Finite Group Databasebeta

← C2×#10593645 #11923028

Subgroups — C2×#10593645 #11923028

Order 1152.

1182 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 171 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
1C22×C3×C4×A4C211yesmaximal, characteristic
2C22×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic
3C22×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic
4#10593645C214yesmaximal, direct product factor
5C2×SL(2,ℤ/4)⋊C4—33nomaximal
6C2×#5210—31nomaximal
7C23×C3×A4C2211yescharacteristic
8C2×C3×C4×A4—22no—
9C2×C3×C4×A4C2212yes—
10C2×C3⋊SL(2,ℤ/4)—22no—
11C2×C3⋊SL(2,ℤ/4)C414yescomplemented
12C2×C3⋊SL(2,ℤ/4)C2212yes—
13C2×C3⋊SL(2,ℤ/4)C2212yes—
14C2×#3750—41nomaximal
15C24×C3×C4D311yescharacteristic
16C22×C4×A4D313yes—
17C22×SL(2,ℤ/4)—33no—
18C22×SL(2,ℤ/4)—33no—
19C22×#217—31no—
20C22×#217—31no—
21C22×Dic3⋊C4—31no—
22C22×Dic3⋊C4—31no—
23SL(2,ℤ/4)⋊C4—312no—
24#5210—34no—
25#5210—34no—
26C2×C3⋊#95—31no—
27C2×C3⋊#95—31no—
28C22×C3×A4C2×C412yes—
29C22×C3×A4D412yes—
30C22×C3×A4Q812yes—
31C22×C3×A4C2311yescharacteristic
32C22×C32×C4—41no—
33C22×C3⋊Dic3—41no—
34C22×C3⋊Dic3—41no—
35C3×C4×A4—22no—
36C3⋊SL(2,ℤ/4)—22no—
37C3⋊SL(2,ℤ/4)C2×C414yescomplemented
38#3750—44no—
39C2×#385—91noSylow
40C25×C3C2×D311yescharacteristic
41C23×A4C2×D313yes—
42C23×C3×C4—22no—
43C23×C3×C4—31no—
44C23×C3×C4—31no—
45C23×C3×C4—32no—
46C23×C3×C4—62no—
47C23×C3×C4C2×D312yes—
48C23×Dic3—31no—
49C23×Dic3—31no—
50C23×Dic3—31no—
51C23×Dic3—31no—
52C2×C4×A4—26no—
53C2×C4×A4C2×D316yes—
54C2×SL(2,ℤ/4)—312no—
55C2×SL(2,ℤ/4)—36no—
56C2×SL(2,ℤ/4)—36no—
57C2×SL(2,ℤ/4)—66no—
58C2×#217—32no—
59C2×#217—34no—
60C2×#217—34no—
61C2×#217—32no—
62C2×#217—32no—
63C2×#217—32no—
64C2×#217—62no—
65C2×#217—62no—
66C2×Dic3⋊C4—34no—
67C2×Dic3⋊C4—34no—
68C2×Dic3⋊C4—64no—
69C2×Dic3⋊C4—61no—
70C2×Dic3⋊C4—62no—
71C2×Dic3⋊C4—61no—
72C2×Dic3⋊C4—123no—
73C3⋊#95—34no—
74C3⋊#95—34no—
75C23×C32—41no—
76C2×C3×A4C4⋊C414yescomplemented
77C2×C3×A4C22×C411yescharacteristic
78C2×C3×A4C2×D411yescharacteristic
79C2×C3×A4C2×Q811yescharacteristic
80C2×C32×C4—42no—
81C2×C32×C4—82no—
82C2×C3⋊Dic3—44no—
83C2×C3⋊Dic3—42no—
84C2×C3⋊Dic3—42no—
85C2×C3⋊Dic3—82no—
86C24×C4C3⋊D311yescharacteristic
87C22×C4⋊C4—91no—
88C22×C4⋊C4—91no—
89C22×C22⋊C4—91no—
90C22×C22⋊C4—91no—
91#385—94no—
92#385—94no—
93C2×#95—91no—
94C2×#95—91no—
95C24×C3—31no—
96C24×C3—32no—
97C24×C3—32no—
98C24×C3—31no—
99C24×C3—32no—
100C24×C3Dic612yes—
101C24×C3C4×D312yes—
