Finite Group Databasebeta

← C4×#878 #73442

Subgroups — C4×#878 #73442

Order 384.

656 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic3C211yesmaximal, characteristic
2C2×#878C211yesmaximal, characteristic
3C2×C4×Dic6C211yesmaximal, characteristic, complemented
4C3×C4×C22⋊C4C211yesmaximal, characteristic
5C4×#217C211yesmaximal, characteristic
6#4950C211yesmaximal, characteristic
7#4946C211yesmaximal, characteristic
8#4942C211yesmaximal, characteristic
9C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
10C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
11C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
12#4655C211yesmaximal, characteristic, complemented
13#4654C211yesmaximal, characteristic, complemented
14#4647C211yesmaximal, characteristic, complemented
15#4646C211yesmaximal, characteristic, complemented
16C4×C22⋊Q8—31nomaximal, Sylow
17C23×C3×C4C2211yescharacteristic
18C23×Dic3C2211yescharacteristic
19C23×Dic3C2211yescharacteristic
20C22×Dic6C2211yescharacteristic
21C2×C3×C22⋊C4C2211yescharacteristic
22C2×C3×C22⋊C4C2211yescharacteristic
23C2×C3×C42C2211yescharacteristic
24C2×C3×C42C2211yescharacteristic
25C2×#217C2211yescharacteristic
26C2×#217C2211yescharacteristic
27C2×C4⋊Dic3C2211yescharacteristic
28C2×C4⋊Dic3C2211yescharacteristic
29C2×C4⋊Dic3C2211yescharacteristic
30C2×Dic3⋊C4C2211yescharacteristic
31C2×Dic3⋊C4C2211yescharacteristic
32C2×Dic3⋊C4C2211yescharacteristic
33C2×Dic3⋊C4C2211yescharacteristic
34C2×Dic3⋊C4C2211yescharacteristic
35C2×Dic3⋊C4C2211yescharacteristic
36C2×C4×Dic3—24no—
37C2×C4×Dic3C2211yescharacteristic
38C2×C4×Dic3C2211yescharacteristic
39C2×C4×Dic3C2211yescharacteristic
40C2×C4×Dic3C2211yescharacteristic
41C2×C4×Dic3C2211yescharacteristic
42C2×C4×Dic3C2211yescharacteristic
43#878C418yesdirect product factor
44C4×Dic6—24no—
45C3×#95C2211yescharacteristic
46C3×#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C2×C22⋊Q8—31no—
56C2×C4×Q8—31no—
57C22×C42—31no—
58#391—31no—
59#389—31no—
60#387—31no—
61#387—31no—
62#385—31no—
63#385—31no—
64#380—31no—
65C4×C4⋊C4—31no—
66C4×C4⋊C4—31no—
67C4×C4⋊C4—31no—
68C4×C22⋊C4—31no—
69C4×C22⋊C4D311yescharacteristic
70C24×C3C2311yescharacteristic
71C22×C3×C4—22no—
72C22×C3×C4—22no—
73C22×C3×C4Q814yescomplemented
74C22×C3×C4C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×Dic3—22no—
81C22×Dic3—22no—
82C22×Dic3—22no—
83C22×Dic3—22no—
84C22×Dic3—22no—
85C22×Dic3C2×C414yes—
86C22×Dic3C2311yescharacteristic
87C22×Dic3C2311yescharacteristic
88C22×Dic3C2311yescharacteristic
89C22×Dic3C2311yescharacteristic
90C22×Dic3C2311yescharacteristic
91C22×Dic3C2311yescharacteristic
92C22×Dic3C2311yescharacteristic
93C22×Dic3C2311yescharacteristic
94C2×Dic6—22no—
95C2×Dic6—22no—
96C2×Dic6C2×C414yescomplemented
97C3×C22⋊C4—22no—
98C3×C22⋊C4C2×C414yes—
99C3×C42—22no—
100C3×C42—22no—
101#217—22no—
102#217C2×C414yes—
103C4⋊Dic3—22no—
104C4⋊Dic3—22no—
