Finite Group Databasebeta

← #11860420

Subgroups — #11860420

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#41×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic
3C2×#63843C211yesmaximal, characteristic, complemented
4C3×#5232C211yesmaximal, characteristic
5#10591582C212yesmaximal, complemented
6#10591581C212yesmaximal, complemented
7#10591446C212yesmaximal, complemented
8#10591445C212yesmaximal, complemented
9#10591130C211yesmaximal, characteristic, complemented
10#10591100C211yesmaximal, characteristic, complemented
11#10591060C211yesmaximal, characteristic, complemented
12Dic3×#137—31nomaximal
13#78867—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16Q8×C3⋊Dic3C2211yescharacteristic
17Q8×C3⋊Dic3C2211yescharacteristic
18D4×C3⋊Dic3—21no—
19D4×C3⋊Dic3—21no—
20D4×C3⋊Dic3C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic
22#64135—21no—
23#64135C2211yescharacteristic
24C2×C4×C3⋊Dic3—21no—
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C3×#951C418yescomplemented
27C2×C3×#216C2212yes—
28C2×C3×#214C2212yes—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×#208C2211yescharacteristic
31C2×C3×#208C2211yescharacteristic
32C2×Dic3⋊Dic3—21no—
33C2×Dic32—21no—
34#63843—21no—
35#63843—21no—
36#63843C2212yes—
37#63843C2212yes—
38C3×#835C2212yes—
39C3×#832C2212yes—
40#63575C2212yes—
41#63573C2212yes—
42#63566C2212yes—
43#63566C2212yes—
44#63555C2212yes—
45#63553C2212yes—
46C2×C3×#137—31no—
47Dic3×#41—31no—
48Dic3×#41—31no—
49Dic3×#41—61no—
50C2×#951D311yescharacteristic
51C2×Q8×Dic3—31no—
52C2×#887—31no—
53C3×#417—31no—
54#5232D311yescharacteristic
55#5225—31no—
56#5184—32no—
57Dic3×Q16—32no—
58#5164—32no—
59Dic3×SD16—32no—
60#5121—31no—
61#5120—31no—
62Dic3×M16—31no—
63Dic3×M16—31no—
64#4964—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—
77C22×C3⋊Dic3—21no—
78C22×C3⋊Dic3D411yescharacteristic
79C22×C3⋊Dic3D411yescharacteristic
80C22×C3×Dic3—21no—
81C22×C3×Dic3—21no—
82C2×C3×Dic6—21no—
83C2×C3×Dic6—22no—
84C2×C3×Dic6C2×C414yescomplemented
85C2×C3×Dic6C2312yes—
86#3757—21no—
87#3757—21no—
88#3757—21no—
89C4⋊(C3⋊Dic3)—21no—
90C4⋊(C3⋊Dic3)—21no—
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92C4⋊(C3⋊Dic3)C2311yescharacteristic
93C4×C3⋊Dic3—21no—
94C4×C3⋊Dic3—21no—
95C4×C3⋊Dic3—21no—
96C4×C3⋊Dic3D411yescharacteristic
97C4×C3⋊Dic3D411yescharacteristic
98C4×C3⋊Dic3C2311yescharacteristic
99C4×C3⋊Dic3C2311yescharacteristic
100C3×#216C2×C418yescomplemented
101C3×#214C2×C418yescomplemented
102C3×C4⋊Dic3—21no—
103C3×C4⋊Dic3C2312yes—
104C3×#208—22no—
105C3×#208C2×C414yescomplemented
106C2×C3×C3⋊C8C2312yes—
107C2×C3×C3⋊C8C2312yes—
108Dic3⋊Dic3—22no—
109Dic3⋊Dic3—22no—
110Dic32—22no—
