Finite Group Databasebeta

← #11860412

Subgroups — #11860412

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×#64151C211yesmaximal, characteristic
2C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
3#10594954C211yesmaximal, characteristic
4C3×#5225C211yesmaximal, characteristic, complemented
5#10591541C212yesmaximal, complemented
6#10591540C212yesmaximal, complemented
7#10591537C212yesmaximal, complemented
8#10591536C212yesmaximal, complemented
9#10591139C211yesmaximal, characteristic, complemented
10#10591106C211yesmaximal, characteristic
11Dic3×#208C211yesmaximal, characteristic, complemented
12C4×#942—31nomaximal
13#78946—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C2×#3828C2211yescharacteristic
16C2×#3756C2212yes—
17#64151C418yescomplemented
18C2×#3755C2212yes—
19C2×#3748C2211yescharacteristic
20C3×Q8×Dic3—21no—
21C3×Q8×Dic3—21no—
22C3×Q8×Dic3C2212yes—
23C3×Q8×Dic3C2212yes—
24C3×#926C2211yescharacteristic
25C2×C3×C4⋊Dic3—21no—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4×Dic3—21no—
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30#63952—21no—
31#63952—21no—
32#63894C2211yescharacteristic
33#63894C2211yescharacteristic
34C4×#624—21no—
35#63874—21no—
36#63844C2211yescharacteristic
37#63844C2211yescharacteristic
38C3×#835C2212yes—
39C3×#835C2212yes—
40#63576C2212yes—
41#63574C2212yes—
42#63567C2212yes—
43#63564C2212yes—
44#63554C2212yes—
45Dic3×C3⋊C8C2212yes—
46C2×C3×C4×Q8—31no—
47C2×Q8×Dic3D311yescharacteristic, complemented
48C2×#942—31no—
49C2×#942—31no—
50C2×#942—61no—
51#5522—31no—
52C4×#235—31no—
53C3×#419—31no—
54#5225D311yescharacteristic, complemented
55#5133—31no—
56Dic3×M16—31no—
57#5030—32no—
58C4×#216—32no—
59#5026—32no—
60C4×#215—32no—
61#4995—31no—
62#4966—31no—
63#4964—31no—
64C4×#208—31no—
65#4817—32no—
66#4790—32no—
67#4789—32no—
68#4788—32no—
69C2×C32×Q8—21no—
70C2×C32×Q8—22no—
71C2×C32×Q8C2×C414yescomplemented
72C2×C32×Q8C2312yes—
73C22×C32×C4—21no—
74C22×C32×C4C2311yescharacteristic
75C2×#638—21no—
76#3828—22no—
77#3828C2×C414yes—
78C2×C4⋊(C3⋊D3)C2311yescharacteristic
79C2×C4×C3⋊D3—21no—
80C2×#634C2311yescharacteristic
81C22×C3×Dic3—21no—
82C22×C3×Dic3D411yescharacteristic
83C22×C3×Dic3D411yescharacteristic
84C2×#624—21no—
85C2×#624—21no—
86#3756C2×C418yescomplemented
87#3755C2×C418yescomplemented
88#3748C2×C414yescomplemented
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#217—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3—22no—
94C3×C4⋊Dic3C2312yes—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4×Dic3—21no—
98C3×C4×Dic3—22no—
99C3×C4×Dic3—22no—
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C3×#208—22no—
105C2×C3×C3⋊C8C2312yes—
106#3724—21no—
107#3724—21no—
108#3722—21no—
109#3722—21no—
110Dic32—21no—
111Dic32—21no—
112C4×#137—91noSylow
113C22×C3×Q8—21no—
114C22×C3×Q8C2×D311yescharacteristic
115C22×C3×Q8C2×D311yescharacteristic
116C2×#235—31no—
117C2×#235—31no—
118C2×#235—61no—
119C2×C3×M16—31no—
120C3×C4×Q8—32no—
121C3×C4×Q8—32no—
122C3×C4×Q8—61no—
123C3×C4×Q8—61no—
124C3×#117—31no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C4⋊C4—61no—
127C2×C3×C42—31no—
128C2×C3×C42—61no—
129Q8×Dic3—21no—
130Q8×Dic3—21no—
