Finite Group Databasebeta

← #11866260

Subgroups — #11866260

Order 1152.

1050 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63794C211yesmaximal, characteristic
2C2×D3×#204C211yesmaximal, characteristic, complemented
3#10593994C211yesmaximal, characteristic, complemented
4#10593893C211yesmaximal, characteristic, complemented
5#10592543C211yesmaximal, characteristic, complemented
6C3×#4841C211yesmaximal, characteristic, complemented
7C3×#4839C211yesmaximal, characteristic, complemented
8#10590948C211yesmaximal, characteristic, complemented
9#10590770C211yesmaximal, characteristic, complemented
10#10590760C211yesmaximal, characteristic, complemented
11#10590754C211yesmaximal, characteristic, complemented
12#10590752C211yesmaximal, characteristic, complemented
13#10590690C211yesmaximal, characteristic, complemented
14#10590379C211yesmaximal, characteristic, complemented
15#10590366C211yesmaximal, characteristic, complemented
16#80430—31nomaximal
17#79087—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×#3745C2211yescharacteristic
22C2×#3744C2211yescharacteristic
23#64084C2211yescharacteristic, complemented
24C4×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×C4×D12C2211yescharacteristic
30C3×#872C2211yescharacteristic
31C3×#869C2211yescharacteristic, complemented
32#63921—21no—
33D3×(C2×D3)⋊C4—21no—
34#63904—21no—
35#63895—21no—
36#63895—21no—
37#63894C2211yescharacteristic
38Dic3×D12C2211yescharacteristic
39#63890—21no—
40#63890—21no—
41#63881—21no—
42#63866C2211yescharacteristic, complemented
43#63864C2211yescharacteristic, complemented
44#63841C2211yescharacteristic
45C2×#3717C2211yescharacteristic
46C2×#3717C2211yescharacteristic
47C2×#3716C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49#63794—24no—
50D3×#204—24no—
51C32×C4⋊C8C2211yescharacteristic, complemented
52#63648C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54C3×#816C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×D3×SD16—31no—
65C2×#908—31no—
66C22×#204—31no—
67#5724—31no—
68#5545—31no—
69#5526—31no—
70#5521—31no—
71C3×#461—31no—
72C3×#424—31no—
73#5165—31no—
74#5162—31no—
75#5120—31no—
76#5113—31no—
77#5083—31no—
78#5016—31no—
79#4844—31no—
80#4844—31no—
81#4844—31no—
82#4844—31no—
83#4844—31no—
84#4844—61no—
85#4841—31no—
86#4841—31no—
87#4841—31no—
88#4841D311yescharacteristic, complemented
89#4839D311yescharacteristic, complemented
90#4819—31no—
91#4818—31no—
92#4804—31no—
93#4802—31no—
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×#634C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#624—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111D3×D12—22no—
112D3×D12D414yes—
113#3799—22no—
114#3799—22no—
115D3×Dic6—22no—
116D3×Dic6—22no—
117C2×C32×C8C2311yescharacteristic
118C2×C32×C8C2311yescharacteristic
119C32×C42C2311yescharacteristic
120#3752—21no—
121#3752—21no—
122#3752—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3745—22no—
125#3744—22no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×#204—22no—
138C3×#204—22no—
139C3×ΓL(1,𝔽25)—22no—
140C3×D3×C8—22no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143#3722—21no—
144#3722—21no—
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148Dic32—21no—
149#3717—22no—
150#3717—22no—
151#3716—22no—
152#3714—22no—
153#3042—91noSylow
154C2×#239—31no—
