Finite Group Databasebeta

← #11896059

Subgroups — #11896059

Order 1152.

732 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#627C211yesmaximal, characteristic, complemented
2#10595387C211yesmaximal, characteristic
3#10592884C211yesmaximal, characteristic
4C3×#5184C211yesmaximal, characteristic, complemented
5C3×#5182C211yesmaximal, characteristic, complemented
6#10591632C211yesmaximal, characteristic
7#10591623C211yesmaximal, characteristic, complemented
8#10591607C211yesmaximal, characteristic
9#10591582C211yesmaximal, characteristic, complemented
10#10591544C211yesmaximal, characteristic, complemented
11#10591536C211yesmaximal, characteristic
12#10590893C211yesmaximal, characteristic
13#10590816C211yesmaximal, characteristic, complemented
14#10590786C211yesmaximal, characteristic, complemented
15#10590759C211yesmaximal, characteristic
16#80464—31nomaximal
17#79815—31nomaximal
18C2×C32×Q16C2211yescharacteristic
19#64156C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C3×#944C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27#63919—21no—
28#63919C2211yescharacteristic
29#63918—21no—
30#63918—21no—
31#63918C2211yescharacteristic
32#63918C2211yescharacteristic
33C4×#627—21no—
34C4×#627C2211yescharacteristic
35#63895—21no—
36#63894C2211yescharacteristic
37#63868—21no—
38#63864C2211yescharacteristic
39#63848—21no—
40#63843C2211yescharacteristic
41#63836—21no—
42#63662C2211yescharacteristic
43#63648C2211yescharacteristic
44#63641C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52#63574C2211yescharacteristic
53#63573C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63555C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5732—31no—
62#5568—31no—
63Q8×Dic6—31no—
64Q8×Dic6—31no—
65C3×#462—31no—
66C3×#441—31no—
67#5185—31no—
68#5185—31no—
69#5185—31no—
70#5185—61no—
71#5184—31no—
72#5184D311yescharacteristic, complemented
73#5182D311yescharacteristic, complemented
74#5079—31no—
75#5028—31no—
76C4×#215—31no—
77#5020—31no—
78#4870—31no—
79#4854—31no—
80#4842—31no—
81#4831—31no—
82#4794—31no—
83#4794—31no—
84#4794—31no—
85#4792—31no—
86#4791—31no—
87#4791—31no—
88#4789—31no—
89#4788—31no—
90#4714—31no—
91#4701—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C3×Dic6C2311yescharacteristic
96C2×#627—21no—
97C2×#627—21no—
98C2×#627—21no—
99C2×#627D411yescharacteristic
100C2×#624—21no—
101C32×Q16—22no—
102C2×C32×C8C2311yescharacteristic
103#3755—22no—
104#3752—21no—
105#3752—21no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4×C3⋊Dic3—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#216—22no—
112C3×C4⋊Dic3—21no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×C4×Dic3—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#3722—21no—
135#3722—21no—
136#3722—21no—
137Dic32—21no—
138#3369—91noSylow
139C2×C3×Q16—21no—
140C2×C3×Q16—31no—
141C2×C3×Q16C2×D311yescharacteristic
142C2×C3×Q16C2×D311yescharacteristic
143C3×C4⋊Q8—31no—
144C3×C4×Q8—31no—
145C3×C4×Q8—31no—
146C3×C4×Q8—31no—
147#947—31no—
148#947—31no—
149#947—31no—
150#947—61no—
151Q8×Dic3—31no—
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154Q8×Dic3—61no—
155Q8×Dic3C2×D311yescharacteristic
156Q8×Dic3C2×D311yescharacteristic
157Q8×Dic3C2×D311yescharacteristic
158#944C2×D311yescharacteristic
159C2×#216C2×D311yescharacteristic
160C2×#215—31no—
161C2×#215—31no—
162C2×#215—61no—
163#898—61no—
164#898—61no—
165#898—61no—
166#897—61no—
167#896—61no—
168#893—31no—
169#892—61no—
170#888—31no—
171#888—31no—
172#888—31no—
173#888—31no—
174#888—61no—
175#888—61no—
176#888—61no—
177#888—61no—
178#887—31no—
179#876—61no—
180#875—31no—
181C4×D12—31no—
182#872—61no—
183#869—31no—
184#869—31no—
185#869—61no—
186#869—61no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—61no—
190C4×Dic6—61no—
191C3×#106—31no—
192C3×C4⋊C8—31no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#97—31no—
198#835—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—61no—
203#835C2×D311yescharacteristic
204#835C2×D311yescharacteristic
205#835C2×D311yescharacteristic
