Finite Group Databasebeta

← #11784938

Subgroups — #11784938

Order 1152.

1175 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic
2#10592932C211yesmaximal, characteristic, complemented
3C3×#5236C211yesmaximal, characteristic, complemented
4#10591231C211yesmaximal, characteristic, complemented
5#10591110C211yesmaximal, characteristic, complemented
6#10591083C211yesmaximal, characteristic, complemented
7#10591071C211yesmaximal, characteristic, complemented
8#72146—31nomaximal
9#70413—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C3×#1010—21no—
12C3×#1010C412yescomplemented
13C3×#1009—21no—
14C3×#1009C412yescomplemented
15C3×D3×#41—22no—
16C3×D3×#41—22no—
17C3×#1007—21no—
18C3×#1004—21no—
19C3×#1004—22no—
20C2×C3×#235—22no—
21C2×C3×#235C2211yescharacteristic
22C2×C3×#235C2211yescharacteristic
23#64135C2211yescharacteristic, complemented
24C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
25C3×#926C2211yescharacteristic, complemented
26C2×C3×#208C2211yescharacteristic, complemented
27#63662—21no—
28#63659—21no—
29C3×#837—22no—
30#63580—22no—
31#63568—22no—
32#63565—21no—
33#63562—21no—
34(C2×D3)⋊(C3⋊C8)—22no—
35C3×#585—31no—
36#5964D311yescharacteristic
37C3×#421—31no—
38#5240—31no—
39#5236—31no—
40#5236D311yescharacteristic, complemented
41#5234—31no—
42#5233—31no—
43#5233—31no—
44#5233—31no—
45#5233—61no—
46#5139—31no—
47#5129—31no—
48#5006—31no—
49#5002—31no—
50C32×#41—21no—
51C32×#41—21no—
52C32×#41C2×C412yes—
53C32×#41D412yes—
54C2×C32×Q8D411yescharacteristic
55C2×C32×D4—21no—
56C2×C32×D4D411yescharacteristic
57C22×C32×C4—21no—
58C22×C32×C4C2311yescharacteristic
59C2×C3×#67—24no—
60C2×C3×#67—21no—
61C2×C3×#67D412yes—
62C3×#239—22no—
63C3×#239—22no—
64C3×D3×Q8—22no—
65C3×D3×Q8—22no—
66C3×#237—24no—
67C3×#237—22no—
68C3×#237—22no—
69C3×#237—24no—
70C3×D3×D4—24no—
71C3×D3×D4—22no—
72C3×D3×D4—24no—
73C3×D3×D4—22no—
74C3×#235—24no—
75C3×#235—24no—
76C3×#235—21no—
77C3×#235—21no—
78C3×#235—21no—
79C3×#235—21no—
80C3×#235—21no—
81C3×#235—21no—
82C3×#235—22no—
83C3×#235—22no—
84C3×#235C2×C412yes—
85C3×#235D412yes—
86C2×C3×D12—22no—
87C2×C3×D12C2×C411yescharacteristic
88C2×C3×D12D411yescharacteristic
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3—21no—
91C2×C3×C4×D3D412yes—
92C2×C3×Dic6—22no—
93C2×C3×Dic6C2×C411yescharacteristic
94C2×C3×Dic6D411yescharacteristic
95#3757—21no—
96C4⋊(C3⋊Dic3)—21no—
97C4×C3⋊Dic3—21no—
98C2×C3⋊(C3⋊C8)—21no—
99C2×C3⋊(C3⋊C8)—21no—
100C2×C3⋊(C3⋊C8)—21no—
101C3×#217—21no—
102C3×C4⋊Dic3—21no—
103C3×C4×Dic3—21no—
104C3×#208—21no—
105C3×#208—21no—
106C2×C3×C3⋊C8—21no—
107#1794—91noSylow
108C3×2−1+4—32no—
109C3×2−1+4—61no—
110C3×2−1+4—61no—
111C3×H(5,𝔽2)—32no—
112C3×H(5,𝔽2)—62no—
113C3×H(5,𝔽2)—61no—
114C3×H(5,𝔽2)—61no—
115C2×C3×#41—21no—
116C2×C3×#41—31no—
117C2×C3×#41—31no—
118C2×C3×#41—62no—
119C2×C3×#41—62no—
120C2×C3×#41—62no—
121C2×C3×#41C2×D311yescharacteristic
122C2×C3×#41C2×D311yescharacteristic