155C2×D3×Q8—31no—
156C2×D3×D4—31no—
157C2×#235—31no—
158C22×D12—31no—
159C22×Dic6—31no—
160C2×C3×SD16—31no—
161C2×C3×SD16—31no—
162C2×C3×M16—31no—
163C22×C3×C8—31no—
164C3×C4⋊Q8—31no—
165C3×C4×D4—31no—
166C3×#117—31no—
167#947—31no—
168#944—31no—
169C2×#215—31no—
170C2×#215—31no—
171D4×Dic3—31no—
172C2×#214—31no—
173C2×#213—31no—
174C4×#67—61no—
175C2×(C2×D3)⋊C4—61no—
176#926—31no—
177#914—64no—
178D3×SD16—64no—
179#908—64no—
180C2×D24—31no—
181C2×D24—31no—
182C2×D24—31no—
183C2×D24—61no—
184C2×#204—31no—
185C2×#204—31no—
186C2×#204—31no—
187C2×#204—31no—
188C2×#204—31no—
189C2×#204—61no—
190C2×#204—64no—
191C2×#204C2×D311yescharacteristic
192C2×#204C2×D311yescharacteristic
193C2×ΓL(1,𝔽25)C2×D311yescharacteristic
194C2×D3×C8C2×D311yescharacteristic
195#897—61no—
196#897—61no—
197#896—61no—
198#896—61no—
199#894—61no—
200#894—61no—
201#893—31no—
202#893—61no—
203#893—61no—
204#892—31no—
205#886—61no—
206#886—61no—
207#67⋊C4—61no—
208D3×C22⋊C4—61no—
209D3×C22⋊C4—61no—
210D3×C22⋊C4—61no—
211#875—31no—
212#875—31no—
213#875—31no—
214#875—61no—
215C4×D12—31no—
216C4×D12—31no—
217C4×D12—31no—
218C4×D12—31no—
219C4×D12—61no—
220C4×D12C2×D311yescharacteristic
221#872C2×D311yescharacteristic
222#869—31no—
223#869C2×D311yescharacteristic, complemented
224C3×C4⋊C8—21no—
225C3×C4⋊C8—31no—
226C3×C4⋊C8—31no—
227C3×C4⋊C8—31no—
228C3×C4⋊C8C2×D311yescharacteristic, complemented
229C3×C4⋊C8C2×D311yescharacteristic, complemented
230C3×#103—31no—
231C3×#103—31no—
232#835—31no—
233#835—31no—
234#821—31no—
235#821—31no—
236#821—31no—
237#821—61no—
238#816—31no—
239#816—31no—
240#816—31no—
241#816—31no—
242#816—31no—
243#816—61no—
244#816C2×D311yescharacteristic, complemented
245#816C2×D311yescharacteristic, complemented
246Dic3⋊C8C2×D311yescharacteristic, complemented
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#810—31no—
249#809—31no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251C22×C3⋊D3—21no—
252C22×C3⋊D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3C2×D411yescharacteristic
255C2×D32—24no—
256C2×D32—81no—
257C2×D32—81no—
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—21no—
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)C2×D412yes—
267C4×C3⋊D3—81no—
268#634—21no—
269#634—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C3×D12—21no—
277C3×D12C2×D412yes—
278C3×C4×D3—81no—
279C3×C4×D3C2×D412yes—
280C3×C4×D3#4112yes—
281C3×Dic6—21no—
282C3×Dic6—21no—
283C3×Dic6—21no—
284C3×Dic6—21no—
285#627—42no—
286#626—24no—
287#626—42no—
288#624—42no—
289#624—81no—
290D3×Dic3—42no—
291D3×Dic3—81no—
292C32×C8—21no—
293C32×C8—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×AGL(1,ℤ/8)—91no—
297C22×SD16—91no—
298#536—91no—
299#518—91no—
300#463—91no—
301#463—91no—
302#463—91no—
303#463—91no—
304#461—31no—
305#461—91no—
306#461—91no—
307#461—91no—
308#424—31no—
309#419—91no—
310#416—91no—
311C23×D3—61no—
312C23×D3—61no—
313C2×C3×Q8—31no—
314C2×C3×Q8—31no—
315C2×C3×D4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—61no—
318C2×#67—61no—
319C2×#67—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322#239—62no—
323#239—62no—
324D3×Q8—62no—
325D3×Q8—62no—
326D3×D4—34no—
327D3×D4—62no—
328#235—62no—
329#235—62no—
330C2×D12—31no—
331C2×D12—31no—
332C2×D12—34no—
333C2×D12—31no—
334C2×D12—31no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—62no—
