Finite Group Databasebeta

← #11866224

Subgroups — #11866224

Order 1152.

1114 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595426C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic, complemented
3C2×D3×D24C211yesmaximal, characteristic, complemented
4#10594604C211yesmaximal, characteristic, complemented
5#10592518C211yesmaximal, characteristic, complemented
6C3×#4819C211yesmaximal, characteristic, complemented
7C3×#4804C211yesmaximal, characteristic, complemented
8#10591570C211yesmaximal, characteristic, complemented
9#10591568C211yesmaximal, characteristic, complemented
10#10590765C211yesmaximal, characteristic, complemented
11#10590749C211yesmaximal, characteristic, complemented
12#10590694C211yesmaximal, characteristic, complemented
13#10590592C211yesmaximal, characteristic, complemented
14#10590551C211yesmaximal, characteristic, complemented
15#10590547C211yesmaximal, characteristic, complemented
16#80536—31nomaximal
17#78862—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21#64156C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic, complemented
23C2×#3745C2211yescharacteristic
24#64102C2211yescharacteristic, complemented
25C3×#947C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic, complemented
27C2×C3×D24C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#893C2211yescharacteristic, complemented
30C3×#892C2211yescharacteristic
31#63939—24no—
32#63922—21no—
33#63922—21no—
34#63921—21no—
35D3×(C2×D3)⋊C4—21no—
36#63914C2211yescharacteristic, complemented
37#63911C2211yescharacteristic, complemented
38#63906—21no—
39#63906—21no—
40C4×#626—21no—
41#63898C2211yescharacteristic, complemented
42#63894C2211yescharacteristic, complemented
43#63880—21no—
44#63855C2211yescharacteristic
45C2×#3714C2211yescharacteristic
46C2×#3714C2211yescharacteristic
47C2×#3714C2211yescharacteristic, complemented
48C2×#3713C2211yescharacteristic, complemented
49C2×#3711C2211yescharacteristic
50D3×D24—24no—
51C32×#103C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63572C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#5830—31no—
64C2×#949—31no—
65C2×#914—31no—
66C2×D3×D8—31no—
67C22×D24—31no—
68#5674—31no—
69#5545—31no—
70#5521—31no—
71C3×#463—31no—
72C3×#416—31no—
73#5165—31no—
74#5150—31no—
75#5102—31no—
76#5057—31no—
77#5015—31no—
78#5001—31no—
79#4843—31no—
80#4839—31no—
81#4819—31no—
82#4819—31no—
83#4819—31no—
84#4819—31no—
85#4819—61no—
86#4819D311yescharacteristic, complemented
87#4804D311yescharacteristic, complemented
88#4786—31no—
89#4786—31no—
90#4786—31no—
91#4786—31no—
92#4786—31no—
93#4770—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C3×#239—22no—
101C3×#239—22no—
102C2×C3×D12—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#625—21no—
114C2×#625—21no—
115C2×#624—21no—
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12—22no—
119D3×D12—22no—
120D3×D12D414yescomplemented
121C2×C32×C8C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3755—22no—
124#3752—21no—
125#3752—21no—
126#3752—21no—
127C4×C3⋊Dic3C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129#3745—22no—
130C3×#215—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4×Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×D24—22no—
141C3×D3×C8—22no—
142Dic3⋊Dic3D411yescharacteristic
143Dic3⋊Dic3D411yescharacteristic
144#3722—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3D411yescharacteristic
147(C2×D3)⋊Dic3D411yescharacteristic
148#3714—22no—
149#3714—22no—
150#3714—22no—
