Finite Group Databasebeta

← #11857573

Subgroups — #11857573

Order 1152.

1511 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64297C211yesmaximal, characteristic
2C3×#5516C211yesmaximal, characteristic, complemented
3#10594818C211yesmaximal, characteristic, complemented
4#10592705C211yesmaximal, characteristic, complemented
5C3×#5006C211yesmaximal, characteristic, complemented
6#10591232C211yesmaximal, characteristic, complemented
7#10591231C211yesmaximal, characteristic, complemented
8#10590405C218yesmaximal, complemented
9#82556—31nomaximal
10#78689—31nomaximal
11C2×#3828C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×#3804C2214yes—
15C2×#3799C412yescomplemented
16C2×#3797C412yescomplemented
17#64297—22no—
18#64297—22no—
19#64297—22no—
20#64297—22no—
21C2×#3796C412yescomplemented
22C2×D3×Dic6C412yescomplemented
23C32×#117C2211yescharacteristic
24#64135C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C3×#926C2211yescharacteristic
27C3×#887—22no—
28C3×#877C2214yes—
29C3×C4×Dic6—22no—
30#63955C2214yes—
31#63843—22no—
32Dic3×Dic6—22no—
33#63633C2214yes—
34C3×#806C2214yes—
35#63581C2214yes—
36#63580C2214yes—
37C2×#1010—31no—
38C2×#1007—31no—
39C3×#519—31no—
40#5812—31no—
41#5516—31no—
42#5516D311yescharacteristic, complemented
43C3×#410—31no—
44#5240—31no—
45#5006—31no—
46#5006—31no—
47#5006—31no—
48#5006—31no—
49#5006—31no—
50#5006—38no—
51#5006—61no—
52#5006D311yescharacteristic, complemented
53#4740—38no—
54C22×C32×C4C2311yescharacteristic
55C2×#638C2312yes—
56#3828—21no—
57#3828—21no—
58#3828—21no—
59#3828—21no—
60C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
61C2×C4×C3⋊D3C2×C412yes—
62C2×#634C2×C411yescharacteristic
63C2×C3×#67C2312yes—
64C22×C3×Dic3C2312yes—
65C3×#235—21no—
66C3×#235—21no—
67C3×#235—21no—
68C3×#235—21no—
69C2×C3×D12C2×C411yescharacteristic
70C2×C3×C4×D3C2×C412yes—
71C2×C3×Dic6C2×C411yescharacteristic
72C2×C3×Dic6C2×C412yes—
73C2×C3×Dic6C2×C412yes—
74C2×C3×Dic6D412yes—
75C2×C3×Dic6D412yes—
76C2×C3×Dic6D412yes—
77C2×C3×Dic6D412yes—
78C2×#627C2×C414yes—
79C2×#626C2×C414yes—
80C2×#624C2×C414yes—
81#3804—28no—
82#3804—28no—
83C2×D3×Dic3C2×C414yes—
84#3799—24no—
85#3799—24no—
86#3797—24no—
87#3797—24no—
88#3796—24no—
89#3796—24no—
90D3×Dic6—24no—
91D3×Dic6—24no—
92C32×C4⋊C4—21no—
93C32×C22⋊C4C2312yes—
94C32×C42—21no—
95#3757C2312yes—
96C4⋊(C3⋊Dic3)—21no—
97C4×C3⋊Dic3—21no—
98C3×#217C2312yes—
99C3×#217C2312yes—
100C3×C4⋊Dic3—21no—
101C3×C4⋊Dic3—21no—
102C3×Dic3⋊C4—24no—
103C3×C4×Dic3—21no—
104C3×C4×Dic3—21no—
105C3×C4×Dic3—24no—
106Dic3⋊Dic3—24no—
107Dic32—24no—
108#2884—91noSylow
109C2×C3×#41—31no—
110C22×C3×Q8—31no—
111#1010—62no—
112#1010—62no—
113#1010—62no—
114#1010—62no—
115#1007—62no—
116#1007—62no—
117#1007—62no—
118#1007—62no—
119C2×#239—32no—
120C2×#239—32no—
121C2×D3×Q8—32no—
