Finite Group Databasebeta

← #11860419

Subgroups — #11860419

Order 1152.

1097 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64160C211yesmaximal, characteristic
2C3×Dic3×#41C211yesmaximal, characteristic
3C2×#63844C211yesmaximal, characteristic, complemented
4C3×#5232C211yesmaximal, characteristic
5#10591541C212yesmaximal, complemented
6#10591537C212yesmaximal, complemented
7#10591405C212yesmaximal, complemented
8#10591401C212yesmaximal, complemented
9#10591139C211yesmaximal, characteristic, complemented
10#10591107C211yesmaximal, characteristic, complemented
11Dic3×#208C211yesmaximal, characteristic, complemented
12C4×#951—31nomaximal
13#78867—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C22×#634C2211yescharacteristic
16#64160C418yescomplemented
17C2×#3756C2212yes—
18C2×#3754C2212yes—
19C2×#3748C2211yescharacteristic
20C3×Q8×Dic3C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×D4×Dic3—21no—
23C3×D4×Dic3—21no—
24C3×D4×Dic3C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C3×#926—21no—
27C3×#926C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4×Dic3—21no—
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×#208C2211yescharacteristic
32C2×#3724—21no—
33C2×Dic32—21no—
34#63844—21no—
35#63844—21no—
36#63844C2212yes—
37#63844C2212yes—
38C3×#835C2212yes—
39C3×#832C2212yes—
40#63576C2212yes—
41#63574C2212yes—
42#63567C2212yes—
43#63567C2212yes—
44#63554C2212yes—
45Dic3×C3⋊C8C2212yes—
46C3×C4×#41—31no—
47Dic3×#41D311yescharacteristic
48C2×#951—31no—
49C2×#951—31no—
50C2×#951—61no—
51C2×#887—31no—
52C2×C4×Dic6—31no—
53C3×#417—31no—
54#5232D311yescharacteristic
55#5120—31no—
56Dic3×M16—31no—
57#5030—32no—
58C4×#216—32no—
59#5018—32no—
60C4×#214—32no—
61#5004—31no—
62#4995—31no—
63#4964—31no—
64C4×#208—31no—
65#4790—32no—
66#4789—32no—
67#4758—32no—
68#4757—32no—
69C32×#41—22no—
70C32×#41C2×C414yes—
71C2×C32×Q8C2311yescharacteristic
72C2×C32×D4—21no—
73C2×C32×D4C2311yescharacteristic
74C22×C32×C4—21no—
75C22×C32×C4C2311yescharacteristic
76C22×C3⋊Dic3—21no—
77C2×#634—21no—
78C2×#634—22no—
79C2×#634C2×C414yescomplemented
80C2×#634C2312yes—
81C22×C3×Dic3—21no—
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
84C22×C3×Dic3D411yescharacteristic
85C22×C3×Dic3D411yescharacteristic
86#3756C2×C418yescomplemented
87#3754C2×C418yescomplemented
88#3748C2×C414yescomplemented
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#217—21no—
91C3×#217—21no—
92C3×#217—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3C2312yes—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4×Dic3—21no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3—21no—
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C3×C4×Dic3C2311yescharacteristic