131Q8×Dic3C2×D312yes—
132Q8×Dic3C2×D312yes—
133C2×#216—32no—
134C2×#216—32no—
135C2×#216—62no—
136#942—38no—
137#942—38no—
138#942—68no—
139C2×#215—32no—
140C2×#215—32no—
141C2×#215—62no—
142C4×#67—61no—
143C4×#67—61no—
144#926C2×D311yescharacteristic
145C2×C4⋊Dic3—21no—
146C2×C4⋊Dic3C2×D311yescharacteristic
147C2×C4×Dic3—21no—
148C2×C4×Dic3C2×D311yescharacteristic
149C2×#208—31no—
150C2×#208—31no—
151C2×#208—61no—
152C2×#208C2×D311yescharacteristic
153#893—31no—
154#893—31no—
155#887—31no—
156#887—31no—
157#67⋊C4—61no—
158#67⋊C4—61no—
159C4×D12—31no—
160C4×D12—31no—
161#872—61no—
162#872—61no—
163C42×D3—61no—
164C42×D3—61no—
165C4×Dic6—31no—
166C4×Dic6—31no—
167C3×#103—32no—
168C3×#103—32no—
169#835C2×D312yes—
170#835C2×D312yes—
171#821—32no—
172#816—32no—
173#815—32no—
174C8×Dic3—32no—
175#810—32no—
176#809—32no—
177#808—32no—
178#808—32no—
179#807—32no—
180#807—32no—
181#803—32no—
182C4×C3⋊C8—32no—
183C23×C32C2×D411yescharacteristic
184C22×C3⋊D3—21no—
185C32×Q8—24no—
186C32×Q8—22no—
187C32×Q8C22×C414yes—
188C2×C32×C4—24no—
189C2×C32×C4—22no—
190C2×C32×C4C22×C412yes—
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4#4112yes—
193C2×C32×C4C2411yescharacteristic
194#638—24no—
195C2×C3⋊Dic3—21no—
196C4⋊(C3⋊D3)—21no—
197C4⋊(C3⋊D3)C22×C412yes—
198C4×C3⋊D3—24no—
199#634—21no—
200#634C22×C412yes—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—41no—
206C2×C3×Dic3—42no—
207C2×C3×Dic3C2×D411yescharacteristic
208C2×C3×Dic3C2×D411yescharacteristic
209C2×C3×Dic3C2×D411yescharacteristic
210C2×C3×Dic3C2×D411yescharacteristic
211#624—42no—
212#624—42no—
213C3⋊(C3⋊C8)C22×C414yes—
214C3×C3⋊C8—22no—
215C2×#137—91no—
216C4×#41—91no—
217C2×C4×Q8—31no—
218#441—92no—
219#440—92no—
220C4×Q16—92no—
221C4×SD16—92no—
222#428—91no—
223#419—31no—
224#417—91no—
225C4×M16—91no—
226C2×C3×Q8—22no—
227C2×C3×Q8—21no—
228C2×C3×Q8—22no—
229C2×C3×Q8—21no—
230C2×C3×Q8—24no—
231C2×C3×Q8—22no—
232C2×C3×Q8—42no—
233C2×C3×Q8—41no—
234C2×C3×Q8C4×D314yescomplemented
235C2×C3×Q8C4×D314yescomplemented
236C2×C3×Q8C22×D312yes—
237C2×C3×Q8C22×D312yes—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—41no—
244C22×C3×C4—61no—
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C2×#67—61no—
248C2×#67—61no—
249C2×#67—121no—
250C22×Dic3—21no—
251C22×Dic3#6711yescharacteristic
252C22×Dic3#6711yescharacteristic
253#235—34no—
254#235—34no—
255#235—64no—
256#235—62no—
257#235—62no—
258#235—122no—
259C2×D12—31no—
260C2×D12—31no—
261C2×D12—61no—
262C2×C4×D3—61no—
263C2×C4×D3—61no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×C4×D3—61no—
267C2×C4×D3—61no—
268C2×C4×D3—121no—
269C2×Dic6—31no—
270C2×Dic6—31no—
271C2×Dic6—61no—
272C3×M16—62no—
273C2×C3×C8—32no—
274C3×C4⋊C4—31no—
275C3×C4⋊C4—32no—
276C3×C4⋊C4—31no—
277C3×C4⋊C4—62no—
278C3×C4⋊C4—62no—
279C3×C4⋊C4—61no—
280C3×C22⋊C4—61no—
281C3×C42—31no—
282C3×C42—31no—
283C3×C42—31no—
284C3×C42—31no—
285C3×C42—62no—
286C3×C42—62no—
287C3×C42—61no—
288#217—21no—
289#216—38no—
290#216—38no—
291#216—68no—
292#215—38no—
293#215—38no—
294#215—68no—
295(C2×D3)⋊C4—61no—
296(C2×D3)⋊C4—61no—
297(C2×D3)⋊C4—61no—
298(C2×D3)⋊C4—61no—
299C4⋊Dic3—21no—
300C4⋊Dic3—22no—
301C4⋊Dic3—22no—
302C4⋊Dic3C22×D311yescharacteristic