123#1010—21no—
124#1010Dic312yescomplemented
125#1009—21no—
126#1009Dic312yescomplemented
127D3×#41—22no—
128D3×#41—22no—
129#1007—21no—
130#1004—21no—
131#1004—22no—
132C2×#235—22no—
133C2×#235C2×D311yescharacteristic
134C2×#235C2×D311yescharacteristic
135C2×C3×M16—31no—
136C3×#117—31no—
137#926—31no—
138#926—31no—
139#926—61no—
140#926C2×D311yescharacteristic, complemented
141C2×#208C2×D311yescharacteristic, complemented
142C22×C3⋊C8—31no—
143C22×C3⋊C8—31no—
144C22×C3⋊C8—61no—
145C3×#104—62no—
146#837—22no—
147#837—62no—
148#835—61no—
149#835—62no—
150#835—61no—
151#835—61no—
152#834—62no—
153#832—61no—
154#832—62no—
155#832—61no—
156#832—61no—
157#830—62no—
158#825—62no—
159(C2×D3)⋊C8—62no—
160#810—61no—
161#809—61no—
162#806—62no—
163C23×C32—21no—
164C23×C32C2×D411yescharacteristic
165C22×C3×D3—24no—
166C22×C3×D3—21no—
167C22×C3×D3C22⋊C412yes—
168C32×Q8—21no—
169C32×Q8C22⋊C412yes—
170C32×D4—22no—
171C32×D4—22no—
172C32×D4—21no—
173C32×D4C22⋊C412yes—
174C2×C32×C4—21no—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4C22×C411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C3⋊Dic3—41no—
184C3×#67—24no—
185C3×#67—24no—
186C3×#67—22no—
187C3×#67—22no—
188C3×#67—22no—
189C3×#67—22no—
190C2×C3×Dic3—24no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—41no—
193C2×C3×Dic3C22⋊C412yes—
194C3×D12—24no—
195C3×D12—21no—
196C3×D12—21no—
197C3×D12—21no—
198C3×D12C22⋊C412yes—
199C3×C4×D3—24no—
200C3×C4×D3—24no—
201C3×C4×D3—22no—
202C3×C4×D3—22no—
203C3×C4×D3—22no—
204C3×C4×D3—22no—
205C3×Dic6—24no—
206C3×Dic6—21no—
207C3×Dic6—21no—
208C3×Dic6—21no—
209C3×Dic6C22⋊C412yes—
210C3⋊(C3⋊C8)—41no—
211C3×C3⋊C8—41no—
212#585—31no—
213#421—31no—
214#421—91no—
215#416—91no—
216#416—91no—
217#410—91no—
218#408—91no—
219C3×#41—21no—
220C3×#41—21no—
221C3×#41—21no—
222C3×#41—21no—
223C3×#41—22no—
224C3×#41—22no—
225C3×#41—32no—
226C3×#41—32no—
227C3×#41—41no—
228C3×#41—41no—
229C3×#41—62no—
230C3×#41—62no—
231C3×#41—64no—
232C3×#41—64no—
233C3×#41—64no—
234C3×#41—64no—
235C3×#41—62no—
236C3×#41—62no—
237C3×#41—62no—
238C3×#41—62no—
239C3×#41—61no—
240C3×#41—61no—
241C3×#41—61no—
242C3×#41—61no—
243C3×#41—61no—
244C3×#41—61no—
245C3×#41C4×D312yes—
246C3×#41C2×Dic312yes—
247C3×#41#6712yes—
248C3×#41#6712yes—
249C2×C3×Q8—21no—
250C2×C3×Q8—31no—
251C2×C3×Q8—31no—
252C2×C3×Q8—62no—
253C2×C3×Q8—62no—
254C2×C3×Q8—62no—
255C2×C3×Q8D1211yescharacteristic
256C2×C3×Q8#6711yescharacteristic
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—32no—
261C2×C3×D4—31no—
262C2×C3×D4—31no—
263C2×C3×D4—41no—
264C2×C3×D4—62no—
265C2×C3×D4—64no—
266C2×C3×D4—64no—
267C2×C3×D4—62no—
268C2×C3×D4—64no—
269C2×C3×D4—61no—
270C2×C3×D4—62no—
271C2×C3×D4D1211yescharacteristic
272C2×C3×D4#6711yescharacteristic
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—32no—
277C22×C3×C4—41no—
278C22×C3×C4—64no—
279C22×C3×C4—61no—
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C2×#67—24no—
