Finite Group Databasebeta

← #11866335

Subgroups — #11866335

Order 1152.

1036 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63800C211yesmaximal, characteristic, complemented
2C2×D3×#204C211yesmaximal, characteristic, complemented
3#10594000C211yesmaximal, characteristic
4#10593885C211yesmaximal, characteristic, complemented
5#10592544C211yesmaximal, characteristic, complemented
6C3×#4848C211yesmaximal, characteristic, complemented
7C3×#4839C211yesmaximal, characteristic, complemented
8#10590954C211yesmaximal, characteristic, complemented
9#10590939C211yesmaximal, characteristic, complemented
10#10590879C211yesmaximal, characteristic, complemented
11#10590861C211yesmaximal, characteristic, complemented
12#10590859C211yesmaximal, characteristic, complemented
13#10590799C211yesmaximal, characteristic, complemented
14#10590377C211yesmaximal, characteristic, complemented
15#10590368C211yesmaximal, characteristic, complemented
16#80385—31nomaximal
17#79099—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×#3746C2211yescharacteristic, complemented
22C2×#3744C2211yescharacteristic
23#64084C2211yescharacteristic
24C4×#634C2211yescharacteristic, complemented
25C2×C3×#204C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic, complemented
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#874C2211yescharacteristic
30C3×#872C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic, complemented
32#63922—21no—
33#63922—21no—
34#63911C2211yescharacteristic
35#63886—21no—
36#63886—21no—
37#63878—21no—
38#63877—21no—
39#63860C2211yescharacteristic
40#63844C2211yescharacteristic, complemented
41Dic3×Dic6C2211yescharacteristic, complemented
42#63841C2211yescharacteristic
43#63838—21no—
44#63837—21no—
45C2×#3719C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47C2×#3716C2211yescharacteristic
48C2×#3716C2211yescharacteristic, complemented
49#63800—24no—
50D3×#204—24no—
51C32×C4⋊C8C2211yescharacteristic, complemented
52#63648C2211yescharacteristic
53#63643C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63564C2211yescharacteristic
61#63563C2211yescharacteristic
62#63563C2211yescharacteristic, complemented
63C2×#915—31no—
64C2×D3×SD16—31no—
65C2×#909—31no—
66C22×#204—31no—
67#5715—31no—
68#5572—31no—
69#5525—31no—
70#5516—31no—
71C3×#460—31no—
72C3×#424—31no—
73#5166—31no—
74#5163—31no—
75#5131—31no—
76#5113—31no—
77#5075—31no—
78#5028—31no—
79#4848—31no—
80#4848—31no—
81#4848—31no—
82#4848D311yescharacteristic, complemented
83#4845—31no—
84#4845—31no—
85#4845—31no—
86#4845—31no—
87#4845—31no—
88#4845—61no—
89#4839D311yescharacteristic, complemented
90#4772—31no—
91#4770—31no—
92#4767—31no—
93#4762—31no—
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×D12—21no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#625—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111D3×D12—22no—
112D3×D12—22no—
113#3795—22no—
114#3795—22no—
115D3×Dic6—22no—
116D3×Dic6D414yescomplemented
117C2×C32×C8C2311yescharacteristic
118C2×C32×C8C2311yescharacteristic
119C32×C42C2311yescharacteristic
120#3752—21no—
121#3752—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123#3750—21no—
124C4×C3⋊Dic3—21no—
125#3746—22no—
126#3744—22no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
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—
141#3724—21no—
142Dic3⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146Dic32—21no—
147Dic32—21no—
148Dic32—21no—
149#3719—22no—
150#3717—22no—
151#3716—22no—
152#3716—22no—
153#3043—91noSylow
154C2×D3×Q8—31no—
155C2×#237—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×#127—31no—
165C3×C4×Q8—31no—
166C3×#117—31no—
167Q8×Dic3—31no—
168C2×#216—31no—
169C2×#215—31no—
170#940—31no—
171#939—61no—
172#939—61no—
173#937—61no—
174#937—61no—
175#936—31no—
176C2×#214—31no—
177C2×#214—31no—
178#926—31no—
179#915—64no—
180D3×SD16—64no—
181#909—64no—
182C2×Dic12—31no—
183C2×Dic12—31no—
184C2×Dic12—31no—
185C2×Dic12—61no—
186C2×#204—31no—