105C4⋊Dic3C2×C414yescomplemented
106Dic3⋊C4—22no—
107Dic3⋊C4—22no—
108Dic3⋊C4—22no—
109Dic3⋊C4—22no—
110Dic3⋊C4C2×C414yescomplemented
111Dic3⋊C4C2×C414yescomplemented
112C4×Dic3—22no—
113C4×Dic3—22no—
114C4×Dic3—22no—
115C4×Dic3—22no—
116C4×Dic3—22no—
117C4×Dic3D414yes—
118C22×Q8—31no—
119C23×C4—31no—
120C23×C4—31no—
121C23×C4C2×D311yescharacteristic
122C22⋊Q8—38no—
123C4×Q8—64no—
124C2×C4⋊C4—31no—
125C2×C4⋊C4—31no—
126C2×C4⋊C4—31no—
127C2×C4⋊C4—31no—
128C2×C4⋊C4—31no—
129C2×C4⋊C4—31no—
130C2×C4⋊C4—31no—
131C2×C4⋊C4—31no—
132C2×C4⋊C4—31no—
133C2×C22⋊C4—31no—
134C2×C22⋊C4—31no—
135C2×C22⋊C4C2×D311yescharacteristic
136C2×C22⋊C4C2×D311yescharacteristic
137C2×C42—31no—
138C2×C42—31no—
139C2×C42—31no—
140C2×C42—31no—
141C2×C42—31no—
142C2×C42—31no—
143C2×C42—64no—
144C2×C42C2×D311yescharacteristic
145C2×C42C2×D311yescharacteristic
146#95—31no—
147#95—31no—
148#95—31no—
149#95—31no—
150#95—31no—
151#95—31no—
152#95—31no—
153#95—31no—
154#95C2×D311yescharacteristic
155#95C2×D311yescharacteristic
156C23×C3—21no—
157C23×C3—21no—
158C23×C3—21no—
159C23×C3—21no—
160C23×C3C22×C412yes—
161C23×C3C2×Q812yes—
162C23×C3#4112yes—
163C23×C3C2411yescharacteristic
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—28no—
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×C4C22×C412yes—
178C2×C3×C4C22×C412yes—
179C2×C3×C4C2×D412yes—
180C2×C3×C4C2×Q812yes—
181C2×C3×C4C2×Q812yes—
182C2×C3×C4#4112yes—
183C2×Dic3—28no—
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—28no—
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×Dic3C22×C412yes—
205C2×Dic3C2×D412yes—
206C2×Dic3C2×D412yes—
207C2×Dic3#4112yes—
208C2×Dic3#4112yes—
209Dic6—28no—
210C24C22×D311yescharacteristic
211C2×Q8—34no—
212C2×Q8—62no—
213C2×Q8—62no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—31no—
217C22×C4—34no—
218C22×C4—31no—
219C22×C4—31no—
220C22×C4—31no—
221C22×C4—31no—
222C22×C4—31no—
223C22×C4—31no—
224C22×C4—31no—
225C22×C4—62no—
226C22×C4—62no—
227C22×C4—62no—
228C22×C4—62no—
229C22×C4—62no—
230C22×C4Dic614yescomplemented
231C22×C4C22×D311yescharacteristic
232C22×C4C22×D311yescharacteristic
233C22×C4C22×D311yescharacteristic
234C22×C4C22×D311yescharacteristic
235C22×C4C22×D311yescharacteristic
236C22×C4C22×D311yescharacteristic
237C4⋊C4—34no—
238C4⋊C4—34no—
239C4⋊C4—34no—
240C4⋊C4—62no—
241C4⋊C4—62no—
242C4⋊C4—62no—
243C4⋊C4—62no—
244C4⋊C4—62no—
245C4⋊C4—62no—
246C22⋊C4—22no—
247C22⋊C4—34no—
248C22⋊C4—62no—
249C22⋊C4C4×D314yes—
250C42—22no—
251C42—22no—
252C42—34no—
253C42—62no—
254C42—62no—
255C42—62no—
256C42—62no—
257C42—62no—
258C22×C3—22no—
259C22×C3—22no—
260C22×C3—22no—
261C22×C3—22no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3C4×Q814yescomplemented
265C22×C3C23×C411yescharacteristic
266C22×C3C22×D411yescharacteristic
267C22×C3C22×Q811yescharacteristic
268C22×C3C2×#4111yescharacteristic
269C22×C3C2×#4111yescharacteristic
270C22×C3C2×#4111yescharacteristic
