Finite Group Databasebeta

← C4×#64259 #11922831

Subgroups — C4×#64259 #11922831

Order 1152.

790 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 790 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64259C211yesmaximal, characteristic
2C3×C42×A4C211yesmaximal, characteristic
3C4⋊(C3⋊SL(2,ℤ/4))C211yesmaximal, characteristic
4#10593645C212yesmaximal
5C4×C3⋊SL(2,ℤ/4)C212yesmaximal
6C4×A4⋊Q8—33nomaximal
7C4×#924—31nomaximal
8C2×C3×C4×A4C2211yescharacteristic
9C2×C3×C4×A4C2211yescharacteristic
10C2×C3×C4×A4C2211yescharacteristic
11C2×C3⋊SL(2,ℤ/4)C2212yes—
12C2×C3⋊SL(2,ℤ/4)C2212yes—
13#64259C414yesdirect product factor
14C4×#634—41nomaximal
15C2×A4⋊Q8—33no—
16C22×C3×C42D311yescharacteristic
17C2×#924—31no—
18C2×C4×Dic6—31no—
19C42×A4D313yes—
20C4⋊SL(2,ℤ/4)—33no—
21SL(2,ℤ/4)⋊C4—36no—
22C4×SL(2,ℤ/4)—36no—
23#5212—31no—
24#5210—32no—
25C4×#217—32no—
26C4×C4⋊Dic3—31no—
27#4933—32no—
28C4×Dic3⋊C4—32no—
29#4929—31no—
30#4928—31no—
31C22×C3×A4C2311yescharacteristic
32C2×#634—41no—
33C3×C4×A4—21no—
34C3×C4×A4C2×C412yes—
35C3×C4×A4Q812yescomplemented
36C3⋊SL(2,ℤ/4)—22no—
37C3⋊SL(2,ℤ/4)C2×C414yes—
38C32×C42—41no—
39C4⋊(C3⋊Dic3)—41no—
40#3750—42no—
41C4×C3⋊Dic3—42no—
42C4×C22⋊Q8—91noSylow
43C23×C3×C4C2×D311yescharacteristic
44C23×C3×C4C2×D311yescharacteristic
45C23×C3×C4C2×D311yescharacteristic
46C22×Dic6—31no—
47C2×C4×A4C2×D313yes—
48C2×C4×A4C2×D313yes—
49C2×C4×A4C2×D313yes—
50C2×SL(2,ℤ/4)—36no—
51C2×SL(2,ℤ/4)—36no—
52A4⋊Q8—312no—
53C2×C3×C42—31no—
54C2×C3×C42—31no—
55C2×C3×C42—31no—
56C2×C3×C42—31no—
57C2×#217—32no—
58C2×#217—32no—
59C2×C4⋊Dic3—31no—
60C2×C4⋊Dic3—31no—
61C2×C4⋊Dic3—31no—
62#924—34no—
63#924—34no—
64C2×Dic3⋊C4—32no—
65C2×Dic3⋊C4—32no—
66C2×Dic3⋊C4—32no—
67C2×C4×Dic3—32no—
68C2×C4×Dic3—32no—
69C4×Dic6—61no—
70C4×Dic6—61no—
71C4×Dic6—61no—
72C4×Dic6—61no—
73C4×Dic6—123no—
74C3⋊#95—32no—
75C3⋊#95—32no—
76C3⋊#95—32no—
77C3⋊#95—32no—
78C3⋊#95—32no—
79C2×C3×A4C22×C411yescharacteristic
80C2×C3×A4C2×Q811yescharacteristic
81C2×C3×A4#4111yescharacteristic
82C2×C32×C4—41no—
83C2×C32×C4—41no—
84C2×C32×C4—41no—
85C2×C3⋊Dic3—42no—
86C2×C3⋊Dic3—42no—
87#634—44no—
88C2×C22⋊Q8—91no—
89C2×C4×Q8—91no—
90C22×C42C3⋊D311yescharacteristic
91#391—91no—
92#389—91no—
93#387—92no—
94#385—92no—
95#380—91no—
96C4×C4⋊C4—92no—
97C4×C4⋊C4—91no—
98C4×C22⋊C4—92no—
99C24×C3C22×D311yescharacteristic
100C22×A4C22×D313yes—
101C22×C3×C4—21no—
102C22×C3×C4—31no—
103C22×C3×C4—31no—
104C22×C3×C4—31no—
105C22×C3×C4—31no—
106C22×C3×C4—31no—
107C22×C3×C4—32no—
108C22×C3×C4—32no—
109C22×C3×C4—31no—
110C22×C3×C4—61no—
111C22×C3×C4Dic612yescomplemented
112C22×C3×C4C4×D312yes—
113C22×Dic3—32no—
114C22×Dic3—32no—
115C22×Dic3—32no—
116C22×Dic3—32no—
117C2×Dic6—34no—
118C2×Dic6—61no—
119C2×Dic6—62no—
120C2×Dic6—61no—
121C2×Dic6—123no—
122C4×A4—23no—
123C4×A4Dic616yescomplemented
