Finite Group Databasebeta

← C4×#63694 #11920383

Subgroups — C4×#63694 #11920383

Order 1152.

900 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 900 conjugacy classes of subgroups — too many to draw. Only its 84 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×C4×C22⋊C9C211yesmaximal, characteristic, complemented
2C2×#63694C211yesmaximal, characteristic
3C2×C4×(C22⋊C9)⋊C2C211yesmaximal, characteristic, complemented
4#10589534C211yesmaximal, characteristic, complemented
5(C2×(C22⋊C9)⋊C2)⋊C4C211yesmaximal, characteristic, complemented
6((C22⋊C9)⋊C4)⋊C4C211yesmaximal, characteristic, complemented
7C4×(C22⋊C9)⋊C4C211yesmaximal, characteristic, complemented
8C4×#953—31nomaximal
9C23×C22⋊C9C2211yescharacteristic
10C22×(C22⋊C9)⋊C2C2211yescharacteristic
11C2×C4×C22⋊C9—22no—
12C2×C4×C22⋊C9C2211yescharacteristic
13C2×C4×C22⋊C9C2211yescharacteristic
14#63694C414yesdirect product factor
15C2×(C22⋊C9)⋊C4C2211yescharacteristic
16C2×(C22⋊C9)⋊C4C2211yescharacteristic
17C2×(C22⋊C9)⋊C4C2211yescharacteristic
18C4×(C22⋊C9)⋊C2—22no—
19C4×#611—41nomaximal
20C24×C3×C4D311yescharacteristic
21C2×#953—31no—
22C2×C4×#67—31no—
23C2×C4×#67—31no—
24C2×C4×#67—31no—
25#5247—31no—
26#5213—31no—
27#5213—31no—
28#5213—31no—
29#5210—31no—
30#5210—31no—
31#5210—31no—
32C4×#217—31no—
33C4×#217—31no—
34C4×#217—31no—
35C22×C22⋊C9—21no—
36C22×C22⋊C9—21no—
37C22×C22⋊C9C2×C412yescomplemented
38C22×C22⋊C9C2311yescharacteristic
39C2×(C22⋊C9)⋊C2—21no—
40C2×(C22⋊C9)⋊C2—21no—
41C2×(C22⋊C9)⋊C2C2×C412yescomplemented
42C22×C4×C9—41no—
43C2×#611—41no—
44C2×C4×D9—41no—
45C4×C22⋊C9—21no—
46C4×C22⋊C9D412yescomplemented
47(C22⋊C9)⋊C4—21no—
48(C22⋊C9)⋊C4—21no—
49(C22⋊C9)⋊C4C2×C412yescomplemented
50#3676—41no—
51(C2×D9)⋊C4—41no—
52Dic9⋊C4—41no—
53C4×Dic9—41no—
54C4×#120—91noSylow
55C25×C3C2×D311yescharacteristic
56C23×C3×C4—22no—
57C23×C3×C4—31no—
58C23×C3×C4—31no—
59C23×C3×C4—31no—
60C23×C3×C4—31no—
61C23×C3×C4—62no—
62C23×C3×C4C2×D311yescharacteristic
63C23×C3×C4C2×D311yescharacteristic
64C22×#67—31no—
65C22×#67—31no—
66C22×#67—31no—
67C22×C4×D3—31no—
68#953—34no—
69#953—34no—
70C2×#217—31no—
71C2×#217—31no—
72C2×#217—31no—
73C2×#217—31no—
74C2×#217—31no—
75C2×#217—31no—
76C2×#217—31no—
77C2×#217—31no—
78C2×#217—31no—
79C4×#67—62no—
80C4×#67—64no—
81C4×#67—61no—
82C4×#67—61no—
83C4×#67—61no—
84C4×#67—62no—
85C4×#67—61no—
86C2×(C2×D3)⋊C4—31no—
87C2×(C2×D3)⋊C4—31no—
88C2×(C2×D3)⋊C4—31no—
89C2×Dic3⋊C4—31no—
90C2×Dic3⋊C4—31no—
91C2×Dic3⋊C4—31no—
92C2×C4×Dic3—31no—
93C2×C4×Dic3—31no—