271C22×C3C2×#4111yescharacteristic
272C3×C4—22no—
273C3×C4—22no—
274C3×C4—22no—
275C3×C4—41no—
276C3×C4—41no—
277C3×C4C22⋊Q814yescomplemented
278Dic3—22no—
279Dic3—22no—
280Dic3—22no—
281Dic3—22no—
282Dic3—22no—
283Dic3—41no—
284Dic3—41no—
285Dic3C4×D414yes—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23C2×Dic612yes—
291C23C2×C4×D312yes—
292C23#23512yes—
293C23C23×D311yescharacteristic
294Q8—68no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—28no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—32no—
309C2×C4—32no—
310C2×C4—32no—
311C2×C4—32no—
312C2×C4—32no—
313C2×C4—32no—
314C2×C4—32no—
315C2×C4—32no—
316C2×C4—68no—
317C2×C4—68no—
318C2×C4—61no—
319C2×C4—61no—
320C2×C4—61no—
321C2×C4—61no—
322C2×C4—61no—
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×C4C2×Dic612yes—
335C2×C4C2×Dic612yes—
336C2×C4C2×C4×D312yes—
337C2×C4C2×C4×D312yes—
338C2×C4D3×D412yes—
339C2×C4#23712yes—
340C2×C3—24no—
341C2×C3C2×C4×D411yescharacteristic
342C2×C3C2×C4×Q811yescharacteristic
343C2×C3C4×#4111yescharacteristic
344C2×C3C2×C22⋊Q811yescharacteristic
345C2×C3#52511yescharacteristic
346C2×C3#52911yescharacteristic
347C2×C3#53311yescharacteristic
348C22—22no—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22C4×Dic614yescomplemented
355C22C22×Dic611yescharacteristic
356C22C22×C4×D311yescharacteristic
357C22C2×#23511yescharacteristic
358C22C2×D3×D411yescharacteristic
359C22C2×#23711yescharacteristic
360C22D3×#4111yescharacteristic
361C22D3×#4111yescharacteristic
362C4—22no—
363C4—22no—
364C4—22no—
365C4—34no—
366C4—41no—
367C4—41no—
368C4—62no—
369C4—62no—
370C4—62no—
371C4—62no—
372C4—62no—
373C4—121no—
374C4—121no—
375C4#87814yesdirect product factor
376C3C4×C22⋊Q811yescharacteristic, complemented, Sylow
377C2—24no—
378C2C2×C4×Dic611yescharacteristic
379C2C2×#87811yescharacteristic
380C2#551711yescharacteristic
381C2C4×#23711yescharacteristic
382C2#553811yescharacteristic
383C2C4×D3×D411yescharacteristic
384C2#554711yescharacteristic
subgroupG/H
centerC22×C4C22×D3
commutatorC22×C3C23×C4
FrattiniC23C23×D3
FittingC3×C4×C22⋊C4C2
socle, cosocleC23×C3C24
prime radicalC24×C3C23
hypercenterC4×C22⋊C4D3
hypocenterC3C4×C22⋊Q8
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic6C2semidirect
9. C4×C4⋊Dic3C2semidirect
10. C4×Dic3⋊C4C2semidirect
11. C4×Dic3⋊C4C2semidirect
12. #4655C2semidirect
13. #4654C2semidirect
14. #4647C2semidirect
15. #4646C2semidirect
43. #878C4direct (N × H)
73. C22×C3×C4Q8semidirect
96. C2×Dic6C2×C4semidirect
105. C4⋊Dic3C2×C4semidirect
110. Dic3⋊C4C2×C4semidirect
111. Dic3⋊C4C2×C4semidirect
230. C22×C4Dic6semidirect
264. C22×C3C4×Q8semidirect
277. C3×C4C22⋊Q8semidirect
354. C22C4×Dic6semidirect
375. C4#878direct (N × H)
376. C3C4×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic32
C2×#8782
C2×C4×Dic62
C3×C4×C22⋊C42
C4×#2172
#49502
#49462
#49422
C4×C4⋊Dic32
C4×Dic3⋊C42
#46552
#46542
#46472
#46462
C4×C22⋊Q83