Finite Group Databasebeta

← C2×#10593643 #11923026

Subgroups — C2×#10593643 #11923026

Order 1152.

862 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 862 conjugacy classes of subgroups — too many to draw. Only its 163 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
2#10593643C214yesmaximal, direct product factor
3C2×C3⋊(A4⋊C8)C212yesmaximal, complemented
4C2×#5409—33nomaximal
5C2×#5207—31nomaximal
6C23×C3×A4C411yescharacteristic
7C2×C3×C4×A4C412yes—
8C2×C3×C4×A4C411yescharacteristic
9C2×C3×C4×A4C2211yescharacteristic
10C2×C3×C4×A4C2212yes—
11C2×#3748—41nomaximal
12C3⋊(A4⋊C8)C2214yescomplemented
13C24×C3×C4D311yescharacteristic
14C22×C4×A4D313yes—
15C22×#208—31no—
16C22×#208—31no—
17#5409—312no—
18C2×A4⋊C8—36no—
19#5207—34no—
20#5207—34no—
21C2×#830—32no—
22C2×#830—32no—
23C22×C3×A4—22no—
24C22×C3×A4C2×C412yes—
25C22×C3×A4C2×C411yescharacteristic
26C22×C32×C4—41no—
27C3×C4×A4C2×C411yescharacteristic
28C3×C4×A4C2×C412yes—
29C3×C4×A4C2311yescharacteristic
30#3748—44no—
31C2×C3⋊(C3⋊C8)—42no—
32C2×#407—91noSylow
33C25×C3Dic311yescharacteristic
34C23×A4Dic313yes—
35C23×C3×C4—31no—
36C23×C3×C4—31no—
37C23×C3×C4—31no—
38C23×C3×C4—32no—
39C23×C3×C4—31no—
40C23×C3×C4—32no—
41C23×C3×C4Dic312yes—
42C23×C3×C4Dic311yescharacteristic
43C23×C3×C4C2×D311yescharacteristic
44C23×C3×C4C2×D312yes—
45C2×C4×A4Dic316yes—
46C2×C4×A4Dic313yes—
47C2×C4×A4C2×D313yes—
48C2×C4×A4C2×D316yes—
49C2×#208—34no—
50C2×#208—34no—
51C2×#208—61no—
52C2×#208—61no—
53C2×#208—62no—
54C2×#208—62no—
55C2×#208—61no—
56C2×#208—61no—
57C2×#208—123no—
58C22×C3⋊C8—32no—
59C22×C3⋊C8—32no—
60A4⋊C8—312no—
61#830—38no—
62#830—34no—
63#830—34no—
64C23×C32—41no—
65C2×C3×A4—22no—
66C2×C3×A4M1612yescomplemented
67C2×C3×A4C22×C411yescharacteristic
68C2×C32×C4—41no—
69C2×C32×C4—42no—
70C2×C32×C4—41no—
71C2×C32×C4—42no—
72C3⋊(C3⋊C8)—44no—
73C24×C4C3⋊D311yescharacteristic
74C22×M16—91no—
75C22×M16—91no—
76#407—94no—
77#407—94no—
78C2×C22⋊C8—92no—
79C2×C22⋊C8—92no—
80C24×C3—22no—
81C24×C3—31no—
82C24×C3—31no—
83C24×C3—32no—
84C24×C3—62no—
85C24×C3C2×Dic312yes—
86C24×C3C2×Dic311yescharacteristic
87C22×A4—26no—
88C22×A4C2×Dic316yes—
89C22×A4C2×Dic313yes—
90C22×C3×C4—31no—
91C22×C3×C4—31no—
92C22×C3×C4—32no—
93C22×C3×C4—31no—
94C22×C3×C4—32no—
95C22×C3×C4—31no—
96C22×C3×C4—32no—
97C22×C3×C4—32no—
98C22×C3×C4—31no—
99C22×C3×C4—31no—
100C22×C3×C4—32no—
101C22×C3×C4—31no—
102C22×C3×C4—32no—
103C22×C3×C4—32no—
104C22×C3×C4—32no—
105C22×C3×C4—32no—
106C22×C3×C4—31no—
107C22×C3×C4—32no—
108C22×C3×C4—31no—
109C22×C3×C4—32no—
110C22×C3×C4—43no—
111C22×C3×C4—61no—
112C22×C3×C4—62no—
113C22×C3×C4—61no—
114C22×C3×C4—61no—
115C22×C3×C4—62no—
116C22×C3×C4C2×Dic311yescharacteristic
117C22×C3×C4C2×Dic312yes—
118C22×C3×C4S411yescharacteristic
119C22×C3×C4C22×D311yescharacteristic
120C4×A4C2×Dic313yes—
121C4×A4C2×Dic316yes—
122C4×A4C22×D313yes—
123#208—64no—
124#208—64no—
125#208—64no—
