Finite Group Databasebeta

← #11784908

Subgroups — #11784908

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 671 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64298C211yesmaximal, characteristic
2C2×#63651C211yesmaximal, characteristic, complemented
3C2×C3×#825C211yesmaximal, characteristic, complemented
4C3×#5133C211yesmaximal, characteristic, complemented
5#10591213C211yesmaximal, characteristic, complemented
6C2×#63569C211yesmaximal, characteristic, complemented
7#10591087C211yesmaximal, characteristic, complemented
8#70387—31nomaximal
9#70308—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C2×#3805—22no—
14#64298—22no—
15#64298—22no—
16#64298—22no—
17#64298C414yescomplemented
18C2×#3795—21no—
19C2×#3795—21no—
20C2×D3×Dic6—21no—
21C2×D3×Dic6—21no—
22C2×C32×M16C2211yescharacteristic
23C2×#3748C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26#63651—22no—
27C3×#825—22no—
28C3×#821—21no—
29C3×#816—21no—
30#63579—22no—
31#63569—22no—
32#63565—21no—
33#63562—21no—
34C2×#1010—31no—
35C2×#1010—31no—
36C2×C3×#104—31no—
37C3×#417—31no—
38C2×#837—31no—
39#5232—31no—
40C2×#825D311yescharacteristic, complemented
41C2×#824—31no—
42C2×#824—31no—
43C2×#824—61no—
44#5133D311yescharacteristic, complemented
45#4973—31no—
46#4966—31no—
47#4929—31no—
48C2×#805—31no—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3D412yes—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634C2×C412yes—
56C2×#634D412yes—
57C2×C3×#67—21no—
58C2×C3×#67—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C3×#235—21no—
62C3×#235—21no—
63C3×#235—21no—
64C3×#235—21no—
65C3×#235C2×C412yes—
66C3×#235C2×C412yes—
67C3×#235D412yes—
68C3×#235D412yes—
69C2×C3×D12D411yescharacteristic
70C2×C3×D12D411yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×C4×D3—21no—
73C2×C3×Dic6D411yescharacteristic
74C2×C3×Dic6D411yescharacteristic
75C2×#627—22no—
76C2×#625—22no—
77#3805—28no—
78#3805—28no—
79C2×D3×Dic3—22no—
80C2×D3×Dic3—22no—
81#3795—24no—
82#3795—24no—
83#3795—24no—
84#3795—24no—
85D3×Dic6—24no—
86D3×Dic6—24no—
87D3×Dic6—24no—
88D3×Dic6—24no—
89C32×M16—21no—
90C32×M16—21no—
91C2×C32×C8—21no—
92#3748—21no—
93#3748—21no—
94C2×C3⋊(C3⋊C8)—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3—21no—
97C3×C4×Dic3—21no—
98C3×C4×Dic3—21no—
99#1793—91noSylow
100C2×C3×#41—31no—
101C2×C3×#41—31no—
102#1010—34no—
103#1010—34no—
104#1010—62no—
105#1010—62no—
106#1010—62no—
107#1010—62no—
108#1010—62no—
109#1010—62no—
110C2×D3×Q8—61no—
111C2×D3×Q8—61no—
112C2×#237—61no—
113C2×#237—61no—
114C2×#237—62no—
115C2×#237—62no—
116C2×#235—61no—
117C2×#235—61no—
118C2×#235C2×D311yescharacteristic
119C2×#235C2×D311yescharacteristic
120C22×Dic6—31no—
121C22×Dic6—31no—
122C22×Dic6—61no—
123C22×Dic6—61no—
124C22×Dic6—61no—
125C2×C3×M16—21no—
126C2×C3×M16C2×D311yescharacteristic
127C2×C3×M16C2×D311yescharacteristic
128C2×C3×C4⋊C4—31no—
129C2×C3×C42—31no—
130C2×C4⋊Dic3C2×D311yescharacteristic
131C2×C4×Dic3C2×D311yescharacteristic
132C2×#208—31no—
133C2×#208—31no—
134C2×#208—61no—
135C3×#104—62no—
136C3×#103—61no—
137C3×#102—61no—
138#837—62no—
139#835—61no—
140#832—61no—
141C3⋊#95—62no—
142C3⋊#95—62no—
143#825—22no—
144#824—62no—
145#824—62no—
146#824—64no—
147#821—21no—
148#816—21no—
149#810—61no—
150#809—61no—
