Finite Group Databasebeta

← #11866194

Subgroups — #11866194

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
1C2×C3×#911C211yesmaximal, characteristic, complemented
2#10595303C211yesmaximal, characteristic, complemented
3#10595215C211yesmaximal, characteristic, complemented
4C2×D3×#213C211yesmaximal, characteristic, complemented
5#10592849C211yesmaximal, characteristic, complemented
6C3×#5150C211yesmaximal, characteristic, complemented
7#10591476C211yesmaximal, characteristic, complemented
8#10591471C211yesmaximal, characteristic, complemented
9#10591433C211yesmaximal, characteristic, complemented
10#10591428C211yesmaximal, characteristic, complemented
11#10591420C211yesmaximal, characteristic, complemented
12#10590939C211yesmaximal, characteristic, complemented
13#10590754C211yesmaximal, characteristic, complemented
14#10590750C211yesmaximal, characteristic, complemented
15#10590695C211yesmaximal, characteristic, complemented
16#83934—31nomaximal
17#80334—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×C32×D8C2211yescharacteristic, complemented
22#64149C2211yescharacteristic, complemented
23D4×C3⋊Dic3C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic
25C3×#940C2211yescharacteristic, complemented
26C3×D4×Dic3C2211yescharacteristic, complemented
27C2×C3×#214C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic, complemented
30C3×#911—24no—
31C2×C3×#204C2211yescharacteristic, complemented
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33#63983—21no—
34#63983—21no—
35#63978—21no—
36#63978—21no—
37#67⋊Dic3—21no—
38Dic3×#67—21no—
39D3×#217—21no—
40C2×(C2×D3)⋊Dic3—21no—
41D3×#213—24no—
42#63898C2211yescharacteristic, complemented
43Dic3×D12C2211yescharacteristic, complemented
44#63864C2211yescharacteristic, complemented
45#63863C2211yescharacteristic, complemented
46#63855C2211yescharacteristic
47#63841C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63659C2211yescharacteristic, complemented
52#63648C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57#63572C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64#5830—31no—
65#5798—31no—
66C22×#213—31no—
67C2×#911D311yescharacteristic, complemented
68C2×D3×D8—31no—
69#5715—31no—
70#5545—31no—
71C3×#459—31no—
72#5233—31no—
73#5165—31no—
74#5165—31no—
75#5165—31no—
76#5165—31no—
77#5153—31no—
78#5150—31no—
79#5150—31no—
80#5150—31no—
81#5150—31no—
82#5150—61no—
83#5150D311yescharacteristic, complemented
84#5131—31no—
85#5119—31no—
86#5072—31no—
87#5016—31no—
88#4844—31no—
89#4839—31no—
90#4787—31no—
91#4786—31no—
92#4772—31no—
93#4770—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C2×#638—21no—
100C22×C3⋊Dic3—21no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C22×C3×Dic3—21no—
107C22×C3×Dic3—21no—
108C3×#237—22no—
109C3×#237—22no—
110C3×D3×D4—22no—
111C3×D3×D4D414yescomplemented
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×#626—21no—
117C2×D3×Dic3—21no—
118C2×D3×Dic3—21no—
119D3×D12—22no—
120D3×D12—22no—
121C32×D8—22no—
122C2×C32×C8C2311yescharacteristic
123#3757—21no—
124#3753—22no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C4×C3⋊Dic3C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#214—22no—
130C3×#213—22no—
131C3×#213—22no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×#204—22no—
137C3×ΓL(1,𝔽25)—22no—
138Dic3⋊Dic3D411yescharacteristic
139Dic3⋊Dic3D411yescharacteristic