151#3713—22no—
152#3711—22no—
153#3041—91noSylow
154C2×C3×#41—31no—
155C2×#239C2×D311yescharacteristic
156C2×D3×D4—31no—
157C2×D3×D4—31no—
158C22×D12—31no—
159C22×D12—31no—
160C2×C3×SD16—31no—
161C2×C3×D8—31no—
162C22×C3×C8—31no—
163C3×#124—31no—
164C3×C4×D4—31no—
165C3×#117—31no—
166#949—64no—
167#947—31no—
168#947—31no—
169#947—61no—
170#947C2×D311yescharacteristic, complemented
171C2×#215—31no—
172C2×#215—31no—
173C2×#215—61no—
174C2×#215C2×D311yescharacteristic, complemented
175#940—31no—
176#940—31no—
177#940—31no—
178#937—61no—
179#937—61no—
180D4×Dic3—31no—
181C2×#213—31no—
182C2×#213—31no—
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—31no—
186#930—61no—
187#930—61no—
188C4×#67—61no—
189C2×(C2×D3)⋊C4—61no—
190#926—31no—
191C2×#208—31no—
192#914—64no—
193D3×D8—64no—
194C2×D24—31no—
195C2×D24—31no—
196C2×D24—31no—
197C2×D24—31no—
198C2×D24—31no—
199C2×D24—61no—
200C2×D24—64no—
201C2×D24C2×D311yescharacteristic
202C2×ΓL(1,𝔽25)—31no—
203C2×D3×C8C2×D311yescharacteristic
204#893—31no—
205#893—31no—
206#893—31no—
207#893—31no—
208#893—61no—
209#893C2×D311yescharacteristic, complemented
210#892C2×D311yescharacteristic
211#884—61no—
212#884—61no—
213#882—61no—
214#882—61no—
215#67⋊C4—61no—
216D3×C22⋊C4—61no—
217D3×C22⋊C4—61no—
218D3×C22⋊C4—61no—
219#874—31no—
220C4×D12—31no—
221C4×D12—61no—
222C4×D12—61no—
223#872—31no—
224C3×C4⋊C8—31no—
225C3×#103—21no—
226C3×#103—31no—
227C3×#103C2×D311yescharacteristic, complemented
228C3×#103C2×D311yescharacteristic, complemented
229C3×#102—31no—
230C3×#102—31no—
231C3×#102—31no—
232#835C2×D311yescharacteristic, complemented
233#832—31no—
234#821—31no—
235#821C2×D311yescharacteristic, complemented
236Dic3⋊C8—31no—
237Dic3⋊C8—31no—
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—61no—
242Dic3⋊C8C2×D311yescharacteristic, complemented
243#809—31no—
244#809—31no—
245#809—31no—
246#809—31no—
247#809—61no—
248#809C2×D311yescharacteristic, complemented
249#809C2×D311yescharacteristic, complemented
250C4⋊(C3⋊C8)—31no—
251C22×C3⋊D3—21no—
252C22×C3⋊D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C2×D32—24no—
258C2×D32—42no—
259C2×D32—81no—
260C2×D32—81no—
261C2×D32—81no—
262C2×D32—81no—
263C32×Q8—21no—
264C32×Q8—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C2×C3⋊Dic3C2×D411yescharacteristic
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)C2×D412yes—
274C4×C3⋊D3—81no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—42no—
285C3×D12C2×D412yes—
286C3×C4×D3—42no—
287C3×C4×D3—81no—
288C3×C4×D3C2×D412yes—
289C3×C4×D3#4112yes—
290#626—24no—
291#626—42no—
292#626—81no—
293#626—81no—
294#625—81no—
295#625—81no—
296#624—81no—
297D3×Dic3—81no—
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×AGL(1,ℤ/8)—91no—
303C22×D8—91no—
304#535—91no—
305#518—91no—
306#463—31no—
307#463—91no—
308#463—91no—
309#463—91no—
310#459—91no—
311#459—91no—
312#459—91no—
313#459—91no—
314#424—91no—
315#418—91no—
316#416—31no—
317C23×D3—61no—
318C23×D3—61no—
319C23×D3—61no—
320C23×D3—61no—
321C3×#41—62no—
322C3×#41—62no—
323C2×C3×Q8—21no—
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—61no—
330C22×C3×C4—31no—
331C22×C3×C4—61no—
332C22×C3×C4—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C22×Dic3—61no—
342#239—22no—
343#239—22no—
344D3×D4—34no—
345D3×D4—62no—
346D3×D4—62no—
347D3×D4—62no—
348C2×D12—21no—
349C2×D12—31no—
350C2×D12—31no—
351C2×D12—34no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—62no—
357C2×D12—62no—
