Finite Group Databasebeta

← C4×#894 #73757

Subgroups — C4×#894 #73757

Order 384.

688 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#894C211yesmaximal, characteristic
2C2×C4×D12C211yesmaximal, characteristic
3C2×C42×D3C211yesmaximal, characteristic, complemented
4C3×C4×C4⋊C4C211yesmaximal, characteristic, complemented
5#4990C211yesmaximal, characteristic, complemented
6#4989C211yesmaximal, characteristic, complemented
7#4980C211yesmaximal, characteristic, complemented
8C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
9C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
12#4669C211yesmaximal, characteristic, complemented
13#4665C211yesmaximal, characteristic
14#4664C211yesmaximal, characteristic, complemented
15#4655C211yesmaximal, characteristic, complemented
16C4×#123—31nomaximal, Sylow
17C22×D12C2211yescharacteristic
18C22×C4×D3C2211yescharacteristic
19C22×C4×D3C2211yescharacteristic
20C22×C4×D3C2211yescharacteristic
21C22×C4×D3C2211yescharacteristic
22C2×C3×C4⋊C4C2211yescharacteristic
23C2×C3×C4⋊C4C2211yescharacteristic
24C2×C3×C42C2211yescharacteristic
25C2×C3×C42C2211yescharacteristic
26C2×C3×C42C2211yescharacteristic
27C2×(C2×D3)⋊C4C2211yescharacteristic
28C2×(C2×D3)⋊C4C2211yescharacteristic
29C2×(C2×D3)⋊C4C2211yescharacteristic
30C2×(C2×D3)⋊C4C2211yescharacteristic
31C2×(C2×D3)⋊C4C2211yescharacteristic
32C2×(C2×D3)⋊C4C2211yescharacteristic
33C2×(C2×D3)⋊C4C2211yescharacteristic
34C2×(C2×D3)⋊C4C2211yescharacteristic
35C2×C4⋊Dic3C2211yescharacteristic
36C2×Dic3⋊C4C2211yescharacteristic
37C2×Dic3⋊C4C2211yescharacteristic
38C2×C4×Dic3C2211yescharacteristic
39C2×C4×Dic3C2211yescharacteristic
40C2×C4×Dic3C2211yescharacteristic
41C2×C4×Dic3C2211yescharacteristic
42#894C418yesdirect product factor
43C4×D12—24no—
44C42×D3—24no—
45C3×#95C2211yescharacteristic
46C3×#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C2×#123—31no—
56C2×C4×D4—31no—
57C22×C42—31no—
58#388—31no—
59#388—31no—
60#387—31no—
61#387—31no—
62#386—31no—
63#385—31no—
64#381—31no—
65C4×C4⋊C4—31no—
66C4×C4⋊C4D311yescharacteristic, complemented
67C4×C22⋊C4—31no—
68C4×C22⋊C4—31no—
69C4×C22⋊C4—31no—
70C23×D3C2311yescharacteristic
71C23×D3C2311yescharacteristic
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
85C2×D12—22no—
86C2×D12—22no—
87C2×D12C2×C414yes—
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×D3C2×C414yescomplemented
99C2×C4×D3D414yes—
100C3×C4⋊C4—22no—
101C3×C4⋊C4C2×C414yescomplemented
102C3×C42—22no—
103C3×C42—22no—
104C3×C42—22no—
105(C2×D3)⋊C4—22no—
106(C2×D3)⋊C4—22no—
107(C2×D3)⋊C4—22no—
108(C2×D3)⋊C4—22no—
109(C2×D3)⋊C4—22no—
110(C2×D3)⋊C4C2×C414yescomplemented
111(C2×D3)⋊C4C2×C414yescomplemented
112(C2×D3)⋊C4C2×C414yescomplemented
113C4⋊Dic3—22no—
114Dic3⋊C4—22no—
115Dic3⋊C4C2×C414yescomplemented
116C4×Dic3—22no—
117C4×Dic3—22no—
118C4×Dic3—22no—
119C4×Dic3—22no—
120C22×D4—31no—
121C23×C4—31no—
122C23×C4—31no—
123C23×C4—31no—
124C23×C4—31no—
125#123—38no—
126C4×D4—64no—