122C2×D3×Q8—32no—
123C2×D3×Q8—32no—
124C2×#237—34no—
125C2×#237—32no—
126C2×#235—31no—
127C2×#235—31no—
128C2×#235—34no—
129C2×#235—32no—
130C2×#235—61no—
131C2×#235C2×D311yescharacteristic
132C22×Dic6—32no—
133C22×Dic6C2×D311yescharacteristic
134C3×C4×Q8—62no—
135C3×C4×Q8—62no—
136C3×#117—21no—
137C3×#117—31no—
138C3×#117—31no—
139C3×#117—34no—
140C3×#117C2×D311yescharacteristic
141C3×#117C2×D311yescharacteristic
142Q8×Dic3—62no—
143Q8×Dic3—62no—
144#926—31no—
145#926—31no—
146#926—34no—
147#926—61no—
148#926C2×D311yescharacteristic
149#926C2×D311yescharacteristic
150#887—22no—
151#887—62no—
152#877—34no—
153#877C2×D314yes—
154C4×Dic6—22no—
155C4×Dic6—62no—
156C3×#99—34no—
157#834—34no—
158#806—34no—
159#806—34no—
160#806—34no—
161#806—34no—
162#806—34no—
163#806—64no—
164#806C2×D314yes—
165C23×C32C2411yescharacteristic
166C22×C3⋊D3C22×C412yes—
167C22×C3×D3C22×C412yes—
168C2×C32×C4—22no—
169C2×C32×C4C22×C411yescharacteristic
170C2×C32×C4C22×C411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175#638—22no—
176#638—22no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3C22×C412yes—
179C4⋊(C3⋊D3)—21no—
180C4⋊(C3⋊D3)—21no—
181C4×C3⋊D3—22no—
182C4×C3⋊D3—22no—
183#634—21no—
184#634—21no—
185C3×#67—22no—
186C3×#67—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3C22×C412yes—
190C2×C3×Dic3C22×C414yes—
191C2×C3×Dic3C2×D414yes—
192C2×C3×Dic3C2×D414yes—
193C3×D12—21no—
194C3×D12—21no—
195C3×C4×D3—22no—
196C3×C4×D3—22no—
197C3×Dic6—21no—
198C3×Dic6—21no—
199C3×Dic6C22⋊C414yes—
200C3×Dic6C22⋊C414yes—
201C3×Dic6C22⋊C414yes—
202C3×Dic6C22⋊C414yes—
203#627—28no—
204#626—28no—
205#624—28no—
206D3×Dic3—28no—
207C2×2−1+4—91no—
208#519—31no—
209#519—91no—
210#410—31no—
211#410—98no—
212#410—91no—
213#410—91no—
214#410—91no—
215C3×#41—61no—
216C3×#41—61no—
217C3×#41—61no—
218C3×#41—61no—
219C2×C3×Q8—32no—
220C2×C3×Q8—32no—
221C2×C3×Q8—31no—
222C2×C3×Q8—32no—
223C2×C3×Q8—32no—
224C2×C3×Q8—32no—
225C2×C3×Q8—32no—
226C2×C3×D4—32no—
227C2×C3×D4—31no—
228C22×C3×C4—21no—
229C22×C3×C4—32no—
230C22×C3×C4—32no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—32no—
234C2×#67—32no—
235C2×#67—34no—
236C2×#67—62no—
237C2×#67C22×D312yes—
238C22×Dic3—34no—
239C22×Dic3C22×D312yes—
240#239—64no—
241#239—64no—
242#239—64no—
243#239—64no—
244D3×Q8—64no—
245D3×Q8—64no—
246D3×Q8—64no—
247D3×Q8—64no—
248D3×Q8—64no—
249D3×Q8—64no—
250#237—68no—
251#237—68no—
252#237—64no—
253#237—64no—
254#235—21no—
255#235—21no—
256#235—21no—
257#235—21no—
258#235—68no—
259#235—68no—
260#235—61no—
261#235—61no—
262#235—61no—
263#235—61no—
264#235—61no—
265#235—61no—
266#235—61no—
267#235—61no—
268#235—64no—
269#235—64no—
270#235—121no—
271#235—121no—
272#235—121no—
273#235—121no—
274C2×D12—34no—
275C2×D12—31no—
276C2×D12—31no—
277C2×D12—61no—
278C2×D12C4×D311yescharacteristic
