Finite Group Databasebeta

← C2×#10593187 #11921934

Subgroups — C2×#10593187 #11921934

Order 1152.

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

normal subgroups only

This group has 692 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×A4×Dic6C211yesmaximal, characteristic, complemented
2C2×C3×C4⋊S4C211yesmaximal, characteristic
3C2×C3⋊(A4⋊C8)C211yesmaximal, characteristic, complemented
4#10593187C214yesmaximal, direct product factor
5C2×#5417—31nomaximal
6C2×#5040—31nomaximal
7C22×C3×S4—21no—
8C2×C3×C4×A4C2211yescharacteristic
9C2×Dic3×A4—21no—
10A4×Dic6—21no—
11A4×Dic6C2212yescomplemented
12C3×C4⋊S4—21no—
13C3×C4⋊S4C2212yes—
14C2×#3715—41nomaximal
15C3⋊(A4⋊C8)C2212yescomplemented
16C23×Dic6D311yescharacteristic, complemented
17C2×Q8×A4—31no—
18C2×C4⋊S4D311yescharacteristic
19C2×C3×#121—31no—
20C22×#214—31no—
21C22×#214—31no—
22#5417—34no—
23C2×A4⋊C8—31no—
24C2×A4⋊C8—61no—
25C2×#830—31no—
26#5040—34no—
27#5040—34no—
28C2×#810—31no—
29C2×#810—31no—
30C22×C3×A4D411yescharacteristic
31C2×C3×S4—22no—
32C2×C3×S4—42no—
33C2×C3×D12—41no—
34C2×C3×Dic6—41no—
35C3×C4×A4D411yescharacteristic
36C3×C4×A4C2311yescharacteristic
37Dic3×A4—22no—
38C2×C3⋊(C3⋊C8)—41no—
39#3715—44no—
40C2×#448—91noSylow
41C22×S4—21no—
42C22×C3×D4—31no—
43C22×C3×D4—61no—
44C23×C3×C4C2×D311yescharacteristic
45C23×Dic3—21no—
46C22×Dic6—21no—
47C22×Dic6—31no—
48C22×Dic6—31no—
49C22×Dic6—32no—
50C22×Dic6—61no—
51C22×Dic6—61no—
52C22×Dic6C2×D312yescomplemented
53Q8×A4—32no—
54Q8×A4—61no—
55C2×C4×A4—21no—
56C2×C4×A4—61no—
57C2×C4×A4C2×D311yescharacteristic
58C4⋊S4—21no—
59C4⋊S4C2×D312yes—
60C3×#121—32no—
61C3×#121—32no—
62C3×#121—61no—
63C3×#121—61no—
64C2×C3×C4⋊C4—31no—
65C2×C3×C22⋊C4—61no—
66C2×#215—121no—
67C2×#214—34no—
68C2×#214—34no—
69C2×#214—62no—
70C2×#214—62no—
71C2×#214—62no—
72C2×#214—61no—
73C2×#214—61no—
74C22×C3⋊C8—31no—
75C22×C3⋊C8—31no—
76A4⋊C8—32no—
77A4⋊C8—62no—
78#830—32no—
79#830—32no—
80#810—34no—
81#810—34no—
82C22×C3×D3—81no—
83C2×C3×A4SD1612yescomplemented
84C2×C3×A4C2×D411yescharacteristic
85C3×S4—42no—
86C2×C32×C4—41no—
87C2×C3×Dic3—81no—
88C3×D12—42no—
89C3×D12—81no—
90C3×Dic6—42no—
91C3×Dic6—81no—
92C3⋊(C3⋊C8)—42no—
93C23×Q8—31no—
94C22×SD16—91no—
95C22×SD16—91no—
96C2×#121—31no—
97#448—94no—
98#448—94no—
99C2×#103—91no—
100C2×#103—91no—
101C2×C22⋊C8—91no—
102C24×C3—61no—
103C24×C3#6711yescharacteristic
104C22×A4—21no—
105C22×A4#6711yescharacteristic
106C2×S4—22no—
107C2×S4—42no—
108C2×C3×Q8—121no—
109C2×C3×D4—32no—
110C2×C3×D4—61no—
111C2×C3×D4—61no—
112C2×C3×D4—61no—
113C2×C3×D4—61no—
114C2×C3×D4—62no—
115C2×C3×D4—62no—
116C2×C3×D4—61no—
117C2×C3×D4—122no—
118C2×C3×D4—122no—
119C22×C3×C4—31no—
120C22×C3×C4—31no—
121C22×C3×C4—31no—
122C22×C3×C4—31no—
123C22×C3×C4—61no—
124C22×C3×C4#6711yescharacteristic
125C22×C3×C4C22×D311yescharacteristic
126C22×Dic3—22no—
127C22×Dic3—61no—
128C22×Dic3—62no—
129C22×Dic3—61no—
130C2×D12—41no—
131C2×Dic6—32no—
132C2×Dic6—32no—
133C2×Dic6—32no—
134C2×Dic6—31no—
135C2×Dic6—32no—
136C2×Dic6—32no—
137C2×Dic6—61no—
138C2×Dic6—61no—
139C2×Dic6—61no—
