Finite Group Databasebeta

← #80789

Subgroups — #80789

Order 384.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5643C211yesmaximal, characteristic, complemented
2#5619C211yesmaximal, characteristic, complemented
3C3×#468C211yesmaximal, characteristic, complemented
4#5176C211yesmaximal, characteristic, complemented
5Dic3×SD16C211yesmaximal, characteristic, complemented
6#5135C211yesmaximal, characteristic, complemented
7#5122C211yesmaximal, characteristic, complemented
8#5048C211yesmaximal, characteristic, complemented
9#5038C211yesmaximal, characteristic, complemented
10#4876C211yesmaximal, characteristic, complemented
11#4872C211yesmaximal, characteristic, complemented
12#4817C211yesmaximal, characteristic, complemented
13#4800C211yesmaximal, characteristic, complemented
14#4785C211yesmaximal, characteristic, complemented
15#4760C211yesmaximal, characteristic, complemented
16#3179—31nomaximal, Sylow
17C2×C3×SD16C2211yescharacteristic
18C2×C3×M16C2211yescharacteristic
19C3×C22⋊Q8C2211yescharacteristic
20C3×#121C2211yescharacteristic
21#947C2211yescharacteristic
22Q8×Dic3C2211yescharacteristic
23C2×#215C2211yescharacteristic
24#940C2211yescharacteristic
25#939—21no—
26#938—21no—
27D4×Dic3C2211yescharacteristic
28C2×#213C2211yescharacteristic
29#930C2211yescharacteristic
30#930C2211yescharacteristic
31#926C2211yescharacteristic
32C22×C3⋊C8C2211yescharacteristic
33C2×D24C2211yescharacteristic
34#898—21no—
35#897—21no—
36#893C2211yescharacteristic
37#893C2211yescharacteristic
38#890C2211yescharacteristic
39#888C2211yescharacteristic
40#886—21no—
41#885—21no—
42#883—21no—
43#883—21no—
44C3×#107C2211yescharacteristic
45C3×#103C2211yescharacteristic
46C3×#102C2211yescharacteristic
47#835C2211yescharacteristic
48#832C2211yescharacteristic
49#821C2211yescharacteristic
50#821C2211yescharacteristic
51#817C2211yescharacteristic
52#815C2211yescharacteristic
53#815C2211yescharacteristic
54C8×Dic3C2211yescharacteristic
55C8×Dic3C2211yescharacteristic
56#809C2211yescharacteristic
57#809C2211yescharacteristic
58#808C2211yescharacteristic
59#807C2211yescharacteristic
60#542—31no—
61#540—31no—
62#501—31no—
63#496—31no—
64#488—31no—
65#486—31no—
66#469—31no—
67#468D311yescharacteristic, complemented
68#466—31no—
69#465—31no—
70#442—31no—
71#440—31no—
72C4×SD16—31no—
73C4×D8—31no—
74#405—31no—
75C2×C3×Q8C2311yescharacteristic
76C2×C3×D4—21no—
77C2×C3×D4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C2×#67—21no—
80C2×#67—21no—
81C2×#67—21no—
82C2×#67—21no—
83C22×Dic3—21no—
84C2×D12C2311yescharacteristic
85C2×D12C2311yescharacteristic
86C2×C4×D3—21no—
87C2×C4×D3—21no—
88C2×Dic6—21no—
89C3×SD16—22no—
90C3×M16—22no—
91C2×C3×C8C2311yescharacteristic
92C2×C3×C8C2311yescharacteristic
93C3×C4⋊C4—21no—
94C3×C4⋊C4C2311yescharacteristic
95C3×C4⋊C4C2311yescharacteristic
96C3×C22⋊C4—21no—
97C3×C22⋊C4—21no—
98#217—21no—
99#217D411yescharacteristic
100#217D411yescharacteristic
101#215—22no—
102#213—22no—
103(C2×D3)⋊C4—21no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109C4⋊Dic3—21no—
110C4⋊Dic3—21no—
111C4⋊Dic3D411yescharacteristic
112C4⋊Dic3D411yescharacteristic
113C4⋊Dic3C2311yescharacteristic
114C4⋊Dic3C2311yescharacteristic
115Dic3⋊C4—21no—
116Dic3⋊C4—21no—
117C4×Dic3—21no—
118C4×Dic3C2311yescharacteristic
119C4×Dic3C2311yescharacteristic
120C2×C3⋊C8—22no—
121C2×C3⋊C8C2311yescharacteristic
122C2×C3⋊C8C2311yescharacteristic
123D24—22no—
124C2×SD16—31no—
125C2×SD16C2×D311yescharacteristic
126C2×D8—31no—
127C2×D8—31no—
128C2×M16C2×D311yescharacteristic
129C22×C8—31no—
130C4⋊Q8—31no—
131#127—31no—
132#126—61no—
133#125—31no—
134#124—31no—
135#124—61no—
136#123—61no—
137#123—61no—
138#123—61no—
139C22⋊Q8—61no—
140C22⋊Q8C2×D311yescharacteristic
141#121—31no—
142#121—31no—
143#121—61no—
144#121—61no—
145#121C2×D311yescharacteristic
146C4×Q8—31no—
147C4×D4—31no—
148C4×D4—31no—
149C4×D4—31no—
150#117—31no—
151#107—31no—
152#107C2×D311yescharacteristic
153#106—31no—
154#106—31no—
155#103—31no—
156#103C2×D311yescharacteristic
157#102—31no—
158#102—31no—
159#102—31no—
160#102—31no—