358C2×D12—62no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—61no—
362C2×D12—61no—
363C2×D12C22×D311yescharacteristic
364C2×D12C22×D311yescharacteristic
365C2×D12C22×D311yescharacteristic
366C2×C4×D3—21no—
367C2×C4×D3—21no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—121no—
374C2×C4×D3C22×D311yescharacteristic
375C3×SD16—62no—
376C3×D8—62no—
377C2×C3×C8—21no—
378C2×C3×C8—31no—
379C2×C3×C8—31no—
380C2×C3×C8—62no—
381C2×C3×C8C22×D311yescharacteristic
382C2×C3×C8C22×D311yescharacteristic
383C3×C4⋊C4—21no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4C22×D311yescharacteristic
386C3×C4⋊C4C22×D311yescharacteristic
387C3×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389C3×C22⋊C4—61no—
390C3×C22⋊C4—61no—
391C3×C42—31no—
392C3×C42—61no—
393#217—31no—
394#217—31no—
395#217—61no—
396#215—22no—
397#215—62no—
398#215—62no—
399#215—122no—
400#213—62no—
401#213—62no—
402#213—62no—
403#213—62no—
404#213—62no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—31no—
410(C2×D3)⋊C4—31no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—121no—
421(C2×D3)⋊C4—121no—
422(C2×D3)⋊C4—121no—
423C4⋊Dic3—31no—
424C4⋊Dic3—31no—
425C4⋊Dic3C22×D311yescharacteristic
426Dic3⋊C4—31no—
427Dic3⋊C4—31no—
428C4×Dic3—21no—
429C4×Dic3—31no—
430C4×Dic3—31no—
431C4×Dic3—61no—
432C4×Dic3C22×D311yescharacteristic
433#208—62no—
434C2×C3⋊C8—31no—
435C2×C3⋊C8—31no—
436C2×C3⋊C8—61no—
437C2×C3⋊C8C22×D311yescharacteristic
438C2×C3⋊C8C22×D311yescharacteristic
439D24—22no—
440D24—62no—
441D24—62no—
442D24—62no—
443D24—62no—
444D24—62no—
445D24—122no—
446ΓL(1,𝔽25)—62no—
447D3×C8—22no—
448C22×C32C22×D411yescharacteristic
449C2×C3⋊D3—22no—
450C2×C3⋊D3—41no—
451C2×C3⋊D3—41no—
452C2×C3⋊D3—41no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—22no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3#12112yes—
467D32—84no—
468D32—84no—
469C32×C4—41no—
470C32×C4—41no—
471C32×C4C22×D411yescharacteristic
472C32×C4C2×#4111yescharacteristic
473C3⋊Dic3—21no—
474C3⋊Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C2×#41—31no—
480C22×D4—91no—
481C22×D4—91no—
482AGL(1,ℤ/8)—184no—
483C2×SD16—31no—
484C2×SD16—91no—
485C2×D8—31no—
486C2×D8—91no—
487C2×D8—91no—
488C2×D8—91no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—184no—
492C2×M16—91no—
493C22×C8—31no—
494#127—91no—
495#127—91no—
496#124—31no—
497#124—91no—
498#121—181no—
499#121—181no—
500#120—181no—
501#120—181no—
502C4×D4—31no—
503C4×D4—91no—
504C4×D4—91no—
505C4×D4—91no—
506C4×D4—181no—
507C4×D4—181no—
508#117—31no—
509#117—91no—
510C2×C22⋊C4—181no—
511C2×C22⋊C4—181no—
512C4⋊C8—31no—
513C4⋊C8—91no—
514C4⋊C8—91no—
515C4⋊C8—91no—
516#103—31no—
517#103D3211yescharacteristic, complemented
518#102—31no—
519#102—31no—
520#102—31no—
521#102—91no—
522#102—91no—
523#102—91no—
524C23×C3—31no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3—61no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—64no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—64no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—121no—
538C22×D3—121no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—241no—
542C22×D3—241no—
543C22×D3—241no—
544C22×D3—241no—
545C22×D3—241no—
546C22×D3—241no—
547C22×D3—241no—
548C22×D3—241no—
549C22×D3D3×D411yescharacteristic
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—41no—
555C3×Q8—41no—
556C3×D4—32no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—122no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—31no—
569C2×C3×C4—32no—
