Finite Group Databasebeta

← #81389

Subgroups — #81389

Order 384.

364 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5616C211yesmaximal, characteristic, complemented
2#5532C211yesmaximal, characteristic, complemented
3C3×#482C211yesmaximal, characteristic, complemented
4#5038C211yesmaximal, characteristic, complemented
5#4998C211yesmaximal, characteristic, complemented
6#4885C211yesmaximal, characteristic, complemented
7#4874C211yesmaximal, characteristic, complemented
8#4870C211yesmaximal, characteristic, complemented
9#4860C211yesmaximal, characteristic, complemented
10#4784C211yesmaximal, characteristic, complemented
11#4775C211yesmaximal, characteristic, complemented
12#4761C211yesmaximal, characteristic, complemented
13#4756C211yesmaximal, characteristic, complemented
14#4737C211yesmaximal, characteristic, complemented
15#67⋊C8C211yesmaximal, characteristic, complemented
16#3341—31nomaximal, Sylow
17C3×#121C2211yescharacteristic
18C3×#117C2211yescharacteristic
19#939—21no—
20#938C2211yescharacteristic
21#936—21no—
22D4×Dic3C2211yescharacteristic
23C2×#213C2211yescharacteristic
24#930C2211yescharacteristic
25C4×#67C2211yescharacteristic
26#926C2211yescharacteristic
27C22×C3⋊C8C2211yescharacteristic
28C2×D3×C8C2211yescharacteristic
29#895C2211yescharacteristic
30#893C2211yescharacteristic
31#892C2211yescharacteristic
32#892C2211yescharacteristic
33#888C2211yescharacteristic
34#888C2211yescharacteristic
35#885—21no—
36#885—21no—
37#884—21no—
38#877—21no—
39#875—21no—
40#872—21no—
41C3×#107C2211yescharacteristic
42C3×#106C2211yescharacteristic
43C3×#102C2211yescharacteristic
44C3×#102C2211yescharacteristic
45C3×C22⋊C8C2211yescharacteristic
46#832C2211yescharacteristic
47#821C2211yescharacteristic
48#821C2211yescharacteristic
49(C2×D3)⋊C8C2211yescharacteristic
50#818C2211yescharacteristic
51#817C2211yescharacteristic
52Dic3⋊C8C2211yescharacteristic
53C8×Dic3C2211yescharacteristic
54#809C2211yescharacteristic
55#808C2211yescharacteristic
56#808C2211yescharacteristic
57#807C2211yescharacteristic
58#807C2211yescharacteristic
59#807C2211yescharacteristic
60#555—31no—
61#555—31no—
62#500—31no—
63#482—31no—
64#482—31no—
65#482—31no—
66#482D311yescharacteristic, complemented
67#476—31no—
68#476—31no—
69#466—31no—
70#466—31no—
71C4×D8—31no—
72C8×D4—31no—
73#427—31no—
74#427—31no—
75C2×C3×D4—21no—
76C2×C3×D4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C2×#67—21no—
79C2×#67—21no—
80C2×#67D411yescharacteristic
81C22×Dic3—21no—
82C2×D12—21no—
83C2×D12C2311yescharacteristic
84C2×C4×D3—21no—
85C2×C4×D3C2311yescharacteristic
86C2×Dic6—21no—
87C2×Dic6—21no—
88C2×C3×C8C2311yescharacteristic
89C2×C3×C8C2311yescharacteristic
90C3×C4⋊C4C2311yescharacteristic
91C3×C4⋊C4C2311yescharacteristic
92C3×C4⋊C4C2311yescharacteristic
93C3×C22⋊C4—21no—
94C3×C22⋊C4—21no—
95C3×C42—21no—
96#217—21no—
97#217—21no—
98#217—21no—
99#217D411yescharacteristic
100#213—22no—
101(C2×D3)⋊C4—21no—
102(C2×D3)⋊C4—21no—
103(C2×D3)⋊C4—21no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4D411yescharacteristic
107C4⋊Dic3C2311yescharacteristic
108C4⋊Dic3C2311yescharacteristic
109C4⋊Dic3C2311yescharacteristic
110Dic3⋊C4—21no—
111Dic3⋊C4—21no—
112Dic3⋊C4D411yescharacteristic
113C4×Dic3—21no—
114C4×Dic3—21no—
115C4×Dic3—21no—
116C4×Dic3C2311yescharacteristic
117C2×C3⋊C8—22no—
118C2×C3⋊C8C2311yescharacteristic
119C2×C3⋊C8C2311yescharacteristic
120D3×C8—22no—
121C2×D8—31no—
122C22×C8—31no—
123C22×C8—31no—
124C4⋊Q8—31no—
125C4⋊Q8—31no—
126#124—61no—
127#124—61no—
128#124—61no—
129#124—61no—
130#121—31no—
131#121—31no—
132#121—31no—
133#121—61no—
134#121—61no—
135#121C2×D311yescharacteristic
136C4×D4—31no—
137C4×D4—31no—
138C4×D4—31no—
139#117—31no—
140#117—31no—
141#117—31no—
142#117—61no—
143#117—61no—
144#117C2×D311yescharacteristic
145#107—31no—
146#107—31no—
147#107—31no—
148#107—31no—
149#107C2×D311yescharacteristic
150#106—31no—
151#106—31no—
152#106—31no—
153#106C2×D311yescharacteristic
154C4⋊C8—31no—
155#102—31no—
156#102—31no—
157#102—31no—
