Finite Group Databasebeta

← #79772

Subgroups — #79772

Order 384.

492 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#916C211yesmaximal, characteristic
2C4×#239C211yesmaximal, characteristic, complemented
3C4×#237C211yesmaximal, characteristic, complemented
4C3×#440C211yesmaximal, characteristic, complemented
5#5164C211yesmaximal, characteristic, complemented
6#5030C211yesmaximal, characteristic, complemented
7#5014C211yesmaximal, characteristic, complemented
8#4889C211yesmaximal, characteristic, complemented
9#4880C211yesmaximal, characteristic, complemented
10#4804C211yesmaximal, characteristic, complemented
11#4789C211yesmaximal, characteristic, complemented
12#4785C211yesmaximal, characteristic, complemented
13#4772C211yesmaximal, characteristic, complemented
14#4710C211yesmaximal, characteristic, complemented
15D3×#97C211yesmaximal, characteristic, complemented
16#2943—31nomaximal, Sylow
17C2×#239C2211yescharacteristic
18C2×#237C2211yescharacteristic
19C2×C3×SD16C2211yescharacteristic
20C3×C4×Q8C2211yescharacteristic
21C3×C4×D4C2211yescharacteristic
22Q8×Dic3C2211yescharacteristic
23C2×#216C2211yescharacteristic
24D4×Dic3C2211yescharacteristic
25C2×#213C2211yescharacteristic
26C4×#67—21no—
27C2×C4×Dic3—21no—
28#916C418yescomplemented
29C2×#204C2211yescharacteristic
30C2×D3×C8C2211yescharacteristic
31C2×D3×C8C2211yescharacteristic
32#893—21no—
33#893C2211yescharacteristic
34#892—21no—
35#892C2211yescharacteristic
36#892C2211yescharacteristic
37#887C2211yescharacteristic
38#67⋊C4—21no—
39#877—21no—
40C4×D12—21no—
41C4×D12C2211yescharacteristic
42C42×D3—21no—
43C42×D3C2211yescharacteristic
44C4×Dic6C2211yescharacteristic
45C3×#107C2211yescharacteristic
46C3×#103C2211yescharacteristic
47C3×#102C2211yescharacteristic
48C3×#97C2211yescharacteristic
49#835C2211yescharacteristic
50#832C2211yescharacteristic
51#821C2211yescharacteristic
52#818C2211yescharacteristic
53#816C2211yescharacteristic
54#815C2211yescharacteristic
55#815C2211yescharacteristic
56#810C2211yescharacteristic
57#809C2211yescharacteristic
58#808C2211yescharacteristic
59#808C2211yescharacteristic
60#803C2211yescharacteristic
61C2×#135—31no—
62C4×#41—31no—
63C4×#41—31no—
64#442—31no—
65#442—31no—
66#441—31no—
67#441—31no—
68#440—31no—
69#440—31no—
70#440—31no—
71#440D311yescharacteristic, complemented
72#427—31no—
73#416—31no—
74#416—31no—
75C2×#97—31no—
76C2×C3×Q8C2311yescharacteristic
77C2×C3×D4C2311yescharacteristic
78C22×C3×C4—21no—
79C2×#67—21no—
80C22×Dic3—21no—
81C22×Dic3—21no—
82#239—22no—
83#239C2×C414yescomplemented
84#237—22no—
85#237C2×C414yescomplemented
86C2×D12—21no—
87C2×D12C2311yescharacteristic
88C2×C4×D3—21no—
89C2×C4×D3—21no—
90C2×C4×D3—21no—
91C2×C4×D3D411yescharacteristic
92C2×C4×D3D411yescharacteristic
93C2×C4×D3C2311yescharacteristic
94C2×Dic6C2311yescharacteristic
95C3×SD16C2×C414yescomplemented
96C2×C3×C8C2311yescharacteristic
97C2×C3×C8C2311yescharacteristic
98C3×C4⋊C4—21no—
99C3×C4⋊C4C2311yescharacteristic
