Finite Group Databasebeta

← #11895597

Subgroups — #11895597

Order 1152.

720 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595387C211yesmaximal, characteristic
2#10594321C211yesmaximal, characteristic, complemented
3#10592499C211yesmaximal, characteristic
4C3×#4796C211yesmaximal, characteristic, complemented
5C3×#4795C211yesmaximal, characteristic, complemented
6#10591623C211yesmaximal, characteristic, complemented
7#10591579C211yesmaximal, characteristic
8Dic3×#216C211yesmaximal, characteristic, complemented
9#10590818C211yesmaximal, characteristic, complemented
10#10590801C211yesmaximal, characteristic
11#10590764C211yesmaximal, characteristic
12#10590645C211yesmaximal, characteristic, complemented
13#10590537C211yesmaximal, characteristic
14#10590495C211yesmaximal, characteristic, complemented
15#10590458C211yesmaximal, characteristic
16#81216—31nomaximal
17#80463—31nomaximal
18#64156C2211yescharacteristic
19#64099C2211yescharacteristic
20C3×Q8×Dic3C2211yescharacteristic
21C3×#944C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic
24C3×#890C2211yescharacteristic
25C3×#887C2211yescharacteristic
26#63918—21no—
27#63918C2211yescharacteristic
28C4×#627C2211yescharacteristic
29#63895—21no—
30#63894C2211yescharacteristic
31#63868—21no—
32#63864C2211yescharacteristic
33#63848—21no—
34#63846—21no—
35#63845—21no—
36#63843C2211yescharacteristic
37#63843C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39#63837—21no—
40#63836—21no—
41C2×#3717C2211yescharacteristic
42C32×#103C2211yescharacteristic
43#63662C2211yescharacteristic
44#63648C2211yescharacteristic
45C8×C3⋊Dic3C2211yescharacteristic
46#63636C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#818C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63575C2211yescharacteristic
54#63572C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5732—31no—
62#5685—31no—
63#5570—31no—
64#5568—31no—
65C3×#479—31no—
66C3×#462—31no—
67#5185—31no—
68#5185—31no—
69Dic3×Q16—31no—
70Dic3×Q16—31no—
71#5079—31no—
72#5068—31no—
73C4×#216—31no—
74C4×#215—31no—
75#4890—31no—
76#4873—31no—
77#4857—31no—
78#4852—31no—
79#4846—31no—
80#4845—31no—
81#4830—31no—
82#4830—31no—
83#4800—31no—
84#4800—31no—
85#4800—31no—
86#4800—61no—
87#4798—31no—
88#4796—31no—
89#4796D311yescharacteristic, complemented
90#4795D311yescharacteristic, complemented
91#4792—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C3×Dic6C2311yescharacteristic
95C2×C3×Dic6C2311yescharacteristic
96C2×#627—21no—
97C2×#627D411yescharacteristic
98C2×#624—21no—
99C2×C32×C8C2311yescharacteristic
100C32×C4⋊C4C2311yescharacteristic
101#3752—21no—
102#3752—21no—
103C4⋊(C3⋊Dic3)—21no—
104C4⋊(C3⋊Dic3)C2311yescharacteristic
105#3750—21no—
106C4×C3⋊Dic3C2311yescharacteristic