338C2×D12—61no—
339C2×D12—61no—
340C2×D12C22×D311yescharacteristic
341C2×C4×D3—21no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3—121no—
351C2×C4×D3C22×D311yescharacteristic
352C2×Dic6—31no—
353C2×Dic6—31no—
354C2×Dic6—61no—
355C2×Dic6—62no—
356C2×Dic6—62no—
357C2×Dic6—61no—
358C2×Dic6—61no—
359C2×Dic6C22×D311yescharacteristic
360C2×Dic6C22×D311yescharacteristic
361C3×SD16—62no—
362C3×SD16—62no—
363C3×M16—62no—
364C2×C3×C8—21no—
365C2×C3×C8—21no—
366C2×C3×C8—31no—
367C2×C3×C8—31no—
368C2×C3×C8—62no—
369C2×C3×C8C22×D311yescharacteristic
370C2×C3×C8C22×D311yescharacteristic
371C2×C3×C8C22×D311yescharacteristic
372C2×C3×C8C22×D311yescharacteristic
373C3×C4⋊C4—31no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—61no—
377C3×C4⋊C4—61no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4—31no—
380C3×C22⋊C4—61no—
381C3×C42—21no—
382C3×C42—31no—
383C3×C42C22×D311yescharacteristic
384C3×C42C22×D311yescharacteristic
385#217—61no—
386#217—61no—
387#215—62no—
388#215—62no—
389#214—62no—
390#213—62no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—121no—
407(C2×D3)⋊C4—121no—
408(C2×D3)⋊C4—121no—
409(C2×D3)⋊C4D1211yescharacteristic
410(C2×D3)⋊C4D1211yescharacteristic
411C4⋊Dic3—21no—
412C4⋊Dic3—21no—
413C4⋊Dic3—31no—
414C4⋊Dic3—31no—
415C4⋊Dic3—61no—
416C4⋊Dic3—61no—
417C4⋊Dic3—61no—
418C4⋊Dic3C22×D311yescharacteristic
419Dic3⋊C4—61no—
420Dic3⋊C4—61no—
421Dic3⋊C4D1211yescharacteristic
422Dic3⋊C4D1211yescharacteristic
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428D24—62no—
429D24—62no—
430D24—62no—
431D24—122no—
432#204—22no—
433#204—22no—
434#204—62no—
435#204—62no—
436#204—62no—
437#204—62no—
438#204—62no—
439#204—122no—
440ΓL(1,𝔽25)—22no—
441D3×C8—22no—
442C22×C32C22×D411yescharacteristic
443C2×C3⋊D3—22no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—41no—
446C2×C3⋊D3—41no—
447C2×C3⋊D3—41no—
448C2×C3⋊D3—41no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—22no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3#12112yes—
455D32—84no—
456C32×C4—21no—
457C32×C4—21no—
458C32×C4C22×D411yescharacteristic
459C32×C4C2×#4111yescharacteristic
460C3⋊Dic3—41no—
461C3⋊Dic3—41no—
462C3×Dic3—21no—
463C3×Dic3—21no—
464C3×Dic3—41no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—91no—
469C22×Q8—91no—
470C22×D4—91no—
471AGL(1,ℤ/8)—184no—
472C2×SD16—31no—
473C2×SD16—31no—
474C2×SD16—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—184no—
479C2×D8—91no—
480C2×D8—91no—
481C2×M16—31no—
482C22×C8—31no—
483C4⋊Q8—31no—
484C4⋊Q8—91no—
485#124—91no—
486#124—91no—
487#123—181no—
488#123—181no—
489C22⋊Q8—181no—
490C22⋊Q8—181no—
491C4×D4—31no—
492C4×D4—91no—
493C4×D4—91no—
494C4×D4—91no—
495C4×D4—181no—
496C4×D4—181no—
497#117—31no—
498#117—91no—
499C2×C22⋊C4—181no—
500C2×C22⋊C4—181no—
501C4⋊C8—31no—
502C4⋊C8—31no—
503C4⋊C8—31no—
504C4⋊C8D3211yescharacteristic, complemented
505#103—31no—
506#103—31no—
507#103—91no—
508#103—91no—
509#103—91no—
510#103—91no—
511#102—91no—
512#102—91no—
513C23×C3—31no—
514C23×C3—61no—
515C22×D3—21no—
516C22×D3—64no—
517C22×D3—61no—
518C22×D3—61no—
519C22×D3—64no—
520C22×D3—61no—
521C22×D3—61no—
522C22×D3—121no—
523C22×D3—121no—
524C22×D3—241no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3—241no—
528C22×D3C2×D1211yescharacteristic
529C3×Q8—61no—
