Finite Group Databasebeta

← #81312

Subgroups — #81312

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#5619C211yesmaximal, characteristic, complemented
2#5504C211yesmaximal, characteristic, complemented
3C3×#481C211yesmaximal, characteristic, complemented
4#5037C211yesmaximal, characteristic, complemented
5#4967C211yesmaximal, characteristic, complemented
6#4871C211yesmaximal, characteristic, complemented
7#4869C211yesmaximal, characteristic, complemented
8#4857C211yesmaximal, characteristic, complemented
9#4852C211yesmaximal, characteristic, complemented
10#4786C211yesmaximal, characteristic, complemented
11#4762C211yesmaximal, characteristic, complemented
12#4757C211yesmaximal, characteristic, complemented
13#4756C211yesmaximal, characteristic, complemented
14#4734C211yesmaximal, characteristic, complemented
15#4720C211yesmaximal, characteristic, complemented
16#3119—31nomaximal, Sylow
17C2×#235C2211yescharacteristic
18C3×#121C2211yescharacteristic
19C2×C3×C4⋊C4C2211yescharacteristic
20#940C2211yescharacteristic
21#939—21no—
22#938—21no—
23D4×Dic3C2211yescharacteristic
24C2×#214C2211yescharacteristic
25C2×#213C2211yescharacteristic
26#930C2211yescharacteristic
27C4×#67—21no—
28C4×#67—21no—
29#926C2211yescharacteristic
30C2×D24C2211yescharacteristic
31C2×#204C2211yescharacteristic
32#893C2211yescharacteristic
33#893C2211yescharacteristic
34#893C2211yescharacteristic
35#892—21no—
36D3×C4⋊C4—21no—
37#890C2211yescharacteristic
38#887C2211yescharacteristic
39#887C2211yescharacteristic
40#886—21no—
41#883—21no—
42C3×#106C2211yescharacteristic
43C3×#106C2211yescharacteristic
44C3×#102C2211yescharacteristic
45C3×#102C2211yescharacteristic
46C3×C22⋊C8C2211yescharacteristic
47#830C2211yescharacteristic
48#821C2211yescharacteristic
49#816C2211yescharacteristic
50#815C2211yescharacteristic
51Dic3⋊C8C2211yescharacteristic
52Dic3⋊C8C2211yescharacteristic
53C8×Dic3C2211yescharacteristic
54#810C2211yescharacteristic
55#809C2211yescharacteristic
56#809C2211yescharacteristic
57#809C2211yescharacteristic
58#807C2211yescharacteristic
59#807C2211yescharacteristic
60#540—31no—
61#520—31no—
62#481D311yescharacteristic, complemented
63#480—31no—
64#479—31no—
65#478—31no—
66#460—31no—
67#459—31no—
68#449—31no—
69#449—31no—
70#442—31no—
71#440—31no—
72C4×SD16—31no—
73C4×D8—31no—
74#433—31no—
75C2×C3×D4—21no—
76C2×C3×D4C2311yescharacteristic
77C22×C3×C4—21no—
78C22×C3×C4C2311yescharacteristic
79C2×#67—21no—
80C2×#67—21no—
81C2×#67—21no—
82C2×#67—21no—
83C22×Dic3—21no—
84#235—22no—
85#235—22no—
86C2×D12C2311yescharacteristic
87C2×D12C2311yescharacteristic
88C2×C4×D3—21no—
89C2×C4×D3—21no—
90C2×C4×D3—21no—
91C2×C4×D3—21no—
92C2×Dic6C2311yescharacteristic
93C2×C3×C8C2311yescharacteristic
94C2×C3×C8C2311yescharacteristic
95C3×C4⋊C4—21no—
96C3×C4⋊C4C2311yescharacteristic
97C3×C4⋊C4C2311yescharacteristic
98C3×C4⋊C4C2311yescharacteristic
99C3×C22⋊C4—21no—
100#217—21no—
101#217D411yescharacteristic
102#217D411yescharacteristic
103#214—22no—
104#213—22no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109C4⋊Dic3—21no—
110C4⋊Dic3D411yescharacteristic
111C4⋊Dic3D411yescharacteristic
112C4⋊Dic3C2311yescharacteristic
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115Dic3⋊C4—21no—
116C4×Dic3—21no—
117C4×Dic3—21no—
118C4×Dic3C2311yescharacteristic
119C4×Dic3C2311yescharacteristic
120C2×C3⋊C8C2311yescharacteristic
121C2×C3⋊C8C2311yescharacteristic
122D24—22no—
123#204—22no—
124C2×#41—31no—
125C2×SD16—31no—
126C2×SD16—31no—
127C2×D8—31no—
128C2×D8—31no—
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—61no—
148C2×C4⋊C4C2×D311yescharacteristic
149#107—31no—
150#107—31no—
151#106C2×D311yescharacteristic
152#106C2×D311yescharacteristic
153C4⋊C8—31no—
154C4⋊C8—31no—
