Finite Group Databasebeta

← #75307

Subgroups — #75307

Order 384.

652 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#894C211yesmaximal, characteristic
2C2×#893C211yesmaximal, characteristic
3C2×#872C211yesmaximal, characteristic, complemented
4C3×#387C211yesmaximal, characteristic, complemented
5#4976C211yesmaximal, characteristic, complemented
6Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
7C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
8#4669C211yesmaximal, characteristic, complemented
9#4669C211yesmaximal, characteristic, complemented
10#4668C211yesmaximal, characteristic, complemented
11#4668C211yesmaximal, characteristic, complemented
12#4666C211yesmaximal, characteristic, complemented
13#4665C211yesmaximal, characteristic
14D3×#95C211yesmaximal, characteristic, complemented
15#4652C211yesmaximal, characteristic, complemented
16#2359—31nomaximal, Sylow
17C22×D12C2211yescharacteristic
18C22×C4×D3C2211yescharacteristic
19C22×C4×D3C2211yescharacteristic
20C22×C4×D3C2211yescharacteristic
21C22×C4×D3C2211yescharacteristic
22C2×C3×C4⋊C4C2211yescharacteristic
23C2×C3×C4⋊C4C2211yescharacteristic
24C2×C3×C42C2211yescharacteristic
25C2×(C2×D3)⋊C4C2211yescharacteristic
26C2×(C2×D3)⋊C4C2211yescharacteristic
27C2×(C2×D3)⋊C4C2211yescharacteristic
28C2×(C2×D3)⋊C4C2211yescharacteristic
29C2×(C2×D3)⋊C4C2211yescharacteristic
30C2×(C2×D3)⋊C4C2211yescharacteristic
31C2×(C2×D3)⋊C4C2211yescharacteristic
32C2×(C2×D3)⋊C4C2211yescharacteristic
33C2×C4⋊Dic3C2211yescharacteristic
34C2×Dic3⋊C4C2211yescharacteristic
35C2×Dic3⋊C4C2211yescharacteristic
36C2×Dic3⋊C4C2211yescharacteristic
37C2×Dic3⋊C4C2211yescharacteristic
38C2×C4×Dic3C2211yescharacteristic
39C2×C4×Dic3C2211yescharacteristic
40C2×C4×Dic3C2211yescharacteristic
41C2×C4×Dic3C2211yescharacteristic
42#894C418yescomplemented
43#893—24no—
44#872—24no—
45C3×#95C2211yescharacteristic
46C3×#95C2211yescharacteristic
47C3×#95C2211yescharacteristic
48C3×#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C2×#123—31no—
56C2×C4×D4—31no—
57C2×#117—31no—
58#389—31no—
59#388—31no—
60#388—31no—
61#387—31no—
62#387D311yescharacteristic, complemented
63#386—31no—
64#385—31no—
65#385—31no—
66C4×C4⋊C4—31no—
67C4×C22⋊C4—31no—
68C4×C22⋊C4—31no—
69C2×#95—31no—
70C23×D3C2311yescharacteristic
71C23×D3C2311yescharacteristic
72C22×C3×C4C2311yescharacteristic
73C22×C3×C4C2311yescharacteristic
74C22×C3×C4C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×Dic3C2311yescharacteristic
80C22×Dic3C2311yescharacteristic
81C22×Dic3C2311yescharacteristic
82C22×Dic3C2311yescharacteristic
83C22×Dic3C2311yescharacteristic
84C22×Dic3C2311yescharacteristic
85C2×D12—22no—
86C2×D12—22no—
87C2×D12C2×C414yes—
88C2×C4×D3—22no—
89C2×C4×D3—22no—
90C2×C4×D3—22no—
91C2×C4×D3—22no—
92C2×C4×D3—22no—
93C2×C4×D3—22no—
94C2×C4×D3—22no—
95C2×C4×D3—22no—
96C2×C4×D3—41no—
97C2×C4×D3—41no—
98C2×C4×D3—41no—
99C2×C4×D3C2×C414yescomplemented
100C3×C4⋊C4—22no—
101C3×C4⋊C4C2×C414yescomplemented
102C3×C42—22no—
103(C2×D3)⋊C4—22no—
104(C2×D3)⋊C4—22no—
105(C2×D3)⋊C4—22no—
106(C2×D3)⋊C4—41no—
107(C2×D3)⋊C4C2×C414yescomplemented