102C24×C3#6712yes—
103C24×C3C22×D311yescharacteristic
104C22×A4Dic616yes—
105C22×A4C4×D316yes—
106C22×A4#6716yes—
107C22×A4C22×D313yes—
108C22×C3×C4—22no—
109C22×C3×C4—32no—
110C22×C3×C4—34no—
111C22×C3×C4—31no—
112C22×C3×C4—32no—
113C22×C3×C4—32no—
114C22×C3×C4—43no—
115C22×C3×C4—62no—
116C22×C3×C4—62no—
117C22×C3×C4—61no—
118C22×C3×C4—62no—
119C22×C3×C4—64no—
120C22×C3×C4—64no—
121C22×C3×C4—62no—
122C22×C3×C4S411yescharacteristic
123C22×Dic3—32no—
124C22×Dic3—32no—
125C22×Dic3—34no—
126C22×Dic3—34no—
127C22×Dic3—32no—
128C22×Dic3—32no—
129C22×Dic3—62no—
130C22×Dic3—61no—
131C22×Dic3—62no—
132C22×Dic3—62no—
133C22×Dic3—61no—
134C22×Dic3—62no—
135C22×Dic3—61no—
136C22×Dic3—62no—
137C22×Dic3—62no—
138C22×Dic3—62no—
139C22×Dic3—62no—
140C22×Dic3—61no—
141C22×Dic3—123no—
142C22×Dic3—123no—
143C4×A4—26no—
144SL(2,ℤ/4)—312no—
145SL(2,ℤ/4)—66no—
146#217—38no—
147#217—34no—
148#217—34no—
149#217—64no—
150#217—62no—
151#217—62no—
152Dic3⋊C4—68no—
153Dic3⋊C4—64no—
154Dic3⋊C4—64no—
155Dic3⋊C4—1212no—
156C22×C32—42no—
157C22×C32—42no—
158C22×C32—42no—
159C22×C32—41no—
160C3×A4C2×C4⋊C411yescharacteristic, complemented
161C32×C4—82no—
162C3⋊Dic3—44no—
163C3⋊Dic3—82no—
164C25C2×C3⋊D311yescharacteristic
165C23×C4—22no—
166C23×C4—31no—
167C23×C4—31no—
168C23×C4—32no—
169C23×C4—62no—
170C23×C4—91no—
171C23×C4—91no—
172C23×C4—91no—
173C23×C4—91no—
174C23×C4C2×C3⋊D312yes—
175C2×C4⋊C4—94no—
176C2×C4⋊C4—94no—
177C2×C4⋊C4—184no—
178C2×C4⋊C4—181no—
179C2×C4⋊C4—182no—
180C2×C4⋊C4—181no—
181C2×C22⋊C4—92no—
182C2×C22⋊C4—94no—
183C2×C22⋊C4—94no—
184C2×C22⋊C4—92no—
185C2×C22⋊C4—92no—
186C2×C22⋊C4—92no—
187C2×C22⋊C4—182no—
188C2×C22⋊C4—182no—
189#95—94no—
190#95—94no—
191C23×C3—32no—
192C23×C3—32no—
193C23×C3—32no—
194C23×C3—32no—
195C23×C3—32no—
196C23×C3—32no—
197C23×C3—31no—
198C23×C3—31no—
199C23×C3—32no—
200C23×C3—31no—
201C23×C3—32no—
202C23×C3—31no—
203C23×C3—32no—
204C23×C3—34no—
205C23×C3—34no—
206C23×C3—34no—
207C23×C3—31no—
208C23×C3—43no—
209C23×C3—61no—
210C23×C3—61no—
211C23×C3—61no—
212C23×C3—64no—
213C23×C3Dic3⋊C414yescomplemented
214C23×C3C2×Dic611yescharacteristic
215C23×C3C2×C4×D311yescharacteristic
216C23×C3C2×#6711yescharacteristic
217C23×C3C2×S411yescharacteristic
218C2×A4Dic3⋊C4112yescomplemented
219C2×A4C2×Dic613yes—
220C2×A4C2×C4×D313yes—
221C2×A4C2×#6713yes—
222C2×C3×C4—22no—
223C2×C3×C4—34no—
224C2×C3×C4—32no—
225C2×C3×C4—46no—
226C2×C3×C4—62no—
227C2×C3×C4—62no—
228C2×C3×C4—64no—