126#208—64no—
127#208—1212no—
128C2×C3⋊C8—34no—
129C2×C3⋊C8—34no—
130C2×C3⋊C8—62no—
131C2×C3⋊C8—62no—
132C2×C3⋊C8—62no—
133C2×C3⋊C8—62no—
134C2×C3⋊C8—126no—
135C22×C32—41no—
136C22×C32—42no—
137C22×C32—82no—
138C3×A4C2×M1611yescharacteristic, complemented
139C32×C4—41no—
140C32×C4—42no—
141C32×C4—41no—
142C25C3⋊Dic311yescharacteristic
143C23×C4—31no—
144C23×C4—31no—
145C23×C4—32no—
146C23×C4—31no—
147C23×C4—31no—
148C23×C4—32no—
149C23×C4C3⋊Dic312yes—
150C23×C4C3⋊Dic311yescharacteristic
151C23×C4C2×C3⋊D311yescharacteristic
152C23×C4C2×C3⋊D312yes—
153C2×M16—94no—
154C2×M16—94no—
155C2×M16—181no—
156C2×M16—181no—
157C2×M16—182no—
158C2×M16—182no—
159C2×M16—181no—
160C2×M16—181no—
161C22×C8—92no—
162C22×C8—92no—
163C22⋊C8—98no—
164C22⋊C8—94no—
165C22⋊C8—94no—
166C23×C3—22no—
167C23×C3—31no—
168C23×C3—31no—
169C23×C3—32no—
170C23×C3—32no—
171C23×C3—34no—
172C23×C3—32no—
173C23×C3—32no—
174C23×C3—31no—
175C23×C3—43no—
176C23×C3—62no—
177C23×C3—62no—
178C23×C3—62no—
179C23×C3—61no—
180C23×C3—64no—
181C23×C3—62no—
182C23×C3—64no—
183C23×C3#20812yescomplemented
184C23×C3SL(2,ℤ/4)11yescharacteristic
185C23×C3C22×Dic311yescharacteristic
186C2×A4—26no—
187C2×A4#20816yescomplemented
188C2×A4C22×Dic313yes—
189C2×C3×C4—31no—
190C2×C3×C4—32no—
191C2×C3×C4—32no—
192C2×C3×C4—31no—
193C2×C3×C4—31no—
194C2×C3×C4—32no—
195C2×C3×C4—31no—
196C2×C3×C4—32no—
197C2×C3×C4—32no—
198C2×C3×C4—32no—
199C2×C3×C4—32no—
200C2×C3×C4—31no—
201C2×C3×C4—31no—
202C2×C3×C4—32no—
203C2×C3×C4—31no—
204C2×C3×C4—32no—
205C2×C3×C4—31no—
206C2×C3×C4—46no—
207C2×C3×C4—43no—
208C2×C3×C4—43no—
209C2×C3×C4—46no—
210C2×C3×C4—61no—
211C2×C3×C4—62no—
212C2×C3×C4—61no—
213C2×C3×C4—62no—
214C2×C3×C4SL(2,ℤ/4)12yes—
215C2×C3×C4SL(2,ℤ/4)11yescharacteristic
216C2×C3×C4C2×S412yes—
217C2×C3×C4C2×S411yescharacteristic
218C3⋊C8—64no—
219C3⋊C8—64no—
220C3⋊C8—1212no—
221C2×C32—42no—
222C2×C32—41no—
223C2×C32—82no—
224C24—22no—
225C24—31no—
226C24—31no—
227C24—32no—
228C24—62no—
229C24C2×C3⋊Dic312yes—
230C24C2×C3⋊Dic311yescharacteristic
231C22×C4—31no—
232C22×C4—32no—
233C22×C4—32no—
234C22×C4—31no—
235C22×C4—31no—
236C22×C4—31no—
237C22×C4—32no—
238C22×C4—31no—
239C22×C4—32no—
240C22×C4—31no—
241C22×C4—32no—
242C22×C4—31no—
243C22×C4—32no—
244C22×C4—32no—
245C22×C4—32no—
246C22×C4—32no—
247C22×C4—31no—
248C22×C4—32no—
249C22×C4—31no—
250C22×C4—32no—
251C22×C4—61no—
252C22×C4—62no—
253C22×C4—61no—
254C22×C4—61no—
255C22×C4—62no—
256C22×C4C2×C3⋊Dic311yescharacteristic
257C22×C4C2×C3⋊Dic312yes—
258C22×C4C3⋊S411yescharacteristic
259C22×C4C22×C3⋊D311yescharacteristic
260M16—184no—
261M16—184no—
262M16—184no—
263M16—184no—
264C2×C8—94no—
265C2×C8—94no—
266C2×C8—182no—
267C2×C8—182no—
268C2×C8—182no—
269C2×C8—182no—
270C22×C3—22no—
271C22×C3—32no—
272C22×C3—31no—
273C22×C3—32no—
274C22×C3—32no—
275C22×C3—31no—
276C22×C3—31no—
277C22×C3—34no—
278C22×C3—32no—
279C22×C3—43no—
