Finite Group Databasebeta

← #11857957

Subgroups — #11857957

Order 1152.

1639 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic
2C3×D3×#117C211yesmaximal, characteristic, complemented
3C2×D3×#208C211yesmaximal, characteristic, complemented
4#10592700C211yesmaximal, characteristic, complemented
5C3×#5004C211yesmaximal, characteristic, complemented
6#10591099C211yesmaximal, characteristic, complemented
7#10591096C211yesmaximal, characteristic, complemented
8#10590610C214yesmaximal, complemented
9#10590609C214yesmaximal, complemented
10#82213—31nomaximal
11#78956—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#626—21no—
16C22×#624—21no—
17C2×#3799—21no—
18C2×#3799—21no—
19C2×#3799—24no—
20C2×#3799C418yescomplemented
21C2×#3799C2212yes—
22C2×#3799C2212yes—
23C32×#117C2211yescharacteristic
24C2×#3748C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C3×#892C2212yescomplemented
28C3×D3×C4⋊C4C2212yescomplemented
29C3×D3×C22⋊C4—21no—
30C3×#877—21no—
31C3×#872—21no—
32C3×C42×D3—21no—
33C2×#3711C2212yescomplemented
34D3×#208—24no—
35C2×D3×C3⋊C8C2212yescomplemented
36#63636C2214yescomplemented
37C3×#810C2214yescomplemented
38#63565C2214yescomplemented
39#63564C2214yescomplemented
40C22×#239—31no—
41C22×#235—31no—
42C2×C3×#117—31no—
43C22×#208—31no—
44C2×D3×M16—31no—
45D3×#117D311yescharacteristic, complemented
46C3×#419—31no—
47#5225—31no—
48#5131—31no—
49#5004—31no—
50#5004D311yescharacteristic, complemented
51#5002—34no—
52#5001—31no—
53#5001—31no—
54#5001—31no—
55#5001—61no—
56#4966—34no—
57#4804—34no—
58#4803—34no—
59C23×C3⋊D3—21no—
60C23×C3×D3D411yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)—22no—
64C2×C4⋊(C3⋊D3)C2×C414yescomplemented
65C2×C4⋊(C3⋊D3)C2312yes—
66C22×C3×Dic3—21no—
67C22×C3×Dic3D411yescharacteristic
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3C2×C414yes—
70C2×C3×C4×D3D411yescharacteristic
71C2×C3×C4×D3D411yescharacteristic
72C2×C3×C4×D3D414yes—
73C2×C3×C4×D3C2311yescharacteristic
74C2×C3×C4×D3C2311yescharacteristic
75C2×C3×Dic6—21no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6C2×C414yescomplemented
78C2×C3×Dic6C2312yes—
79C2×#626—28no—
80C2×#626—22no—
81C2×#626—22no—
82C2×#624—28no—
83C2×#624—22no—
84C2×#624—22no—
85#3799—28no—
86#3799—28no—
87#3799—24no—
88#3799—24no—
89#3799C2×C418yes—
90#3799C2×C418yescomplemented
91C32×C4⋊C4C2312yes—
92C32×C22⋊C4—21no—
93C32×C42—21no—
94#3748—22no—
95C2×C3⋊(C3⋊C8)C2312yes—
96C3×#217—21no—
97C3×(C2×D3)⋊C4—22no—
98C3×C4⋊Dic3C2312yes—
99C3×Dic3⋊C4—22no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3—22no—
102C3×#208—22no—
103C2×C3×C3⋊C8C2312yes—
104#3711—24no—
105D3×C3⋊C8—24no—
106#2896—91noSylow
107C22×C3×Q8—31no—
108C23×C3×C4—31no—
109C22×#67—61no—
110C2×#239—38no—
111C2×#239—32no—
112C2×#239—32no—
