Finite Group Databasebeta

← #81490

Subgroups — #81490

Order 384.

388 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
1#5632C211yesmaximal, characteristic
2#5511C211yesmaximal, characteristic
3C3×#484C211yesmaximal, characteristic, complemented
4#5051C211yesmaximal, characteristic, complemented
5C2×#810C211yesmaximal, characteristic, complemented
6#4887C211yesmaximal, characteristic, complemented
7#4884C211yesmaximal, characteristic, complemented
8#4875C211yesmaximal, characteristic, complemented
9#4873C211yesmaximal, characteristic, complemented
10#4809C211yesmaximal, characteristic, complemented
11D3×#103C211yesmaximal, characteristic, complemented
12#4795C211yesmaximal, characteristic, complemented
13#4792C211yesmaximal, characteristic, complemented
14#4739C211yesmaximal, characteristic, complemented
15#67⋊C8C211yesmaximal, characteristic
16#3299—31nomaximal, Sylow
17C2×D3×Q8C2211yescharacteristic
18C22×Dic6C2211yescharacteristic
19C3×C22⋊Q8C2211yescharacteristic
20C2×C3×C4⋊C4C2211yescharacteristic
21#944C2211yescharacteristic
22C2×#216C2211yescharacteristic
23C4×#67—21no—
24C4×#67C2211yescharacteristic
25#924—21no—
26#924C2211yescharacteristic
27C22×C3⋊C8C2211yescharacteristic
28C2×Dic12C2211yescharacteristic
29C2×Dic12C2211yescharacteristic
30C2×D3×C8C2211yescharacteristic
31#897C2211yescharacteristic
32#897C2211yescharacteristic
33#896—21no—
34#896—21no—
35D3×C4⋊C4C2211yescharacteristic
36#889—21no—
37#888—21no—
38#888C2211yescharacteristic
39#887C2211yescharacteristic
40#887C2211yescharacteristic
41#67⋊C4—21no—
42#878—21no—
43C3×#107C2211yescharacteristic
44C3×#107C2211yescharacteristic
45C3×#103C2211yescharacteristic
46C3×#103C2211yescharacteristic
47C3×C22⋊C8C2211yescharacteristic
48#835C2211yescharacteristic
49(C2×D3)⋊C8C2211yescharacteristic
50#816C2211yescharacteristic
51#816C2211yescharacteristic
52Dic3⋊C8C2211yescharacteristic
53C8×Dic3C2211yescharacteristic
54#810C2211yescharacteristic
55#810C2211yescharacteristic
56#810C2211yescharacteristic
57#810C2211yescharacteristic
58#810C2211yescharacteristic
59#807C2211yescharacteristic
60#554—31no—
61D4×Q8—31no—
62#487—31no—
63#484—31no—
64#484D311yescharacteristic, complemented
65#477—31no—
66#467—31no—
67#467—31no—
68#462—31no—
69#451—31no—
70#451—31no—
71C4×Q16—31no—
72C8×D4—31no—
73C2×#103—31no—
74C2×#103—31no—
75C2×C3×Q8C2311yescharacteristic
76C22×C3×C4—21no—
77C22×C3×C4C2311yescharacteristic
78C2×#67D411yescharacteristic
79C22×Dic3—21no—
80D3×Q8—22no—
81D3×Q8—41no—
82C2×C4×D3—21no—
83C2×C4×D3—21no—
84C2×C4×D3C2311yescharacteristic
85C2×Dic6—22no—
86C2×Dic6—21no—
87C2×Dic6—21no—
88C2×Dic6—21no—
89C2×Dic6—41no—
90C2×Dic6C2311yescharacteristic
91C2×Dic6C2311yescharacteristic
92C2×Dic6C2311yescharacteristic
93C2×C3×C8C2311yescharacteristic
94C2×C3×C8C2311yescharacteristic
95C3×C4⋊C4—21no—
96C3×C4⋊C4—21no—
97C3×C4⋊C4C2311yescharacteristic
98C3×C4⋊C4C2311yescharacteristic
99C3×C4⋊C4C2311yescharacteristic
100C3×C22⋊C4—21no—
101#217—21no—
102#217D411yescharacteristic
103#216—41no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4D411yescharacteristic
107C4⋊Dic3—21no—
108C4⋊Dic3—21no—
109C4⋊Dic3C2311yescharacteristic
110Dic3⋊C4—21no—
111Dic3⋊C4—21no—
112Dic3⋊C4—21no—
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115Dic3⋊C4—21no—
116Dic3⋊C4—21no—
117Dic3⋊C4D411yescharacteristic
118C4×Dic3—21no—
119C4×Dic3—21no—
120C4×Dic3C2311yescharacteristic
121C2×C3⋊C8—41no—
122C2×C3⋊C8C2311yescharacteristic
123C2×C3⋊C8C2311yescharacteristic
124Dic12—22no—
125Dic12—41no—
126D3×C8—41no—
127C22×Q8—31no—
128C22×Q8—31no—
129C2×Q16—31no—
130C2×Q16—31no—
131C2×Q16—31no—
132C22×C8—31no—
133C22×C8—31no—
134C4⋊Q8—31no—
135C4⋊Q8—31no—
136C4⋊Q8—61no—
137#125—61no—
138C22⋊Q8—31no—
139C22⋊Q8—31no—
140C22⋊Q8—31no—
141C22⋊Q8—61no—
142C22⋊Q8—61no—
143C22⋊Q8—61no—
144C22⋊Q8—61no—
145C22⋊Q8C2×D311yescharacteristic
146C4×Q8—31no—
147C4×Q8—31no—
148C4×D4—31no—
149C4×D4—61no—
150C4×D4—61no—
151C2×C4⋊C4—31no—
152C2×C4⋊C4C2×D311yescharacteristic
153#107—31no—
154#107C2×D311yescharacteristic
155#107C2×D311yescharacteristic
156C4⋊C8—31no—
