Finite Group Databasebeta

← #11866193

Subgroups — #11866193

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
1C3×#5545C211yesmaximal, characteristic, complemented
2C2×#63932C211yesmaximal, characteristic, complemented
3C2×D3×#213C211yesmaximal, characteristic, complemented
4#10594000C211yesmaximal, characteristic, complemented
5#10592715C211yesmaximal, characteristic, complemented
6C3×#5015C211yesmaximal, characteristic, complemented
7#10591481C211yesmaximal, characteristic, complemented
8#10591468C211yesmaximal, characteristic, complemented
9#10590608C211yesmaximal, characteristic, complemented
10#10590592C211yesmaximal, characteristic, complemented
11#10590547C211yesmaximal, characteristic, complemented
12#10590530C211yesmaximal, characteristic, complemented
13#10590366C211yesmaximal, characteristic, complemented
14#10590347C211yesmaximal, characteristic, complemented
15#10590324C211yesmaximal, characteristic, complemented
16#82540—31nomaximal
17#80334—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic, complemented
22C2×#3754C2211yescharacteristic, complemented
23C2×#3753C2211yescharacteristic
24#64084C2211yescharacteristic, complemented
25C3×D4×Dic3C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic, complemented
28C3×C4×#67—21no—
29C2×C3×(C2×D3)⋊C4—21no—
30C3×#893C2211yescharacteristic, complemented
31C3×#892C2211yescharacteristic
32C3×#67⋊C4—21no—
33C3×D3×C22⋊C4—21no—
34C3×#874C2211yescharacteristic, complemented
35C3×C4×D12C2211yescharacteristic, complemented
36C3×#872C2211yescharacteristic
37#63932—24no—
38D3×#213—24no—
39#63922—21no—
40#63922—21no—
41#63911C2211yescharacteristic, complemented
42#63886—21no—
43#63886—21no—
44#63860C2211yescharacteristic, complemented
45C2×#3716C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic
47C2×#3713C2211yescharacteristic
48C2×#3713C2211yescharacteristic, complemented
49C2×#3711C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63637C2211yescharacteristic, complemented
52#63636C2211yescharacteristic, complemented
53C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic, complemented
56C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63562C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C3×#518—31no—
64C2×#932—31no—
65C22×#213—31no—
66C2×#911—31no—
67C2×D3×D8—31no—
68#5715—31no—
69#5545D311yescharacteristic, complemented
70#5525—31no—
71C3×#459—31no—
72#5153—31no—
73#5150—31no—
74#5072—31no—
75#5016—31no—
76#5016—31no—
77#5016—31no—
78#5016—31no—
79#5016—31no—
80#5016—61no—
81#5015—31no—
82#5015—31no—
83#5015—31no—
84#5015D311yescharacteristic, complemented
85#5002—31no—
86#5001—31no—
87#4999—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
97C22×C32×C4—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C3×D3×D4—22no—
103C3×D3×D4D414yescomplemented
104C2×C3×D12—21no—
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#625—21no—
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12—22no—
119#3795—22no—
120#3795—22no—
121C32×C4⋊C4C2311yescharacteristic
122C32×C22⋊C4—21no—
123C32×C42C2311yescharacteristic
124#3754—22no—
125#3753—22no—
126#3752—21no—
127#3752—21no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#217—21no—
131C3×#213—22no—
132C3×#213—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4D411yescharacteristic
140C3×Dic3⋊C4D411yescharacteristic
141C3×C4×Dic3—21no—
142C3×C4×Dic3C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147#3716—22no—
148#3714—22no—
149#3713—22no—
150#3713—22no—
151#3711—22no—
152D3×C3⋊C8—22no—
153#3041—91noSylow
154C22×C3×D4—31no—
155C2×#237—31no—
156C2×D3×D4—31no—
157C2×D3×D4C2×D311yescharacteristic
158C2×#235—31no—
159C22×D12—31no—
160C2×C3×D8—31no—