113C2×#239—64no—
114C2×#239—61no—
115C2×#239—61no—
116C2×#235—38no—
117C2×#235—32no—
118C2×#235—32no—
119C2×#235—64no—
120C2×#235—61no—
121C2×#235—61no—
122C22×D12—31no—
123C22×D12—31no—
124C22×D12—61no—
125C22×D12—61no—
126C22×C4×D3—61no—
127C22×C4×D3—61no—
128C22×C4×D3C2×D311yescharacteristic
129C22×Dic6C2×D311yescharacteristic
130C2×C3×M16—31no—
131C3×#117—21no—
132C3×#117—31no—
133C3×#117—32no—
134C3×#117—61no—
135C3×#117—61no—
136C3×#117C2×D311yescharacteristic
137C3×#117C2×D311yescharacteristic
138C2×C3×C4⋊C4—32no—
139C2×C3×C22⋊C4—61no—
140C2×C3×C42—61no—
141#926C2×D311yescharacteristic
142C2×#208—31no—
143C2×#208—31no—
144C2×#208—32no—
145C2×#208—61no—
146C2×#208—64no—
147C2×#208C2×D311yescharacteristic
148C22×C3⋊C8—32no—
149D3×M16—64no—
150C2×ΓL(1,𝔽25)—32no—
151C2×D3×C8—32no—
152#892C2×D312yescomplemented
153D3×C4⋊C4C2×D312yescomplemented
154D3×C22⋊C4—21no—
155#877—21no—
156#872—21no—
157C42×D3—21no—
158C3×#103—34no—
159#835—34no—
160#821—34no—
161#810—34no—
162#810C2×D314yescomplemented
163#809—34no—
164#809—34no—
165#809—34no—
166#809—64no—
167C23×C32C2×D411yescharacteristic
168C22×C3⋊D3—24no—
169C22×C3⋊D3—22no—
170C22×C3⋊D3—44no—
171C22×C3×D3—42no—
172C22×C3×D3C22⋊C414yes—
173C22×C3×D3C2×D411yescharacteristic
174C22×C3×D3C2×D411yescharacteristic
175C2×C32×C4—22no—
176C2×C32×C4C22×C412yes—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C4⋊(C3⋊D3)—24no—
181C4⋊(C3⋊D3)—22no—
182C4⋊(C3⋊D3)C22×C414yes—
183C2×C3×Dic3—24no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3C22⋊C414yes—
187C2×C3×Dic3C2×D411yescharacteristic
188C2×C3×Dic3C2×D411yescharacteristic
189C3×C4×D3—44no—
190C3×C4×D3C22⋊C414yes—
191C3×C4×D3C22⋊C414yes—
192C3×C4×D3C22×C412yes—
193C3×C4×D3C22×C412yes—
194C3×C4×D3C2×D412yes—
195C3×C4×D3C2×D412yes—
196C3×Dic6—24no—
197C3×Dic6—22no—
198C3×Dic6C22×C414yes—
199#626—28no—
200#626—28no—
201#624—28no—
202#624—28no—
203C3⋊(C3⋊C8)—22no—
204C3×C3⋊C8—22no—
205C22×#41—91no—
206C22×M16—91no—
207C2×#117—31no—
208#419—31no—
209#419—91no—
210#418—91no—
211#418—91no—
212#417—94no—
213#416—94no—
214C24×C3—31no—
215C23×D3—61no—
216C23×D3—61no—
217C23×D3—121no—
218C23×D3#6711yescharacteristic
219C2×C3×Q8—34no—
220C2×C3×Q8—32no—
221C2×C3×Q8—62no—
222C2×C3×Q8—61no—
223C22×C3×C4—21no—
224C22×C3×C4—31no—
225C22×C3×C4—34no—
226C22×C3×C4—34no—
227C22×C3×C4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×C3×C4—62no—
232C22×C3×C4—61no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—68no—
236C2×#67—62no—
237C2×#67—62no—
238C22×Dic3—21no—
239C22×Dic3#6711yescharacteristic
240#239—38no—
241#239—38no—
242#239—68no—
243#239—68no—
244#239—64no—
245#239—64no—
246#235—38no—
247#235—38no—
248#235—68no—
249#235—68no—
250#235—64no—
251#235—64no—
252C2×D12—34no—
253C2×D12—34no—
254C2×D12—32no—