530C3×Q8—61no—
531C3×Q8—61no—
532C3×Q8—61no—
533C3×D4—32no—
534C3×D4—61no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—31no—
539C2×C3×C4—32no—
540C2×C3×C4—32no—
541C2×C3×C4—31no—
542C2×C3×C4—31no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—241no—
547C2×C3×C4C2×D1211yescharacteristic
548C2×C3×C4C2×D1211yescharacteristic
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553#67—64no—
554#67—122no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—122no—
565C2×Dic3—241no—
566C2×Dic3C2×D1211yescharacteristic
567C2×Dic3C2×D1211yescharacteristic
568C2×Dic3C2×D1211yescharacteristic
569D12—21no—
570D12—32no—
571D12—32no—
572D12—62no—
573D12—64no—
574D12—61no—
575D12—61no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—61no—
580D12—121no—
581D12—121no—
582D12—121no—
583D12—122no—
584D12D3×D412yes—
585C4×D3—81no—
586C4×D3—122no—
587C4×D3—122no—
588C4×D3—122no—
589C4×D3—241no—
590C4×D3—241no—
591C4×D3—241no—
592C4×D3—241no—
593C4×D3—241no—
594C4×D3—242no—
595C4×D3D3×D412yes—
596C4×D3#23912yes—
597Dic6—21no—
598Dic6—21no—
599Dic6—21no—
600Dic6—21no—
601Dic6—61no—
602Dic6—61no—
603Dic6—61no—
604Dic6—61no—
605Dic6—121no—
606Dic6—121no—
607Dic6—122no—
608Dic6—122no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8—21no—
613C3×C8—41no—
614C3×C8—41no—
615C3×C8—61no—
616C3×C8—61no—
617C3⋊C8—21no—
618C3⋊C8—21no—
619C2×C32C2×#12111yescharacteristic
620C2×C32#57711yescharacteristic
621C2×C32#57711yescharacteristic
622C3⋊D3—42no—
623C3⋊D3—81no—
624C3×D3—22no—
625C3×D3—42no—
626C24—181no—
627#41—182no—
628#41—182no—
629C2×Q8—31no—
630C2×Q8—31no—
631C2×Q8—91no—
632C2×Q8—181no—
633C2×Q8—182no—
634C2×Q8—182no—
635C2×D4—31no—
636C2×D4—94no—
637C2×D4—91no—
638C2×D4—91no—
639C2×D4—182no—
640C2×D4—181no—
641C2×D4—181no—
642C22×C4—31no—
643C22×C4—61no—
644C22×C4—181no—
645C22×C4—181no—
646C22×C4—181no—
647C22×C4—181no—
648C22×C4—181no—
649SD16—62no—
650SD16—62no—
651SD16—182no—
652SD16—182no—
653SD16—182no—
654SD16—182no—
655D8—182no—
656D8—182no—
657M16—62no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—62no—
661C2×C8C2×D3211yescharacteristic
662C2×C8C2×D3211yescharacteristic
663C4⋊C4—31no—
664C4⋊C4—31no—
665C4⋊C4—31no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4—91no—
669C4⋊C4—181no—
670C4⋊C4—181no—
671C22⋊C4—31no—
672C22⋊C4—31no—
673C22⋊C4—61no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C42—31no—
683C42—181no—
684C42C2×D3211yescharacteristic
685C22×C3—21no—
686C22×C3—32no—
687C22×C3—61no—
688C22×C3—61no—
689C22×C3—62no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3C22×D1211yescharacteristic
693C22×C3C2×D3×D411yescharacteristic
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—22no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—62no—
700C2×D3—62no—
701C2×D3—122no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—241no—
713C2×D3—241no—
714C2×D3—241no—
715C2×D3—241no—
716C2×D3—241no—
717C2×D3—244no—
718C2×D3—244no—
719C2×D3#89512yes—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—32no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—61no—
730C3×C4—61no—
731C3×C4—121no—
732C3×C4—121no—
733C3×C4—121no—
734C3×C4C2×D3×D411yescharacteristic
735C3×C4C2×D3×D411yescharacteristic
736C3×C4C2×#23911yescharacteristic
737C3×C4D3×#4111yescharacteristic
738Dic3—21no—
739Dic3—21no—
740Dic3—41no—
