Finite Group Databasebeta

← C2×#10593649 #11923037

Subgroups — C2×#10593649 #11923037

Order 1152.

934 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 934 conjugacy classes of subgroups — too many to draw. Only its 99 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×C3×D4×A4C211yesmaximal, characteristic, complemented
2C2×C4⋊(C3⋊S4)C211yesmaximal, characteristic, complemented
3#10593649C214yesmaximal, direct product factor
4C2×C3⋊(A4⋊C8)C211yesmaximal, characteristic, complemented
5C2×#5415—33nomaximal
6C2×#5217—31nomaximal
7C23×C3×A4—21no—
8C22×C3⋊S4—21no—
9C3×D4×A4—21no—
10C3×D4×A4C2212yescomplemented
11C2×C3×C4×A4C2211yescharacteristic
12C4⋊(C3⋊S4)—21no—
13C4⋊(C3⋊S4)C2212yescomplemented
14C2×#3753—41nomaximal
15C3⋊(A4⋊C8)C2212yescomplemented
16C23×C3×D4D311yescharacteristic, complemented
17C2×D4×A4D313yescomplemented
18C2×C4⋊S4—33no—
19C22×#213—31no—
20C22×#213—31no—
21C2×#930—31no—
22#5415—312no—
23C2×A4⋊C8—33no—
24#5217—34no—
25#5217—34no—
26C2×#832—31no—
27C2×#832—31no—
28C2×#830—31no—
29C22×C3×A4—22no—
30C22×C3×A4—42no—
31C22×C3×A4D411yescharacteristic
32C2×C3⋊S4—22no—
33C2×C3⋊S4—42no—
34C2×C32×D4—41no—
35C2×C4⋊(C3⋊D3)—41no—
36C3×C4×A4D411yescharacteristic
37C3×C4×A4C2311yescharacteristic
38#3753—44no—
39C2×C3⋊(C3⋊C8)—41no—
40C2×#447—91noSylow
41C25×C3—21no—
42C23×A4—23no—
43C22×S4—63no—
44C22×C3×D4—21no—
45C22×C3×D4—31no—
46C22×C3×D4—31no—
47C22×C3×D4—32no—
48C22×C3×D4—61no—
49C22×C3×D4—61no—
50C22×C3×D4C2×D312yescomplemented
51C23×C3×C4C2×D311yescharacteristic
52C22×#67—61no—
53C22×D12—31no—
54D4×A4—23no—
55D4×A4C2×D316yescomplemented
56C2×C4×A4C2×D313yes—
57C4⋊S4—36no—
58C4⋊S4—63no—
59C2×#213—34no—
60C2×#213—34no—
61C2×#213—62no—
62C2×#213—62no—
63C2×#213—62no—
64C2×#213—61no—
65C2×#213—61no—
66C2×#213—123no—
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—
75A4⋊C8—36no—
76#832—34no—
77#832—34no—
78#830—32no—
79#830—32no—
80C23×C32—81no—
81C22×C3⋊D3—81no—
82C2×C3×A4—42no—
83C2×C3×A4D812yescomplemented
84C2×C3×A4C2×D411yescharacteristic
85C3⋊S4—42no—
86C32×D4—42no—
87C32×D4—81no—
88C2×C32×C4—41no—
89C4⋊(C3⋊D3)—42no—
90C4⋊(C3⋊D3)—81no—
91C3⋊(C3⋊C8)—42no—
92C23×D4C3⋊D311yescharacteristic, complemented
93C22×D8—91no—
94C22×D8—91no—
95C2×#121—91no—
96#447—94no—
97#447—94no—
98C2×#102—91no—
99C2×#102—91no—
100C2×C22⋊C8—91no—
101C24×C3—22no—
102C24×C3—42no—
103C24×C3—61no—
104C24×C3—61no—
105C24×C3—62no—
106C24×C3—122no—
107C24×C3#6711yescharacteristic
