Finite Group Databasebeta

← #11872590

Subgroups — #11872590

Order 1152.

788 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594984C211yesmaximal, characteristic
2#10594818C211yesmaximal, characteristic, complemented
3#10592419C211yesmaximal, characteristic, complemented
4C3×#4738C211yesmaximal, characteristic
5C3×#4723C211yesmaximal, characteristic, complemented
6#10591185C211yesmaximal, characteristic, complemented
7#10591090C211yesmaximal, characteristic
8#10590817C211yesmaximal, characteristic, complemented
9#10590816C211yesmaximal, characteristic, complemented
10#10590796C211yesmaximal, characteristic, complemented
11#10590796C211yesmaximal, characteristic, complemented
12#10590791C211yesmaximal, characteristic, complemented
13#10590790C211yesmaximal, characteristic, complemented
14#10590779C211yesmaximal, characteristic, complemented
15#10590775C211yesmaximal, characteristic, complemented
16#81497—31nomaximal
17#80032—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19#64135C2211yescharacteristic
20C3×#930C2211yescharacteristic
21C3×#926C2211yescharacteristic
22C3×#924C2211yescharacteristic
23C2×C3×#204C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25#63969—21no—
26#63959—21no—
27#63955—21no—
28#63955—21no—
29#63919C2211yescharacteristic
30#63898C2211yescharacteristic
31#63893—21no—
32#63863C2211yescharacteristic
33#63861—21no—
34#63843C2211yescharacteristic
35#63843C2211yescharacteristic
36#63843C2211yescharacteristic
37#63843C2211yescharacteristic
38#63843C2211yescharacteristic
39Dic3×Dic6—21no—
40Dic3×Dic6—21no—
41C2×#3718C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C32×C22⋊C8C2211yescharacteristic
44#63657C2211yescharacteristic
45#63642C2211yescharacteristic
46#63641C2211yescharacteristic
47#63641C2211yescharacteristic
48C8×C3⋊Dic3C2211yescharacteristic
49C3×#818C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55#63576C2211yescharacteristic
56#63574C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61#5812—31no—
62#5643—31no—
63#5603—31no—
64#5516—31no—
65C3×#485—31no—
66C3×#448—31no—
67#5228—31no—
68#5166—31no—
69#5166—31no—
70#5164—31no—
71Dic3×SD16—31no—
72#5050—31no—
73#5035—31no—
74#5003—31no—
75#4889—31no—
76#4875—31no—
77#4854—31no—
78#4852—31no—
79#4798—31no—
80#4798—31no—
81#4793—31no—
82#4791—31no—
83#4790—31no—
84#4790—31no—
85#4789—31no—
86#4789—31no—
87#4738D311yescharacteristic
88#4723D311yescharacteristic, complemented
89#4720—31no—
90#4720—31no—
91#4720—61no—
92C22×C32×C4C2311yescharacteristic
93C2×C3×#67—21no—
94C22×C3×Dic3—21no—
95C2×C3×D12C2311yescharacteristic
96C2×C3×Dic6—21no—
97C2×C3×Dic6—22no—
98C2×C3×Dic6—22no—
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#627—21no—
103C2×D3×Dic3—21no—
104C2×C32×C8C2311yescharacteristic
105C2×C32×C8C2311yescharacteristic
106#3757D411yescharacteristic
107#3757D411yescharacteristic
108C4⋊(C3⋊Dic3)D411yescharacteristic
109C4⋊(C3⋊Dic3)D411yescharacteristic
110C4×C3⋊Dic3C2311yescharacteristic
111C4×C3⋊Dic3C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×#217—21no—
115C3×#217—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×C4×Dic3—21no—
123C3×#204—22no—
124C3×#204—22no—
125#3724—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139#3718—22no—
140#3718—22no—
141#3121—91noSylow
142C22×C3×Q8—31no—
143C22×Dic6C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C3×C22⋊Q8—31no—
147C3×#121—31no—
148C3×#117—31no—