206#821—31no—
207#821—31no—
208#821—31no—
209#821—31no—
210#821—61no—
211#817—31no—
212#817C2×D311yescharacteristic
213#816—31no—
214#816C2×D311yescharacteristic
215#815—31no—
216#815—31no—
217#815C2×D311yescharacteristic
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8—61no—
222Dic3⋊C8C2×D311yescharacteristic
223C8×Dic3—31no—
224#810—31no—
225#809—31no—
226#809—31no—
227#808—31no—
228#808—31no—
229#808—31no—
230C4⋊(C3⋊C8)—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⋊Dic3C2×D411yescharacteristic
242C2×C3⋊Dic3C2×D411yescharacteristic
243C4⋊(C3⋊D3)—21no—
244C4⋊(C3⋊D3)—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C3×Dic6—21no—
254C3×Dic6—21no—
255#627—22no—
256#627—81no—
257#627—81no—
258#627—81no—
259#624—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—91no—
273#464—91no—
274#462—31no—
275#446—91no—
276#441—31no—
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×D12—31no—
287C2×D12—31no—
288C2×D12—61no—
289C2×C4×D3—61no—
290C2×C4×D3—61no—
291C2×Dic6—31no—
292C2×Dic6—31no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6—61no—
299C2×Dic6C22×D311yescharacteristic
300C3×Q16—22no—
301C3×Q16—22no—
302C3×Q16—42no—
303C3×Q16—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—31no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C42—31no—
318C3×C42—31no—
319C3×C42—61no—
320C3×C42—61no—
321C3×C42—61no—
322#216—22no—
323#215—62no—
324#215—62no—
325#215—122no—
326(C2×D3)⋊C4—61no—
327(C2×D3)⋊C4—61no—
328(C2×D3)⋊C4—61no—
329(C2×D3)⋊C4—61no—
330(C2×D3)⋊C4—61no—
331(C2×D3)⋊C4—61no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—121no—
337(C2×D3)⋊C4—121no—
338C4⋊Dic3—21no—
339C4⋊Dic3—21no—
340C4⋊Dic3—21no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—31no—
344C4⋊Dic3—31no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—121no—
352C4⋊Dic3C22×D311yescharacteristic
353C4⋊Dic3C22×D311yescharacteristic
354C4⋊Dic3C22×D311yescharacteristic
355Dic3⋊C4—21no—
356Dic3⋊C4—21no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366C4×Dic3—21no—
367C4×Dic3—21no—
368C4×Dic3—21no—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—121no—
377C4×Dic3C22×D311yescharacteristic
378C4×Dic3C22×D311yescharacteristic
379C2×C3⋊C8—31no—
380C2×C3⋊C8—31no—
381C2×C3⋊C8—61no—
382C2×C3⋊C8C22×D311yescharacteristic
383C2×C3⋊C8C22×D311yescharacteristic
384C22×C32C22×D411yescharacteristic
385C2×C3⋊D3—41no—
386C2×C3⋊D3—41no—
387C2×C3⋊D3—41no—
388C32×C4—22no—
389C32×C4—41no—
390C32×C4C2×#4111yescharacteristic
391C32×C42−1+411yescharacteristic
392C3⋊Dic3—21no—
393C3⋊Dic3—21no—
394C3⋊Dic3—41no—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3—41no—
402C3×Dic3#13712yes—
403C2×Q16—31no—
404C2×Q16D3211yescharacteristic
405C2×SD16—91no—
406C4⋊Q8—31no—
407C4⋊Q8—91no—
408C4⋊Q8—91no—
409C4⋊Q8—91no—
410C4⋊Q8—181no—
411C4⋊Q8—181no—
412C4⋊Q8—181no—
413#126—181no—
414#126—181no—
415#124—91no—
416#124—91no—
417C22⋊Q8—181no—
418C4×Q8—31no—
419C4×Q8—31no—
420C4×Q8—31no—
421C4×Q8—91no—
422C4×Q8—91no—
423C4×Q8—91no—
424C4×Q8—181no—
425C4×D4—91no—
426#117—181no—
427#106—31no—
428#106—91no—
429#106—91no—
430C4⋊C8—31no—
431C4⋊C8—91no—
432C4⋊C8—91no—
433#103—31no—
434#103—31no—
435#103—31no—
436#103—31no—
437#103—91no—
438#103—91no—
439#103—91no—
440#102—91no—
441#102—91no—
442#102—91no—
443#97—31no—
444#97—91no—
445C4×C8—91no—
446C22×D3—61no—
447C22×D3—61no—
448C22×D3—121no—
449C3×Q8—21no—
450C3×Q8—21no—
451C3×Q8—21no—
452C3×Q8—21no—
453C3×Q8—21no—
454C3×Q8—21no—
455C3×Q8—22no—
456C3×Q8—41no—
457C3×Q8—41no—
458C3×Q8—41no—
459C3×Q8—61no—
460C3×Q8—61no—
461C3×Q8#23512yes—
462C3×Q8#23712yes—
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×C4—61no—
478C2×C3×C4C23×D311yescharacteristic
479C2×C3×C4C23×D311yescharacteristic
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—31no—
487C2×Dic3—31no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—121no—
493C2×Dic3D3×D411yescharacteristic
494C2×Dic3D3×D411yescharacteristic
495C2×Dic3D3×D411yescharacteristic
496C2×Dic3D3×D411yescharacteristic
497D12—61no—
498D12—61no—
499D12—61no—