280C22×C3—46no—
281C22×C3—62no—
282C22×C3—62no—
283C22×C3—64no—
284C22×C3—61no—
285C22×C3—62no—
286C22×C3—64no—
287C22×C3—62no—
288C22×C3—86no—
289C22×C3C2×#20811yescharacteristic, complemented
290C22×C3C2×SL(2,ℤ/4)12yes—
291C22×C3C2×SL(2,ℤ/4)11yescharacteristic
292A4C2×#20813yescomplemented
293C3×C4—31no—
294C3×C4—31no—
295C3×C4—32no—
296C3×C4—46no—
297C3×C4—43no—
298C3×C4—43no—
299C3×C4C2×SL(2,ℤ/4)12yes—
300C3×C4C2×SL(2,ℤ/4)11yescharacteristic
301C3×C4C22×S411yescharacteristic
302C32—41noSylow
303C23—22no—
304C23—31no—
305C23—31no—
306C23—32no—
307C23—32no—
308C23—34no—
309C23—32no—
310C23—32no—
311C23—31no—
312C23—62no—
313C23—62no—
314C23—62no—
315C23—61no—
316C23—64no—
317C23—62no—
318C23—64no—
319C23#374812yescomplemented
320C23C3⋊SL(2,ℤ/4)11yescharacteristic
321C23C22×C3⋊Dic311yescharacteristic
322C2×C4—31no—
323C2×C4—32no—
324C2×C4—32no—
325C2×C4—31no—
326C2×C4—31no—
327C2×C4—32no—
328C2×C4—32no—
329C2×C4—31no—
330C2×C4—32no—
331C2×C4—32no—
332C2×C4—32no—
333C2×C4—31no—
334C2×C4—31no—
335C2×C4—32no—
336C2×C4—31no—
337C2×C4—32no—
338C2×C4—31no—
339C2×C4—61no—
340C2×C4—62no—
341C2×C4—61no—
342C2×C4—62no—
343C2×C4C3⋊SL(2,ℤ/4)11yescharacteristic
344C2×C4C3⋊SL(2,ℤ/4)12yes—
345C2×C4C2×C3⋊S412yes—
346C2×C4C2×C3⋊S411yescharacteristic
347C8—184no—
348C8—184no—
349C2×C3—22no—
350C2×C3—31no—
351C2×C3—31no—
352C2×C3—32no—
353C2×C3—46no—
354C2×C3—43no—
355C2×C3—62no—
356C2×C3—86no—
357C2×C3#540912yescomplemented
358C2×C3C22×SL(2,ℤ/4)11yescharacteristic
359C22—22no—
360C22—32no—
361C22—31no—
362C22—32no—
363C22—32no—
364C22—31no—
365C22—31no—
366C22—34no—
367C22—32no—
368C22—62no—
369C22—62no—
370C22—64no—
371C22—61no—
372C22—62no—
373C22—64no—
374C22—62no—
375C22C2×#374811yescharacteristic, complemented
376C22C2×C3⋊SL(2,ℤ/4)12yes—
377C22C2×C3⋊SL(2,ℤ/4)11yescharacteristic
378C4—31no—
379C4—31no—
380C4—32no—
381C4C2×C3⋊SL(2,ℤ/4)12yes—
382C4C2×C3⋊SL(2,ℤ/4)11yescharacteristic
383C4C22×C3⋊S411yescharacteristic
384C3—43no—
385C3C2×#540911yescharacteristic, complemented
386C2—22no—
387C2—31no—
388C2—31no—
389C2—32no—
390C2—62no—
391C2#1059364312yesdirect product factor
392C2C22×C3⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC2×C4C2×C3⋊S4
commutatorC2×C3×A4C22×C4
FrattiniC4C22×C3⋊S4
FittingC24×C3×C4D3
socleC24×C3C2×Dic3
prime radicalC23×C3×A4C4
cosocleC3×C4×A4C23
hypercenterC22×C4C3⋊S4
hypocenterC3×A4C2×M16
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593643C2direct (N × H)
3. C2×C3⋊(A4⋊C8)C2semidirect
12. C3⋊(A4⋊C8)C22semidirect
66. C2×C3×A4M16semidirect
138. C3×A4C2×M16semidirect
183. C23×C3#208semidirect
187. C2×A4#208semidirect
289. C22×C3C2×#208semidirect
292. A4C2×#208semidirect
319. C23#3748semidirect
357. C2×C3#5409semidirect
375. C22C2×#3748semidirect
385. C3C2×#5409semidirect
391. C2#10593643direct (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
#105936432
C2×C3⋊(A4⋊C8)2
C2×#54093
C2×#52073
C2×#37484