Finite Group Databasebeta

← #11865883

Subgroups — #11865883

Order 1152.

1166 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595153C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic, complemented
3C2×#63794C211yesmaximal, characteristic, complemented
4D3×#893C211yesmaximal, characteristic, complemented
5#10592485C211yesmaximal, characteristic, complemented
6C3×#4787C211yesmaximal, characteristic, complemented
7C3×#4771C211yesmaximal, characteristic, complemented
8#10591433C211yesmaximal, characteristic, complemented
9#10591432C211yesmaximal, characteristic, complemented
10#10590770C211yesmaximal, characteristic, complemented
11#10590748C211yesmaximal, characteristic, complemented
12#10590663C211yesmaximal, characteristic, complemented
13#10590609C211yesmaximal, characteristic, complemented
14#10590565C211yesmaximal, characteristic, complemented
15#10590534C211yesmaximal, characteristic, complemented
16#80534—31nomaximal
17#78910—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×C4×D32—21no—
21C2×#3799C2211yescharacteristic
22#64149C2211yescharacteristic, complemented
23C2×#3753C2211yescharacteristic
24C2×#3745C2211yescharacteristic
25#64102C2211yescharacteristic
26C3×#936C2211yescharacteristic, complemented
27C2×C3×#213C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
30C3×#893C2211yescharacteristic
31C3×D3×C4⋊C4C2211yescharacteristic
32#63971—21no—
33#63971—21no—
34#63952—21no—
35#63952—21no—
36#63925—24no—
37D3×(C2×D3)⋊C4—21no—
38#63904—21no—
39#63898C2211yescharacteristic
40#63894C2211yescharacteristic
41#63881—21no—
42C4×D3×Dic3C2211yescharacteristic
43#63873C2211yescharacteristic, complemented
44#63864C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic
46C2×#3717C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3711C2211yescharacteristic
50#63794—24no—
51C32×#102C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#810C2211yescharacteristic, complemented
59#63572C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63#5832—31no—
64C2×#949—31no—
65C2×#914—31no—
66C2×#911—31no—
67C2×#908—31no—
68#5668—31no—
69C4×D3×D4—31no—
70C2×#893—31no—
71C3×#463—31no—
72C3×#417—31no—
73#5162—31no—
74#5150—31no—
75#5118—31no—
76#5057—31no—
77#5016—31no—
78#4966—31no—
79#4844—31no—
80#4837—31no—
81#4819—31no—
82#4819—31no—
83#4818—31no—
84#4818—31no—
85#4818—31no—
86#4803—31no—
87#4787—31no—
88#4787D311yescharacteristic, complemented
89#4786—31no—
90#4786—31no—
91#4786—31no—
92#4786—61no—
93#4771D311yescharacteristic, complemented
94C22×D32—21no—
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C3×#237—22no—
104C3×#237—22no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#626—21no—
112C2×#626—21no—
113C2×#624—21no—
114C2×#624—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3D411yescharacteristic
117C2×D3×Dic3D411yescharacteristic
118D3×D12—22no—
119D3×D12D414yescomplemented
120C4×D32—44no—
121#3799—22no—
122#3799—22no—
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125#3753—22no—
126#3752—21no—
127C4×C3⋊Dic3C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129#3745—22no—
130C3×#217—21no—
131C3×#217—21no—
132C3×#213—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—22no—
140C3×ΓL(1,𝔽25)—22no—
141#3724—21no—
142#3724—21no—
143#3722—21no—
144#3722—21no—
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147Dic32D411yescharacteristic
148Dic32D411yescharacteristic
149#3717—22no—
150#3717—22no—
151#3715—22no—
152#3714—22no—
153#3711—22no—
154#3036—91noSylow
155C2×C3×#41—31no—