107C2×C3⋊(C3⋊C8)C2311yescharacteristic
108C3×#216—22no—
109C3×C4⋊Dic3—21no—
110C3×C4⋊Dic3—21no—
111C3×C4⋊Dic3C2311yescharacteristic
112C3×C4⋊Dic3C2311yescharacteristic
113C3×Dic3⋊C4—21no—
114C3×Dic3⋊C4—21no—
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4—21no—
117C3×C4×Dic3—21no—
118C3×C4×Dic3—21no—
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C3×Dic12—22no—
124#3724D411yescharacteristic
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3D411yescharacteristic
130Dic3⋊Dic3D411yescharacteristic
131#3722—21no—
132#3722—21no—
133#3722—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32—21no—
137#3717—22no—
138#3364—91noSylow
139C2×C3×Q16—31no—
140C2×C3×Q16—31no—
141C3×C4⋊Q8—31no—
142C3×#125—31no—
143C3×C4×Q8—31no—
144C3×C4×Q8—31no—
145#947—31no—
146#947—31no—
147#947—31no—
148#947—61no—
149Q8×Dic3—31no—
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152Q8×Dic3C2×D311yescharacteristic
153#944C2×D311yescharacteristic
154C2×#216C2×D311yescharacteristic
155C2×#215—31no—
156C2×Dic12C2×D311yescharacteristic
157C2×#204—31no—
158#898—61no—
159#898—61no—
160#898—61no—
161#897—61no—
162#896—61no—
163#893—31no—
164#892—61no—
165#890—31no—
166#890—31no—
167#890—61no—
168#890—61no—
169#890—61no—
170#890C2×D311yescharacteristic
171#889—61no—
172#889—61no—
173#888—31no—
174#888—61no—
175#887—31no—
176#887—31no—
177#887—61no—
178#887C2×D311yescharacteristic
179#876—61no—
180#875—31no—
181C4×D12—31no—
182#872—61no—
183#869—31no—
184#869—61no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C3×#107—31no—
190C3×#106—31no—
191C3×C4⋊C8—31no—
192C3×C4⋊C8—31no—
193C3×#103—21no—
194C3×#103—31no—
195C3×#103—31no—
196C3×#103C2×D311yescharacteristic
197C3×#103C2×D311yescharacteristic
198#835—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#835—61no—
204#835C2×D311yescharacteristic
205#821—31no—
206#821—31no—
207#821—31no—
208#821—61no—
209#818—31no—
210#818C2×D311yescharacteristic
211#816—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8C2×D311yescharacteristic
215Dic3⋊C8C2×D311yescharacteristic
216C8×Dic3—31no—
217C8×Dic3—31no—
218C8×Dic3—31no—
219C8×Dic3—31no—
220C8×Dic3—61no—
221#810—31no—
222#810—31no—
223#810C2×D311yescharacteristic
224#809—31no—
225#809—31no—
226#809—31no—
227#809—61no—
228#808C2×D311yescharacteristic
229#807—31no—
230C4×C3⋊C8—31no—
231C4×C3⋊C8—31no—
232C22×C3⋊D3—21no—
233C32×Q8—21no—
234C32×Q8—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4C2411yescharacteristic
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3C2×D411yescharacteristic
240C2×C3⋊Dic3C2×D411yescharacteristic
241C4⋊(C3⋊D3)—21no—
242C4⋊(C3⋊D3)—21no—
243C2×C3×Dic3—21no—
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×Dic6—21no—
252C3×Dic6—21no—
253C3×Dic6—21no—