140C2×Dic6—62no—
141C2×Dic6—64no—
142C2×Dic6—61no—
143C2×Dic6—62no—
144C2×Dic6—61no—
145C2×Dic6S411yescharacteristic, complemented
146C4×A4—21no—
147C4×A4—21no—
148C4×A4—62no—
149C4×A4#6711yescharacteristic
150C4×A4C22×D311yescharacteristic
151C3×C4⋊C4—32no—
152C3×C4⋊C4—61no—
153C3×C22⋊C4—62no—
154C3×C22⋊C4—62no—
155#215—124no—
156#214—68no—
157#214—64no—
158#214—64no—
159C2×C3⋊C8—32no—
160C2×C3⋊C8—32no—
161C2×C3⋊C8—61no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8—61no—
165C2×C3⋊C8—121no—
166C2×C3⋊C8—241no—
167C22×C32—41no—
168C2×C3×D3—82no—
169C2×C3×D3—162no—
170C3×A4C2×SD1611yescharacteristic, complemented
171C32×C4—41no—
172C32×C4—41no—
173C3×Dic3—82no—
174C22×Q8—32no—
175C22×Q8—61no—
176C22×Q8—91no—
177C22×Q8—91no—
178C22×Q8—92no—
179C22×Q8—181no—
180C22×Q8—181no—
181C22×D4—31no—
182C22×D4—61no—
183C23×C4—61no—
184C23×C4D3211yescharacteristic
185C2×SD16—94no—
186C2×SD16—94no—
187C2×SD16—181no—
188C2×SD16—182no—
189C2×SD16—182no—
190C2×SD16—182no—
191C2×SD16—181no—
192C22×C8—91no—
193C22×C8—91no—
194#121—32no—
195#121—32no—
196#121—61no—
197#121—61no—
198C2×C4⋊C4—31no—
199C2×C22⋊C4—61no—
200#103—94no—
201#103—94no—
202C22⋊C8—92no—
203C22⋊C8—92no—
204C23×C3—31no—
205C23×C3—31no—
206C23×C3—32no—
207C23×C3—62no—
208C23×C3—121no—
209C23×C3—122no—
210C23×C3—122no—
211C23×C3—121no—
212C23×C3#21512yescomplemented
213C23×C3C2×#6711yescharacteristic
214C22×D3—81no—
215C2×A4—22no—
216C2×A4—21no—
217C2×A4#21412yescomplemented
218C2×A4C2×#6711yescharacteristic
219S4—42no—
220C3×Q8—122no—
221C3×Q8—241no—
222C3×D4—62no—
223C3×D4—62no—
224C3×D4—121no—
225C3×D4—124no—
226C3×D4—122no—
227C3×D4—122no—
228C3×D4—121no—
229C2×C3×C4—31no—
230C2×C3×C4—31no—
231C2×C3×C4—31no—
232C2×C3×C4—31no—
233C2×C3×C4—31no—
234C2×C3×C4—31no—
235C2×C3×C4—31no—
236C2×C3×C4—41no—
237C2×C3×C4—61no—
238C2×C3×C4—62no—
239C2×C3×C4—81no—
240C2×C3×C4—122no—
241C2×C3×C4—241no—
242C2×C3×C4C2×S411yescharacteristic
243C2×Dic3—21no—
244C2×Dic3—62no—
245C2×Dic3—62no—
246C2×Dic3—62no—
247C2×Dic3—61no—
248C2×Dic3—62no—
249D12—42no—
250D12—81no—
251Dic6—21no—
252Dic6—34no—
253Dic6—32no—
254Dic6—62no—
255Dic6—62no—
256Dic6—62no—
257Dic6—61no—
258Dic6C2×S412yescomplemented
259C3⋊C8—62no—
260C3⋊C8—62no—
261C3⋊C8—122no—
262C3⋊C8—242no—
263C2×C32—42no—
264C2×C32—41no—
265C3×D3—162no—
266C24—61no—
267C24#62511yescharacteristic
268C2×Q8—31no—
269C2×Q8—92no—
270C2×Q8—92no—
271C2×Q8—92no—
272C2×Q8—92no—
273C2×Q8—92no—
274C2×Q8—91no—
275C2×Q8—181no—
276C2×Q8—181no—
277C2×Q8—181no—
278C2×Q8—182no—
279C2×Q8—181no—
280C2×Q8—181no—
281C2×Q8—182no—
282C2×Q8—184no—
283C2×D4—32no—
284C2×D4—61no—
285C2×D4—61no—
286C2×D4—61no—
287C2×D4—61no—
288C2×D4—62no—
289C2×D4—62no—
290C2×D4—61no—
291C2×D4—122no—
292C2×D4—122no—
293C22×C4—31no—
294C22×C4—31no—
295C22×C4—31no—
296C22×C4—31no—
297C22×C4—61no—
298C22×C4—62no—
299C22×C4—181no—
300C22×C4—182no—
301C22×C4—181no—
302C22×C4#62511yescharacteristic
303C22×C4C2×D3211yescharacteristic
304SD16—184no—
305SD16—188no—
306SD16—184no—
307C2×C8—92no—
308C2×C8—92no—
309C2×C8—181no—
310C2×C8—181no—
311C2×C8—181no—
