Finite Group Databasebeta

← C2×#10593666 #11923094

Subgroups — C2×#10593666 #11923094

Order 1152.

2198 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 2198 conjugacy classes of subgroups — too many to draw. Only its 227 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
1C24×C3×A4C211yesmaximal, characteristic
2C22×C3⋊SL(2,ℤ/4)C212yesmaximal, complemented
3#10593666C214yesmaximal, direct product factor
4C2×#5432—33nomaximal
5C2×#5247—31nomaximal
6C23×C3×A4—24no—
7C23×C3×A4C414yescomplemented
8C23×C3×A4C2212yes—
9C23×C3×A4C2211yescharacteristic
10C2×C3⋊SL(2,ℤ/4)—24no—
11C2×C3⋊SL(2,ℤ/4)C2214yescomplemented
12C2×#3757—41nomaximal
13C26×C3D311yescharacteristic
14C24×A4D313yes—
15C22×SL(2,ℤ/4)—36no—
16C22×#217—32no—
17C22×#217—31no—
18C22×#217—31no—
19C22×#217—32no—
20#5432—312no—
21#5247—34no—
22#5247—34no—
23C24×C32—41no—
24C22×C3×A4—28no—
25C22×C3×A4—24no—
26C22×C3×A4C2×C412yes—
27C22×C3×A4C2×C414yescomplemented
28C22×C3×A4D414yes—
29C22×C3×A4C2311yescharacteristic
30C22×C3⋊Dic3—42no—
31C3⋊SL(2,ℤ/4)—24no—
32#3757—44no—
33C2×#379—91noSylow
34C25×C3—24no—
35C25×C3—31no—
36C25×C3—31no—
37C25×C3—34no—
38C25×C3—32no—
39C25×C3—64no—
40C25×C3Dic314yescomplemented
41C25×C3C2×D312yes—
42C25×C3C2×D311yescharacteristic
43C23×A4—212no—
44C23×A4Dic3112yescomplemented
45C23×A4C2×D316yes—
46C23×A4C2×D313yes—
47C23×Dic3—32no—
48C23×Dic3—32no—
49C2×SL(2,ℤ/4)—312no—
50C2×SL(2,ℤ/4)—612no—
51C2×#217—34no—
52C2×#217—38no—
53C2×#217—34no—
54C2×#217—34no—
55C2×#217—34no—
56C2×#217—64no—
57C2×#217—68no—
58C2×#217—64no—
59C2×#217—61no—
60C2×#217—62no—
61C2×#217—64no—
62C2×#217—61no—
63C2×#217—123no—
64C23×C32—44no—
65C23×C32—41no—
66C23×C32—42no—
67C23×C32—84no—
68C2×C3×A4—24no—
69C2×C3×A4C22⋊C414yescomplemented
70C2×C3×A4C22×C411yescharacteristic
71C2×C3×A4C2×D412yes—
72C2×C3⋊Dic3—44no—
73C2×C3⋊Dic3—84no—
74C26C3⋊D311yescharacteristic
75C22×C22⋊C4—92no—
76C22×C22⋊C4—91no—
77C22×C22⋊C4—91no—
78C22×C22⋊C4—92no—
79#379—94no—
80#379—94no—
81C24×C3—28no—
82C24×C3—24no—
83C24×C3—31no—
84C24×C3—34no—
85C24×C3—32no—
86C24×C3—31no—
87C24×C3—32no—
88C24×C3—34no—
89C24×C3—38no—
90C24×C3—34no—
91C24×C3—34no—
92C24×C3—32no—
93C24×C3—32no—
94C24×C3—31no—
95C24×C3—38no—
96C24×C3—34no—
97C24×C3—43no—
98C24×C3—64no—
99C24×C3—64no—
100C24×C3—68no—
101C24×C3—64no—
102C24×C3—62no—
103C24×C3—61no—
104C24×C3—64no—
105C24×C3—64no—
106C24×C3—68no—
107C24×C3—616no—
108C24×C3—68no—