149#947—31no—
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154Q8×Dic3—31no—
155Q8×Dic3—61no—
156Q8×Dic3—61no—
157C2×#216—31no—
158C2×#216—31no—
159C2×#216—31no—
160C2×#216—31no—
161#936—31no—
162#936—61no—
163#935—61no—
164D4×Dic3—31no—
165#930C2×D311yescharacteristic
166#926—31no—
167#926—31no—
168#926—61no—
169#926—61no—
170#926—61no—
171#926C2×D311yescharacteristic
172#924C2×D311yescharacteristic
173C2×#204C2×D311yescharacteristic
174C2×#204C2×D311yescharacteristic
175#898—61no—
176#897—61no—
177#893—31no—
178#888—31no—
179#888—31no—
180#887—31no—
181#887—31no—
182#887—31no—
183#887—31no—
184#887—31no—
185#885—61no—
186#883—61no—
187#879—61no—
188#878—61no—
189#877—61no—
190#877—61no—
191C4×Dic6—61no—
192C4×Dic6—61no—
193C3×#107—31no—
194C3×#106—31no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#103—31no—
198C3×#103—31no—
199C3×C22⋊C8—21no—
200C3×C22⋊C8C2×D311yescharacteristic
201C3×C22⋊C8C2×D311yescharacteristic
202#835—31no—
203#835—31no—
204#832—31no—
205#832—31no—
206#830—31no—
207#830—31no—
208#830—61no—
209#818C2×D311yescharacteristic
210#817C2×D311yescharacteristic
211#816C2×D311yescharacteristic
212#816C2×D311yescharacteristic
213#816C2×D311yescharacteristic
214#816C2×D311yescharacteristic
215#815—31no—
216#815—31no—
217#815—61no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8—31no—
222Dic3⋊C8—61no—
223Dic3⋊C8—61no—
224C8×Dic3—31no—
225C8×Dic3—31no—
226C8×Dic3—61no—
227#810—31no—
228#810—31no—
229#809—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4C2×D411yescharacteristic
240C2×C32×C4C2411yescharacteristic
241C2×C3⋊Dic3C2×D411yescharacteristic
242C2×C3⋊Dic3C2×D411yescharacteristic
243C2×C3⋊Dic3C2×D411yescharacteristic
244C2×C3⋊Dic3C2×D411yescharacteristic
245C3×#67—81no—
246C2×C3×Dic3—24no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C3×D12—21no—
255C3×D12—21no—
256C3×Dic6—24no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6—21no—
261C3×Dic6#4112yes—
262C3×Dic6#4112yes—
263#627—81no—
264D3×Dic3—81no—
265C32×C8—21no—
266C32×C8—21no—
267C3⋊(C3⋊C8)—21no—
268C3⋊(C3⋊C8)—21no—
269#542—91no—
270#519—91no—
271#485—31no—
272#482—91no—
273#477—91no—
274#475—91no—
275#464—91no—
276#464—91no—
277#451—91no—
278#448—31no—
279#441—91no—
280#440—91no—
281C4×Q16—91no—
282C4×SD16—91no—
283#433—91no—
284C2×C3×Q8—31no—
285C2×C3×Q8—31no—
286C2×C3×Q8—31no—
287C2×C3×Q8—62no—
288C2×C3×Q8—62no—
289C2×C3×Q8—61no—
290C2×C3×D4—31no—
291C2×C3×D4—61no—
292C22×C3×C4—21no—
293C22×C3×C4—61no—
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C2×#67—21no—
297C22×Dic3—21no—
298C22×Dic3—61no—
299C2×D12C22×D311yescharacteristic
300C2×C4×D3—61no—
301C2×Dic6—21no—
302C2×Dic6—22no—
303C2×Dic6—22no—
304C2×Dic6—61no—
305C2×Dic6—61no—
306C2×Dic6C22×D311yescharacteristic
307C2×Dic6C22×D311yescharacteristic
308C2×Dic6C22×D311yescharacteristic
309C3×SD16—62no—
310C3×SD16—62no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8C22×D311yescharacteristic
314C2×C3×C8C22×D311yescharacteristic
315C2×C3×C8C22×D311yescharacteristic
316C2×C3×C8C22×D311yescharacteristic
317C3×C4⋊C4—31no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—61no—
322C3×C22⋊C4—61no—
323C3×C22⋊C4—61no—
324C3×C22⋊C4—61no—
325C3×C42—61no—
326#217—21no—
327#217—21no—
328#217—31no—
329#217—31no—
330#217—31no—
331#217—31no—
332#217—61no—
333#217—61no—
334#217—61no—
335#217—61no—
336#217—61no—
337#216—62no—
338#216—62no—
339#216—62no—
