Finite Group Databasebeta

← #11921989

Subgroups — #11921989

Order 1152.

892 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 892 conjugacy classes of subgroups — too many to draw. Only its 87 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×C4×C3⋊S4C211yesmaximal, characteristic
2C2×(C3⋊S4)⋊C4C212yesmaximal
3A4×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C3×C4⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
5#10593238C212yesmaximal, complemented
6C4⋊C4×S4—31nomaximal
7#74010—31nomaximal
8C22×C3⋊S4C2211yescharacteristic
9C2×C3×C4×A4C2211yescharacteristic
10C2×Dic3×A4C2212yes—
11C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
12C4×C3⋊S4C414yescomplemented
13C2×C3×SL(2,ℤ/4)C2212yes—
14(C3⋊S4)⋊C4—24no—
15#63900—41nomaximal
16C2×C4×S4—31no—
17C2×C4×S4—32no—
18C2×C4×S4—61no—
19C2×C4×#67—31no—
20C22×C4⋊Dic3D311yescharacteristic, complemented
21C2×D3×C4⋊C4—31no—
22C2×#67⋊C4—32no—
23A4×C4⋊C4—31no—
24C4⋊SL(2,ℤ/4)D311yescharacteristic, complemented
25SL(2,ℤ/4)⋊C4—32no—
26C3×#380—31no—
27#4987—31no—
28#4975—31no—
29Dic3×C4⋊C4—31no—
30#4946—32no—
31#4668—32no—
32#4647—32no—
33C22×C3×A4C2311yescharacteristic
34C2×C3⋊S4C2×C412yes—
35C2×C3⋊S4D412yes—
36C2×C3⋊S4Q812yes—
37C2×C4×C3⋊D3—41no—
38C3×C4×A4C2×C412yescomplemented
39C2×#624—42no—
40Dic3×A4—22no—
41C3⋊SL(2,ℤ/4)C2×C412yescomplemented
42C3×SL(2,ℤ/4)—22no—
43C3×C4⋊Dic3—41no—
44C3×C4⋊Dic3—41no—
45#3724—42no—
46D4×C4⋊C4—91noSylow
47C22×S4—31no—
48C22×S4—61no—
49C23×C3×C4C2×D311yescharacteristic
50C22×#67—31no—
51C23×Dic3C2×D312yes—
52C22×C4×D3—31no—
53C22×C4×D3—32no—
54C2×C4×A4—21no—
55C2×C4×A4—32no—
56C2×C4×A4C2×D311yescharacteristic
57C2×SL(2,ℤ/4)—31no—
58C2×SL(2,ℤ/4)—61no—
59C2×SL(2,ℤ/4)C2×D312yes—
60C4×S4—34no—
61C4×S4—64no—
62C4×S4—64no—
63C2×C3×C4⋊C4—31no—
64C2×C3×C4⋊C4—31no—
65C2×C3×C22⋊C4—32no—
66C2×#217—31no—
67C4×#67—34no—
68C4×#67—34no—
69C2×(C2×D3)⋊C4—31no—
70C2×(C2×D3)⋊C4—32no—
71C2×C4⋊Dic3—31no—
72C2×C4⋊Dic3—32no—
73C2×C4⋊Dic3—31no—
74C2×Dic3⋊C4—31no—
75C2×Dic3⋊C4—32no—
76C2×Dic3⋊C4—32no—
77C2×Dic3⋊C4—32no—
78C2×C4×Dic3—31no—
79C2×C4×Dic3—32no—
80D3×C4⋊C4—61no—
81D3×C4⋊C4—62no—
82D3×C4⋊C4—61no—
83D3×C4⋊C4—121no—
84#67⋊C4—64no—
85#67⋊C4—64no—
86C3×#95—32no—
87C3⋊#95—32no—
88C3⋊#95—32no—
89C22×C3⋊D3—41no—
90C2×C3×A4C22×C411yescharacteristic
91C2×C3×A4C2×D411yescharacteristic
92C2×C3×A4C2×Q811yescharacteristic
93C3⋊S4C4⋊C414yescomplemented
94C2×C32×C4—41no—
95C2×C3⋊Dic3—41no—
96C4×C3⋊D3—44no—
97C2×C3×Dic3—42no—
98C2×C3×Dic3—42no—
99#624—84no—
100C2×C4×D4—92no—
101C2×C4×D4—91no—
102C22×C4⋊C4—31no—
103C22×C4⋊C4—91no—
104#389—92no—
