Finite Group Databasebeta

← #76568

Subgroups — #76568

Order 384.

432 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#944C211yesmaximal, characteristic
2C2×#889C211yesmaximal, characteristic
3C3×#391C211yesmaximal, characteristic
4#5230C211yesmaximal, characteristic
5#4985C211yesmaximal, characteristic
6#4933C211yesmaximal, characteristic
7#4928C211yesmaximal, characteristic
8#4658C211yesmaximal, characteristic
9#4657C211yesmaximal, characteristic
10#4657C211yesmaximal, characteristic
11#4656C211yesmaximal, characteristic
12#4654C211yesmaximal, characteristic
13#4654C211yesmaximal, characteristic
14#4652C211yesmaximal, characteristic
15#4646C211yesmaximal, characteristic
16#2713—31nomaximal, Sylow
17C22×C3×Q8C2211yescharacteristic
18C22×Dic6C2211yescharacteristic
19C2×C3×C4⋊C4C2211yescharacteristic
20C2×C3×C42C2211yescharacteristic
21#944—24no—
22C2×C4⋊Dic3C2211yescharacteristic
23C2×C4⋊Dic3C2211yescharacteristic
24C2×C4⋊Dic3C2211yescharacteristic
25C2×Dic3⋊C4C2211yescharacteristic
26C2×Dic3⋊C4C2211yescharacteristic
27C2×Dic3⋊C4C2211yescharacteristic
28C2×Dic3⋊C4C2211yescharacteristic
29C2×Dic3⋊C4C2211yescharacteristic
30C2×Dic3⋊C4C2211yescharacteristic
31C2×Dic3⋊C4C2211yescharacteristic
32C2×Dic3⋊C4C2211yescharacteristic
33C2×Dic3⋊C4C2211yescharacteristic
34C2×Dic3⋊C4C2211yescharacteristic
35C2×C4×Dic3C2211yescharacteristic
36C2×C4×Dic3C2211yescharacteristic
37#889—24no—
38C3×#95C2211yescharacteristic
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
54C2×C4⋊Q8—31no—
55C2×#125—31no—
56#400—31no—
57#400—31no—
58#398—31no—
59#398—31no—
60#395—31no—
61#395—31no—
62#391—31no—
63#391D311yescharacteristic
64#389—31no—
65#387—31no—
66#387—31no—
67#387—31no—
68#387—31no—
69C2×C3×Q8—22no—
70C2×C3×Q8—22no—
71C2×C3×Q8—41no—
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
85C22×Dic3C2311yescharacteristic
86C22×Dic3C2311yescharacteristic
87C2×Dic6—22no—
88C2×Dic6—22no—
89C2×Dic6—41no—
90C3×C4⋊C4—22no—
91C3×C42—41no—
92C4⋊Dic3—22no—
93C4⋊Dic3—41no—
94C4⋊Dic3Q814yescomplemented
95Dic3⋊C4—22no—
96Dic3⋊C4—22no—
97Dic3⋊C4—22no—
98Dic3⋊C4—22no—
99Dic3⋊C4—22no—
100Dic3⋊C4—22no—
101Dic3⋊C4—22no—
102Dic3⋊C4—41no—
103Dic3⋊C4—41no—
104Dic3⋊C4D414yes—
105C4×Dic3—22no—
106C4×Dic3—22no—
107C22×Q8—31no—
108C22×Q8C2×D311yescharacteristic
109C4⋊Q8—64no—
110#125—64no—
111C2×C4⋊C4—31no—
112C2×C4⋊C4—31no—
113C2×C4⋊C4—31no—
114C2×C4⋊C4—31no—
115C2×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
125C2×C42—31no—
126C2×C42—31no—
127C2×C42C2×D311yescharacteristic
128#95—31no—
129#95—31no—
130#95—31no—
131#95—31no—
132#95—31no—
133#95—31no—
134#95—31no—
135#95—31no—
136#95—31no—
137#95—31no—
138#95—31no—
139#95—31no—
140#95C2×D311yescharacteristic
141#95C2×D311yescharacteristic
142#95C2×D311yescharacteristic
143#95C2×D311yescharacteristic
144C23×C3C2411yescharacteristic
145C3×Q8—44no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
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×C4C2×D412yes—
165C2×C3×C4C2×Q812yes—
166C2×C3×C4#4112yes—
167C2×Dic3—21no—
168C2×Dic3—21no—
169C2×Dic3—21no—
170C2×Dic3—21no—
171C2×Dic3—21no—
172C2×Dic3—21no—
173C2×Dic3—21no—
174C2×Dic3—21no—
175C2×Dic3—21no—
176C2×Dic3—21no—