127C2×C4⋊C4—31no—
128C2×C4⋊C4—31no—
129C2×C4⋊C4—31no—
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×C22⋊C4—31no—
139C2×C22⋊C4—31no—
140C2×C42—31no—
141C2×C42—31no—
142C2×C42—31no—
143C2×C42—31no—
144C2×C42—64no—
145C2×C42C2×D311yescharacteristic
146C2×C42C2×D311yescharacteristic
147C2×C42C2×D311yescharacteristic
148#95—31no—
149#95—31no—
150#95—31no—
151#95—31no—
152#95—31no—
153#95—31no—
154#95—31no—
155#95—31no—
156#95C2×D311yescharacteristic
157#95C2×D311yescharacteristic
158C23×C3C2411yescharacteristic
159C22×D3—21no—
160C22×D3—21no—
161C22×D3—21no—
162C22×D3—21no—
163C22×D3—21no—
164C22×D3—21no—
165C22×D3—21no—
166C22×D3—21no—
167C22×D3—21no—
168C22×D3—21no—
169C22×D3C22×C412yes—
170C22×D3C22×C412yes—
171C22×D3C2×D412yes—
172C22×D3#4112yes—
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×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4C22×C412yes—
188C2×C3×C4C22×C412yes—
189C2×C3×C4C22×C412yes—
190C2×C3×C4C2×D412yes—
191C2×C3×C4#4112yes—
192C2×C3×C4#4112yes—
193C2×C3×C4#4112yes—
194C2×Dic3—21no—
195C2×Dic3—21no—
196C2×Dic3—21no—
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3—21no—
200C2×Dic3—21no—
201C2×Dic3—21no—
202C2×Dic3—21no—
203C2×Dic3—21no—
204C2×Dic3—21no—
205C2×Dic3—21no—
206C2×Dic3—21no—
207C2×Dic3—21no—
208C2×Dic3C22×C412yes—
209C2×Dic3C22×C412yes—
210C2×Dic3C2×D412yes—
211C2×Dic3#4112yes—
212D12—28no—
213C4×D3—28no—
214C4×D3—28no—
215C4×D3—28no—
216C4×D3—44no—
217C24—31no—
218C24—31no—
219C2×D4—34no—
220C2×D4—62no—
221C2×D4—62no—
222C22×C4—31no—
223C22×C4—31no—
224C22×C4—31no—
225C22×C4—31no—
226C22×C4—34no—
227C22×C4—34no—
228C22×C4—31no—
229C22×C4—31no—
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×C4C22×D311yescharacteristic
241C22×C4C22×D311yescharacteristic
242C22×C4C22×D311yescharacteristic
243C22×C4C22×D311yescharacteristic
244C22×C4C22×D311yescharacteristic
245C22×C4C22×D311yescharacteristic
246C22×C4C22×D311yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—34no—
249C4⋊C4—62no—
250C4⋊C4—62no—
251C4⋊C4C4×D314yescomplemented
252C22⋊C4—34no—
253C22⋊C4—34no—
254C22⋊C4—34no—
255C22⋊C4—62no—
256C22⋊C4—62no—
257C22⋊C4—62no—
258C22⋊C4—62no—
259C22⋊C4—62no—
260C42—22no—
261C42—22no—
262C42—22no—
263C42—62no—
264C42—62no—
265C42—62no—
266C42—62no—
267C22×C3C23×C411yescharacteristic
268C22×C3C22×D411yescharacteristic
269C22×C3C2×#4111yescharacteristic
270C22×C3C2×#4111yescharacteristic
271C22×C3C2×#4111yescharacteristic
272C22×C3C2×#4111yescharacteristic
273C22×C3C2×#4111yescharacteristic
274C2×D3—22no—
275C2×D3—22no—
276C2×D3—22no—
277C2×D3—22no—
278C2×D3—22no—
279C2×D3—22no—
280C2×D3—22no—
281C2×D3—22no—
282C2×D3—22no—
283C2×D3—41no—
284C2×D3—41no—
285C2×D3—41no—
286C2×D3—41no—
287C2×D3C4×D414yes—
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—22no—
292C3×C4—41no—
293C3×C4—41no—
294C3×C4#12314yescomplemented
295Dic3—22no—
296Dic3—22no—
297Dic3—22no—
298Dic3—22no—
299Dic3—41no—
300Dic3—41no—
301C23—32no—
302C23—32no—
