Finite Group Databasebeta

← #11922000

Subgroups — #11922000

Order 1152.

908 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 75 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⋊S4)C211yesmaximal, characteristic, complemented
2C2×C3×C4×S4C211yesmaximal, characteristic, complemented
3C2×#64207C212yesmaximal, complemented
4A4×C4⋊Dic3C211yesmaximal, characteristic, complemented
5#10593242C212yesmaximal, complemented
6#85310—31nomaximal
7#82352—31nomaximal
8C22×C3⋊S4C2212yes—
9C22×C3×S4C2211yescharacteristic
10C2×C3×C4×A4C2211yescharacteristic
11C2×Dic3×A4C2212yes—
12C4⋊(C3⋊S4)—22no—
13C2×C3×SL(2,ℤ/4)C2211yescharacteristic
14C3×C4×S4—22no—
15#64207—24no—
16#63909—41nomaximal
17C2×C4⋊S4—32no—
18C2×C4⋊S4—31no—
19C2×C4⋊S4—61no—
20C2×C4×S4D311yescharacteristic, complemented
21C2×C3×C4×D4—31no—
22C2×#939—32no—
23C2×#930—31no—
24C2×#930—31no—
25C22×C4⋊Dic3D311yescharacteristic, complemented
26A4×C4⋊C4—31no—
27(C2×S4)⋊C4—32no—
28#5212—31no—
29#4994—32no—
30#4961—32no—
31#4958—32no—
32#4939—31no—
33#4928—31no—
34C22×C3×A4C2311yescharacteristic
35C2×C3⋊S4—22no—
36C2×C3⋊S4—22no—
37C2×C3⋊S4—22no—
38C2×C3×S4—21no—
39C2×C3×S4—21no—
40C2×C3×S4D412yescomplemented
41C2×C4⋊(C3⋊D3)—41no—
42C2×C3×C4×D3—41no—
43C3×C4×A4D412yescomplemented
44C2×#626—42no—
45Dic3×A4—22no—
46C3×SL(2,ℤ/4)—21no—
47C3×C4⋊Dic3—41no—
48#3722—42no—
49#2416—91noSylow
50C22×S4—32no—
51C22×S4—62no—
52C22×S4C2×D311yescharacteristic
53C22×C3×D4—31no—
54C23×C3×C4—31no—
55C23×C3×C4C2×D311yescharacteristic
56C22×#67—32no—
57C22×#67—32no—
58C23×Dic3C2×D312yes—
59C22×D12—31no—
60C2×C4×A4—21no—
61C2×C4×A4—32no—
62C2×C4×A4C2×D311yescharacteristic
63C2×SL(2,ℤ/4)C2×D311yescharacteristic
64C4⋊S4—64no—
65C4⋊S4—64no—
66C4⋊S4—62no—
67C4×S4—22no—
68C3×C4×D4—62no—
69C3×C4×D4—62no—
70C2×C3×C4⋊C4—31no—
71C2×C3×C22⋊C4—31no—
72C2×C3×C22⋊C4—31no—
73C2×C3×C42—31no—
74C2×#217—32no—
75#939—64no—
76#939—64no—
77#930—61no—
78#930—62no—
79#930—62no—
80#930—62no—
81#930—61no—
82C2×(C2×D3)⋊C4—32no—
83C2×(C2×D3)⋊C4—32no—
84C2×(C2×D3)⋊C4—32no—
85C2×(C2×D3)⋊C4—32no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—32no—
89C2×C4⋊Dic3—31no—
90C2×Dic3⋊C4—32no—
91#895—121no—
92C3⋊#95—32no—
93C3⋊#95—32no—
94C22×C3⋊D3—42no—
95C22×C3×D3—41no—
96C2×C3×A4C2×D411yescharacteristic
97C2×C3×A4C2×D411yescharacteristic
98C2×C3×A4#4111yescharacteristic
99C3⋊S4—42no—
100C3×S4—22no—
101C2×C32×C4—41no—
102C4⋊(C3⋊D3)—82no—
103C2×C3×Dic3—41no—
104C2×C3×Dic3—42no—
105C3×C4×D3—82no—
106#626—84no—
107C2×#121—92no—
108C2×#121—91no—
109C2×#121—91no—
110C2×C4×D4—31no—
111C22×C4⋊C4—31no—
112#396—92no—
113#394—92no—
114#390—91no—
115#389—91no—
116#386—92no—
117#380—91no—
118C24×C3—31no—
119C24×C3C22×D311yescharacteristic
120C23×D3—32no—
121C22×A4—21no—
