Finite Group Databasebeta

← #11866222

Subgroups — #11866222

Order 1152.

1122 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595303C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic, complemented
3C2×D3×D24C211yesmaximal, characteristic, complemented
4#10594604C211yesmaximal, characteristic, complemented
5#10592485C211yesmaximal, characteristic, complemented
6C3×#4786C211yesmaximal, characteristic, complemented
7C3×#4772C211yesmaximal, characteristic, complemented
8#10591433C211yesmaximal, characteristic, complemented
9#10591429C211yesmaximal, characteristic, complemented
10#10590770C211yesmaximal, characteristic, complemented
11#10590751C211yesmaximal, characteristic, complemented
12#10590694C211yesmaximal, characteristic, complemented
13#10590592C211yesmaximal, characteristic, complemented
14#10590540C211yesmaximal, characteristic, complemented
15#10590534C211yesmaximal, characteristic, complemented
16#80334—31nomaximal
17#78862—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21#64149C2211yescharacteristic, complemented
22C2×#3753C2211yescharacteristic, complemented
23C2×#3745C2211yescharacteristic
24#64102C2211yescharacteristic, complemented
25C3×#940C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic, complemented
27C2×C3×D24C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#893C2211yescharacteristic, complemented
30C3×#892C2211yescharacteristic
31#63983—21no—
32#63983—21no—
33#63978—21no—
34#63978—21no—
35#63925—24no—
36#63921—21no—
37D3×(C2×D3)⋊C4—21no—
38C4×#626—21no—
39#63898C2211yescharacteristic, complemented
40#63894C2211yescharacteristic, complemented
41#63880—21no—
42#63864C2211yescharacteristic, complemented
43#63863C2211yescharacteristic, complemented
44#63855C2211yescharacteristic
45C2×#3717C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, complemented
47C2×#3714C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3711C2211yescharacteristic
50D3×D24—24no—
51C32×#102C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, 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×#911—31no—
66C2×D3×D8—31no—
67C22×D24—31no—
68#5715—31no—
69#5545—31no—
70#5521—31no—
71C3×#459—31no—
72C3×#416—31no—
73#5153—31no—
74#5150—31no—
75#5102—31no—
76#5072—31no—
77#5016—31no—
78#5001—31no—
79#4844—31no—
80#4839—31no—
81#4819—31no—
82#4819—31no—
83#4819—31no—
84#4819—31no—
85#4787—31no—
86#4786—31no—
87#4786—31no—
88#4786—31no—
89#4786—31no—
90#4786—61no—
91#4786D311yescharacteristic, complemented
92#4772D311yescharacteristic, complemented
93#4770—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C2×#638—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C22×C3×Dic3—21no—
106C3×#237—22no—
107C3×#237—22no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#626—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#3753—22no—
124#3752—21no—
125C4×C3⋊Dic3C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3745—22no—
128C3×#213—22no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×D24—22no—
137C3×D3×C8—22no—
138Dic3⋊Dic3D411yescharacteristic
139Dic3⋊Dic3D411yescharacteristic
140#3722—21no—
141#3722—21no—
142#3722—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3D411yescharacteristic
147(C2×D3)⋊Dic3D411yescharacteristic
148#3717—22no—
149#3715—22no—
150#3714—22no—
151#3714—22no—
152#3711—22no—
153#3041—91noSylow
154C2×C3×#41—31no—
155C2×#237C2×D311yescharacteristic
156C2×D3×D4—31no—
157C2×D3×D4—31no—
158C22×D12—31no—
159C22×D12—31no—
160C2×C3×D8—31no—
161C2×C3×D8—31no—
162C22×C3×C8—31no—
163C3×#127—31no—
164C3×C4×D4—31no—
165C3×#117—31no—
166#949—64no—
167#947—31no—
168#947—31no—
169C2×#215—31no—
170C2×#215—31no—
171#940—31no—
172#940—31no—
173#940—61no—
174#940C2×D311yescharacteristic, complemented
175#939—61no—
176#939—61no—
177#937—61no—
178#937—61no—
179#937—61no—
180#937—61no—
181#936—31no—
182D4×Dic3—31no—
183C2×#214—31no—
184C2×#213—31no—
185C2×#213—31no—
186C2×#213—31no—
187C2×#213—31no—
188C2×#213—61no—
189C2×#213C2×D311yescharacteristic, complemented
190#930—61no—
191#930—61no—
192C4×#67—61no—
193C2×(C2×D3)⋊C4—61no—