255C2×D12—32no—
256C2×D12—62no—
257C2×D12—64no—
258C2×D12—68no—
259C2×D12—62no—
260C2×D12—62no—
261C2×D12—62no—
262C2×D12—62no—
263C2×D12—61no—
264C2×D12—61no—
265C2×D12—122no—
266C2×D12—121no—
267C2×C4×D3—22no—
268C2×C4×D3—68no—
269C2×C4×D3—62no—
270C2×C4×D3—62no—
271C2×C4×D3—68no—
272C2×C4×D3—62no—
273C2×C4×D3—62no—
274C2×C4×D3C4×D314yes—
275C2×C4×D3D1214yes—
276C2×C4×D3#6711yescharacteristic
277C2×C4×D3#6711yescharacteristic
278C2×C4×D3C22×D311yescharacteristic
279C2×C4×D3C22×D311yescharacteristic
280C2×Dic6—22no—
281C2×Dic6—21no—
282C2×Dic6C4×D314yescomplemented
283C2×Dic6C22×D312yes—
284C3×M16—62no—
285C2×C3×C8—32no—
286C3×C4⋊C4—22no—
287C3×C4⋊C4—32no—
288C3×C4⋊C4—62no—
289C3×C4⋊C4C22×D312yes—
290C3×C4⋊C4C22×D312yes—
291C3×C22⋊C4—21no—
292C3×C22⋊C4—21no—
293C3×C22⋊C4—41no—
294C3×C22⋊C4—62no—
295C3×C22⋊C4—61no—
296C3×C42—21no—
297C3×C42—21no—
298C3×C42—41no—
299C3×C42—62no—
300C3×C42—61no—
301#217—21no—
302(C2×D3)⋊C4—22no—
303C4⋊Dic3C22×D312yes—
304Dic3⋊C4—22no—
305C4×Dic3—21no—
306C4×Dic3—22no—
307#208—22no—
308#208—64no—
309#208—62no—
310#208—62no—
311#208—122no—
312C2×C3⋊C8—32no—
313C2×C3⋊C8—32no—
314C2×C3⋊C8—62no—
315C2×C3⋊C8—64no—
316C2×C3⋊C8C22×D312yes—
317ΓL(1,𝔽25)—64no—
318D3×C8—64no—
319C22×C32—22no—
320C22×C32C2×C22⋊C412yes—
321C22×C32C22×D411yescharacteristic
322C2×C3⋊D3—24no—
323C2×C3⋊D3—48no—
324C2×C3⋊D3—44no—
325C2×C3×D3—22no—
326C2×C3×D3—22no—
327C2×C3×D3—44no—
328C2×C3×D3C2×C22⋊C412yes—
329C2×C3×D3C2×C22⋊C412yes—
330C32×C4—42no—
331C32×C4C2×C22⋊C412yes—
332C32×C4C23×C411yescharacteristic
333C32×C4C22×D411yescharacteristic
334C3×Dic3—24no—
335C3×Dic3—42no—
336C3×Dic3C2×C22⋊C412yes—
337C3×Dic3C2×C22⋊C412yes—
338C2×#41—92no—
339C2×#41—92no—
340C2×#41—98no—
341C2×#41—184no—
342C2×#41—181no—
343C2×#41—181no—
344C22×Q8—31no—
345C22×D4—91no—
346C22×D4—181no—
347C23×C4—31no—
348C23×C4—181no—
349C2×M16—31no—
350C2×M16—92no—
351C2×M16—91no—
352C2×M16—184no—
353C22×C8—92no—
354#117—31no—
355#117—32no—
356#117—61no—
357#117—61no—
358#117D3211yescharacteristic
359C2×C4⋊C4—32no—
360C2×C22⋊C4—61no—
361C2×C42—61no—
362#103—34no—
363#103—94no—
364#102—94no—
365#102—94no—
366C23×C3—21no—
367C23×C3—31no—
368C23×C3—31no—
369C23×C3—34no—
370C23×C3—122no—
371C23×C3D3×D411yescharacteristic
372C23×C3C2×#6711yescharacteristic
373C22×D3—42no—
374C22×D3—64no—
375C22×D3—64no—
376C22×D3—62no—
377C22×D3—62no—
378C22×D3—122no—
379C22×D3—124no—
380C22×D3—124no—
381C22×D3—124no—
382C22×D3—244no—
383C22×D3(C2×D3)⋊C414yes—
384C22×D3C2×#6711yescharacteristic
385C22×D3C2×#6711yescharacteristic
386C3×Q8—34no—
387C3×Q8—64no—
388C3×Q8—62no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—34no—
396C2×C3×C4—31no—
397C2×C3×C4—31no—
398C2×C3×C4—34no—
399C2×C3×C4—34no—
400C2×C3×C4—32no—
401C2×C3×C4—32no—