158#102—31no—
159#102C2×D311yescharacteristic
160#102C2×D311yescharacteristic
161C22⋊C8—31no—
162C22⋊C8C2×D311yescharacteristic
163C4×C8—31no—
164C23×C3—21no—
165C23×C3C2×D411yescharacteristic
166C22×D3—21no—
167C22×D3C2×D411yescharacteristic
168C3×D4—21no—
169C3×D4—21no—
170C3×D4—81no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4C2×D411yescharacteristic
177C2×C3×C4C2411yescharacteristic
178#67—22no—
179#67—81no—
180#67—81no—
181C2×Dic3—21no—
182C2×Dic3—21no—
183C2×Dic3—21no—
184C2×Dic3—42no—
185C2×Dic3C2×D411yescharacteristic
186C2×Dic3C2×D411yescharacteristic
187C2×Dic3C2×D411yescharacteristic
188D12—21no—
189D12—21no—
190D12—81no—
191C4×D3—21no—
192C4×D3—21no—
193C4×D3—42no—
194Dic6—81no—
195Dic6—81no—
196C3×C8—21no—
197C3×C8—21no—
198C3⋊C8—21no—
199C3⋊C8#4112yes—
200C2×Q8—61no—
201C2×Q8—61no—
202C2×D4—21no—
203C2×D4—31no—
204C2×D4—31no—
205C2×D4—61no—
206C2×D4—61no—
207C2×D4—61no—
208C2×D4C22×D311yescharacteristic
209C22×C4—31no—
210C22×C4—61no—
211C22×C4—61no—
212C22×C4C22×D311yescharacteristic
213D8—62no—
214C2×C8—31no—
215C2×C8—31no—
216C2×C8—62no—
217C2×C8—62no—
218C2×C8C22×D311yescharacteristic
219C2×C8C22×D311yescharacteristic
220C4⋊C4—31no—
221C4⋊C4—31no—
222C4⋊C4—31no—
223C4⋊C4—31no—
224C4⋊C4—61no—
225C4⋊C4—61no—
226C4⋊C4C22×D311yescharacteristic
227C4⋊C4C22×D311yescharacteristic
228C4⋊C4C22×D311yescharacteristic
229C22⋊C4—21no—
230C22⋊C4—21no—
231C22⋊C4—31no—
232C22⋊C4—31no—
233C22⋊C4—61no—
234C22⋊C4—61no—
235C22⋊C4—61no—
236C22⋊C4—61no—
237C22⋊C4—61no—
238C22⋊C4—61no—
239C22⋊C4—61no—
240C22⋊C4—61no—
241C42—21no—
242C42—31no—
243C42—61no—
244C42—61no—
245C42—61no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—41no—
250C22×C3—41no—
251C22×C3—41no—
252C22×C3C22×D411yescharacteristic
253C2×D3—21no—
254C2×D3—21no—
255C2×D3—21no—
256C2×D3—41no—
257C2×D3—41no—
258C2×D3—41no—
259C3×C4—21no—
260C3×C4—41no—
261C3×C4—41no—
262C3×C4—41no—
263C3×C4C2×#4111yescharacteristic
264C3×C42−1+411yescharacteristic
265Dic3—21no—
266Dic3—21no—
267Dic3—41no—
268Dic3—41no—
269Dic3—41no—
270Dic3#13512yes—
271C23—21no—
272C23—31no—
273C23—61no—
274C23D3×D411yescharacteristic
275Q8—241no—
276Q8—241no—
277D4—21no—
278D4—21no—
279D4—62no—
280D4—61no—
281D4—61no—
282D4—81no—
283D4—241no—
284D4—241no—
285D4—241no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—31no—
292C2×C4—31no—
293C2×C4—31no—
294C2×C4—61no—
295C2×C4—61no—
296C2×C4—61no—
297C2×C4—61no—
298C2×C4—61no—
299C2×C4—122no—
300C2×C4—122no—
301C2×C4D3×D411yescharacteristic
302C2×C4C23×D311yescharacteristic
303C8—21no—
304C8—21no—
305C8—32no—
306C8—61no—
307C2×C3—41no—
308C2×C3—81no—
309C2×C3#54711yescharacteristic
310C2×C3C2×#13511yescharacteristic
311C2×C3#57611yescharacteristic
312D3—41no—
313D3—81no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—61no—
321C22—61no—
322C22—61no—
323C22—121no—
324C22—121no—
325C22—121no—
326C22C2×D3×D411yescharacteristic
327C4—21no—
328C4—32no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—61no—
333C4—61no—
334C4—121no—
335C4—121no—
336C4—121no—
337C4D3×#4111yescharacteristic
338C4#101011yescharacteristic
339C3#334111yescharacteristic, complemented, Sylow
340C2—41no—
341C2—81no—
342C2—121no—
343C2—241no—
344C2#565511yescharacteristic
345C2D3×#13511yescharacteristic
346C2#577411yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#482C2
socleC22×C3C22×D4
hypercenter#482D3
hypocenterC3#3341
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #5616C2semidirect
2. #5532C2semidirect
3. C3×#482C2semidirect
4. #5038C2semidirect
5. #4998C2semidirect
6. #4885C2semidirect
7. #4874C2semidirect
8. #4870C2semidirect
9. #4860C2semidirect
10. #4784C2semidirect
11. #4775C2semidirect
12. #4761C2semidirect
13. #4756C2semidirect
14. #4737C2semidirect
15. #67⋊C8C2semidirect
66. #482D3semidirect
339. C3#3341semidirect

Maximal subgroups

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

subgroupindex
#56162
#55322
C3×#4822
#50382
#49982
#48852
#48742
#48702
#48602
#47842
#47752
#47612
#47562
#47372
#67⋊C82
#33413