229C2×C3×C4—64no—
230C2×C3×C4—62no—
231C2×C3×C4—62no—
232C2×C3×C4—86no—
233C2×C3×C4C2×S412yes—
234C2×Dic3—34no—
235C2×Dic3—34no—
236C2×Dic3—62no—
237C2×Dic3—62no—
238C2×Dic3—68no—
239C2×Dic3—62no—
240C2×Dic3—64no—
241C2×Dic3—64no—
242C2×Dic3—62no—
243C2×Dic3—62no—
244C2×Dic3—62no—
245C2×Dic3—62no—
246C2×Dic3—62no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—126no—
250C2×Dic3—1212no—
251C2×Dic3—126no—
252C2×Dic3—124no—
253C2×Dic3—122no—
254C2×Dic3—122no—
255C2×Dic3—246no—
256C2×C32—41no—
257C2×C32—41no—
258C2×C32—44no—
259C2×C32—41no—
260C24—31no—
261C24—31no—
262C24—32no—
263C24—32no—
264C24—32no—
265C24#63412yes—
266C24C4×C3⋊D312yes—
267C24#63812yes—
268C24C22×C3⋊D311yescharacteristic
269C22×C4—22no—
270C22×C4—32no—
271C22×C4—34no—
272C22×C4—31no—
273C22×C4—32no—
274C22×C4—32no—
275C22×C4—62no—
276C22×C4—62no—
277C22×C4—61no—
278C22×C4—62no—
279C22×C4—64no—
280C22×C4—64no—
281C22×C4—62no—
282C22×C4—92no—
283C22×C4—92no—
284C22×C4—94no—
285C22×C4—94no—
286C22×C4—92no—
287C22×C4—92no—
288C22×C4—182no—
289C22×C4—181no—
290C22×C4—182no—
291C22×C4—182no—
292C22×C4—181no—
293C22×C4—182no—
294C22×C4—182no—
295C22×C4—182no—
296C22×C4—181no—
297C22×C4—182no—
298C22×C4—182no—
299C22×C4—181no—
300C22×C4C3⋊S411yescharacteristic
301C4⋊C4—188no—
302C4⋊C4—184no—
303C4⋊C4—184no—
304C22⋊C4—98no—
305C22⋊C4—94no—
306C22⋊C4—94no—
307C22⋊C4—184no—
308C22⋊C4—182no—
309C22⋊C4—182no—
310C22×C3—34no—
311C22×C3—31no—
312C22×C3—31no—
313C22×C3—31no—
314C22×C3—31no—
315C22×C3—31no—
316C22×C3—32no—
317C22×C3—31no—
318C22×C3—31no—
319C22×C3—32no—
320C22×C3—34no—
321C22×C3—34no—
322C22×C3—34no—
323C22×C3—34no—
324C22×C3—31no—
325C22×C3—31no—
326C22×C3—32no—
327C22×C3—46no—
328C22×C3—46no—
329C22×C3—46no—
330C22×C3—43no—
331C22×C3—61no—
332C22×C3—62no—
333C22×C3—62no—
334C22×C3—62no—
335C22×C3C2×Dic3⋊C411yescharacteristic, complemented
336C22×C3A4⋊Q812yes—
337C22×C3C4×S412yes—
338C22×C3GL(2,ℤ/4)12yes—
339C22×C3C22×S411yescharacteristic
340A4C2×Dic3⋊C413yescomplemented
341C3×C4—22no—
342C3×C4—62no—
343C3×C4—86no—
344Dic3—64no—
345Dic3—64no—
346Dic3—1212no—
347Dic3—122no—
348Dic3—122no—
349Dic3—246no—
350C32—41noSylow
351C23—32no—
352C23—32no—
353C23—32no—
354C23—32no—
355C23—32no—
356C23—32no—
357C23—31no—
358C23—31no—
359C23—32no—
360C23—31no—
361C23—32no—
362C23—31no—
363C23—32no—
364C23—34no—
365C23—34no—
366C23—34no—
367C23—31no—
368C23—61no—
369C23—64no—
370C23—61no—
371C23—61no—
372C23#375014yescomplemented
