Finite Group Databasebeta

← #80073

Subgroups — #80073

Order 384.

396 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#5827C211yesmaximal, characteristic, complemented
2#5619C211yesmaximal, characteristic, complemented
3C3×#449C211yesmaximal, characteristic, complemented
4#5238C211yesmaximal, characteristic, complemented
5#5163C211yesmaximal, characteristic, complemented
6Dic3×SD16C211yesmaximal, characteristic, complemented
7#5152C211yesmaximal, characteristic, complemented
8#5150C211yesmaximal, characteristic, complemented
9#5033C211yesmaximal, characteristic, complemented
10#4817C211yesmaximal, characteristic, complemented
11#4799C211yesmaximal, characteristic, complemented
12#4763C211yesmaximal, characteristic, complemented
13#4756C211yesmaximal, characteristic, complemented
14#4735C211yesmaximal, characteristic, complemented
15#4720C211yesmaximal, characteristic, complemented
16#3119—31nomaximal, Sylow
17C2×C3×#41C2211yescharacteristic
18C2×C3×SD16C2211yescharacteristic
19C2×C3×D8C2211yescharacteristic
20C3×#121C2211yescharacteristic
21Q8×Dic3C2211yescharacteristic
22Q8×Dic3C2211yescharacteristic
23C2×#215C2211yescharacteristic
24#940C2211yescharacteristic
25#939—21no—
26#938—21no—
27D4×Dic3—21no—
28D4×Dic3—21no—
29D4×Dic3C2211yescharacteristic
30D4×Dic3C2211yescharacteristic
31D4×Dic3C2211yescharacteristic
32C2×#213C2211yescharacteristic
33#930C2211yescharacteristic
34#926—21no—
35#926C2211yescharacteristic
36C2×C4⋊Dic3—21no—
37C2×C4⋊Dic3C2211yescharacteristic
38#893C2211yescharacteristic
39#890C2211yescharacteristic
40#886—21no—
41#883—21no—
42C3×#103C2211yescharacteristic
43C3×#102C2211yescharacteristic
44C3×C22⋊C8C2211yescharacteristic
45#835C2211yescharacteristic
46#832C2211yescharacteristic
47#832C2211yescharacteristic
48#832C2211yescharacteristic
49#830C2211yescharacteristic
50#821C2211yescharacteristic
51#821C2211yescharacteristic
52#817C2211yescharacteristic
53#817C2211yescharacteristic
54#815C2211yescharacteristic
55Dic3⋊C8C2211yescharacteristic
56Dic3⋊C8C2211yescharacteristic
57C8×Dic3C2211yescharacteristic
58#807C2211yescharacteristic
59#807C2211yescharacteristic
60#540—31no—
61#520—31no—
62#481—31no—
63#480—31no—
64#479—31no—
65#478—31no—
66#460—31no—
67#459—31no—
68#449—31no—
69#449D311yescharacteristic, complemented
70#442—31no—
71#440—31no—
72C4×SD16—31no—
73C4×D8—31no—
74#433—31no—
75C3×#41—22no—
76C3×#41—22no—
77C2×C3×Q8C2311yescharacteristic
78C2×C3×D4—21no—
79C2×C3×D4—21no—
80C2×C3×D4C2311yescharacteristic
81C2×C3×D4C2311yescharacteristic
82C22×C3×C4—21no—
83C22×C3×C4C2311yescharacteristic
84C2×#67—21no—
85C2×#67—21no—
86C2×#67—21no—
87C22×Dic3—21no—
88C22×Dic3—21no—
89C22×Dic3—21no—
90C22×Dic3—21no—
91C2×D12C2311yescharacteristic
92C2×C4×D3—21no—
93C3×SD16—22no—
94C3×D8—22no—
95C2×C3×C8C2311yescharacteristic
96C2×C3×C8C2311yescharacteristic
97C3×C4⋊C4C2311yescharacteristic
98C3×C22⋊C4—21no—
99#217—21no—
100#217—21no—
101#217—21no—
102#217D411yescharacteristic
103#217D411yescharacteristic
104#215—22no—
105#213—22no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4—21no—
108C4⋊Dic3—21no—
109C4⋊Dic3—21no—
110C4⋊Dic3—21no—
111C4⋊Dic3—21no—
112C4⋊Dic3D411yescharacteristic
113C4⋊Dic3D411yescharacteristic
114C4⋊Dic3C2311yescharacteristic
115C4⋊Dic3C2311yescharacteristic
116C4⋊Dic3C2311yescharacteristic
117Dic3⋊C4—21no—
118C4×Dic3—21no—
119C4×Dic3—21no—
120C4×Dic3C2311yescharacteristic
121C4×Dic3C2311yescharacteristic
122C2×C3⋊C8C2311yescharacteristic
123C2×C3⋊C8C2311yescharacteristic
124C2×#41C2×D311yescharacteristic
125C2×SD16—31no—
126C2×SD16C2×D311yescharacteristic
127C2×D8—31no—
128C2×D8C2×D311yescharacteristic
129#127—31no—
130#125—31no—
131#123—61no—
132#123—61no—
133#121—31no—
134#121—61no—
135#121—61no—
136#121C2×D311yescharacteristic
137C4×Q8—31no—
138C4×Q8—31no—
139C4×D4—31no—
140C4×D4—31no—
141C4×D4—31no—
142C4×D4—31no—
143C4×D4—61no—
144C4×D4—61no—
145#117—31no—
146#117—61no—
147C2×C4⋊C4—31no—
148C2×C4⋊C4—61no—
149#107—31no—
150#107—31no—
151#106—31no—
152#106—31no—
153C4⋊C8—31no—
154C4⋊C8—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
163C22⋊C8—31no—