100C3×C4⋊C4C2311yescharacteristic
101C3×C22⋊C4—21no—
102C3×C42—21no—
103C3×C42C2311yescharacteristic
104#217—21no—
105#216C2×C414yescomplemented
106#213C2×C414yescomplemented
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110(C2×D3)⋊C4—21no—
111C4⋊Dic3—21no—
112C4⋊Dic3C2311yescharacteristic
113C4⋊Dic3C2311yescharacteristic
114Dic3⋊C4—21no—
115Dic3⋊C4—21no—
116C4×Dic3—21no—
117C4×Dic3—21no—
118C4×Dic3—21no—
119C4×Dic3—21no—
120C4×Dic3—21no—
121C4×Dic3D411yescharacteristic
122C4×Dic3D411yescharacteristic
123C4×Dic3C2311yescharacteristic
124C2×C3⋊C8C2311yescharacteristic
125C2×C3⋊C8C2311yescharacteristic
126#204C2×C414yescomplemented
127D3×C8—22no—
128D3×C8C2×C414yescomplemented
129C2×#41—31no—
130C2×#41—31no—
131#135—38no—
132C2×Q16—31no—
133C2×SD16—31no—
134C2×SD16C2×D311yescharacteristic
135C2×D8—31no—
136C22×C8—31no—
137C22×C8—31no—
138C4×Q8—31no—
139C4×Q8—31no—
140C4×Q8—31no—
141C4×Q8C2×D311yescharacteristic
142C4×D4—31no—
143C4×D4—31no—
144C4×D4—31no—
145C4×D4—61no—
146C4×D4—61no—
147C4×D4—61no—
148C4×D4—61no—
149C4×D4C2×D311yescharacteristic
150#117—31no—
151#117—31no—
152#117—61no—
153#117—61no—
154C2×C42—31no—
155C2×C42—61no—
156C2×C42—61no—
157#107—31no—
158#107C2×D311yescharacteristic
159#106—31no—
160#106—31no—
161#103—31no—
162#103—31no—
163#103—31no—
164#103C2×D311yescharacteristic
165#102—31no—
166#102—31no—
167#102—31no—
168#102C2×D311yescharacteristic
169#97—31no—
170#97—31no—
171#97—31no—
172#97C2×D311yescharacteristic
173C23×C3—21no—
174C22×D3—21no—
175C22×D3C2×D411yescharacteristic
176C3×Q8—21no—
177C3×Q8C22×C412yes—
178C3×D4—21no—
179C3×D4C22×C412yes—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—42no—
184C2×C3×C4C2×D411yescharacteristic
185C2×C3×C4C2×D411yescharacteristic
186C2×C3×C4C2411yescharacteristic
187#67—24no—
188C2×Dic3—21no—
189C2×Dic3—24no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—42no—
193C2×Dic3C2×D411yescharacteristic
194C2×Dic3C2×D411yescharacteristic
195C2×Dic3C2×D411yescharacteristic
196D12—24no—
197D12—21no—
198D12C22×C412yes—
199C4×D3—24no—
200C4×D3—41no—
201C4×D3—41no—
202C4×D3—42no—
203C4×D3—42no—
204C4×D3C22×C412yes—
205C4×D3#4112yes—
206Dic6—21no—
207Dic6C22×C412yes—
208C3×C8—21no—
209C3×C8C22×C412yes—
210C3⋊C8—21no—
211C3⋊C8C22×C412yes—
212#41—34no—
213#41—34no—
214#41—62no—
215#41—62no—
216C2×Q8—31no—
217C2×Q8C22×D311yescharacteristic
218C2×D4—31no—
219C2×D4—61no—
220C2×D4—61no—
221C2×D4C22×D311yescharacteristic
222C22×C4—21no—
223C22×C4—31no—
224C22×C4—31no—
225C22×C4—31no—
226C22×C4—61no—
227C22×C4—61no—
228C22×C4—61no—
229C22×C4—61no—
230C22×C4—61no—
231Q16—34no—
232SD16—34no—
233SD16C4×D314yescomplemented
234D8—34no—
235C2×C8—31no—
236C2×C8—34no—
237C2×C8—31no—
238C2×C8—62no—
239C2×C8C22×D311yescharacteristic
240C2×C8C22×D311yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—31no—
243C4⋊C4—31no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4C22×D311yescharacteristic
248C4⋊C4C22×D311yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—61no—