106C3×#208—22no—
107C2×C3×C3⋊C8C2312yes—
108#3724—22no—
109#3724—22no—
110Dic32—22no—
111Dic32—22no—
112C4×#137—91noSylow
113C2×C3×#41—21no—
114C2×C3×#41C2×D311yescharacteristic
115C2×C3×#41C2×D311yescharacteristic
116C22×Dic6—31no—
117C22×Dic6—31no—
118C22×Dic6—61no—
119C2×C3×M16—31no—
120C3×C4×Q8—31no—
121C3×C4×Q8—31no—
122C3×C4×D4—31no—
123C3×C4×D4—31no—
124C3×C4×D4—61no—
125C3×C4×D4—61no—
126C3×#117—31no—
127C3×#117—61no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C42—31no—
130C2×C3×C42—61no—
131#951—38no—
132#951—38no—
133#951—68no—
134Q8×Dic3C2×D311yescharacteristic
135Q8×Dic3C2×D311yescharacteristic
136C2×#216—32no—
137C2×#216—32no—
138C2×#216—62no—
139D4×Dic3—21no—
140D4×Dic3—21no—
141D4×Dic3C2×D311yescharacteristic
142D4×Dic3C2×D311yescharacteristic
143C2×#214—32no—
144C2×#214—32no—
145C2×#214—62no—
146#926—21no—
147#926C2×D311yescharacteristic
148C2×C4⋊Dic3C2×D311yescharacteristic
149C2×Dic3⋊C4—61no—
150C2×Dic3⋊C4—61no—
151C2×C4×Dic3—21no—
152C2×C4×Dic3—61no—
153C2×C4×Dic3—61no—
154C2×C4×Dic3C2×D311yescharacteristic
155C2×#208—31no—
156C2×#208—31no—
157C2×#208—61no—
158C2×#208C2×D311yescharacteristic
159#887—32no—
160#887—32no—
161#887—61no—
162#887—61no—
163C4×Dic6—32no—
164C4×Dic6—32no—
165C4×Dic6—61no—
166C4×Dic6—61no—
167C3×#103—32no—
168C3×#102—32no—
169#835C2×D312yes—
170#832C2×D312yes—
171#816—32no—
172#816—32no—
173#815—32no—
174C8×Dic3—32no—
175#810—32no—
176#810—32no—
177#808—32no—
178#808—32no—
179#807—32no—
180#807—32no—
181#803—32no—
182C4×C3⋊C8—32no—
183C23×C32—21no—
184C23×C32C2×D411yescharacteristic
185C32×Q8—21no—
186C32×Q8C22×C412yes—
187C32×D4—24no—
188C32×D4—21no—
189C32×D4C22×C412yes—
190C2×C32×C4—21no—
191C2×C32×C4—24no—
192C2×C32×C4C22×C412yes—
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4#4112yes—
195C2×C32×C4C2411yescharacteristic
196C2×C3⋊Dic3—24no—
197C2×C3⋊Dic3—22no—
198#634—24no—
199#634—22no—
200#634C22×C414yes—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—41no—
206C2×C3×Dic3—42no—
207C2×C3×Dic3—42no—
208C2×C3×Dic3—42no—
209C2×C3×Dic3C2×D411yescharacteristic
210C2×C3×Dic3C2×D411yescharacteristic
211C2×C3×Dic3C2×D411yescharacteristic
212C2×C3×Dic3C2×D411yescharacteristic
213C3⋊(C3⋊C8)C22×C414yes—
214C3×C3⋊C8—22no—
215C2×#137—91no—
216C4×#41—31no—
217C2×C4×Q8—91no—
218#441—92no—
219#440—92no—
220C4×Q16—92no—
221C4×SD16—92no—
222#428—91no—
223#419—91no—
224#417—31no—
225C4×M16—91no—
226C3×#41—22no—
227C3×#41—22no—
228C3×#41—24no—
229C3×#41—42no—
230C3×#41C4×D314yes—
231C3×#41C4×D314yes—
232C2×C3×Q8—21no—
233C2×C3×Q8C22×D311yescharacteristic
234C2×C3×Q8C22×D311yescharacteristic
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—41no—
239C2×C3×D4C22×D311yescharacteristic