570C2×C3×C4—32no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—61no—
576C2×C3×C4—122no—
577C2×C3×C4—241no—
578C2×C3×C4C23×D311yescharacteristic
579C2×C3×C4C23×D311yescharacteristic
580#67—64no—
581#67—122no—
582#67—241no—
583#67—241no—
584#67—241no—
585#67—241no—
586#67—241no—
587#67—241no—
588C2×Dic3—21no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—241no—
596C2×Dic3D3×D411yescharacteristic
597C2×Dic3D3×D411yescharacteristic
598C2×Dic3D3×D411yescharacteristic
599D12—21no—
600D12—21no—
601D12—21no—
602D12—21no—
603D12—21no—
604D12—32no—
605D12—32no—
606D12—42no—
607D12—62no—
608D12—64no—
609D12—61no—
610D12—61no—
611D12—61no—
612D12—61no—
613D12—61no—
614D12—61no—
615D12—121no—
616D12—121no—
617D12—121no—
618D12—122no—
619D12—241no—
620D12—241no—
621D12D3×D412yes—
622C4×D3—42no—
623C4×D3—81no—
624C4×D3—241no—
625C4×D3—241no—
626C4×D3—241no—
627C4×D3—241no—
628C4×D3—241no—
629C4×D3—242no—
630C4×D3#23512yes—
631C4×D3D3×D412yes—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—41no—
635C3×C8—61no—
636C3×C8—61no—
637C3⋊C8—21no—
638C3⋊C8—21no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C2×C32C2×#12111yescharacteristic
643C2×C32#57611yescharacteristic
644C2×C32#57611yescharacteristic
645C3⋊D3—42no—
646C3⋊D3—81no—
647C3×D3—22no—
648C3×D3—42no—
649C3×D3—81no—
650C3×D3—81no—
651C24—181no—
652C24—181no—
653#41—62no—
654#41—62no—
655C2×Q8C2×D3211yescharacteristic
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—61no—
660C2×D4—94no—
661C2×D4—91no—
662C2×D4—91no—
663C2×D4—182no—
664C2×D4—182no—
665C2×D4—182no—
666C2×D4—181no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4—181no—
672C22×C4—31no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—181no—
678SD16—62no—
679SD16—182no—
680D8—62no—
681D8—182no—
682D8—182no—
683D8—182no—
684D8—182no—
685D8—182no—
686M16—182no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—62no—
690C2×C8—91no—
691C2×C8C2×D3211yescharacteristic
692C4⋊C4—31no—
693C4⋊C4—91no—
694C4⋊C4—91no—
695C4⋊C4C2×D3211yescharacteristic
696C22⋊C4—61no—
697C22⋊C4—61no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—91no—
701C22⋊C4—91no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C42—31no—
708C42—61no—
709C42—91no—
710C22×C3—21no—
711C22×C3—32no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—62no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3C2×D3×D411yescharacteristic
724C22×C3C2×D3×D411yescharacteristic
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—22no—
728C2×D3—41no—
729C2×D3—41no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—62no—
737C2×D3—62no—
738C2×D3—122no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—241no—
750C2×D3—241no—
751C2×D3—241no—
752C2×D3—241no—
753C2×D3—241no—
754C2×D3—244no—
755C2×D3—244no—
756C2×D3—244no—
757C2×D3—244no—
758C2×D3#88412yes—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—32no—
762C3×C4—41no—
763C3×C4—41no—
764C3×C4—41no—
765C3×C4—41no—
766C3×C4—61no—
767C3×C4—61no—
768C3×C4—81no—
769C3×C4—81no—
770C3×C4—121no—
771C3×C4C2×#23511yescharacteristic
772C3×C4C2×D3×D411yescharacteristic
773C3×C4C2×D3×D411yescharacteristic
774C3×C4D3×#4111yescharacteristic
775Dic3—21no—
776Dic3—21no—
777Dic3—41no—
778Dic3—61no—
779Dic3—61no—
780Dic3—61no—
781Dic3—61no—
782Dic3—121no—
783Dic3—121no—
784Dic3#88412yes—
785C32#304111yescharacteristic, complemented, Sylow
786C23—31no—
787C23—61no—
788C23—61no—
789C23—61no—
790C23—184no—
791C23—181no—
792C23—181no—
793C23—362no—
794C23—721no—
795C23—721no—
796C23—721no—
797C23—721no—
