Finite Group Databasebeta

← #11860408

Subgroups — #11860408

Order 1152.

1123 conjugacy classes of subgroups.

The subgroup lattice has 659 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595993C211yesmaximal, characteristic
2C2×#63843C211yesmaximal, characteristic, complemented
3C2×#63833C211yesmaximal, characteristic
4C3×#5004C211yesmaximal, characteristic, complemented
5C3×#4995C211yesmaximal, characteristic, complemented
6#10591106C211yesmaximal, characteristic
7#10591060C211yesmaximal, characteristic, complemented
8#10590485C212yesmaximal, complemented
9#10590484C212yesmaximal, complemented
10#10590483C212yesmaximal, complemented
11#10590482C212yesmaximal, complemented
12#79200—31nomaximal
13#78946—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18#64102C2211yescharacteristic
19#64102C2211yescharacteristic
20#64096C2211yescharacteristic
21#64096C2211yescharacteristic
22#64090—21no—
23#64090—21no—
24#64081—21no—
25C42×C3⋊D3—21no—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic
29C2×Dic3⋊Dic3—21no—
30C2×Dic32—21no—
31#63843—21no—
32#63843—21no—
33#63843C2212yes—
34#63843C2212yes—
35C2×#3719C2212yes—
36#63833C418yescomplemented
37C2×#3717C2212yes—
38C3×#810C2212yes—
39C3×#810C2212yes—
40C3×#808C2212yes—
41C3×#807C2212yes—
42#63567C2212yes—
43#63564C2212yes—
44#63555C2212yes—
45#63553C2212yes—
46C2×Q8×Dic3—31no—
47C2×#942—31no—
48C2×#909—31no—
49#5522—31no—
50#5522—31no—
51#5522—61no—
52C2×#887—31no—
53C3×#428—31no—
54C3×#419—31no—
55#5133—31no—
56Dic3×M16—31no—
57Dic3×M16—31no—
58#5004D311yescharacteristic, complemented
59#4995D311yescharacteristic, complemented
60#4966—31no—
61#4889—32no—
62#4873—32no—
63#4853—32no—
64#4852—32no—
65#4817—32no—
66#4790—32no—
67#4789—32no—
68#4788—32no—
69C22×C32×C4C2311yescharacteristic
70C2×#638—21no—
71C22×C3⋊Dic3D411yescharacteristic
72C22×C3⋊Dic3D411yescharacteristic
73#3828—22no—
74#3828C2×C414yes—
75C2×C4⋊(C3⋊D3)C2311yescharacteristic
76C2×C4×C3⋊D3—21no—
77C2×C4×C3⋊D3—21no—
78C2×C4×C3⋊D3—21no—
79C2×#634C2311yescharacteristic
80C22×C3×Dic3—21no—
81C22×C3×Dic3—21no—
82C2×C3×Dic6—21no—
83C2×C3×Dic6—22no—
84C2×C3×Dic6C2×C414yescomplemented
85C2×C3×Dic6C2312yes—
86C32×C4⋊C4C2311yescharacteristic
87C32×C4⋊C4C2311yescharacteristic
88C32×C22⋊C4—21no—
89C32×C42—21no—
90#3752—21no—
91#3752—21no—
92#3750—21no—
93#3750—21no—
94C4×C3⋊Dic3—21no—
95C4×C3⋊Dic3—21no—
96C4×C3⋊Dic3D411yescharacteristic
97C4×C3⋊Dic3D411yescharacteristic
98C4×C3⋊Dic3C2311yescharacteristic
99C4×C3⋊Dic3C2311yescharacteristic
100C3×C4⋊Dic3—21no—
101C3×C4⋊Dic3C2312yes—
102C3×#208—22no—
103C3×#208C2×C414yescomplemented
104C2×C3×C3⋊C8C2312yes—
105C2×C3×C3⋊C8C2312yes—
106Dic3⋊Dic3—22no—
107Dic3⋊Dic3—22no—
108Dic32—22no—
109Dic32—22no—
110#3719C2×C418yescomplemented
