Finite Group Databasebeta

← C4×#889 #73622

Subgroups — C4×#889 #73622

Order 384.

484 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#889C211yesmaximal, characteristic
2C3×C4×C4⋊C4C211yesmaximal, characteristic
3#4980C211yesmaximal, characteristic
4#4978C211yesmaximal, characteristic
5#4976C211yesmaximal, characteristic
6C4×C4⋊Dic3C211yesmaximal, characteristic
7C4×Dic3⋊C4C211yesmaximal, characteristic
8C4×Dic3⋊C4C211yesmaximal, characteristic
9C4×Dic3⋊C4C211yesmaximal, characteristic
10C4×Dic3⋊C4C211yesmaximal, characteristic
11C42×Dic3C211yesmaximal, characteristic
12#4653C211yesmaximal, characteristic
13#4652C211yesmaximal, characteristic
14#4650C211yesmaximal, characteristic
15#4647C211yesmaximal, characteristic
16C4×#125—31nomaximal, Sylow
17C2×C3×C4⋊C4C2211yescharacteristic
18C2×C3×C4⋊C4C2211yescharacteristic
19C2×C3×C42C2211yescharacteristic
20C2×C3×C42C2211yescharacteristic
21C2×C3×C42C2211yescharacteristic
22C2×C4⋊Dic3C2211yescharacteristic
23C2×C4⋊Dic3C2211yescharacteristic
24C2×Dic3⋊C4C2211yescharacteristic
25C2×Dic3⋊C4C2211yescharacteristic
26C2×Dic3⋊C4C2211yescharacteristic
27C2×Dic3⋊C4C2211yescharacteristic
28C2×Dic3⋊C4C2211yescharacteristic
29C2×Dic3⋊C4C2211yescharacteristic
30C2×Dic3⋊C4C2211yescharacteristic
31C2×Dic3⋊C4C2211yescharacteristic
32C2×C4×Dic3C2211yescharacteristic
33C2×C4×Dic3C2211yescharacteristic
34C2×C4×Dic3C2211yescharacteristic
35C2×C4×Dic3C2211yescharacteristic
36C2×C4×Dic3C2211yescharacteristic
37C2×C4×Dic3C2211yescharacteristic
38C2×C4×Dic3C2211yescharacteristic
39C2×C4×Dic3C2211yescharacteristic
40#889C418yesdirect product factor
41C3×#95C2211yescharacteristic
42C3×#95C2211yescharacteristic
43C3⋊#95C2211yescharacteristic
44C3⋊#95C2211yescharacteristic
45C3⋊#95C2211yescharacteristic
46C3⋊#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C2×#125—31no—
54#389—31no—
55#389—31no—
56#387—31no—
57#387—31no—
58#387—31no—
59#387—31no—
60#382—31no—
61C4×C4⋊C4—31no—
62C4×C4⋊C4—31no—
63C4×C4⋊C4—31no—
64C4×C4⋊C4—31no—
65C4×C4⋊C4—31no—
66C4×C4⋊C4D311yescharacteristic
67C43—31no—
68C22×C3×C4C2311yescharacteristic
69C22×C3×C4C2311yescharacteristic
70C22×C3×C4C2311yescharacteristic
71C22×C3×C4C2311yescharacteristic
72C22×C3×C4C2311yescharacteristic
73C22×C3×C4C2311yescharacteristic
74C22×C3×C4C2311yescharacteristic
75C22×Dic3C2311yescharacteristic
76C22×Dic3C2311yescharacteristic
77C22×Dic3C2311yescharacteristic
78C22×Dic3C2311yescharacteristic
79C22×Dic3C2311yescharacteristic
80C22×Dic3C2311yescharacteristic
81C22×Dic3C2311yescharacteristic
82C22×Dic3C2311yescharacteristic
83C3×C4⋊C4—22no—
84C3×C4⋊C4C2×C414yes—
85C3×C42—22no—
86C3×C42—22no—
87C3×C42—22no—
88C4⋊Dic3—22no—
89C4⋊Dic3C2×C414yes—
90Dic3⋊C4—22no—
91Dic3⋊C4—22no—
92Dic3⋊C4—22no—
93Dic3⋊C4—22no—
94Dic3⋊C4C2×C414yes—
95Dic3⋊C4C2×C414yes—
96Dic3⋊C4C2×C414yes—
97Dic3⋊C4C2×C414yes—
98C4×Dic3—22no—
99C4×Dic3—22no—
100C4×Dic3—22no—
101C4×Dic3—22no—
102C4×Dic3—22no—
103C4×Dic3—22no—
104C4×Dic3C2×C414yes—
105C4×Dic3Q814yes—
106#125—38no—
107C2×C4⋊C4—31no—
108C2×C4⋊C4—31no—
109C2×C4⋊C4—31no—
110C2×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
118C2×C4⋊C4C2×D311yescharacteristic
119C2×C42—31no—
120C2×C42—31no—
121C2×C42—31no—
122C2×C42—31no—
123C2×C42—31no—
124C2×C42—31no—
125C2×C42—31no—
126C2×C42—31no—
127C2×C42C2×D311yescharacteristic
128C2×C42C2×D311yescharacteristic
129C2×C42C2×D311yescharacteristic
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
142C23×C3C2411yescharacteristic
143C2×C3×C4—21no—
144C2×C3×C4—21no—
145C2×C3×C4—21no—
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×C4C22×C412yes—
158C2×C3×C4C22×C412yes—
