Finite Group Databasebeta

← #11922500

Subgroups — #11922500

Order 1152.

856 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 856 conjugacy classes of subgroups — too many to draw. Only its 95 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×Dic3×A4C211yesmaximal, characteristic
2#10593666C211yesmaximal, characteristic
3C3×#5432C211yesmaximal, characteristic
4Dic3⋊SL(2,ℤ/4)C212yesmaximal, complemented
5Dic3×SL(2,ℤ/4)C212yesmaximal, complemented
6#85482—31nomaximal
7#73817—31nomaximal
8C23×C3×A4C2211yescharacteristic
9C2×Dic3×A4C414yescomplemented
10C2×Dic3×A4C2211yescharacteristic
11C2×Dic3×A4C2211yescharacteristic
12C2×C3⋊SL(2,ℤ/4)C2212yes—
13C2×C3×SL(2,ℤ/4)C2212yes—
14#63955—41nomaximal
15C24×Dic3D311yescharacteristic
16C22×C4×A4—31no—
17C2×#877—31no—
18C2×#877—31no—
19#5432—31no—
20#5432—61no—
21#5432D311yescharacteristic
22C4⋊SL(2,ℤ/4)—32no—
23C4×SL(2,ℤ/4)—32no—
24C3×#379—31no—
25#5247—31no—
26#4943—31no—
27#4943—31no—
28#4942—32no—
29#4942—32no—
30Dic3×C22⋊C4—32no—
31Dic3×C22⋊C4—32no—
32C22×C3×A4—22no—
33C22×C3×A4C2×C412yes—
34C22×C3×A4C2311yescharacteristic
35C22×C3×Dic3—41no—
36Dic3×A4C2×C412yes—
37Dic3×A4C2×C412yes—
38C3⋊SL(2,ℤ/4)—22no—
39C3×SL(2,ℤ/4)—22no—
40#3757—41no—
41C3×#217—41no—
42Dic3⋊Dic3—42no—
43Dic32—42no—
44#2280—91noSylow
45C25×C3C2×D311yescharacteristic
46C23×A4—21no—
47C23×A4C2×D311yescharacteristic
48C23×Dic3—31no—
49C23×Dic3—31no—
50C23×Dic3—31no—
51C23×Dic3—31no—
52C23×Dic3—34no—
53C23×Dic3Dic314yescomplemented
54C23×Dic3C2×D311yescharacteristic
55C23×Dic3C2×D311yescharacteristic
56C2×C4×A4—34no—
57C2×C4×A4—31no—
58C2×C4×A4—31no—
59C2×SL(2,ℤ/4)—32no—
60C2×SL(2,ℤ/4)—62no—
61C2×SL(2,ℤ/4)C2×D312yes—
62C2×C3×C22⋊C4—32no—
63C2×C3×C22⋊C4—31no—
64C2×C3×C22⋊C4—31no—
65C2×C3×C22⋊C4—32no—
66C2×#217—32no—
67C2×#217—31no—
68C2×#217—31no—
69C2×#217—32no—
70#926—121no—
71C2×Dic3⋊C4—32no—
72C2×Dic3⋊C4—32no—
73C2×C4×Dic3—32no—
74C2×C4×Dic3—32no—
75#877—64no—
76#877—61no—
77#877—61no—
78#877—61no—
79#877—61no—
80C3⋊#95—32no—
81C3⋊#95—32no—
82C3⋊#95—32no—
83C3⋊#95—32no—
84C23×C32—41no—
85C2×C3×A4—22no—
86C2×C3×A4C22×C411yescharacteristic
87C2×C3×A4#4112yes—
88C2×C3⋊Dic3—42no—
89C2×C3×Dic3—42no—
90C2×C3×Dic3—44no—
91C2×C3×Dic3—41no—
92C2×C3×Dic3—41no—
93C24×C4—31no—
94C2×#117—91no—
95C2×#117—91no—
96#381—91no—
97#381—91no—
98#380—92no—
99#380—92no—
100#379—31no—