161C2×C3×D8—31no—
162C3×#127—31no—
163C3×C4×D4—21no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—61no—
168C3×C4×D4—61no—
169C3×C4×D4C2×D311yescharacteristic, complemented
170C3×C4×D4C2×D311yescharacteristic, complemented
171C3×#117—31no—
172C3×#117—31no—
173C2×C3×C22⋊C4—61no—
174C2×C3×C22⋊C4—61no—
175#940—31no—
176#939—61no—
177#939—61no—
178#937—61no—
179#937—61no—
180#936—31no—
181D4×Dic3C2×D311yescharacteristic, complemented
182C2×#214—31no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—61no—
186#932—64no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213—31no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—61no—
195C2×#213—64no—
196C2×#213C2×D311yescharacteristic
197C2×#213C2×D311yescharacteristic, complemented
198C4×#67—21no—
199C2×(C2×D3)⋊C4—21no—
200C2×#208—31no—
201C22×C3⋊C8—31no—
202#911—64no—
203D3×D8—64no—
204C2×D24—31no—
205C2×#204—31no—
206C2×ΓL(1,𝔽25)—31no—
207C2×D3×C8—31no—
208#895—61no—
209#895—61no—
210#893C2×D311yescharacteristic, complemented
211#892C2×D311yescharacteristic
212#882—61no—
213#882—61no—
214#67⋊C4—21no—
215D3×C22⋊C4—21no—
216#875—31no—
217#875—31no—
218#875—31no—
219#875—61no—
220#874—31no—
221#874C2×D311yescharacteristic, complemented
222C4×D12C2×D311yescharacteristic, complemented
223#872C2×D311yescharacteristic
224C3×C4⋊C8—31no—
225C3×#102—31no—
226C3×#102—31no—
227#832—31no—
228#832—31no—
229#821—31no—
230#816—31no—
231Dic3⋊C8—31no—
232Dic3⋊C8—31no—
233#810—31no—
234#810—31no—
235#810—31no—
236#810—61no—
237#809—31no—
238#809—31no—
239#809—31no—
240#809—31no—
241#809—31no—
242#809—61no—
243#809C2×D311yescharacteristic, complemented
244#809C2×D311yescharacteristic, complemented
245C4⋊(C3⋊C8)—31no—
246C4⋊(C3⋊C8)—31no—
247C4⋊(C3⋊C8)—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—61no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251C23×C32—21no—
252C22×C3⋊D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—24no—
255C22×C3×D3—21no—
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×D4C2×D412yes—
265C2×C32×C4—21no—
266C2×C32×C4—81no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273#634—21no—
274#634—21no—
275C3×#67—24no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—81no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—81no—
287C3×D12—81no—
288C3×D12C2×D412yes—
289C3×C4×D3—81no—
290C3×C4×D3—81no—
291C3×C4×D3C2×D412yes—
292C3×C4×D3#4112yes—
293#626—42no—
294#626—81no—
295#626—81no—
296#625—42no—
297D3×Dic3—42no—
298C3⋊(C3⋊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—31no—
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—
321C2×C3×D4—21no—
322C2×C3×D4—34no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—62no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4C22×D311yescharacteristic
331C2×C3×D4C22×D311yescharacteristic
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—31no—
335C22×C3×C4—41no—
336C22×C3×C4—61no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C2×#67—21no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C22×Dic3—21no—
346C22×Dic3—61no—
347#237—62no—
348#237—62no—
349D3×D4—22no—
350D3×D4—62no—
351D3×D4—62no—
352D3×D4D1214yescomplemented
353#235—62no—
354#235—62no—
355C2×D12—21no—
356C2×D12—21no—
357C2×D12—31no—
358C2×D12—31no—
359C2×D12—61no—
360C2×D12—62no—
361C2×D12—62no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12C22×D311yescharacteristic
366C2×D12C22×D311yescharacteristic
367C2×D12C22×D311yescharacteristic
368C2×C4×D3—21no—
369C2×C4×D3—21no—
370C2×C4×D3—61no—
371C2×C4×D3C22×D311yescharacteristic
372C2×Dic6—31no—
373C2×Dic6—31no—
374C2×Dic6—61no—
375C3×D8—62no—
376C3×D8—62no—
377C2×C3×C8—31no—
378C2×C3×C8—31no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—31no—