500D12—61no—
501D12—121no—
502D12—121no—
503C4×D3—122no—
504C4×D3—122no—
505Dic6—21no—
506Dic6—21no—
507Dic6—62no—
508Dic6—62no—
509Dic6—241no—
510Dic6—241no—
511Dic6—241no—
512Dic6—241no—
513Dic6—241no—
514Dic6—241no—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—41no—
518C3×C8—61no—
519C3×C8—61no—
520C3⋊C8—21no—
521C3⋊C8—21no—
522C3⋊C8—61no—
523C3⋊C8—61no—
524C3⋊C8—121no—
525C2×C32#54811yescharacteristic
526C2×C32C2×#13711yescharacteristic
527C2×C32#57711yescharacteristic
528C3⋊D3—81no—
529C2×Q8—31no—
530C2×Q8—91no—
531C2×Q8—181no—
532C2×Q8—181no—
533C2×Q8—181no—
534C2×Q8C2×D3211yescharacteristic
535C2×Q8C2×D3211yescharacteristic
536C2×D4—91no—
537C22×C4—181no—
538Q16—22no—
539Q16—62no—
540SD16—182no—
541C2×C8—31no—
542C2×C8—31no—
543C2×C8—91no—
544C2×C8C2×D3211yescharacteristic
545C4⋊C4—31no—
546C4⋊C4—31no—
547C4⋊C4—31no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—91no—
554C4⋊C4—91no—
555C4⋊C4—91no—
556C4⋊C4—91no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C22⋊C4—181no—
563C22⋊C4—181no—
564C22⋊C4—181no—
565C22⋊C4—181no—
566C22⋊C4—181no—
567C42—31no—
568C42—31no—
569C42—61no—
570C42—61no—
571C42—61no—
572C42—91no—
573C42—181no—
574C42—181no—
575C22×C3—21no—
576C22×C3C2×D3×D411yescharacteristic
577C22×C3C2×D3×D411yescharacteristic
578C2×D3—121no—
579C2×D3—121no—
580C2×D3—121no—
581C2×D3—121no—
582C2×D3—121no—
583C2×D3—121no—
584C2×D3—241no—
585C2×D3—241no—
586C2×D3—241no—
587C3×C4—22no—
588C3×C4—22no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—32no—
592C3×C4—42no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—61no—
596C3×C4—61no—
597C3×C4—61no—
598C3×C4—81no—
599C3×C4—121no—
600C3×C4—121no—
601C3×C4—121no—
602C3×C4—121no—
603C3×C4C2×#23511yescharacteristic
604C3×C4C2×#23711yescharacteristic
605C3×C4#101011yescharacteristic
606C3×C4#101011yescharacteristic
607Dic3—21no—
608Dic3—21no—
609Dic3—21no—
610Dic3—41no—
611Dic3—41no—
612Dic3—41no—
613Dic3—41no—
614Dic3—61no—
615Dic3—61no—
616Dic3—61no—
617Dic3—61no—
618Dic3—121no—
619Dic3—121no—
620Dic3—121no—
621Dic3—121no—
622Dic3—241no—
623Dic3#91812yes—
624C32#336911yescharacteristic, complemented, Sylow
625C23—181no—
626Q8—21no—
627Q8—21no—
628Q8—21no—
629Q8—61no—
630Q8—61no—
631Q8—182no—
632Q8—721no—
633Q8—721no—
634Q8—721no—
635Q8#380412yes—
636D4—181no—
637D4—181no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—31no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—91no—
649C2×C4—91no—
650C2×C4—181no—
651C2×C4—362no—
652C2×C4C22×D3211yescharacteristic
653C8—21no—
654C8—61no—
655C8—61no—
656C8—181no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3#555211yescharacteristic
661C2×C3#559811yescharacteristic
662C2×C3C2×#91811yescharacteristic
663C2×C3D3×#13711yescharacteristic
664C2×C3#577811yescharacteristic
665C2×C3#577811yescharacteristic
666D3—241no—
667D3—241no—
668D3—481no—
669C22—361no—
670C22—361no—
671C22—361no—
672C22D32×D411yescharacteristic
673C4—22no—
674C4—32no—
675C4—41no—
676C4—61no—
677C4—61no—
678C4—61no—
679C4—121no—
680C4—121no—
681C4—121no—
682C4—121no—
683C4—181no—
684C4—181no—
685C4—361no—
686C4#6430911yescharacteristic
687C4C2×#380411yescharacteristic
688C3—21no—
689C3#7981511yescharacteristic, complemented
690C3#8046411yescharacteristic, complemented
691C2—721no—
692C2D3×#91811yescharacteristic
693C2#1059476711yescharacteristic
694C2#1059514111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
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
4. C3×#5184C2semidirect
5. C3×#5182C2semidirect
7. #10591623C2semidirect
9. #10591582C2semidirect
10. #10591544C2semidirect
13. #10590816C2semidirect
14. #10590786C2semidirect
72. #5184D3semidirect
73. #5182D3semidirect
624. C32#3369semidirect
689. C3#79815semidirect
690. C3#80464semidirect

Maximal subgroups

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

subgroupindex
Q8×#6272
#105953872
#105928842
C3×#51842
C3×#51822
#105916322
#105916232
#105916072
#105915822
#105915442
#105915362
#105908932
#105908162
#105907862
#105907592
#804643
#798153