283C2×#67—21no—
284C2×#67#6712yes—
285#239—22no—
286#239—22no—
287D3×Q8—22no—
288D3×Q8—22no—
289#237—24no—
290#237—22no—
291#237—22no—
292#237—24no—
293D3×D4—24no—
294D3×D4—22no—
295D3×D4—24no—
296D3×D4—22no—
297#235—24no—
298#235—24no—
299#235—21no—
300#235—21no—
301#235—21no—
302#235—21no—
303#235—21no—
304#235—21no—
305#235—22no—
306#235—22no—
307#235C2×Dic312yes—
308#235#6712yes—
309C2×D12—22no—
310C2×D12C2×Dic311yescharacteristic
311C2×D12#6711yescharacteristic
312C2×C4×D3—24no—
313C2×C4×D3—21no—
314C2×C4×D3#6712yes—
315C2×Dic6—22no—
316C2×Dic6C2×Dic311yescharacteristic
317C2×Dic6#6711yescharacteristic
318C3×M16—61no—
319C3×M16—61no—
320C2×C3×C8—61no—
321C3×C4⋊C4—61no—
322C3×C22⋊C4—61no—
323C3×C42—61no—
324#217—21no—
325#217—61no—
326#217—61no—
327#217—121no—
328C4⋊Dic3—21no—
329C4⋊Dic3—62no—
330C4⋊Dic3—61no—
331C4⋊Dic3—61no—
332C4×Dic3—21no—
333C4×Dic3—61no—
334C4×Dic3—61no—
335C4×Dic3—121no—
336#208—21no—
337#208—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—62no—
340C2×C3⋊C8—61no—
341C2×C3⋊C8—61no—
342C2×C3⋊C8—61no—
343C2×C3⋊C8—61no—
344C2×C3⋊C8—61no—
345C2×C3⋊C8—61no—
346C2×C3⋊C8—121no—
347C2×C3⋊C8—121no—
348C22×C32—22no—
349C22×C32—41no—
350C22×C32—81no—
351C22×C32C2×C22⋊C411yescharacteristic
352C22×C32#12011yescharacteristic
353C22×C32#12011yescharacteristic
354C2×C3×D3—22no—
355C2×C3×D3—22no—
356C2×C3×D3—42no—
357C2×C3×D3—81no—
358C2×C3×D3—84no—
359C32×C4—22no—
360C32×C4C2×C22⋊C411yescharacteristic
361C32×C4C2×C22⋊C411yescharacteristic
362C32×C4#12011yescharacteristic
363C32×C4#12011yescharacteristic
364C3⋊Dic3—81no—
365C3×Dic3—22no—
366C3×Dic3—22no—
367C3×Dic3—81no—
3682−1+4—32no—
3692−1+4—61no—
3702−1+4—61no—
371H(5,𝔽2)—32no—
372H(5,𝔽2)—62no—
373H(5,𝔽2)—61no—
374H(5,𝔽2)—61no—
375C2×#41—31no—
376C2×#41—31no—
377C2×#41—62no—
378C2×#41—62no—
379C2×#41—62no—
380C2×#41D3211yescharacteristic
381C2×M16—31no—
382C22×C8—91no—
383#117—31no—
384#117—91no—
385#104—62no—
386#104—182no—
387#103—181no—
388#103—181no—
389#102—181no—
390#102—181no—
391#99—182no—
392C22⋊C8—182no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—32no—
397C23×C3—41no—
398C23×C3—64no—
399C23×C3—61no—
400C23×C3D3×D411yescharacteristic
401C23×C3C2×#6711yescharacteristic
402C22×D3—24no—
403C22×D3—21no—
404C22×D3#21712yes—
405C3×Q8—21no—
406C3×Q8—21no—
407C3×Q8—22no—
408C3×Q8—32no—
409C3×Q8—41no—
410C3×Q8—64no—
411C3×Q8—61no—
412C3×Q8—61no—
413C3×Q8—61no—
414C3×Q8(C2×D3)⋊C412yes—
415C3×Q8#21712yes—
416C3×D4—22no—
417C3×D4—22no—
418C3×D4—22no—
419C3×D4—22no—
420C3×D4—21no—
421C3×D4—21no—
422C3×D4—22no—
423C3×D4—32no—
424C3×D4—41no—
425C3×D4—42no—
426C3×D4—42no—
427C3×D4—64no—
428C3×D4—64no—
429C3×D4—64no—
430C3×D4—62no—
431C3×D4—62no—
432C3×D4—62no—
433C3×D4—62no—
434C3×D4—61no—
435C3×D4—61no—
436C3×D4—61no—
437C3×D4(C2×D3)⋊C412yes—
438C3×D4#21712yes—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—32no—
452C2×C3×C4—42no—