177C2×Dic3—21no—
178C2×Dic3—21no—
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×Dic3C2×D412yes—
188C2×Dic3C2×D412yes—
189C2×Dic3C2×Q812yes—
190C2×Dic3C2×Q812yes—
191Dic6—44no—
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—41no—
195C2×Q8—62no—
196C2×Q8—62no—
197C2×Q8—121no—
198C22×C4—31no—
199C22×C4—31no—
200C22×C4—31no—
201C22×C4—31no—
202C22×C4—31no—
203C22×C4—31no—
204C22×C4—31no—
205C22×C4—31no—
206C22×C4C22×D311yescharacteristic
207C22×C4C22×D311yescharacteristic
208C22×C4C22×D311yescharacteristic
209C22×C4C22×D311yescharacteristic
210C22×C4C22×D311yescharacteristic
211C22×C4C22×D311yescharacteristic
212C22×C4C22×D311yescharacteristic
213C4⋊C4—22no—
214C4⋊C4—34no—
215C4⋊C4—34no—
216C4⋊C4—62no—
217C4⋊C4—62no—
218C4⋊C4—62no—
219C4⋊C4—62no—
220C4⋊C4—62no—
221C4⋊C4—62no—
222C4⋊C4—62no—
223C4⋊C4—62no—
224C4⋊C4—121no—
225C4⋊C4—121no—
226C4⋊C4—121no—
227C42—41no—
228C42—62no—
229C42—62no—
230C22×C3C22×D411yescharacteristic
231C22×C3C22×Q811yescharacteristic
232C22×C3C2×#4111yescharacteristic
233C22×C3H(5,𝔽2)11yescharacteristic
234C22×C32−1+411yescharacteristic
235C22×C32−1+411yescharacteristic
236C22×C32−1+411yescharacteristic
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—22no—
240C3×C4—41no—
241C3×C4—41no—
242C3×C4—41no—
243C3×C4—41no—
244Dic3—22no—
245Dic3—22no—
246Dic3—22no—
247Dic3—22no—
248Dic3—41no—
249Dic3—41no—
250Dic3—41no—
251Dic3—41no—
252C23C23×D311yescharacteristic
253Q8—44no—
254Q8—124no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—32no—
274C2×C4—32no—
275C2×C4—32no—
276C2×C4—32no—
277C2×C4—61no—
278C2×C4—61no—
279C2×C4—61no—
280C2×C4—61no—
281C2×C4—61no—
282C2×C4—61no—
283C2×C4—61no—
284C2×C4—61no—
285C2×C4—61no—
286C2×C4—61no—
287C2×C4—61no—
288C2×C4—61no—
289C2×C4—61no—
290C2×C4—61no—
291C2×C4—61no—
292C2×C4—61no—
293C2×C4—61no—
294C2×C4—61no—
295C2×C4—61no—
296C2×C4—61no—
297C2×C4#23512yes—
298C2×C4D3×D412yes—
299C2×C4D3×Q812yes—
300C2×C3#53611yescharacteristic
301C2×C3#54111yescharacteristic
302C2×C3#54411yescharacteristic
303C2×C3#54611yescharacteristic
304C2×C3D4×Q811yescharacteristic
305C2×C3#55711yescharacteristic
306C2×C3#56311yescharacteristic
307C22C2×#23511yescharacteristic
308C22C2×D3×D411yescharacteristic
309C22#100411yescharacteristic
310C22C2×D3×Q811yescharacteristic
311C22#100711yescharacteristic
312C22#101011yescharacteristic
313C22#101011yescharacteristic
314C4—22no—
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—62no—
322C4—62no—
323C4—62no—
324C4—62no—
325C4—121no—
326C4—121no—
327C4—121no—
328C4—121no—
329C3#271311yescharacteristic, complemented, Sylow
330C2#549011yescharacteristic
331C2#556711yescharacteristic
332C2#558311yescharacteristic
333C2#562311yescharacteristic
334C2#564611yescharacteristic
335C2#567511yescharacteristic
336C2#572711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#391C2
hypercenter#391D3
hypocenterC3#2713
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
94. C4⋊Dic3Q8semidirect
329. C3#2713semidirect

Maximal subgroups

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

subgroupindex
C2×#9442
C2×#8892
C3×#3912
#52302
#49852
#49332
#49282
#46582
#46572
#46562
#46542
#46522
#46462
#27133