Finite Group Databasebeta

← #76001

Subgroups — #76001

Order 384.

492 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#889C211yesmaximal, characteristic, complemented
2C2×#872C211yesmaximal, characteristic
3C3×#389C211yesmaximal, characteristic, complemented
4#4994C211yesmaximal, characteristic
5#4994C211yesmaximal, characteristic
6#4993C211yesmaximal, characteristic
7#4993C211yesmaximal, characteristic
8#4976C211yesmaximal, characteristic, complemented
9#4976C211yesmaximal, characteristic, complemented
10#4975C211yesmaximal, characteristic, complemented
11#4933C211yesmaximal, characteristic, complemented
12#4667C211yesmaximal, characteristic
13#4666C211yesmaximal, characteristic
14#4655C211yesmaximal, characteristic, complemented
15#4647C211yesmaximal, characteristic, complemented
16#2441—31nomaximal, Sylow
17C22×C4×D3C2211yescharacteristic
18C2×C3×C4⋊C4C2211yescharacteristic
19C2×C3×C4⋊C4C2211yescharacteristic
20C2×C3×C4⋊C4C2211yescharacteristic
21C2×C3×C4⋊C4C2211yescharacteristic
22C2×C3×C42C2211yescharacteristic
23C2×(C2×D3)⋊C4C2211yescharacteristic
24C2×(C2×D3)⋊C4C2211yescharacteristic
25C2×(C2×D3)⋊C4C2211yescharacteristic
26C2×(C2×D3)⋊C4C2211yescharacteristic
27C2×(C2×D3)⋊C4C2211yescharacteristic
28C2×(C2×D3)⋊C4C2211yescharacteristic
29C2×C4⋊Dic3C2211yescharacteristic
30C2×C4⋊Dic3C2211yescharacteristic
31C2×Dic3⋊C4C2211yescharacteristic
32C2×Dic3⋊C4C2211yescharacteristic
33C2×Dic3⋊C4C2211yescharacteristic
34C2×Dic3⋊C4C2211yescharacteristic
35C2×Dic3⋊C4C2211yescharacteristic
36C2×Dic3⋊C4C2211yescharacteristic
37C2×Dic3⋊C4C2211yescharacteristic
38C2×Dic3⋊C4C2211yescharacteristic
39C2×Dic3⋊C4C2211yescharacteristic
40C2×Dic3⋊C4C2211yescharacteristic
41C2×C4×Dic3C2211yescharacteristic
42C2×C4×Dic3C2211yescharacteristic
43C2×C4×Dic3C2211yescharacteristic
44#889—24no—
45#872—24no—
46C3×#95C2211yescharacteristic
47C3×#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C2×#125—31no—
55C2×#117—31no—
56#399—31no—
57#399—31no—
58#396—31no—
59#396—31no—
60#389—31no—
61#389—31no—
62#389—31no—
63#389D311yescharacteristic, complemented
64#387—31no—
65#387—31no—
66#384—31no—
67#380—31no—
68C4×C22⋊C4—31no—
69C23×D3C2311yescharacteristic
70C22×C3×C4C2311yescharacteristic
71C22×C3×C4C2311yescharacteristic
72C22×C3×C4C2311yescharacteristic
73C22×C3×C4C2311yescharacteristic
74C22×C3×C4C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×Dic3C2311yescharacteristic
78C22×Dic3C2311yescharacteristic
79C22×Dic3C2311yescharacteristic
80C22×Dic3C2311yescharacteristic
81C22×Dic3C2311yescharacteristic
82C22×Dic3C2311yescharacteristic
83C22×Dic3C2311yescharacteristic
84C2×C4×D3—22no—
85C2×C4×D3—22no—
86C2×C4×D3Q814yes—
87C3×C4⋊C4—22no—
88C3×C4⋊C4—22no—
89C3×C4⋊C4—41no—
90C3×C4⋊C4—41no—
91C3×C42—22no—
92(C2×D3)⋊C4—22no—
93(C2×D3)⋊C4—22no—
94(C2×D3)⋊C4—22no—
95(C2×D3)⋊C4—22no—
96(C2×D3)⋊C4—41no—
97(C2×D3)⋊C4—41no—
98C4⋊Dic3—22no—
99C4⋊Dic3—41no—
100Dic3⋊C4—22no—
101Dic3⋊C4—22no—
102Dic3⋊C4—22no—
103Dic3⋊C4—22no—
104Dic3⋊C4—22no—
105Dic3⋊C4—22no—
106Dic3⋊C4—22no—
107Dic3⋊C4—22no—
108Dic3⋊C4—41no—
109Dic3⋊C4D414yes—
110C4×Dic3—22no—
111C4×Dic3—22no—
112C4×Dic3—22no—
113C23×C4—31no—
114#125—64no—
115#117—64no—
116C2×C4⋊C4—31no—
117C2×C4⋊C4—31no—
118C2×C4⋊C4—31no—
119C2×C4⋊C4—31no—
120C2×C4⋊C4—31no—
121C2×C4⋊C4—31no—
122C2×C4⋊C4—31no—
123C2×C4⋊C4—31no—
124C2×C4⋊C4—31no—
125C2×C4⋊C4—31no—
126C2×C4⋊C4—31no—
127C2×C4⋊C4—31no—
128C2×C4⋊C4C2×D311yescharacteristic
129C2×C4⋊C4C2×D311yescharacteristic
130C2×C4⋊C4C2×D311yescharacteristic
131C2×C4⋊C4C2×D311yescharacteristic
132C2×C22⋊C4—31no—
133C2×C22⋊C4—31no—
134C2×C22⋊C4—31no—
135C2×C22⋊C4—31no—
136C2×C22⋊C4—31no—
137C2×C22⋊C4—31no—
138C2×C42—31no—
139C2×C42—31no—
140C2×C42—31no—
141C2×C42C2×D311yescharacteristic
142#95—31no—
143#95—31no—
144#95—31no—
145#95—31no—
146#95—31no—
147#95—31no—
148#95C2×D311yescharacteristic
149#95C2×D311yescharacteristic
150C23×C3C2411yescharacteristic
151C22×D3—21no—
152C22×D3—21no—
153C22×D3—21no—