402C2×C3×C4—32no—
403C2×C3×C4—32no—
404C2×C3×C4—42no—
405C2×C3×C4—64no—
406C2×C3×C4—62no—
407C2×C3×C4—62no—
408C2×C3×C4—124no—
409C2×C3×C4C2×C4×D312yes—
410C2×C3×C4C2×C4×D312yes—
411C2×C3×C4C2×D1212yes—
412C2×C3×C4D3×D412yes—
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4C2×#6711yescharacteristic
415C2×C3×C4C23×D311yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417#67—68no—
418#67—68no—
419C2×Dic3—24no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3(C2×D3)⋊C414yes—
423C2×Dic3C2×#6711yescharacteristic
424C2×Dic3C2×#6711yescharacteristic
425D12—34no—
426D12—34no—
427D12—64no—
428D12—68no—
429D12—68no—
430D12—64no—
431D12—64no—
432D12—62no—
433D12—62no—
434D12—122no—
435D12—124no—
436C4×D3—44no—
437C4×D3—68no—
438C4×D3—68no—
439C4×D3—68no—
440C4×D3—68no—
441C4×D3(C2×D3)⋊C414yes—
442C4×D3(C2×D3)⋊C414yes—
443C4×D3C2×C4×D312yes—
444C4×D3C2×C4×D312yes—
445C4×D3C2×D1212yes—
446C4×D3C2×D1212yes—
447Dic6—24no—
448Dic6—22no—
449Dic6C2×C4×D314yes—
450C3×C8—62no—
451C3⋊C8—22no—
452C3⋊C8—62no—
453C3⋊C8—62no—
454C3⋊C8—122no—
455C2×C32—22no—
456C2×C32C22×C22⋊C411yescharacteristic
457C2×C32#57512yes—
458C3⋊D3—44no—
459C3×D3—22no—
460C3×D3—22no—
461C24—31no—
462C24—181no—
463#41—98no—
464#41—98no—
465#41—184no—
466#41—184no—
467#41—188no—
468#41—188no—
469C2×Q8—32no—
470C2×Q8—34no—
471C2×Q8—62no—
472C2×Q8—61no—
473C2×D4—92no—
474C2×D4—94no—
475C2×D4—182no—
476C2×D4—182no—
477C2×D4—188no—
478C2×D4—182no—
479C2×D4—181no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—34no—
484C22×C4—34no—
485C22×C4—31no—
486C22×C4—31no—
487C22×C4—62no—
488C22×C4—61no—
489C22×C4—182no—
490C22×C4—182no—
491C22×C4—188no—
492C22×C4C2×D3211yescharacteristic
493M16—62no—
494M16—184no—
495M16—182no—
496C2×C8—32no—
497C2×C8—92no—
498C2×C8—184no—
499C4⋊C4—32no—
500C4⋊C4—62no—
501C4⋊C4C2×D3212yes—
502C22⋊C4—21no—
503C22⋊C4—62no—
504C22⋊C4—61no—
505C42—21no—
506C42—62no—
507C42—61no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—21no—
511C22×C3—22no—
512C22×C3—32no—
513C22×C3—32no—
514C22×C3—42no—
515C22×C3—62no—
516C22×C3—62no—
517C22×C3—124no—
518C22×C3D3×C22⋊C412yes—
519C22×C3C2×(C2×D3)⋊C412yes—
520C22×C3C2×D3×D411yescharacteristic
521C22×C3C22×#6711yescharacteristic
522C2×D3—22no—
523C2×D3—22no—
524C2×D3—44no—
525C2×D3—64no—
526C2×D3—64no—
527C2×D3—124no—
528C2×D3—128no—
529C2×D3—128no—
530C2×D3—124no—
531C2×D3—124no—
532C2×D3—244no—
533C2×D3—248no—
534C2×D3C2×(C2×D3)⋊C412yes—
535C2×D3C2×(C2×D3)⋊C412yes—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—22no—
539C3×C4—32no—
540C3×C4—32no—
541C3×C4—42no—
542C3×C4—42no—
543C3×C4—64no—
544C3×C4—82no—
545C3×C4—122no—
546C3×C4D3×C22⋊C412yes—
547C3×C4C2×(C2×D3)⋊C412yes—
548C3×C4C22×C4×D311yescharacteristic
549C3×C4C22×C4×D311yescharacteristic
550C3×C4C22×D1211yescharacteristic
