Finite Group Databasebeta

← #11921961

Subgroups — #11921961

Order 1152.

660 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 71 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×#64259C211yesmaximal, characteristic
2C2×#64204C211yesmaximal, characteristic
3A4×Dic3⋊C4C211yesmaximal, characteristic
4C3×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic
5Dic3⋊SL(2,ℤ/4)C211yesmaximal, characteristic
6SL(2,ℤ/4)⋊Dic3C211yesmaximal, characteristic
7Dic3×SL(2,ℤ/4)C211yesmaximal, characteristic
8#85303—31nomaximal
9#74416—31nomaximal
10C2×C3×C4×A4C2211yescharacteristic
11C2×Dic3×A4C2211yescharacteristic
12C2×Dic3×A4C2211yescharacteristic
13C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
14C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
15#64259—22no—
16C2×C3×SL(2,ℤ/4)C2211yescharacteristic
17C2×C3×SL(2,ℤ/4)C2211yescharacteristic
18#64204—22no—
19#63840—41nomaximal
20C2×A4⋊Q8—31no—
21C2×A4⋊Q8—31no—
22C2×A4⋊Q8—61no—
23C2×#924—31no—
24C22×Dic3⋊C4D311yescharacteristic
25C2×#888—31no—
26C2×#878—31no—
27A4×C4⋊C4—31no—
28C4⋊SL(2,ℤ/4)—31no—
29SL(2,ℤ/4)⋊C4—31no—
30SL(2,ℤ/4)⋊C4D311yescharacteristic
31C4×SL(2,ℤ/4)—31no—
32C3×#385—31no—
33#4982—31no—
34#4979—31no—
35#4975—31no—
36#4950—31no—
37#4942—31no—
38Dic3×C22⋊C4—31no—
39#4657—31no—
40#4656—31no—
41#4647—31no—
42#4647—31no—
43C22×C3×A4C2311yescharacteristic
44C2×#634—41no—
45C3×C4×A4—21no—
46C2×#627—41no—
47Dic3×A4—21no—
48Dic3×A4Q812yescomplemented
49C3⋊SL(2,ℤ/4)—21no—
50C3⋊SL(2,ℤ/4)D412yes—
51C3×SL(2,ℤ/4)—21no—
52C3×SL(2,ℤ/4)Q812yescomplemented
53C3×Dic3⋊C4—41no—
54C3×Dic3⋊C4—41no—
55Dic3⋊Dic3—41no—
56Dic3⋊Dic3—41no—
57Dic32—41no—
58#2440—91noSylow
59C23×C3×C4C2×D311yescharacteristic
60C23×Dic3C2×D311yescharacteristic
61C23×Dic3C2×D311yescharacteristic
62C22×Dic6—31no—
63C22×Dic6—31no—
64C2×C4×A4—21no—
65C2×C4×A4—31no—
66C2×C4×A4—31no—
67C2×C4×A4C2×D311yescharacteristic
68C2×SL(2,ℤ/4)—31no—
69C2×SL(2,ℤ/4)—31no—
70C2×SL(2,ℤ/4)—61no—
71C2×SL(2,ℤ/4)—61no—
72C2×SL(2,ℤ/4)C2×D311yescharacteristic
73C2×SL(2,ℤ/4)C2×D311yescharacteristic
74A4⋊Q8—62no—
75A4⋊Q8—62no—
76A4⋊Q8—64no—
77C2×C3×C4⋊C4—31no—
78C2×C3×C4⋊C4—31no—
79C2×C3×C22⋊C4—31no—
80C2×C3×C22⋊C4—31no—
81C2×#217—31no—
82C2×#217—31no—
83C2×C4⋊Dic3—31no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—31no—
87#924—62no—
88#924—62no—
89C2×Dic3⋊C4—31no—
90C2×Dic3⋊C4—31no—
91C2×Dic3⋊C4—31no—
92C2×Dic3⋊C4—31no—
93C2×Dic3⋊C4—31no—
94C2×Dic3⋊C4—31no—
95C2×Dic3⋊C4—31no—
96C2×Dic3⋊C4—31no—
97C2×Dic3⋊C4—31no—
98C2×Dic3⋊C4—31no—
99C2×C4×Dic3—31no—
100C2×C4×Dic3—31no—
101#888—61no—
102#888—61no—
103#888—61no—
104#888—61no—
105#888—121no—
106#878—62no—
107#878—62no—
108C3×#95—31no—
109C3×#95—31no—
110C3⋊#95—31no—
111C3⋊#95—31no—
112C3⋊#95—31no—
113C3⋊#95—31no—
114C3⋊#95—31no—
