Finite Group Databasebeta

← D3×#387 #75295

Subgroups — D3×#387 #75295

Order 384.

712 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊C4C211yesmaximal, characteristic
2C2×D3×C4⋊C4C211yesmaximal, characteristic
3C2×C42×D3C211yesmaximal, characteristic
4C3×#387C211yesmaximal, characteristic, complemented
5#4980C211yesmaximal, characteristic, complemented
6#4978C211yesmaximal, characteristic, complemented
7#4933C211yesmaximal, characteristic, complemented
8D3×#95C211yesmaximal, characteristic
9D3×#95C211yesmaximal, characteristic
10D3×#95C211yesmaximal, characteristic
11D3×#95C211yesmaximal, characteristic
12#4655C211yesmaximal, characteristic, complemented
13#4654C211yesmaximal, characteristic, complemented
14#4653C211yesmaximal, characteristic, complemented
15#4652C211yesmaximal, characteristic, complemented
16C2×#387—31nomaximal, Sylow
17C22×C4×D3C2211yescharacteristic
18C22×C4×D3C2211yescharacteristic
19C22×C4×D3C2211yescharacteristic
20C22×C4×D3C2211yescharacteristic
21C22×C4×D3C2211yescharacteristic
22C22×C4×D3C2211yescharacteristic
23C22×C4×D3C2211yescharacteristic
24C2×C3×C4⋊C4C2211yescharacteristic
25C2×C3×C4⋊C4C2211yescharacteristic
26C2×C3×C42C2211yescharacteristic
27C2×C4⋊Dic3C2211yescharacteristic
28C2×C4⋊Dic3C2211yescharacteristic
29C2×Dic3⋊C4C2211yescharacteristic
30C2×Dic3⋊C4C2211yescharacteristic
31C2×Dic3⋊C4C2211yescharacteristic
32C2×Dic3⋊C4C2211yescharacteristic
33C2×C4×Dic3C2211yescharacteristic
34C2×C4×Dic3C2211yescharacteristic
35C2×C4×Dic3C2211yescharacteristic
36D3×C4⋊C4—24no—
37D3×C4⋊C4C418yescomplemented
38C42×D3—24no—
39C3×#95C2211yescharacteristic
40C3×#95C2211yescharacteristic
41C3×#95C2211yescharacteristic
42C3×#95C2211yescharacteristic
43C3⋊#95C2211yescharacteristic
44C3⋊#95C2211yescharacteristic
45C3⋊#95C2211yescharacteristic
46C3⋊#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C22×C4⋊C4—31no—
56C22×C4⋊C4—31no—
57C22×C42—31no—
58#387—31no—
59#387—31no—
60#387—31no—
61#387—31no—
62#387—31no—
63#387—31no—
64#387—31no—
65#387D311yescharacteristic, direct product factor
66C2×#95—31no—
67C2×#95—31no—
68C2×#95—31no—
69C2×#95—31no—
70C23×D3C2311yescharacteristic
71C22×C3×C4C2311yescharacteristic
72C22×C3×C4C2311yescharacteristic
73C22×C3×C4C2311yescharacteristic
74C22×C3×C4C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×Dic3C2311yescharacteristic
79C22×Dic3C2311yescharacteristic
80C22×Dic3C2311yescharacteristic
81C22×Dic3C2311yescharacteristic
82C22×Dic3C2311yescharacteristic
83C22×Dic3C2311yescharacteristic
84C22×Dic3C2311yescharacteristic
85C2×C4×D3—22no—
86C2×C4×D3—22no—
87C2×C4×D3—22no—
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—22no—
97C2×C4×D3—22no—
98C2×C4×D3—22no—
99C2×C4×D3—22no—
100C2×C4×D3—22no—
101C2×C4×D3C2×C414yes—
102C2×C4×D3C2×C414yes—
103C2×C4×D3C2×C414yes—
104C2×C4×D3D414yes—
105C2×C4×D3Q814yes—
106C3×C4⋊C4—22no—
