Finite Group Databasebeta

← #11866333

Subgroups — #11866333

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63801C211yesmaximal, characteristic, complemented
2C2×D3×#204C211yesmaximal, characteristic, complemented
3#10594001C211yesmaximal, characteristic
4#10593885C211yesmaximal, characteristic, complemented
5#10592547C211yesmaximal, characteristic, complemented
6C3×#4845C211yesmaximal, characteristic, complemented
7C3×#4839C211yesmaximal, characteristic, complemented
8#10590939C211yesmaximal, characteristic, complemented
9#10590879C211yesmaximal, characteristic, complemented
10#10590813C211yesmaximal, characteristic, complemented
11#10590801C211yesmaximal, characteristic, complemented
12#10590799C211yesmaximal, characteristic, complemented
13#10590690C211yesmaximal, characteristic, complemented
14#10590378C211yesmaximal, characteristic, complemented
15#10590367C211yesmaximal, characteristic, complemented
16#80600—31nomaximal
17#79099—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×#3744C2211yescharacteristic
22C2×#3744C2211yescharacteristic, complemented
23#64083C2211yescharacteristic
24C4×#634C2211yescharacteristic, complemented
25C2×C3×Dic12C2211yescharacteristic, complemented
26C2×C3×#204C2211yescharacteristic
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#875C2211yescharacteristic
30C3×#872C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic, complemented
32#63923—21no—
33#63923—21no—
34#63911C2211yescharacteristic
35#63910—21no—
36#63910—21no—
37#63878—21no—
38#63877—21no—
39#63864C2211yescharacteristic
40#63844C2211yescharacteristic, complemented
41Dic3×Dic6C2211yescharacteristic, complemented
42#63841C2211yescharacteristic
43#63838—21no—
44#63837—21no—
45C2×#3719C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic
49#63801—24no—
50D3×#204—24no—
51C32×C4⋊C8C2211yescharacteristic, complemented
52#63648C2211yescharacteristic
53#63648C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63564C2211yescharacteristic
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic
63C2×#918—31no—
64C2×D3×SD16—31no—
65C2×#909—31no—
66C22×#204—31no—
67#5674—31no—
68#5572—31no—
69#5525—31no—
70#5516—31no—
71C3×#464—31no—
72C3×#424—31no—
73#5185—31no—
74#5163—31no—
75#5131—31no—
76#5113—31no—
77#5054—31no—
78#5027—31no—
79#4848—31no—
80#4848—31no—
81#4848—31no—
82#4848—31no—
83#4848—31no—
84#4848—61no—
85#4845—31no—
86#4845—31no—
87#4845—31no—
88#4845D311yescharacteristic, complemented
89#4839D311yescharacteristic, complemented
90#4804—31no—
91#4798—31no—
92#4770—31no—
93#4762—31no—
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#624—21no—
110C2×D3×Dic3—21no—
111D3×D12—22no—
112D3×D12—22no—
113#3799—22no—
114#3799—22no—
115D3×Dic6—22no—
116D3×Dic6D414yescomplemented
117C2×C32×C8C2311yescharacteristic
118C2×C32×C8C2311yescharacteristic
119C32×C42C2311yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122C4×C3⋊Dic3—21no—
123#3744—22no—
124#3744—22no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
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×Dic12—22no—
138C3×#204—22no—
139C3×ΓL(1,𝔽25)—22no—
140C3×D3×C8—22no—
141#3724—21no—
142Dic3⋊Dic3—21no—
143#3722—21no—
144#3722—21no—
145(C2×D3)⋊Dic3—21no—
146Dic32—21no—
147Dic32—21no—
148Dic32—21no—
149#3719—22no—
150#3717—22no—
151#3717—22no—
152#3716—22no—
153#3043—91noSylow
154C2×#239—31no—
155C2×D3×Q8—31no—
156C2×D3×D4—31no—
157C2×#235—31no—
158C22×D12—31no—
159C22×Dic6—31no—
160C2×C3×Q16—31no—
161C2×C3×SD16—31no—
162C2×C3×M16—31no—
163C22×C3×C8—31no—
164C3×#124—31no—
165C3×C4×Q8—31no—
166C3×#117—31no—
167#947—31no—
168Q8×Dic3—31no—
169C2×#216—31no—
170C2×#215—31no—
171C2×#215—31no—
172#940—31no—