122C22×A4C22×D311yescharacteristic
123C2×S4—21no—
124C2×S4—21no—
125C2×S4—64no—
126C2×S4—62no—
127C2×S4—62no—
128C2×S4—62no—
129C2×S4—122no—
130C2×S4—122no—
131C2×S4D1212yescomplemented
132C2×C3×D4—32no—
133C2×C3×D4—32no—
134C2×C3×D4—61no—
135C2×C3×D4—61no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C22×C3×C4—31no—
139C22×C3×C4—31no—
140C22×C3×C4—32no—
141C22×C3×C4—31no—
142C22×C3×C4—31no—
143C22×C3×C4—31no—
144C22×C3×C4—61no—
145C22×C3×C4—62no—
146C22×C3×C4—62no—
147C22×C3×C4—61no—
148C22×C3×C4D1212yescomplemented
149C2×#67—62no—
150C2×#67—62no—
151C2×#67—64no—
152C2×#67—62no—
153C2×#67—62no—
154C2×#67—62no—
155C2×#67—62no—
156C2×#67—62no—
157C2×#67—62no—
158C2×#67—122no—
159C22×Dic3—22no—
160C22×Dic3—32no—
161C22×Dic3—32no—
162C22×Dic3—32no—
163C22×Dic3—62no—
164C2×D12—61no—
165C2×D12—62no—
166C2×D12—62no—
167C2×D12—61no—
168C2×D12—121no—
169C2×D12—122no—
170C2×D12—241no—
171C2×C4×D3—41no—
172C4×A4—22no—
173C4×A4—62no—
174C4×A4#6712yescomplemented
175SL(2,ℤ/4)—21no—
176C3×C4⋊C4—62no—
177C3×C4⋊C4—121no—
178C3×C22⋊C4—62no—
179C3×C22⋊C4—61no—
180C3×C22⋊C4—61no—
181C3×C42—62no—
182#217—64no—
183(C2×D3)⋊C4—62no—
184(C2×D3)⋊C4—64no—
185(C2×D3)⋊C4—64no—
186(C2×D3)⋊C4—62no—
187(C2×D3)⋊C4—122no—
188(C2×D3)⋊C4—122no—
189C4⋊Dic3—31no—
190C4⋊Dic3—32no—
191C4⋊Dic3—61no—
192C4⋊Dic3—62no—
193C4⋊Dic3S411yescharacteristic, complemented
194Dic3⋊C4—64no—
195C22×C32—41no—
196C2×C3⋊D3—82no—
197C2×C3⋊D3—82no—
198C2×C3⋊D3—82no—
199C2×C3×D3—42no—
200C2×C3×D3—81no—
201C2×C3×D3—81no—
202C3×A4#12111yescharacteristic, complemented
203C32×C4—42no—
204C3×Dic3—82no—
205C3×Dic3—81no—
206C22×D4—31no—
207C22×D4—91no—
208C22×D4—92no—
209C22×D4—92no—
210C23×C4—31no—
211C23×C4—32no—
212C23×C4D3211yescharacteristic
213#121—181no—
214#121—182no—
215#121—181no—
216#121—182no—
217#121—184no—
218#121—184no—
219#121—182no—
220C4×D4—62no—
221C4×D4—62no—
222C2×C4⋊C4—31no—
223C2×C4⋊C4—91no—
224C2×C4⋊C4—91no—
225C2×C4⋊C4—92no—
226C2×C4⋊C4—91no—
227C2×C4⋊C4—92no—
228C2×C22⋊C4—31no—
229C2×C22⋊C4—31no—
230C2×C22⋊C4—92no—
231C2×C22⋊C4—92no—
232C2×C22⋊C4—92no—
233C2×C22⋊C4—92no—
234C2×C22⋊C4—92no—
235C2×C42—31no—
236#95—92no—
237#95—92no—
238C23×C3—31no—
239C23×C3—31no—
240C23×C3—31no—
241C23×C3—31no—
242C23×C3—32no—
243C23×C3—61no—
244C23×C3—61no—
245C23×C3—61no—
246C23×C3—61no—
247C23×C3—61no—
248C23×C3—61no—
249C23×C3C2×D1211yescharacteristic
250C23×C3D3×D411yescharacteristic
251C23×C3#23911yescharacteristic
252C22×D3—41no—
253C22×D3—62no—
254C22×D3—62no—
255C22×D3—62no—
256C22×D3—62no—
257C22×D3—62no—
258C22×D3—62no—
259C22×D3—62no—
260C22×D3—122no—
261C22×D3—242no—
262C2×A4—21no—
263C2×A4—21no—
264C2×A4—21no—
265C2×A4C2×D1211yescharacteristic
266C2×A4#23511yescharacteristic