303C4⋊Dic3C22×D312yes—
304C4⋊Dic3C22×D311yescharacteristic
305Dic3⋊C4—61no—
306Dic3⋊C4—61no—
307Dic3⋊C4—61no—
308Dic3⋊C4—61no—
309C4×Dic3—21no—
310C4×Dic3—22no—
311C4×Dic3—22no—
312C4×Dic3—61no—
313C4×Dic3—61no—
314C4×Dic3—61no—
315C4×Dic3—61no—
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×C32C4×D412yes—
331C22×C32C22×D411yescharacteristic
332C2×C3⋊D3—22no—
333C2×C3⋊D3—41no—
334C2×C3⋊D3—41no—
335C32×C4—24no—
336C32×C4C4×D412yes—
337C32×C4C23×C411yescharacteristic
338C32×C4C2×#4111yescharacteristic
339C3⋊Dic3—22no—
340C3×Dic3—21no—
341C3×Dic3—21no—
342C3×Dic3—21no—
343C3×Dic3—41no—
344C3×Dic3—41no—
345C3×Dic3—42no—
346C3×Dic3#13712yescomplemented
347C2×#41—91no—
348C22×Q8D3211yescharacteristic
349#137—98no—
350C2×Q16—92no—
351C2×SD16—92no—
352C2×M16—31no—
353C2×M16—91no—
354C4×Q8—32no—
355C4×Q8—32no—
356C4×Q8—61no—
357C4×Q8—61no—
358C4×Q8—91no—
359C4×Q8—91no—
360C4×D4—91no—
361C4×D4—91no—
362C4×D4—181no—
363C4×D4—181no—
364#117—31no—
365#117—181no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—61no—
368C2×C42—31no—
369C2×C42—61no—
370C2×C42—181no—
371#107—92no—
372#106—92no—
373#103—32no—
374#103—32no—
375#103—92no—
376#102—92no—
377#97—92no—
378C4×C8—92no—
379C23×C3—21no—
380C23×C3D3×D411yescharacteristic
381C23×C3C2×#6711yescharacteristic
382C22×D3—61no—
383C22×D3—61no—
384C22×D3—121no—
385C3×Q8—24no—
386C3×Q8—24no—
387C3×Q8—22no—
388C3×Q8—22no—
389C3×Q8—24no—
390C3×Q8—42no—
391C3×Q8—44no—
392C3×Q8C2×C4×D314yes—
393C3×Q8C2×C4×D314yes—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—21no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—31no—
403C2×C3×C4—31no—
404C2×C3×C4—31no—
405C2×C3×C4—31no—
406C2×C3×C4—42no—
407C2×C3×C4—44no—
408C2×C3×C4—62no—
409C2×C3×C4—62no—
410C2×C3×C4—61no—
411C2×C3×C4—61no—
412C2×C3×C4—121no—
413C2×C3×C4—122no—
414C2×C3×C4C2×C4×D312yes—
415C2×C3×C4C2×C4×D312yes—
416C2×C3×C4#23512yes—
417C2×C3×C4D3×D411yescharacteristic
418C2×C3×C4#23712yes—
419C2×C3×C4C2×#6711yescharacteristic
420C2×C3×C4C23×D311yescharacteristic
421C2×C3×C4C23×D311yescharacteristic
422#67—64no—
423#67—64no—
424#67—124no—
425C2×Dic3—22no—
426C2×Dic3—21no—
427C2×Dic3—21no—
428C2×Dic3—22no—
429C2×Dic3—41no—
430C2×Dic3—42no—
431C2×Dic3—61no—
432C2×Dic3—61no—
433C2×Dic3—121no—
434C2×Dic3C2×#6711yescharacteristic
435C2×Dic3C2×#6711yescharacteristic
436C2×Dic3C2×#6711yescharacteristic
437C2×Dic3C2×#6711yescharacteristic
438D12—32no—
439D12—32no—
440D12—62no—
441D12—61no—
442D12—61no—
443D12—121no—
444C4×D3—64no—
445C4×D3—64no—
446C4×D3—124no—
447C4×D3—122no—
448C4×D3—122no—
449C4×D3—122no—
450C4×D3—122no—
451Dic6—32no—
452Dic6—32no—
453Dic6—62no—
454Dic6—61no—
455Dic6—61no—
456Dic6—121no—
457C3×C8—62no—
458C3⋊C8—22no—
459C3⋊C8—34no—
460C3⋊C8—34no—
461C3⋊C8—64no—
462C2×C32—22no—
463C2×C32C2×C4×D411yescharacteristic
464C2×C32C2×#13711yescharacteristic
465C2×C32#57511yescharacteristic
466C3⋊D3—42no—
467#41—94no—
468#41—182no—
469C2×Q8—22no—
470C2×Q8—21no—
471C2×Q8—91no—
472C2×Q8#62414yescomplemented
473C2×Q8C2×D3212yes—
474C2×D4—91no—
475C2×D4—181no—
476C22×C4—21no—
477C22×C4—31no—
478C22×C4—31no—
479C22×C4—61no—
480C22×C4—181no—
481C22×C4—181no—
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—62no—