156C2×#239—31no—
157C2×#237C2×D311yescharacteristic
158C2×D3×D4—31no—
159C2×#235—31no—
160C22×D12—31no—
161C22×C4×D3—61no—
162C22×C4×D3—61no—
163C2×C3×SD16—31no—
164C2×C3×D8—31no—
165C2×C3×M16—31no—
166C3×#124—31no—
167C3×C4×D4—31no—
168C2×C3×C4⋊C4—31no—
169#949—64no—
170#947—31no—
171#944—31no—
172#944—31no—
173C2×#215—31no—
174C2×#215—31no—
175C2×#215—31no—
176#940—31no—
177#940—31no—
178#940—61no—
179#939—61no—
180#939—61no—
181#936C2×D311yescharacteristic, complemented
182D4×Dic3—31no—
183C2×#214—31no—
184C2×#213—31no—
185C2×#213—31no—
186C2×#213—31no—
187C2×#213—61no—
188C2×#213C2×D311yescharacteristic
189C4×#67—61no—
190C4×#67—61no—
191C4×#67—61no—
192C2×(C2×D3)⋊C4—61no—
193C2×C4×Dic3—31no—
194C2×#208—31no—
195#914—64no—
196#911—64no—
197#908—64no—
198C2×D24—31no—
199C2×D24—31no—
200C2×D24—31no—
201C2×D24—61no—
202C2×#204—31no—
203C2×#204—31no—
204C2×#204C2×D311yescharacteristic
205C2×ΓL(1,𝔽25)—31no—
206C2×ΓL(1,𝔽25)C2×D311yescharacteristic
207#893—31no—
208#893—31no—
209#893—31no—
210#893—31no—
211#893—61no—
212#893—61no—
213#893—61no—
214#893C2×D311yescharacteristic
215D3×C4⋊C4C2×D311yescharacteristic
216#884—61no—
217#884—61no—
218#67⋊C4—61no—
219#67⋊C4—61no—
220#67⋊C4—61no—
221D3×C22⋊C4—61no—
222#875—31no—
223C4×D12—31no—
224C42×D3—31no—
225C3×C4⋊C8—31no—
226C3×#103—31no—
227C3×#103—31no—
228C3×#103—31no—
229C3×#102—21no—
230C3×#102—31no—
231C3×#102C2×D311yescharacteristic, complemented
232C3×#102C2×D311yescharacteristic, complemented
233#835—31no—
234#832C2×D311yescharacteristic, complemented
235#821—31no—
236#816C2×D311yescharacteristic, complemented
237Dic3⋊C8—31no—
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—61no—
243Dic3⋊C8C2×D311yescharacteristic, complemented
244#810—31no—
245#810C2×D311yescharacteristic, complemented
246#810C2×D311yescharacteristic, complemented
247#809—31no—
248#809—31no—
249#809—31no—
250#809—61no—
251C4⋊(C3⋊C8)—31no—
252C23×C32—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—42no—
260C32×D4—21no—
261C32×D4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2411yescharacteristic
264#638—42no—
265#638—42no—
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)C2×D412yes—
272C4×C3⋊D3—42no—
273C3×#67—42no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—42no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C3×D12—21no—
282C3×D12C2×D412yes—
283C3×C4×D3—42no—
284C3×C4×D3—42no—
285C3×C4×D3C2×D412yes—
286C3×C4×D3#4112yes—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#626—24no—
292#626—42no—
293#624—42no—
294#624—42no—
295D3×Dic3—22no—
296D3×Dic3—41no—
297D3×Dic3—42no—
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×AGL(1,ℤ/8)—91no—
303C2×AGL(1,ℤ/8)—91no—
304#532—91no—
305C2×C4×D4—91no—
306#463—31no—
307#463—91no—
308#463—91no—
309#463—91no—
310#461—91no—
311#461—91no—
312#459—91no—
313#459—91no—
314#423—91no—
315#417—31no—
316#417—91no—
317C23×D3—61no—
318C23×D3—61no—
319C3×#41—62no—
320C3×#41—62no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×D4—21no—
324C2×C3×D4—31no—
325C2×C3×D4—61no—
326C2×C3×D4C22×D311yescharacteristic
327C2×C3×D4C22×D311yescharacteristic
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C22×C3×C4—61no—
332C2×#67—21no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—121no—
340C2×#67—121no—
341C22×Dic3—21no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—61no—
345#239—62no—
346#239—62no—
347#237—22no—
348#237—22no—
349D3×D4—34no—
350D3×D4—62no—
351#235—62no—
352#235—62no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—34no—