741Dic3—41no—
742Dic3—41no—
743Dic3—121no—
744Dic3—121no—
745Dic3—121no—
746Dic3—121no—
747Dic3—241no—
748Dic3—241no—
749Dic3#89512yes—
750C32#304211yescharacteristic, complemented, Sylow
751C23—31no—
752C23—61no—
753C23—184no—
754C23—181no—
755C23—181no—
756C23—721no—
757C23—721no—
758Q8—61no—
759Q8—61no—
760Q8—61no—
761Q8—61no—
762Q8—181no—
763Q8—181no—
764Q8—362no—
765D4—32no—
766D4—61no—
767D4—92no—
768D4—184no—
769D4—181no—
770D4—181no—
771D4—181no—
772D4—362no—
773C2×C4—31no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—31no—
777C2×C4—31no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—181no—
782C2×C4—181no—
783C2×C4—241no—
784C2×C4—362no—
785C2×C4—362no—
786C2×C4—721no—
787C2×C4—721no—
788C2×C4—721no—
789C2×C4D3×D1211yescharacteristic
790C2×C4D3×D1211yescharacteristic
791C2×C4C22×D3211yescharacteristic
792C8—21no—
793C8—21no—
794C8—61no—
795C8—61no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—62no—
800C2×C3—122no—
801C2×C3C2×#89511yescharacteristic
802C2×C3D3×#12111yescharacteristic
803C2×C3#575111yescharacteristic
804C2×C3#575111yescharacteristic
805C2×C3#576211yescharacteristic
806C2×C3#577811yescharacteristic
807D3—22no—
808D3—42no—
809D3—122no—
810D3—122no—
811D3—242no—
812D3—241no—
813D3—241no—
814D3—481no—
815C22—32no—
816C22—61no—
817C22—61no—
818C22—62no—
819C22—121no—
820C22—121no—
821C22—182no—
822C22—361no—
823C22—361no—
824C22—361no—
825C22—361no—
826C22—361no—
827C22—724no—
828C22C2×D3×D1211yescharacteristic
829C4—21no—
830C4—21no—
831C4—32no—
832C4—61no—
833C4—61no—
834C4—121no—
835C4—121no—
836C4—121no—
837C4—361no—
838C4—361no—
839C4D32×D411yescharacteristic
840C4D3×#23911yescharacteristic
841C3—21no—
842C3#7908711yescharacteristic, complemented
843C3#8043011yescharacteristic, complemented
844C2—62no—
845C2—122no—
846C2—362no—
847C2—721no—
848C2D3×#89511yescharacteristic
849C2#1059467711yescharacteristic
850C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#63794C2
hypercenterC4⋊C8D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×D3×#204C2semidirect
3. #10593994C2semidirect
4. #10593893C2semidirect
5. #10592543C2semidirect
6. C3×#4841C2semidirect
7. C3×#4839C2semidirect
8. #10590948C2semidirect
9. #10590770C2semidirect
10. #10590760C2semidirect
11. #10590754C2semidirect
12. #10590752C2semidirect
13. #10590690C2semidirect
14. #10590379C2semidirect
15. #10590366C2semidirect
23. #64084C22semidirect
31. C3×#869C22semidirect
42. #63866C22semidirect
43. #63864C22semidirect
51. C32×C4⋊C8C22semidirect
52. #63648C22semidirect
53. #63643C22semidirect
54. C3×#816C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
60. #63566C22semidirect
61. #63566C22semidirect
62. #63564C22semidirect
88. #4841D3semidirect
89. #4839D3semidirect
223. #869C2×D3semidirect
228. C3×C4⋊C8C2×D3semidirect
229. C3×C4⋊C8C2×D3semidirect
244. #816C2×D3semidirect
245. #816C2×D3semidirect
246. Dic3⋊C8C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
504. C4⋊C8D32semidirect
750. C32#3042semidirect
842. C3#79087semidirect
843. C3#80430semidirect

Maximal subgroups

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

subgroupindex
C2×#637942
C2×D3×#2042
#105939942
#105938932
#105925432
C3×#48412
C3×#48392
#105909482
#105907702
#105907602
#105907542
#105907522
#105906902
#105903792
#105903662
#804303
#790873