173C2×#214—31no—
174#926—31no—
175#918—64no—
176D3×SD16—64no—
177#909—64no—
178C2×Dic12—31no—
179C2×Dic12C2×D311yescharacteristic, complemented
180C2×#204—31no—
181C2×#204—31no—
182C2×#204—31no—
183C2×#204—31no—
184C2×#204—31no—
185C2×#204—31no—
186C2×#204—31no—
187C2×#204—61no—
188C2×#204—61no—
189C2×#204—64no—
190C2×#204C2×D311yescharacteristic
191C2×ΓL(1,𝔽25)C2×D311yescharacteristic
192C2×D3×C8C2×D311yescharacteristic
193#895—61no—
194#895—61no—
195#892—31no—
196#892—61no—
197#887—31no—
198#887—61no—
199#887—61no—
200#887—61no—
201#884—61no—
202#884—61no—
203#882—61no—
204#882—61no—
205#882—61no—
206#882—61no—
207#877—61no—
208#877—61no—
209#875—31no—
210#875C2×D311yescharacteristic
211#874—31no—
212#874—31no—
213#874—31no—
214#874—61no—
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×#103—31no—
231C3×#102—31no—
232#835—31no—
233#832—31no—
234#821—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—31no—
239#821—31no—
240#821—31no—
241#821—61no—
242#821—61no—
243#821C2×D311yescharacteristic
244#816—31no—
245#816C2×D311yescharacteristic, complemented
246Dic3⋊C8C2×D311yescharacteristic, complemented
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#809—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—
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—21no—
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)—21no—
267C4⋊(C3⋊D3)—81no—
268C4⋊(C3⋊D3)—81no—
269#634—21no—
270#634C2×D412yes—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×C4×D3C2×D412yes—
280C3×C4×D3#4112yes—
281C3×Dic6—21no—
282C3×Dic6—21no—
283C3×Dic6—21no—
284C3×Dic6C2×D412yes—
285#627—24no—
286#626—42no—
287#626—42no—
288#626—81no—
289#626—81no—
290#624—42no—
291D3×Dic3—24no—
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—31no—
301#464—91no—
302#464—91no—
303#464—91no—
304#460—91no—
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×Q8—31no—
315C2×C3×D4—31no—
316C22×C3×C4—31no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C22×Dic3—61no—
322#239—62no—
323#239—62no—
324D3×Q8—34no—
325D3×Q8—62no—
326D3×D4—62no—
327D3×D4—62no—
328#235—62no—
329#235—62no—
330C2×D12—31no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—62no—
337C2×D12—62no—
338C2×D12—61no—
339C2×D12—61no—
340C2×D12—61no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12—61no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—121no—
347C2×D12—121no—
348C2×D12C22×D311yescharacteristic
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3C22×D311yescharacteristic
353C2×Dic6—31no—
354C2×Dic6—31no—
355C2×Dic6—34no—
356C2×Dic6—61no—
357C2×Dic6—62no—
358C2×Dic6—61no—
359C2×Dic6—61no—
360C2×Dic6C22×D311yescharacteristic
361C2×Dic6C22×D311yescharacteristic
362C3×Q16—62no—
363C3×SD16—62no—
364C3×M16—62no—
365C2×C3×C8—21no—
366C2×C3×C8—21no—
367C2×C3×C8—31no—
368C2×C3×C8—31no—
369C2×C3×C8—62no—
370C2×C3×C8C22×D311yescharacteristic
371C2×C3×C8C22×D311yescharacteristic
372C2×C3×C8C22×D311yescharacteristic
373C2×C3×C8C22×D311yescharacteristic
374C3×C4⋊C4—31no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—61no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4—31no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C42—21no—
383C3×C42—31no—
384C3×C42—61no—
385C3×C42C22×D311yescharacteristic
386C3×C42C22×D311yescharacteristic
387#217—61no—
388#216—62no—
389#215—62no—
390#215—62no—
391#214—62no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
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)⋊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—22no—
429Dic12—62no—
430#204—22no—
431#204—62no—
432#204—62no—
433#204—62no—
434#204—62no—
435#204—62no—
436#204—62no—
437#204—62no—
438#204—122no—