109C24×C3—616no—
110C24×C3C2×Dic312yes—
111C24×C3C2×Dic314yescomplemented
112C24×C3#6714yes—
113C24×C3S411yescharacteristic
114C24×C3C22×D311yescharacteristic
115C22×A4—224no—
116C22×A4—212no—
117C22×A4C2×Dic316yes—
118C22×A4C2×Dic3112yescomplemented
119C22×A4#67112yes—
120C22×A4C22×D313yes—
121C22×Dic3—34no—
122C22×Dic3—34no—
123C22×Dic3—64no—
124C22×Dic3—64no—
125C22×Dic3—64no—
126C22×Dic3—64no—
127C22×Dic3—64no—
128C22×Dic3—62no—
129C22×Dic3—62no—
130C22×Dic3—126no—
131SL(2,ℤ/4)—612no—
132#217—68no—
133#217—64no—
134#217—616no—
135#217—68no—
136#217—64no—
137#217—64no—
138#217—64no—
139#217—1212no—
140C22×C32—42no—
141C22×C32—44no—
142C22×C32—44no—
143C22×C32—41no—
144C22×C32—84no—
145C22×C32—88no—
146C3×A4C2×C22⋊C411yescharacteristic, complemented
147C3⋊Dic3—84no—
148C25—24no—
149C25—31no—
150C25—31no—
151C25—34no—
152C25—32no—
153C25—64no—
154C25C3⋊Dic314yescomplemented
155C25C2×C3⋊D312yes—
156C25C2×C3⋊D311yescharacteristic
157C23×C4—92no—
158C23×C4—92no—
159C2×C22⋊C4—98no—
160C2×C22⋊C4—94no—
161C2×C22⋊C4—94no—
162C2×C22⋊C4—94no—
163C2×C22⋊C4—94no—
164C2×C22⋊C4—184no—
165C2×C22⋊C4—188no—
166C2×C22⋊C4—184no—
167C2×C22⋊C4—181no—
168C2×C22⋊C4—182no—
169C2×C22⋊C4—184no—
170C2×C22⋊C4—181no—
171C23×C3—24no—
172C23×C3—24no—
173C23×C3—32no—
174C23×C3—32no—
175C23×C3—34no—
176C23×C3—34no—
177C23×C3—31no—
178C23×C3—31no—
179C23×C3—34no—
180C23×C3—32no—
181C23×C3—32no—
182C23×C3—34no—
183C23×C3—31no—
184C23×C3—34no—
185C23×C3—38no—
186C23×C3—38no—
187C23×C3—316no—
188C23×C3—34no—
189C23×C3—34no—
190C23×C3—34no—
191C23×C3—38no—
192C23×C3—32no—
193C23×C3—46no—
194C23×C3—43no—
195C23×C3—412no—
196C23×C3—64no—
197C23×C3—68no—
198C23×C3—64no—
199C23×C3—68no—
200C23×C3—616no—
201C23×C3—68no—
202C23×C3—64no—
203C23×C3—61no—
204C23×C3—62no—
205C23×C3—64no—
206C23×C3—62no—
207C23×C3—64no—
208C23×C3—616no—
209C23×C3—68no—
210C23×C3—64no—
211C23×C3—68no—
212C23×C3—68no—
213C23×C3—616no—
214C23×C3—616no—
215C23×C3—68no—
216C23×C3—632no—
217C23×C3—64no—
218C23×C3—812no—
219C23×C3#21714yescomplemented
220C23×C3SL(2,ℤ/4)14yescomplemented
221C23×C3C22×Dic311yescharacteristic
222C23×C3C2×#6712yes—
223C23×C3C2×S412yes—
224C23×C3C2×S411yescharacteristic
225C2×A4—212no—
226C2×A4#217112yescomplemented
227C2×A4C22×Dic313yes—
228C2×A4C2×#6716yes—
229C2×Dic3—64no—
230C2×Dic3—64no—
231C2×Dic3—64no—
232C2×Dic3—64no—
233C2×Dic3—64no—
234C2×Dic3—64no—
235C2×Dic3—1212no—