303C23—32no—
304C23—32no—
305C23—61no—
306C23—61no—
307C23—61no—
308C23—61no—
309C23—61no—
310C23—61no—
311C23—61no—
312C23—61no—
313C23—61no—
314C23—61no—
315C23C23×D311yescharacteristic
316D4—68no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—32no—
332C2×C4—32no—
333C2×C4—32no—
334C2×C4—32no—
335C2×C4—68no—
336C2×C4—68no—
337C2×C4—61no—
338C2×C4—61no—
339C2×C4—61no—
340C2×C4—61no—
341C2×C4—61no—
342C2×C4—61no—
343C2×C4—61no—
344C2×C4—61no—
345C2×C4—68no—
346C2×C4—61no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—61no—
352C2×C4—124no—
353C2×C4C2×C4×D312yes—
354C2×C4C2×C4×D312yes—
355C2×C4C2×C4×D312yes—
356C2×C4#23512yes—
357C2×C4#23512yes—
358C2×C4D3×D412yes—
359C2×C4#23912yes—
360C2×C3C2×C4×D411yescharacteristic
361C2×C3C4×#4111yescharacteristic
362C2×C3C4×#4111yescharacteristic
363C2×C3C2×#12311yescharacteristic
364C2×C3#52511yescharacteristic
365C2×C3#52911yescharacteristic
366C2×C3#52911yescharacteristic
367D3—24no—
368D3—42no—
369C22—34no—
370C22—62no—
371C22—62no—
372C22—62no—
373C22—62no—
374C22—62no—
375C22—62no—
376C22—62no—
377C22—62no—
378C22—62no—
379C22—121no—
380C22—121no—
381C22—121no—
382C22—121no—
383C22C22×C4×D311yescharacteristic
384C22C2×#23511yescharacteristic
385C22C2×#23511yescharacteristic
386C22C2×D3×D411yescharacteristic
387C22C2×#23911yescharacteristic
388C22D3×#4111yescharacteristic
389C22D3×#4111yescharacteristic
390C4—22no—
391C4—22no—
392C4—22no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—62no—
397C4—62no—
398C4—62no—
399C4—62no—
400C4—121no—
401C4—121no—
402C4#89414yesdirect product factor
403C3C4×#12311yescharacteristic, complemented, Sylow
404C2—64no—
405C2—122no—
406C2C4×#23511yescharacteristic
407C2C2×#89411yescharacteristic
408C2#552811yescharacteristic
409C2C4×D3×D411yescharacteristic
410C2#554711yescharacteristic
411C2C4×#23911yescharacteristic
412C2#558011yescharacteristic
subgroupG/H
centerC22×C4C22×D3
commutatorC22×C3C23×C4
FrattiniC23C23×D3
FittingC3×C4×C4⋊C4C2
socle, cosocleC23×C3C24
prime radicalC22×D12C22
hypercenterC4×C4⋊C4D3
hypocenterC3C4×#123
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C42×D3C2semidirect
4. C3×C4×C4⋊C4C2semidirect
5. #4990C2semidirect
6. #4989C2semidirect
7. #4980C2semidirect
8. C4×(C2×D3)⋊C4C2semidirect
9. C4×(C2×D3)⋊C4C2semidirect
10. C4×(C2×D3)⋊C4C2semidirect
11. C4×Dic3⋊C4C2semidirect
12. #4669C2semidirect
14. #4664C2semidirect
15. #4655C2semidirect
42. #894C4direct (N × H)
66. C4×C4⋊C4D3semidirect
98. C2×C4×D3C2×C4semidirect
101. C3×C4⋊C4C2×C4semidirect
110. (C2×D3)⋊C4C2×C4semidirect
111. (C2×D3)⋊C4C2×C4semidirect
112. (C2×D3)⋊C4C2×C4semidirect
115. Dic3⋊C4C2×C4semidirect
251. C4⋊C4C4×D3semidirect
294. C3×C4#123semidirect
402. C4#894direct (N × H)
403. C3C4×#123semidirect

Maximal subgroups

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

subgroupindex
C2×#8942
C2×C4×D122
C2×C42×D32
C3×C4×C4⋊C42
#49902
#49892
#49802
C4×(C2×D3)⋊C42
C4×Dic3⋊C42
#46692
#46652
#46642
#46552
C4×#1233