551C3×C4C2×D3×D411yescharacteristic
552Dic3—24no—
553Dic3—42no—
554Dic3C2×(C2×D3)⋊C412yes—
555Dic3C2×(C2×D3)⋊C412yes—
556C32#289611yescharacteristic, complemented, Sylow
557C23—31no—
558C23—31no—
559C23—34no—
560C23—122no—
561C23—182no—
562C23—184no—
563C23—364no—
564C23D3×#6711yescharacteristic
565Q8—34no—
566Q8—62no—
567Q8—64no—
568D4—94no—
569D4—188no—
570D4—188no—
571D4—182no—
572D4—184no—
573C2×C4—22no—
574C2×C4—31no—
575C2×C4—31no—
576C2×C4—34no—
577C2×C4—32no—
578C2×C4—32no—
579C2×C4—32no—
580C2×C4—32no—
581C2×C4—34no—
582C2×C4—34no—
583C2×C4—62no—
584C2×C4—64no—
585C2×C4—62no—
586C2×C4—124no—
587C2×C4—188no—
588C2×C4—188no—
589C2×C4C4×D3212yes—
590C2×C4D3×D1212yes—
591C2×C4D3×#6711yescharacteristic
592C2×C4C22×D3211yescharacteristic
593C8—62no—
594C8—182no—
595C2×C3—22no—
596C2×C3—22no—
597C2×C3—22no—
598C2×C3—21no—
599C2×C3—42no—
600C2×C3—62no—
601C2×C3—62no—
602C2×C3C2×D3×C22⋊C411yescharacteristic
603C2×C3#577712yes—
604C2×C3C22×(C2×D3)⋊C411yescharacteristic
605C2×C3#582212yes—
606D3—22no—
607D3—22no—
608D3—124no—
609D3—124no—
610D3—244no—
611C22—22no—
612C22—32no—
613C22—32no—
614C22—62no—
615C22—62no—
616C22—124no—
617C22—184no—
618C22—368no—
619C22—364no—
620C22D3×(C2×D3)⋊C412yes—
621C22C2×D3×#6711yescharacteristic
622C4—32no—
623C4—32no—
624C4—42no—
625C4—64no—
626C4—122no—
627C4D3×(C2×D3)⋊C412yes—
628C4C2×C4×D3211yescharacteristic
629C4C2×D3×D1211yescharacteristic
630C3—21no—
631C3#7895611yescharacteristic, complemented
632C3#8221311yescharacteristic, complemented
633C2—22no—
634C2—62no—
635C2—62no—
636C2—364no—
637C2C2×D3×(C2×D3)⋊C411yescharacteristic
638C2#1059547012yes—
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×#3799C2
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2896
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×D3×#117C2semidirect
3. C2×D3×#208C2semidirect
4. #10592700C2semidirect
5. C3×#5004C2semidirect
6. #10591099C2semidirect
7. #10591096C2semidirect
8. #10590610C2semidirect
9. #10590609C2semidirect
20. C2×#3799C4semidirect
27. C3×#892C22semidirect
28. C3×D3×C4⋊C4C22semidirect
33. C2×#3711C22semidirect
35. C2×D3×C3⋊C8C22semidirect
36. #63636C22semidirect
37. C3×#810C22semidirect
38. #63565C22semidirect
39. #63564C22semidirect
45. D3×#117D3semidirect
50. #5004D3semidirect
64. C2×C4⋊(C3⋊D3)C2×C4semidirect
77. C2×C3×Dic6C2×C4semidirect
90. #3799C2×C4semidirect
152. #892C2×D3semidirect
153. D3×C4⋊C4C2×D3semidirect
162. #810C2×D3semidirect
282. C2×Dic6C4×D3semidirect
556. C32#2896semidirect
631. C3#78956semidirect
632. C3#82213semidirect

Maximal subgroups

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

subgroupindex
C22×#37992
C3×D3×#1172
C2×D3×#2082
#105927002
C3×#50042
#105910992
#105910962
#105906102
#105906092
#822133
#789563