Finite Group Databasebeta

← C2×#10593177 #11921867

Subgroups — C2×#10593177 #11921867

Order 1152.

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

normal subgroups only

This group has 640 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×#64259C211yesmaximal, characteristic, complemented
2C2×C3×C4⋊S4C211yesmaximal, characteristic
3C2×A4×C3⋊C8C211yesmaximal, characteristic, complemented
4#10593177C214yesmaximal, direct product factor
5C2×#5401—31nomaximal
6C2×#5041—31nomaximal
7C22×C3×S4—21no—
8C2×C3×C4×A4C2211yescharacteristic
9C2×C3⋊SL(2,ℤ/4)—21no—
10#64259—21no—
11#64259C2212yescomplemented
12C3×C4⋊S4—21no—
13C3×C4⋊S4C2212yes—
14C2×#3716—41nomaximal
15A4×C3⋊C8C2212yescomplemented
16C2×C4⋊S4D311yescharacteristic
17C2×A4⋊Q8—31no—
18C2×A4⋊Q8—61no—
19C2×C3×#121—31no—
20C22×#214—31no—
21C2×#924—31no—
22C23×C3⋊C8D311yescharacteristic, complemented
23C2×C8×A4—31no—
24#5401—34no—
25C2×#832—31no—
26#5041—34no—
27#5041—34no—
28C2×#810—31no—
29C2×#808—31no—
30C22×C3×A4D411yescharacteristic
31C2×C3×S4—22no—
32C2×C3×S4—42no—
33C2×#634—41no—
34C2×C3×D12—41no—
35C3×C4×A4D411yescharacteristic
36C3×C4×A4C2311yescharacteristic
37C3⋊SL(2,ℤ/4)—22no—
38C2×C3×C3⋊C8—41no—
39#3716—44no—
40C2×#465—91noSylow
41C22×S4—21no—
42C22×C3×D4—31no—
43C22×C3×D4—61no—
44C23×C3×C4C2×D311yescharacteristic
45C22×Dic6—31no—
46C2×C4×A4—21no—
47C2×C4×A4C2×D311yescharacteristic
48C2×SL(2,ℤ/4)—62no—
49C2×SL(2,ℤ/4)—61no—
50C4⋊S4—21no—
51C4⋊S4C2×D312yes—
52A4⋊Q8—32no—
53A4⋊Q8—62no—
54A4⋊Q8—62no—
55A4⋊Q8—61no—
56C3×#121—32no—
57C3×#121—32no—
58C3×#121—61no—
59C3×#121—61no—
60C2×C3×C4⋊C4—31no—
61C2×C3×C22⋊C4—61no—
62C2×#217—61no—
63C2×#214—34no—
64C2×#214—61no—
65C2×#214—62no—
66C2×#214—61no—
67C2×C4⋊Dic3—31no—
68#924—32no—
69#924—32no—
70#924—61no—
71#924—61no—
72C2×Dic3⋊C4—61no—
73C22×C3⋊C8—31no—
74C22×C3⋊C8—31no—
75C22×C3⋊C8—32no—
76C22×C3⋊C8C2×D312yescomplemented
77C2×#204—121no—
78C8×A4—32no—
79#832—34no—
80#810—34no—
81#808—34no—
82C22×C3×D3—81no—
83C2×C3×A4SD1612yescomplemented
84C2×C3×A4C2×D411yescharacteristic
85C3×S4—42no—
86C2×C32×C4—41no—
87C2×C3⋊Dic3—81no—
88#634—42no—
89#634—81no—
90C3×D12—42no—
91C3×D12—81no—
92C3×C3⋊C8—42no—
93C22×SD16—91no—
94C23×C8—31no—
95C2×C22⋊Q8—91no—
96C2×#121—31no—
97#465—94no—
98#465—94no—
99C2×#106—91no—
100C2×#103—91no—
101C2×#102—91no—
102C24×C3—61no—
103C24×C3D1211yescharacteristic
104C22×A4—21no—
105C22×A4#6711yescharacteristic
106C2×S4—22no—
107C2×S4—42no—
108C2×C3×D4—32no—
109C2×C3×D4—61no—
110C2×C3×D4—61no—
111C2×C3×D4—61no—
112C2×C3×D4—61no—
113C2×C3×D4—62no—
114C2×C3×D4—62no—
115C2×C3×D4—61no—
116C2×C3×D4—122no—
117C2×C3×D4—122no—
118C22×C3×C4—31no—
119C22×C3×C4—31no—
120C22×C3×C4—31no—
121C22×C3×C4—31no—
122C22×C3×C4—61no—
123C22×C3×C4D1211yescharacteristic
124C22×C3×C4C22×D311yescharacteristic
125C22×Dic3—61no—
126C22×Dic3—61no—
127C2×D12—41no—
128C2×Dic6—32no—
129C2×Dic6—61no—
130C2×Dic6—61no—