453C2×C3×C4—42no—
454C2×C3×C4—41no—
455C2×C3×C4—64no—
456C2×C3×C4—64no—
457C2×C3×C4—64no—
458C2×C3×C4—61no—
459C2×C3×C4—62no—
460C2×C3×C4—62no—
461C2×C3×C4—62no—
462C2×C3×C4—62no—
463C2×C3×C4—121no—
464C2×C3×C4C2×C4×D311yescharacteristic
465C2×C3×C4C2×D1211yescharacteristic
466C2×C3×C4D3×D411yescharacteristic
467C2×C3×C4D3×D411yescharacteristic
468C2×C3×C4D3×D411yescharacteristic
469C2×C3×C4C22×Dic311yescharacteristic
470C2×C3×C4C2×#6711yescharacteristic
471C2×C3×C4C2×#6711yescharacteristic
472C2×C3×C4C2×#6711yescharacteristic
473C2×C3×C4C2×#6711yescharacteristic
474C2×C3×C4C2×#6711yescharacteristic
475C2×C3×C4C2×#6711yescharacteristic
476#67—24no—
477#67—24no—
478#67—22no—
479#67—22no—
480#67—22no—
481#67—22no—
482C2×Dic3—24no—
483C2×Dic3—21no—
484C2×Dic3—41no—
485C2×Dic3—122no—
486C2×Dic3—121no—
487C2×Dic3—121no—
488C2×Dic3#21712yes—
489D12—24no—
490D12—21no—
491D12—21no—
492D12—21no—
493D12#21712yes—
494C4×D3—24no—
495C4×D3—24no—
496C4×D3—22no—
497C4×D3—22no—
498C4×D3—22no—
499C4×D3—22no—
500Dic6—24no—
501Dic6—21no—
502Dic6—21no—
503Dic6—21no—
504Dic6#21712yes—
505C3×C8—121no—
506C3⋊C8—41no—
507C3⋊C8—122no—
508C3⋊C8—121no—
509C3⋊C8—121no—
510C2×C32—21no—
511C2×C32—21no—
512C2×C32—21no—
513C2×C32—42no—
514C2×C32#37911yescharacteristic
515C3×D3—42no—
516C3×D3—42no—
517#41—21no—
518#41—21no—
519#41—32no—
520#41—32no—
521#41—62no—
522#41—62no—
523#41—64no—
524#41—64no—
525#41—64no—
526#41—64no—
527#41—62no—
528#41—62no—
529#41—62no—
530#41—62no—
531#41—61no—
532#41—61no—
533#41—61no—
534#41—61no—
535#41—61no—
536#41—61no—
537#41D3×Dic312yes—
538#41#62512yes—
539C2×Q8—31no—
540C2×Q8—31no—
541C2×Q8—62no—
542C2×Q8—62no—
543C2×Q8—62no—
544C2×Q8#62611yescharacteristic
545C2×D4—21no—
546C2×D4—32no—
547C2×D4—31no—
548C2×D4—31no—
549C2×D4—62no—
550C2×D4—64no—
551C2×D4—64no—
552C2×D4—62no—
553C2×D4—64no—
554C2×D4—61no—
555C2×D4—62no—
556C2×D4#62611yescharacteristic
557C22×C4—21no—
558C22×C4—32no—
559C22×C4—64no—
560C22×C4—61no—
561C22×C4C2×D3211yescharacteristic
562M16—61no—
563M16—61no—
564C2×C8—61no—
565C2×C8—181no—
566C2×C8—181no—
567C2×C8—181no—
568C4⋊C4—61no—
569C4⋊C4—181no—
570C22⋊C4—61no—
571C22⋊C4—181no—
572C42—61no—
573C42—181no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—42no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—42no—
583C22×C3—62no—
584C22×C3—62no—
585C22×C3—81no—
586C22×C3—81no—
587C22×C3—82no—
588C22×C3—122no—
589C22×C3—241no—
590C22×C3—244no—
591C22×C3D3×C22⋊C411yescharacteristic
592C22×C3#88211yescharacteristic
593C22×C3#93711yescharacteristic
594C22×C3C2×#21711yescharacteristic
595C22×C3#95311yescharacteristic
596C22×C3#95311yescharacteristic
597C2×D3—22no—
598C2×D3—22no—
599C2×D3—42no—
600C2×D3—81no—
601C2×D3—84no—
602C3×C4—22no—
603C3×C4—22no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—42no—
609C3×C4—62no—
610C3×C4—62no—
611C3×C4—241no—
612C3×C4D3×C22⋊C411yescharacteristic
613C3×C4#88211yescharacteristic