236C2×Dic3—128no—
237C2×Dic3—124no—
238C2×Dic3—124no—
239C2×Dic3—2412no—
240C2×C32—41no—
241C2×C32—42no—
242C2×C32—44no—
243C2×C32—84no—
244C24—28no—
245C24—24no—
246C24—31no—
247C24—31no—
248C24—32no—
249C24—34no—
250C24—34no—
251C24—32no—
252C24—38no—
253C24—32no—
254C24—32no—
255C24—31no—
256C24—34no—
257C24—34no—
258C24—38no—
259C24—34no—
260C24—64no—
261C24—64no—
262C24—68no—
263C24—64no—
264C24—62no—
265C24—61no—
266C24—64no—
267C24—64no—
268C24—68no—
269C24—616no—
270C24—68no—
271C24—616no—
272C24C2×C3⋊Dic312yes—
273C24C2×C3⋊Dic314yescomplemented
274C24#63814yes—
275C24C3⋊S411yescharacteristic
276C24C22×C3⋊D311yescharacteristic
277C22×C4—94no—
278C22×C4—94no—
279C22×C4—184no—
280C22×C4—184no—
281C22×C4—184no—
282C22×C4—184no—
283C22×C4—184no—
284C22×C4—182no—
285C22×C4—182no—
286C22⋊C4—188no—
287C22⋊C4—184no—
288C22⋊C4—1816no—
289C22⋊C4—188no—
290C22⋊C4—184no—
291C22⋊C4—184no—
292C22⋊C4—184no—
293C22×C3—24no—
294C22×C3—28no—
295C22×C3—34no—
296C22×C3—31no—
297C22×C3—32no—
298C22×C3—31no—
299C22×C3—31no—
300C22×C3—32no—
301C22×C3—32no—
302C22×C3—32no—
303C22×C3—34no—
304C22×C3—38no—
305C22×C3—34no—
306C22×C3—34no—
307C22×C3—38no—
308C22×C3—34no—
309C22×C3—46no—
310C22×C3—412no—
311C22×C3—412no—
312C22×C3—43no—
313C22×C3—64no—
314C22×C3—68no—
315C22×C3—64no—
316C22×C3—616no—
317C22×C3—61no—
318C22×C3—64no—
319C22×C3—62no—
320C22×C3—64no—
321C22×C3—68no—
322C22×C3—616no—
323C22×C3—64no—
324C22×C3—68no—
325C22×C3—824no—
326C22×C3—812no—
327C22×C3C2×#21711yescharacteristic, complemented
328C22×C3C2×SL(2,ℤ/4)12yes—
329C22×C3C2×SL(2,ℤ/4)14yescomplemented
330C22×C3GL(2,ℤ/4)14yes—
331C22×C3C22×S411yescharacteristic
332A4C2×#21713yescomplemented
333Dic3—124no—
334Dic3—124no—
335Dic3—2412no—
336C32—41noSylow
337C23—24no—
338C23—24no—
339C23—32no—
340C23—32no—
341C23—34no—
342C23—34no—
343C23—31no—
344C23—31no—
345C23—34no—
346C23—32no—
347C23—32no—
348C23—34no—
349C23—31no—
350C23—34no—
351C23—38no—
352C23—38no—
353C23—316no—
354C23—34no—
355C23—34no—
356C23—34no—
357C23—38no—
358C23—32no—
359C23—68no—
360C23—64no—
361C23—616no—
362C23—68no—
363C23—64no—
364C23—68no—
365C23—64no—
366C23—64no—
367C23—61no—
368C23—62no—
369C23—64no—
370C23—62no—
371C23—616no—
372C23—68no—
373C23—68no—
374C23—64no—
375C23—616no—
376C23—68no—
377C23—616no—
378C23—68no—
379C23—632no—
380C23—64no—
381C23#375714yescomplemented
382C23C3⋊SL(2,ℤ/4)14yescomplemented