111#3717C2×C418yescomplemented
112C4×#137—91noSylow
113C22×C3×Q8—31no—
114C2×#235—31no—
115C2×#235—31no—
116C2×#235—61no—
117C22×Dic6C2×D311yescharacteristic
118C2×C3×M16—31no—
119C2×C3×M16—31no—
120C3×#117—21no—
121C3×#117C2×D311yescharacteristic
122C3×#117C2×D311yescharacteristic
123C2×C3×C4⋊C4—31no—
124Q8×Dic3—32no—
125Q8×Dic3—32no—
126Q8×Dic3—61no—
127Q8×Dic3—61no—
128C2×#216—32no—
129#942—38no—
130C2×#215—32no—
131C2×C4⋊Dic3—61no—
132C2×C4⋊Dic3C2×D311yescharacteristic
133C2×Dic3⋊C4—61no—
134C2×C4×Dic3—31no—
135C2×C4×Dic3—31no—
136C2×C4×Dic3—61no—
137C2×C4×Dic3—61no—
138C2×C4×Dic3—61no—
139C2×#208C2×D311yescharacteristic
140C2×#208C2×D311yescharacteristic
141#909—38no—
142C2×Dic12—32no—
143C2×#204—32no—
144#893—31no—
145#893—31no—
146#893—31no—
147#893—31no—
148#893—61no—
149#893—61no—
150#887—32no—
151#887—32no—
152#887—31no—
153#887—31no—
154#887—31no—
155#887—31no—
156#887—61no—
157#887—61no—
158#887—61no—
159#887—61no—
160#67⋊C4—61no—
161#67⋊C4—61no—
162#67⋊C4—61no—
163#67⋊C4—61no—
164#67⋊C4—62no—
165#67⋊C4—62no—
166#872—61no—
167#872—61no—
168#872—62no—
169C42×D3—61no—
170C42×D3—61no—
171C42×D3—62no—
172C3×#107—32no—
173C3×#106—32no—
174C3×#103—32no—
175C3×#103—32no—
176#821—32no—
177#816—32no—
178#815—32no—
179#815—32no—
180C8×Dic3—32no—
181C8×Dic3—32no—
182#810—32no—
183#810C2×D312yes—
184#810C2×D312yes—
185#809—32no—
186#808C2×D312yes—
187#807C2×D312yes—
188C23×C32C2×D411yescharacteristic
189C22×C3⋊D3—21no—
190C2×C32×C4—21no—
191C2×C32×C4—21no—
192C2×C32×C4C22×C412yes—
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4#4112yes—
195C2×C32×C4C2411yescharacteristic
196#638—24no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3—41no—
200C2×C3⋊Dic3C2×D411yescharacteristic
201C2×C3⋊Dic3C2×D411yescharacteristic
202C2×C3⋊Dic3C2×D411yescharacteristic
203C2×C3⋊Dic3C2×D411yescharacteristic
204C4⋊(C3⋊D3)—21no—
205C4⋊(C3⋊D3)C22×C412yes—
206C4×C3⋊D3—24no—
207C4×C3⋊D3—42no—
208C4×C3⋊D3—42no—
209#634—21no—
210#634C22×C412yes—
211C2×C3×Dic3—24no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—42no—
215C3×Dic6—24no—
216C3×Dic6—22no—
217C3×Dic6C22×C414yes—
218C3×C3⋊C8—22no—
219C3×C3⋊C8C22×C414yes—
220C2×#137—91no—
221C4×#41—91no—
222C2×C4×Q8—91no—
223#441—92no—
224#440—92no—
225C4×Q16—92no—
226C4×SD16—92no—
227#428—31no—
228#419—31no—
229#417—91no—
230C4×M16—91no—
231C2×C3×Q8—34no—
232C2×C3×Q8—32no—
233C2×C3×Q8—61no—
234C2×C3×Q8—62no—
235C22×C3×C4—21no—
236C22×C3×C4—61no—
237C22×C3×C4—61no—
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C2×#67—62no—
241C2×#67—61no—
242C2×#67—61no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—31no—
246C22×Dic3—31no—
247C22×Dic3—31no—
248C22×Dic3—31no—
249C22×Dic3—61no—
250C22×Dic3—61no—
251#235—34no—
252#235—34no—