108C23×D3—61no—
109C22×A4—26no—
110C22×A4—46no—
111C22×A4#6713yes—
112C2×S4—66no—
113C2×S4—126no—
114C2×C3×D4—32no—
115C2×C3×D4—32no—
116C2×C3×D4—32no—
117C2×C3×D4—32no—
118C2×C3×D4—32no—
119C2×C3×D4—31no—
120C2×C3×D4—43no—
121C2×C3×D4—61no—
122C2×C3×D4—61no—
123C2×C3×D4—61no—
124C2×C3×D4—62no—
125C2×C3×D4—61no—
126C2×C3×D4—61no—
127C2×C3×D4—62no—
128C2×C3×D4—64no—
129C2×C3×D4S411yescharacteristic, complemented
130C22×C3×C4—31no—
131C22×C3×C4—31no—
132C22×C3×C4—31no—
133C22×C3×C4—31no—
134C22×C3×C4#6711yescharacteristic
135C22×C3×C4C22×D311yescharacteristic
136C2×#67—62no—
137C2×#67—62no—
138C2×#67—122no—
139C2×#67—122no—
140C22×Dic3—61no—
141C2×D12—32no—
142C2×D12—61no—
143C2×D12—61no—
144C2×D12—61no—
145C2×D12—61no—
146C2×D12—61no—
147C2×D12—123no—
148C4×A4#6713yes—
149C4×A4C22×D313yes—
150#213—68no—
151#213—64no—
152#213—64no—
153#213—1212no—
154(C2×D3)⋊C4—62no—
155(C2×D3)⋊C4—62no—
156C4⋊Dic3—32no—
157C4⋊Dic3—61no—
158C2×C3⋊C8—32no—
159C2×C3⋊C8—32no—
160C2×C3⋊C8—61no—
161C2×C3⋊C8—61no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8—123no—
165C22×C32—41no—
166C22×C32—82no—
167C22×C32—162no—
168C2×C3⋊D3—82no—
169C2×C3⋊D3—162no—
170C3×A4C2×D811yescharacteristic, complemented
171C32×C4—41no—
172C32×C4—41no—
173C25—21no—
174C22×D4—21no—
175C22×D4—31no—
176C22×D4—31no—
177C22×D4—32no—
178C22×D4—61no—
179C22×D4—61no—
180C22×D4—91no—
181C22×D4—181no—
182C22×D4C2×C3⋊D312yescomplemented
183C23×C4C2×C3⋊D311yescharacteristic
184C2×D8—94no—
185C2×D8—94no—
186C2×D8—182no—
187C2×D8—182no—
188C2×D8—182no—
189C2×D8—181no—
190C2×D8—181no—
191C22×C8—91no—
192C22×C8—91no—
193#121—92no—
194#121—92no—
195#121—181no—
196#121—181no—
197C2×C4⋊C4—91no—
198C2×C22⋊C4—181no—
199#102—94no—
200#102—94no—
201C22⋊C8—92no—
202C22⋊C8—92no—
203C23×C3—21no—
204C23×C3—31no—
205C23×C3—31no—
206C23×C3—32no—
207C23×C3—42no—
208C23×C3—62no—
209C23×C3—62no—
210C23×C3—62no—
211C23×C3—62no—
212C23×C3—61no—
213C23×C3—83no—
214C23×C3—122no—
215C23×C3—122no—
216C23×C3—122no—
217C23×C3—124no—
218C23×C3—122no—
219C23×C3—122no—
220C23×C3—124no—
221C23×C3#21312yescomplemented
222C23×C3C2×#6711yescharacteristic
223C22×D3—62no—
224C22×D3—121no—
225C22×D3—122no—
226C22×D3—122no—
227C22×D3—121no—
228C22×D3—243no—
229C2×A4—46no—
230C2×A4#21316yescomplemented
231C2×A4C2×#6713yes—
232S4—126no—
233C3×D4—21no—
234C3×D4—34no—
235C3×D4—32no—
236C3×D4—46no—
237C3×D4—62no—
238C3×D4—62no—
239C3×D4—62no—
240C3×D4—61no—
241C3×D4—83no—