157#103—31no—
158#103—31no—
159#103—31no—
160#103—31no—
161#103—31no—
162#103—31no—
163#103—31no—
164#103—31no—
165#103C2×D311yescharacteristic
166#103C2×D311yescharacteristic
167C22⋊C8—31no—
168C22⋊C8C2×D311yescharacteristic
169C4×C8—31no—
170C23×C3C2×D411yescharacteristic
171C22×D3C2×D411yescharacteristic
172C3×Q8—21no—
173C3×Q8—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—81no—
181C2×C3×C4C2×D411yescharacteristic
182C2×C3×C4C2411yescharacteristic
183#67Q1614yescomplemented
184C2×Dic3—21no—
185C2×Dic3—21no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—42no—
189C2×Dic3C2×D411yescharacteristic
190C2×Dic3C2×D411yescharacteristic
191C2×Dic3C2×D411yescharacteristic
192C4×D3—21no—
193C4×D3—21no—
194C4×D3—42no—
195C4×D3—81no—
196Dic6—21no—
197Dic6—21no—
198Dic6—21no—
199Dic6—21no—
200Dic6—21no—
201Dic6—42no—
202Dic6—42no—
203Dic6—81no—
204Dic6#4112yes—
205C3×C8—21no—
206C3×C8—21no—
207C3⋊C8—21no—
208C3⋊C8—21no—
209C2×Q8—31no—
210C2×Q8—31no—
211C2×Q8—31no—
212C2×Q8—61no—
213C2×Q8—61no—
214C2×Q8—62no—
215C2×Q8—61no—
216C2×Q8—62no—
217C2×Q8—121no—
218C2×Q8—121no—
219C2×Q8C22×D311yescharacteristic
220C2×D4—31no—
221C22×C4—21no—
222C22×C4—31no—
223C22×C4—61no—
224C22×C4—61no—
225C22×C4—61no—
226C22×C4C22×D311yescharacteristic
227Q16—62no—
228Q16—121no—
229Q16—121no—
230C2×C8—31no—
231C2×C8—31no—
232C2×C8—121no—
233C2×C8—121no—
234C2×C8C22×D311yescharacteristic
235C2×C8C22×D311yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—31no—
239C4⋊C4—31no—
240C4⋊C4—61no—
241C4⋊C4—61no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4—61no—
248C4⋊C4—61no—
249C4⋊C4C22×D311yescharacteristic
250C4⋊C4C22×D311yescharacteristic
251C4⋊C4C22×D311yescharacteristic
252C22⋊C4—21no—
253C22⋊C4—31no—
254C22⋊C4—31no—
255C22⋊C4—61no—
256C22⋊C4—61no—
257C22⋊C4—61no—
258C42—31no—
259C42—61no—
260C42—61no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3C2×Q1612yes—
264C22×C3C22×D411yescharacteristic
265C2×D3—21no—
266C2×D3—21no—
267C2×D3C2×Q1612yes—
268C3×C4—21no—
269C3×C4—41no—
270C3×C4—41no—
271C3×C4—41no—
272C3×C4—41no—
273C3×C4C2×#4111yescharacteristic
274C3×C4H(5,𝔽2)11yescharacteristic
275Dic3—22no—
276Dic3—21no—
277Dic3—21no—
278Dic3—41no—
279Dic3—41no—
280Dic3—41no—
281Dic3C2×Q1612yes—
282C23—31no—
283C23D3×D411yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—32no—
287Q8—61no—
288Q8—61no—
289Q8—61no—
290Q8—61no—
291Q8—61no—
292Q8—122no—
293Q8—122no—
294Q8—241no—
295D4—34no—
296C2×C4—21no—
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—61no—
306C2×C4—61no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—81no—
312C2×C4—122no—
313C2×C4—122no—
314C2×C4—241no—
315C2×C4D3×D411yescharacteristic
316C2×C4C23×D311yescharacteristic
317C8—21no—
318C8—21no—
319C8—61no—
320C8—61no—
321C2×C3—22no—
322C2×C3#54611yescharacteristic
323C2×C3C22×Q1611yescharacteristic
324C2×C3#57711yescharacteristic
325D3—22no—
326C22—21no—
327C22—21no—
328C22—32no—
329C22—61no—
330C22—61no—
331C22D3×Q1612yes—
332C22C2×D3×D411yescharacteristic
333C4—21no—
334C4—32no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—61no—
340C4—62no—
341C4—61no—
342C4—121no—
343C4—121no—
344C4—121no—
345C4D3×#4111yescharacteristic
346C4#100911yescharacteristic
347C3#329911yescharacteristic, complemented, Sylow
348C2—22no—
349C2—62no—
350C2#565411yescharacteristic
351C2C2×D3×Q1611yescharacteristic
352C2#577511yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#484C2
socleC22×C3C22×D4
prime radicalC2×#67D4
hypercenter#484D3
hypocenterC3#3299
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. C3×#484C2semidirect
4. #5051C2semidirect
5. C2×#810C2semidirect
6. #4887C2semidirect
7. #4884C2semidirect
8. #4875C2semidirect
9. #4873C2semidirect
10. #4809C2semidirect
11. D3×#103C2semidirect
12. #4795C2semidirect
13. #4792C2semidirect
14. #4739C2semidirect
64. #484D3semidirect
183. #67Q16semidirect
347. C3#3299semidirect

Maximal subgroups

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

subgroupindex
#56322
#55112
C3×#4842
#50512
C2×#8102
#48872
#48842
#48752
#48732
#48092
D3×#1032
#47952
#47922
#47392
#67⋊C82
#32993