253#235—64no—
254#235—64no—
255#235—62no—
256#235—62no—
257C2×D12—31no—
258C2×D12—31no—
259C2×D12—61no—
260C2×C4×D3—62no—
261C2×C4×D3—61no—
262C2×C4×D3—61no—
263C2×C4×D3—61no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×C4×D3—61no—
267C2×C4×D3—62no—
268C2×C4×D3—62no—
269C2×Dic6—21no—
270C2×Dic6—22no—
271C2×Dic6—31no—
272C2×Dic6—31no—
273C2×Dic6—61no—
274C2×Dic6C4×D314yescomplemented
275C2×Dic6C22×D312yes—
276C3×M16—34no—
277C3×M16—62no—
278C2×C3×C8—32no—
279C2×C3×C8—32no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—32no—
283C3×C4⋊C4—61no—
284C3×C4⋊C4C22×D311yescharacteristic
285C3×C4⋊C4C22×D311yescharacteristic
286C3×C4⋊C4C22×D311yescharacteristic
287C3×C4⋊C4C22×D311yescharacteristic
288C3×C22⋊C4—22no—
289C3×C22⋊C4—21no—
290C3×C22⋊C4—21no—
291C3×C42—22no—
292C3×C42—21no—
293C3×C42—21no—
294#216—38no—
295#215—38no—
296(C2×D3)⋊C4—61no—
297(C2×D3)⋊C4—61no—
298(C2×D3)⋊C4—61no—
299(C2×D3)⋊C4—61no—
300(C2×D3)⋊C4—62no—
301(C2×D3)⋊C4—62no—
302C4⋊Dic3—21no—
303C4⋊Dic3—62no—
304C4⋊Dic3—62no—
305C4⋊Dic3C22×D312yes—
306Dic3⋊C4—62no—
307Dic3⋊C4—62no—
308Dic3⋊C4—61no—
309Dic3⋊C4—61no—
310Dic3⋊C4—61no—
311Dic3⋊C4—61no—
312Dic3⋊C4—62no—
313Dic3⋊C4—62no—
314C4×Dic3—31no—
315C4×Dic3—31no—
316C4×Dic3—31no—
317C4×Dic3—31no—
318C4×Dic3—31no—
319C4×Dic3—31no—
320C4×Dic3—31no—
321C4×Dic3—31no—
322C4×Dic3—61no—
323C4×Dic3—61no—
324C4×Dic3—61no—
325C4×Dic3—61no—
326C4×Dic3—62no—
327C4×Dic3—62no—
328C4×Dic3—62no—
329C4×Dic3—62no—
330C4×Dic3—61no—
331C4×Dic3—61no—
332C4×Dic3—61no—
333C4×Dic3—61no—
334C4×Dic3—62no—
335C4×Dic3—62no—
336#208—22no—
337#208C4×D314yescomplemented
338C2×C3⋊C8C22×D312yes—
339C2×C3⋊C8C22×D312yes—
340Dic12—38no—
341#204—38no—
342C22×C32—21no—
343C22×C32—21no—
344C22×C32C4×D412yes—
345C22×C32C22×D411yescharacteristic
346C2×C3⋊D3—22no—
347C2×C3⋊D3—41no—
348C2×C3⋊D3—41no—
349C32×C4—41no—
350C32×C4—41no—
351C32×C4C4×D412yes—
352C32×C4C23×C411yescharacteristic
353C32×C4C2×#4111yescharacteristic
354C3⋊Dic3—22no—
355C3⋊Dic3—21no—
356C3⋊Dic3—21no—
357C3⋊Dic3—21no—
358C3⋊Dic3#13712yescomplemented
359C3×Dic3—24no—
360C3×Dic3—42no—
361C2×#41—91no—
362C22×Q8—31no—
363#137—98no—
364C2×Q16—92no—
365C2×SD16—92no—
366C2×M16—31no—
367C2×M16—31no—
368C4×Q8—92no—
369C4×Q8—92no—
370C4×Q8—91no—
371C4×Q8—91no—
372C4×Q8—181no—
373C4×Q8—181no—
374C4×D4—91no—
375C4×D4—91no—
376C4×D4—181no—
377C4×D4—181no—
378#117—181no—
379#117D3211yescharacteristic
380C2×C4⋊C4—31no—
381C2×C4⋊C4—181no—
382C2×C42—91no—
383C2×C42—181no—
384C2×C42—181no—
385#107—32no—
386#106—32no—
387#103—32no—
388#103—32no—
389#103—92no—
390#102—92no—
391#97—92no—
392C4×C8—92no—
393C23×C3—21no—
394C23×C3D3×D411yescharacteristic
395C23×C3D3×D411yescharacteristic
396C22×D3—62no—
397C22×D3—61no—
398C22×D3—61no—
