Finite Group Databasebeta

← C2×#10593178 #11921868

Subgroups — C2×#10593178 #11921868

Order 1152.

656 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 71 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×C4⋊(C3⋊S4)C211yesmaximal, characteristic
2C2×C3×A4⋊Q8C211yesmaximal, characteristic, complemented
3C2×A4×C3⋊C8C211yesmaximal, characteristic, complemented
4#10593178C214yesmaximal, direct product factor
5C2×#5401—31nomaximal
6C2×#5048—31nomaximal
7C22×C3⋊S4—21no—
8C2×C3×C4×A4C2211yescharacteristic
9C4⋊(C3⋊S4)—21no—
10C4⋊(C3⋊S4)C2212yes—
11C2×C3×SL(2,ℤ/4)—21no—
12C3×A4⋊Q8—21no—
13C3×A4⋊Q8C2212yescomplemented
14C2×#3717—41nomaximal
15A4×C3⋊C8C2212yescomplemented
16C2×C4⋊S4—31no—
17C2×C4⋊S4—61no—
18C2×A4⋊Q8D311yescharacteristic, complemented
19C2×C3×C22⋊Q8—31no—
20C22×#215—31no—
21C2×#930—31no—
22C23×C3⋊C8D311yescharacteristic, complemented
23C2×C8×A4—31no—
24#5401—34no—
25C2×#835—31no—
26#5048—34no—
27#5048—34no—
28C2×#809—31no—
29C2×#808—31no—
30C22×C3×A4D411yescharacteristic
31C2×C3⋊S4—22no—
32C2×C3⋊S4—42no—
33C2×C4⋊(C3⋊D3)—41no—
34C2×C3×Dic6—41no—
35C3×C4×A4D411yescharacteristic
36C3×C4×A4C2311yescharacteristic
37C3×SL(2,ℤ/4)—22no—
38C2×C3×C3⋊C8—41no—
39#3717—44no—
40C2×#465—91noSylow
41C22×S4—62no—
42C22×S4—61no—
43C22×C3×Q8—31no—
44C23×C3×C4C2×D311yescharacteristic
45C22×#67—61no—
46C22×D12—31no—
47C2×C4×A4—21no—
48C2×C4×A4C2×D311yescharacteristic
49C2×SL(2,ℤ/4)—21no—
50C4⋊S4—32no—
51C4⋊S4—62no—
52C4⋊S4—62no—
53C4⋊S4—61no—
54A4⋊Q8—21no—
55A4⋊Q8C2×D312yescomplemented
56C3×C22⋊Q8—32no—
57C3×C22⋊Q8—32no—
58C3×C22⋊Q8—61no—
59C3×C22⋊Q8—61no—
60C2×C3×C4⋊C4—31no—
61C2×C3×C4⋊C4—61no—
62C2×C3×C22⋊C4—61no—
63C2×#215—34no—
64C2×#215—61no—
65C2×#215—62no—
66C2×#215—61no—
67#930—32no—
68#930—32no—
69#930—61no—
70#930—61no—
71C2×(C2×D3)⋊C4—61no—
72C2×C4⋊Dic3—31no—
73C22×C3⋊C8—31no—
74C22×C3⋊C8—31no—
75C22×C3⋊C8—32no—
76C22×C3⋊C8C2×D312yescomplemented
77C2×#204—121no—
78C8×A4—32no—
79#835—34no—
80#809—34no—
81#808—34no—
82C22×C3⋊D3—81no—
83C2×C3×A4SD1612yescomplemented
84C2×C3×A4C2×D411yescharacteristic
85C3⋊S4—42no—
86C2×C32×C4—41no—
87C4⋊(C3⋊D3)—42no—
88C4⋊(C3⋊D3)—81no—
89C2×C3×Dic3—81no—
90C3×Dic6—42no—
91C3×Dic6—81no—
92C3×C3⋊C8—42no—
93C22×SD16—91no—
94C23×C8—31no—
95C2×C22⋊Q8—31no—
96C2×#121—91no—
97#465—94no—
98#465—94no—
99C2×#106—91no—
100C2×#103—91no—
101C2×#102—91no—
102C24×C3D1211yescharacteristic
103C23×D3—61no—
104C22×A4—21no—
105C22×A4#6711yescharacteristic
106C2×S4—64no—
107C2×S4—62no—
108C2×S4—124no—
109C2×S4—122no—
110C2×C3×Q8—32no—
111C2×C3×Q8—61no—
112C2×C3×Q8—61no—
113C2×C3×Q8—61no—
114C2×C3×Q8—61no—
115C2×C3×Q8—61no—
116C22×C3×C4—31no—
117C22×C3×C4—31no—
118C22×C3×C4—31no—
119C22×C3×C4—31no—
120C22×C3×C4—61no—
121C22×C3×C4—61no—
122C22×C3×C4D1211yescharacteristic
123C22×C3×C4C22×D311yescharacteristic
124C2×#67—62no—
125C2×#67—62no—
126C2×#67—122no—
127C2×#67—122no—
128C22×Dic3—61no—
129C2×D12—32no—
130C2×D12—61no—
131C2×D12—61no—
132C2×D12—61no—
133C2×D12—61no—
134C2×D12—61no—
135C2×D12—121no—