240C2×C3×D4C22×D311yescharacteristic
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—31no—
245C22×C3×C4—31no—
246C22×C3×C4—41no—
247C22×C3×C4—61no—
248C22×C3×C4—61no—
249C22×C3×C4—61no—
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—61no—
256C22×Dic3—61no—
257C22×Dic3—121no—
258C22×Dic3#6711yescharacteristic
259C22×Dic3#6711yescharacteristic
260C2×Dic6—34no—
261C2×Dic6—34no—
262C2×Dic6—32no—
263C2×Dic6—32no—
264C2×Dic6—62no—
265C2×Dic6—64no—
266C2×Dic6—62no—
267C2×Dic6—61no—
268C2×Dic6—62no—
269C2×Dic6—61no—
270C2×Dic6—122no—
271C2×Dic6—121no—
272C3×M16—62no—
273C2×C3×C8—32no—
274C3×C4⋊C4—31no—
275C3×C4⋊C4—32no—
276C3×C4⋊C4—31no—
277C3×C4⋊C4—61no—
278C3×C4⋊C4—61no—
279C3×C4⋊C4—61no—
280C3×C22⋊C4—61no—
281C3×C22⋊C4—61no—
282C3×C22⋊C4—61no—
283C3×C42—31no—
284C3×C42—31no—
285C3×C42—31no—
286C3×C42—31no—
287C3×C42—61no—
288C3×C42—61no—
289C3×C42—61no—
290#217—21no—
291#217—21no—
292#217—21no—
293#216—38no—
294#216—38no—
295#216—68no—
296#214—38no—
297#214—38no—
298#214—68no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3C22×D311yescharacteristic
303C4⋊Dic3C22×D312yes—
304C4⋊Dic3C22×D311yescharacteristic
305Dic3⋊C4—62no—
306Dic3⋊C4—62no—
307Dic3⋊C4—62no—
308Dic3⋊C4—62no—
309C4×Dic3—21no—
310C4×Dic3—21no—
311C4×Dic3—21no—
312C4×Dic3—62no—
313C4×Dic3—62no—
314C4×Dic3—62no—
315C4×Dic3—62no—
316C4×Dic3#6711yescharacteristic
317C4×Dic3#6711yescharacteristic
318C4×Dic3C22×D311yescharacteristic
319C4×Dic3C22×D311yescharacteristic
320#208—22no—
321#208—34no—
322#208—34no—
323#208—64no—
324C2×C3⋊C8—32no—
325C2×C3⋊C8—32no—
326C2×C3⋊C8—62no—
327C2×C3⋊C8C22×D312yes—
328C22×C32—21no—
329C22×C32—21no—
330C22×C32—22no—
331C22×C32—41no—
332C22×C32—41no—
333C22×C32C4×D412yes—
334C22×C32C22×D411yescharacteristic
335C32×C4—22no—
336C32×C4C4×D412yes—
337C32×C4C23×C411yescharacteristic
338C32×C4C2×#4111yescharacteristic
339C3⋊Dic3—24no—
340C3×Dic3—21no—
341C3×Dic3—21no—
342C3×Dic3—21no—
343C3×Dic3—41no—
344C3×Dic3—42no—
345C3×Dic3—41no—
346C3×Dic3#13712yescomplemented
347C2×#41D3211yescharacteristic
348C22×Q8—91no—
349#137—98no—
350C2×Q16—92no—
351C2×SD16—92no—
352C2×M16—31no—
353C2×M16—91no—
354C4×Q8—31no—
355C4×Q8—31no—
356C4×Q8—92no—
357C4×Q8—92no—
358C4×Q8—181no—
359C4×Q8—181no—
360C4×D4—31no—
361C4×D4—31no—
362C4×D4—61no—
363C4×D4—61no—
364#117—31no—
365#117—61no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—181no—
368C2×C42—31no—
369C2×C42—61no—
370C2×C42—181no—
371#107—92no—
372#106—92no—
373#103—32no—
374#103—92no—
375#103—92no—
376#102—32no—
377#97—92no—
378C4×C8—92no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—41no—
383C23×C3D3×D411yescharacteristic
384C23×C3C2×#6711yescharacteristic
385C3×Q8—21no—
386C3×Q8—21no—
387C3×Q8—22no—
388C3×Q8—41no—