187C2×#204—31no—
188C2×#204—31no—
189C2×#204—31no—
190C2×#204—31no—
191C2×#204—61no—
192C2×#204—64no—
193C2×#204C2×D311yescharacteristic
194C2×#204C2×D311yescharacteristic, complemented
195C2×ΓL(1,𝔽25)C2×D311yescharacteristic
196C2×D3×C8C2×D311yescharacteristic
197#895—61no—
198#895—61no—
199#892—31no—
200#892—61no—
201#887—31no—
202#887—61no—
203#887—61no—
204#887—61no—
205#882—61no—
206#882—61no—
207#877—61no—
208#877—61no—
209#875—31no—
210#875—31no—
211#875—31no—
212#875—61no—
213#874—31no—
214#874C2×D311yescharacteristic
215#872—61no—
216#872C2×D311yescharacteristic
217C4×Dic6—31no—
218C4×Dic6—31no—
219C4×Dic6—31no—
220C4×Dic6—31no—
221C4×Dic6—61no—
222C4×Dic6—61no—
223C4×Dic6C2×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×#102—31no—
231C3×#102—31no—
232#832—31no—
233#832—31no—
234#821—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—31no—
239#821—61no—
240#821C2×D311yescharacteristic
241#821C2×D311yescharacteristic, complemented
242#816—31no—
243#816—31no—
244#816—31no—
245#816—61no—
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—42no—
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—
263C2×C3⋊Dic3—21no—
264C4⋊(C3⋊D3)—21no—
265C4⋊(C3⋊D3)—21no—
266#634—21no—
267#634—21no—
268#634—21no—
269#634C2×D412yes—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—81no—
280C3×D12—81no—
281C3×C4×D3C2×D412yes—
282C3×C4×D3#4112yes—
283C3×Dic6—21no—
284C3×Dic6C2×D412yes—
285#627—24no—
286#626—42no—
287#626—81no—
288#626—81no—
289#625—42no—
290D3×Dic3—24no—
291D3×Dic3—42no—
292C32×C8—21no—
293C32×C8—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×#137—91no—
297C22×SD16—91no—
298#535—91no—
299#519—91no—
300#464—91no—
301#464—91no—
302#464—91no—
303#464—91no—
304#460—31no—
305#460—91no—
306#460—91no—
307#460—91no—
308#424—31no—
309#418—91no—
310#416—91no—
311C23×D3—61no—
312C23×D3—61no—
313C2×C3×Q8—31no—
314C2×C3×D4—31no—
315C2×C3×D4—31no—
316C2×C3×D4—61no—
317C2×C3×D4—61no—
318C22×C3×C4—31no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326D3×Q8—34no—
327D3×Q8—62no—
328#237—62no—
329#237—62no—
330D3×D4—62no—
331D3×D4—62no—
332#235—62no—
333#235—62no—
334C2×D12—21no—
335C2×D12—21no—
336C2×D12—31no—
337C2×D12—31no—
338C2×D12—61no—
339C2×D12—62no—
340C2×D12—62no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12—61no—
344C2×D12C22×D311yescharacteristic
345C2×D12C22×D311yescharacteristic
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3C22×D311yescharacteristic
349C2×Dic6—31no—
350C2×Dic6—31no—
351C2×Dic6—34no—
352C2×Dic6—31no—
353C2×Dic6—31no—
354C2×Dic6—61no—
355C2×Dic6—61no—
356C2×Dic6—62no—
357C2×Dic6—61no—
358C2×Dic6—61no—
359C2×Dic6C22×D311yescharacteristic
360C3×SD16—62no—
361C3×SD16—62no—
362C3×M16—62no—
363C2×C3×C8—21no—
364C2×C3×C8—21no—
365C2×C3×C8—31no—
366C2×C3×C8—31no—
367C2×C3×C8—62no—
368C2×C3×C8C22×D311yescharacteristic
369C2×C3×C8C22×D311yescharacteristic
370C2×C3×C8C22×D311yescharacteristic
371C2×C3×C8C22×D311yescharacteristic
372C3×C4⋊C4—31no—
373C3×C4⋊C4—31no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—61no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—31no—
378C3×C42—21no—
379C3×C42—31no—
380C3×C42—61no—
381C3×C42C22×D311yescharacteristic
382C3×C42C22×D311yescharacteristic
383#217—61no—
384#217—61no—
385#217—61no—
386#216—62no—
387#215—62no—
388#214—62no—
389#214—62no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
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—121no—
398(C2×D3)⋊C4—121no—
399(C2×D3)⋊C4D1211yescharacteristic
400(C2×D3)⋊C4D1211yescharacteristic
401C4⋊Dic3—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3C22×D311yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—121no—
413Dic3⋊C4D1211yescharacteristic
414Dic3⋊C4D1211yescharacteristic
415C4×Dic3—21no—
416C4×Dic3—61no—
417C4×Dic3—61no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—121no—
425C4×Dic3C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428Dic12—62no—
429Dic12—62no—
430Dic12—62no—