340#216—62no—
341(C2×D3)⋊C4—21no—
342(C2×D3)⋊C4—61no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345C4⋊Dic3—31no—
346C4⋊Dic3—31no—
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3C22×D311yescharacteristic
357C4⋊Dic3C22×D311yescharacteristic
358C4⋊Dic3C22×D311yescharacteristic
359C4⋊Dic3C22×D311yescharacteristic
360Dic3⋊C4—21no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368C4×Dic3—21no—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—31no—
372C4×Dic3—31no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—61no—
390C2×C3⋊C8—61no—
391#204—22no—
392#204—22no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32C22×D411yescharacteristic
397C2×C3×D3—41no—
398C2×C3×D3—41no—
399C2×C3×D3—41no—
400C32×C4—21no—
401C32×C4C2×#4111yescharacteristic
402C32×C4C2×#4111yescharacteristic
403C3⋊Dic3—21no—
404C3⋊Dic3—21no—
405C3⋊Dic3—21no—
406C3⋊Dic3—21no—
407C3×Dic3—22no—
408C3×Dic3—22no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C3×Dic3—41no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C22×Q8—31no—
415C2×Q16—91no—
416C2×Q16—91no—
417C2×SD16—31no—
418C2×SD16—31no—
419C4⋊Q8—91no—
420#126—181no—
421#124—91no—
422#124—181no—
423#123—181no—
424C22⋊Q8—31no—
425C22⋊Q8—181no—
426#121—31no—
427C4×Q8—91no—
428C4×Q8—91no—
429C4×Q8—91no—
430C4×Q8—91no—
431C4×Q8—91no—
432C4×Q8—181no—
433C4×Q8—181no—
434C4×D4—91no—
435#117—31no—
436#117—91no—
437#117—181no—
438#117—181no—
439#107—31no—
440#107—91no—
441#106—31no—
442#106—91no—
443C4⋊C8—91no—
444C4⋊C8—91no—
445#103—31no—
446#103—31no—
447#103—31no—
448#103—31no—
449#103—91no—
450#103—91no—
451#102—91no—
452#102—91no—
453C22⋊C8—91no—
454C22⋊C8D3211yescharacteristic
455#97—91no—
456C4×C8—91no—
457C23×C3—21no—
458C23×C3—61no—
459C23×C3D3×D411yescharacteristic
460C23×C3D3×D411yescharacteristic
461C22×D3—21no—
462C3×Q8—32no—
463C3×Q8—32no—
464C3×Q8—64no—
465C3×Q8—61no—
466C3×Q8—61no—
467C3×Q8—61no—
468C3×Q8—61no—
469C3×D4—61no—
470C3×D4—61no—
471C3×D4—241no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—64no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4D3×D411yescharacteristic
489C2×C3×C4D3×D411yescharacteristic
490C2×C3×C4C23×D311yescharacteristic
491C2×C3×C4C23×D311yescharacteristic
492#67—81no—
493C2×Dic3—24no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—31no—
502C2×Dic3—31no—
503C2×Dic3—31no—
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—31no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—241no—
514D12—21no—
515D12—21no—
516C4×D3—241no—
517Dic6—24no—
518Dic6—21no—
519Dic6—21no—
520Dic6—21no—
521Dic6—21no—
522Dic6—241no—
523Dic6—241no—
524Dic6#23712yes—
525Dic6#23712yes—
526C3×C8—21no—
527C3×C8—21no—
528C3×C8—21no—
529C3×C8—21no—
530C3×C8—41no—
531C3×C8—41no—
532C3⋊C8—61no—
533C3⋊C8—61no—
534C3⋊C8—61no—
535C3⋊C8—61no—
536C3⋊C8—121no—
537C3⋊C8—121no—
538C2×C32—41no—
539C2×C32#52511yescharacteristic
540C2×C32#57711yescharacteristic
541C2×C32#57811yescharacteristic
542C3×D3—81no—
543C2×Q8—31no—
544C2×Q8—31no—
545C2×Q8—31no—
546C2×Q8—62no—
547C2×Q8—62no—
548C2×Q8—61no—
549C2×Q8—181no—
550C2×D4—31no—
551C2×D4—61no—
552C22×C4—61no—
553C22×C4—181no—
554C22×C4C2×D3211yescharacteristic
555Q16—182no—
556Q16—182no—
557SD16—62no—
558SD16—62no—
559C2×C8—91no—
560C2×C8—91no—
561C2×C8C2×D3211yescharacteristic
562C2×C8C2×D3211yescharacteristic
563C4⋊C4—31no—
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—31no—
567C4⋊C4—61no—
568C4⋊C4—91no—