383C23C22×C3⋊Dic311yescharacteristic
384C23C2×#63812yes—
385C23C2×C3⋊S412yes—
386C23C2×C3⋊S411yescharacteristic
387C2×C4—184no—
388C2×C4—184no—
389C2×C4—184no—
390C2×C4—184no—
391C2×C4—184no—
392C2×C4—184no—
393C2×C4—368no—
394C2×C4—364no—
395C2×C4—364no—
396C2×C3—24no—
397C2×C3—32no—
398C2×C3—31no—
399C2×C3—31no—
400C2×C3—34no—
401C2×C3—412no—
402C2×C3—43no—
403C2×C3—46no—
404C2×C3—64no—
405C2×C3—812no—
406C2×C3#543214yescomplemented
407C2×C3C22×SL(2,ℤ/4)11yescharacteristic
408C2×C3C2×GL(2,ℤ/4)12yes—
409C22—28no—
410C22—24no—
411C22—34no—
412C22—31no—
413C22—32no—
414C22—38no—
415C22—34no—
416C22—34no—
417C22—31no—
418C22—31no—
419C22—32no—
420C22—32no—
421C22—32no—
422C22—34no—
423C22—38no—
424C22—34no—
425C22—64no—
426C22—68no—
427C22—64no—
428C22—616no—
429C22—61no—
430C22—64no—
431C22—62no—
432C22—64no—
433C22—68no—
434C22—616no—
435C22—68no—
436C22—64no—
437C22C2×#375711yescharacteristic, complemented
438C22C2×C3⋊SL(2,ℤ/4)12yes—
439C22C2×C3⋊SL(2,ℤ/4)14yescomplemented
440C22#6426914yes—
441C22C22×C3⋊S411yescharacteristic
442C4—364no—
443C4—364no—
444C3—43no—
445C3C2×#543211yescharacteristic, complemented
446C2—24no—
447C2—32no—
448C2—31no—
449C2—31no—
450C2—34no—
451C2—64no—
452C2#1059366614yesdirect product factor
453C2C22×C3⋊SL(2,ℤ/4)11yescharacteristic
454C2C2×#6426912yes—
subgroupG/H
centerC23C2×C3⋊S4
commutatorC2×C3×A4C22×C4
FrattiniC22C22×C3⋊S4
FittingC26×C3D3
socleC25×C3C2×D3
prime radicalC24×C3×A4C2
cosocleC22×C3×A4C23
hypercenterC24C3⋊S4
hypocenterC3×A4C2×C22⋊C4
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C22×C3⋊SL(2,ℤ/4)C2semidirect
3. #10593666C2direct (N × H)
7. C23×C3×A4C4semidirect
11. C2×C3⋊SL(2,ℤ/4)C22semidirect
27. C22×C3×A4C2×C4semidirect
40. C25×C3Dic3semidirect
44. C23×A4Dic3semidirect
69. C2×C3×A4C22⋊C4semidirect
111. C24×C3C2×Dic3semidirect
118. C22×A4C2×Dic3semidirect
146. C3×A4C2×C22⋊C4semidirect
154. C25C3⋊Dic3semidirect
219. C23×C3#217semidirect
220. C23×C3SL(2,ℤ/4)semidirect
226. C2×A4#217semidirect
273. C24C2×C3⋊Dic3semidirect
327. C22×C3C2×#217semidirect
329. C22×C3C2×SL(2,ℤ/4)semidirect
332. A4C2×#217semidirect
381. C23#3757semidirect
382. C23C3⋊SL(2,ℤ/4)semidirect
406. C2×C3#5432semidirect
437. C22C2×#3757semidirect
439. C22C2×C3⋊SL(2,ℤ/4)semidirect
445. C3C2×#5432semidirect
452. C2#10593666direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C3×A42
C22×C3⋊SL(2,ℤ/4)2
#105936662
C2×#54323
C2×#52473
C2×#37574