242C3×D4C2×S412yescomplemented
243C2×C3×C4—31no—
244C2×C3×C4—31no—
245C2×C3×C4—31no—
246C2×C3×C4—31no—
247C2×C3×C4—31no—
248C2×C3×C4—31no—
249C2×C3×C4—31no—
250C2×C3×C4—43no—
251C2×C3×C4—61no—
252C2×C3×C4C2×S411yescharacteristic
253#67—124no—
254#67—122no—
255#67—122no—
256C2×Dic3—62no—
257C2×Dic3—122no—
258D12—62no—
259D12—62no—
260D12—126no—
261D12—121no—
262D12—121no—
263D12—243no—
264C3⋊C8—62no—
265C3⋊C8—62no—
266C3⋊C8—126no—
267C2×C32—42no—
268C2×C32—41no—
269C2×C32—162no—
270C3⋊D3—162no—
271C24—22no—
272C24—42no—
273C24—61no—
274C24—61no—
275C24—62no—
276C24—122no—
277C24—181no—
278C24#63811yescharacteristic
279C2×D4—32no—
280C2×D4—32no—
281C2×D4—32no—
282C2×D4—32no—
283C2×D4—32no—
284C2×D4—31no—
285C2×D4—61no—
286C2×D4—61no—
287C2×D4—61no—
288C2×D4—62no—
289C2×D4—61no—
290C2×D4—61no—
291C2×D4—62no—
292C2×D4—64no—
293C2×D4—92no—
294C2×D4—181no—
295C2×D4—181no—
296C2×D4—181no—
297C2×D4—181no—
298C2×D4—182no—
299C2×D4—182no—
300C2×D4—181no—
301C2×D4—362no—
302C2×D4—362no—
303C2×D4C3⋊S411yescharacteristic, complemented
304C22×C4—31no—
305C22×C4—31no—
306C22×C4—31no—
307C22×C4—31no—
308C22×C4—181no—
309C22×C4#63811yescharacteristic
310C22×C4C22×C3⋊D311yescharacteristic
311D8—188no—
312D8—184no—
313D8—184no—
314C2×C8—92no—
315C2×C8—92no—
316C2×C8—181no—
317C2×C8—181no—
318C2×C8—181no—
319C2×C8—181no—
320C4⋊C4—92no—
321C4⋊C4—181no—
322C22⋊C4—182no—
323C22⋊C4—182no—
324C22×C3—22no—
325C22×C3—32no—
326C22×C3—31no—
327C22×C3—32no—
328C22×C3—32no—
329C22×C3—31no—
330C22×C3—31no—
331C22×C3—42no—
332C22×C3—43no—
333C22×C3—61no—
334C22×C3—62no—
335C22×C3—86no—
336C22×C3—122no—
337C22×C3—122no—
338C22×C3—124no—
339C22×C3—122no—
340C22×C3—122no—
341C22×C3—124no—
342C22×C3—122no—
343C22×C3—166no—
344C22×C3C2×#21311yescharacteristic, complemented
345C22×C3GL(2,ℤ/4)11yescharacteristic
346C2×D3—122no—
347C2×D3—122no—
348C2×D3—122no—
349C2×D3—246no—
350C2×D3—242no—
351C2×D3—242no—
352C2×D3—486no—
353A4C2×#21313yescomplemented
354C3×C4—31no—
355C3×C4—31no—
356C3×C4—43no—
357C3×C4—43no—
358C3×C4GL(2,ℤ/4)11yescharacteristic
359C3×C4C22×S411yescharacteristic
360Dic3—122no—
361C32—41noSylow
362C23—21no—
363C23—31no—
364C23—31no—
365C23—32no—
366C23—42no—
367C23—62no—
368C23—62no—
369C23—62no—
370C23—62no—
371C23—61no—
372C23—122no—
373C23—122no—
374C23—122no—
375C23—124no—
376C23—122no—
377C23—122no—
378C23—124no—
379C23—182no—
380C23—361no—
381C23—362no—
382C23—362no—
383C23—361no—
384C23#375312yescomplemented
