Finite Group Databasebeta

← #79841

Subgroups — #79841

Order 384.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5581C211yesmaximal, characteristic
2Q8×D12C211yesmaximal, characteristic
3C3×#441C211yesmaximal, characteristic, complemented
4#5186C211yesmaximal, characteristic, complemented
5#5186C211yesmaximal, characteristic, complemented
6#5031C211yesmaximal, characteristic, complemented
7#5022C211yesmaximal, characteristic, complemented
8#4868C211yesmaximal, characteristic, complemented
9#4862C211yesmaximal, characteristic, complemented
10#4816C211yesmaximal, characteristic, complemented
11#4813C211yesmaximal, characteristic, complemented
12#4802C211yesmaximal, characteristic, complemented
13D3×#103C211yesmaximal, characteristic, complemented
14#4706C211yesmaximal, characteristic
15#4703C211yesmaximal, characteristic, complemented
16#3312—31nomaximal, Sylow
17C2×D3×Q8C2211yescharacteristic
18C2×D3×Q8C2211yescharacteristic
19C2×C3×Q16C2211yescharacteristic
20C3×C4×Q8C2211yescharacteristic
21C3×C4×Q8C2211yescharacteristic
22#946C2211yescharacteristic
23#946C2211yescharacteristic
24C2×#216C2211yescharacteristic
25C2×#216C2211yescharacteristic
26C2×ΓL(1,𝔽25)C2211yescharacteristic
27C2×D3×C8C2211yescharacteristic
28#897—21no—
29#897—21no—
30#897C2211yescharacteristic
31#897C2211yescharacteristic
32#894—21no—
33#892C2211yescharacteristic
34D3×C4⋊C4C2211yescharacteristic
35#889—21no—
36#876—21no—
37C4×D12—21no—
38C4×D12C2211yescharacteristic
39#872—21no—
40#870C2211yescharacteristic
41#869—21no—
42#869C2211yescharacteristic
43C3×#106C2211yescharacteristic
44C3×#103C2211yescharacteristic
45C3×#103C2211yescharacteristic
46C3×#97C2211yescharacteristic
47#835C2211yescharacteristic
48#835C2211yescharacteristic
49(C2×D3)⋊C8C2211yescharacteristic
50(C2×D3)⋊C8C2211yescharacteristic
51#816C2211yescharacteristic
52#816C2211yescharacteristic
53#816C2211yescharacteristic
54#816C2211yescharacteristic
55#810C2211yescharacteristic
56#810C2211yescharacteristic
57#808C2211yescharacteristic
58#807C2211yescharacteristic
59C4⋊(C3⋊C8)C2211yescharacteristic
60#552—31no—
61D4×Q8—31no—
62#491—31no—
63#485—31no—
64#483—31no—
65#479—31no—
66#470—31no—
67#467—31no—
68#462—31no—
69#451—31no—
70#451—31no—
71#441D311yescharacteristic, complemented
72#435—31no—
73#419—31no—
74C2×#103—31no—
75C2×C3×Q8C2311yescharacteristic
76C2×C3×Q8C2311yescharacteristic
77D3×Q8—22no—
78D3×Q8—22no—
79D3×Q8—41no—
80D3×Q8—41no—
81C2×D12D411yescharacteristic
82C2×C4×D3—21no—
83C2×C4×D3—21no—
84C2×C4×D3—21no—
85C2×C4×D3C2311yescharacteristic
86C2×C4×D3C2311yescharacteristic
87C2×Dic6—21no—
88C2×Dic6—21no—
89C2×Dic6C2311yescharacteristic
90C2×Dic6C2311yescharacteristic
91C3×Q16—22no—
92C2×C3×C8C2311yescharacteristic
93C2×C3×C8C2311yescharacteristic
94C3×C4⋊C4—21no—
95C3×C4⋊C4—21no—
96C3×C4⋊C4C2311yescharacteristic
97C3×C4⋊C4C2311yescharacteristic
98C3×C42—21no—
99C3×C42—21no—
100C3×C42C2311yescharacteristic
101#216—41no—
102#216—41no—
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)⋊C4D411yescharacteristic
109(C2×D3)⋊C4D411yescharacteristic
110C4⋊Dic3—21no—
111C4⋊Dic3—21no—
112C4⋊Dic3—21no—
113C4⋊Dic3—21no—
114C4⋊Dic3D411yescharacteristic
115C4⋊Dic3C2311yescharacteristic
116C4⋊Dic3C2311yescharacteristic
117Dic3⋊C4—21no—
118Dic3⋊C4—21no—
119Dic3⋊C4—21no—
120Dic3⋊C4—21no—
121Dic3⋊C4—21no—
122C4×Dic3—21no—
123C2×C3⋊C8C2311yescharacteristic
124C2×C3⋊C8C2311yescharacteristic
125ΓL(1,𝔽25)—41no—
126D3×C8—41no—
127C22×Q8—31no—
128C22×Q8—31no—
129C2×Q16—31no—
130C2×Q16—31no—
131C2×Q16C2×D311yescharacteristic
132C2×M16—31no—
133C22×C8—31no—
134C4⋊Q8—31no—
135C4⋊Q8—61no—
136#126—61no—
137#125—31no—
138#125—61no—
139#123—61no—
140C22⋊Q8—31no—
141C22⋊Q8—31no—
142C22⋊Q8—31no—
143C22⋊Q8—31no—
144C22⋊Q8—61no—
145C22⋊Q8—61no—
146C4×Q8C2×D311yescharacteristic
147C4×Q8C2×D311yescharacteristic
148C4×D4—31no—
149C4×D4—61no—
150#117—31no—
151#117—61no—