279C2×C4×D3—34no—
280C2×C4×D3—32no—
281C2×C4×D3—32no—
282C2×C4×D3—34no—
283C2×C4×D3—34no—
284C2×C4×D3—62no—
285C2×C4×D3C4×D312yes—
286C2×Dic6—31no—
287C2×Dic6—31no—
288C2×Dic6—34no—
289C2×Dic6—34no—
290C2×Dic6—61no—
291C2×Dic6—64no—
292C2×Dic6—64no—
293C2×Dic6C4×D311yescharacteristic
294C2×Dic6C4×D312yes—
295C2×Dic6C4×D312yes—
296C2×Dic6D1212yes—
297C2×Dic6D1212yes—
298C2×Dic6#6712yes—
299C2×Dic6#6712yes—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—41no—
303C3×C4⋊C4—64no—
304C3×C4⋊C4—61no—
305C3×C4⋊C4—61no—
306C3×C22⋊C4—22no—
307C3×C22⋊C4—32no—
308C3×C22⋊C4—32no—
309C3×C22⋊C4C22×D312yes—
310C3×C22⋊C4C22×D312yes—
311C3×C42—21no—
312C3×C42—21no—
313C3×C42—41no—
314C3×C42—64no—
315C3×C42—61no—
316C3×C42—61no—
317#217—32no—
318#217—32no—
319#217—62no—
320#217C22×D312yes—
321#217C22×D312yes—
322C4⋊Dic3—21no—
323C4⋊Dic3—21no—
324C4⋊Dic3—64no—
325C4⋊Dic3—61no—
326C4⋊Dic3—61no—
327C4⋊Dic3—121no—
328Dic3⋊C4—24no—
329Dic3⋊C4—64no—
330C4×Dic3—21no—
331C4×Dic3—21no—
332C4×Dic3—24no—
333C4×Dic3—64no—
334C4×Dic3—61no—
335C4×Dic3—61no—
336C4×Dic3—64no—
337C4×Dic3—121no—
338C22×C32—41no—
339C22×C32C23×C411yescharacteristic
340C22×C32C22×D411yescharacteristic
341C22×C32C22×D411yescharacteristic
342C2×C3⋊D3—22no—
343C2×C3⋊D3—42no—
344C2×C3×D3—22no—
345C2×C3×D3—42no—
346C32×C4—42no—
347C32×C4C2×C22⋊C411yescharacteristic
348C32×C4C2×C22⋊C411yescharacteristic
349C32×C4C2×C22⋊C411yescharacteristic
350C32×C4C2×C22⋊C411yescharacteristic
351C3⋊Dic3—22no—
352C3⋊Dic3—42no—
353C3×Dic3—22no—
354C3×Dic3—42no—
355C3×Dic3—42no—
356C3×Dic3C2×C22⋊C418yes—
3572−1+4—182no—
3582−1+4—182no—
3592−1+4—182no—
3602−1+4—182no—
361C2×#41—31no—
362C2×#41—94no—
363C2×#41—92no—
364C2×#41—92no—
365C2×#41—91no—
366C22×Q8—31no—
367C22×Q8—92no—
368C22×Q8—92no—
369C4×Q8—62no—
370C4×Q8—62no—
371C4×Q8—182no—
372C4×Q8—182no—
373#117—31no—
374#117—31no—
375#117—34no—
376#117—94no—
377#117—91no—
378#117D3211yescharacteristic
379#99—34no—
380#99—94no—
381#99—94no—
382#99—94no—
383C23×C3—21no—
384C23×C3—32no—
385C23×C3C23×D311yescharacteristic
386C23×C3C23×D311yescharacteristic
387C22×D3—32no—
388C22×D3—32no—
389C22×D3—62no—
390C22×D3C2×C4×D312yes—
391C3×Q8—34no—
392C3×Q8—34no—
393C3×Q8—34no—
394C3×Q8—34no—
395C3×Q8—61no—
396C3×Q8—61no—
397C3×D4—62no—
398C3×D4—62no—
399C3×D4—61no—
400C3×D4—61no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—34no—
410C2×C3×C4—34no—
411C2×C3×C4—34no—
412C2×C3×C4—32no—
413C2×C3×C4—42no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4—62no—
418C2×C3×C4C2×C4×D311yescharacteristic
419C2×C3×C4C2×C4×D311yescharacteristic
420C2×C3×C4C2×C4×D311yescharacteristic
421C2×C3×C4C2×C4×D311yescharacteristic
422C2×C3×C4C2×D1211yescharacteristic
423C2×C3×C4C2×D1211yescharacteristic
424C2×C3×C4D3×D411yescharacteristic
425C2×C3×C4D3×D411yescharacteristic
