Finite Group Databasebeta

← #11896061

Subgroups — #11896061

Order 1152.

730 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#627C211yesmaximal, characteristic, complemented
2#10595384C211yesmaximal, characteristic
3#10592883C211yesmaximal, characteristic, complemented
4C3×#5185C211yesmaximal, characteristic
5C3×#5182C211yesmaximal, characteristic, complemented
6#10591630C211yesmaximal, characteristic, complemented
7#10591624C211yesmaximal, characteristic
8#10591623C211yesmaximal, characteristic, complemented
9#10591612C211yesmaximal, characteristic
10#10591576C211yesmaximal, characteristic, complemented
11Dic3×#215C211yesmaximal, characteristic
12#10590866C211yesmaximal, characteristic
13#10590803C211yesmaximal, characteristic, complemented
14#10590757C211yesmaximal, characteristic
15#10590646C211yesmaximal, characteristic, complemented
16#80582—31nomaximal
17#80464—31nomaximal
18C2×C32×Q16C2211yescharacteristic
19Q8×C3⋊Dic3C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21C3×#947C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×#944C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27#63919—21no—
28#63919C2211yescharacteristic
29#63918—21no—
30#63918—21no—
31#63918C2211yescharacteristic
32#63918C2211yescharacteristic
33C4×#627—21no—
34C4×#627C2211yescharacteristic
35#63893—21no—
36Dic3×D12C2211yescharacteristic
37#63878—21no—
38#63863C2211yescharacteristic
39#63862—21no—
40#63861—21no—
41Dic3×Dic6C2211yescharacteristic
42#63662C2211yescharacteristic
43#63662C2211yescharacteristic
44#63644C2211yescharacteristic
45#63642C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52#63573C2211yescharacteristic
53#63573C2211yescharacteristic
54#63572C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5732—31no—
62#5671—31no—
63Q8×Dic6—31no—
64Q8×Dic6—31no—
65C3×#464—31no—
66C3×#462—31no—
67#5185—31no—
68#5185D311yescharacteristic
69#5184—31no—
70#5184—31no—
71#5184—31no—
72#5184—61no—
73#5182D311yescharacteristic, complemented
74#5166—31no—
75Dic3×SD16—31no—
76#5079—31no—
77#5055—31no—
78#5030—31no—
79C4×#215—31no—
80#4851—31no—
81#4842—31no—
82#4831—31no—
83#4828—31no—
84#4794—31no—
85#4794—31no—
86#4792—31no—
87#4791—31no—
88#4791—31no—
89#4791—31no—
90#4765—31no—
91#4761—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×Dic6C2311yescharacteristic
96C2×#627—21no—
97C2×#627—21no—
98C2×#627—21no—
99C2×#627D411yescharacteristic
100C2×D3×Dic3—21no—
101C32×Q16—22no—
102C2×C32×C8C2311yescharacteristic
103C4⋊(C3⋊Dic3)—21no—
104C4⋊(C3⋊Dic3)—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4×C3⋊Dic3—21no—
108C4×C3⋊Dic3—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#216—22no—
112C3×#215—22no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3—21no—
123C3×C4×Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127#3724—21no—
128#3724D411yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138#3369—91noSylow
139C2×C3×Q16—21no—
140C2×C3×Q16—31no—
141C2×C3×Q16C2×D311yescharacteristic
142C2×C3×Q16C2×D311yescharacteristic
143C2×C3×SD16—31no—
144C3×C4⋊Q8—31no—
145C3×#124—31no—
146C3×C4×Q8—31no—
147C3×C4×Q8—31no—
148#947—31no—
149#947C2×D311yescharacteristic
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154Q8×Dic3—31no—