107C3×C4⋊C4C2×C414yescomplemented
108C3×C42—22no—
109C4⋊Dic3—22no—
110C4⋊Dic3C2×C414yescomplemented
111Dic3⋊C4—22no—
112Dic3⋊C4—22no—
113Dic3⋊C4C2×C414yescomplemented
114Dic3⋊C4C2×C414yescomplemented
115C4×Dic3—22no—
116C4×Dic3—22no—
117C4×Dic3—22no—
118C23×C4—31no—
119C23×C4—31no—
120C23×C4—31no—
121C23×C4—31no—
122C23×C4—31no—
123C23×C4—31no—
124C23×C4—31no—
125C2×C4⋊C4—31no—
126C2×C4⋊C4—31no—
127C2×C4⋊C4—31no—
128C2×C4⋊C4—38no—
129C2×C4⋊C4—31no—
130C2×C4⋊C4—31no—
131C2×C4⋊C4—31no—
132C2×C4⋊C4—64no—
133C2×C4⋊C4C2×D311yescharacteristic
134C2×C4⋊C4C2×D311yescharacteristic
135C2×C42—31no—
136C2×C42—31no—
137C2×C42—31no—
138C2×C42—64no—
139C2×C42C2×D311yescharacteristic
140#95—31no—
141#95—31no—
142#95—31no—
143#95—31no—
144#95—31no—
145#95—31no—
146#95—31no—
147#95—31no—
148#95—31no—
149#95—31no—
150#95—31no—
151#95—31no—
152#95C2×D311yescharacteristic
153#95C2×D311yescharacteristic
154#95C2×D311yescharacteristic
155#95C2×D311yescharacteristic
156C23×C3C2411yescharacteristic
157C22×D3C22×C412yes—
158C22×D3C2×D412yes—
159C22×D3C2×Q812yes—
160C22×D3#4112yes—
161C22×D3#4112yes—
162C22×D3#4112yes—
163C22×D3#4112yes—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
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×C4C22×C412yes—
181C2×C3×C4C22×C412yes—
182C2×C3×C4C22×C412yes—
183C2×C3×C4C2×D412yes—
184C2×C3×C4C2×Q812yes—
185C2×Dic3—21no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—21no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—21no—
195C2×Dic3—21no—
196C2×Dic3—21no—
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3—21no—
200C2×Dic3—21no—
201C2×Dic3C22×C412yes—
202C2×Dic3C22×C412yes—
203C2×Dic3C22×C412yes—
204C2×Dic3C2×D412yes—
205C2×Dic3C2×Q812yes—
206C4×D3—28no—
207C4×D3—28no—
208C4×D3—28no—
209C4×D3—28no—
210C4×D3—28no—
211C4×D3—44no—
212C4×D3—44no—
213C24—31no—
214C22×C4—31no—
215C22×C4—31no—
216C22×C4—31no—
217C22×C4—31no—
218C22×C4—31no—
219C22×C4—34no—
220C22×C4—34no—
221C22×C4—34no—
222C22×C4—34no—
223C22×C4—34no—
224C22×C4—31no—
225C22×C4—31no—
226C22×C4—62no—
227C22×C4—62no—
228C22×C4—62no—
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—62no—
238C22×C4—62no—
239C22×C4—62no—
240C22×C4—62no—
241C22×C4—62no—
242C22×C4C22×D311yescharacteristic
243C22×C4C22×D311yescharacteristic
244C22×C4C22×D311yescharacteristic
245C22×C4C22×D311yescharacteristic
246C22×C4C22×D311yescharacteristic
247C22×C4C22×D311yescharacteristic
248C22×C4C22×D311yescharacteristic
249C4⋊C4—22no—
250C4⋊C4—34no—
251C4⋊C4—34no—
252C4⋊C4—34no—
253C4⋊C4—62no—
254C4⋊C4—62no—
255C4⋊C4—62no—
256C4⋊C4C4×D314yescomplemented
257C42—22no—
258C42—62no—
259C42—62no—
260C42—62no—
261C22×C3C23×C411yescharacteristic
262C22×C3C22×D411yescharacteristic
263C22×C3C22×Q811yescharacteristic
264C22×C3C2×#4111yescharacteristic
265C22×C3C2×#4111yescharacteristic
266C22×C3C2×#4111yescharacteristic