389C3×Q8C2×C4×D312yes—
390C3×Q8C2×C4×D312yes—
391C3×D4—24no—
392C3×D4—24no—
393C3×D4—21no—
394C3×D4—21no—
395C3×D4—22no—
396C3×D4—41no—
397C3×D4—44no—
398C3×D4C2×C4×D312yes—
399C3×D4C2×C4×D312yes—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—24no—
403C2×C3×C4—24no—
404C2×C3×C4—21no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—21no—
408C2×C3×C4—31no—
409C2×C3×C4—31no—
410C2×C3×C4—31no—
411C2×C3×C4—31no—
412C2×C3×C4—44no—
413C2×C3×C4—41no—
414C2×C3×C4—62no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—62no—
418C2×C3×C4—122no—
419C2×C3×C4—121no—
420C2×C3×C4—122no—
421C2×C3×C4—122no—
422C2×C3×C4C2×C4×D312yes—
423C2×C3×C4C2×C4×D312yes—
424C2×C3×C4#23512yes—
425C2×C3×C4D3×D411yescharacteristic
426C2×C3×C4#23712yes—
427C2×C3×C4C2×#6711yescharacteristic
428C2×C3×C4C23×D311yescharacteristic
429C2×C3×C4C23×D311yescharacteristic
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—41no—
435C2×Dic3—42no—
436C2×Dic3—42no—
437C2×Dic3—42no—
438C2×Dic3—64no—
439C2×Dic3—64no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—122no—
443C2×Dic3—124no—
444C2×Dic3C2×#6711yescharacteristic
445C2×Dic3C2×#6711yescharacteristic
446C2×Dic3C2×#6711yescharacteristic
447C2×Dic3C2×#6711yescharacteristic
448Dic6—34no—
449Dic6—34no—
450Dic6—64no—
451Dic6—64no—
452Dic6—64no—
453Dic6—62no—
454Dic6—62no—
455Dic6—122no—
456Dic6—124no—
457C3×C8—62no—
458C3⋊C8—22no—
459C3⋊C8—34no—
460C3⋊C8—34no—
461C3⋊C8—64no—
462C2×C32—22no—
463C2×C32—42no—
464C2×C32C2×C4×D411yescharacteristic
465C2×C32C2×#13711yescharacteristic
466C2×C32#57511yescharacteristic
467#41—22no—
468#41#62414yes—
469C2×Q8—92no—
470C2×Q8—94no—
471C2×Q8—182no—
472C2×Q8—181no—
473C2×Q8C2×D3211yescharacteristic
474C2×D4—21no—
475C2×D4C2×D3211yescharacteristic
476C22×C4—21no—
477C22×C4—31no—
478C22×C4—31no—
479C22×C4—61no—
480C22×C4—61no—
481C22×C4—61no—
482C22×C4—181no—
483C22×C4C2×D3211yescharacteristic
484Q16—98no—
485SD16—98no—
486M16—62no—
487M16—94no—
488C2×C8—32no—
489C2×C8—92no—
490C4⋊C4—32no—
491C4⋊C4—31no—
492C4⋊C4—31no—
493C4⋊C4—61no—
494C4⋊C4—61no—
495C4⋊C4—61no—
496C4⋊C4—182no—
497C4⋊C4—182no—
498C22⋊C4—61no—
499C22⋊C4—61no—
500C22⋊C4—61no—
501C42—31no—
502C42—31no—
503C42—31no—
504C42—31no—
505C42—61no—
506C42—61no—
507C42—61no—
508C42—182no—
509C42—182no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—21no—
517C22×C3—22no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—42no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—81no—
526C22×C3—81no—
527C22×C3#67⋊C412yes—
528C22×C3C4×#6712yes—
529C22×C3C2×D3×D411yescharacteristic
530C22×C3C22×#6711yescharacteristic
531C3×C4—22no—
532C3×C4—22no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—22no—
536C3×C4—32no—
537C3×C4—42no—