105#385—92no—
106#385—92no—
107#384—91no—
108#380—31no—
109#380—91no—
110C4×C4⋊C4—91no—
111C24×C3C22×D311yescharacteristic
112C23×D3—31no—
113C22×A4—21no—
114C22×A4C22×D311yescharacteristic
115C2×S4—32no—
116C2×S4—32no—
117C2×S4—32no—
118C2×S4—62no—
119C2×S4—62no—
120C2×S4—62no—
121C22×C3×C4—31no—
122C22×C3×C4—31no—
123C22×C3×C4—32no—
124C22×C3×C4—32no—
125C22×C3×C4—32no—
126C22×C3×C4C4×D312yescomplemented
127C2×#67—32no—
128C2×#67—32no—
129C2×#67—32no—
130C2×#67—32no—
131C2×#67—32no—
132C2×#67—32no—
133C22×Dic3—22no—
134C22×Dic3—31no—
135C22×Dic3—31no—
136C22×Dic3—31no—
137C22×Dic3—32no—
138C22×Dic3—32no—
139C22×Dic3—62no—
140C2×C4×D3—34no—
141C2×C4×D3—61no—
142C2×C4×D3—62no—
143C2×C4×D3—61no—
144C2×C4×D3—62no—
145C2×C4×D3—64no—
146C2×C4×D3—62no—
147C2×C4×D3—121no—
148C2×C4×D3—122no—
149C2×C4×D3—122no—
150C2×C4×D3—241no—
151C4×A4—22no—
152C4×A4—62no—
153C4×A4C4×D312yescomplemented
154SL(2,ℤ/4)—22no—
155SL(2,ℤ/4)—32no—
156SL(2,ℤ/4)—62no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—62no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—121no—
161C3×C22⋊C4—62no—
162C3×C22⋊C4—62no—
163#217—32no—
164#217—32no—
165(C2×D3)⋊C4—34no—
166(C2×D3)⋊C4—64no—
167C4⋊Dic3—31no—
168C4⋊Dic3—32no—
169C4⋊Dic3—41no—
170C4⋊Dic3—61no—
171C4⋊Dic3S411yescharacteristic, complemented
172Dic3⋊C4—34no—
173Dic3⋊C4—64no—
174Dic3⋊C4—62no—
175Dic3⋊C4—62no—
176Dic3⋊C4—122no—
177Dic3⋊C4—122no—
178C4×Dic3—34no—
179C4×Dic3—64no—
180C22×C32—41no—
181C2×C3⋊D3—42no—
182C2×C3⋊D3—42no—
183C2×C3⋊D3—42no—
184C3×A4C2×C4⋊C411yescharacteristic, complemented
185C32×C4—42no—
186C3⋊Dic3—42no—
187C3×Dic3—82no—
188C3×Dic3—82no—
189C22×D4—91no—
190C23×C4—32no—
191C23×C4—91no—
192C23×C4—92no—
193C23×C4D3211yescharacteristic
194C4×D4—94no—
195C4×D4—94no—
196C4×D4—184no—
197C4×D4—184no—
198C2×C4⋊C4—31no—
199C2×C4⋊C4—31no—
200C2×C4⋊C4—91no—
201C2×C4⋊C4—91no—
202C2×C4⋊C4—91no—
203C2×C4⋊C4—92no—
204C2×C4⋊C4—92no—
205C2×C4⋊C4—92no—
206C2×C4⋊C4—92no—
207C2×C4⋊C4—181no—
208C2×C4⋊C4—182no—
209C2×C4⋊C4—181no—
210C2×C22⋊C4—32no—
211C2×C22⋊C4—91no—
212C2×C22⋊C4—91no—
213C2×C22⋊C4—92no—
214C2×C42—91no—
215C2×C42—92no—
216#95—32no—
217#95—92no—
218#95—92no—
219C23×C3—31no—
220C23×C3—31no—
221C23×C3—31no—
222C23×C3—31no—
223C23×C3C2×C4×D311yescharacteristic
224C23×C3D3×D411yescharacteristic
225C23×C3D3×Q811yescharacteristic
226C22×D3—32no—
227C22×D3—32no—
228C22×D3—32no—
229C22×D3—61no—
230C22×D3—61no—
231C22×D3—61no—
232C22×D3—61no—
233C22×D3—121no—
234C22×D3—241no—
235C2×A4—21no—
236C2×A4—21no—
237C2×A4—21no—
238C2×A4C2×C4×D311yescharacteristic
239C2×A4D3×D411yescharacteristic