101#379—91no—
102C4×C22⋊C4—92no—
103C4×C22⋊C4—92no—
104C24×C3—22no—
105C24×C3—31no—
106C24×C3—31no—
107C24×C3—32no—
108C24×C3—62no—
109C24×C3C2×Dic312yes—
110C24×C3C22×D311yescharacteristic
111C22×A4—22no—
112C22×A4—22no—
113C22×A4—21no—
114C22×A4—42no—
115C22×A4C4×D312yes—
116C22×A4C22×D311yescharacteristic
117C22×C3×C4—32no—
118C22×C3×C4—32no—
119C22×C3×C4—121no—
120C22×Dic3—31no—
121C22×Dic3—34no—
122C22×Dic3—34no—
123C22×Dic3—31no—
124C22×Dic3—31no—
125C22×Dic3—31no—
126C22×Dic3—31no—
127C22×Dic3—31no—
128C22×Dic3—31no—
129C22×Dic3—34no—
130C22×Dic3—34no—
131C22×Dic3—34no—
132C22×Dic3—32no—
133C22×Dic3—32no—
134C22×Dic3—32no—
135C22×Dic3—32no—
136C22×Dic3—62no—
137C22×Dic3—62no—
138C22×Dic3—62no—
139C22×Dic3—61no—
140C22×Dic3C2×Dic312yes—
141C22×Dic3C2×Dic312yes—
142C22×Dic3S411yescharacteristic
143C4×A4—32no—
144C4×A4—32no—
145SL(2,ℤ/4)—22no—
146SL(2,ℤ/4)—62no—
147SL(2,ℤ/4)—122no—
148C3×C22⋊C4—62no—
149C3×C22⋊C4—61no—
150C3×C22⋊C4—62no—
151C3×C22⋊C4—64no—
152C3×C22⋊C4—62no—
153C3×C22⋊C4—61no—
154#217—41no—
155#217—62no—
156#217—61no—
157#217—62no—
158#217—64no—
159#217—62no—
160#217—61no—
161#217—121no—
162#217—241no—
163C4⋊Dic3—122no—
164Dic3⋊C4—62no—
165Dic3⋊C4—64no—
166Dic3⋊C4—62no—
167C4×Dic3—62no—
168C4×Dic3—64no—
169C4×Dic3—62no—
170C4×Dic3—122no—
171C22×C32—42no—
172C22×C32—41no—
173C22×C32—82no—
174C3×A4#11711yescharacteristic, complemented
175C3⋊Dic3—82no—
176C3×Dic3—42no—
177C3×Dic3—42no—
178C3×Dic3—82no—
179C25D3211yescharacteristic
180C23×C4—34no—
181C23×C4—31no—
182C23×C4—31no—
183C23×C4—91no—
184C23×C4—91no—
185C23×C4—91no—
186C23×C4—91no—
187C23×C4—94no—
188#117—181no—
189#117—181no—
190#117—181no—
191#117—184no—
192#117—181no—
193C2×C4⋊C4—92no—
194C2×C4⋊C4—92no—
195C2×C22⋊C4—31no—
196C2×C22⋊C4—31no—
197C2×C22⋊C4—32no—
198C2×C22⋊C4—32no—
199C2×C22⋊C4—91no—
200C2×C22⋊C4—91no—
201C2×C22⋊C4—92no—
202C2×C22⋊C4—92no—
203C2×C42—92no—
204C2×C42—92no—
205#95—92no—
206#95—92no—
207#95—92no—
208#95—92no—
209C23×C3—22no—
210C23×C3—31no—
211C23×C3—32no—
212C23×C3—32no—
213C23×C3—31no—
214C23×C3—34no—
215C23×C3—32no—
216C23×C3—32no—
217C23×C3—31no—
218C23×C3—41no—
219C23×C3—62no—
220C23×C3—62no—
221C23×C3—62no—
222C23×C3—61no—
223C23×C3—64no—
224C23×C3—62no—
225C23×C3—64no—
226C23×C3—81no—
227C23×C3#23512yes—
228C23×C3C22×Dic311yescharacteristic
229C23×C3C2×S411yescharacteristic