399C3×Q8—34no—
400C3×Q8—64no—
401C3×Q8—62no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—21no—
412C2×C3×C4—64no—
413C2×C3×C4—62no—
414C2×C3×C4—62no—
415C2×C3×C4—122no—
416C2×C3×C4C2×C4×D312yes—
417C2×C3×C4C2×C4×D312yes—
418C2×C3×C4D3×D411yescharacteristic
419C2×C3×C4D3×D411yescharacteristic
420C2×C3×C4#23712yes—
421C2×C3×C4#23912yes—
422C2×C3×C4C23×D311yescharacteristic
423C2×C3×C4C23×D311yescharacteristic
424#67—68no—
425#67—64no—
426#67—64no—
427C2×Dic3—24no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—31no—
431C2×Dic3—31no—
432C2×Dic3—31no—
433C2×Dic3—31no—
434C2×Dic3—31no—
435C2×Dic3—31no—
436C2×Dic3—31no—
437C2×Dic3—31no—
438C2×Dic3—42no—
439C2×Dic3—61no—
440C2×Dic3—61no—
441C2×Dic3—61no—
442C2×Dic3—61no—
443C2×Dic3—62no—
444C2×Dic3—62no—
445C2×Dic3—62no—
446C2×Dic3—61no—
447C2×Dic3—61no—
448C2×Dic3—122no—
449C2×Dic3—121no—
450C2×Dic3—121no—
451C2×Dic3—122no—
452D12—32no—
453D12—32no—
454D12—62no—
455D12—62no—
456D12—61no—
457D12—61no—
458C4×D3—68no—
459C4×D3—64no—
460C4×D3—64no—
461C4×D3—122no—
462C4×D3—122no—
463C4×D3—124no—
464C4×D3—124no—
465C4×D3—122no—
466C4×D3—122no—
467Dic6—24no—
468Dic6—22no—
469Dic6—32no—
470Dic6—32no—
471Dic6—62no—
472Dic6—62no—
473Dic6—61no—
474Dic6—61no—
475Dic6C2×C4×D314yes—
476C3×C8—34no—
477C3×C8—62no—
478C3⋊C8—22no—
479C3⋊C8C2×C4×D314yes—
480C2×C32—22no—
481C2×C32C2×C4×D411yescharacteristic
482C2×C32C2×#13711yescharacteristic
483C2×C32#57511yescharacteristic
484C3⋊D3—42no—
485#41—94no—
486#41—182no—
487C2×Q8—32no—
488C2×Q8—34no—
489C2×Q8—62no—
490C2×Q8—61no—
491C2×Q8—91no—
492C2×D4—91no—
493C2×D4—181no—
494C22×C4—61no—
495C22×C4—61no—
496C22×C4—91no—
497C22×C4—91no—
498C22×C4—181no—
499C22×C4—181no—
500C22×C4—181no—
501C22×C4C2×D3211yescharacteristic
502Q16—98no—
503SD16—98no—
504M16—34no—
505M16—62no—
506C2×C8—32no—
507C2×C8—32no—
508C4⋊C4—32no—
509C4⋊C4—61no—
510C4⋊C4—181no—
511C4⋊C4—181no—
512C4⋊C4—182no—
513C4⋊C4—182no—
514C4⋊C4C2×D3211yescharacteristic
515C4⋊C4C2×D3211yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—181no—
518C22⋊C4—181no—
519C42—21no—
520C42—91no—
521C42—91no—
522C42—91no—
523C42—91no—
524C42—181no—
525C42—181no—
526C42—182no—
527C42—182no—
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—22no—
534C22×C3—41no—
535C22×C3—41no—
536C22×C3#67⋊C412yes—
537C22×C3#89312yes—
538C22×C3C2×D3×D411yescharacteristic
539C22×C3C2×D3×D411yescharacteristic
540C2×D3—64no—
541C2×D3—62no—
542C2×D3—62no—
543C2×D3—122no—
544C2×D3—122no—
545C2×D3—121no—
546C2×D3—121no—
547C2×D3—121no—
548C2×D3—121no—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—22no—
552C3×C4—42no—
553C3×C4—42no—
554C3×C4—41no—
555C3×C4—41no—
556C3×C4—41no—
557C3×C4—41no—
558C3×C4—64no—
559C3×C4—122no—
560C3×C4#67⋊C412yes—
561C3×C4#89312yes—