115C3⋊#95—31no—
116C2×C3×A4C2×D411yescharacteristic
117C2×C3×A4C2×Q811yescharacteristic
118C2×C3×A4C2×Q811yescharacteristic
119C2×C32×C4—41no—
120C2×C3⋊Dic3—41no—
121C2×C3⋊Dic3—41no—
122#634—82no—
123C2×C3×Dic3—41no—
124C2×C3×Dic3—41no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—41no—
127#627—82no—
128C2×C4⋊Q8—91no—
129C2×C22⋊Q8—91no—
130C2×C22⋊Q8—91no—
131C22×C4⋊C4—31no—
132#398—91no—
133#398—91no—
134#395—91no—
135#395—91no—
136#389—91no—
137#389—91no—
138#385—31no—
139#385—91no—
140#384—91no—
141#380—91no—
142C4×C22⋊C4—91no—
143C24×C3C22×D311yescharacteristic
144C22×A4—21no—
145C22×A4C22×D311yescharacteristic
146C22×C3×C4—21no—
147C22×C3×C4—31no—
148C22×C3×C4—31no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—61no—
154C22×Dic3—21no—
155C22×Dic3—31no—
156C22×Dic3—31no—
157C22×Dic3—32no—
158C22×Dic3—31no—
159C22×Dic3—31no—
160C22×Dic3—31no—
161C22×Dic3—31no—
162C22×Dic3—31no—
163C22×Dic3—31no—
164C22×Dic3—61no—
165C22×Dic3Dic612yescomplemented
166C2×Dic6—62no—
167C2×Dic6—61no—
168C2×Dic6—62no—
169C2×Dic6—61no—
170C2×Dic6—61no—
171C2×Dic6—61no—
172C2×Dic6—121no—
173C2×Dic6—121no—
174C2×Dic6—121no—
175C2×Dic6—121no—
176C2×Dic6—241no—
177C4×A4—22no—
178C4×A4—21no—
179C4×A4—32no—
180C4×A4—61no—
181SL(2,ℤ/4)—21no—
182SL(2,ℤ/4)—32no—
183SL(2,ℤ/4)—62no—
184SL(2,ℤ/4)—62no—
185SL(2,ℤ/4)—61no—
186SL(2,ℤ/4)Dic612yescomplemented
187C3×C4⋊C4—61no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—121no—
190C3×C4⋊C4—121no—
191C3×C22⋊C4—32no—
192C3×C22⋊C4—32no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195#217—32no—
196#217—32no—
197#217—61no—
198#217—61no—
199C4⋊Dic3—62no—
200C4⋊Dic3—61no—
201C4⋊Dic3—62no—
202C4⋊Dic3—61no—
203C4⋊Dic3—121no—
204C4⋊Dic3—121no—
205Dic3⋊C4—31no—
206Dic3⋊C4—31no—
207Dic3⋊C4—31no—
208Dic3⋊C4—41no—
209Dic3⋊C4—61no—
210Dic3⋊C4—62no—
211Dic3⋊C4—62no—
212Dic3⋊C4—61no—
213Dic3⋊C4—62no—
214Dic3⋊C4—62no—
215Dic3⋊C4—62no—
216Dic3⋊C4—61no—
217Dic3⋊C4—121no—
218Dic3⋊C4S411yescharacteristic
219C4×Dic3—61no—
220C4×Dic3—62no—
221C4×Dic3—61no—
222C4×Dic3—121no—
223C22×C32—41no—
224C3×A4C4⋊Q811yescharacteristic, complemented
225C32×C4—81no—
226C3⋊Dic3—42no—
227C3⋊Dic3—81no—
228C3×Dic3—42no—
229C3×Dic3—42no—
230C3×Dic3—81no—
231C3×Dic3—81no—
232C22×Q8—91no—
233C22×Q8—91no—
234C23×C4—31no—
235C23×C4—31no—
236C23×C4D3211yescharacteristic
237C4⋊Q8—181no—
238C4⋊Q8—181no—
239C4⋊Q8—181no—
240C4⋊Q8—181no—
241C22⋊Q8—182no—
242C22⋊Q8—182no—
243C22⋊Q8—182no—
244C22⋊Q8—182no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4—31no—
247C2×C4⋊C4—91no—
248C2×C4⋊C4—91no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—91no—
251C2×C4⋊C4—91no—
252C2×C4⋊C4—91no—
253C2×C4⋊C4—91no—
254C2×C4⋊C4—91no—
255C2×C4⋊C4—91no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4—91no—