124C4×A4C4×D316yes—
125SL(2,ℤ/4)—312no—
126SL(2,ℤ/4)—66no—
127C3×C42—31no—
128C3×C42—31no—
129C3×C42—31no—
130C3×C42—43no—
131C3×C42—61no—
132C3×C42S411yescharacteristic
133#217—34no—
134#217—34no—
135#217—62no—
136#217—62no—
137C4⋊Dic3—34no—
138C4⋊Dic3—61no—
139C4⋊Dic3—62no—
140C4⋊Dic3—61no—
141C4⋊Dic3—123no—
142Dic3⋊C4—38no—
143Dic3⋊C4—62no—
144Dic3⋊C4—64no—
145Dic3⋊C4—62no—
146Dic3⋊C4—126no—
147C4×Dic3—62no—
148C4×Dic3—64no—
149C4×Dic3—62no—
150C4×Dic3—126no—
151C22×C32—41no—
152C3×A4C4×Q811yescharacteristic, complemented
153C32×C4—42no—
154C32×C4—42no—
155C32×C4—81no—
156C3⋊Dic3—44no—
157C3⋊Dic3—82no—
158C22×Q8—91no—
159C23×C4C2×C3⋊D311yescharacteristic
160C23×C4C2×C3⋊D311yescharacteristic
161C23×C4C2×C3⋊D311yescharacteristic
162C22⋊Q8—94no—
163C22⋊Q8—94no—
164C4×Q8—181no—
165C4×Q8—181no—
166C4×Q8—181no—
167C4×Q8—181no—
168C2×C4⋊C4—92no—
169C2×C4⋊C4—91no—
170C2×C4⋊C4—91no—
171C2×C4⋊C4—92no—
172C2×C4⋊C4—91no—
173C2×C4⋊C4—92no—
174C2×C22⋊C4—92no—
175C2×C22⋊C4—92no—
176C2×C42—31no—
177C2×C42—31no—
178C2×C42—31no—
179C2×C42—31no—
180C2×C42—92no—
181C2×C42—92no—
182#95—92no—
183#95—92no—
184#95—92no—
185#95—92no—
186#95—92no—
187C23×C3—31no—
188C23×C3—31no—
189C23×C3—31no—
190C23×C3—31no—
191C23×C3C2×Dic611yescharacteristic
192C23×C3C2×C4×D311yescharacteristic
193C23×C3#23511yescharacteristic
194C2×A4C2×Dic613yes—
195C2×A4C2×C4×D313yes—
196C2×A4#23513yes—
197C2×C3×C4—31no—
198C2×C3×C4—31no—
199C2×C3×C4—32no—
200C2×C3×C4—32no—
201C2×C3×C4—32no—
202C2×C3×C4—32no—
203C2×C3×C4—32no—
204C2×C3×C4—32no—
205C2×C3×C4—32no—
206C2×C3×C4—31no—
207C2×C3×C4—43no—
208C2×C3×C4—43no—
209C2×C3×C4—43no—
210C2×C3×C4—61no—
211C2×C3×C4—61no—
212C2×C3×C4—61no—
213C2×C3×C4—61no—
214C2×C3×C4—61no—
215C2×C3×C4C2×S411yescharacteristic
216C2×C3×C4C2×S411yescharacteristic
217C2×C3×C4C2×S411yescharacteristic
218C2×Dic3—34no—
219C2×Dic3—34no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—62no—
224C2×Dic3—62no—
225C2×Dic3—62no—
226C2×Dic3—62no—
227C2×Dic3—62no—
228C2×Dic3—62no—
229C2×Dic3—62no—
230C2×Dic3—126no—
231C2×Dic3—126no—
232Dic6—64no—
233Dic6—64no—
234Dic6—1212no—
235C2×C32—41no—
236C2×C32—41no—
237C2×C32—41no—
238C24C22×C3⋊D311yescharacteristic
239C2×Q8—94no—
240C2×Q8—181no—
241C2×Q8—182no—
242C2×Q8—181no—
243C22×C4—21no—
244C22×C4—31no—
245C22×C4—31no—
246C22×C4—31no—
247C22×C4—31no—
248C22×C4—31no—
249C22×C4—32no—
250C22×C4—32no—
251C22×C4—31no—
252C22×C4—61no—
253C22×C4—92no—
254C22×C4—92no—
255C22×C4—92no—
256C22×C4—92no—
257C22×C4#63412yescomplemented
258C22×C4C4×C3⋊D312yes—
259C4⋊C4—98no—
260C4⋊C4—94no—
261C4⋊C4—182no—
262C4⋊C4—181no—
263C4⋊C4—184no—
264C4⋊C4—182no—
265C4⋊C4—182no—
266C4⋊C4—181no—
267C22⋊C4—94no—
268C22⋊C4—94no—
269C22⋊C4—182no—
270C22⋊C4—182no—
271C42—31no—
272C42—31no—
273C42—31no—
274C42—61no—
275C42—182no—
276C42—184no—
277C42—182no—