194#926—31no—
195C2×#208—31no—
196#911—64no—
197D3×D8—64no—
198C2×D24—31no—
199C2×D24—31no—
200C2×D24—31no—
201C2×D24—31no—
202C2×D24—61no—
203C2×D24—64no—
204C2×D24C2×D311yescharacteristic
205C2×#204—31no—
206C2×ΓL(1,𝔽25)—31no—
207C2×D3×C8C2×D311yescharacteristic
208#893—31no—
209#893—31no—
210#893—31no—
211#893—31no—
212#893—61no—
213#893C2×D311yescharacteristic, complemented
214#892C2×D311yescharacteristic
215#67⋊C4—61no—
216D3×C22⋊C4—61no—
217D3×C22⋊C4—61no—
218D3×C22⋊C4—61no—
219#875—31no—
220C4×D12—31no—
221C4×D12—61no—
222C4×D12—61no—
223#872—31no—
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#103—31no—
227C3×#102—21no—
228C3×#102—31no—
229C3×#102—31no—
230C3×#102C2×D311yescharacteristic, complemented
231C3×#102C2×D311yescharacteristic, complemented
232#832—31no—
233#832C2×D311yescharacteristic, complemented
234#821—31no—
235#816C2×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#810C2×D311yescharacteristic, complemented
244#809—31no—
245#809—31no—
246#809—31no—
247#809—31no—
248#809—61no—
249#809C2×D311yescharacteristic, complemented
250C4⋊(C3⋊C8)—31no—
251C23×C32—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×D4—21no—
264C32×D4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C2411yescharacteristic
267#638—81no—
268#638—81no—
269C2×C3⋊Dic3C2×D411yescharacteristic
270C2×C3⋊Dic3C2×D411yescharacteristic
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)C2×D412yes—
275C4×C3⋊D3—81no—
276C3×#67—42no—
277C3×#67—81no—
278C3×#67—81no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—42no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12C2×D412yes—
289C3×C4×D3—81no—
290C3×C4×D3C2×D412yes—
291C3×C4×D3#4112yes—
292C3×Dic6—21no—
293C3×Dic6—21no—
294#626—24no—
295#626—42no—
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—91no—
307#463—91no—
308#463—91no—
309#463—91no—
310#459—31no—
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—31no—
324C2×C3×D4—21no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4C22×D311yescharacteristic
331C2×C3×D4C22×D311yescharacteristic
332C22×C3×C4—31no—
333C22×C3×C4—61no—
334C22×C3×C4—61no—
335C2×#67—21no—
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—121no—
345C2×#67—121no—
346C22×Dic3—21no—
347C22×Dic3—61no—
348#237—22no—
349#237—22no—
350D3×D4—34no—
351D3×D4—62no—
352D3×D4—62no—
353D3×D4—62no—
354C2×D12—31no—
355C2×D12—31no—
356C2×D12—34no—
357C2×D12—31no—
358C2×D12—31no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—62no—
362C2×D12—62no—
363C2×D12—62no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12C22×D311yescharacteristic
367C2×D12C22×D311yescharacteristic
368C2×C4×D3—21no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—121no—
375C2×C4×D3C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C3×D8—62no—
378C3×D8—62no—
379C2×C3×C8—21no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C2×C3×C8—62no—
383C2×C3×C8C22×D311yescharacteristic
384C2×C3×C8C22×D311yescharacteristic
385C3×C4⋊C4—21no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4C22×D311yescharacteristic
388C3×C4⋊C4C22×D311yescharacteristic
389C3×C22⋊C4—61no—
390C3×C22⋊C4—61no—
391C3×C42—31no—
392C3×C42—61no—
393#217—31no—
394#217—31no—
395#217—61no—
396#217—61no—
397#217—61no—
398#215—62no—
399#215—62no—
400#214—62no—
401#213—22no—
402#213—62no—
403#213—62no—
404#213—62no—
405#213—62no—
406#213—122no—
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—61no—
421(C2×D3)⋊C4—61no—
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—122no—
445#204—62no—
446ΓL(1,𝔽25)—62no—
447D3×C8—22no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32C22×D411yescharacteristic
452C2×C3⋊D3—22no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—22no—
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×C4C22×D411yescharacteristic
471C32×C4C2×#4111yescharacteristic
472C3⋊Dic3—21no—
473C3⋊Dic3—21no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C2×#41—31no—
480C22×D4—91no—
481C22×D4—91no—
482AGL(1,ℤ/8)—184no—
483C2×SD16—91no—
484C2×SD16—91no—
485C2×D8—31no—
486C2×D8—31no—
487C2×D8—91no—