94C2×C4×Dic3—31no—
95C3⋊#95—31no—
96C3⋊#95—31no—
97C3⋊#95—31no—
98C3⋊#95—31no—
99C3⋊#95—31no—
100C3⋊#95—31no—
101C23×C9—41no—
102C22×D9—41no—
103C2×C22⋊C9—22no—
104C2×C22⋊C9C22×C411yescharacteristic
105C2×C22⋊C9C2×D411yescharacteristic
106C2×C22⋊C9#4111yescharacteristic
107(C22⋊C9)⋊C2—22no—
108C2×C4×C9—41no—
109C2×C4×C9—41no—
110C2×C4×C9—82no—
111#611—44no—
112C2×Dic9—41no—
113C2×Dic9—41no—
114C2×Dic9—41no—
115C4×D9—82no—
116C24×C4D911yescharacteristic, complemented
117C2×#120—91no—
118C2×C4×D4—91no—
119C2×C4×D4—91no—
120C2×C4×D4—91no—
121#386—91no—
122#386—91no—
123#386—91no—
124#385—91no—
125#385—91no—
126#385—91no—
127#379—91no—
128C4×C22⋊C4—91no—
129C4×C22⋊C4—91no—
130C4×C22⋊C4—91no—
131C24×C3—21no—
132C24×C3—21no—
133C24×C3—31no—
134C24×C3—31no—
135C24×C3—32no—
136C24×C3—61no—
137C24×C3—61no—
138C24×C3C4×D312yes—
139C24×C3C22×D311yescharacteristic
140C23×D3—31no—
141C22×C3×C4—21no—
142C22×C3×C4—31no—
143C22×C3×C4—31no—
144C22×C3×C4—31no—
145C22×C3×C4—32no—
146C22×C3×C4—34no—
147C22×C3×C4—31no—
148C22×C3×C4—31no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—62no—
152C22×C3×C4—62no—
153C22×C3×C4—61no—
154C22×C3×C4—61no—
155C22×C3×C4—62no—
156C22×C3×C4—62no—
157C22×C3×C4—62no—
158C22×C3×C4—62no—
159C22×C3×C4—62no—
160C22×C3×C4#6712yes—
161C22×C3×C4S411yescharacteristic
162C2×#67—34no—
163C2×#67—32no—
164C2×#67—34no—
165C2×#67—32no—
166C2×#67—61no—
167C2×#67—62no—
168C2×#67—61no—
169C2×#67—61no—
170C2×#67—62no—
171C2×#67—62no—
172C2×#67—61no—
173C2×#67—61no—
174C2×#67—61no—
175C22×Dic3—31no—
176C22×Dic3—31no—
177C22×Dic3—31no—
178C22×Dic3—31no—
179C22×Dic3—31no—
180C22×Dic3—31no—
181C22×Dic3—31no—
182C2×C4×D3—61no—
183C2×C4×D3—62no—
184C2×C4×D3—62no—
185C2×C4×D3—61no—
186#217—34no—
187#217—32no—
188#217—34no—
189#217—32no—
190#217—61no—
191#217—62no—
192#217—61no—
193#217—61no—
194#217—62no—
195#217—62no—
196#217—61no—
197#217—61no—
198#217—61no—
199(C2×D3)⋊C4—62no—
200(C2×D3)⋊C4—62no—
201(C2×D3)⋊C4—61no—
202(C2×D3)⋊C4—61no—
203Dic3⋊C4—62no—
204Dic3⋊C4—62no—
205Dic3⋊C4—61no—
206Dic3⋊C4—61no—
207C4×Dic3—62no—
208C4×Dic3—62no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C22×C9—42no—
212C22×C9—41no—
213C22×C9—81no—
214C22×C9—81no—
215C2×D9—42no—
216C2×D9—81no—
217C2×D9—81no—
218C22⋊C9C4×D411yescharacteristic, complemented
219C4×C9—42no—
220C4×C9—81no—
221Dic9—42no—
222Dic9—81no—
223Dic9—81no—
224C25C2×D911yescharacteristic
225C22×D4—91no—
226C22×D4—91no—
227C22×D4—91no—
228C23×C4—22no—
229C23×C4—31no—
230C23×C4—31no—
231C23×C4—31no—
232C23×C4—31no—