151#805—62no—
152C23×C32C2×D411yescharacteristic
153C22×C3×D3—21no—
154C22×C3×D3—21no—
155C2×C32×C4C22×C411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3C22⋊C414yes—
164#634—22no—
165#634—22no—
166#634—22no—
167#634—22no—
168C3×#67—22no—
169C3×#67—22no—
170C3×#67—22no—
171C3×#67—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—41no—
176C2×C3×Dic3—41no—
177C2×C3×Dic3—42no—
178C2×C3×Dic3—41no—
179C3×D12—21no—
180C3×D12—21no—
181C3×D12C22⋊C412yes—
182C3×D12C22⋊C412yes—
183C3×C4×D3—22no—
184C3×C4×D3—22no—
185C3×C4×D3—22no—
186C3×C4×D3—22no—
187C3×Dic6—21no—
188C3×Dic6—21no—
189C3×Dic6C22⋊C412yes—
190C3×Dic6C22⋊C412yes—
191#627—28no—
192#625—28no—
193D3×Dic3—28no—
194D3×Dic3—28no—
195C32×C8—41no—
196C3⋊(C3⋊C8)—41no—
197C2×2−1+4—91no—
198C2×#104—31no—
199C2×#104—91no—
200#417—31no—
201#417—91no—
202C2×#101—91no—
203#391—91no—
204C3×#41—32no—
205C3×#41—32no—
206C3×#41—32no—
207C3×#41—32no—
208C3×#41—61no—
209C3×#41—61no—
210C3×#41—61no—
211C3×#41—61no—
212C2×C3×Q8—31no—
213C2×C3×Q8—31no—
214C2×C3×D4—31no—
215C2×C3×D4—31no—
216C2×C3×D4—61no—
217C2×C3×D4—61no—
218C22×C3×C4—21no—
219C22×C3×C4—61no—
220C22×C3×C4—61no—
221C22×C3×C4—61no—
222C22×C3×C4—61no—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C2×#67—21no—
226C2×#67—21no—
227C2×#67—62no—
228C2×#67—62no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—32no—
232C22×Dic3—32no—
233C22×Dic3—62no—
234C22×Dic3—62no—
235C22×Dic3—62no—
236D3×Q8—64no—
237D3×Q8—64no—
238D3×Q8—64no—
239D3×Q8—64no—
240#237—64no—
241#237—64no—
242#237—64no—
243#237—64no—
244#237—68no—
245#237—68no—
246#237—68no—
247#237—68no—
248#235—21no—
249#235—21no—
250#235—21no—
251#235—21no—
252#235—64no—
253#235—64no—
254#235—64no—
255#235—64no—
256#235C4×D312yes—
257#235C4×D312yes—
258#235D1212yes—
259#235#6712yes—
260C2×D12D1211yescharacteristic
261C2×D12#6711yescharacteristic
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—62no—
265C2×C4×D3—62no—
266C2×Dic6—32no—
267C2×Dic6—32no—
268C2×Dic6—32no—
269C2×Dic6—32no—
270C2×Dic6—62no—
271C2×Dic6—62no—
272C2×Dic6—64no—
273C2×Dic6—64no—
274C2×Dic6—62no—
275C2×Dic6—62no—
276C2×Dic6—61no—
277C2×Dic6—61no—
278C2×Dic6—61no—
279C2×Dic6—61no—
280C2×Dic6—61no—
281C2×Dic6—61no—
282C2×Dic6—61no—
283C2×Dic6—61no—
284C2×Dic6—64no—
285C2×Dic6—64no—
286C2×Dic6—121no—
287C2×Dic6—121no—
288C2×Dic6—121no—
289C2×Dic6—121no—
290C2×Dic6D1211yescharacteristic
291C2×Dic6#6711yescharacteristic
292C3×M16—22no—
293C3×M16—21no—
294C3×M16—21no—
295C3×M16—21no—
296C3×M16—21no—
297C3×M16—41no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8—41no—
301C3×C4⋊C4—61no—
302C3×C4⋊C4—61no—
303C3×C42—61no—
304C3×C42—61no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4×Dic3—21no—
308C4×Dic3—21no—
309#208—62no—
310#208—61no—
311#208—61no—
312#208—61no—
313#208—61no—
314#208—121no—
315C2×C3⋊C8—61no—
316C2×C3⋊C8—61no—
317C2×C3⋊C8—121no—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32C2×C22⋊C411yescharacteristic
321C22×C32#12011yescharacteristic
322C22×C32#12011yescharacteristic
323C2×C3×D3—22no—
324C2×C3×D3—22no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C2×C3×D3—41no—
329C32×C4C2×C22⋊C411yescharacteristic
330C32×C4C2×C22⋊C411yescharacteristic
331C32×C4#12011yescharacteristic
332C32×C4#12011yescharacteristic