254C3×Dic6#4112yes—
255#627—22no—
256#627—42no—
257#624—42no—
258C32×C8—21no—
259C3⋊(C3⋊C8)—21no—
260C3×C3⋊C8—21no—
261C3×C3⋊C8—21no—
262#557—91no—
263#556—91no—
264#488—91no—
265#488—91no—
266#487—91no—
267#479—31no—
268#479—91no—
269#474—91no—
270#464—91no—
271#464—91no—
272#462—31no—
273C8×Q8—91no—
274C4×Q16—91no—
275C4×Q16—91no—
276C4×SD16—91no—
277C2×C3×Q8—21no—
278C2×C3×Q8—31no—
279C2×C3×Q8—31no—
280C2×C3×Q8C22×D311yescharacteristic
281C2×C3×Q8C22×D311yescharacteristic
282C2×D12—31no—
283C2×D12—31no—
284C2×D12—61no—
285C2×C4×D3—61no—
286C2×C4×D3—61no—
287C2×Dic6—31no—
288C2×Dic6—31no—
289C2×Dic6—61no—
290C2×Dic6—61no—
291C2×Dic6C22×D311yescharacteristic
292C2×Dic6C22×D311yescharacteristic
293C3×Q16—62no—
294C3×Q16—62no—
295C2×C3×C8—21no—
296C2×C3×C8—31no—
297C2×C3×C8—31no—
298C2×C3×C8C22×D311yescharacteristic
299C2×C3×C8C22×D311yescharacteristic
300C3×C4⋊C4—21no—
301C3×C4⋊C4—31no—
302C3×C4⋊C4—31no—
303C3×C4⋊C4—61no—
304C3×C4⋊C4—61no—
305C3×C4⋊C4—61no—
306C3×C4⋊C4—61no—
307C3×C4⋊C4—61no—
308C3×C4⋊C4—61no—
309C3×C4⋊C4C22×D311yescharacteristic
310C3×C4⋊C4C22×D311yescharacteristic
311C3×C42—31no—
312C3×C42—31no—
313C3×C42—61no—
314C3×C42—61no—
315#216—22no—
316#215—62no—
317(C2×D3)⋊C4—61no—
318(C2×D3)⋊C4—61no—
319(C2×D3)⋊C4—61no—
320(C2×D3)⋊C4—61no—
321(C2×D3)⋊C4—61no—
322(C2×D3)⋊C4—61no—
323(C2×D3)⋊C4—61no—
324(C2×D3)⋊C4—61no—
325(C2×D3)⋊C4—61no—
326(C2×D3)⋊C4—61no—
327(C2×D3)⋊C4—121no—
328(C2×D3)⋊C4—121no—
329C4⋊Dic3—21no—
330C4⋊Dic3—21no—
331C4⋊Dic3—31no—
332C4⋊Dic3—31no—
333C4⋊Dic3—31no—
334C4⋊Dic3—31no—
335C4⋊Dic3—61no—
336C4⋊Dic3—61no—
337C4⋊Dic3—61no—
338C4⋊Dic3—61no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—121no—
343C4⋊Dic3C22×D311yescharacteristic
344C4⋊Dic3C22×D311yescharacteristic
345Dic3⋊C4—21no—
346Dic3⋊C4—21no—
347Dic3⋊C4—21no—
348Dic3⋊C4—21no—
349Dic3⋊C4—31no—
350Dic3⋊C4—31no—
351Dic3⋊C4—31no—
352Dic3⋊C4—31no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—121no—
360C4×Dic3—21no—
361C4×Dic3—21no—
362C4×Dic3—31no—
363C4×Dic3—31no—
364C4×Dic3—61no—
365C4×Dic3—61no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3C22×D311yescharacteristic
372C4×Dic3C22×D311yescharacteristic
373C2×C3⋊C8—31no—
374C2×C3⋊C8—31no—
375C2×C3⋊C8—61no—
376C2×C3⋊C8C22×D311yescharacteristic
377C2×C3⋊C8C22×D311yescharacteristic
378Dic12—22no—
379#204—62no—
380C22×C32C22×D411yescharacteristic
381C2×C3⋊D3—41no—
382C2×C3⋊D3—41no—
383C2×C3⋊D3—41no—
384C32×C4—41no—
385C32×C4—41no—
386C32×C4C2×#4111yescharacteristic
387C32×C42−1+411yescharacteristic
388C3⋊Dic3—21no—
389C3⋊Dic3—21no—
390C3⋊Dic3—41no—
391C3×Dic3—22no—
392C3×Dic3—21no—
393C3×Dic3—21no—
394C3×Dic3—21no—
395C3×Dic3—41no—
396C3×Dic3—41no—
397C3×Dic3—41no—
398C3×Dic3#13512yes—
399C2×Q16—31no—
400C2×Q16—31no—
401C2×SD16—91no—