798Q8—21no—
799Q8—21no—
800D4—32no—
801D4—61no—
802D4—61no—
803D4—61no—
804D4—61no—
805D4—61no—
806D4—92no—
807D4—122no—
808D4—184no—
809D4—181no—
810D4—181no—
811D4—181no—
812D4—362no—
813D4—721no—
814D4—721no—
815D4—721no—
816D4—721no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—31no—
820C2×C4—32no—
821C2×C4—32no—
822C2×C4—31no—
823C2×C4—31no—
824C2×C4—61no—
825C2×C4—91no—
826C2×C4—91no—
827C2×C4—122no—
828C2×C4—241no—
829C2×C4—721no—
830C2×C4—721no—
831C2×C4—721no—
832C2×C4C22×D3211yescharacteristic
833C8—21no—
834C8—61no—
835C8—61no—
836C8—181no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—62no—
841C2×C3—122no—
842C2×C3—241no—
843C2×C3—241no—
844C2×C3C2×#88411yescharacteristic
845C2×C3D3×#12111yescharacteristic
846C2×C3#576911yescharacteristic
847C2×C3#576911yescharacteristic
848C2×C3#576911yescharacteristic
849C2×C3#577411yescharacteristic
850D3—22no—
851D3—42no—
852D3—81no—
853D3—81no—
854D3—122no—
855D3—122no—
856D3—242no—
857D3—241no—
858D3—241no—
859D3—481no—
860C22—32no—
861C22—61no—
862C22—61no—
863C22—62no—
864C22—121no—
865C22—121no—
866C22—121no—
867C22—121no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—121no—
872C22—182no—
873C22—361no—
874C22—361no—
875C22—361no—
876C22—361no—
877C22—361no—
878C22—724no—
879C22—724no—
880C22D32×D411yescharacteristic
881C4—32no—
882C4—41no—
883C4—41no—
884C4—61no—
885C4—61no—
886C4—121no—
887C4—181no—
888C4—181no—
889C4D3×#23511yescharacteristic
890C4D32×D411yescharacteristic
891C3—21no—
892C3#7886211yescharacteristic, complemented
893C3#8053611yescharacteristic, complemented
894C2—62no—
895C2—122no—
896C2—241no—
897C2—241no—
898C2—362no—
899C2—721no—
900C2D3×#88411yescharacteristic
901C2#1059475511yescharacteristic
902C2#1059477111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3041
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
1. #10595426C2semidirect
2. C2×#63939C2semidirect
3. C2×D3×D24C2semidirect
4. #10594604C2semidirect
5. #10592518C2semidirect
6. C3×#4819C2semidirect
7. C3×#4804C2semidirect
8. #10591570C2semidirect
9. #10591568C2semidirect
10. #10590765C2semidirect
11. #10590749C2semidirect
12. #10590694C2semidirect
13. #10590592C2semidirect
14. #10590551C2semidirect
15. #10590547C2semidirect
21. #64156C22semidirect
22. C2×#3755C22semidirect
24. #64102C22semidirect
25. C3×#947C22semidirect
26. C2×C3×#215C22semidirect
29. C3×#893C22semidirect
36. #63914C22semidirect
37. #63911C22semidirect
41. #63898C22semidirect
42. #63894C22semidirect
47. C2×#3714C22semidirect
48. C2×#3713C22semidirect
51. C32×#103C22semidirect
52. #63641C22semidirect
53. #63636C22semidirect
54. C3×#835C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#809C22semidirect
58. C3×#809C22semidirect
59. #63572C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
86. #4819D3semidirect
87. #4804D3semidirect
120. D3×D12D4semidirect
170. #947C2×D3semidirect
174. C2×#215C2×D3semidirect
209. #893C2×D3semidirect
227. C3×#103C2×D3semidirect
228. C3×#103C2×D3semidirect
232. #835C2×D3semidirect
235. #821C2×D3semidirect
242. Dic3⋊C8C2×D3semidirect
248. #809C2×D3semidirect
249. #809C2×D3semidirect
517. #103D32semidirect
785. C32#3041semidirect
892. C3#78862semidirect
893. C3#80536semidirect

Maximal subgroups

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

subgroupindex
#105954262
C2×#639392
C2×D3×D242
#105946042
#105925182
C3×#48192
C3×#48042
#105915702
#105915682
#105907652
#105907492
#105906942
#105905922
#105905512
#105905472
#805363
#788623