562C3×C4C22×C4×D311yescharacteristic
563C3×C4C22×C4×D311yescharacteristic
564C3×C4C2×#23711yescharacteristic
565C3×C4C2×#23911yescharacteristic
566Dic3—24no—
567Dic3—32no—
568Dic3—32no—
569Dic3—42no—
570Dic3—62no—
571Dic3—64no—
572Dic3—62no—
573Dic3—62no—
574Dic3—62no—
575Dic3—61no—
576Dic3—61no—
577Dic3—61no—
578Dic3—61no—
579Dic3—61no—
580Dic3—61no—
581Dic3—121no—
582Dic3—121no—
583C32C4×#13711yescharacteristic, complemented, Sylow
584C23—181no—
585C23#381111yescharacteristic
586Q8—34no—
587Q8—62no—
588Q8—64no—
589Q8—92no—
590Q8—181no—
591D4—92no—
592D4—184no—
593D4—181no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—62no—
597C2×C4—64no—
598C2×C4—62no—
599C2×C4—91no—
600C2×C4—91no—
601C2×C4—91no—
602C2×C4—91no—
603C2×C4—122no—
604C2×C4—182no—
605C2×C4—181no—
606C2×C4—184no—
607C2×C4—362no—
608C2×C4—362no—
609C2×C4—361no—
610C2×C4#379612yes—
611C2×C4C4×D3212yes—
612C2×C4#381111yescharacteristic
613C2×C4C22×D3211yescharacteristic
614C8—34no—
615C8—62no—
616C2×C3—22no—
617C2×C3—22no—
618C2×C3—21no—
619C2×C3—21no—
620C2×C3—21no—
621C2×C3—42no—
622C2×C3C2×#67⋊C411yescharacteristic
623C2×C3C2×#89311yescharacteristic
624C2×C3#577311yescharacteristic
625C2×C3D3×#13711yescharacteristic
626C2×C3D3×#13711yescharacteristic
627C2×C3#577711yescharacteristic
628D3—124no—
629D3—122no—
630D3—122no—
631C22—21no—
632C22—21no—
633C22—182no—
634C22—361no—
635C22—361no—
636C22#6388112yes—
637C22C2×#381111yescharacteristic
638C4—41no—
639C4—41no—
640C4—64no—
641C4—92no—
642C4—122no—
643C4—182no—
644C4—181no—
645C4—181no—
646C4—181no—
647C4#6388112yes—
648C4C2×#379611yescharacteristic
649C4C2×C4×D3211yescharacteristic
650C3—21no—
651C3#7894611yescharacteristic, complemented
652C3#7920011yescharacteristic, complemented
653C2—22no—
654C2—362no—
655C2C2×#6388111yescharacteristic
656C2#1059546811yescharacteristic
657C2#1059547111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32C4×#137
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. C2×#63843C2semidirect
4. C3×#5004C2semidirect
5. C3×#4995C2semidirect
7. #10591060C2semidirect
8. #10590485C2semidirect
9. #10590484C2semidirect
10. #10590483C2semidirect
11. #10590482C2semidirect
36. #63833C4semidirect
58. #5004D3semidirect
59. #4995D3semidirect
84. C2×C3×Dic6C2×C4semidirect
103. C3×#208C2×C4semidirect
110. #3719C2×C4semidirect
111. #3717C2×C4semidirect
274. C2×Dic6C4×D3semidirect
337. #208C4×D3semidirect
358. C3⋊Dic3#137semidirect
583. C32C4×#137semidirect
651. C3#78946semidirect
652. C3#79200semidirect

Maximal subgroups

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

subgroupindex
#105959932
C2×#638432
C2×#638332
C3×#50042
C3×#49952
#105911062
#105910602
#105904852
#105904842
#105904832
#105904822
#792003
#789463