131C2×Dic6—61no—
132C2×Dic6—61no—
133C2×Dic6—61no—
134C2×Dic6—121no—
135C2×Dic6—241no—
136C4×A4—21no—
137C4×A4—21no—
138C4×A4#6711yescharacteristic
139C4×A4C22×D311yescharacteristic
140SL(2,ℤ/4)—64no—
141SL(2,ℤ/4)—62no—
142C2×C3×C8—121no—
143C3×C4⋊C4—32no—
144C3×C4⋊C4—61no—
145C3×C22⋊C4—62no—
146C3×C22⋊C4—62no—
147#217—62no—
148#217—62no—
149#214—64no—
150#214—64no—
151C4⋊Dic3—32no—
152C4⋊Dic3—61no—
153Dic3⋊C4—62no—
154Dic3⋊C4—62no—
155C2×C3⋊C8—31no—
156C2×C3⋊C8—32no—
157C2×C3⋊C8—32no—
158C2×C3⋊C8—32no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8S411yescharacteristic, complemented
161#204—124no—
162C22×C32—41no—
163C2×C3×D3—82no—
164C2×C3×D3—162no—
165C3×A4C2×SD1611yescharacteristic, complemented
166C32×C4—41no—
167C32×C4—41no—
168C3⋊Dic3—82no—
169C22×Q8—91no—
170C22×D4—31no—
171C22×D4—61no—
172C23×C4D3211yescharacteristic
173C2×SD16—94no—
174C2×SD16—181no—
175C2×SD16—182no—
176C2×SD16—181no—
177C22×C8—32no—
178C22×C8—91no—
179C22×C8—91no—
180C22×C8—92no—
181C22⋊Q8—92no—
182C22⋊Q8—92no—
183C22⋊Q8—181no—
184C22⋊Q8—181no—
185#121—32no—
186#121—32no—
187#121—61no—
188#121—61no—
189C2×C4⋊C4—31no—
190C2×C4⋊C4—91no—
191C2×C4⋊C4—181no—
192C2×C22⋊C4—61no—
193C2×C22⋊C4—181no—
194#106—94no—
195#103—94no—
196#102—94no—
197C23×C3—31no—
198C23×C3—31no—
199C23×C3—32no—
200C23×C3—62no—
201C23×C3—121no—
202C23×C3—122no—
203C23×C3—122no—
204C23×C3—121no—
205C23×C3#20412yescomplemented
206C23×C3C2×D1211yescharacteristic
207C22×D3—81no—
208C2×A4—22no—
209C2×A4—21no—
210C2×A4#21412yescomplemented
211C2×A4C2×#6711yescharacteristic
212S4—42no—
213C3×D4—62no—
214C3×D4—62no—
215C3×D4—121no—
216C3×D4—124no—
217C3×D4—122no—
218C3×D4—122no—
219C3×D4—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—81no—
231C2×C3×C4—122no—
232C2×C3×C4C2×S411yescharacteristic
233C2×Dic3—62no—
234C2×Dic3—62no—
235C2×Dic3—121no—
236C2×Dic3—122no—
237C2×Dic3—121no—
238C2×Dic3—241no—
239C2×Dic3—242no—
240D12—42no—
241D12—81no—
242Dic6—62no—
243Dic6—62no—
244Dic6—122no—
245Dic6—121no—
246Dic6—121no—
247Dic6—242no—
248Dic6—241no—
249Dic6—242no—
250C3×C8—122no—
251C3⋊C8—32no—
252C3⋊C8C2×S412yescomplemented
253C2×C32—41no—
254C2×C32—42no—
255C3×D3—162no—
256C24—61no—
257C24#62611yescharacteristic
258C2×Q8—92no—
259C2×Q8—181no—
260C2×Q8—181no—
261C2×Q8—181no—
262C2×Q8—181no—
263C2×Q8—181no—
264C2×D4—32no—
265C2×D4—61no—
266C2×D4—61no—
267C2×D4—61no—
268C2×D4—61no—
269C2×D4—62no—
270C2×D4—62no—
271C2×D4—61no—
272C2×D4—122no—
273C2×D4—122no—
274C22×C4—31no—
275C22×C4—31no—
276C22×C4—31no—
277C22×C4—31no—
278C22×C4—61no—
279C22×C4—181no—
280C22×C4—181no—
281C22×C4#62611yescharacteristic
282C22×C4C2×D3211yescharacteristic
283SD16—184no—
284SD16—184no—
285C2×C8—31no—
286C2×C8—92no—
287C2×C8—92no—
288C2×C8—91no—
289C2×C8—92no—
290C2×C8—181no—
291C4⋊C4—32no—
292C4⋊C4—61no—
293C4⋊C4—92no—
294C4⋊C4—181no—
295C4⋊C4—182no—
296C4⋊C4—182no—
297C22⋊C4—62no—
298C22⋊C4—62no—