402C4⋊Q8—31no—
403C4⋊Q8—91no—
404C4⋊Q8—181no—
405#126—181no—
406#126—181no—
407#125—31no—
408#125—91no—
409#125—181no—
410#125—181no—
411#124—91no—
412#124—91no—
413C22⋊Q8—181no—
414C4×Q8—31no—
415C4×Q8—31no—
416C4×Q8—91no—
417C4×Q8—91no—
418C4×Q8—91no—
419C4×Q8—91no—
420C4×Q8—181no—
421C4×D4—91no—
422#117—181no—
423#107—31no—
424#107—91no—
425#106—31no—
426C4⋊C8—31no—
427C4⋊C8—31no—
428C4⋊C8—91no—
429#103—31no—
430#103—31no—
431#103—91no—
432#103—91no—
433#103—91no—
434#103—91no—
435#103D3211yescharacteristic
436#102—91no—
437#102—91no—
438#102—91no—
439C4×C8—91no—
440C4×C8—91no—
441C4×C8—91no—
442C22×D3—61no—
443C22×D3—61no—
444C22×D3—121no—
445C3×Q8—21no—
446C3×Q8—21no—
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—32no—
450C3×Q8—41no—
451C3×Q8—41no—
452C3×Q8—61no—
453C3×Q8—61no—
454C3×Q8—61no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—31no—
461C2×C3×C4—31no—
462C2×C3×C4—31no—
463C2×C3×C4—31no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4C23×D311yescharacteristic
471C2×C3×C4C23×D311yescharacteristic
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—31no—
477C2×Dic3—31no—
478C2×Dic3—31no—
479C2×Dic3—31no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—121no—
485C2×Dic3D3×D411yescharacteristic
486C2×Dic3D3×D411yescharacteristic
487C2×Dic3D3×D411yescharacteristic
488C2×Dic3D3×D411yescharacteristic
489D12—61no—
490D12—61no—
491D12—61no—
492D12—61no—
493D12—121no—
494D12—121no—
495C4×D3—122no—
496C4×D3—122no—
497Dic6—21no—
498Dic6—21no—
499Dic6—21no—
500Dic6—62no—
501Dic6—62no—
502Dic6—122no—
503Dic6—122no—
504Dic6#23712yes—
505C3×C8—21no—
506C3×C8—21no—
507C3×C8—41no—
508C3×C8—61no—
509C3×C8—61no—
510C3⋊C8—21no—
511C3⋊C8—21no—
512C3⋊C8—61no—
513C3⋊C8—61no—
514C3⋊C8—121no—
515C2×C32#54811yescharacteristic
516C2×C32C2×#13511yescharacteristic
517C2×C32#57811yescharacteristic
518C3⋊D3—81no—
519C2×Q8—31no—
520C2×Q8—31no—
521C2×Q8—91no—
522C2×Q8—181no—
523C2×Q8C2×D3211yescharacteristic
524C2×D4—91no—
525C22×C4—181no—
526Q16—62no—
527Q16—62no—
528SD16—182no—
529C2×C8—31no—
530C2×C8—31no—
531C2×C8—91no—
532C2×C8C2×D3211yescharacteristic
533C4⋊C4—31no—
534C4⋊C4—31no—
535C4⋊C4—61no—
536C4⋊C4—61no—
537C4⋊C4—61no—
538C4⋊C4—61no—
539C4⋊C4—61no—
540C4⋊C4—61no—
541C4⋊C4—91no—
542C4⋊C4—91no—
543C4⋊C4—91no—
544C4⋊C4—91no—
545C4⋊C4—181no—
546C4⋊C4—181no—
547C4⋊C4—181no—
548C4⋊C4—181no—
549C4⋊C4—181no—
550C4⋊C4—181no—
551C4⋊C4C2×D3211yescharacteristic
552C22⋊C4—181no—
553C22⋊C4—181no—
554C22⋊C4—181no—
555C22⋊C4—181no—
556C22⋊C4—181no—
557C42—31no—
558C42—31no—
559C42—61no—
560C42—61no—
561C42—91no—
562C42—181no—
563C42—181no—
564C42—181no—
565C22×C3—21no—
566C22×C3C2×D3×D411yescharacteristic
567C22×C3C2×D3×D411yescharacteristic
568C2×D3—121no—
569C2×D3—121no—