426C2×C3×C4D3×D411yescharacteristic
427C2×C3×C4D3×D411yescharacteristic
428C2×C3×C4C2×#6711yescharacteristic
429C2×C3×C4C2×#6711yescharacteristic
430#67—22no—
431#67—22no—
432#67—62no—
433#67—62no—
434#67—62no—
435#67—62no—
436#67—68no—
437#67—122no—
438#67—122no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—32no—
442C2×Dic3—32no—
443C2×Dic3—62no—
444C2×Dic3—68no—
445C2×Dic3—62no—
446C2×Dic3—62no—
447C2×Dic3—122no—
448C2×Dic3C2×C4×D312yes—
449C2×Dic3C2×C4×D314yes—
450C2×Dic3C2×D1214yes—
451C2×Dic3C2×#6714yes—
452D12—21no—
453D12—21no—
454D12—68no—
455D12—61no—
456D12—61no—
457D12—61no—
458D12—61no—
459D12—121no—
460D12—121no—
461C4×D3—22no—
462C4×D3—22no—
463C4×D3—68no—
464C4×D3—68no—
465C4×D3—62no—
466C4×D3—62no—
467C4×D3—62no—
468C4×D3—62no—
469C4×D3—68no—
470C4×D3—122no—
471C4×D3—122no—
472Dic6—21no—
473Dic6—21no—
474Dic6—68no—
475Dic6—61no—
476Dic6—61no—
477Dic6—61no—
478Dic6—61no—
479Dic6—68no—
480Dic6—121no—
481Dic6—121no—
482Dic6(C2×D3)⋊C414yes—
483Dic6(C2×D3)⋊C414yes—
484Dic6(C2×D3)⋊C414yes—
485Dic6(C2×D3)⋊C414yes—
486C2×C32—21no—
487C2×C32—21no—
488C2×C32—21no—
489C2×C32C22×C22⋊C411yescharacteristic
490C3⋊D3—42no—
491C3×D3—42no—
492#41—61no—
493#41—61no—
494#41—61no—
495#41—61no—
496#41—188no—
497#41—188no—
498#41—184no—
499#41—184no—
500#41—184no—
501#41—184no—
502#41—181no—
503#41—181no—
504#41—181no—
505#41—181no—
506C2×Q8—32no—
507C2×Q8—32no—
508C2×Q8—31no—
509C2×Q8—32no—
510C2×Q8—32no—
511C2×Q8—32no—
512C2×Q8—32no—
513C2×Q8—94no—
514C2×Q8—91no—
515C2×Q8—184no—
516C2×Q8—184no—
517C2×Q8—184no—
518C2×Q8—184no—
519C2×D4—32no—
520C2×D4—31no—
521C2×D4—94no—
522C2×D4—92no—
523C2×D4—91no—
524C22×C4—32no—
525C22×C4—32no—
526C22×C4—94no—
527C22×C4—94no—
528C22×C4—92no—
529C22×C4C2×D3211yescharacteristic
530C4⋊C4—21no—
531C4⋊C4—64no—
532C4⋊C4—61no—
533C4⋊C4—61no—
534C4⋊C4—184no—
535C4⋊C4—181no—
536C22⋊C4—32no—
537C22⋊C4—32no—
538C22⋊C4—92no—
539C22⋊C4C2×D3212yes—
540C42—21no—
541C42—64no—
542C42—61no—
543C42—61no—
544C42—184no—
545C42—181no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—41no—
550C22×C3—41no—
551C22×C3—62no—
552C22×C3—81no—
553C22×C3—122no—
554C22×C3C22×C4×D311yescharacteristic
555C22×C3C22×C4×D311yescharacteristic
556C22×C3C22×D1211yescharacteristic
557C22×C3C2×D3×D411yescharacteristic
558C22×C3C2×D3×D411yescharacteristic
559C22×C3C22×#6711yescharacteristic
560C2×D3—22no—
561C2×D3—42no—
562C2×D3—62no—
563C2×D3—62no—
564C2×D3—122no—
565C2×D3—122no—
566C2×D3—122no—
567C2×D3—242no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—21no—
571C3×C4—21no—
572C3×C4—38no—
573C3×C4—42no—
574C3×C4—42no—
575C3×C4—62no—
576C3×C4—82no—
577C3×C4—122no—
578C3×C4—122no—
579C3×C4D3×C22⋊C411yescharacteristic
580C3×C4D3×C22⋊C411yescharacteristic
581C3×C4D3×C22⋊C411yescharacteristic
582C3×C4D3×C22⋊C411yescharacteristic