152C2×C4⋊C4—31no—
153#107—31no—
154#106—31no—
155#106C2×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⋊C8—31no—
169#97C2×D311yescharacteristic
170C22×D3C2×D411yescharacteristic
171C22×D3C2×D411yescharacteristic
172C3×Q8—21no—
173C3×Q8—21no—
174C3×Q8—21no—
175C3×Q8#4112yes—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4C2×D411yescharacteristic
181C2×C3×C4C2×D411yescharacteristic
182C2×C3×C4C2411yescharacteristic
183C2×Dic3—21no—
184C2×Dic3—21no—
185C2×Dic3—21no—
186C2×Dic3—21no—
187C2×Dic3C2×D411yescharacteristic
188C2×Dic3C2×D411yescharacteristic
189D12—22no—
190C4×D3—21no—
191C4×D3—21no—
192C4×D3—21no—
193C4×D3—21no—
194C4×D3—42no—
195C4×D3—42no—
196C4×D3—42no—
197Dic6—21no—
198Dic6—21no—
199Dic6—21no—
200Dic6—21no—
201Dic6—42no—
202Dic6—42no—
203C3×C8—21no—
204C3×C8—21no—
205C3⋊C8—21no—
206C3⋊C8—21no—
207C2×Q8—31no—
208C2×Q8—31no—
209C2×Q8—61no—
210C2×Q8—61no—
211C2×Q8—62no—
212C2×Q8—62no—
213C2×Q8—121no—
214C2×Q8—121no—
215C2×Q8C22×D311yescharacteristic
216C2×Q8C22×D311yescharacteristic
217C2×D4—31no—
218C22×C4—31no—
219C22×C4—31no—
220C22×C4—61no—
221C22×C4—61no—
222C22×C4—61no—
223Q16—22no—
224Q16—121no—
225Q16—121no—
226M16—121no—
227C2×C8—31no—
228C2×C8—31no—
229C2×C8—121no—
230C2×C8C22×D311yescharacteristic
231C2×C8C22×D311yescharacteristic
232C4⋊C4—21no—
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⋊C4—61no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4C22×D311yescharacteristic
247C4⋊C4C22×D311yescharacteristic
248C22⋊C4—31no—
249C22⋊C4—31no—
250C22⋊C4—61no—
251C22⋊C4—61no—
252C22⋊C4—61no—
253C22⋊C4—61no—
254C22⋊C4—61no—
255C42—21no—
256C42—21no—
257C42—61no—
258C42C22×D311yescharacteristic
259C22×C3C22×D411yescharacteristic
260C2×D3—21no—
261C2×D3—21no—
262C2×D3—21no—
263C2×D3—21no—
264C2×D3—21no—
265C2×D3#13712yes—
266C3×C4—22no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—41no—
270C3×C4—41no—
271C3×C4—41no—
272C3×C4C2×#4111yescharacteristic
273C3×C4H(5,𝔽2)11yescharacteristic
274Dic3—21no—
275Dic3—21no—
276Dic3—41no—
277Dic3—41no—
278Dic3—41no—
279Dic3—41no—
280C23—31no—
281C23—31no—
282Q8—21no—
283Q8—21no—
284Q8—21no—
285Q8—61no—
286Q8—61no—
287Q8—61no—
288Q8—61no—
289Q8—122no—
290Q8—122no—
291Q8#23512yes—
292D4—62no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—31no—
298C2×C4—31no—
299C2×C4—61no—
300C2×C4—61no—
301C2×C4—61no—
302C2×C4—61no—
303C2×C4—61no—
304C2×C4—61no—
305C2×C4—61no—
306C2×C4—61no—
307C2×C4—122no—
308C2×C4—122no—
309C2×C4—122no—
310C2×C4D3×D411yescharacteristic
311C2×C4D3×D411yescharacteristic
312C2×C4C23×D311yescharacteristic
313C8—21no—
314C8—21no—
315C8—61no—
316C8—61no—
317C2×C3#54611yescharacteristic
318C2×C3C2×#13711yescharacteristic
319C2×C3#57811yescharacteristic
320D3—22no—
321D3—41no—
322C22—32no—
323C22—61no—
324C22—61no—
325C22—61no—
326C22—61no—
327C22—61no—
328C22C2×D3×D411yescharacteristic
329C4—21no—
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—61no—
336C4—61no—
337C4—121no—
338C4—121no—
339C4—121no—
340C4—121no—
341C4C2×#23511yescharacteristic
342C4#100911yescharacteristic
343C3#331211yescharacteristic, complemented, Sylow
344C2—62no—
345C2—121no—
346C2#555011yescharacteristic
347C2D3×#13711yescharacteristic
348C2#577911yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#441C2
socleC22×C3C22×D4
prime radicalC2×D12D4
hypercenter#441D3
hypocenterC3#3312
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. C3×#441C2semidirect
4. #5186C2semidirect
5. #5186C2semidirect
6. #5031C2semidirect
7. #5022C2semidirect
8. #4868C2semidirect
9. #4862C2semidirect
10. #4816C2semidirect
11. #4813C2semidirect
12. #4802C2semidirect
13. D3×#103C2semidirect
15. #4703C2semidirect
71. #441D3semidirect
343. C3#3312semidirect

Maximal subgroups

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

subgroupindex
#55812
Q8×D122
C3×#4412
#51862
#50312
#50222
#48682
#48622
#48162
#48132
#48022
D3×#1032
#47062
#47032
#33123