111Dic32—22no—
112C4×#137—91noSylow
113C2×C3×#41—21no—
114C2×C3×#41C2×D311yescharacteristic
115C2×C3×#41C2×D311yescharacteristic
116C22×C3×Q8—31no—
117C22×Dic6C2×D311yescharacteristic
118C3×#137—38no—
119C2×C3×Q16—32no—
120C2×C3×SD16—32no—
121C2×C3×M16—31no—
122C2×C3×M16—31no—
123C2×C3×C4⋊C4—31no—
124#951Dic318yescomplemented
125Q8×Dic3—31no—
126Q8×Dic3—31no—
127Q8×Dic3—31no—
128Q8×Dic3—31no—
129Q8×Dic3—32no—
130Q8×Dic3—32no—
131Q8×Dic3—61no—
132Q8×Dic3—61no—
133Q8×Dic3—61no—
134Q8×Dic3—61no—
135C2×#216C2×D312yes—
136D4×Dic3—31no—
137D4×Dic3—31no—
138D4×Dic3—31no—
139D4×Dic3—31no—
140D4×Dic3—61no—
141D4×Dic3—61no—
142D4×Dic3—61no—
143D4×Dic3—61no—
144D4×Dic3—61no—
145D4×Dic3—61no—
146D4×Dic3—62no—
147D4×Dic3—62no—
148C2×#214C2×D312yes—
149#926—31no—
150#926—31no—
151#926—61no—
152#926—61no—
153#926—61no—
154#926—62no—
155C2×C4⋊Dic3—61no—
156C2×C4⋊Dic3C2×D311yescharacteristic
157C2×Dic3⋊C4—61no—
158C2×C4×Dic3—31no—
159C2×C4×Dic3—31no—
160C2×C4×Dic3—61no—
161C2×C4×Dic3—61no—
162C2×C4×Dic3—61no—
163C2×C4×Dic3—61no—
164C2×C4×Dic3—61no—
165C2×C4×Dic3—62no—
166C2×#208C2×D311yescharacteristic
167C2×#208C2×D311yescharacteristic
168#887—32no—
169#887—32no—
170#887—61no—
171#887—61no—
172C3×#103—32no—
173C3×#102—32no—
174#835—32no—
175#835—32no—
176#835C2×D312yes—
177#832C2×D312yes—
178#818—32no—
179#817—32no—
180#816—32no—
181#816—32no—
182#815—32no—
183#815—32no—
184C8×Dic3—32no—
185C8×Dic3—32no—
186#808—32no—
187#807—32no—
188C23×C32—21no—
189C23×C32C2×D411yescharacteristic
190C32×Q8—21no—
191C32×Q8C22×C412yes—
192C32×D4—24no—
193C32×D4—21no—
194C32×D4C22×C412yes—
195C2×C32×C4—21no—
196C2×C32×C4—24no—
197C2×C32×C4C22×C412yes—
198C2×C32×C4C2×D411yescharacteristic
199C2×C32×C4#4112yes—
200C2×C32×C4C2411yescharacteristic
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—41no—
205C2×C3⋊Dic3—42no—
206C2×C3⋊Dic3—42no—
207C2×C3⋊Dic3C2×D411yescharacteristic
208C2×C3⋊Dic3C2×D411yescharacteristic
209C2×C3⋊Dic3C2×D411yescharacteristic
210C2×C3⋊Dic3C2×D411yescharacteristic
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—31no—
221C4×#41—91no—
222C2×C4×Q8—91no—
223#441—92no—
224#440—92no—
225C4×Q16—92no—
226C4×SD16—92no—
227#428—91no—
228#419—91no—
229#417—31no—
230C4×M16—91no—
231C3×#41—24no—
232C3×#41—22no—
233C3×#41—22no—
234C3×#41—24no—
235C3×#41C4×D314yes—
236C3×#41C2×Dic314yes—
237C2×C3×Q8—21no—
238C2×C3×Q8—34no—
239C2×C3×Q8—32no—
240C2×C3×Q8—61no—
241C2×C3×Q8—62no—
242C2×C3×Q8C22×D311yescharacteristic
243C2×C3×Q8C22×D311yescharacteristic
244C2×C3×D4—22no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4C22×D311yescharacteristic
249C2×C3×D4C22×D311yescharacteristic
250C22×C3×C4—22no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—61no—