614C3×C4C2×(C2×D3)⋊C411yescharacteristic
615C3×C4#93711yescharacteristic
616C3×C4C2×#21711yescharacteristic
617C3×C4C2×#21711yescharacteristic
618C3×C4#95311yescharacteristic
619C3×C4#95311yescharacteristic
620Dic3—22no—
621Dic3—22no—
622Dic3—81no—
623Dic3—242no—
624Dic3—241no—
625Dic3—241no—
626C32#179411yescharacteristic, complemented, Sylow
627C23—21no—
628C23—32no—
629C23—64no—
630C23—61no—
631C23D3×#6711yescharacteristic
632Q8—21no—
633Q8—32no—
634Q8—64no—
635Q8—61no—
636Q8—61no—
637Q8—61no—
638Q8(C2×D3)⋊Dic312yes—
639D4—22no—
640D4—22no—
641D4—21no—
642D4—32no—
643D4—64no—
644D4—64no—
645D4—64no—
646D4—62no—
647D4—62no—
648D4—62no—
649D4—62no—
650D4—61no—
651D4—61no—
652D4—61no—
653D4(C2×D3)⋊Dic312yes—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—32no—
658C2×C4—64no—
659C2×C4—64no—
660C2×C4—64no—
661C2×C4—61no—
662C2×C4—62no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—62no—
666C2×C4—121no—
667C2×C4—361no—
668C2×C4C2×D3×Dic311yescharacteristic
669C2×C4C2×#62511yescharacteristic
670C2×C4C2×#62611yescharacteristic
671C2×C4D3×#6711yescharacteristic
672C2×C4D3×#6711yescharacteristic
673C2×C4D3×#6711yescharacteristic
674C8—121no—
675C8—361no—
676C2×C3—22no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—41no—
685C2×C3—41no—
686C2×C3—42no—
687C2×C3—42no—
688C2×C3—82no—
689C2×C3—122no—
690C2×C3—122no—
691C2×C3#495511yescharacteristic
692C2×C3#524711yescharacteristic
693D3—42no—
694D3—42no—
695C22—22no—
696C22—41no—
697C22—62no—
698C22—62no—
699C22—81no—
700C22—122no—
701C22—241no—
702C22—244no—
703C22D3×#21711yescharacteristic
704C22#6397611yescharacteristic
705C22#6397711yescharacteristic
706C4—22no—
707C4—62no—
708C4—62no—
709C4—241no—
710C4—721no—
711C4C2×(C2×D3)⋊Dic311yescharacteristic
712C4D3×#21711yescharacteristic
713C4#6397611yescharacteristic
714C4#6397711yescharacteristic
715C3—21no—
716C3#7041311yescharacteristic, complemented
717C3#7214611yescharacteristic, complemented
718C2—21no—
719C2—21no—
720C2—21no—
721C2—42no—
722C2—122no—
723C2—122no—
724C2#1059170611yescharacteristic
subgroupG/H
centerC4#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#379
prime radicalC3×#5964C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1794
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10592932C2semidirect
3. C3×#5236C2semidirect
4. #10591231C2semidirect
5. #10591110C2semidirect
6. #10591083C2semidirect
7. #10591071C2semidirect
12. C3×#1010C4semidirect
14. C3×#1009C4semidirect
23. #64135C22semidirect
24. C22×C3⋊(C3⋊C8)C22semidirect
25. C3×#926C22semidirect
26. C2×C3×#208C22semidirect
40. #5236D3semidirect
124. #1010Dic3semidirect
126. #1009Dic3semidirect
140. #926C2×D3semidirect
141. C2×#208C2×D3semidirect
626. C32#1794semidirect
716. C3#70413semidirect
717. C3#72146semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
#105929322
C3×#52362
#105912312
#105911102
#105910832
#105910712
#721463
#704133