356C2×D12—31no—
357C2×D12—31no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—62no—
361C2×D12—61no—
362C2×D12—61no—
363C2×D12C22×D311yescharacteristic
364C2×C4×D3—21no—
365C2×C4×D3—21no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—121no—
376C2×C4×D3—124no—
377C2×C4×D3—124no—
378C2×C4×D3C22×D311yescharacteristic
379C2×Dic6C22×D311yescharacteristic
380C2×Dic6C22×D311yescharacteristic
381C3×SD16—62no—
382C3×D8—62no—
383C3×M16—62no—
384C2×C3×C8—21no—
385C2×C3×C8—31no—
386C2×C3×C8—31no—
387C2×C3×C8C22×D311yescharacteristic
388C2×C3×C8C22×D311yescharacteristic
389C3×C4⋊C4—21no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4C22×D311yescharacteristic
393C3×C4⋊C4C22×D311yescharacteristic
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C42—31no—
398#217—21no—
399#217—21no—
400#217—61no—
401#215—62no—
402#215—62no—
403#215—62no—
404#214—62no—
405#213—22no—
406#213—62no—
407#213—62no—
408#213—62no—
409#213—122no—
410(C2×D3)⋊C4—21no—
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—
421C4⋊Dic3C22×D311yescharacteristic
422Dic3⋊C4—21no—
423Dic3⋊C4—61no—
424Dic3⋊C4—61no—
425Dic3⋊C4—61no—
426Dic3⋊C4—61no—
427C4×Dic3—31no—
428C4×Dic3—31no—
429C4×Dic3—31no—
430C4×Dic3—31no—
431C4×Dic3—31no—
432C4×Dic3—31no—
433C4×Dic3—61no—
434C4×Dic3C22×D311yescharacteristic
435#208—62no—
436C2×C3⋊C8—31no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—61no—
439C2×C3⋊C8C22×D311yescharacteristic
440C2×C3⋊C8C22×D311yescharacteristic
441D24—62no—
442D24—62no—
443D24—62no—
444D24—122no—
445#204—22no—
446#204—62no—
447#204—62no—
448ΓL(1,𝔽25)—22no—
449ΓL(1,𝔽25)—62no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32C22×D411yescharacteristic
454C2×C3⋊D3—22no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—22no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3#12112yes—
466D32—48no—
467C32×C4—41no—
468C32×C4C22×D411yescharacteristic
469C32×C4C2×#4111yescharacteristic
470C3⋊Dic3—21no—
471C3⋊Dic3AGL(1,ℤ/8)12yescomplemented
472C3×Dic3—21no—
473C3×Dic3—21no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C3×Dic3#12112yes—
478C2×#41—31no—
479C2×#41—91no—
480C22×D4—91no—
481C23×C4—181no—
482AGL(1,ℤ/8)—184no—
483AGL(1,ℤ/8)—184no—
484C2×SD16—31no—
485C2×SD16—91no—
486C2×SD16—91no—
487C2×SD16—91no—
488C2×D8—31no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—91no—
492C2×M16—31no—
493C2×M16—91no—
494C4⋊Q8—91no—
495#127—91no—
496#124—31no—
497#124—91no—
498#121—181no—
499#121—181no—
500C4×D4—31no—
501C4×D4—91no—
502C4×D4—91no—
503C4×D4—91no—
504C4×D4—181no—
505C4×D4—181no—
506C4×D4—181no—
507C4×D4—181no—
508C2×C4⋊C4—31no—
509C2×C22⋊C4—181no—
510C2×C42—91no—
511C4⋊C8—31no—
512C4⋊C8—91no—
513C4⋊C8—91no—
514C4⋊C8—91no—
515#103—31no—
516#103—31no—
517#103—31no—
518#103—91no—
519#102—31no—
520#102—91no—
521#102—91no—
522#102D3211yescharacteristic, complemented
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—31no—
526C23×C3—41no—
527C23×C3—61no—
528C22×D3—21no—
529C22×D3—64no—
530C22×D3—61no—
531C22×D3—61no—
532C22×D3—64no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—121no—
536C22×D3—121no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3D3×D411yescharacteristic
542C3×Q8—61no—
543C3×Q8—61no—
544C3×Q8—61no—
545C3×Q8—61no—
546C3×D4—21no—
547C3×D4—21no—
548C3×D4—21no—
549C3×D4—21no—
550C3×D4—32no—
551C3×D4—41no—
552C3×D4—41no—
553C3×D4—61no—
554C3×D4—122no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—31no—
559C2×C3×C4—32no—