140#3722—21no—
141#3722—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3D411yescharacteristic
148(C2×D3)⋊Dic3D411yescharacteristic
149Dic32—21no—
150#3714—22no—
151#3713—22no—
152D3×C3⋊C8—22no—
153#3041—91noSylow
154C2×C3×#41—31no—
155C22×C3×D4—31no—
156C2×#237C2×D311yescharacteristic
157C2×D3×D4—31no—
158C2×D3×D4C2×D311yescharacteristic
159C22×D12—31no—
160C3×AGL(1,ℤ/8)—64no—
161C2×C3×SD16—31no—
162C2×C3×SD16—31no—
163C2×C3×D8—21no—
164C2×C3×D8—31no—
165C2×C3×D8—31no—
166C2×C3×D8C2×D311yescharacteristic, complemented
167C2×C3×D8C2×D311yescharacteristic, complemented
168C2×C3×M16—31no—
169C3×#127—31no—
170C3×C4×D4—31no—
171C2×#217—61no—
172C2×#217—61no—
173#947—31no—
174#947—31no—
175#940—31no—
176#940—31no—
177#940—61no—
178#940C2×D311yescharacteristic, complemented
179#939—61no—
180#939—61no—
181#937—61no—
182#937—61no—
183#937—61no—
184#937—61no—
185#936—31no—
186D4×Dic3—31no—
187D4×Dic3—31no—
188D4×Dic3—31no—
189D4×Dic3—31no—
190D4×Dic3—61no—
191D4×Dic3—61no—
192D4×Dic3—61no—
193D4×Dic3C2×D311yescharacteristic, complemented
194C2×#214C2×D311yescharacteristic, complemented
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213—61no—
201C2×#213—64no—
202C2×#213C2×D311yescharacteristic
203C2×#213C2×D311yescharacteristic, complemented
204#930—61no—
205#930—61no—
206C4×#67—61no—
207C2×(C2×D3)⋊C4—61no—
208#926—31no—
209#926—31no—
210C22×C3⋊C8—31no—
211#911—24no—
212D3×D8—64no—
213C2×D24—31no—
214C2×#204C2×D311yescharacteristic, complemented
215C2×ΓL(1,𝔽25)C2×D311yescharacteristic
216C2×D3×C8—31no—
217#893—31no—
218#892—31no—
219#67⋊C4—61no—
220D3×C22⋊C4—61no—
221#875—31no—
222C4×D12—31no—
223#872—31no—
224C3×C4⋊C8—31no—
225C3×#102—31no—
226C3×#102—31no—
227#835—31no—
228#835—31no—
229#832—31no—
230#832—31no—
231#832—31no—
232#832—61no—
233#832C2×D311yescharacteristic, complemented
234#821—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—61no—
239#821C2×D311yescharacteristic, complemented
240#816—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—61no—
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#810—31no—
249#809—31no—
250C4⋊(C3⋊C8)—31no—
251C23×C32—21no—
252C23×C32—21no—
253C22×C3⋊D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—24no—
256C22×C3×D3—21no—
257C22×C3×D3—81no—
258C22×C3×D3—81no—
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—81no—
262C2×D32—81no—
263C32×D4—21no—
264C32×D4—21no—
265C32×D4—21no—
266C32×D4C2×D412yes—
267C2×C32×C4C2411yescharacteristic
268#638—81no—
269#638—81no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—81no—
272C2×C3⋊Dic3C2×D411yescharacteristic
273C2×C3⋊Dic3C2×D411yescharacteristic
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C3×#67—24no—
277C3×#67—42no—
278C3×#67—81no—
279C3×#67—81no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3—81no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12C2×D412yes—
291C3×C4×D3C2×D412yes—
292C3×C4×D3#4112yes—
293C3×Dic6—21no—
294C3×Dic6—21no—
295#626—42no—
296D3×Dic3—81no—
297D3×Dic3—81no—
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×AGL(1,ℤ/8)—31no—
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—91no—
317C24×C3—61no—
318C23×D3—21no—
319C23×D3—61no—
320C23×D3—61no—
321C3×#41—62no—
322C3×#41—62no—
323C2×C3×Q8—31no—
324C2×C3×D4—21no—
325C2×C3×D4—21no—
326C2×C3×D4—34no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—62no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C2×C3×D4C22×D311yescharacteristic