267C2×A4C2×#6711yescharacteristic
268S4—22no—
269S4—124no—
270S4—122no—
271C3×D4—62no—
272C3×D4—62no—
273C3×D4—62no—
274C3×D4—62no—
275C2×C3×C4—31no—
276C2×C3×C4—32no—
277C2×C3×C4—32no—
278C2×C3×C4—32no—
279C2×C3×C4—32no—
280C2×C3×C4—41no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—61no—
285C2×C3×C4—61no—
286C2×C3×C4—61no—
287C2×C3×C4—61no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—81no—
291C2×C3×C4—122no—
292C2×C3×C4—122no—
293C2×C3×C4—122no—
294C2×C3×C4C2×S411yescharacteristic
295#67—124no—
296#67—124no—
297#67—122no—
298#67—122no—
299#67—122no—
300#67—122no—
301C2×Dic3—32no—
302C2×Dic3—41no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3C2×S412yes—
311D12—122no—
312D12—122no—
313D12—242no—
314D12—244no—
315D12—244no—
316C4×D3—82no—
317C2×C32—41no—
318C2×C32—41no—
319C2×C32—41no—
320C3⋊D3—162no—
321C3×D3—82no—
322C24—31no—
323C24—92no—
324C24C2×D3211yescharacteristic
325C2×D4—32no—
326C2×D4—32no—
327C2×D4—61no—
328C2×D4—61no—
329C2×D4—61no—
330C2×D4—61no—
331C2×D4—182no—
332C2×D4—181no—
333C2×D4—182no—
334C2×D4—182no—
335C2×D4—182no—
336C2×D4—184no—
337C2×D4—182no—
338C2×D4—182no—
339C2×D4—182no—
340C2×D4—182no—
341C2×D4—182no—
342C2×D4—182no—
343C2×D4—181no—
344C2×D4—362no—
345C22×C4—31no—
346C22×C4—31no—
347C22×C4—32no—
348C22×C4—31no—
349C22×C4—31no—
350C22×C4—31no—
351C22×C4—62no—
352C22×C4—61no—
353C22×C4—62no—
354C22×C4—61no—
355C22×C4—62no—
356C22×C4—92no—
357C22×C4—92no—
358C22×C4—92no—
359C22×C4—182no—
360C22×C4#62612yescomplemented
361C4⋊C4—31no—
362C4⋊C4—62no—
363C4⋊C4—92no—
364C4⋊C4—91no—
365C4⋊C4—181no—
366C4⋊C4—184no—
367C4⋊C4—182no—
368C22⋊C4—62no—
369C22⋊C4—61no—
370C22⋊C4—61no—
371C22⋊C4—182no—
372C22⋊C4—184no—
373C22⋊C4—184no—
374C22⋊C4—182no—
375C22⋊C4—184no—
376C22⋊C4—362no—
377C42—62no—
378C22×C3—31no—
379C22×C3—31no—
380C22×C3—31no—
381C22×C3—31no—
382C22×C3—31no—
383C22×C3—31no—
384C22×C3—31no—
385C22×C3—31no—
386C22×C3—31no—
387C22×C3—41no—
388C22×C3—61no—
389C22×C3—62no—
390C22×C3—62no—
391C22×C3—62no—
392C22×C3—81no—
393C22×C3—121no—
394C22×C3—121no—
395C22×C3—121no—
396C22×C3—121no—
397C22×C3#89511yescharacteristic, complemented
398C22×C3C22×S411yescharacteristic
399C2×D3—42no—
400C2×D3—81no—
401C2×D3—81no—
402C2×D3—122no—
403C2×D3—122no—
404C2×D3—122no—
405C2×D3—122no—
406C2×D3—122no—
407C2×D3—122no—
408C2×D3—122no—
409C2×D3—242no—
410C2×D3—242no—
411C2×D3—242no—
412C2×D3—244no—
413C2×D3—482no—
414C2×D3—482no—
415A4—21no—
416A4#93011yescharacteristic, complemented
417C3×C4—32no—
418C3×C4—42no—
419C3×C4—62no—
420C3×C4—82no—
421C3×C4—121no—
422C3×C4—121no—
423C3×C4—242no—
424C3×C4C4⋊S412yescomplemented
425Dic3—22no—
426Dic3—62no—
427Dic3—81no—
428Dic3—122no—
429C32—41noSylow
430C23—31no—
431C23—31no—
432C23—31no—