259C2×C4⋊C4—91no—
260C2×C4⋊C4—91no—
261C2×C22⋊C4—31no—
262C2×C22⋊C4—31no—
263C2×C22⋊C4—91no—
264C2×C22⋊C4—91no—
265C2×C42—91no—
266C2×C42—91no—
267#95—31no—
268#95—31no—
269#95—91no—
270#95—91no—
271#95—91no—
272#95—91no—
273#95—91no—
274#95—91no—
275C23×C3—31no—
276C23×C3—31no—
277C23×C3—31no—
278C23×C3—31no—
279C23×C3C2×Dic611yescharacteristic
280C23×C3D3×D411yescharacteristic
281C23×C3D3×Q811yescharacteristic
282C2×A4—21no—
283C2×A4—21no—
284C2×A4—21no—
285C2×A4C2×Dic611yescharacteristic
286C2×A4D3×D411yescharacteristic
287C2×A4D3×Q811yescharacteristic
288C2×C3×C4—32no—
289C2×C3×C4—32no—
290C2×C3×C4—31no—
291C2×C3×C4—41no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—61no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4—61no—
300C2×C3×C4—61no—
301C2×C3×C4—61no—
302C2×C3×C4—61no—
303C2×C3×C4—61no—
304C2×C3×C4—61no—
305C2×C3×C4—61no—
306C2×C3×C4—81no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4C2×S411yescharacteristic
310C2×Dic3—31no—
311C2×Dic3—32no—
312C2×Dic3—32no—
313C2×Dic3—32no—
314C2×Dic3—32no—
315C2×Dic3—32no—
316C2×Dic3—31no—
317C2×Dic3—41no—
318C2×Dic3—41no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—61no—
324C2×Dic3—61no—
325C2×Dic3—61no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—61no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—241no—
337C2×Dic3—241no—
338C2×Dic3C2×S411yescharacteristic
339C2×Dic3C2×S411yescharacteristic
340Dic6—122no—
341Dic6—122no—
342Dic6—122no—
343Dic6—122no—
344Dic6—242no—
345Dic6—242no—
346Dic6—244no—
347C2×C32—41no—
348C2×C32—41no—
349C2×C32—41no—
350C24C2×D3211yescharacteristic
351C2×Q8—181no—
352C2×Q8—181no—
353C2×Q8—182no—
354C2×Q8—182no—
355C2×Q8—181no—
356C2×Q8—181no—
357C2×Q8—361no—
358C2×Q8—361no—
359C22×C4—21no—
360C22×C4—31no—
361C22×C4—31no—
362C22×C4—31no—
363C22×C4—31no—
364C22×C4—31no—
365C22×C4—31no—
366C22×C4—32no—
367C22×C4—61no—
368C22×C4—61no—
369C22×C4—91no—
370C22×C4—91no—
371C22×C4—91no—
372C22×C4—92no—
373C22×C4—91no—
374C22×C4—91no—
375C22×C4—91no—
376C22×C4—91no—
377C22×C4—91no—
378C22×C4—181no—
379C4⋊C4—31no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C4⋊C4—91no—
383C4⋊C4—91no—
384C4⋊C4—91no—
385C4⋊C4—121no—
386C4⋊C4—181no—
387C4⋊C4—181no—
388C4⋊C4—181no—
389C4⋊C4—182no—
390C4⋊C4—182no—
391C4⋊C4—182no—
392C4⋊C4—182no—
393C4⋊C4—182no—
394C4⋊C4—182no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C4⋊C4—182no—
398C4⋊C4—361no—
399C22⋊C4—32no—
400C22⋊C4—32no—
401C22⋊C4—61no—
402C22⋊C4—61no—
403C22⋊C4—92no—
404C22⋊C4—92no—
405C22⋊C4—181no—
406C22⋊C4—181no—
407C42—181no—
408C42—181no—
409C42—182no—
410C22×C3—31no—
411C22×C3—31no—
412C22×C3—31no—
413C22×C3—31no—
414C22×C3—31no—
415C22×C3—31no—
416C22×C3—31no—
417C22×C3—31no—
418C22×C3—31no—
419C22×C3—41no—