431Dic12—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—41no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—41no—
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
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—22no—
461C3⋊Dic3—41no—
462C3⋊Dic3—41no—
463C3×Dic3—22no—
464C3×Dic3—21no—
465C3×Dic3—21no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—91no—
469C22×Q8—91no—
470C22×D4—91no—
471#137—184no—
472C2×Q16—91no—
473C2×Q16—91no—
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—91no—
479C2×SD16—91no—
480C2×SD16—184no—
481C2×M16—31no—
482C22×C8—31no—
483#127—31no—
484#127—91no—
485#124—91no—
486#124—91no—
487#121—181no—
488#121—181no—
489#120—181no—
490#120—181no—
491C4×Q8—31no—
492C4×Q8—91no—
493C4×Q8—91no—
494C4×Q8—91no—
495C4×Q8—181no—
496C4×Q8—181no—
497#117—31no—
498#117—91no—
499#117—181no—
500#117—181no—
501C4⋊C8—31no—
502C4⋊C8—31no—
503C4⋊C8—31no—
504C4⋊C8D3211yescharacteristic, complemented
505#103—91no—
506#103—91no—
507#102—31no—
508#102—31no—
509#102—91no—
510#102—91no—
511#102—91no—
512#102—91no—
513C23×C3—31no—
514C23×C3—61no—
515C23×C3—61no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—61no—
519C22×D3—61no—
520C22×D3—121no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—241no—
524C22×D3—241no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3C2×D1211yescharacteristic
528C3×Q8—32no—
529C3×Q8—61no—
530C3×D4—61no—
531C3×D4—61no—
532C3×D4—61no—
533C3×D4—61no—
534C3×D4—241no—
535C3×D4—241no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—31no—
540C2×C3×C4—32no—
541C2×C3×C4—32no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4C2×D1211yescharacteristic
547C2×C3×C4C2×D1211yescharacteristic
548C2×C3×C4D3×D411yescharacteristic
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4C23×D311yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552#67—122no—
553#67—122no—
554#67—122no—
555#67—241no—
556#67—241no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—64no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—121no—
567C2×Dic3—121no—
568C2×Dic3—121no—
569C2×Dic3—122no—
570C2×Dic3C2×D1211yescharacteristic
571C2×Dic3C2×D1211yescharacteristic
572C2×Dic3C2×D1211yescharacteristic
573D12—21no—
574D12—21no—
575D12—21no—
576D12—21no—
577D12—61no—
578D12—61no—
579D12—61no—
580D12—61no—
581D12—81no—
582D12—81no—
583D12—121no—
584D12—121no—
585D12—122no—
586D12—241no—
587D12—241no—
588C4×D3—64no—
589C4×D3—122no—
590C4×D3D3×D412yes—
591C4×D3#23912yes—
592Dic6—21no—
593Dic6—32no—
594Dic6—32no—
595Dic6—62no—
596Dic6—64no—
597Dic6—61no—
598Dic6—61no—
599Dic6—64no—
600Dic6—61no—
601Dic6—61no—
602Dic6—61no—
603Dic6—61no—
604Dic6—121no—
605Dic6—121no—
606Dic6—121no—
607Dic6D3×D412yes—
608C3×C8—21no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8—41no—
613C3×C8—41no—
614C3×C8—61no—
615C3×C8—61no—
616C3⋊C8—21no—
617C3⋊C8—21no—
618C2×C32C2×#12111yescharacteristic
619C2×C32#57711yescharacteristic
620C2×C32#57711yescharacteristic
621C3⋊D3—81no—
622C3×D3—22no—
623C3×D3—81no—
624C3×D3—81no—
625C24—181no—
626#41—182no—
627#41—182no—
628C2×Q8—31no—
629C2×Q8—94no—
630C2×Q8—91no—
631C2×Q8—91no—
632C2×Q8—181no—
633C2×Q8—182no—
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—61no—
637C2×D4—61no—
638C2×D4—91no—
639C2×D4—182no—
640C2×D4—182no—
641C2×D4—181no—
642C2×D4—181no—
643C2×D4—181no—
644C2×D4—181no—
645C22×C4—31no—
646C22×C4—181no—
647C22×C4—181no—
648Q16—182no—
649Q16—182no—
650SD16—62no—
651SD16—62no—
652SD16—182no—
653SD16—182no—
654SD16—182no—
655SD16—182no—
656M16—62no—
657C2×C8—31no—
658C2×C8—31no—
659C2×C8—62no—
660C2×C8C2×D3211yescharacteristic
661C2×C8C2×D3211yescharacteristic
662C4⋊C4—31no—
663C4⋊C4—31no—
664C4⋊C4—31no—
665C4⋊C4—61no—
666C4⋊C4—91no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C22⋊C4—31no—
671C22⋊C4—31no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C42—31no—
678C42—61no—
679C42—181no—
680C42—181no—
681C42—181no—
682C42—181no—
683C42C2×D3211yescharacteristic
684C22×C3—21no—