136C2×D12—241no—
137C2×Dic6—41no—
138C4×A4—21no—
139C4×A4—21no—
140C4×A4#6711yescharacteristic
141C4×A4C22×D311yescharacteristic
142SL(2,ℤ/4)—22no—
143C2×C3×C8—121no—
144C3×C4⋊C4—32no—
145C3×C4⋊C4—61no—
146C3×C4⋊C4—62no—
147C3×C4⋊C4—62no—
148C3×C22⋊C4—62no—
149C3×C22⋊C4—62no—
150#215—64no—
151#215—64no—
152(C2×D3)⋊C4—62no—
153(C2×D3)⋊C4—62no—
154C4⋊Dic3—32no—
155C4⋊Dic3—61no—
156C2×C3⋊C8—31no—
157C2×C3⋊C8—32no—
158C2×C3⋊C8—32no—
159C2×C3⋊C8—32no—
160C2×C3⋊C8—61no—
161C2×C3⋊C8S411yescharacteristic, complemented
162#204—124no—
163C22×C32—41no—
164C2×C3⋊D3—82no—
165C2×C3⋊D3—162no—
166C3×A4C2×SD1611yescharacteristic, complemented
167C32×C4—41no—
168C32×C4—41no—
169C3×Dic3—82no—
170C22×Q8—31no—
171C22×D4—91no—
172C22×D4—181no—
173C23×C4D3211yescharacteristic
174C2×SD16—94no—
175C2×SD16—181no—
176C2×SD16—182no—
177C2×SD16—181no—
178C22×C8—32no—
179C22×C8—91no—
180C22×C8—91no—
181C22×C8—92no—
182C22⋊Q8—32no—
183C22⋊Q8—32no—
184C22⋊Q8—61no—
185C22⋊Q8—61no—
186#121—92no—
187#121—92no—
188#121—181no—
189#121—181no—
190C2×C4⋊C4—31no—
191C2×C4⋊C4—61no—
192C2×C4⋊C4—91no—
193C2×C22⋊C4—61no—
194C2×C22⋊C4—181no—
195#106—94no—
196#103—94no—
197#102—94no—
198C23×C3—31no—
199C23×C3—31no—
200C23×C3—32no—
201C23×C3#20412yescomplemented
202C23×C3C2×D1211yescharacteristic
203C22×D3—62no—
204C22×D3—121no—
205C22×D3—122no—
206C22×D3—122no—
207C22×D3—121no—
208C22×D3—241no—
209C22×D3—242no—
210C2×A4—22no—
211C2×A4—21no—
212C2×A4#21512yescomplemented
213C2×A4C2×#6711yescharacteristic
214S4—124no—
215S4—122no—
216C3×Q8—62no—
217C3×Q8—62no—
218C3×Q8—121no—
219C3×Q8—121no—
220C2×C3×C4—31no—
221C2×C3×C4—31no—
222C2×C3×C4—31no—
223C2×C3×C4—31no—
224C2×C3×C4—31no—
225C2×C3×C4—31no—
226C2×C3×C4—31no—
227C2×C3×C4—41no—
228C2×C3×C4—61no—
229C2×C3×C4—62no—
230C2×C3×C4—62no—
231C2×C3×C4—81no—
232C2×C3×C4—122no—
233C2×C3×C4—121no—
234C2×C3×C4—121no—
235C2×C3×C4C2×S411yescharacteristic
236#67—124no—
237#67—122no—
238#67—122no—
239C2×Dic3—62no—
240C2×Dic3—81no—
241C2×Dic3—122no—
242D12—62no—
243D12—62no—
244D12—122no—
245D12—121no—
246D12—121no—
247D12—242no—
248D12—241no—
249D12—242no—
250Dic6—42no—
251Dic6—81no—
252C3×C8—122no—
253C3⋊C8—32no—
254C3⋊C8C2×S412yescomplemented
255C2×C32—41no—
256C2×C32—42no—
257C3⋊D3—162no—
258C24—181no—
259C24#62611yescharacteristic
260C2×Q8—32no—
261C2×Q8—61no—
262C2×Q8—61no—
263C2×Q8—61no—
264C2×Q8—61no—
265C2×Q8—61no—
266C2×D4—92no—
267C2×D4—181no—
268C2×D4—181no—
269C2×D4—181no—
270C2×D4—181no—
271C2×D4—182no—
272C2×D4—182no—
273C2×D4—181no—
274C2×D4—362no—
275C2×D4—362no—
276C22×C4—31no—
277C22×C4—31no—
278C22×C4—31no—
279C22×C4—31no—
280C22×C4—61no—
281C22×C4—61no—
282C22×C4—181no—
283C22×C4#62611yescharacteristic
284C22×C4C2×D3211yescharacteristic
285SD16—184no—
286SD16—184no—
287C2×C8—31no—
288C2×C8—92no—
289C2×C8—92no—
290C2×C8—91no—
291C2×C8—92no—
292C2×C8—181no—
293C4⋊C4—32no—
294C4⋊C4—61no—
295C4⋊C4—62no—
296C4⋊C4—62no—
297C4⋊C4—92no—
298C4⋊C4—181no—
299C22⋊C4—62no—
300C22⋊C4—62no—
301C22⋊C4—182no—
302C22⋊C4—182no—
303C22×C3—32no—