569C4⋊C4—91no—
570C4⋊C4—181no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4—181no—
574C4⋊C4—181no—
575C4⋊C4—181no—
576C22⋊C4—61no—
577C22⋊C4—61no—
578C22⋊C4—61no—
579C22⋊C4—91no—
580C22⋊C4—91no—
581C22⋊C4—181no—
582C22⋊C4—181no—
583C22⋊C4—181no—
584C42—61no—
585C42—91no—
586C42—91no—
587C42—181no—
588C42—181no—
589C42—181no—
590C42—181no—
591C42—181no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—121no—
603C22×C3—121no—
604C22×C3—121no—
605C22×C3C2×D3×D411yescharacteristic
606C22×C3C2×D3×D411yescharacteristic
607C2×D3—41no—
608C2×D3—41no—
609C2×D3—41no—
610C3×C4—21no—
611C3×C4—21no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—41no—
615C3×C4—62no—
616C3×C4—62no—
617C3×C4—121no—
618C3×C4—121no—
619C3×C4—121no—
620C3×C4—121no—
621C3×C4—121no—
622C3×C4C2×#23711yescharacteristic
623C3×C4C2×#23711yescharacteristic
624C3×C4D3×#4111yescharacteristic
625C3×C4D3×#4111yescharacteristic
626Dic3—22no—
627Dic3—22no—
628Dic3—41no—
629Dic3—41no—
630Dic3—41no—
631Dic3—41no—
632Dic3—41no—
633Dic3—61no—
634Dic3—61no—
635Dic3—61no—
636Dic3—61no—
637Dic3—61no—
638Dic3—61no—
639Dic3—61no—
640Dic3—61no—
641Dic3—121no—
642Dic3—121no—
643Dic3—121no—
644Dic3—121no—
645C32#312111yescharacteristic, complemented, Sylow
646C23—61no—
647C23#380211yescharacteristic
648Q8—32no—
649Q8—32no—
650Q8—64no—
651Q8—61no—
652Q8—61no—
653Q8—61no—
654Q8—61no—
655Q8—721no—
656D4—61no—
657D4—61no—
658D4—241no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—64no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—91no—
670C2×C4—91no—
671C2×C4—91no—
672C2×C4—91no—
673C2×C4—721no—
674C2×C4#380211yescharacteristic
675C2×C4C22×D3211yescharacteristic
676C8—21no—
677C8—21no—
678C8—181no—
679C8—181no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—41no—
684C2×C3—41no—
685C2×C3—81no—
686C2×C3—241no—
687C2×C3#558611yescharacteristic
688C2×C3#565611yescharacteristic
689C2×C3#576211yescharacteristic
690C2×C3#577011yescharacteristic
691C2×C3#577911yescharacteristic
692C2×C3#577911yescharacteristic
693D3—81no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—121no—
698C22—121no—
699C22—121no—
700C22C2×#380211yescharacteristic
701C4—21no—
702C4—62no—
703C4—62no—
704C4—121no—
705C4—121no—
706C4—121no—
707C4—121no—
708C4—121no—
709C4—181no—
710C4—181no—
711C4—181no—
712C4—181no—
713C4D3×#23711yescharacteristic
714C4D3×#23711yescharacteristic
715C3—21no—
716C3#8003211yescharacteristic, complemented
717C3#8149711yescharacteristic, complemented
718C2—41no—
719C2—241no—
720C2#1059408211yescharacteristic
721C2#1059468611yescharacteristic
722C2#1059472311yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC3×#930C22
hypercenterC22⋊C8D32
hypocenterC32#3121
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10594818C2semidirect
3. #10592419C2semidirect
5. C3×#4723C2semidirect
6. #10591185C2semidirect
8. #10590817C2semidirect
9. #10590816C2semidirect
10. #10590796C2semidirect
11. #10590796C2semidirect
12. #10590791C2semidirect
13. #10590790C2semidirect
14. #10590779C2semidirect
15. #10590775C2semidirect
88. #4723D3semidirect
645. C32#3121semidirect
716. C3#80032semidirect
717. C3#81497semidirect

Maximal subgroups

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

subgroupindex
#105949842
#105948182
#105924192
C3×#47382
C3×#47232
#105911852
#105910902
#105908172
#105908162
#105907962
#105907912
#105907902
#105907792
#105907752
#814973
#800323