154C22×D3—21no—
155C22×D3—21no—
156C22×D3—21no—
157C22×D3C2×Q812yes—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
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×C4C2×D412yes—
177C2×C3×C4C2×Q812yes—
178C2×C3×C4#4112yes—
179C2×Dic3—21no—
180C2×Dic3—21no—
181C2×Dic3—21no—
182C2×Dic3—21no—
183C2×Dic3—21no—
184C2×Dic3—21no—
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×Dic3C2×D412yes—
196C2×Dic3C2×D412yes—
197C2×Dic3C2×Q812yes—
198C2×Dic3#4112yes—
199C2×Dic3#4112yes—
200C4×D3—28no—
201C24—31no—
202C22×C4—31no—
203C22×C4—31no—
204C22×C4—31no—
205C22×C4—34no—
206C22×C4—31no—
207C22×C4—31no—
208C22×C4—31no—
209C22×C4—31no—
210C22×C4—62no—
211C22×C4—62no—
212C22×C4C22×D311yescharacteristic
213C22×C4C22×D311yescharacteristic
214C22×C4C22×D311yescharacteristic
215C22×C4C22×D311yescharacteristic
216C22×C4C22×D311yescharacteristic
217C22×C4C22×D311yescharacteristic
218C22×C4C22×D311yescharacteristic
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—34no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—62no—
225C4⋊C4—62no—
226C4⋊C4—62no—
227C4⋊C4—62no—
228C4⋊C4—62no—
229C4⋊C4—62no—
230C4⋊C4—62no—
231C4⋊C4—62no—
232C4⋊C4—62no—
233C4⋊C4—121no—
234C4⋊C4—121no—
235C22⋊C4—62no—
236C22⋊C4—62no—
237C22⋊C4—62no—
238C22⋊C4—62no—
239C22⋊C4—121no—
240C22⋊C4—121no—
241C42—22no—
242C42—62no—
243C42—62no—
244C42—62no—
245C22×C3C22×D411yescharacteristic
246C22×C3C22×Q811yescharacteristic
247C22×C3C2×#4111yescharacteristic
248C22×C3C2×#4111yescharacteristic
249C22×C3C2×#4111yescharacteristic
250C22×C3H(5,𝔽2)11yescharacteristic
251C22×C32−1+411yescharacteristic
252C2×D3—22no—
253C2×D3—22no—
254C2×D3—22no—
255C2×D3—41no—
256C2×D3—41no—
257C2×D3—41no—
258C2×D3—41no—
259C3×C4—22no—
260C3×C4—22no—
261C3×C4—22no—
262C3×C4—41no—
263C3×C4—41no—
264C3×C4—41no—
265C3×C4—41no—
266Dic3—22no—
267Dic3—22no—
268Dic3—41no—
269Dic3—41no—
270Dic3—41no—
271Dic3—41no—
272Dic3C22⋊Q814yes—
273C23—32no—
274C23—61no—
275C23—61no—
276C23—61no—
277C23—61no—
278C23—61no—
279C23—61no—
280C23C23×D311yescharacteristic
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—32no—
300C2×C4—32no—
301C2×C4—32no—
302C2×C4—32no—
303C2×C4—32no—
304C2×C4—68no—
305C2×C4—61no—
306C2×C4—61no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—61no—
318C2×C4—61no—
319C2×C4—61no—
320C2×C4—61no—
321C2×C4#23512yes—
322C2×C4D3×D412yes—
323C2×C4D3×Q812yes—
324C2×C3C2×C22⋊Q811yescharacteristic
325C2×C3#53311yescharacteristic
326C2×C3#54411yescharacteristic
327C2×C3#54711yescharacteristic
328C2×C3#55011yescharacteristic
329C2×C3#55211yescharacteristic
330C2×C3#55311yescharacteristic
331D3—42no—
332C22—62no—
333C22—62no—
334C22—62no—
335C22—121no—
336C22—121no—
337C22—121no—
338C22—121no—
339C22C2×#23511yescharacteristic
340C22C2×D3×D411yescharacteristic
341C22#100411yescharacteristic
342C22C2×D3×Q811yescharacteristic
343C22#100711yescharacteristic
344C22D3×#4111yescharacteristic
345C22D3×#4111yescharacteristic
346C4—22no—
347C4—22no—
348C4—22no—
349C4—34no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—62no—
355C4—62no—
356C4—121no—
357C4—121no—
358C4—121no—
359C4—121no—
360C3#244111yescharacteristic, complemented, Sylow
361C2—122no—
362C2#550711yescharacteristic
363C2#554011yescharacteristic
364C2#557811yescharacteristic
365C2#559911yescharacteristic
366C2D3×C22⋊Q811yescharacteristic
367C2#569311yescharacteristic
368C2#572911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#389C2
prime radicalC23×D3C23
hypercenter#389D3
hypocenterC3#2441
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#889C2semidirect
3. C3×#389C2semidirect
8. #4976C2semidirect
9. #4976C2semidirect
10. #4975C2semidirect
11. #4933C2semidirect
14. #4655C2semidirect
15. #4647C2semidirect
63. #389D3semidirect
360. C3#2441semidirect

Maximal subgroups

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

subgroupindex
C2×#8892
C2×#8722
C3×#3892
#49942
#49932
#49762
#49752
#49332
#46672
#46662
#46552
#46472
#24413