255C22×C3×C4—61no—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D311yescharacteristic
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—31no—
261C22×Dic3—31no—
262C22×Dic3—31no—
263C22×Dic3—31no—
264C22×Dic3—61no—
265C22×Dic3—61no—
266C22×Dic3—61no—
267C22×Dic3—61no—
268C22×Dic3—61no—
269C22×Dic3—61no—
270C22×Dic3—62no—
271C22×Dic3—62no—
272C2×Dic6—21no—
273C2×Dic6—22no—
274C2×Dic6C2×Dic314yescomplemented
275C2×Dic6C22×D312yes—
276C3×Q16—38no—
277C3×SD16—38no—
278C3×M16—34no—
279C3×M16—62no—
280C2×C3×C8—32no—
281C2×C3×C8—32no—
282C3×C4⋊C4—32no—
283C3×C4⋊C4—61no—
284#217—61no—
285#217—61no—
286#217—61no—
287#217—61no—
288#217—62no—
289#217—62no—
290#217—62no—
291#217—61no—
292#217—61no—
293#216C2×Dic318yescomplemented
294#214C2×Dic318yescomplemented
295C4⋊Dic3—21no—
296C4⋊Dic3—31no—
297C4⋊Dic3—31no—
298C4⋊Dic3—31no—
299C4⋊Dic3—31no—
300C4⋊Dic3—61no—
301C4⋊Dic3—61no—
302C4⋊Dic3—62no—
303C4⋊Dic3—62no—
304C4⋊Dic3—61no—
305C4⋊Dic3—61no—
306C4⋊Dic3—61no—
307C4⋊Dic3—61no—
308C4⋊Dic3—62no—
309C4⋊Dic3—62no—
310C4⋊Dic3C22×D312yes—
311Dic3⋊C4—62no—
312Dic3⋊C4—62no—
313C4×Dic3—31no—
314C4×Dic3—31no—
315C4×Dic3—31no—
316C4×Dic3—31no—
317C4×Dic3—31no—
318C4×Dic3—31no—
319C4×Dic3—31no—
320C4×Dic3—31no—
321C4×Dic3—61no—
322C4×Dic3—61no—
323C4×Dic3—61no—
324C4×Dic3—61no—
325C4×Dic3—62no—
326C4×Dic3—62no—
327C4×Dic3—62no—
328C4×Dic3—62no—
329C4×Dic3—61no—
330C4×Dic3—61no—
331C4×Dic3—61no—
332C4×Dic3—61no—
333C4×Dic3—62no—
334C4×Dic3—62no—
335C4×Dic3—62no—
336C4×Dic3—61no—
337C4×Dic3—61no—
338#208—22no—
339#208C2×Dic314yescomplemented
340C2×C3⋊C8C22×D312yes—
341C2×C3⋊C8C22×D312yes—
342C22×C32—22no—
343C22×C32—21no—
344C22×C32—21no—
345C22×C32—41no—
346C22×C32—41no—
347C22×C32C4×D412yes—
348C22×C32C22×D411yescharacteristic
349C32×C4—22no—
350C32×C4C4×D412yes—
351C32×C4C23×C411yescharacteristic
352C32×C4C2×#4111yescharacteristic
353C3⋊Dic3—21no—
354C3⋊Dic3—21no—
355C3⋊Dic3—21no—
356C3⋊Dic3—41no—
357C3⋊Dic3—41no—
358C3⋊Dic3#13712yescomplemented
359C3×Dic3—24no—
360C3×Dic3—42no—
361C2×#41D3211yescharacteristic
362C22×Q8—31no—
363#137—38no—
364C2×Q16—32no—
365C2×SD16—32no—
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—91no—
379#117—181no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—181no—
382C2×C42—91no—
383C2×C42—181no—
384C2×C42—181no—
385#107—92no—
386#106—92no—
387#103—32no—
388#103—92no—
389#103—92no—
390#102—32no—
391#97—92no—
392C4×C8—92no—
393C23×C3—22no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3D3×D411yescharacteristic
398C23×C3D3×D411yescharacteristic
399C3×Q8—22no—
400C3×Q8—21no—
401C3×Q8—21no—
402C3×Q8—22no—
403C3×Q8—34no—
404C3×Q8—64no—
405C3×Q8—62no—