337C2×C3×D4C22×D311yescharacteristic
338C22×C3×C4—31no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—21no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—121no—
351C2×#67—121no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3—61no—
358C22×Dic3—121no—
359#237—22no—
360#237—22no—
361D3×D4—22no—
362D3×D4—62no—
363D3×D4—62no—
364D3×D4#6714yescomplemented
365C2×D12—31no—
366C2×D12—31no—
367C2×D12—61no—
368C2×D12—62no—
369C2×D12—62no—
370C2×D12—61no—
371C2×D12C22×D311yescharacteristic
372C2×D12C22×D311yescharacteristic
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C3×SD16—62no—
378C3×SD16—62no—
379C3×D8—22no—
380C3×D8—22no—
381C3×D8—42no—
382C3×D8—62no—
383C3×D8—62no—
384C3×M16—62no—
385C2×C3×C8—21no—
386C2×C3×C8—31no—
387C2×C3×C8—31no—
388C2×C3×C8C22×D311yescharacteristic
389C2×C3×C8C22×D311yescharacteristic
390C3×C4⋊C4—31no—
391C3×C22⋊C4—61no—
392C3×C42—31no—
393#217—21no—
394#217—31no—
395#217—31no—
396#217—61no—
397#217—61no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—121no—
404#214—22no—
405#213—22no—
406#213—22no—
407#213—62no—
408#213—62no—
409#213—62no—
410#213—62no—
411#213—62no—
412#213—122no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
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—61no—
423(C2×D3)⋊C4—61no—
424C4⋊Dic3—31no—
425C4⋊Dic3—31no—
426C4⋊Dic3—31no—
427C4⋊Dic3—31no—
428C4⋊Dic3—61no—
429C4⋊Dic3C22×D311yescharacteristic
430Dic3⋊C4—31no—
431Dic3⋊C4—31no—
432C4×Dic3—31no—
433C4×Dic3—31no—
434C4×Dic3—61no—
435C4×Dic3—61no—
436C4×Dic3—61no—
437C4×Dic3C22×D311yescharacteristic
438C2×C3⋊C8—31no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—61no—
441C2×C3⋊C8—62no—
442C2×C3⋊C8C22×D311yescharacteristic
443C2×C3⋊C8C22×D311yescharacteristic
444D24—62no—
445#204—22no—
446ΓL(1,𝔽25)—22no—
447D3×C8—62no—
448C22×C32—22no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32C22×D411yescharacteristic
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—84no—
467C2×C3×D3#12112yes—
468D32—84no—
469C32×C4C22×D411yescharacteristic
470C32×C4C2×#4111yescharacteristic
471C3⋊Dic3—21no—
472C3⋊Dic3—21no—
473C3⋊Dic3—41no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C2×#41—31no—
480C22×D4—31no—
481C22×D4—91no—
482AGL(1,ℤ/8)—64no—
483C2×SD16—31no—
484C2×SD16—31no—
485C2×D8—31no—
486C2×D8—31no—
487C2×D8—91no—
488C2×D8—91no—
489C2×D8—91no—
490C2×D8—184no—
491C2×D8D3211yescharacteristic, complemented
492C2×M16—31no—
493C22×C8—91no—
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—91no—
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—91no—
517#103—91no—
518#102—31no—
519#102—31no—
520#102—91no—
521#102—91no—
522#102—91no—
523#102—91no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—31no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—64no—
532C23×C3—61no—
533C23×C3—61no—
534C23×C3—241no—
535C23×C3—241no—
536C22×D3—21no—
537C22×D3—24no—
538C22×D3—21no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—81no—
542C22×D3—81no—
543C22×D3—121no—
544C22×D3—122no—
545C22×D3—122no—
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—21no—
558C3×D4—21no—
559C3×D4—22no—
560C3×D4—32no—
561C3×D4—41no—
562C3×D4—41no—
563C3×D4—41no—
564C3×D4—64no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—122no—
569C3×D4—241no—
570C3×D4—241no—
571C3×D4D3×D412yes—
572C3×D4C2×#6712yes—