155Q8×Dic3—61no—
156Q8×Dic3—61no—
157Q8×Dic3C2×D311yescharacteristic
158Q8×Dic3C2×D311yescharacteristic
159#944C2×D311yescharacteristic
160C2×#216C2×D311yescharacteristic
161C2×#215C2×D311yescharacteristic
162#936—31no—
163D4×Dic3—31no—
164#898—61no—
165#898—61no—
166#897—61no—
167#892—61no—
168#888—31no—
169#888—31no—
170#888—31no—
171#888—31no—
172#888—61no—
173#888—61no—
174#888—61no—
175#888—61no—
176#879—61no—
177#879—61no—
178#878—61no—
179#877—61no—
180C4×D12—31no—
181#869—31no—
182#869—31no—
183#869—61no—
184#869—61no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C4×Dic6—61no—
190C3×C4⋊C8—31no—
191C3×C4⋊C8—31no—
192C3×#103—31no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#102—31no—
196#835—31no—
197#835—31no—
198#835—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—61no—
203#835—61no—
204#835C2×D311yescharacteristic
205#835C2×D311yescharacteristic
206#832—31no—
207#832—31no—
208#821—31no—
209#821C2×D311yescharacteristic
210#817—31no—
211#817—31no—
212#817—31no—
213#817—31no—
214#817—61no—
215#816—31no—
216#816C2×D311yescharacteristic
217#815—31no—
218#815—31no—
219#815—31no—
220#815—61no—
221Dic3⋊C8—31no—
222Dic3⋊C8—31no—
223Dic3⋊C8C2×D311yescharacteristic
224Dic3⋊C8C2×D311yescharacteristic
225C8×Dic3—31no—
226#810—31no—
227#809—31no—
228#808—31no—
229#808—31no—
230#803—31no—
231C4×C3⋊C8—31no—
232C22×C3×D3—21no—
233C32×Q8—21no—
234C32×Q8—21no—
235C32×Q8—21no—
236C32×Q8#4112yes—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4C2411yescharacteristic
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3C2×D411yescharacteristic
243C2×C3⋊Dic3C2×D411yescharacteristic
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×D12—21no—
252C3×D12—21no—
253C3×Dic6—21no—
254C3×Dic6—21no—
255#627—22no—
256#627—81no—
257#627—81no—
258#627—81no—
259D3×Dic3—42no—
260C32×C8—21no—
261C3⋊(C3⋊C8)—21no—
262C3×C3⋊C8—21no—
263C3×C3⋊C8—21no—
264Q82—91no—
265#556—91no—
266#489—91no—
267#489—91no—
268#487—91no—
269#476—91no—
270#475—91no—
271#475—91no—
272#464—31no—
273#464—91no—
274#462—31no—
275#446—91no—
276#441—91no—
277#441—91no—
278C4×SD16—91no—
279C2×C3×Q8—21no—
280C2×C3×Q8—21no—
281C2×C3×Q8—31no—
282C2×C3×Q8C22×D311yescharacteristic
283C2×C3×Q8C22×D311yescharacteristic
284C2×C3×Q8C22×D311yescharacteristic
285C2×C3×Q8C22×D311yescharacteristic
286C2×C3×D4—31no—
287C22×Dic3—61no—
288C2×D12C22×D311yescharacteristic
289C2×C4×D3—61no—
290C2×Dic6—31no—
291C2×Dic6—31no—
292C2×Dic6—61no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6C22×D311yescharacteristic
299C3×Q16—24no—
300C3×Q16—22no—
301C3×Q16—22no—
302C3×Q16—62no—
303C3×SD16—62no—
304C2×C3×C8—21no—
305C2×C3×C8—31no—
306C2×C3×C8—31no—
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C22×D311yescharacteristic
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C22⋊C4—61no—
316C3×C22⋊C4—61no—
317C3×C42—31no—
318C3×C42—31no—
319C3×C42—61no—
320C3×C42—61no—
321#217—61no—
322#217—61no—
323#217—61no—
324#216—22no—
325#215—22no—
326(C2×D3)⋊C4—21no—
327(C2×D3)⋊C4—21no—
328(C2×D3)⋊C4—61no—
329(C2×D3)⋊C4—61no—
330(C2×D3)⋊C4—61no—
331C4⋊Dic3—21no—
332C4⋊Dic3—21no—
333C4⋊Dic3—31no—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—31no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—121no—