570C2×D3—121no—
571C2×D3—121no—
572C2×D3—121no—
573C2×D3—121no—
574C2×D3—241no—
575C2×D3—241no—
576C2×D3—241no—
577C3×C4—21no—
578C3×C4—21no—
579C3×C4—32no—
580C3×C4—41no—
581C3×C4—41no—
582C3×C4—41no—
583C3×C4—41no—
584C3×C4—62no—
585C3×C4—61no—
586C3×C4—61no—
587C3×C4—61no—
588C3×C4—81no—
589C3×C4—81no—
590C3×C4—121no—
591C3×C4—121no—
592C3×C4—121no—
593C3×C4C2×#23711yescharacteristic
594C3×C4#100711yescharacteristic
595C3×C4D3×#4111yescharacteristic
596C3×C4#101011yescharacteristic
597Dic3—21no—
598Dic3—21no—
599Dic3—21no—
600Dic3—22no—
601Dic3—41no—
602Dic3—41no—
603Dic3—41no—
604Dic3—61no—
605Dic3—61no—
606Dic3—61no—
607Dic3—61no—
608Dic3—121no—
609Dic3—121no—
610Dic3—121no—
611Dic3—121no—
612Dic3—241no—
613Dic3#91912yes—
614C32#336411yescharacteristic, complemented, Sylow
615C23—181no—
616Q8—21no—
617Q8—21no—
618Q8—32no—
619Q8—61no—
620Q8—61no—
621Q8—61no—
622Q8—182no—
623Q8—362no—
624D4—181no—
625D4—181no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—31no—
629C2×C4—31no—
630C2×C4—31no—
631C2×C4—31no—
632C2×C4—61no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—91no—
637C2×C4—91no—
638C2×C4—181no—
639C2×C4—362no—
640C2×C4C22×D3211yescharacteristic
641C8—21no—
642C8—61no—
643C8—61no—
644C8—181no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3#559811yescharacteristic
649C2×C3#563311yescharacteristic
650C2×C3C2×#91911yescharacteristic
651C2×C3D3×#13511yescharacteristic
652C2×C3#577911yescharacteristic
653C2×C3#577911yescharacteristic
654D3—241no—
655D3—241no—
656D3—481no—
657C22—361no—
658C22—361no—
659C22—361no—
660C22D32×D411yescharacteristic
661C4—32no—
662C4—41no—
663C4—41no—
664C4—62no—
665C4—61no—
666C4—61no—
667C4—61no—
668C4—121no—
669C4—121no—
670C4—121no—
671C4—181no—
672C4—181no—
673C4—361no—
674C4#6429711yescharacteristic
675C4D3×#23711yescharacteristic
676C3—21no—
677C3#8046311yescharacteristic, complemented
678C3#8121611yescharacteristic, complemented
679C2—721no—
680C2#1059407411yescharacteristic
681C2#1059475211yescharacteristic
682C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenter#103D32
hypocenterC32#3364
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. #10594321C2semidirect
4. C3×#4796C2semidirect
5. C3×#4795C2semidirect
6. #10591623C2semidirect
8. Dic3×#216C2semidirect
9. #10590818C2semidirect
12. #10590645C2semidirect
14. #10590495C2semidirect
89. #4796D3semidirect
90. #4795D3semidirect
614. C32#3364semidirect
677. C3#80463semidirect
678. C3#81216semidirect

Maximal subgroups

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

subgroupindex
#105953872
#105943212
#105924992
C3×#47962
C3×#47952
#105916232
#105915792
Dic3×#2162
#105908182
#105908012
#105907642
#105906452
#105905372
#105904952
#105904582
#812163
#804633