573C2×C3×C4—21no—
574C2×C3×C4—31no—
575C2×C3×C4—32no—
576C2×C3×C4—32no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—122no—
582C2×C3×C4—241no—
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585#67—24no—
586#67—42no—
587#67—81no—
588#67—81no—
589#67—122no—
590#67—241no—
591#67—241no—
592#67—241no—
593#67—241no—
594#67—242no—
595#67—242no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—31no—
599C2×Dic3—31no—
600C2×Dic3—31no—
601C2×Dic3—31no—
602C2×Dic3—42no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—81no—
608C2×Dic3—121no—
609C2×Dic3—241no—
610C2×Dic3—241no—
611C2×Dic3—241no—
612C2×Dic3—241no—
613C2×Dic3—242no—
614C2×Dic3D3×D411yescharacteristic
615C2×Dic3D3×D411yescharacteristic
616C2×Dic3D3×D411yescharacteristic
617D12—21no—
618D12—21no—
619D12—21no—
620D12—61no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—121no—
625D12—121no—
626D12—122no—
627D12C2×#6712yes—
628C4×D3—241no—
629C4×D3—241no—
630C4×D3#23712yes—
631C4×D3C2×#6712yes—
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—42no—
645C2×C32—81no—
646C2×C32C2×#12111yescharacteristic
647C2×C32#57611yescharacteristic
648C2×C32#57611yescharacteristic
649C3⋊D3—81no—
650C3×D3—22no—
651C3×D3—42no—
652C3×D3—81no—
653C24—61no—
654C24—181no—
655#41—62no—
656#41—62no—
657C2×Q8—31no—
658C2×D4—34no—
659C2×D4—31no—
660C2×D4—31no—
661C2×D4—62no—
662C2×D4—61no—
663C2×D4—61no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—91no—
667C2×D4—182no—
668C2×D4—182no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4—181no—
672C2×D4C2×D3211yescharacteristic
673C2×D4C2×D3211yescharacteristic
674C22×C4—31no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—181no—
678C22×C4—181no—
679C22×C4—181no—
680SD16—62no—
681SD16—62no—
682D8—22no—
683D8—62no—
684D8—62no—
685D8—182no—
686D8—182no—
687D8—182no—
688M16—62no—
689C2×C8—31no—
690C2×C8—31no—
691C2×C8—91no—
692C2×C8—182no—
693C2×C8C2×D3211yescharacteristic
694C4⋊C4—31no—
695C4⋊C4—91no—
696C4⋊C4—91no—
697C4⋊C4—91no—
698C22⋊C4—61no—
699C22⋊C4—91no—
700C22⋊C4—91no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C42—31no—
710C42—91no—
711C42—181no—
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—21no—
715C22×C3—32no—
716C22×C3—42no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—62no—
730C22×C3—81no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—81no—
734C22×C3—81no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—244no—
741C22×C3C2×D3×D411yescharacteristic
742C22×C3C2×D3×D411yescharacteristic
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—22no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—84no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—121no—
757C2×D3—121no—
758C2×D3—241no—
759C2×D3—241no—
760C2×D3—241no—
761C2×D3—244no—
762C2×D3—244no—
763C2×D3#93912yes—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—32no—
767C3×C4—61no—
768C3×C4—61no—
769C3×C4—121no—
770C3×C4—121no—
771C3×C4C2×D3×D411yescharacteristic
772C3×C4C2×#23711yescharacteristic
773C3×C4D3×#4111yescharacteristic
774C3×C4C22×#6711yescharacteristic
775Dic3—21no—
776Dic3—21no—
777Dic3—41no—
778Dic3—41no—
779Dic3—62no—
780Dic3—61no—
781Dic3—61no—
782Dic3—61no—
783Dic3—61no—
784Dic3—121no—
785Dic3—121no—
786Dic3—121no—
787Dic3—241no—
788Dic3#93912yes—
789C32#304111yescharacteristic, complemented, Sylow
790C23—21no—
791C23—21no—
792C23—31no—