333C3⋊Dic3—24no—
334C3×Dic3—22no—
335C3×Dic3—22no—
336C3×Dic3—42no—
337C3×Dic3—81no—
3382−1+4—94no—
3392−1+4—182no—
3402−1+4—182no—
3412−1+4—182no—
342C2×#41—31no—
343C2×#41—31no—
344C2×#41—181no—
345C2×#41—181no—
346C2×#41—182no—
347C22×Q8—91no—
348C22×Q8—181no—
349C22×Q8—181no—
350C2×M16—91no—
351C2×M16D3211yescharacteristic
352C2×C4⋊C4—31no—
353C2×C42—31no—
354#104—62no—
355#104—182no—
356#103—61no—
357#103—181no—
358#102—61no—
359#102—181no—
360#101—182no—
361#95—182no—
362C23×C3—21no—
363C23×C3—61no—
364C23×C3—61no—
365C23×C3D3×D411yescharacteristic
366C23×C3D3×D411yescharacteristic
367C22×D3—21no—
368C22×D3—21no—
369C3×Q8—32no—
370C3×Q8—32no—
371C3×Q8—61no—
372C3×Q8—61no—
373C3×D4—32no—
374C3×D4—32no—
375C3×D4—62no—
376C3×D4—62no—
377C3×D4—62no—
378C3×D4—62no—
379C3×D4—61no—
380C3×D4—61no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—61no—
388C2×C3×C4—61no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—121no—
395C2×C3×C4—121no—
396C2×C3×C4—122no—
397C2×C3×C4—121no—
398C2×C3×C4C2×C4×D311yescharacteristic
399C2×C3×C4C2×C4×D311yescharacteristic
400C2×C3×C4C2×D1211yescharacteristic
401C2×C3×C4C2×D1211yescharacteristic
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4C2×#6711yescharacteristic
409C2×C3×C4C2×#6711yescharacteristic
410#67—22no—
411#67—22no—
412#67—22no—
413#67—22no—
414#67—68no—
415#67—68no—
416C2×Dic3—21no—
417C2×Dic3—21no—
418C2×Dic3—22no—
419C2×Dic3—34no—
420C2×Dic3—34no—
421C2×Dic3—41no—
422C2×Dic3—41no—
423C2×Dic3—42no—
424C2×Dic3—41no—
425C2×Dic3—64no—
426C2×Dic3—68no—
427C2×Dic3—68no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—122no—
433C2×Dic3—122no—
434D12—21no—
435D12—21no—
436D12(C2×D3)⋊C412yes—
437D12(C2×D3)⋊C412yes—
438C4×D3—22no—
439C4×D3—22no—
440C4×D3—22no—
441C4×D3—22no—
442C4×D3—68no—
443C4×D3—68no—
444Dic6—21no—
445Dic6—21no—
446Dic6—68no—
447Dic6—68no—
448Dic6—62no—
449Dic6—62no—
450Dic6—62no—
451Dic6—62no—
452Dic6—62no—
453Dic6—62no—
454Dic6—62no—
455Dic6—62no—
456Dic6—122no—
457Dic6—122no—
458Dic6—122no—
459Dic6—122no—
460Dic6(C2×D3)⋊C412yes—
461Dic6(C2×D3)⋊C412yes—
462C3×C8—42no—
463C3×C8—41no—
464C3×C8—41no—
465C3⋊C8—122no—
466C3⋊C8—121no—
467C3⋊C8—121no—
468C2×C32—21no—
469C2×C32—21no—
470C2×C32#37911yescharacteristic
471C2×C32#45411yescharacteristic
472C2×C32#45611yescharacteristic
473C3×D3—42no—
474C3×D3—42no—
475#41—32no—
476#41—32no—
477#41—32no—
478#41—32no—
479#41—61no—
480#41—61no—
481#41—61no—
482#41—61no—
483#41—184no—
484#41—184no—
485#41—184no—
486#41—184no—
487#41—188no—
488#41—188no—
489C2×Q8—31no—
490C2×Q8—31no—
491C2×Q8—92no—
492C2×Q8—92no—
493C2×Q8—182no—
494C2×Q8—184no—
495C2×Q8—184no—
496C2×Q8—184no—
497C2×Q8—184no—
498C2×Q8—181no—
499C2×Q8—181no—
500C2×Q8—181no—
501C2×Q8—181no—
502C2×D4—31no—
503C2×D4—31no—
504C2×D4—61no—
505C2×D4—61no—
506C2×D4—182no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—92no—
512C22×C4—182no—
513C22×C4—182no—
514C22×C4C2×D3211yescharacteristic
515M16—21no—
516M16—21no—
517M16—181no—
518M16—181no—
519C2×C8—21no—
520C2×C8—181no—
521C4⋊C4—61no—
522C4⋊C4—61no—
523C42—61no—
524C42—61no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—62no—
535C22×C3—62no—
536C22×C3—121no—
537C22×C3—121no—
538C22×C3—121no—
539C22×C3—121no—
540C22×C3D3×C22⋊C411yescharacteristic