420C22×C3—61no—
421C22×C3—81no—
422C22×C3#88811yescharacteristic, complemented
423C22×C3C22×S411yescharacteristic
424A4—21no—
425A4#88811yescharacteristic, complemented
426C3×C4—21no—
427C3×C4—62no—
428C3×C4—61no—
429C3×C4—62no—
430C3×C4—81no—
431C3×C4—82no—
432C3×C4—122no—
433C3×C4—121no—
434C3×C4—121no—
435C3×C4—241no—
436Dic3—21no—
437Dic3—32no—
438Dic3—42no—
439Dic3—62no—
440Dic3—62no—
441Dic3—61no—
442Dic3—81no—
443Dic3—122no—
444Dic3—121no—
445Dic3—121no—
446Dic3—242no—
447Dic3—241no—
448Dic3—242no—
449Dic3A4⋊Q812yescomplemented
450C32—41noSylow
451C23—31no—
452C23—31no—
453C23—31no—
454C23—31no—
455C23D3×Dic611yescharacteristic
456C23D3×Dic611yescharacteristic
457C23#381111yescharacteristic
458Q8—362no—
459Q8—362no—
460Q8—362no—
461Q8—362no—
462C2×C4—31no—
463C2×C4—32no—
464C2×C4—32no—
465C2×C4—31no—
466C2×C4—31no—
467C2×C4—61no—
468C2×C4—61no—
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—61no—
479C2×C4—61no—
480C2×C4—61no—
481C2×C4—92no—
482C2×C4—92no—
483C2×C4—91no—
484C2×C4—92no—
485C2×C4—92no—
486C2×C4—92no—
487C2×C4—91no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—181no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4D3×S411yescharacteristic
504C2×C3—31no—
505C2×C3—31no—
506C2×C3—31no—
507C2×C3—31no—
508C2×C3—41no—
509C2×C3—41no—
510C2×C3—41no—
511C2×C3—81no—
512C2×C3—81no—
513C2×C3—81no—
514C2×C3C2×A4⋊Q811yescharacteristic
515C2×C3D4×S411yescharacteristic
516C2×C3Q8×S411yescharacteristic
517C22—31no—
518C22—31no—
519C22—31no—
520C22—31no—
521C22—31no—
522C22—31no—
523C22—31no—
524C22—31no—
525C22—31no—
526C22—61no—
527C22#6384011yescharacteristic, complemented
528C22C2×D3×S411yescharacteristic
529C4—21no—
530C4—32no—
531C4—62no—
532C4—62no—
533C4—61no—
534C4—61no—
535C4—92no—
536C4—121no—
537C4—121no—
538C4—182no—
539C4—181no—
540C4—182no—
541C4—361no—
542C4—361no—
543C3—41no—
544C3—81no—
545C3#8530311yescharacteristic, complemented
546C2—31no—
547C2—31no—
548C2—31no—
549C2—31no—
550C2Dic6×S411yescharacteristic
551C2D3×A4⋊Q811yescharacteristic
552C2#1059647311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, prime radical, cosocleC22×C3×A4C23
FittingC23×C3×C4C2×D3
socleC24×C3C22×D3
hypercenterC2×C4D3×S4
hypocenterC3×A4C4⋊Q8
LCSG ▷ C22×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
48. Dic3×A4Q8semidirect
52. C3×SL(2,ℤ/4)Q8semidirect
165. C22×Dic3Dic6semidirect
186. SL(2,ℤ/4)Dic6semidirect
224. C3×A4C4⋊Q8semidirect
422. C22×C3#888semidirect
425. A4#888semidirect
449. Dic3A4⋊Q8semidirect
527. C22#63840semidirect
545. C3#85303semidirect

Maximal subgroups

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

subgroupindex
C2×#642592
C2×#642042
A4×Dic3⋊C42
C3×SL(2,ℤ/4)⋊C42
Dic3⋊SL(2,ℤ/4)2
SL(2,ℤ/4)⋊Dic32
Dic3×SL(2,ℤ/4)2
#853033
#744163
#638404