251C22⋊C4—61no—
252C22⋊C4—61no—
253C22⋊C4—61no—
254C22⋊C4—61no—
255C42—21no—
256C42—31no—
257C42—31no—
258C42—31no—
259C42—61no—
260C42—61no—
261C42—61no—
262C42—61no—
263C42—61no—
264C42C22×D311yescharacteristic
265C22×C3—22no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3C22×D411yescharacteristic
269C2×D3—21no—
270C2×D3—21no—
271C2×D3—22no—
272C2×D3—41no—
273C2×D3—41no—
274C2×D3C4×D412yes—
275C3×C4—22no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—41no—
279C3×C4—41no—
280C3×C4C23×C411yescharacteristic
281C3×C4C2×#4111yescharacteristic
282Dic3—22no—
283Dic3—21no—
284Dic3—21no—
285Dic3—41no—
286Dic3—41no—
287Dic3C4×D412yes—
288C23—21no—
289C23—31no—
290C23—61no—
291Q8—21no—
292Q8—32no—
293Q8—61no—
294Q8C2×C4×D312yes—
295D4—21no—
296D4—32no—
297D4—64no—
298D4—64no—
299D4—61no—
300D4C2×C4×D312yes—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—31no—
305C2×C4—32no—
306C2×C4—32no—
307C2×C4—31no—
308C2×C4—31no—
309C2×C4—42no—
310C2×C4—64no—
311C2×C4—64no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—121no—
316C2×C4—121no—
317C2×C4—122no—
318C2×C4—122no—
319C2×C4—122no—
320C2×C4D3×D411yescharacteristic
321C2×C4D3×D411yescharacteristic
322C2×C4C23×D311yescharacteristic
323C8—21no—
324C8—32no—
325C8—61no—
326C8C2×C4×D312yes—
327C2×C3—42no—
328C2×C3C2×C4×D411yescharacteristic
329C2×C3#57511yescharacteristic
330C2×C3#57511yescharacteristic
331D3—22no—
332D3—42no—
333C22—22no—
334C22—32no—
335C22—41no—
336C22—41no—
337C22—61no—
338C22—61no—
339C22—62no—
340C22—121no—
341C22—121no—
342C22C2×D3×D411yescharacteristic
343C4—21no—
344C4—21no—
345C4—22no—
346C4—32no—
347C4—41no—
348C4—41no—
349C4—61no—
350C4—61no—
351C4—62no—
352C4—121no—
353C4—121no—
354C4C22×C4×D311yescharacteristic
355C4D3×#4111yescharacteristic
356C3#294311yescharacteristic, complemented, Sylow
357C2—42no—
358C2—62no—
359C2—122no—
360C2C4×D3×D411yescharacteristic
361C2#577311yescharacteristic
362C2#577711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutatorC3×C4C23×C4
FrattiniC2×C4C23×D3
FittingC3×#440C2
socleC22×C3C22×D4
prime radicalC2×#916C2
cosocleC2×C3×C4C24
hypercenter#440D3
hypocenterC3#2943
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×#239C2semidirect
3. C4×#237C2semidirect
4. C3×#440C2semidirect
5. #5164C2semidirect
6. #5030C2semidirect
7. #5014C2semidirect
8. #4889C2semidirect
9. #4880C2semidirect
10. #4804C2semidirect
11. #4789C2semidirect
12. #4785C2semidirect
13. #4772C2semidirect
14. #4710C2semidirect
15. D3×#97C2semidirect
28. #916C4semidirect
71. #440D3semidirect
83. #239C2×C4semidirect
85. #237C2×C4semidirect
95. C3×SD16C2×C4semidirect
105. #216C2×C4semidirect
106. #213C2×C4semidirect
126. #204C2×C4semidirect
128. D3×C8C2×C4semidirect
233. SD16C4×D3semidirect
356. C3#2943semidirect

Maximal subgroups

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

subgroupindex
C2×#9162
C4×#2392
C4×#2372
C3×#4402
#51642
#50302
#50142
#48892
#48802
#48042
#47892
#47852
#47722
#47102
D3×#972
#29433