488C2×D8—91no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—184no—
492C2×M16—91no—
493C22×C8—31no—
494#127—31no—
495#127—91no—
496#124—91no—
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#103—31no—
518#102—31no—
519#102—31no—
520#102—91no—
521#102—91no—
522#102—91no—
523#102D3211yescharacteristic, complemented
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—31no—
527C23×C3—41no—
528C23×C3—61no—
529C23×C3—61no—
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—64no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—64no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—121no—
539C22×D3—121no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—241no—
543C22×D3—241no—
544C22×D3—241no—
545C22×D3—241no—
546C22×D3—241no—
547C22×D3—241no—
548C22×D3—241no—
549C22×D3—241no—
550C22×D3D3×D411yescharacteristic
551C3×Q8—61no—
552C3×Q8—61no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—32no—
558C3×D4—41no—
559C3×D4—41no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—122no—
564C3×D4—241no—
565C3×D4—241no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—31no—
570C2×C3×C4—32no—
571C2×C3×C4—32no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—41no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—122no—
578C2×C3×C4—241no—
579C2×C3×C4C23×D311yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581#67—42no—
582#67—64no—
583#67—81no—
584#67—81no—
585#67—122no—
586#67—241no—
587#67—241no—
588#67—241no—
589#67—241no—
590#67—242no—
591#67—242no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—31no—
598C2×Dic3—42no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—241no—
602C2×Dic3D3×D411yescharacteristic
603C2×Dic3D3×D411yescharacteristic
604C2×Dic3D3×D411yescharacteristic
605D12—21no—
606D12—21no—
607D12—21no—
608D12—32no—
609D12—32no—
610D12—62no—
611D12—64no—
612D12—61no—
613D12—61no—
614D12—61no—
615D12—61no—
616D12—61no—
617D12—61no—
618D12—121no—
619D12—121no—
620D12—121no—
621D12—122no—
622D12D3×D412yes—
623C4×D3—81no—
624C4×D3—241no—
625C4×D3—241no—
626C4×D3—241no—
627C4×D3—241no—
628C4×D3—242no—
629C4×D3—241no—
630C4×D3#23512yes—
631C4×D3D3×D412yes—
632Dic6—21no—
633Dic6—21no—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—41no—
637C3×C8—61no—
638C3×C8—61no—
639C3⋊C8—21no—
640C3⋊C8—21no—
641C3⋊C8—61no—
642C3⋊C8—61no—
643C3⋊C8—121no—
644C2×C32—81no—
645C2×C32C2×#12111yescharacteristic
646C2×C32#57611yescharacteristic
647C2×C32#57611yescharacteristic
648C3⋊D3—42no—
649C3⋊D3—81no—
650C3×D3—22no—
651C3×D3—42no—
652C3×D3—81no—
653C24—181no—
654C24—181no—
655#41—62no—
656#41—62no—
657C2×Q8—31no—
658C2×D4—31no—
659C2×D4—31no—
660C2×D4—61no—
661C2×D4—61no—
662C2×D4—61no—
663C2×D4—94no—
664C2×D4—91no—
665C2×D4—91no—
666C2×D4—182no—
667C2×D4—182no—
668C2×D4—182no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4C2×D3211yescharacteristic
674C22×C4—31no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—181no—
678C22×C4—181no—
679C22×C4—181no—
680SD16—182no—
681SD16—182no—
682D8—62no—
683D8—62no—
684D8—182no—
685D8—182no—
686D8—182no—
687D8—182no—
688M16—182no—
689C2×C8—31no—
690C2×C8—31no—
691C2×C8—62no—
692C2×C8—91no—
693C2×C8C2×D3211yescharacteristic
694C4⋊C4—31no—
695C4⋊C4—91no—
696C4⋊C4—91no—
697C4⋊C4C2×D3211yescharacteristic
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—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C42—31no—
710C42—61no—
711C42—91no—
712C22×C3—21no—
713C22×C3—32no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—62no—
723C22×C3—81no—
724C22×C3—81no—
725C22×C3—81no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3C2×D3×D411yescharacteristic
732C22×C3C2×D3×D411yescharacteristic
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—22no—
736C2×D3—41no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—62no—
742C2×D3—62no—
743C2×D3—122no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—241no—
755C2×D3—241no—
756C2×D3—241no—
757C2×D3—241no—
758C2×D3—241no—
759C2×D3—244no—
760C2×D3—244no—
761C2×D3—244no—
762C2×D3—244no—
763C2×D3#88412yes—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—32no—