161#102—31no—
162#102C2×D311yescharacteristic
163#97—31no—
164#97—31no—
165C4×C8—31no—
166C4×C8—31no—
167C23×C3—21no—
168C23×C3C2×D411yescharacteristic
169C22×D3—21no—
170C22×D3—21no—
171C3×Q8—21no—
172C3×Q8—21no—
173C3×D4—21no—
174C3×D4—21no—
175C3×D4—81no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4C2×D411yescharacteristic
182C2×C3×C4C2411yescharacteristic
183#67—81no—
184#67—81no—
185#67—81no—
186#67—81no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—81no—
190C2×Dic3C2×D411yescharacteristic
191C2×Dic3C2×D411yescharacteristic
192C2×Dic3C2×D411yescharacteristic
193C2×Dic3C2×D411yescharacteristic
194D12—21no—
195D12—21no—
196D12—21no—
197D12—21no—
198C4×D3—81no—
199C4×D3—81no—
200Dic6—81no—
201C3×C8—21no—
202C3×C8#4112yes—
203C3⋊C8—21no—
204C3⋊C8#4112yes—
205C2×Q8—61no—
206C2×Q8C22×D311yescharacteristic
207C2×D4—21no—
208C2×D4—31no—
209C2×D4—31no—
210C2×D4—61no—
211C2×D4—61no—
212C2×D4—61no—
213C2×D4—61no—
214C2×D4C22×D311yescharacteristic
215C22×C4—61no—
216C22×C4—61no—
217C22×C4—61no—
218C22×C4C22×D311yescharacteristic
219SD16—22no—
220SD16—62no—
221D8—62no—
222D8—62no—
223M16—22no—
224C2×C8—31no—
225C2×C8—31no—
226C2×C8—62no—
227C2×C8C22×D311yescharacteristic
228C2×C8C22×D311yescharacteristic
229C4⋊C4—21no—
230C4⋊C4—31no—
231C4⋊C4—31no—
232C4⋊C4—31no—
233C4⋊C4—31no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4C22×D311yescharacteristic
239C4⋊C4C22×D311yescharacteristic
240C22⋊C4—21no—
241C22⋊C4—21no—
242C22⋊C4—31no—
243C22⋊C4—31no—
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4—61no—
247C22⋊C4—61no—
248C22⋊C4—61no—
249C22⋊C4—61no—
250C22⋊C4—61no—
251C42—31no—
252C42—31no—
253C42—61no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—41no—
258C22×C3—41no—
259C22×C3—41no—
260C22×C3C22×D411yescharacteristic
261C2×D3—41no—
262C2×D3—41no—
263C2×D3—41no—
264C2×D3—41no—
265C2×D3—41no—
266C2×D3—41no—
267C3×C4—21no—
268C3×C4—41no—
269C3×C4—41no—
270C3×C4—41no—
271C3×C4C2×#4111yescharacteristic
272C3×C4C2×#4111yescharacteristic
273Dic3—21no—
274Dic3—21no—
275Dic3—21no—
276Dic3—21no—
277Dic3—41no—
278Dic3—41no—
279C23—21no—
280C23—61no—
281C23—61no—
282C23D3×D411yescharacteristic
283Q8—21no—
284Q8—21no—
285Q8—241no—
286D4—21no—
287D4—21no—
288D4—61no—
289D4—61no—
290D4—61no—
291D4—61no—
292D4—81no—
293D4—241no—
294D4—241no—
295D4—241no—
296D4—241no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—31no—
303C2×C4—31no—
304C2×C4—31no—
305C2×C4—31no—
306C2×C4—61no—
307C2×C4—61no—
308C2×C4—241no—
309C2×C4—241no—
310C2×C4—241no—
311C2×C4D3×D411yescharacteristic
312C2×C4C23×D311yescharacteristic
313C8—21no—
314C8—32no—
315C8—61no—
316C8#23712yes—
317C2×C3—41no—
318C2×C3—81no—
319C2×C3#53211yescharacteristic
320C2×C3#57611yescharacteristic
321C2×C3#57711yescharacteristic
322D3—81no—
323D3—81no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—121no—
331C22—121no—
332C22—121no—
333C22—121no—
334C22—121no—
335C22—121no—
336C22C2×D3×D411yescharacteristic
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—61no—
342C4—61no—
343C4—61no—
344C4—61no—
345C4—121no—
346C4—121no—
347C4C2×#23711yescharacteristic
348C4D3×#4111yescharacteristic
349C3#317911yescharacteristic, complemented, Sylow
350C2—41no—
351C2—81no—
352C2—241no—
353C2—241no—
354C2#559611yescharacteristic
355C2#577411yescharacteristic
356C2#577811yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#468C2
socleC22×C3C22×D4
hypercenter#468D3
hypocenterC3#3179
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #5643C2semidirect
2. #5619C2semidirect
3. C3×#468C2semidirect
4. #5176C2semidirect
5. Dic3×SD16C2semidirect
6. #5135C2semidirect
7. #5122C2semidirect
8. #5048C2semidirect
9. #5038C2semidirect
10. #4876C2semidirect
11. #4872C2semidirect
12. #4817C2semidirect
13. #4800C2semidirect
14. #4785C2semidirect
15. #4760C2semidirect
67. #468D3semidirect
349. C3#3179semidirect

Maximal subgroups

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

subgroupindex
#56432
#56192
C3×#4682
#51762
Dic3×SD162
#51352
#51222
#50482
#50382
#48762
#48722
#48172
#48002
#47852
#47602
#31793