541C22×C3D3×C22⋊C411yescharacteristic
542C22×C3#88211yescharacteristic
543C22×C3#88211yescharacteristic
544C22×C3#93711yescharacteristic
545C22×C3#93711yescharacteristic
546C2×D3—22no—
547C2×D3—22no—
548C2×D3—41no—
549C2×D3—41no—
550C2×D3—41no—
551C2×D3—41no—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—21no—
555C3×C4—21no—
556C3×C4—62no—
557C3×C4—62no—
558C3×C4—122no—
559C3×C4—241no—
560C3×C4D3×C22⋊C411yescharacteristic
561C3×C4D3×C22⋊C411yescharacteristic
562C3×C4#88211yescharacteristic
563C3×C4#88211yescharacteristic
564C3×C4C2×(C2×D3)⋊C411yescharacteristic
565C3×C4C2×(C2×D3)⋊C411yescharacteristic
566C3×C4#93711yescharacteristic
567C3×C4#93711yescharacteristic
568Dic3—22no—
569Dic3—22no—
570Dic3—42no—
571Dic3—64no—
572Dic3—64no—
573Dic3—81no—
574Dic3—124no—
575C32#179311yescharacteristic, complemented, Sylow
576C23—61no—
577C23—61no—
578C23#380211yescharacteristic
579Q8—32no—
580Q8—32no—
581Q8—61no—
582Q8—61no—
583Q8—188no—
584Q8—182no—
585Q8—182no—
586Q8—182no—
587Q8—182no—
588D4—32no—
589D4—32no—
590D4—62no—
591D4—62no—
592D4—62no—
593D4—62no—
594D4—61no—
595D4—61no—
596D4—188no—
597C2×C4—61no—
598C2×C4—61no—
599C2×C4—62no—
600C2×C4—62no—
601C2×C4—62no—
602C2×C4—62no—
603C2×C4—62no—
604C2×C4—94no—
605C2×C4—121no—
606C2×C4—121no—
607C2×C4—122no—
608C2×C4—121no—
609C2×C4—188no—
610C2×C4—188no—
611C2×C4—182no—
612C2×C4—182no—
613C2×C4C4×D3211yescharacteristic
614C2×C4D3×D1211yescharacteristic
615C2×C4D3×D1211yescharacteristic
616C2×C4D3×#6711yescharacteristic
617C2×C4D3×#6711yescharacteristic
618C2×C4#381111yescharacteristic
619C8—41no—
620C8—361no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—41no—
629C2×C3—41no—
630C2×C3—122no—
631C2×C3—122no—
632C2×C3#482611yescharacteristic
633C2×C3#482711yescharacteristic
634C2×C3#495511yescharacteristic
635C2×C3#495511yescharacteristic
636C2×C3#520111yescharacteristic
637C2×C3#520511yescharacteristic
638D3—42no—
639D3—42no—
640C22—21no—
641C22—21no—
642C22—62no—
643C22—62no—
644C22—121no—
645C22—121no—
646C22—121no—
647C22—121no—
648C22#6392111yescharacteristic
649C22#6392211yescharacteristic
650C22#6392211yescharacteristic
651C4—62no—
652C4—62no—
653C4—122no—
654C4—184no—
655C4—241no—
656C4D3×(C2×D3)⋊C411yescharacteristic
657C4D3×(C2×D3)⋊C411yescharacteristic
658C4#6392311yescharacteristic
659C4#6398311yescharacteristic
660C3—21no—
661C3#7030811yescharacteristic, complemented
662C3#7038711yescharacteristic, complemented
663C2—21no—
664C2—21no—
665C2—122no—
666C2—122no—
667C2#1059101711yescharacteristic
668C2#1059101911yescharacteristic
669C2#1059139911yescharacteristic
subgroupG/H
centerC22#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC2×#64298C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1793
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63651C2semidirect
3. C2×C3×#825C2semidirect
4. C3×#5133C2semidirect
5. #10591213C2semidirect
6. C2×#63569C2semidirect
7. #10591087C2semidirect
17. #64298C4semidirect
40. C2×#825D3semidirect
44. #5133D3semidirect
575. C32#1793semidirect
661. C3#70308semidirect
662. C3#70387semidirect

Maximal subgroups

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

subgroupindex
C2×#642982
C2×#636512
C2×C3×#8252
C3×#51332
#105912132
C2×#635692
#105910872
#703873
#703083