233C23×C4—62no—
234C23×C4—91no—
235C23×C4C2×D911yescharacteristic
236C23×C4C2×D911yescharacteristic
237#120—94no—
238#120—94no—
239C4×D4—182no—
240C4×D4—184no—
241C4×D4—181no—
242C4×D4—181no—
243C4×D4—181no—
244C4×D4—182no—
245C4×D4—181no—
246C2×C4⋊C4—91no—
247C2×C4⋊C4—91no—
248C2×C4⋊C4—91no—
249C2×C22⋊C4—91no—
250C2×C22⋊C4—91no—
251C2×C22⋊C4—91no—
252C2×C22⋊C4—91no—
253C2×C22⋊C4—91no—
254C2×C22⋊C4—91no—
255C2×C22⋊C4—91no—
256C2×C22⋊C4—91no—
257C2×C22⋊C4—91no—
258C2×C22⋊C4—91no—
259C2×C22⋊C4—91no—
260C2×C22⋊C4—91no—
261C2×C42—91no—
262C2×C42—91no—
263C2×C42—91no—
264#95—91no—
265#95—91no—
266#95—91no—
267#95—91no—
268#95—91no—
269#95—91no—
270C23×C3—22no—
271C23×C3—31no—
272C23×C3—32no—
273C23×C3—31no—
274C23×C3—31no—
275C23×C3—31no—
276C23×C3—32no—
277C23×C3—32no—
278C23×C3—32no—
279C23×C3—32no—
280C23×C3—31no—
281C23×C3—61no—
282C23×C3—61no—
283C23×C3—61no—
284C23×C3—61no—
285C23×C3—62no—
286C23×C3—61no—
287C23×C3—61no—
288C23×C3—62no—
289C23×C3—62no—
290C23×C3—61no—
291C23×C3—64no—
292C23×C3C2×C4×D311yescharacteristic
293C23×C3#23511yescharacteristic
294C23×C3C2×#6711yescharacteristic
295C23×C3C2×S411yescharacteristic
296C22×D3—32no—
297C22×D3—61no—
298C22×D3—61no—
299C22×D3—61no—
300C22×D3—61no—
301C22×D3—61no—
302C22×D3—61no—
303C2×C3×C4—22no—
304C2×C3×C4—31no—
305C2×C3×C4—32no—
306C2×C3×C4—32no—
307C2×C3×C4—32no—
308C2×C3×C4—32no—
309C2×C3×C4—31no—
310C2×C3×C4—62no—
311C2×C3×C4—61no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—62no—
315C2×C3×C4—64no—
316C2×C3×C4—62no—
317C2×C3×C4—61no—
318C2×C3×C4C2×S411yescharacteristic
319C2×C3×C4C2×S411yescharacteristic
320#67—62no—
321#67—62no—
322#67—62no—
323#67—68no—
324#67—64no—
325#67—62no—
326#67—64no—
327C2×Dic3—32no—
328C2×Dic3—32no—
329C2×Dic3—32no—
330C2×Dic3—61no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C4×D3—122no—
349C4×D3—122no—
350C2×C9—41no—
351C2×C9—41no—
352C2×C9—41no—
353C2×C9—82no—
354D9—82no—
355C24—21no—
356C24—21no—
357C24—31no—
358C24—31no—
359C24—32no—
360C24—61no—
361C24—61no—
362C24—91no—
363C24C4×D912yescomplemented
364C24C22×D911yescharacteristic
365C2×D4—94no—
366C2×D4—92no—
367C2×D4—94no—
368C2×D4—92no—
369C2×D4—181no—
370C2×D4—182no—
371C2×D4—181no—
372C2×D4—181no—
373C2×D4—182no—
374C2×D4—182no—
375C2×D4—181no—
376C2×D4—181no—
377C2×D4—181no—
378C22×C4—21no—
379C22×C4—31no—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—32no—
383C22×C4—34no—
384C22×C4—31no—
385C22×C4—31no—
386C22×C4—31no—
387C22×C4—31no—
388C22×C4—62no—
389C22×C4—62no—