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—41no—
447C2×C3⋊D3—41no—
448C2×C3⋊D3—41no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
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—22no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—91no—
469C22×Q8—91no—
470C22×D4—91no—
471#137—184no—
472C2×Q16—31no—
473C2×Q16—91no—
474C2×SD16—31no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—91no—
479C2×SD16—91no—
480C2×SD16—184no—
481C2×M16—31no—
482C22×C8—31no—
483#127—91no—
484#127—91no—
485#124—31no—
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—31no—
506#103—91no—
507#102—31no—
508#102—91no—
509#102—91no—
510#102—91no—
511#102—91no—
512#102—91no—
513C23×C3—31no—
514C23×C3—61no—
515C22×D3—21no—
516C22×D3—61no—
517C22×D3—61no—
518C22×D3—61no—
519C22×D3—61no—
520C22×D3—121no—
521C22×D3—121no—
522C22×D3—122no—
523C22×D3—122no—
524C22×D3—241no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3—241no—
528C22×D3C2×D1211yescharacteristic
529C3×Q8—32no—
530C3×Q8—61no—
531C3×Q8—61no—
532C3×Q8—61no—
533C3×D4—61no—
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×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—241no—
555#67—241no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—64no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—121no—
565C2×Dic3—121no—
566C2×Dic3C2×D1211yescharacteristic
567C2×Dic3C2×D1211yescharacteristic
568C2×Dic3C2×D1211yescharacteristic
569D12—21no—
570D12—21no—
571D12—61no—
572D12—61no—
573D12—61no—
574D12—61no—
575D12—61no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—121no—
580D12—121no—
581D12—121no—
582D12—121no—
583D12—122no—
584D12—122no—
585D12—241no—
586D12—241no—
587D12—241no—
588D12—241no—
589D12—242no—
590D12—242no—
591D12—241no—
592D12—241no—
593C4×D3—64no—
594C4×D3—122no—
595C4×D3—122no—
596C4×D3D3×D412yes—
597C4×D3#23912yes—
598Dic6—21no—
599Dic6—21no—
600Dic6—21no—
601Dic6—32no—
602Dic6—32no—
603Dic6—62no—
604Dic6—64no—
605Dic6—61no—
606Dic6—61no—
607Dic6—64no—
608Dic6—121no—
609Dic6D3×D412yes—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8—21no—
613C3×C8—21no—
614C3×C8—41no—
615C3×C8—41no—
616C3×C8—61no—
617C3×C8—61no—
618C3⋊C8—21no—
619C3⋊C8—21no—
620C2×C32C2×#12111yescharacteristic
621C2×C32#57711yescharacteristic
622C2×C32#57711yescharacteristic
623C3⋊D3—81no—
624C3⋊D3—81no—
625C3×D3—22no—
626C3×D3—81no—
627C24—181no—
628#41—182no—
629#41—182no—
630C2×Q8—31no—
631C2×Q8—31no—
632C2×Q8—94no—
633C2×Q8—91no—
634C2×Q8—181no—
635C2×Q8—182no—
636C2×D4—31no—
637C2×D4—91no—
638C2×D4—91no—
639C2×D4—182no—
640C2×D4—182no—
641C2×D4—181no—
642C2×D4—181no—
643C2×D4—181no—
644C2×D4—181no—
645C2×D4—181no—
646C2×D4—181no—
647C22×C4—31no—
648C22×C4—181no—
649C22×C4—181no—
650Q16—62no—
651Q16—182no—
652SD16—62no—
653SD16—182no—
654SD16—182no—
655SD16—182no—
656SD16—182no—
657SD16—182no—
658M16—62no—
659C2×C8—31no—
660C2×C8—31no—
661C2×C8—62no—
662C2×C8C2×D3211yescharacteristic
663C2×C8C2×D3211yescharacteristic
664C4⋊C4—31no—
665C4⋊C4—31no—
666C4⋊C4—31no—
667C4⋊C4—61no—
668C4⋊C4—91no—
669C4⋊C4—181no—
670C4⋊C4—181no—
671C4⋊C4—181no—
672C22⋊C4—31no—
673C22⋊C4—31no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C42—31no—
680C42—61no—
681C42—181no—
682C42—181no—
683C42—181no—
684C42—181no—
685C42C2×D3211yescharacteristic
686C22×C3—21no—
687C22×C3—32no—
688C22×C3—61no—
689C22×C3—61no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3C22×D1211yescharacteristic
694C22×C3C2×D3×D411yescharacteristic
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—121no—
701C2×D3—121no—
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—241no—
718C2×D3—244no—
719C2×D3—244no—
720C2×D3#89512yes—
