes—
317C2×C4C23×D313yes—
318C2×C3—22no—
319C2×C3—41no—
320C2×C3C22×#4111yescharacteristic
321C2×C3C2×2−1+411yescharacteristic
322C2×C3#58511yescharacteristic
323D3—43no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—63no—
330C22—63no—
331C22—63no—
332C22#100712yes—
333C22C24×D311yescharacteristic
334C4—23no—
335C4—23no—
336C4—21no—
337C4—23no—
338C4—61no—
339C4—61no—
340C4—61no—
341C4—63no—
342C4—63no—
343C4—63no—
344C4—61no—
345C4C2×#23716yes—
346C3#351611yescharacteristic, complemented, Sylow
347C2—22no—
348C2—41no—
349C2—123no—
350C2C22×#23711yescharacteristic
351C2C2×#100711yescharacteristic
352C2#596811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×D4×Q8C2
hypercenterD4×Q8D3
hypocenterC3#3516
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×D4×Q8C2semidirect
2. #5817C2semidirect
3. #5817C2semidirect
4. #5812C2semidirect
5. C2×Q8×Dic3C2semidirect
6. #5732C2semidirect
7. #5731C2semidirect
8. #5643C2semidirect
9. #5639C2semidirect
10. #5635C2semidirect
11. #5624C2semidirect
12. #5574C2semidirect
13. #5569C2semidirect
14. #5565C2semidirect
15. #5538C2semidirect
72. D4×Q8D3semidirect
346. C3#3516semidirect

Maximal subgroups

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

subgroupindex
C3×D4×Q82
#58172
#58122
C2×Q8×Dic32
#57322
#57312
#56432
#56392
#56352
#56242
#55742
#55692
#55652
#55382
#35163