390C22×C4—61no—
391C22×C4—61no—
392C22×C4—62no—
393C22×C4—62no—
394C22×C4—62no—
395C22×C4—62no—
396C22×C4—62no—
397C22×C4—91no—
398C22×C4—91no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—91no—
402C22×C4—91no—
403C22×C4—91no—
404C22×C4—181no—
405C22×C4—182no—
406C22×C4—182no—
407C22×C4—181no—
408C22×C4#61112yescomplemented
409C22×C4(C22⋊C9)⋊C211yescharacteristic, complemented
410C4⋊C4—182no—
411C4⋊C4—182no—
412C4⋊C4—181no—
413C4⋊C4—181no—
414C22⋊C4—94no—
415C22⋊C4—92no—
416C22⋊C4—94no—
417C22⋊C4—92no—
418C22⋊C4—182no—
419C22⋊C4—182no—
420C22⋊C4—181no—
421C22⋊C4—181no—
422C22⋊C4—182no—
423C22⋊C4—181no—
424C22⋊C4—181no—
425C22⋊C4—182no—
426C22⋊C4—182no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C42—181no—
432C42—182no—
433C42—182no—
434C42—181no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—31no—
438C22×C3—31no—
439C22×C3—31no—
440C22×C3—31no—
441C22×C3—31no—
442C22×C3—31no—
443C22×C3—31no—
444C22×C3—31no—
445C22×C3—31no—
446C22×C3—34no—
447C22×C3—32no—
448C22×C3—62no—
449C22×C3—62no—
450C22×C3—62no—
451C22×C3—62no—
452C22×C3—61no—
453C22×C3—62no—
454C22×C3—62no—
455C22×C3—62no—
456C22×C3—61no—
457C22×C3—61no—
458C22×C3C4×#6711yescharacteristic
459C22×C3C4×S412yes—
460C22×C3C22×S411yescharacteristic
461C2×D3—62no—
462C2×D3—62no—
463C2×D3—62no—
464C2×D3—121no—
465C2×D3—121no—
466C2×D3—121no—
467C2×D3—121no—
468C3×C4—21no—
469C3×C4—32no—
470C3×C4—61no—
471C3×C4GL(2,ℤ/4)12yes—
472Dic3—62no—
473Dic3—62no—
474Dic3—62no—
475Dic3—121no—
476Dic3—121no—
477Dic3—121no—
478Dic3—121no—
479C9—41noSylow
480C23—22no—
481C23—31no—
482C23—32no—
483C23—31no—
484C23—31no—
485C23—31no—
486C23—32no—
487C23—32no—
488C23—31no—
489C23—32no—
490C23—32no—
491C23—61no—
492C23—61no—
493C23—61no—
494C23—61no—
495C23—62no—
496C23—61no—
497C23—61no—
498C23—62no—
499C23—62no—
500C23—61no—
501C23—64no—
502C23—92no—
503C23—181no—
504C23—181no—
505C23—181no—
506C23—181no—
507C23—181no—
508C23—181no—
509C23C2×C4×D911yescharacteristic
510C23#369711yescharacteristic
511C23C2×#61111yescharacteristic
512C23C2×(C22⋊C9)⋊C211yescharacteristic
513D4—182no—
514D4—182no—
515D4—182no—
516D4—188no—
517D4—184no—
518D4—182no—
519D4—184no—
520C2×C4—22no—
521C2×C4—31no—
522C2×C4—32no—
523C2×C4—32no—
524C2×C4—32no—
525C2×C4—32no—
526C2×C4—31no—
527C2×C4—62no—
528C2×C4—61no—
529C2×C4—61no—
530C2×C4—61no—
531C2×C4—62no—
532C2×C4—64no—
533C2×C4—62no—
534C2×C4—61no—
535C2×C4—92no—
536C2×C4—92no—
537C2×C4—92no—
538C2×C4—181no—
539C2×C4—181no—
540C2×C4—181no—
541C2×C4—181no—
542C2×C4—181no—