299C22⋊C4—182no—
300C22⋊C4—182no—
301C22×C3—32no—
302C22×C3—31no—
303C22×C3—31no—
304C22×C3—31no—
305C22×C3—32no—
306C22×C3—32no—
307C22×C3—41no—
308C22×C3—61no—
309C22×C3—81no—
310C22×C3—122no—
311C22×C3—122no—
312C22×C3—122no—
313C22×C3—242no—
314C22×C3—242no—
315C22×C3C2×#20411yescharacteristic, complemented
316C22×C3C4⋊S411yescharacteristic
317C2×D3—82no—
318C2×D3—162no—
319A4—21no—
320A4C2×#21411yescharacteristic, complemented
321C3×C4—31no—
322C3×C4—31no—
323C3×C4—41no—
324C3×C4—41no—
325C3×C4—81no—
326C3×C4—81no—
327C3×C4—122no—
328C3×C4C4⋊S411yescharacteristic
329C3×C4C22×S411yescharacteristic
330Dic3—122no—
331Dic3—122no—
332Dic3—242no—
333Dic3—244no—
334C32—41noSylow
335C23—31no—
336C23—31no—
337C23—32no—
338C23—62no—
339C23—121no—
340C23—122no—
341C23—122no—
342C23—121no—
343C23#371612yescomplemented
344C23C2×#62611yescharacteristic
345Q8—182no—
346Q8—182no—
347Q8—361no—
348Q8—361no—
349D4—62no—
350D4—62no—
351D4—121no—
352D4—124no—
353D4—122no—
354D4—122no—
355D4—121no—
356C2×C4—31no—
357C2×C4—31no—
358C2×C4—31no—
359C2×C4—31no—
360C2×C4—31no—
361C2×C4—31no—
362C2×C4—31no—
363C2×C4—61no—
364C2×C4—62no—
365C2×C4—122no—
366C2×C4—182no—
367C2×C4—182no—
368C2×C4—361no—
369C2×C4—362no—
370C2×C4—361no—
371C2×C4D3×S411yescharacteristic
372C8—32no—
373C8—92no—
374C2×C3—31no—
375C2×C3—31no—
376C2×C3—32no—
377C2×C3—41no—
378C2×C3—42no—
379C2×C3—81no—
380C2×C3—82no—
381C2×C3—242no—
382C2×C3#540112yescomplemented
383C2×C3C2×C4⋊S411yescharacteristic
384D3—162no—
385C22—32no—
386C22—31no—
387C22—31no—
388C22—31no—
389C22—32no—
390C22—32no—
391C22—61no—
392C22—122no—
393C22—122no—
394C22—122no—
395C22—242no—
396C22—242no—
397C22C2×#371611yescharacteristic, complemented
398C22#6420711yescharacteristic
399C4—31no—
400C4—31no—
401C4—122no—
402C4—362no—
403C4—362no—
404C4#6420711yescharacteristic
405C4C2×D3×S411yescharacteristic
406C3—41no—
407C3—81no—
408C3C2×#540111yescharacteristic, complemented
409C2—31no—
410C2—31no—
411C2—32no—
412C2—242no—
413C2#1059317712yesdirect product factor
414C2C2×#6420711yescharacteristic
subgroupG/H
centerC22#64207
commutator, cosocleC3×C4×A4C23
FrattiniC4C2×D3×S4
FittingC23×C3×C4C2×D3
socleC24×C3D12
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×#64259C2semidirect
3. C2×A4×C3⋊C8C2semidirect
4. #10593177C2direct (N × H)
11. #64259C22semidirect
15. A4×C3⋊C8C22semidirect
22. C23×C3⋊C8D3semidirect
76. C22×C3⋊C8C2×D3semidirect
83. C2×C3×A4SD16semidirect
160. C2×C3⋊C8S4semidirect
165. C3×A4C2×SD16semidirect
205. C23×C3#204semidirect
210. C2×A4#214semidirect
252. C3⋊C8C2×S4semidirect
315. C22×C3C2×#204semidirect
320. A4C2×#214semidirect
343. C23#3716semidirect
382. C2×C3#5401semidirect
397. C22C2×#3716semidirect
408. C3C2×#5401semidirect
413. C2#10593177direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642592
C2×C3×C4⋊S42
C2×A4×C3⋊C82
#105931772
C2×#54013
C2×#50413
C2×#37164