538C3×C4—61no—
539C3×C4—61no—
540C3×C4—61no—
541C3×C4—121no—
542C3×C4—121no—
543C3×C4—122no—
544C3×C4#67⋊C412yes—
545C3×C4C4×#6712yes—
546C3×C4C22×C4×D311yescharacteristic
547C3×C4C22×C4×D311yescharacteristic
548C3×C4C2×#23511yescharacteristic
549C3×C4C2×#23711yescharacteristic
550Dic3—21no—
551Dic3—21no—
552Dic3—21no—
553Dic3—42no—
554Dic3—41no—
555Dic3—41no—
556Dic3—64no—
557Dic3—64no—
558Dic3—124no—
559Dic3#95112yescomplemented
560C32C4×#13711yescharacteristic, complemented, Sylow
561C23—21no—
562C23D3×#6711yescharacteristic
563Q8—21no—
564Q8—94no—
565Q8—182no—
566Q8—184no—
567Q8C2×#62412yes—
568D4—24no—
569D4—21no—
570D4C2×#62412yes—
571C2×C4—21no—
572C2×C4—24no—
573C2×C4—31no—
574C2×C4—31no—
575C2×C4—31no—
576C2×C4—31no—
577C2×C4—62no—
578C2×C4—61no—
579C2×C4—61no—
580C2×C4—62no—
581C2×C4—122no—
582C2×C4—121no—
583C2×C4—122no—
584C2×C4—122no—
585C2×C4—182no—
586C2×C4—184no—
587C2×C4#380412yes—
588C2×C4C2×#62412yes—
589C2×C4D3×#6711yescharacteristic
590C2×C4C22×D3211yescharacteristic
591C8—62no—
592C8—94no—
593C2×C3—22no—
594C2×C3—22no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—42no—
599C2×C3—42no—
600C2×C3—42no—
601C2×C3—82no—
602C2×C3C2×#67⋊C411yescharacteristic
603C2×C3#577311yescharacteristic
604C2×C3D3×#13711yescharacteristic
605C2×C3C2×C4×#6711yescharacteristic
606C2×C3#582211yescharacteristic
607C2×C3C2×#95111yescharacteristic
608C22—21no—
609C22—21no—
610C22—22no—
611C22—41no—
612C22—41no—
613C22#6395212yes—
614C22C2×D3×#6711yescharacteristic
615C4—22no—
616C4—32no—
617C4—61no—
618C4—61no—
619C4—61no—
620C4—121no—
621C4—121no—
622C4—122no—
623C4—184no—
624C4#6395212yes—
625C4C2×#380411yescharacteristic
626C4C22×#62411yescharacteristic
627C3—21no—
628C3#7886711yescharacteristic, complemented
629C3C4×#95111yescharacteristic, complemented
630C2—22no—
631C2—42no—
632C2D3×#95111yescharacteristic
633C2#1059546911yescharacteristic
634C2C2×#6395211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32C22×D4
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
3. C2×#63844C2semidirect
5. #10591541C2semidirect
6. #10591537C2semidirect
7. #10591405C2semidirect
8. #10591401C2semidirect
9. #10591139C2semidirect
10. #10591107C2semidirect
11. Dic3×#208C2semidirect
16. #64160C4semidirect
79. C2×#634C2×C4semidirect
86. #3756C2×C4semidirect
87. #3754C2×C4semidirect
88. #3748C2×C4semidirect
346. C3×Dic3#137semidirect
559. Dic3#951semidirect
560. C32C4×#137semidirect
628. C3#78867semidirect
629. C3C4×#951semidirect

Maximal subgroups

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

subgroupindex
C2×#641602
C3×Dic3×#412
C2×#638442
C3×#52322
#105915412
#105915372
#105914052
#105914012
#105911392
#105911072
Dic3×#2082
C4×#9513
#788673