543C2×C4—181no—
544C2×C4—181no—
545C2×C4—181no—
546C2×C4—181no—
547C2×C4—181no—
548C2×C4—181no—
549C2×C4—181no—
550C2×C4—181no—
551C2×C4—181no—
552C2×C4—181no—
553C2×C4—181no—
554C2×C4—181no—
555C2×C4—181no—
556C2×C4—362no—
557C2×C4—362no—
558C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
559C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
560C2×C3—22no—
561C2×C3—31no—
562C2×C3—31no—
563C2×C3—31no—
564C2×C3—31no—
565C2×C3—62no—
566C2×C3C2×C4×S411yescharacteristic
567C2×C3#591211yescharacteristic
568C2×C3C2×GL(2,ℤ/4)11yescharacteristic
569D3—122no—
570C22—21no—
571C22—21no—
572C22—31no—
573C22—31no—
574C22—31no—
575C22—31no—
576C22—31no—
577C22—31no—
578C22—31no—
579C22—31no—
580C22—31no—
581C22—34no—
582C22—32no—
583C22—62no—
584C22—62no—
585C22—62no—
586C22—62no—
587C22—61no—
588C22—62no—
589C22—62no—
590C22—62no—
591C22—61no—
592C22—61no—
593C22—182no—
594C22—182no—
595C22—182no—
596C22—361no—
597C22—361no—
598C22—361no—
599C22—361no—
600C22C4×#61111yescharacteristic, complemented
601C22C4×(C22⋊C9)⋊C212yescomplemented
602C22C22×(C22⋊C9)⋊C211yescharacteristic
603C4—21no—
604C4—32no—
605C4—61no—
606C4—182no—
607C4—182no—
608C4—182no—
609C4—361no—
610C4—361no—
611C4—361no—
612C4—361no—
613C4#6369412yesdirect product factor
614C3C4×GL(2,ℤ/4)11yescharacteristic
615C2—22no—
616C2—31no—
617C2—31no—
618C2—31no—
619C2—31no—
620C2—62no—
621C2—362no—
622C2C2×C4×(C22⋊C9)⋊C211yescharacteristic
623C2#1059308711yescharacteristic
624C2C2×#6369411yescharacteristic
subgroupG/H
centerC2×C4C2×(C22⋊C9)⋊C2
commutatorC2×C22⋊C9C22×C4
FrattiniC22×C3C22×S4
FittingC24×C3×C4D3
socleC24×C3C22×D3
prime radicalC2×#63694C2
cosocleC22×C22⋊C9C23
hypercenterC22×C4(C22⋊C9)⋊C2
hypocenterC22⋊C9C4×D4
LCSG ▷ C2×C22⋊C9 ▷ C22⋊C9
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C22⋊C9C2semidirect
3. C2×C4×(C22⋊C9)⋊C2C2semidirect
4. #10589534C2semidirect
5. (C2×(C22⋊C9)⋊C2)⋊C4C2semidirect
6. ((C22⋊C9)⋊C4)⋊C4C2semidirect
7. C4×(C22⋊C9)⋊C4C2semidirect
14. #63694C4direct (N × H)
37. C22×C22⋊C9C2×C4semidirect
41. C2×(C22⋊C9)⋊C2C2×C4semidirect
46. C4×C22⋊C9D4semidirect
49. (C22⋊C9)⋊C4C2×C4semidirect
116. C24×C4D9semidirect
218. C22⋊C9C4×D4semidirect
363. C24C4×D9semidirect
408. C22×C4#611semidirect
409. C22×C4(C22⋊C9)⋊C2semidirect
600. C22C4×#611semidirect
601. C22C4×(C22⋊C9)⋊C2semidirect
613. C4#63694direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊C92
C2×#636942
C2×C4×(C22⋊C9)⋊C22
#105895342
(C2×(C22⋊C9)⋊C2)⋊C42
((C22⋊C9)⋊C4)⋊C42
C4×(C22⋊C9)⋊C42
C4×#9533
C4×#6114