267C22×C3C2×#4111yescharacteristic
268C2×D3#11714yes—
269C2×D3C4×D414yes—
270C2×D3C4×Q814yes—
271C2×D3C22⋊Q814yes—
272C2×D3#12314yes—
273C2×D3#12514yes—
274C2×D3#12614yes—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—22no—
279C3×C4—22no—
280C3×C4—41no—
281C3×C4—41no—
282Dic3—22no—
283Dic3—22no—
284Dic3—22no—
285Dic3—22no—
286Dic3—22no—
287Dic3—41no—
288Dic3—41no—
289C23—32no—
290C23—32no—
291C23—32no—
292C23—32no—
293C23—32no—
294C23—32no—
295C23—32no—
296C23C23×D311yescharacteristic
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—32no—
314C2×C4—32no—
315C2×C4—32no—
316C2×C4—32no—
317C2×C4—32no—
318C2×C4—68no—
319C2×C4—68no—
320C2×C4—68no—
321C2×C4—68no—
322C2×C4—68no—
323C2×C4—61no—
324C2×C4—61no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—61no—
331C2×C4—61no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4—61no—
335C2×C4—61no—
336C2×C4—61no—
337C2×C4—61no—
338C2×C4—61no—
339C2×C4—124no—
340C2×C4—124no—
341C2×C4C2×C4×D312yes—
342C2×C4C2×C4×D312yes—
343C2×C4C2×C4×D312yes—
344C2×C4D3×D412yes—
345C2×C4D3×Q812yes—
346C2×C3C2×#11711yescharacteristic
347C2×C3C2×C4×D411yescharacteristic
348C2×C3C2×C4×Q811yescharacteristic
349C2×C3C2×C22⋊Q811yescharacteristic
350C2×C3C2×#12311yescharacteristic
351C2×C3C2×#12511yescharacteristic
352C2×C3C2×#12611yescharacteristic
353D3#38718yesdirect product factor
354C22—34no—
355C22—34no—
356C22—34no—
357C22—34no—
358C22—34no—
359C22—34no—
360C22—34no—
361C22C22×C4×D311yescharacteristic
362C22C2×D3×D411yescharacteristic
363C22C2×D3×Q811yescharacteristic
364C22D3×#4111yescharacteristic
365C22D3×#4111yescharacteristic
366C22D3×#4111yescharacteristic
367C22D3×#4111yescharacteristic
368C4—22no—
369C4—22no—
370C4—22no—
371C4—22no—
372C4—22no—
373C4—41no—
374C4—41no—
375C4—62no—
376C4—62no—
377C4—62no—
378C4—62no—
379C4—62no—
380C4—121no—
381C4—121no—
382C3C2×#38711yescharacteristic, complemented, Sylow
383C2—38no—
384C2D3×#11711yescharacteristic
385C2C4×D3×D411yescharacteristic
386C2C4×D3×Q811yescharacteristic
387C2D3×C22⋊Q811yescharacteristic
388C2D3×#12311yescharacteristic
389C2D3×#12511yescharacteristic
390C2D3×#12611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC3×#387C2
socle, cosocleC23×C3C24
prime radicalC23×D3C23
hypercenter#387D3
hypocenterC3C2×#387
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
4. C3×#387C2semidirect
5. #4980C2semidirect
6. #4978C2semidirect
7. #4933C2semidirect
12. #4655C2semidirect
13. #4654C2semidirect
14. #4653C2semidirect
15. #4652C2semidirect
37. D3×C4⋊C4C4semidirect
65. #387D3direct (N × H)
107. C3×C4⋊C4C2×C4semidirect
110. C4⋊Dic3C2×C4semidirect
113. Dic3⋊C4C2×C4semidirect
114. Dic3⋊C4C2×C4semidirect
256. C4⋊C4C4×D3semidirect
353. D3#387direct (N × H)
382. C3C2×#387semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊C42
C2×C42×D32
C3×#3872
#49802
#49782
#49332
D3×#952
#46552
#46542
#46532
#46522
C2×#3873