685C22×C3—32no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3C22×D1211yescharacteristic
695C22×C3C2×D3×D411yescharacteristic
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—241no—
711C2×D3—241no—
712C2×D3—241no—
713C2×D3—244no—
714C2×D3—244no—
715C2×D3#89512yes—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—32no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—62no—
726C3×C4—61no—
727C3×C4—61no—
728C3×C4—121no—
729C3×C4C2×D3×D411yescharacteristic
730C3×C4C2×D3×D411yescharacteristic
731C3×C4C2×#23911yescharacteristic
732C3×C4D3×#4111yescharacteristic
733Dic3—21no—
734Dic3—21no—
735Dic3—22no—
736Dic3—41no—
737Dic3—62no—
738Dic3—62no—
739Dic3—122no—
740Dic3—121no—
741Dic3—121no—
742Dic3—121no—
743Dic3—121no—
744Dic3—241no—
745Dic3—241no—
746Dic3#89512yes—
747C32#304311yescharacteristic, complemented, Sylow
748C23—31no—
749C23—61no—
750C23—61no—
751C23—181no—
752C23—362no—
753C23—721no—
754C23—721no—
755Q8—32no—
756Q8—61no—
757Q8—92no—
758Q8—184no—
759Q8—181no—
760Q8—181no—
761Q8—181no—
762D4—61no—
763D4—61no—
764D4—61no—
765D4—61no—
766D4—181no—
767D4—181no—
768D4—241no—
769D4—241no—
770D4—362no—
771D4—362no—
772D4—721no—
773D4—721no—
774C2×C4—31no—
775C2×C4—32no—
776C2×C4—32no—
777C2×C4—31no—
778C2×C4—31no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—184no—
782C2×C4—181no—
783C2×C4—181no—
784C2×C4—181no—
785C2×C4—362no—
786C2×C4D3×D1211yescharacteristic
787C2×C4D3×D1211yescharacteristic
788C2×C4C22×D3211yescharacteristic
789C8—21no—
790C8—21no—
791C8—61no—
792C8—61no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—62no—
797C2×C3—241no—
798C2×C3—241no—
799C2×C3C2×#89511yescharacteristic
800C2×C3D3×#12111yescharacteristic
801C2×C3#575111yescharacteristic
802C2×C3#575111yescharacteristic
803C2×C3#576211yescharacteristic
804C2×C3#577511yescharacteristic
805D3—22no—
806D3—81no—
807D3—81no—
808D3—241no—
809D3—241no—
810D3—481no—
811C22—32no—
812C22—61no—
813C22—61no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—361no—
821C22—361no—
822C22—361no—
823C22—724no—
824C22C2×D3×D1211yescharacteristic
825C4—21no—
826C4—21no—
827C4—32no—
828C4—62no—
829C4—61no—
830C4—61no—
831C4—121no—
832C4—182no—
833C4—361no—
834C4—361no—
835C4D32×D411yescharacteristic
836C4D3×#23911yescharacteristic
837C3—21no—
838C3#7909911yescharacteristic, complemented
839C3#8038511yescharacteristic, complemented
840C2—62no—
841C2—241no—
842C2—241no—
843C2—721no—
844C2D3×#89511yescharacteristic
845C2#1059467711yescharacteristic
846C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10594000C2
hypercenterC4⋊C8D32
hypocenterC32#3043
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
1. C2×#63800C2semidirect
2. C2×D3×#204C2semidirect
4. #10593885C2semidirect
5. #10592544C2semidirect
6. C3×#4848C2semidirect
7. C3×#4839C2semidirect
8. #10590954C2semidirect
9. #10590939C2semidirect
10. #10590879C2semidirect
11. #10590861C2semidirect
12. #10590859C2semidirect
13. #10590799C2semidirect
14. #10590377C2semidirect
15. #10590368C2semidirect
21. C2×#3746C22semidirect
24. C4×#634C22semidirect
26. C2×C3×#204C22semidirect
31. C3×C4×Dic6C22semidirect
40. #63844C22semidirect
41. Dic3×Dic6C22semidirect
45. C2×#3719C22semidirect
48. C2×#3716C22semidirect
51. C32×C4⋊C8C22semidirect
53. #63643C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
62. #63563C22semidirect
82. #4848D3semidirect
89. #4839D3semidirect
116. D3×Dic6D4semidirect
194. C2×#204C2×D3semidirect
223. C4×Dic6C2×D3semidirect
228. C3×C4⋊C8C2×D3semidirect
229. C3×C4⋊C8C2×D3semidirect
241. #821C2×D3semidirect
246. Dic3⋊C8C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
504. C4⋊C8D32semidirect
747. C32#3043semidirect
838. C3#79099semidirect
839. C3#80385semidirect

Maximal subgroups

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

subgroupindex
C2×#638002
C2×D3×#2042
#105940002
#105938852
#105925442
C3×#48482
C3×#48392
#105909542
#105909392
#105908792
#105908612
#105908592
#105907992
#105903772
#105903682
#803853
#790993