494C4⋊C4—62no—
495C4⋊C4—61no—
496C4⋊C4—181no—
497C4⋊C4—181no—
498C22⋊C4—61no—
499C22⋊C4—181no—
500C22⋊C4—181no—
501C42—31no—
502C42—31no—
503C42—31no—
504C42—31no—
505C42—62no—
506C42—62no—
507C42—61no—
508C42—181no—
509C42—181no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—22no—
516C22×C3—41no—
517C22×C3—41no—
518C22×C3#67⋊C412yes—
519C22×C3C4×#6712yes—
520C22×C3C2×D3×D411yescharacteristic
521C22×C3C22×#6711yescharacteristic
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—122no—
525C2×D3—121no—
526C2×D3—121no—
527C2×D3—121no—
528C2×D3—121no—
529C2×D3—241no—
530C2×D3—241no—
531C3×C4—24no—
532C3×C4—24no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—22no—
536C3×C4—32no—
537C3×C4—44no—
538C3×C4—61no—
539C3×C4—61no—
540C3×C4—61no—
541C3×C4—122no—
542C3×C4—121no—
543C3×C4—121no—
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—41no—
554Dic3—41no—
555Dic3—42no—
556Dic3—62no—
557Dic3—62no—
558Dic3—122no—
559Dic3#94212yescomplemented
560C32C4×#13711yescharacteristic, complemented, Sylow
561C23—181no—
562C23D3×#6711yescharacteristic
563Q8—22no—
564Q8—24no—
565Q8—92no—
566Q8—181no—
567Q8C2×#62414yes—
568D4—92no—
569D4—184no—
570D4—181no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—31no—
574C2×C4—31no—
575C2×C4—31no—
576C2×C4—31no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—61no—
580C2×C4—61no—
581C2×C4—121no—
582C2×C4—122no—
583C2×C4—181no—
584C2×C4—184no—
585C2×C4—362no—
586C2×C4—362no—
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×C3C2×#67⋊C411yescharacteristic
600C2×C3D3×#13711yescharacteristic
601C2×C3#577711yescharacteristic
602C2×C3C2×C4×#6711yescharacteristic
603C2×C3C2×#94211yescharacteristic
604C2×C3#582211yescharacteristic
605D3—122no—
606D3—122no—
607D3—242no—
608C22—21no—
609C22—21no—
610C22—182no—
611C22—361no—
612C22—361no—
613C22#6395212yes—
614C22C2×D3×#6711yescharacteristic
615C4—24no—
616C4—32no—
617C4—61no—
618C4—61no—
619C4—61no—
620C4—121no—
621C4—122no—
622C4—121no—
623C4—182no—
624C4#6395212yes—
625C4C2×#380411yescharacteristic
626C4C22×#62411yescharacteristic
627C3—21no—
628C3#7894611yescharacteristic, complemented
629C3C4×#94211yescharacteristic, complemented
630C2—22no—
631C2—362no—
632C2D3×#94211yescharacteristic
633C2#1059531711yescharacteristic
634C2C2×#6395211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C3×Q8×Dic3C2semidirect
4. C3×#5225C2semidirect
5. #10591541C2semidirect
6. #10591540C2semidirect
7. #10591537C2semidirect
8. #10591536C2semidirect
9. #10591139C2semidirect
11. Dic3×#208C2semidirect
17. #64151C4semidirect
47. C2×Q8×Dic3D3semidirect
54. #5225D3semidirect
71. C2×C32×Q8C2×C4semidirect
86. #3756C2×C4semidirect
87. #3755C2×C4semidirect
88. #3748C2×C4semidirect
234. C2×C3×Q8C4×D3semidirect
235. C2×C3×Q8C4×D3semidirect
346. C3×Dic3#137semidirect
472. C2×Q8#624semidirect
559. Dic3#942semidirect
560. C32C4×#137semidirect
628. C3#78946semidirect
629. C3C4×#942semidirect

Maximal subgroups

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

subgroupindex
C2×#641512
C2×C3×Q8×Dic32
#105949542
C3×#52252
#105915412
#105915402
#105915372
#105915362
#105911392
#105911062
Dic3×#2082
C4×#9423
#789463