406C3×Q8C2×C4×D312yes—
407C3×Q8C22×Dic312yes—
408C3×D4—28no—
409C3×D4—22no—
410C3×D4—24no—
411C3×D4—24no—
412C3×D4—21no—
413C3×D4—21no—
414C3×D4—22no—
415C3×D4C2×C4×D312yes—
416C3×D4C22×Dic312yes—
417C2×C3×C4—22no—
418C2×C3×C4—28no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—21no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—21no—
427C2×C3×C4—64no—
428C2×C3×C4—62no—
429C2×C3×C4—62no—
430C2×C3×C4—122no—
431C2×C3×C4C2×C4×D312yes—
432C2×C3×C4D3×D411yescharacteristic
433C2×C3×C4D3×D411yescharacteristic
434C2×C3×C4#23712yes—
435C2×C3×C4#23712yes—
436C2×C3×C4C22×Dic312yes—
437C2×C3×C4C23×D311yescharacteristic
438C2×C3×C4C23×D311yescharacteristic
439C2×Dic3—24no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—31no—
443C2×Dic3—31no—
444C2×Dic3—31no—
445C2×Dic3—31no—
446C2×Dic3—31no—
447C2×Dic3—31no—
448C2×Dic3—31no—
449C2×Dic3—31no—
450C2×Dic3—42no—
451C2×Dic3—61no—
452C2×Dic3—61no—
453C2×Dic3—61no—
454C2×Dic3—61no—
455C2×Dic3—62no—
456C2×Dic3—62no—
457C2×Dic3—62no—
458C2×Dic3—62no—
459C2×Dic3—61no—
460C2×Dic3—61no—
461C2×Dic3—61no—
462C2×Dic3—61no—
463C2×Dic3—122no—
464C2×Dic3—122no—
465C2×Dic3—122no—
466C2×Dic3—121no—
467C2×Dic3—121no—
468C2×Dic3—124no—
469C2×Dic3—122no—
470C2×Dic3—124no—
471C2×Dic3—122no—
472C2×Dic3—122no—
473Dic6—24no—
474Dic6—22no—
475Dic6C22×Dic314yes—
476C3×C8—34no—
477C3×C8—62no—
478C3⋊C8—22no—
479C3⋊C8C22×Dic314yes—
480C2×C32—22no—
481C2×C32—42no—
482C2×C32C2×C4×D411yescharacteristic
483C2×C32C2×#13711yescharacteristic
484C2×C32#57511yescharacteristic
485#41—22no—
486#41D3×Dic314yes—
487C2×Q8—32no—
488C2×Q8—34no—
489C2×Q8—62no—
490C2×Q8—61no—
491C2×Q8C2×D3211yescharacteristic
492C2×D4—21no—
493C2×D4C2×D3211yescharacteristic
494C22×C4—21no—
495C22×C4—61no—
496C22×C4—61no—
497C22×C4—91no—
498C22×C4—91no—
499C22×C4—181no—
500C22×C4—181no—
501C22×C4C2×D3211yescharacteristic
502Q16—38no—
503SD16—38no—
504M16—34no—
505M16—62no—
506C2×C8—32no—
507C2×C8—32no—
508C4⋊C4—32no—
509C4⋊C4—61no—
510C4⋊C4—91no—
511C4⋊C4—91no—
512C4⋊C4—181no—
513C4⋊C4—181no—
514C4⋊C4—182no—
515C4⋊C4—182no—
516C22⋊C4—181no—
517C22⋊C4—181no—
518C22⋊C4—181no—
519C42—91no—
520C42—91no—
521C42—91no—
522C42—91no—
523C42—181no—
524C42—181no—
525C42—182no—
526C42—182no—
527C42—181no—
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—24no—
533C22×C3—22no—
534C22×C3—22no—
535C22×C3—21no—
536C22×C3—22no—
537C22×C3—41no—
538C22×C3—41no—
539C22×C3—42no—
540C22×C3—42no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3—41no—
544C22×C3—41no—
545C22×C3#67⋊C412yes—
546C22×C3D4×Dic312yes—
547C22×C3C2×D3×D411yescharacteristic
548C22×C3C2×D3×D411yescharacteristic
549C3×C4—24no—
550C3×C4—22no—