793C23—64no—
794C23—61no—
795C23—61no—
796C23—181no—
797C23—241no—
798C23—241no—
799C23—362no—
800C23—721no—
801C23—721no—
802Q8—61no—
803Q8—61no—
804D4—21no—
805D4—21no—
806D4—21no—
807D4—32no—
808D4—64no—
809D4—61no—
810D4—61no—
811D4—61no—
812D4—122no—
813D4—181no—
814D4—181no—
815D4—241no—
816D4—241no—
817D4—362no—
818D4—721no—
819D4—721no—
820D4D3×#6712yes—
821C2×C4—31no—
822C2×C4—32no—
823C2×C4—32no—
824C2×C4—31no—
825C2×C4—31no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—91no—
829C2×C4—91no—
830C2×C4—122no—
831C2×C4—181no—
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—42no—
845C2×C3—42no—
846C2×C3—62no—
847C2×C3—82no—
848C2×C3—81no—
849C2×C3—81no—
850C2×C3—122no—
851C2×C3—161no—
852C2×C3—241no—
853C2×C3D3×#12111yescharacteristic
854C2×C3#575711yescharacteristic
855C2×C3#577411yescharacteristic
856C2×C3#577411yescharacteristic
857C2×C3#577411yescharacteristic
858C2×C3C2×#93911yescharacteristic
859D3—22no—
860D3—42no—
861D3—81no—
862D3—241no—
863D3—241no—
864D3—481no—
865C22—22no—
866C22—32no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—61no—
873C22—61no—
874C22—62no—
875C22—121no—
876C22—121no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—244no—
881C22—361no—
882C22—361no—
883C22—361no—
884C22—724no—
885C22D32×D411yescharacteristic
886C4—32no—
887C4—61no—
888C4—61no—
889C4—121no—
890C4—121no—
891C4—181no—
892C4—181no—
893C4—361no—
894C4D3×#23711yescharacteristic
895C4C2×D3×#6711yescharacteristic
896C3—21no—
897C3#8033411yescharacteristic, complemented
898C3#8393411yescharacteristic, complemented
899C2—42no—
900C2—62no—
901C2—81no—
902C2—122no—
903C2—241no—
904C2—721no—
905C2#1059473211yescharacteristic
906C2#1059473511yescharacteristic
907C2D3×#93911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#911C2semidirect
2. #10595303C2semidirect
3. #10595215C2semidirect
4. C2×D3×#213C2semidirect
5. #10592849C2semidirect
6. C3×#5150C2semidirect
7. #10591476C2semidirect
8. #10591471C2semidirect
9. #10591433C2semidirect
10. #10591428C2semidirect
11. #10591420C2semidirect
12. #10590939C2semidirect
13. #10590754C2semidirect
14. #10590750C2semidirect
15. #10590695C2semidirect
21. C2×C32×D8C22semidirect
22. #64149C22semidirect
23. D4×C3⋊Dic3C22semidirect
25. C3×#940C22semidirect
26. C3×D4×Dic3C22semidirect
27. C2×C3×#214C22semidirect
29. C2×C3×#213C22semidirect
31. C2×C3×#204C22semidirect
42. #63898C22semidirect
43. Dic3×D12C22semidirect
44. #63864C22semidirect
45. #63863C22semidirect
51. #63659C22semidirect
52. #63648C22semidirect
53. #63641C22semidirect
54. C3×#832C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. #63572C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
67. C2×#911D3semidirect
83. #5150D3semidirect
111. C3×D3×D4D4semidirect
166. C2×C3×D8C2×D3semidirect
167. C2×C3×D8C2×D3semidirect
178. #940C2×D3semidirect
193. D4×Dic3C2×D3semidirect
194. C2×#214C2×D3semidirect
203. C2×#213C2×D3semidirect
214. C2×#204C2×D3semidirect
233. #832C2×D3semidirect
239. #821C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
364. D3×D4#67semidirect
491. C2×D8D32semidirect
789. C32#3041semidirect
897. C3#80334semidirect
898. C3#83934semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9112
#105953032
#105952152
C2×D3×#2132
#105928492
C3×#51502
#105914762
#105914712
#105914332
#105914282
#105914202
#105909392
#105907542
#105907502
#105906952
#839343
#803343