240C2×A4D3×Q811yescharacteristic
241S4—34no—
242S4—64no—
243C2×C3×C4—31no—
244C2×C3×C4—32no—
245C2×C3×C4—32no—
246C2×C3×C4—32no—
247C2×C3×C4—41no—
248C2×C3×C4—61no—
249C2×C3×C4—62no—
250C2×C3×C4—62no—
251C2×C3×C4—62no—
252C2×C3×C4—62no—
253C2×C3×C4—62no—
254C2×C3×C4—62no—
255C2×C3×C4—81no—
256C2×C3×C4—122no—
257C2×C3×C4C2×S411yescharacteristic
258#67—34no—
259#67—34no—
260#67—34no—
261#67—34no—
262C2×Dic3—32no—
263C2×Dic3—32no—
264C2×Dic3—32no—
265C2×Dic3—32no—
266C2×Dic3—32no—
267C2×Dic3—32no—
268C2×Dic3—42no—
269C2×Dic3—62no—
270C2×Dic3—62no—
271C2×Dic3—61no—
272C2×Dic3—61no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—121no—
278C2×Dic3—241no—
279C2×Dic3C2×S412yes—
280C4×D3—64no—
281C4×D3—64no—
282C4×D3—124no—
283C4×D3—124no—
284C4×D3—124no—
285C4×D3—244no—
286C4×D3—244no—
287C2×C32—41no—
288C2×C32—41no—
289C2×C32—41no—
290C3⋊D3—44no—
291C24—91no—
292C24C2×D3211yescharacteristic
293C2×D4—92no—
294C2×D4—92no—
295C2×D4—92no—
296C2×D4—92no—
297C2×D4—92no—
298C2×D4—92no—
299C22×C4—31no—
300C22×C4—31no—
301C22×C4—32no—
302C22×C4—32no—
303C22×C4—32no—
304C22×C4—62no—
305C22×C4—92no—
306C22×C4—94no—
307C22×C4—91no—
308C22×C4—91no—
309C22×C4—91no—
310C22×C4—92no—
311C22×C4—182no—
312C22×C4—181no—
313C22×C4—182no—
314C22×C4—182no—
315C22×C4—184no—
316C22×C4—181no—
317C22×C4—182no—
318C22×C4—362no—
319C22×C4#62412yescomplemented
320C4⋊C4—31no—
321C4⋊C4—61no—
322C4⋊C4—62no—
323C4⋊C4—61no—
324C4⋊C4—92no—
325C4⋊C4—94no—
326C4⋊C4—91no—
327C4⋊C4—182no—
328C4⋊C4—181no—
329C4⋊C4—182no—
330C4⋊C4—184no—
331C4⋊C4—362no—
332C22⋊C4—62no—
333C22⋊C4—62no—
334C22⋊C4—94no—
335C22⋊C4—92no—
336C22⋊C4—92no—
337C22⋊C4—184no—
338C42—94no—
339C42—184no—
340C22×C3—31no—
341C22×C3—31no—
342C22×C3—31no—
343C22×C3—31no—
344C22×C3—31no—
345C22×C3—31no—
346C22×C3—31no—
347C22×C3—31no—
348C22×C3—31no—
349C22×C3—41no—
350C22×C3—61no—
351C22×C3—81no—
352C22×C3D3×C4⋊C411yescharacteristic, complemented
353C22×C3C22×S411yescharacteristic
354C2×D3—34no—
355C2×D3—62no—
356C2×D3—62no—
357C2×D3—62no—
358C2×D3—62no—
359C2×D3—62no—
360C2×D3—62no—
361C2×D3—122no—
362C2×D3—122no—
363C2×D3—122no—
364C2×D3—242no—
365C2×D3—242no—
366C2×D3—242no—
367A4—21no—
368A4D3×C4⋊C411yescharacteristic, complemented
369C3×C4—32no—
370C3×C4—42no—
371C3×C4—82no—
372C3×C4—122no—
373C3×C4—122no—
374C3×C4—242no—
375C3×C4C4×S412yescomplemented
376Dic3—22no—
377Dic3—34no—
378Dic3—62no—
379Dic3—62no—
380Dic3—62no—
381Dic3—82no—
382Dic3—122no—
383Dic3—242no—
384C32—41noSylow
385C23—31no—
386C23—31no—
387C23—31no—
388C23—31no—
389C23—92no—
390C23—92no—
391C23—92no—
392C23—181no—