349C4⋊Dic3—121no—
350C4⋊Dic3C22×D311yescharacteristic
351C4⋊Dic3C22×D311yescharacteristic
352Dic3⋊C4—21no—
353Dic3⋊C4—21no—
354Dic3⋊C4—31no—
355Dic3⋊C4—31no—
356Dic3⋊C4—31no—
357Dic3⋊C4—31no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363C4×Dic3—21no—
364C4×Dic3—21no—
365C4×Dic3—31no—
366C4×Dic3—31no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—121no—
375C4×Dic3—121no—
376C4×Dic3C22×D311yescharacteristic
377C4×Dic3C22×D311yescharacteristic
378C2×C3⋊C8—31no—
379C2×C3⋊C8—31no—
380C2×C3⋊C8—61no—
381C2×C3⋊C8C22×D311yescharacteristic
382C2×C3⋊C8C22×D311yescharacteristic
383C22×C32C22×D411yescharacteristic
384C2×C3×D3—41no—
385C2×C3×D3—41no—
386C2×C3×D3—41no—
387C32×C4—22no—
388C32×C4—41no—
389C32×C4C2×#4111yescharacteristic
390C32×C42−1+411yescharacteristic
391C3⋊Dic3—21no—
392C3⋊Dic3—21no—
393C3⋊Dic3—41no—
394C3⋊Dic3—41no—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3#13712yes—
402C2×Q16—31no—
403C2×Q16D3211yescharacteristic
404C2×SD16—31no—
405C4⋊Q8—31no—
406C4⋊Q8—91no—
407C4⋊Q8—91no—
408C4⋊Q8—91no—
409C4⋊Q8—181no—
410C4⋊Q8—181no—
411C4⋊Q8—181no—
412#126—181no—
413#126—181no—
414#124—31no—
415#124—91no—
416C22⋊Q8—181no—
417C4×Q8—31no—
418C4×Q8—31no—
419C4×Q8—91no—
420C4×Q8—91no—
421C4×Q8—91no—
422C4×Q8—91no—
423C4×Q8—181no—
424C4×D4—91no—
425#117—181no—
426#106—91no—
427#106—91no—
428#106—91no—
429C4⋊C8—31no—
430C4⋊C8—31no—
431C4⋊C8—91no—
432#103—31no—
433#103—31no—
434#103—31no—
435#103—91no—
436#103—91no—
437#103—91no—
438#103—91no—
439#102—31no—
440#102—91no—
441#102—91no—
442#97—91no—
443#97—91no—
444C4×C8—91no—
445C23×C3—61no—
446C22×D3—21no—
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—22no—
450C3×Q8—21no—
451C3×Q8—21no—
452C3×Q8—21no—
453C3×Q8—21no—
454C3×Q8—22no—
455C3×Q8—41no—
456C3×Q8—41no—
457C3×Q8—61no—
458C3×Q8—61no—
459C3×Q8#23712yes—
460C3×Q8#23712yes—
461C3×D4—61no—
462C3×D4—61no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—31no—
469C2×C3×C4—31no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4C23×D311yescharacteristic
478C2×C3×C4C23×D311yescharacteristic
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—31no—
483C2×Dic3—31no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—121no—
493C2×Dic3—121no—
494C2×Dic3—122no—
495C2×Dic3D3×D411yescharacteristic
496C2×Dic3D3×D411yescharacteristic
497C2×Dic3D3×D411yescharacteristic
498C2×Dic3D3×D411yescharacteristic
499D12—21no—
500D12—21no—
501C4×D3—122no—
502Dic6—21no—
503Dic6—21no—
504Dic6—62no—
505Dic6—62no—
506Dic6—241no—
507Dic6—241no—
508Dic6—241no—
509Dic6—241no—
510Dic6—241no—
511Dic6—241no—
512C3×C8—22no—
513C3×C8—21no—
514C3×C8—21no—
515C3×C8—61no—
516C3×C8—61no—
517C3⋊C8—21no—
518C3⋊C8—21no—
519C3⋊C8—61no—
520C3⋊C8—61no—
521C3⋊C8—121no—
522C2×C32#54811yescharacteristic
523C2×C32C2×#13711yescharacteristic
524C2×C32#57711yescharacteristic
525C3×D3—81no—
526C2×Q8—31no—
527C2×Q8—91no—
528C2×Q8—181no—
529C2×Q8—181no—
530C2×Q8—181no—
531C2×Q8C2×D3211yescharacteristic
532C2×Q8C2×D3211yescharacteristic
533C2×D4—31no—
534C22×C4—181no—
535Q16—22no—
536Q16—62no—
537SD16—62no—
538C2×C8—31no—
539C2×C8—31no—
540C2×C8—91no—
541C2×C8C2×D3211yescharacteristic
542C4⋊C4—31no—
543C4⋊C4—31no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—61no—