721C3×C4—22no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—21no—
727C3×C4—21no—
728C3×C4—32no—
729C3×C4—41no—
730C3×C4—62no—
731C3×C4—61no—
732C3×C4—61no—
733C3×C4—121no—
734C3×C4—121no—
735C3×C4C2×D3×D411yescharacteristic
736C3×C4C2×D3×D411yescharacteristic
737C3×C4C2×#23911yescharacteristic
738C3×C4D3×#4111yescharacteristic
739Dic3—21no—
740Dic3—21no—
741Dic3—22no—
742Dic3—41no—
743Dic3—41no—
744Dic3—62no—
745Dic3—62no—
746Dic3—122no—
747Dic3—121no—
748Dic3—121no—
749Dic3—241no—
750Dic3#89512yes—
751C32#304311yescharacteristic, complemented, Sylow
752C23—31no—
753C23—61no—
754C23—181no—
755C23—181no—
756C23—362no—
757C23—721no—
758C23—721no—
759Q8—32no—
760Q8—61no—
761Q8—61no—
762Q8—61no—
763Q8—92no—
764Q8—184no—
765Q8—181no—
766D4—61no—
767D4—61no—
768D4—181no—
769D4—181no—
770D4—181no—
771D4—181no—
772D4—362no—
773D4—362no—
774D4—721no—
775D4—721no—
776D4—721no—
777D4—721no—
778C2×C4—31no—
779C2×C4—32no—
780C2×C4—32no—
781C2×C4—31no—
782C2×C4—31no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—184no—
787C2×C4—181no—
788C2×C4—181no—
789C2×C4—362no—
790C2×C4D3×D1211yescharacteristic
791C2×C4D3×D1211yescharacteristic
792C2×C4C22×D3211yescharacteristic
793C8—21no—
794C8—21no—
795C8—61no—
796C8—61no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—62no—
801C2×C3—241no—
802C2×C3C2×#89511yescharacteristic
803C2×C3D3×#12111yescharacteristic
804C2×C3#575111yescharacteristic
805C2×C3#575111yescharacteristic
806C2×C3#577011yescharacteristic
807C2×C3#577811yescharacteristic
808D3—22no—
809D3—81no—
810D3—241no—
811D3—241no—
812D3—241no—
813D3—241no—
814D3—481no—
815D3—481no—
816C22—32no—
817C22—61no—
818C22—61no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—361no—
823C22—361no—
824C22—361no—
825C22—361no—
826C22—361no—
827C22—361no—
828C22—724no—
829C22C2×D3×D1211yescharacteristic
830C4—21no—
831C4—21no—
832C4—32no—
833C4—62no—
834C4—61no—
835C4—61no—
836C4—121no—
837C4—121no—
838C4—182no—
839C4—361no—
840C4D32×D411yescharacteristic
841C4D3×#23911yescharacteristic
842C3—21no—
843C3#7909911yescharacteristic, complemented
844C3#8060011yescharacteristic, complemented
845C2—62no—
846C2—241no—
847C2—721no—
848C2—721no—
849C2D3×#89511yescharacteristic
850C2#1059467911yescharacteristic
851C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10594001C2
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×#63801C2semidirect
2. C2×D3×#204C2semidirect
4. #10593885C2semidirect
5. #10592547C2semidirect
6. C3×#4845C2semidirect
7. C3×#4839C2semidirect
8. #10590939C2semidirect
9. #10590879C2semidirect
10. #10590813C2semidirect
11. #10590801C2semidirect
12. #10590799C2semidirect
13. #10590690C2semidirect
14. #10590378C2semidirect
15. #10590367C2semidirect
22. C2×#3744C22semidirect
24. C4×#634C22semidirect
25. C2×C3×Dic12C22semidirect
31. C3×C4×Dic6C22semidirect
40. #63844C22semidirect
41. Dic3×Dic6C22semidirect
45. C2×#3719C22semidirect
47. C2×#3717C22semidirect
51. C32×C4⋊C8C22semidirect
53. #63648C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
61. #63564C22semidirect
88. #4845D3semidirect
89. #4839D3semidirect
116. D3×Dic6D4semidirect
179. C2×Dic12C2×D3semidirect
223. C4×Dic6C2×D3semidirect
228. C3×C4⋊C8C2×D3semidirect
229. C3×C4⋊C8C2×D3semidirect
245. #816C2×D3semidirect
246. Dic3⋊C8C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
504. C4⋊C8D32semidirect
751. C32#3043semidirect
843. C3#79099semidirect
844. C3#80600semidirect

Maximal subgroups

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

subgroupindex
C2×#638012
C2×D3×#2042
#105940012
#105938852
#105925472
C3×#48452
C3×#48392
#105909392
#105908792
#105908132
#105908012
#105907992
#105906902
#105903782
#105903672
#806003
#790993