767C3×C4—41no—
768C3×C4—41no—
769C3×C4—61no—
770C3×C4—61no—
771C3×C4—81no—
772C3×C4—121no—
773C3×C4—121no—
774C3×C4C2×#23511yescharacteristic
775C3×C4C2×D3×D411yescharacteristic
776C3×C4C2×D3×D411yescharacteristic
777C3×C4D3×#4111yescharacteristic
778Dic3—21no—
779Dic3—21no—
780Dic3—41no—
781Dic3—41no—
782Dic3—62no—
783Dic3—61no—
784Dic3—61no—
785Dic3—61no—
786Dic3—61no—
787Dic3—121no—
788Dic3#88412yes—
789C32#304111yescharacteristic, complemented, Sylow
790C23—21no—
791C23—31no—
792C23—61no—
793C23—61no—
794C23—184no—
795C23—181no—
796C23—181no—
797C23—362no—
798C23—721no—
799C23—721no—
800C23—721no—
801C23—721no—
802Q8—61no—
803Q8—61no—
804D4—21no—
805D4—21no—
806D4—32no—
807D4—61no—
808D4—61no—
809D4—61no—
810D4—92no—
811D4—122no—
812D4—184no—
813D4—181no—
814D4—181no—
815D4—181no—
816D4—241no—
817D4—241no—
818D4—362no—
819D4—721no—
820D4—721no—
821C2×C4—21no—
822C2×C4—31no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—31no—
826C2×C4—31no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—91no—
830C2×C4—91no—
831C2×C4—122no—
832C2×C4—241no—
833C2×C4—721no—
834C2×C4—721no—
835C2×C4—721no—
836C2×C4C22×D3211yescharacteristic
837C8—21no—
838C8—61no—
839C8—61no—
840C8—181no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—62no—
845C2×C3—81no—
846C2×C3—81no—
847C2×C3—122no—
848C2×C3—161no—
849C2×C3—241no—
850C2×C3C2×#88411yescharacteristic
851C2×C3D3×#12111yescharacteristic
852C2×C3#575711yescharacteristic
853C2×C3#576911yescharacteristic
854C2×C3#576911yescharacteristic
855C2×C3#577411yescharacteristic
856D3—22no—
857D3—42no—
858D3—81no—
859D3—122no—
860D3—122no—
861D3—242no—
862D3—241no—
863D3—241no—
864D3—481no—
865C22—32no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—61no—
870C22—61no—
871C22—62no—
872C22—121no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22—121no—
877C22—182no—
878C22—361no—
879C22—361no—
880C22—361no—
881C22—361no—
882C22—361no—
883C22—724no—
884C22—724no—
885C22D32×D411yescharacteristic
886C4—32no—
887C4—41no—
888C4—61no—
889C4—61no—
890C4—121no—
891C4—121no—
892C4—181no—
893C4—181no—
894C4D3×#23511yescharacteristic
895C4D32×D411yescharacteristic
896C3—21no—
897C3#7886211yescharacteristic, complemented
898C3#8033411yescharacteristic, complemented
899C2—62no—
900C2—81no—
901C2—122no—
902C2—241no—
903C2—362no—
904C2—721no—
905C2D3×#88411yescharacteristic
906C2#1059473411yescharacteristic
907C2#1059475511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595303C2semidirect
2. C2×#63925C2semidirect
3. C2×D3×D24C2semidirect
4. #10594604C2semidirect
5. #10592485C2semidirect
6. C3×#4786C2semidirect
7. C3×#4772C2semidirect
8. #10591433C2semidirect
9. #10591429C2semidirect
10. #10590770C2semidirect
11. #10590751C2semidirect
12. #10590694C2semidirect
13. #10590592C2semidirect
14. #10590540C2semidirect
15. #10590534C2semidirect
21. #64149C22semidirect
22. C2×#3753C22semidirect
24. #64102C22semidirect
25. C3×#940C22semidirect
26. C2×C3×#213C22semidirect
29. C3×#893C22semidirect
39. #63898C22semidirect
40. #63894C22semidirect
42. #63864C22semidirect
43. #63863C22semidirect
45. C2×#3717C22semidirect
46. C2×#3715C22semidirect
51. C32×#102C22semidirect
52. #63641C22semidirect
53. #63636C22semidirect
54. C3×#832C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#809C22semidirect
59. #63572C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
91. #4786D3semidirect
92. #4772D3semidirect
120. D3×D12D4semidirect
174. #940C2×D3semidirect
189. C2×#213C2×D3semidirect
213. #893C2×D3semidirect
230. C3×#102C2×D3semidirect
231. C3×#102C2×D3semidirect
233. #832C2×D3semidirect
235. #816C2×D3semidirect
242. Dic3⋊C8C2×D3semidirect
243. #810C2×D3semidirect
249. #809C2×D3semidirect
523. #102D32semidirect
789. C32#3041semidirect
897. C3#78862semidirect
898. C3#80334semidirect

Maximal subgroups

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

subgroupindex
#105953032
C2×#639252
C2×D3×D242
#105946042
#105924852
C3×#47862
C3×#47722
#105914332
#105914292
#105907702
#105907512
#105906942
#105905922
#105905402
#105905342
#803343
#788623