159C2×C3×C4C22×C412yes—
160C2×C3×C4C2×Q812yes—
161C2×C3×C4#4112yes—
162C2×C3×C4#4112yes—
163C2×C3×C4#4112yes—
164C2×Dic3—21no—
165C2×Dic3—21no—
166C2×Dic3—21no—
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×Dic3C22×C412yes—
181C2×Dic3C22×C412yes—
182C2×Dic3C22×C412yes—
183C2×Dic3C22×C412yes—
184C2×Dic3C2×Q812yes—
185C2×Dic3C2×Q812yes—
186C2×Dic3#4112yes—
187C2×Dic3#4112yes—
188C22×C4—31no—
189C22×C4—31no—
190C22×C4—31no—
191C22×C4—31no—
192C22×C4—31no—
193C22×C4—31no—
194C22×C4—31no—
195C22×C4—31no—
196C22×C4C22×D311yescharacteristic
197C22×C4C22×D311yescharacteristic
198C22×C4C22×D311yescharacteristic
199C22×C4C22×D311yescharacteristic
200C22×C4C22×D311yescharacteristic
201C22×C4C22×D311yescharacteristic
202C22×C4C22×D311yescharacteristic
203C4⋊C4—22no—
204C4⋊C4—34no—
205C4⋊C4—34no—
206C4⋊C4—34no—
207C4⋊C4—34no—
208C4⋊C4—34no—
209C4⋊C4—62no—
210C4⋊C4—62no—
211C4⋊C4—62no—
212C4⋊C4—62no—
213C4⋊C4—62no—
214C4⋊C4C4×D314yes—
215C42—22no—
216C42—22no—
217C42—22no—
218C42—34no—
219C42—34no—
220C42—62no—
221C42—62no—
222C42—62no—
223C42—62no—
224C42—62no—
225C42—62no—
226C22×C3C23×C411yescharacteristic
227C22×C3C22×Q811yescharacteristic
228C22×C3C2×#4111yescharacteristic
229C22×C3C2×#4111yescharacteristic
230C22×C3C2×#4111yescharacteristic
231C22×C3C2×#4111yescharacteristic
232C22×C3C2×#4111yescharacteristic
233C3×C4—22no—
234C3×C4—22no—
235C3×C4—22no—
236C3×C4—22no—
237C3×C4—41no—
238C3×C4—41no—
239C3×C4#12514yescomplemented
240Dic3—22no—
241Dic3—22no—
242Dic3—22no—
243Dic3—22no—
244Dic3—22no—
245Dic3—41no—
246Dic3—41no—
247Dic3C4×Q814yes—
248C23C23×D311yescharacteristic
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
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—32no—
264C2×C4—32no—
265C2×C4—32no—
266C2×C4—32no—
267C2×C4—32no—
268C2×C4—32no—
269C2×C4—32no—
270C2×C4—32no—
271C2×C4—61no—
272C2×C4—61no—
273C2×C4—61no—
274C2×C4—61no—
275C2×C4—61no—
276C2×C4—61no—
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×C4C2×C4×D312yes—
288C2×C4C2×C4×D312yes—
289C2×C4C2×C4×D312yes—
290C2×C4#23512yes—
291C2×C4#23512yes—
292C2×C4#23712yes—
293C2×C4D3×Q812yes—
294C2×C3C2×C4×Q811yescharacteristic
295C2×C3C4×#4111yescharacteristic
296C2×C3C4×#4111yescharacteristic
297C2×C3C2×#12511yescharacteristic
298C2×C3#52911yescharacteristic
299C2×C3#52911yescharacteristic
300C2×C3#53311yescharacteristic
301C22C22×C4×D311yescharacteristic
302C22C2×#23511yescharacteristic
303C22C2×#23511yescharacteristic
304C22C2×#23711yescharacteristic
305C22C2×D3×Q811yescharacteristic
306C22D3×#4111yescharacteristic
307C22D3×#4111yescharacteristic
308C4—22no—
309C4—22no—
310C4—22no—
311C4—22no—
312C4—34no—
313C4—41no—
314C4—41no—
315C4—62no—
316C4—62no—
317C4—62no—
318C4—62no—
319C4—62no—
320C4—121no—
321C4—121no—
322C4#88914yesdirect product factor
323C3C4×#12511yescharacteristic, complemented, Sylow
324C2C4×#23511yescharacteristic
325C2C2×#88911yescharacteristic
326C2#552811yescharacteristic
327C2C4×#23711yescharacteristic
328C2#553811yescharacteristic
329C2C4×D3×Q811yescharacteristic
330C2#557811yescharacteristic
subgroupG/H
centerC22×C4C22×D3
commutatorC22×C3C23×C4
FrattiniC23C23×D3
FittingC3×C4×C4⋊C4C2
socle, prime radical, cosocleC23×C3C24
hypercenterC4×C4⋊C4D3
hypocenterC3C4×#125
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
40. #889C4direct (N × H)
239. C3×C4#125semidirect
322. C4#889direct (N × H)
323. C3C4×#125semidirect

Maximal subgroups

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

subgroupindex
C2×#8892
C3×C4×C4⋊C42
#49802
#49782
#49762
C4×C4⋊Dic32
C4×Dic3⋊C42
C42×Dic32
#46532
#46522
#46502
#46472
C4×#1253