312C2×C8—181no—
313C4⋊C4—32no—
314C4⋊C4—61no—
315C22⋊C4—62no—
316C22⋊C4—62no—
317C22×C3—32no—
318C22×C3—31no—
319C22×C3—32no—
320C22×C3—32no—
321C22×C3—31no—
322C22×C3—31no—
323C22×C3—41no—
324C22×C3—61no—
325C22×C3—81no—
326C22×C3—122no—
327C22×C3—122no—
328C22×C3—122no—
329C22×C3—242no—
330C22×C3—242no—
331C22×C3C2×#21511yescharacteristic, complemented
332C22×C3GL(2,ℤ/4)11yescharacteristic
333C2×D3—82no—
334C2×D3—162no—
335A4—21no—
336A4C2×#21411yescharacteristic, complemented
337C3×C4—31no—
338C3×C4—31no—
339C3×C4—41no—
340C3×C4—41no—
341C3×C4—81no—
342C3×C4—81no—
343C3×C4—122no—
344C3×C4—242no—
345C3×C4GL(2,ℤ/4)11yescharacteristic
346C3×C4C22×S411yescharacteristic
347Dic3—22no—
348Dic3—62no—
349C32—41noSylow
350C23—31no—
351C23—31no—
352C23—32no—
353C23—62no—
354C23—121no—
355C23—122no—
356C23—122no—
357C23—121no—
358C23#371512yescomplemented
359C23C2×#62511yescharacteristic
360Q8—32no—
361Q8—61no—
362Q8—94no—
363Q8—92no—
364Q8—182no—
365Q8—182no—
366Q8—182no—
367Q8—181no—
368D4—62no—
369D4—62no—
370D4—121no—
371D4—124no—
372D4—122no—
373D4—122no—
374D4—121no—
375C2×C4—31no—
376C2×C4—31no—
377C2×C4—31no—
378C2×C4—31no—
379C2×C4—31no—
380C2×C4—31no—
381C2×C4—31no—
382C2×C4—61no—
383C2×C4—61no—
384C2×C4—62no—
385C2×C4—122no—
386C2×C4—182no—
387C2×C4—182no—
388C2×C4—182no—
389C2×C4—181no—
390C2×C4—182no—
391C2×C4D3×S411yescharacteristic
392C8—182no—
393C8—182no—
394C2×C3—31no—
395C2×C3—31no—
396C2×C3—32no—
397C2×C3—41no—
398C2×C3—42no—
399C2×C3—81no—
400C2×C3—82no—
401C2×C3—242no—
402C2×C3#541712yescomplemented
403C2×C3C2×GL(2,ℤ/4)11yescharacteristic
404D3—162no—
405C22—32no—
406C22—31no—
407C22—31no—
408C22—31no—
409C22—32no—
410C22—32no—
411C22—61no—
412C22—122no—
413C22—122no—
414C22—122no—
415C22—242no—
416C22—242no—
417C22C2×#371511yescharacteristic, complemented
418C22#6420911yescharacteristic
419C4—31no—
420C4—31no—
421C4—62no—
422C4—122no—
423C4—182no—
424C4#6420911yescharacteristic
425C4C2×D3×S411yescharacteristic
426C3—41no—
427C3—81no—
428C3C2×#541711yescharacteristic, complemented
429C2—31no—
430C2—31no—
431C2—32no—
432C2—242no—
433C2#1059318712yesdirect product factor
434C2C2×#6420911yescharacteristic
subgroupG/H
centerC22#64209
commutator, cosocleC3×C4×A4C23
FrattiniC4C2×D3×S4
FittingC23×C3×C4C2×D3
socleC24×C3#67
prime radicalC2×C3×C4⋊S4C2
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
1. C2×A4×Dic6C2semidirect
3. C2×C3⋊(A4⋊C8)C2semidirect
4. #10593187C2direct (N × H)
11. A4×Dic6C22semidirect
15. C3⋊(A4⋊C8)C22semidirect
16. C23×Dic6D3semidirect
52. C22×Dic6C2×D3semidirect
83. C2×C3×A4SD16semidirect
145. C2×Dic6S4semidirect
170. C3×A4C2×SD16semidirect
212. C23×C3#215semidirect
217. C2×A4#214semidirect
258. Dic6C2×S4semidirect
331. C22×C3C2×#215semidirect
336. A4C2×#214semidirect
358. C23#3715semidirect
402. C2×C3#5417semidirect
417. C22C2×#3715semidirect
428. C3C2×#5417semidirect
433. C2#10593187direct (N × H)

Maximal subgroups

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

subgroupindex
C2×A4×Dic62
C2×C3×C4⋊S42
C2×C3⋊(A4⋊C8)2
#105931872
C2×#54173
C2×#50403
C2×#37154