548C4⋊C4—91no—
549C4⋊C4—91no—
550C4⋊C4—91no—
551C4⋊C4—91no—
552C4⋊C4—91no—
553C4⋊C4—181no—
554C4⋊C4—181no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C22⋊C4—61no—
560C22⋊C4—61no—
561C22⋊C4—181no—
562C22⋊C4—181no—
563C22⋊C4—181no—
564C42—31no—
565C42—31no—
566C42—61no—
567C42—61no—
568C42—91no—
569C42—181no—
570C42—181no—
571C42—181no—
572C22×C3—21no—
573C22×C3—121no—
574C22×C3—121no—
575C22×C3—121no—
576C22×C3C2×D3×D411yescharacteristic
577C22×C3C2×D3×D411yescharacteristic
578C2×D3—41no—
579C2×D3—41no—
580C2×D3—41no—
581C3×C4—22no—
582C3×C4—22no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—32no—
586C3×C4—42no—
587C3×C4—42no—
588C3×C4—41no—
589C3×C4—41no—
590C3×C4—61no—
591C3×C4—61no—
592C3×C4—61no—
593C3×C4—121no—
594C3×C4—121no—
595C3×C4—121no—
596C3×C4C2×#23711yescharacteristic
597C3×C4C2×#23711yescharacteristic
598C3×C4#101011yescharacteristic
599C3×C4#101011yescharacteristic
600Dic3—21no—
601Dic3—21no—
602Dic3—21no—
603Dic3—41no—
604Dic3—41no—
605Dic3—41no—
606Dic3—61no—
607Dic3—61no—
608Dic3—61no—
609Dic3—61no—
610Dic3—121no—
611Dic3—121no—
612Dic3—121no—
613Dic3—121no—
614Dic3—121no—
615Dic3—121no—
616Dic3—241no—
617Dic3—241no—
618Dic3#91812yes—
619C32#336911yescharacteristic, complemented, Sylow
620C23—61no—
621Q8—21no—
622Q8—21no—
623Q8—21no—
624Q8—61no—
625Q8—61no—
626Q8—182no—
627Q8—721no—
628Q8—721no—
629Q8—721no—
630Q8#380512yes—
631D4—61no—
632D4—61no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—31no—
636C2×C4—31no—
637C2×C4—31no—
638C2×C4—31no—
639C2×C4—61no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—91no—
643C2×C4—91no—
644C2×C4—181no—
645C2×C4—181no—
646C2×C4—362no—
647C2×C4C22×D3211yescharacteristic
648C8—21no—
649C8—61no—
650C8—61no—
651C8—181no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—241no—
656C2×C3#559811yescharacteristic
657C2×C3#559811yescharacteristic
658C2×C3C2×#91811yescharacteristic
659C2×C3#577011yescharacteristic
660C2×C3D3×#13711yescharacteristic
661C2×C3#577811yescharacteristic
662D3—81no—
663C22—121no—
664C22—121no—
665C22—121no—
666C22D32×D411yescharacteristic
667C4—22no—
668C4—32no—
669C4—41no—
670C4—61no—
671C4—61no—
672C4—61no—
673C4—121no—
674C4—121no—
675C4—121no—
676C4—181no—
677C4—181no—
678C4—361no—
679C4—361no—
680C4#6430911yescharacteristic
681C4C2×#380511yescharacteristic
682C3—21no—
683C3#8046411yescharacteristic, complemented
684C3#8058211yescharacteristic, complemented
685C2—241no—
686C2D3×#91811yescharacteristic
687C2#1059477011yescharacteristic
688C2#1059514211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC2×Q16D32
hypocenterC32#3369
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. Q8×#627C2semidirect
3. #10592883C2semidirect
5. C3×#5182C2semidirect
6. #10591630C2semidirect
8. #10591623C2semidirect
10. #10591576C2semidirect
13. #10590803C2semidirect
15. #10590646C2semidirect
73. #5182D3semidirect
619. C32#3369semidirect
683. C3#80464semidirect
684. C3#80582semidirect

Maximal subgroups

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

subgroupindex
Q8×#6272
#105953842
#105928832
C3×#51852
C3×#51822
#105916302
#105916242
#105916232
#105916122
#105915762
Dic3×#2152
#105908662
#105908032
#105907572
#105906462
#805823
#804643