560C2×C3×C4—32no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—41no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—122no—
568C2×C3×C4—122no—
569C2×C3×C4—122no—
570C2×C3×C4C23×D311yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572#67—42no—
573#67—64no—
574#67—122no—
575#67—122no—
576#67—122no—
577#67—122no—
578#67—122no—
579#67—242no—
580#67—242no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—31no—
585C2×Dic3—31no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—42no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—62no—
592C2×Dic3—121no—
593C2×Dic3—122no—
594C2×Dic3D3×D411yescharacteristic
595C2×Dic3D3×D411yescharacteristic
596C2×Dic3D3×D411yescharacteristic
597D12—21no—
598D12—32no—
599D12—32no—
600D12—62no—
601D12—64no—
602D12—61no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—61no—
608D12—121no—
609D12—121no—
610D12—121no—
611D12—122no—
612D12D3×D412yes—
613C4×D3—42no—
614C4×D3—42no—
615C4×D3—62no—
616C4×D3—122no—
617C4×D3—122no—
618C4×D3—122no—
619C4×D3—122no—
620C4×D3—122no—
621C4×D3—122no—
622C4×D3—121no—
623C4×D3—122no—
624C4×D3—242no—
625C4×D3#23512yes—
626C4×D3D3×D412yes—
627Dic6—21no—
628Dic6—21no—
629Dic6—21no—
630Dic6—21no—
631C3×C8—21no—
632C3×C8—21no—
633C3×C8—41no—
634C3×C8—61no—
635C3×C8—61no—
636C3⋊C8—21no—
637C3⋊C8—21no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—121no—
641C2×C32—81no—
642C2×C32C2×#12111yescharacteristic
643C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
644C2×C32#57511yescharacteristic
645C3⋊D3—42no—
646C3⋊D3—81no—
647C3×D3—22no—
648C3×D3—42no—
649C24—181no—
650#41—62no—
651#41—62no—
652#41—182no—
653#41—182no—
654C2×Q8—31no—
655C2×Q8—31no—
656C2×D4—31no—
657C2×D4—61no—
658C2×D4—94no—
659C2×D4—91no—
660C2×D4—91no—
661C2×D4—182no—
662C2×D4—181no—
663C2×D4—181no—
664C2×D4—181no—
665C2×D4—181no—
666C2×D4C2×D3211yescharacteristic
667C22×C4—31no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—91no—
672C22×C4—91no—
673C22×C4—181no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—364no—
678SD16—62no—
679SD16—182no—
680SD16—182no—
681SD16—182no—
682D8—62no—
683D8—182no—
684D8—182no—
685D8—182no—
686M16—62no—
687M16—182no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—91no—
691C2×C8C2×D3211yescharacteristic
692C4⋊C4—31no—
693C4⋊C4—61no—
694C4⋊C4—181no—
695C4⋊C4—181no—
696C4⋊C4C2×D3211yescharacteristic
697C22⋊C4—61no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C42—31no—
706C42—91no—
707C42—91no—
708C42—91no—
709C22×C3—21no—
710C22×C3—32no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—62no—
720C22×C3—81no—
721C22×C3—81no—
722C22×C3—81no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3C2×D3×D411yescharacteristic
726C22×C3C2×D3×D411yescharacteristic
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—22no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—62no—
733C2×D3—62no—
734C2×D3—122no—
735C2×D3—128no—
736C2×D3—128no—
737C2×D3—121no—
738C2×D3—121no—
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—241no—
748C2×D3—241no—
749C2×D3—241no—
750C2×D3—241no—
751C2×D3—241no—
752C2×D3#88412yes—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—32no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—61no—
759C3×C4—61no—
760C3×C4—81no—
761C3×C4—121no—
762C3×C4—121no—
763C3×C4—121no—
764C3×C4C2×#23511yescharacteristic
765C3×C4C2×D3×D411yescharacteristic
766C3×C4C2×D3×D411yescharacteristic
767C3×C4D3×#4111yescharacteristic
768Dic3—21no—
769Dic3—21no—
770Dic3—32no—
771Dic3—32no—
772Dic3—41no—
773Dic3—41no—
774Dic3—41no—
775Dic3—62no—
776Dic3—61no—
777Dic3—61no—