373C23C2×#63411yescharacteristic
374C23C2×C4×C3⋊D311yescharacteristic
375C23C2×#63811yescharacteristic
376C23C2×C3⋊S411yescharacteristic
377C2×C4—22no—
378C2×C4—34no—
379C2×C4—32no—
380C2×C4—62no—
381C2×C4—62no—
382C2×C4—64no—
383C2×C4—64no—
384C2×C4—62no—
385C2×C4—62no—
386C2×C4—94no—
387C2×C4—94no—
388C2×C4—182no—
389C2×C4—188no—
390C2×C4—182no—
391C2×C4—182no—
392C2×C4—184no—
393C2×C4—184no—
394C2×C4—182no—
395C2×C4—182no—
396C2×C4—182no—
397C2×C4—182no—
398C2×C4—182no—
399C2×C4—182no—
400C2×C4—182no—
401C2×C4—364no—
402C2×C4—362no—
403C2×C4—362no—
404C2×C4C2×C3⋊S412yes—
405C2×C3—31no—
406C2×C3—31no—
407C2×C3—31no—
408C2×C3—34no—
409C2×C3—31no—
410C2×C3—412no—
411C2×C3—43no—
412C2×C3—43no—
413C2×C3—43no—
414C2×C3SL(2,ℤ/4)⋊C414yescomplemented
415C2×C3C2×A4⋊Q811yescharacteristic
416C2×C3C2×C4×S411yescharacteristic
417C2×C3C2×GL(2,ℤ/4)11yescharacteristic
418C22—34no—
419C22—31no—
420C22—31no—
421C22—31no—
422C22—34no—
423C22—34no—
424C22—34no—
425C22—34no—
426C22—31no—
427C22—31no—
428C22—32no—
429C22—31no—
430C22—31no—
431C22—32no—
432C22—31no—
433C22—31no—
434C22—32no—
435C22—61no—
436C22—62no—
437C22—62no—
438C22—62no—
439C22C2×#375011yescharacteristic, complemented
440C22#6425912yes—
441C22C4×C3⋊S412yes—
442C22#6426912yes—
443C22C22×C3⋊S411yescharacteristic
444C4—22no—
445C4—62no—
446C4—184no—
447C4—184no—
448C4—362no—
449C4—362no—
450C3—43no—
451C3C2×SL(2,ℤ/4)⋊C411yescharacteristic, complemented
452C2—31no—
453C2—31no—
454C2—31no—
455C2—34no—
456C2—31no—
457C2#1059364514yesdirect product factor
458C2C2×#6425911yescharacteristic
459C2C2×C4×C3⋊S411yescharacteristic
460C2C2×#6426911yescharacteristic
subgroupG/H
centerC23C2×C3⋊S4
commutatorC2×C3×A4C22×C4
FrattiniC22C22×C3⋊S4
FittingC24×C3×C4D3
socleC25×C3C2×D3
prime radicalC23×C3×A4C22
cosocleC22×C3×A4C23
hypercenterC22×C4C3⋊S4
hypocenterC3×A4C2×C4⋊C4
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10593645C2direct (N × H)
11. C2×C3⋊SL(2,ℤ/4)C4semidirect
37. C3⋊SL(2,ℤ/4)C2×C4semidirect
76. C2×C3×A4C4⋊C4semidirect
160. C3×A4C2×C4⋊C4semidirect
213. C23×C3Dic3⋊C4semidirect
218. C2×A4Dic3⋊C4semidirect
335. C22×C3C2×Dic3⋊C4semidirect
340. A4C2×Dic3⋊C4semidirect
372. C23#3750semidirect
414. C2×C3SL(2,ℤ/4)⋊C4semidirect
439. C22C2×#3750semidirect
451. C3C2×SL(2,ℤ/4)⋊C4semidirect
457. C2#10593645direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×A42
C22×C3⋊SL(2,ℤ/4)2
#105936452
C2×SL(2,ℤ/4)⋊C43
C2×#52103
C2×#37504