583C3×C4C2×(C2×D3)⋊C411yescharacteristic
584C3×C4C2×(C2×D3)⋊C411yescharacteristic
585C3×C4C2×(C2×D3)⋊C411yescharacteristic
586C3×C4C2×(C2×D3)⋊C411yescharacteristic
587Dic3—22no—
588Dic3—42no—
589Dic3—42no—
590Dic3—62no—
591Dic3—62no—
592Dic3—122no—
593Dic3—122no—
594Dic3—122no—
595Dic3—242no—
596Dic3C2×(C2×D3)⋊C418yes—
597C32#288411yescharacteristic, complemented, Sylow
598C23—32no—
599C23—92no—
600C23C22×D3211yescharacteristic
601Q8—34no—
602Q8—34no—
603Q8—34no—
604Q8—34no—
605Q8—61no—
606Q8—61no—
607Q8—188no—
608Q8—181no—
609Q8—181no—
610D4—62no—
611D4—62no—
612D4—61no—
613D4—61no—
614D4—188no—
615D4—182no—
616D4—182no—
617D4—181no—
618D4—181no—
619C2×C4—22no—
620C2×C4—34no—
621C2×C4—34no—
622C2×C4—34no—
623C2×C4—32no—
624C2×C4—62no—
625C2×C4—62no—
626C2×C4—62no—
627C2×C4—62no—
628C2×C4—92no—
629C2×C4—188no—
630C2×C4—188no—
631C2×C4—182no—
632C2×C4—182no—
633C2×C4—182no—
634C2×C4C4×D3211yescharacteristic
635C2×C4C4×D3211yescharacteristic
636C2×C4D3×D1211yescharacteristic
637C2×C4D3×D1211yescharacteristic
638C2×C4D3×#6711yescharacteristic
639C2×C4D3×#6711yescharacteristic
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—41no—
648C2×C3—41no—
649C2×C3—41no—
650C2×C3—122no—
651C2×C3C2×D3×C22⋊C411yescharacteristic
652C2×C3C22×(C2×D3)⋊C411yescharacteristic
653D3—42no—
654D3—122no—
655D3—122no—
656D3—242no—
657C22—41no—
658C22—62no—
659C22—122no—
660C22—182no—
661C22—362no—
662C22C2×C4×D3211yescharacteristic
663C22C2×D3×D1211yescharacteristic
664C22C2×D3×#6711yescharacteristic
665C4—38no—
666C4—42no—
667C4—62no—
668C4—122no—
669C4—122no—
670C4—182no—
671C4—362no—
672C4D3×(C2×D3)⋊C411yescharacteristic
673C4D3×(C2×D3)⋊C411yescharacteristic
674C4D3×(C2×D3)⋊C411yescharacteristic
675C4D3×(C2×D3)⋊C411yescharacteristic
676C3—21no—
677C3#7868911yescharacteristic, complemented
678C3#8255611yescharacteristic, complemented
679C2—21no—
680C2—21no—
681C2—21no—
682C2—122no—
683C2—362no—
684C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2C2×D3×(C2×D3)⋊C4
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC32×#117C22
socleC2×C32C22×C22⋊C4
prime radicalC2×#64297C2
cosocleC23×C32C24
hypercenter#117D32
hypocenterC32#2884
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#5516C2semidirect
3. #10594818C2semidirect
4. #10592705C2semidirect
5. C3×#5006C2semidirect
6. #10591232C2semidirect
7. #10591231C2semidirect
8. #10590405C2semidirect
15. C2×#3799C4semidirect
16. C2×#3797C4semidirect
21. C2×#3796C4semidirect
22. C2×D3×Dic6C4semidirect
42. #5516D3semidirect
52. #5006D3semidirect
597. C32#2884semidirect
677. C3#78689semidirect
678. C3#82556semidirect

Maximal subgroups

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

subgroupindex
C2×#642972
C3×#55162
#105948182
#105927052
C3×#50062
#105912322
#105912312
#105904052
#825563
#786893