381C3×C4⋊C4—31no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4C22×D311yescharacteristic
384C3×C4⋊C4C22×D311yescharacteristic
385C3×C22⋊C4—21no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—31no—
389C3×C22⋊C4—41no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C42—21no—
395C3×C42—31no—
396C3×C42—61no—
397C3×C42C22×D311yescharacteristic
398C3×C42C22×D311yescharacteristic
399#217—21no—
400#217—61no—
401#217—61no—
402#214—62no—
403#214—62no—
404#214—62no—
405#214—122no—
406#213—22no—
407#213—22no—
408#213—62no—
409#213—62no—
410#213—62no—
411#213—62no—
412#213—62no—
413#213—62no—
414#213—62no—
415#213—122no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—21no—
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—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—121no—
426(C2×D3)⋊C4—121no—
427(C2×D3)⋊C4#6711yescharacteristic
428(C2×D3)⋊C4#6711yescharacteristic
429C4⋊Dic3C22×D311yescharacteristic
430Dic3⋊C4#6711yescharacteristic
431Dic3⋊C4#6711yescharacteristic
432C4×Dic3—21no—
433C4×Dic3C22×D311yescharacteristic
434#208—62no—
435C2×C3⋊C8—31no—
436C2×C3⋊C8—31no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—61no—
440C2×C3⋊C8—61no—
441C2×C3⋊C8—62no—
442C2×C3⋊C8C22×D311yescharacteristic
443C2×C3⋊C8C22×D311yescharacteristic
444D24—62no—
445#204—62no—
446ΓL(1,𝔽25)—62no—
447D3×C8—62no—
448C22×C32—22no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32C22×D411yescharacteristic
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—84no—
467C2×C3×D3#12112yes—
468D32—84no—
469C32×C4—21no—
470C32×C4—21no—
471C32×C4—41no—
472C32×C4C22×D411yescharacteristic
473C32×C4C2×#4111yescharacteristic
474C3⋊Dic3—41no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C2×#41—91no—
480C22×D4—31no—
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—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—31no—
504C4×D4—31no—
505C4×D4—61no—
506C4×D4—61no—
507C4×D4D3211yescharacteristic, complemented
508#117—31no—
509#117—31no—
510C2×C22⋊C4—61no—
511C2×C22⋊C4—61no—
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—31no—
527C23×C3—41no—
528C23×C3—64no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3—241no—
533C23×C3—241no—
534C22×D3—21no—
535C22×D3—24no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—81no—
541C22×D3—81no—
542C22×D3—121no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—241no—
546C22×D3—241no—
547C22×D3—241no—
548C22×D3—241no—
549C22×D3C2×#6711yescharacteristic
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—22no—
553C3×D4—32no—
554C3×D4—41no—
555C3×D4—64no—
556C3×D4—61no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—241no—
562C3×D4—241no—
563C3×D4C2×D1212yes—
564C3×D4D3×D412yes—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—31no—
571C2×C3×C4—32no—
572C2×C3×C4—32no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—41no—
576C2×C3×C4—61no—
577C2×C3×C4—81no—
578C2×C3×C4—81no—
579C2×C3×C4—82no—
580C2×C3×C4—241no—
581C2×C3×C4—241no—
582C2×C3×C4—241no—
583C2×C3×C4D3×D411yescharacteristic
584C2×C3×C4D3×D411yescharacteristic
585C2×C3×C4C2×#6711yescharacteristic
586C2×C3×C4C2×#6711yescharacteristic
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589#67—24no—
590#67—122no—
591#67—122no—
592#67—122no—
593#67—241no—
594#67—241no—
595C2×Dic3—21no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—81no—
599C2×Dic3—121no—
600C2×Dic3—122no—
601C2×Dic3C2×#6711yescharacteristic
602C2×Dic3C2×#6711yescharacteristic
603C2×Dic3C2×#6711yescharacteristic
604D12—21no—
605D12—21no—
606D12—21no—
607D12—21no—
608D12—21no—
609D12—61no—
610D12—61no—
611D12—61no—
612D12—61no—
613D12—81no—
614D12—81no—
615D12—121no—
616D12—121no—
617D12—122no—