108(C2×D3)⋊C4C2×C414yescomplemented
109(C2×D3)⋊C4C2×C414yescomplemented
110(C2×D3)⋊C4D414yes—
111C4⋊Dic3—22no—
112Dic3⋊C4—22no—
113Dic3⋊C4—22no—
114Dic3⋊C4—41no—
115Dic3⋊C4C2×C414yescomplemented
116C4×Dic3—22no—
117C4×Dic3—22no—
118C4×Dic3—22no—
119C4×Dic3—41no—
120C22×D4—31no—
121C23×C4—31no—
122C23×C4—31no—
123C23×C4—31no—
124C23×C4—31no—
125#123—38no—
126C4×D4—64no—
127#117—64no—
128C2×C4⋊C4—31no—
129C2×C4⋊C4—31no—
130C2×C4⋊C4—31no—
131C2×C4⋊C4—31no—
132C2×C4⋊C4—31no—
133C2×C4⋊C4C2×D311yescharacteristic
134C2×C4⋊C4C2×D311yescharacteristic
135C2×C22⋊C4—31no—
136C2×C22⋊C4—31no—
137C2×C22⋊C4—31no—
138C2×C22⋊C4—31no—
139C2×C22⋊C4—31no—
140C2×C22⋊C4—31no—
141C2×C22⋊C4—31no—
142C2×C22⋊C4—31no—
143C2×C42—31no—
144C2×C42—31no—
145C2×C42—31no—
146C2×C42—31no—
147C2×C42C2×D311yescharacteristic
148#95—31no—
149#95—31no—
150#95—31no—
151#95—31no—
152#95—31no—
153#95—31no—
154#95C2×D311yescharacteristic
155#95C2×D311yescharacteristic
156#95C2×D311yescharacteristic
157#95C2×D311yescharacteristic
158C23×C3C2411yescharacteristic
159C22×D3—21no—
160C22×D3—21no—
161C22×D3—21no—
162C22×D3—21no—
163C22×D3—21no—
164C22×D3—21no—
165C22×D3—21no—
166C22×D3—21no—
167C22×D3—21no—
168C22×D3—21no—
169C22×D3C22×C412yes—
170C22×D3C22×C412yes—
171C22×D3C2×D412yes—
172C22×D3#4112yes—
173C2×C3×C4—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—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4C22×C412yes—
191C2×C3×C4C22×C412yes—
192C2×C3×C4C22×C412yes—
193C2×C3×C4C2×D412yes—
194C2×Dic3—21no—
195C2×Dic3—21no—
196C2×Dic3—21no—
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3—21no—
200C2×Dic3—21no—
201C2×Dic3—21no—
202C2×Dic3—21no—
203C2×Dic3—21no—
204C2×Dic3—21no—
205C2×Dic3—21no—
206C2×Dic3—21no—
207C2×Dic3C22×C412yes—
208C2×Dic3C22×C412yes—
209C2×Dic3C2×D412yes—
210C2×Dic3#4112yes—
211C2×Dic3#4112yes—
212D12—28no—
213C4×D3—28no—
214C4×D3—44no—
215C4×D3—44no—
216C4×D3—44no—
217C24—31no—
218C24—31no—
219C2×D4—34no—
220C2×D4—62no—
221C2×D4—62no—
222C22×C4—31no—
223C22×C4—31no—
224C22×C4—31no—
225C22×C4—31no—
226C22×C4—31no—
227C22×C4—34no—
228C22×C4—31no—
229C22×C4—62no—
230C22×C4—62no—
231C22×C4—62no—
232C22×C4—62no—
233C22×C4—62no—
234C22×C4—62no—
235C22×C4—62no—
236C22×C4—62no—
237C22×C4—121no—
238C22×C4—121no—
239C22×C4—121no—
240C22×C4C22×D311yescharacteristic
241C22×C4C22×D311yescharacteristic
242C22×C4C22×D311yescharacteristic
243C22×C4C22×D311yescharacteristic
244C22×C4C22×D311yescharacteristic
245C22×C4C22×D311yescharacteristic
246C22×C4C22×D311yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—34no—
249C4⋊C4—62no—
250C4⋊C4—62no—
251C4⋊C4—62no—
252C4⋊C4—121no—
253C4⋊C4C4×D314yescomplemented
254C22⋊C4—34no—
255C22⋊C4—34no—
256C22⋊C4—34no—
257C22⋊C4—34no—
258C22⋊C4—62no—
259C22⋊C4—62no—
260C22⋊C4—62no—
261C22⋊C4—121no—
262C42—22no—
263C42—62no—
264C42—62no—
265C42—62no—
266C42—121no—
267C22×C3C23×C411yescharacteristic
268C22×C3C22×D411yescharacteristic
269C22×C3C2×#4111yescharacteristic
270C22×C3C2×#4111yescharacteristic
271C22×C3C2×#4111yescharacteristic
272C22×C3H(5,𝔽2)11yescharacteristic
273C22×C32−1+411yescharacteristic
274C2×D3—22no—
275C2×D3—22no—