385C23C2×#63811yescharacteristic
386D4—21no—
387D4—34no—
388D4—32no—
389D4—62no—
390D4—62no—
391D4—62no—
392D4—61no—
393D4—182no—
394D4—182no—
395D4—361no—
396D4—364no—
397D4—362no—
398D4—362no—
399D4—361no—
400D4C2×C3⋊S412yescomplemented
401C2×C4—31no—
402C2×C4—31no—
403C2×C4—31no—
404C2×C4—31no—
405C2×C4—31no—
406C2×C4—31no—
407C2×C4—31no—
408C2×C4—61no—
409C2×C4—182no—
410C2×C4—362no—
411C2×C4C2×C3⋊S411yescharacteristic
412C8—182no—
413C8—182no—
414C2×C3—31no—
415C2×C3—31no—
416C2×C3—32no—
417C2×C3—42no—
418C2×C3—46no—
419C2×C3—43no—
420C2×C3—122no—
421C2×C3—166no—
422C2×C3#541512yescomplemented
423C2×C3C2×GL(2,ℤ/4)11yescharacteristic
424D3—242no—
425D3—486no—
426C22—22no—
427C22—32no—
428C22—31no—
429C22—32no—
430C22—32no—
431C22—31no—
432C22—31no—
433C22—42no—
434C22—61no—
435C22—62no—
436C22—122no—
437C22—122no—
438C22—124no—
439C22—122no—
440C22—122no—
441C22—124no—
442C22—122no—
443C22—362no—
444C22—362no—
445C22—362no—
446C22—722no—
447C22—722no—
448C22C2×#375311yescharacteristic, complemented
449C22#6426911yescharacteristic
450C4—31no—
451C4—31no—
452C4—362no—
453C4#6426911yescharacteristic
454C4C22×C3⋊S411yescharacteristic
455C3—43no—
456C3C2×#541511yescharacteristic, complemented
457C2—31no—
458C2—31no—
459C2—32no—
460C2—42no—
461C2—122no—
462C2—722no—
463C2#1059364912yesdirect product factor
464C2C2×#6426911yescharacteristic
subgroupG/H
centerC22#64269
commutator, cosocleC3×C4×A4C23
FrattiniC4C22×C3⋊S4
FittingC23×C3×D4D3
socleC24×C3#67
hypercenterC2×D4C3⋊S4
hypocenterC3×A4C2×D8
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×A4C2semidirect
2. C2×C4⋊(C3⋊S4)C2semidirect
3. #10593649C2direct (N × H)
4. C2×C3⋊(A4⋊C8)C2semidirect
10. C3×D4×A4C22semidirect
13. C4⋊(C3⋊S4)C22semidirect
15. C3⋊(A4⋊C8)C22semidirect
16. C23×C3×D4D3semidirect
17. C2×D4×A4D3semidirect
50. C22×C3×D4C2×D3semidirect
55. D4×A4C2×D3semidirect
83. C2×C3×A4D8semidirect
92. C23×D4C3⋊D3semidirect
129. C2×C3×D4S4semidirect
170. C3×A4C2×D8semidirect
182. C22×D4C2×C3⋊D3semidirect
221. C23×C3#213semidirect
230. C2×A4#213semidirect
242. C3×D4C2×S4semidirect
303. C2×D4C3⋊S4semidirect
344. C22×C3C2×#213semidirect
353. A4C2×#213semidirect
384. C23#3753semidirect
400. D4C2×C3⋊S4semidirect
422. C2×C3#5415semidirect
448. C22C2×#3753semidirect
456. C3C2×#5415semidirect
463. C2#10593649direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
C2×C4⋊(C3⋊S4)2
#105936492
C2×C3⋊(A4⋊C8)2
C2×#54153
C2×#52173
C2×#37534