304C22×C3—31no—
305C22×C3—31no—
306C22×C3—31no—
307C22×C3—32no—
308C22×C3—32no—
309C22×C3—41no—
310C22×C3—61no—
311C22×C3—81no—
312C22×C3C2×#20411yescharacteristic, complemented
313C22×C3C4⋊S411yescharacteristic
314C2×D3—122no—
315C2×D3—122no—
316C2×D3—122no—
317C2×D3—242no—
318C2×D3—244no—
319C2×D3—242no—
320C2×D3—242no—
321C2×D3—482no—
322C2×D3—484no—
323A4—21no—
324A4C2×#21511yescharacteristic, complemented
325C3×C4—31no—
326C3×C4—31no—
327C3×C4—41no—
328C3×C4—41no—
329C3×C4—81no—
330C3×C4—81no—
331C3×C4—122no—
332C3×C4—122no—
333C3×C4C4⋊S411yescharacteristic
334C3×C4C22×S411yescharacteristic
335Dic3—82no—
336Dic3—122no—
337C32—41noSylow
338C23—31no—
339C23—31no—
340C23—32no—
341C23—182no—
342C23—361no—
343C23—362no—
344C23—362no—
345C23—361no—
346C23#371712yescomplemented
347C23C2×#62611yescharacteristic
348Q8—62no—
349Q8—62no—
350Q8—121no—
351Q8—121no—
352D4—182no—
353D4—182no—
354D4—361no—
355D4—364no—
356D4—362no—
357D4—362no—
358D4—361no—
359C2×C4—31no—
360C2×C4—31no—
361C2×C4—31no—
362C2×C4—31no—
363C2×C4—31no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—61no—
367C2×C4—62no—
368C2×C4—62no—
369C2×C4—121no—
370C2×C4—122no—
371C2×C4—121no—
372C2×C4—182no—
373C2×C4—362no—
374C2×C4D3×S411yescharacteristic
375C8—32no—
376C8—92no—
377C2×C3—31no—
378C2×C3—31no—
379C2×C3—32no—
380C2×C3—41no—
381C2×C3—42no—
382C2×C3—81no—
383C2×C3—82no—
384C2×C3#540112yescomplemented
385C2×C3C2×C4⋊S411yescharacteristic
386D3—242no—
387D3—482no—
388D3—484no—
389C22—32no—
390C22—31no—
391C22—31no—
392C22—31no—
393C22—32no—
394C22—32no—
395C22—61no—
396C22—362no—
397C22—362no—
398C22—362no—
399C22—722no—
400C22—722no—
401C22C2×#371711yescharacteristic, complemented
402C22#6420711yescharacteristic
403C4—31no—
404C4—31no—
405C4—122no—
406C4—122no—
407C4—362no—
408C4#6420711yescharacteristic
409C4C2×D3×S411yescharacteristic
410C3—41no—
411C3—81no—
412C3C2×#540111yescharacteristic, complemented
413C2—31no—
414C2—31no—
415C2—32no—
416C2—722no—
417C2#1059317812yesdirect product factor
418C2C2×#6420711yescharacteristic
subgroupG/H
centerC22#64207
commutator, cosocleC3×C4×A4C23
FrattiniC4C2×D3×S4
FittingC23×C3×C4C2×D3
socleC24×C3D12
prime radicalC2×C4⋊(C3⋊S4)C2
hypercenterC2×C4D3×S4
hypocenterC3×A4C2×SD16
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×A4⋊Q8C2semidirect
3. C2×A4×C3⋊C8C2semidirect
4. #10593178C2direct (N × H)
13. C3×A4⋊Q8C22semidirect
15. A4×C3⋊C8C22semidirect
18. C2×A4⋊Q8D3semidirect
22. C23×C3⋊C8D3semidirect
55. A4⋊Q8C2×D3semidirect
76. C22×C3⋊C8C2×D3semidirect
83. C2×C3×A4SD16semidirect
161. C2×C3⋊C8S4semidirect
166. C3×A4C2×SD16semidirect
201. C23×C3#204semidirect
212. C2×A4#215semidirect
254. C3⋊C8C2×S4semidirect
312. C22×C3C2×#204semidirect
324. A4C2×#215semidirect
346. C23#3717semidirect
384. C2×C3#5401semidirect
401. C22C2×#3717semidirect
412. C3C2×#5401semidirect
417. C2#10593178direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊(C3⋊S4)2
C2×C3×A4⋊Q82
C2×A4×C3⋊C82
#105931782
C2×#54013
C2×#50483
C2×#37174