230C2×A4—22no—
231C2×A4—21no—
232C2×A4—22no—
233C2×A4—42no—
234C2×A4C2×C4×D311yescharacteristic
235C2×A4#23712yes—
236C2×C3×C4—62no—
237C2×C3×C4—62no—
238C2×C3×C4—62no—
239C2×C3×C4—62no—
240C2×C3×C4—62no—
241C2×C3×C4—62no—
242C2×C3×C4—121no—
243C2×C3×C4—121no—
244C2×C3×C4—124no—
245C2×Dic3—34no—
246C2×Dic3—31no—
247C2×Dic3—31no—
248C2×Dic3—32no—
249C2×Dic3—32no—
250C2×Dic3—32no—
251C2×Dic3—32no—
252C2×Dic3—34no—
253C2×Dic3—34no—
254C2×Dic3—32no—
255C2×Dic3—32no—
256C2×Dic3—42no—
257C2×Dic3—61no—
258C2×Dic3—61no—
259C2×Dic3—64no—
260C2×Dic3—62no—
261C2×Dic3—62no—
262C2×Dic3—62no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—122no—
267C2×Dic3—242no—
268C2×Dic3SL(2,ℤ/4)14yescomplemented
269C2×Dic3C2×S411yescharacteristic
270C2×Dic3C2×S411yescharacteristic
271C2×C32—42no—
272C2×C32—41no—
273C2×C32—82no—
274C24—22no—
275C24—31no—
276C24—31no—
277C24—32no—
278C24—62no—
279C24D3×Dic312yes—
280C24C2×D3211yescharacteristic
281C22×C4—31no—
282C22×C4—32no—
283C22×C4—32no—
284C22×C4—32no—
285C22×C4—32no—
286C22×C4—91no—
287C22×C4—91no—
288C22×C4—91no—
289C22×C4—91no—
290C22×C4—94no—
291C22×C4—94no—
292C22×C4—91no—
293C22×C4—91no—
294C22×C4—91no—
295C22×C4—92no—
296C22×C4—92no—
297C22×C4—94no—
298C22×C4—94no—
299C22×C4—94no—
300C22×C4—92no—
301C22×C4—92no—
302C22×C4—182no—
303C22×C4—182no—
304C22×C4—181no—
305C22×C4—182no—
306C4⋊C4—182no—
307C4⋊C4—184no—
308C4⋊C4—182no—
309C22⋊C4—62no—
310C22⋊C4—61no—
311C22⋊C4—62no—
312C22⋊C4—64no—
313C22⋊C4—61no—
314C22⋊C4—62no—
315C22⋊C4—182no—
316C22⋊C4—181no—
317C22⋊C4—182no—
318C22⋊C4—184no—
319C22⋊C4—181no—
320C22⋊C4—182no—
321C42—182no—
322C42—184no—
323C42—182no—
324C22×C3—22no—
325C22×C3—32no—
326C22×C3—31no—
327C22×C3—32no—
328C22×C3—32no—
329C22×C3—31no—
330C22×C3—31no—
331C22×C3—34no—
332C22×C3—32no—
333C22×C3—41no—
334C22×C3—42no—
335C22×C3—62no—
336C22×C3—64no—
337C22×C3—62no—
338C22×C3—61no—
339C22×C3—62no—
340C22×C3—64no—
341C22×C3—62no—
342C22×C3—82no—
343C22×C3—81no—
344C22×C3—82no—
345C22×C3—162no—
346C22×C3#92611yescharacteristic, complemented
347C22×C3C2×SL(2,ℤ/4)12yes—
348C22×C3C22×S411yescharacteristic
349A4—21no—
350A4#87711yescharacteristic, complemented
351C3×C4—122no—
352C3×C4—122no—
353C3×C4—122no—
354C3×C4—122no—
355Dic3—32no—
356Dic3—32no—
357Dic3—82no—
358Dic3—122no—
359Dic3—122no—
360Dic3—242no—
361Dic3—482no—