433C23—31no—
434C23—32no—
435C23—61no—
436C23—61no—
437C23—61no—
438C23—61no—
439C23—61no—
440C23—61no—
441C23—182no—
442C23—182no—
443C23—182no—
444C23—182no—
445C23—182no—
446C23—182no—
447C23—182no—
448C23#379911yescharacteristic
449C23D3×D1211yescharacteristic
450C23C2×#62611yescharacteristic
451D4—62no—
452D4—62no—
453D4—62no—
454D4—62no—
455D4—362no—
456D4—364no—
457D4—364no—
458D4—362no—
459D4—362no—
460D4—362no—
461D4—362no—
462D4—362no—
463C2×C4—31no—
464C2×C4—32no—
465C2×C4—32no—
466C2×C4—32no—
467C2×C4—32no—
468C2×C4—32no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—92no—
479C2×C4—122no—
480C2×C4—122no—
481C2×C4—182no—
482C2×C4—182no—
483C2×C4—182no—
484C2×C4—182no—
485C2×C4—182no—
486C2×C4—182no—
487C2×C4—182no—
488C2×C4D3×S411yescharacteristic
489C2×C3—31no—
490C2×C3—31no—
491C2×C3—31no—
492C2×C3—31no—
493C2×C3—41no—
494C2×C3—41no—
495C2×C3—41no—
496C2×C3—81no—
497C2×C3—81no—
498C2×C3—81no—
499C2×C3—122no—
500C2×C3C2×C4⋊S411yescharacteristic
501C2×C3D4×S411yescharacteristic
502C2×C3#591911yescharacteristic
503D3—82no—
504D3—242no—
505D3—482no—
506D3—484no—
507C22—31no—
508C22—31no—
509C22—31no—
510C22—31no—
511C22—31no—
512C22—31no—
513C22—31no—
514C22—31no—
515C22—31no—
516C22—61no—
517C22—62no—
518C22—62no—
519C22—62no—
520C22—121no—
521C22—121no—
522C22—121no—
523C22—121no—
524C22—362no—
525C22—362no—
526C22—362no—
527C22—362no—
528C22—362no—
529C22—362no—
530C22—362no—
531C22#6390911yescharacteristic, complemented
532C22C2×D3×S411yescharacteristic
533C4—32no—
534C4—62no—
535C4—62no—
536C4—121no—
537C4—121no—
538C4—182no—
539C4—362no—
540C4#6420712yescomplemented
541C3—41no—
542C3—81no—
543C3#8531011yescharacteristic, complemented
544C2—31no—
545C2—31no—
546C2—31no—
547C2—31no—
548C2—122no—
549C2—722no—
550C2#1059642111yescharacteristic
551C2D12×S411yescharacteristic
552C2C2×#6420711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, cosocleC22×C3×A4C23
FittingC23×C3×C4C2×D3
socleC24×C3C22×D3
hypercenterC2×C4D3×S4
hypocenterC3×A4#121
LCSG ▷ C22×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊(C3⋊S4)C2semidirect
2. C2×C3×C4×S4C2semidirect
3. C2×#64207C2semidirect
4. A4×C4⋊Dic3C2semidirect
5. #10593242C2semidirect
20. C2×C4×S4D3semidirect
25. C22×C4⋊Dic3D3semidirect
40. C2×C3×S4D4semidirect
43. C3×C4×A4D4semidirect
131. C2×S4D12semidirect
148. C22×C3×C4D12semidirect
174. C4×A4#67semidirect
193. C4⋊Dic3S4semidirect
202. C3×A4#121semidirect
360. C22×C4#626semidirect
397. C22×C3#895semidirect
416. A4#930semidirect
424. C3×C4C4⋊S4semidirect
531. C22#63909semidirect
540. C4#64207semidirect
543. C3#85310semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊(C3⋊S4)2
C2×C3×C4×S42
C2×#642072
A4×C4⋊Dic32
#105932422
#853103
#823523
#639094