778Dic3—121no—
779Dic3#88412yes—
780C32#303611yescharacteristic, complemented, Sylow
781C23—21no—
782C23—31no—
783C23—61no—
784C23—184no—
785C23—181no—
786C23—181no—
787C23—362no—
788C23—362no—
789Q8—61no—
790Q8—61no—
791Q8—61no—
792Q8—61no—
793D4—21no—
794D4—21no—
795D4—32no—
796D4—61no—
797D4—92no—
798D4—122no—
799D4—184no—
800D4—181no—
801D4—181no—
802D4—181no—
803D4—362no—
804D4—362no—
805D4—362no—
806C2×C4—21no—
807C2×C4—31no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—31no—
811C2×C4—31no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—91no—
816C2×C4—91no—
817C2×C4—122no—
818C2×C4—122no—
819C2×C4—122no—
820C2×C4—182no—
821C2×C4—362no—
822C2×C4—362no—
823C2×C4—362no—
824C2×C4—361no—
825C2×C4—362no—
826C2×C4C22×D3211yescharacteristic
827C8—21no—
828C8—61no—
829C8—61no—
830C8—181no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—62no—
835C2×C3—81no—
836C2×C3—81no—
837C2×C3—122no—
838C2×C3—161no—
839C2×C3C2×#88411yescharacteristic
840C2×C3D3×#12111yescharacteristic
841C2×C3#576811yescharacteristic
842C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
843C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
844C2×C3#577711yescharacteristic
845D3—22no—
846D3—42no—
847D3—122no—
848D3—122no—
849D3—242no—
850D3—241no—
851D3—241no—
852D3—481no—
853C22—32no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—61no—
858C22—61no—
859C22—62no—
860C22—121no—
861C22—121no—
862C22—182no—
863C22—368no—
864C22—361no—
865C22—361no—
866C22—361no—
867C22—361no—
868C22—361no—
869C22D32×D411yescharacteristic
870C4—32no—
871C4—41no—
872C4—61no—
873C4—61no—
874C4—92no—
875C4—121no—
876C4—121no—
877C4—121no—
878C4—181no—
879C4D3×#23511yescharacteristic
880C4D32×D411yescharacteristic
881C3—21no—
882C3#7891011yescharacteristic, complemented
883C3#8053411yescharacteristic, complemented
884C2—62no—
885C2—81no—
886C2—122no—
887C2—362no—
888C2—721no—
889C2D3×#88411yescharacteristic
890C2#1059472611yescharacteristic
891C2#1059474611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3036
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. #10595153C2semidirect
2. C2×#63925C2semidirect
3. C2×#63794C2semidirect
4. D3×#893C2semidirect
5. #10592485C2semidirect
6. C3×#4787C2semidirect
7. C3×#4771C2semidirect
8. #10591433C2semidirect
9. #10591432C2semidirect
10. #10590770C2semidirect
11. #10590748C2semidirect
12. #10590663C2semidirect
13. #10590609C2semidirect
14. #10590565C2semidirect
15. #10590534C2semidirect
22. #64149C22semidirect
26. C3×#936C22semidirect
43. #63873C22semidirect
44. #63864C22semidirect
51. C32×#102C22semidirect
52. #63641C22semidirect
53. #63636C22semidirect
54. C3×#832C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#810C22semidirect
59. #63572C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63565C22semidirect
62. #63564C22semidirect
88. #4787D3semidirect
93. #4771D3semidirect
119. D3×D12D4semidirect
181. #936C2×D3semidirect
231. C3×#102C2×D3semidirect
232. C3×#102C2×D3semidirect
234. #832C2×D3semidirect
236. #816C2×D3semidirect
243. Dic3⋊C8C2×D3semidirect
245. #810C2×D3semidirect
246. #810C2×D3semidirect
471. C3⋊Dic3AGL(1,ℤ/8)semidirect
522. #102D32semidirect
780. C32#3036semidirect
882. C3#78910semidirect
883. C3#80534semidirect

Maximal subgroups

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

subgroupindex
#105951532
C2×#639252
C2×#637942
D3×#8932
#105924852
C3×#47872
C3×#47712
#105914332
#105914322
#105907702
#105907482
#105906632
#105906092
#105905652
#105905342
#805343
#789103