362Dic3C2×SL(2,ℤ/4)12yes—
363Dic3C2×SL(2,ℤ/4)12yes—
364C32—41noSylow
365C23—22no—
366C23—31no—
367C23—32no—
368C23—32no—
369C23—31no—
370C23—34no—
371C23—31no—
372C23—32no—
373C23—32no—
374C23—62no—
375C23—62no—
376C23—62no—
377C23—61no—
378C23—64no—
379C23—62no—
380C23—64no—
381C23C2×D3×Dic311yescharacteristic
382C23#380412yes—
383C23D3×S411yescharacteristic
384C2×C4—31no—
385C2×C4—31no—
386C2×C4—34no—
387C2×C4—62no—
388C2×C4—62no—
389C2×C4—62no—
390C2×C4—62no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—92no—
394C2×C4—92no—
395C2×C4—92no—
396C2×C4—92no—
397C2×C4—94no—
398C2×C4—94no—
399C2×C4—91no—
400C2×C4—91no—
401C2×C4—94no—
402C2×C4—92no—
403C2×C4—92no—
404C2×C4—181no—
405C2×C4—181no—
406C2×C4—184no—
407C2×C4—182no—
408C2×C4—182no—
409C2×C4—182no—
410C2×C4—182no—
411C2×C4—182no—
412C2×C4—182no—
413C2×C3—22no—
414C2×C3—32no—
415C2×C3—31no—
416C2×C3—31no—
417C2×C3—42no—
418C2×C3—41no—
419C2×C3—62no—
420C2×C3—82no—
421C2×C3—82no—
422C2×C3—81no—
423C2×C3—162no—
424C2×C3#591212yes—
425C2×C3C22×SL(2,ℤ/4)11yescharacteristic
426C22—22no—
427C22—31no—
428C22—32no—
429C22—32no—
430C22—32no—
431C22—31no—
432C22—31no—
433C22—34no—
434C22—32no—
435C22—62no—
436C22—64no—
437C22—62no—
438C22—61no—
439C22—62no—
440C22—64no—
441C22—62no—
442C22#6395511yescharacteristic, complemented
443C22D3×SL(2,ℤ/4)12yes—
444C22C2×D3×S411yescharacteristic
445C4—32no—
446C4—32no—
447C4—92no—
448C4—92no—
449C4—122no—
450C4—122no—
451C4—362no—
452C4—362no—
453C3—41no—
454C3—81no—
455C3#8548211yescharacteristic, complemented
456C2—22no—
457C2—32no—
458C2—31no—
459C2—31no—
460C2—62no—
461C2#1059646312yes—
462C2C2×D3×SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutatorC2×C3×A4C22×C4
FittingC25×C3C2×D3
socleC24×C3C22×D3
prime radicalC23×C3×A4C22
cosocleC22×C3×A4C23
hypercenterC23D3×S4
hypocenterC3×A4#117
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
4. Dic3⋊SL(2,ℤ/4)C2semidirect
5. Dic3×SL(2,ℤ/4)C2semidirect
9. C2×Dic3×A4C4semidirect
53. C23×Dic3Dic3semidirect
174. C3×A4#117semidirect
268. C2×Dic3SL(2,ℤ/4)semidirect
346. C22×C3#926semidirect
350. A4#877semidirect
442. C22#63955semidirect
455. C3#85482semidirect

Maximal subgroups

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

subgroupindex
C22×Dic3×A42
#105936662
C3×#54322
Dic3⋊SL(2,ℤ/4)2
Dic3×SL(2,ℤ/4)2
#854823
#738173
#639554