164C22⋊C8C2×D311yescharacteristic
165#97—31no—
166C4×C8—31no—
167C23×C3—21no—
168C23×C3—21no—
169C23×C3C2×D411yescharacteristic
170C22×D3—21no—
171C3×Q8—21no—
172C3×Q8#4112yes—
173C3×D4—24no—
174C3×D4—21no—
175C3×D4—21no—
176C3×D4—21no—
177C3×D4—81no—
178C3×D4#4112yes—
179C2×C3×C4—24no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4C2×D411yescharacteristic
185C2×C3×C4C2411yescharacteristic
186#67—81no—
187#67—81no—
188#67—81no—
189C2×Dic3—21no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—81no—
193C2×Dic3—81no—
194C2×Dic3—81no—
195C2×Dic3—81no—
196C2×Dic3C2×D411yescharacteristic
197C2×Dic3C2×D411yescharacteristic
198C2×Dic3C2×D411yescharacteristic
199C2×Dic3C2×D411yescharacteristic
200D12—21no—
201D12—21no—
202C4×D3—81no—
203C3×C8—21no—
204C3×C8—21no—
205C3⋊C8—21no—
206C3⋊C8—21no—
207#41—22no—
208#41—22no—
209C2×Q8C22×D311yescharacteristic
210C2×D4—21no—
211C2×D4—21no—
212C2×D4—31no—
213C2×D4—61no—
214C2×D4—61no—
215C2×D4—61no—
216C2×D4C22×D311yescharacteristic
217C2×D4C22×D311yescharacteristic
218C22×C4—21no—
219C22×C4—61no—
220C22×C4—61no—
221C22×C4—61no—
222C22×C4—61no—
223C22×C4—61no—
224C22×C4C22×D311yescharacteristic
225SD16—22no—
226SD16—62no—
227D8—22no—
228D8—62no—
229C2×C8—31no—
230C2×C8—31no—
231C2×C8C22×D311yescharacteristic
232C2×C8C22×D311yescharacteristic
233C4⋊C4—31no—
234C4⋊C4—31no—
235C4⋊C4—31no—
236C4⋊C4—31no—
237C4⋊C4—31no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4—61no—
241C4⋊C4—61no—
242C4⋊C4—61no—
243C4⋊C4C22×D311yescharacteristic
244C22⋊C4—21no—
245C22⋊C4—31no—
246C22⋊C4—31no—
247C22⋊C4—61no—
248C22⋊C4—61no—
249C22⋊C4—61no—
250C22⋊C4—61no—
251C22⋊C4—61no—
252C42—31no—
253C42—31no—
254C42—61no—
255C42—61no—
256C22×C3—21no—
257C22×C3—22no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—41no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3C22×D411yescharacteristic
266C2×D3—41no—
267C2×D3—41no—
268C2×D3—41no—
269C3×C4—21no—
270C3×C4—22no—
271C3×C4—41no—
272C3×C4C2×#4111yescharacteristic
273C3×C4C2×#4111yescharacteristic
274Dic3—21no—
275Dic3—21no—
276Dic3—21no—
277Dic3—21no—
278Dic3—41no—
279Dic3—41no—
280Dic3—41no—
281C23—21no—
282C23—21no—
283C23—61no—
284C23D3×D411yescharacteristic
285Q8—21no—
286Q8#23712yes—
287D4—24no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—61no—
292D4—61no—
293D4—81no—
294D4—241no—
295D4—241no—
296D4—241no—
297D4#23712yes—
298C2×C4—24no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—31no—
304C2×C4—31no—
305C2×C4—31no—
306C2×C4—31no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—241no—
311C2×C4—241no—
312C2×C4—241no—
313C2×C4—241no—
314C2×C4—241no—
315C2×C4D3×D411yescharacteristic
316C2×C4C23×D311yescharacteristic
317C8—21no—
318C8—21no—
319C8—61no—
320C8—61no—
321C2×C3—41no—
322C2×C3—42no—
323C2×C3—81no—
324C2×C3#52511yescharacteristic
325C2×C3#57611yescharacteristic
326C2×C3#57711yescharacteristic
327D3—81no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—121no—
338C22—121no—
339C22—121no—
340C22C2×D3×D411yescharacteristic
341C4—21no—
342C4—22no—
343C4—41no—
344C4—61no—
345C4—61no—
346C4—61no—
347C4—61no—
348C4—121no—
349C4—121no—
350C4—121no—
351C4C2×#23711yescharacteristic
352C4C2×#23711yescharacteristic
353C3#311911yescharacteristic, complemented, Sylow
354C2—41no—
355C2—42no—
356C2—81no—
357C2—241no—
358C2#558611yescharacteristic
359C2#577011yescharacteristic
360C2#577411yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#449C2
socleC22×C3C22×D4
hypercenter#449D3
hypocenterC3#3119
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #5827C2semidirect
2. #5619C2semidirect
3. C3×#449C2semidirect
4. #5238C2semidirect
5. #5163C2semidirect
6. Dic3×SD16C2semidirect
7. #5152C2semidirect
8. #5150C2semidirect
9. #5033C2semidirect
10. #4817C2semidirect
11. #4799C2semidirect
12. #4763C2semidirect
13. #4756C2semidirect
14. #4735C2semidirect
15. #4720C2semidirect
69. #449D3semidirect
353. C3#3119semidirect

Maximal subgroups

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

subgroupindex
#58272
#56192
C3×#4492
#52382
#51632
Dic3×SD162
#51522
#51502
#50332
#48172
#47992
#47632
#47562
#47352
#47202
#31193