276C2×D3—22no—
277C2×D3—22no—
278C2×D3—22no—
279C2×D3—22no—
280C2×D3—22no—
281C2×D3—22no—
282C2×D3—22no—
283C2×D3—41no—
284C2×D3—41no—
285C2×D3—41no—
286C2×D3—41no—
287C2×D3C4×D414yes—
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—22no—
292C3×C4—41no—
293C3×C4—41no—
294C3×C4—41no—
295Dic3—22no—
296Dic3—22no—
297Dic3—22no—
298Dic3—22no—
299Dic3—22no—
300Dic3—41no—
301C23—32no—
302C23—32no—
303C23—32no—
304C23—32no—
305C23—61no—
306C23—61no—
307C23—61no—
308C23—61no—
309C23—61no—
310C23—61no—
311C23—61no—
312C23—61no—
313C23—61no—
314C23—61no—
315C23C23×D311yescharacteristic
316D4—68no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—32no—
335C2×C4—32no—
336C2×C4—32no—
337C2×C4—32no—
338C2×C4—32no—
339C2×C4—68no—
340C2×C4—61no—
341C2×C4—61no—
342C2×C4—61no—
343C2×C4—61no—
344C2×C4—61no—
345C2×C4—61no—
346C2×C4—61no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—61no—
352C2×C4—61no—
353C2×C4—124no—
354C2×C4—124no—
355C2×C4—124no—
356C2×C4C2×C4×D312yes—
357C2×C4C2×C4×D312yes—
358C2×C4C2×C4×D312yes—
359C2×C4D3×D412yes—
360C2×C3C2×C4×D411yescharacteristic
361C2×C3C4×#4111yescharacteristic
362C2×C3#52011yescharacteristic
363C2×C3#54611yescharacteristic
364C2×C3#54711yescharacteristic
365C2×C3#55111yescharacteristic
366C2×C3#55211yescharacteristic
367D3—24no—
368D3—42no—
369C22—34no—
370C22—62no—
371C22—62no—
372C22—62no—
373C22—62no—
374C22—62no—
375C22—62no—
376C22—62no—
377C22—62no—
378C22—62no—
379C22—121no—
380C22—121no—
381C22—121no—
382C22—121no—
383C22C22×C4×D311yescharacteristic
384C22C2×D3×D411yescharacteristic
385C22#100711yescharacteristic
386C22D3×#4111yescharacteristic
387C22D3×#4111yescharacteristic
388C22D3×#4111yescharacteristic
389C22#100911yescharacteristic
390C4—22no—
391C4—22no—
392C4—22no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—62no—
398C4—62no—
399C4—62no—
400C4—62no—
401C4—62no—
402C4—121no—
403C3#235911yescharacteristic, complemented, Sylow
404C2—64no—
405C2—122no—
406C2#552211yescharacteristic
407C2C4×D3×D411yescharacteristic
408C2#557411yescharacteristic
409C2#563111yescharacteristic
410C2#565411yescharacteristic
411C2#569311yescharacteristic
412C2#570511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC3×#387C2
socle, cosocleC23×C3C24
prime radicalC22×D12C22
hypercenter#387D3
hypocenterC3#2359
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
3. C2×#872C2semidirect
4. C3×#387C2semidirect
5. #4976C2semidirect
6. Dic3×C4⋊C4C2semidirect
7. C4×(C2×D3)⋊C4C2semidirect
8. #4669C2semidirect
9. #4669C2semidirect
10. #4668C2semidirect
11. #4668C2semidirect
12. #4666C2semidirect
14. D3×#95C2semidirect
15. #4652C2semidirect
42. #894C4semidirect
62. #387D3semidirect
99. C2×C4×D3C2×C4semidirect
101. C3×C4⋊C4C2×C4semidirect
107. (C2×D3)⋊C4C2×C4semidirect
108. (C2×D3)⋊C4C2×C4semidirect
109. (C2×D3)⋊C4C2×C4semidirect
115. Dic3⋊C4C2×C4semidirect
253. C4⋊C4C4×D3semidirect
403. C3#2359semidirect

Maximal subgroups

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

subgroupindex
C2×#8942
C2×#8932
C2×#8722
C3×#3872
#49762
Dic3×C4⋊C42
C4×(C2×D3)⋊C42
#46692
#46682
#46662
#46652
D3×#952
#46522
#23593