278C42C3⋊S411yescharacteristic
279C22×C3—31no—
280C22×C3—31no—
281C22×C3—31no—
282C22×C3—31no—
283C22×C3—31no—
284C22×C3—31no—
285C22×C3—31no—
286C22×C3—31no—
287C22×C3—31no—
288C22×C3—43no—
289C22×C3—61no—
290C22×C3C4×Dic611yescharacteristic, complemented
291C22×C3C22×S411yescharacteristic
292A4C4×Dic613yescomplemented
293C3×C4—21no—
294C3×C4—32no—
295C3×C4—32no—
296C3×C4—46no—
297C3×C4—46no—
298C3×C4—61no—
299C3×C4—83no—
300C3×C4A4⋊Q812yescomplemented
301C3×C4C4×S412yes—
302Dic3—64no—
303Dic3—64no—
304Dic3—1212no—
305Dic3—122no—
306Dic3—122no—
307Dic3—246no—
308C32—41noSylow
309C23—31no—
310C23—31no—
311C23—31no—
312C23—31no—
313C23C2×#63411yescharacteristic
314C23C2×C4×C3⋊D311yescharacteristic
315C23#382811yescharacteristic
316Q8—184no—
317Q8—184no—
318C2×C4—31no—
319C2×C4—31no—
320C2×C4—32no—
321C2×C4—32no—
322C2×C4—32no—
323C2×C4—32no—
324C2×C4—32no—
325C2×C4—32no—
326C2×C4—32no—
327C2×C4—31no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—61no—
331C2×C4—61no—
332C2×C4—61no—
333C2×C4—94no—
334C2×C4—94no—
335C2×C4—182no—
336C2×C4—182no—
337C2×C4—182no—
338C2×C4—182no—
339C2×C4—182no—
340C2×C4—182no—
341C2×C4—182no—
342C2×C4—182no—
343C2×C4—182no—
344C2×C4—182no—
345C2×C4C2×C3⋊S411yescharacteristic
346C2×C4C2×C3⋊S411yescharacteristic
347C2×C4C2×C3⋊S411yescharacteristic
348C2×C3—31no—
349C2×C3—31no—
350C2×C3—31no—
351C2×C3—31no—
352C2×C3—43no—
353C2×C3—43no—
354C2×C3—43no—
355C2×C3C2×A4⋊Q811yescharacteristic
356C2×C3C2×C4×S411yescharacteristic
357C2×C3#591211yescharacteristic
358C22—31no—
359C22—31no—
360C22—31no—
361C22—31no—
362C22—31no—
363C22—31no—
364C22—31no—
365C22—31no—
366C22—31no—
367C22—61no—
368C22C4×#63411yescharacteristic, complemented
369C22C22×C3⋊S411yescharacteristic
370C4—21no—
371C4—32no—
372C4—32no—
373C4—61no—
374C4—184no—
375C4—184no—
376C4—362no—
377C4—362no—
378C4#6425912yesdirect product factor
379C4C4×C3⋊S412yes—
380C3—43no—
381C3C4×A4⋊Q811yescharacteristic, complemented
382C2—31no—
383C2—31no—
384C2—31no—
385C2—31no—
386C2C2×#6425911yescharacteristic
387C2C2×C4×C3⋊S411yescharacteristic
388C2#1059657511yescharacteristic
subgroupG/H
centerC2×C4C2×C3⋊S4
commutatorC2×C3×A4C22×C4
FrattiniC22C22×C3⋊S4
FittingC22×C3×C42D3
socleC24×C3C22×D3
prime radical, cosocleC22×C3×A4C23
hypercenterC42C3⋊S4
hypocenterC3×A4C4×Q8
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
13. #64259C4direct (N × H)
35. C3×C4×A4Q8semidirect
111. C22×C3×C4Dic6semidirect
123. C4×A4Dic6semidirect
152. C3×A4C4×Q8semidirect
257. C22×C4#634semidirect
290. C22×C3C4×Dic6semidirect
292. A4C4×Dic6semidirect
300. C3×C4A4⋊Q8semidirect
368. C22C4×#634semidirect
378. C4#64259direct (N × H)
381. C3C4×A4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#642592
C3×C42×A42
C4⋊(C3⋊SL(2,ℤ/4))2
#105936452
C4×C3⋊SL(2,ℤ/4)2
C4×A4⋊Q83
C4×#9243
C4×#6344