551C3×C4—22no—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—22no—
555C3×C4—64no—
556C3×C4—122no—
557C3×C4#67⋊C412yes—
558C3×C4D4×Dic312yes—
559C3×C4C22×C4×D311yescharacteristic
560C3×C4C2×#23711yescharacteristic
561C3×C4C2×#23711yescharacteristic
562C3×C4C23×Dic311yescharacteristic
563Dic3—24no—
564Dic3—32no—
565Dic3—32no—
566Dic3—42no—
567Dic3—62no—
568Dic3—62no—
569Dic3—61no—
570Dic3—61no—
571Dic3—61no—
572Dic3—61no—
573Dic3—61no—
574Dic3—61no—
575Dic3—121no—
576Dic3—121no—
577Dic3—122no—
578Dic3—122no—
579Dic3—121no—
580Dic3—121no—
581Dic3—121no—
582Dic3—121no—
583C32C4×#13711yescharacteristic, complemented, Sylow
584C23—21no—
585C23#381111yescharacteristic
586Q8—21no—
587Q8—34no—
588Q8—62no—
589Q8—64no—
590Q8C2×D3×Dic312yes—
591D4—24no—
592D4—21no—
593D4C2×D3×Dic312yes—
594C2×C4—21no—
595C2×C4—24no—
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—181no—
607C2×C4—362no—
608C2×C4—361no—
609C2×C4—362no—
610C2×C4C2×D3×Dic312yes—
611C2×C4#380512yes—
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×C3—44no—
623C2×C3—42no—
624C2×C3—42no—
625C2×C3C2×#67⋊C411yescharacteristic
626C2×C3#577311yescharacteristic
627C2×C3D3×#13711yescharacteristic
628C2×C3D3×#13711yescharacteristic
629C2×C3#577711yescharacteristic
630C2×C3C2×D4×Dic311yescharacteristic
631C22—21no—
632C22—21no—
633C22—22no—
634C22—41no—
635C22—41no—
636C22#67⋊Dic312yes—
637C22C2×#381111yescharacteristic
638C4—22no—
639C4—64no—
640C4—92no—
641C4—122no—
642C4—181no—
643C4—181no—
644C4—181no—
645C4—361no—
646C4—361no—
647C4#67⋊Dic312yes—
648C4C22×D3×Dic311yescharacteristic
649C4C2×#380511yescharacteristic
650C3—21no—
651C3#7886711yescharacteristic, complemented
652C3Dic3×#13711yescharacteristic, complemented
653C2—22no—
654C2—42no—
655C2#1059546811yescharacteristic
656C2#1059547111yescharacteristic
657C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC22C2×#3811
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×#63843C2semidirect
5. #10591582C2semidirect
6. #10591581C2semidirect
7. #10591446C2semidirect
8. #10591445C2semidirect
9. #10591130C2semidirect
10. #10591100C2semidirect
11. #10591060C2semidirect
26. C3×#951C4semidirect
84. C2×C3×Dic6C2×C4semidirect
100. C3×#216C2×C4semidirect
101. C3×#214C2×C4semidirect
105. C3×#208C2×C4semidirect
124. #951Dic3semidirect
274. C2×Dic6C2×Dic3semidirect
293. #216C2×Dic3semidirect
294. #214C2×Dic3semidirect
339. #208C2×Dic3semidirect
358. C3⋊Dic3#137semidirect
583. C32C4×#137semidirect
651. C3#78867semidirect
652. C3Dic3×#137semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊Dic32
C2×C3×#9512
C2×#638432
C3×#52322
#105915822
#105915812
#105914462
#105914452
#105911302
#105911002
#105910602
Dic3×#1373
#788673