155#103—31no—
156#103—31no—
157#102—31no—
158#102—31no—
159#102—31no—
160#102—31no—
161#102C2×D311yescharacteristic
162#102C2×D311yescharacteristic
163C22⋊C8—31no—
164C22⋊C8C2×D311yescharacteristic
165#97—31no—
166C4×C8—31no—
167C23×C3—21no—
168C23×C3C2×D411yescharacteristic
169C22×D3—21no—
170C22×D3—21no—
171C3×D4—21no—
172C3×D4—21no—
173C3×D4—81no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—81no—
180C2×C3×C4C2×D411yescharacteristic
181C2×C3×C4C2411yescharacteristic
182#67—24no—
183#67—81no—
184#67—81no—
185#67—81no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—81no—
189C2×Dic3C2×D411yescharacteristic
190C2×Dic3C2×D411yescharacteristic
191C2×Dic3C2×D411yescharacteristic
192C2×Dic3C2×D411yescharacteristic
193D12—21no—
194D12—21no—
195D12—21no—
196D12#4112yes—
197C4×D3—24no—
198C4×D3—81no—
199C4×D3—81no—
200C4×D3—81no—
201Dic6—21no—
202Dic6#4112yes—
203C3×C8—21no—
204C3×C8—21no—
205C3⋊C8—21no—
206C3⋊C8—21no—
207#41—62no—
208#41—62no—
209C2×Q8—31no—
210C2×D4—21no—
211C2×D4—31no—
212C2×D4—31no—
213C2×D4—61no—
214C2×D4—61no—
215C2×D4—61no—
216C2×D4—61no—
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—62no—
226SD16—62no—
227D8—62no—
228D8—62no—
229C2×C8—31no—
230C2×C8—31no—
231C2×C8C22×D311yescharacteristic
232C2×C8C22×D311yescharacteristic
233C4⋊C4—21no—
234C4⋊C4—31no—
235C4⋊C4—31no—
236C4⋊C4—31no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4—61no—
241C4⋊C4C22×D311yescharacteristic
242C4⋊C4C22×D311yescharacteristic
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—21no—
258C22×C3—21no—
259C22×C3—41no—
260C22×C3—41no—
261C22×C3—41no—
262C22×C3C22×D411yescharacteristic
263C2×D3—22no—
264C2×D3—41no—
265C2×D3—41no—
266C2×D3—41no—
267C2×D3—41no—
268C2×D3—41no—
269C3×C4—21no—
270C3×C4—41no—
271C3×C4—41no—
272C3×C4—41no—
273C3×C4C2×#4111yescharacteristic
274C3×C4C2×#4111yescharacteristic
275Dic3—22no—
276Dic3—21no—
277Dic3—21no—
278Dic3—21no—
279Dic3—21no—
280Dic3—41no—
281C23—21no—
282C23—61no—
283C23—61no—
284C23D3×D411yescharacteristic
285Q8—32no—
286Q8—61no—
287D4—21no—
288D4—21no—
289D4—32no—
290D4—64no—
291D4—61no—
292D4—61no—
293D4—61no—
294D4—81no—
295D4—241no—
296D4—241no—
297D4—241no—
298C2×C4—21no—
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—64no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—81no—
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—81no—
323C2×C3#52511yescharacteristic
324C2×C3#57611yescharacteristic
325C2×C3#57711yescharacteristic
326D3—42no—
327D3—81no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—62no—
335C22—121no—
336C22—121no—
337C22—121no—
338C22—121no—
339C22—121no—
340C22C2×D3×D411yescharacteristic
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—62no—
346C4—61no—
347C4—61no—
348C4—61no—
349C4—61no—
350C4—121no—
351C4D3×#4111yescharacteristic
352C4D3×#4111yescharacteristic
353C3#311911yescharacteristic, complemented, Sylow
354C2—41no—
355C2—81no—
356C2—122no—
357C2—241no—
358C2#565611yescharacteristic
359C2#576211yescharacteristic
360C2#577411yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#481C2
socleC22×C3C22×D4
hypercenter#481D3
hypocenterC3#3119
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #5619C2semidirect
2. #5504C2semidirect
3. C3×#481C2semidirect
4. #5037C2semidirect
5. #4967C2semidirect
6. #4871C2semidirect
7. #4869C2semidirect
8. #4857C2semidirect
9. #4852C2semidirect
10. #4786C2semidirect
11. #4762C2semidirect
12. #4757C2semidirect
13. #4756C2semidirect
14. #4734C2semidirect
15. #4720C2semidirect
62. #481D3semidirect
353. C3#3119semidirect

Maximal subgroups

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

subgroupindex
#56192
#55042
C3×#4812
#50372
#49672
#48712
#48692
#48572
#48522
#47862
#47622
#47572
#47562
#47342
#47202
#31193