393C23—181no—
394C23—181no—
395C23—181no—
396C23#379711yescharacteristic
397C23#380211yescharacteristic
398C23C2×#62411yescharacteristic
399D4—94no—
400D4—94no—
401D4—94no—
402D4—94no—
403C2×C4—31no—
404C2×C4—32no—
405C2×C4—32no—
406C2×C4—32no—
407C2×C4—32no—
408C2×C4—61no—
409C2×C4—62no—
410C2×C4—62no—
411C2×C4—62no—
412C2×C4—62no—
413C2×C4—62no—
414C2×C4—62no—
415C2×C4—92no—
416C2×C4—92no—
417C2×C4—92no—
418C2×C4—92no—
419C2×C4—92no—
420C2×C4—92no—
421C2×C4—184no—
422C2×C4—182no—
423C2×C4—182no—
424C2×C4—181no—
425C2×C4—181no—
426C2×C4—181no—
427C2×C4—181no—
428C2×C4—184no—
429C2×C4—182no—
430C2×C4—182no—
431C2×C4—364no—
432C2×C4—364no—
433C2×C4D3×S411yescharacteristic
434C2×C3—31no—
435C2×C3—31no—
436C2×C3—31no—
437C2×C3—31no—
438C2×C3—41no—
439C2×C3—41no—
440C2×C3—41no—
441C2×C3—81no—
442C2×C3—81no—
443C2×C3—81no—
444C2×C3C2×C4×S411yescharacteristic
445C2×C3D4×S411yescharacteristic
446C2×C3Q8×S411yescharacteristic
447D3—64no—
448D3—124no—
449D3—244no—
450C22—31no—
451C22—31no—
452C22—31no—
453C22—31no—
454C22—31no—
455C22—31no—
456C22—31no—
457C22—31no—
458C22—31no—
459C22—61no—
460C22—94no—
461C22—182no—
462C22—182no—
463C22—182no—
464C22—182no—
465C22—182no—
466C22—182no—
467C22#6390011yescharacteristic, complemented
468C22C2×D3×S411yescharacteristic
469C4—32no—
470C4—62no—
471C4—94no—
472C4—122no—
473C4—122no—
474C4—182no—
475C4—182no—
476C4—182no—
477C4(C3⋊S4)⋊C412yescomplemented
478C3—41no—
479C3—81no—
480C3C4⋊C4×S411yescharacteristic, complemented
481C2—31no—
482C2—31no—
483C2—31no—
484C2—31no—
485C2—184no—
486C2(C3⋊S4)⋊Q811yescharacteristic
487C2#1059643211yescharacteristic
488C2C2×(C3⋊S4)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutatorC2×C3×A4C22×C4
FittingC23×C3×C4C2×D3
socleC24×C3C22×D3
prime radicalC22×C3⋊S4C22
cosocleC22×C3×A4C23
hypercenterC2×C4D3×S4
hypocenterC3×A4C2×C4⋊C4
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. A4×C4⋊Dic3C2semidirect
4. C3×C4⋊SL(2,ℤ/4)C2semidirect
5. #10593238C2semidirect
12. C4×C3⋊S4C4semidirect
20. C22×C4⋊Dic3D3semidirect
24. C4⋊SL(2,ℤ/4)D3semidirect
38. C3×C4×A4C2×C4semidirect
41. C3⋊SL(2,ℤ/4)C2×C4semidirect
93. C3⋊S4C4⋊C4semidirect
126. C22×C3×C4C4×D3semidirect
153. C4×A4C4×D3semidirect
171. C4⋊Dic3S4semidirect
184. C3×A4C2×C4⋊C4semidirect
319. C22×C4#624semidirect
352. C22×C3D3×C4⋊C4semidirect
368. A4D3×C4⋊C4semidirect
375. C3×C4C4×S4semidirect
467. C22#63900semidirect
477. C4(C3⋊S4)⋊C4semidirect
480. C3C4⋊C4×S4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊S42
C2×(C3⋊S4)⋊C42
A4×C4⋊Dic32
C3×C4⋊SL(2,ℤ/4)2
#105932382
C4⋊C4×S43
#740103
#639004