618D12—241no—
619D12—241no—
620D12C2×D1212yes—
621C4×D3—81no—
622C4×D3—81no—
623C4×D3—122no—
624C4×D3C2×D1212yes—
625C4×D3#23512yes—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—61no—
630Dic6—121no—
631Dic6—121no—
632C3×C8—61no—
633C3×C8—61no—
634C3⋊C8—21no—
635C3⋊C8—21no—
636C3⋊C8—61no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—121no—
641C3⋊C8—121no—
642C2×C32—42no—
643C2×C32C2×#12111yescharacteristic
644C2×C32#57611yescharacteristic
645C2×C32#57611yescharacteristic
646C3⋊D3—81no—
647C3×D3—22no—
648C3×D3—42no—
649C3×D3—81no—
650C3×D3—81no—
651C24—61no—
652C24—181no—
653#41—182no—
654#41—182no—
655C2×Q8—91no—
656C2×D4—34no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—31no—
660C2×D4—62no—
661C2×D4—61no—
662C2×D4—61no—
663C2×D4—61no—
664C2×D4—91no—
665C2×D4—182no—
666C2×D4—182no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4C2×D3211yescharacteristic
672C22×C4—21no—
673C22×C4—31no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—181no—
678SD16—182no—
679SD16—182no—
680D8—62no—
681D8—62no—
682D8—182no—
683D8—182no—
684D8—182no—
685D8—182no—
686M16—182no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—91no—
690C2×C8—91no—
691C2×C8—182no—
692C4⋊C4—31no—
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4C2×D3211yescharacteristic
696C22⋊C4—21no—
697C22⋊C4—31no—
698C22⋊C4—31no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C42—31no—
708C42—61no—
709C42C2×D3211yescharacteristic
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—21no—
713C22×C3—32no—
714C22×C3—42no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—61no—
720C22×C3—61no—
721C22×C3—62no—
722C22×C3—81no—
723C22×C3—81no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—121no—
732C22×C3—244no—
733C22×C3C2×D3×D411yescharacteristic
734C22×C3C22×#6711yescharacteristic
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—22no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—84no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—241no—
754C2×D3—241no—
755C2×D3—241no—
756C2×D3—244no—
757C2×D3—244no—
758C2×D3#93012yes—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—21no—
763C3×C4—21no—
764C3×C4—21no—
765C3×C4—32no—
766C3×C4—41no—
767C3×C4—41no—
768C3×C4—41no—
769C3×C4—41no—
770C3×C4—61no—
771C3×C4—61no—
772C3×C4—81no—
773C3×C4—121no—
774C3×C4C22×D1211yescharacteristic
775C3×C4C2×#23511yescharacteristic
776C3×C4C2×D3×D411yescharacteristic
777C3×C4D3×#4111yescharacteristic
778Dic3—21no—
779Dic3—21no—
780Dic3—41no—
781Dic3—121no—
782Dic3—121no—
783Dic3—241no—
784Dic3#93012yes—
785C32#304111yescharacteristic, complemented, Sylow
786C23—21no—
787C23—31no—
788C23—64no—
789C23—61no—
790C23—61no—
791C23—61no—
792C23—181no—
793C23—241no—
794C23—241no—
795C23—362no—
796C23—721no—
797C23—721no—
798Q8—181no—
799Q8—181no—
800D4—21no—
801D4—32no—
802D4—64no—
803D4—61no—
804D4—61no—
805D4—61no—
806D4—61no—
807D4—61no—
808D4—181no—
809D4—181no—
810D4—241no—
811D4—241no—
812D4—362no—
813D4—362no—
814D4—721no—
815D4—721no—
816D4D3×D1212yes—
817C2×C4—21no—
818C2×C4—31no—
819C2×C4—32no—
820C2×C4—32no—
821C2×C4—31no—
822C2×C4—31no—
823C2×C4—61no—
824C2×C4—81no—
825C2×C4—181no—
826C2×C4—241no—
827C2×C4—241no—
828C2×C4—241no—
829C2×C4—362no—
830C2×C4D3×#6711yescharacteristic
831C2×C4D3×#6711yescharacteristic
832C2×C4C22×D3211yescharacteristic
833C8—61no—
834C8—61no—
835C8—181no—
836C8—181no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—42no—
841C2×C3—42no—
842C2×C3—62no—
843C2×C3—82no—
844C2×C3—122no—
845C2×C3—241no—
846C2×C3—241no—
847C2×C3D3×#12111yescharacteristic
848C2×C3#575711yescharacteristic
849C2×C3#577411yescharacteristic
850C2×C3C2×#93011yescharacteristic
851C2×C3#583511yescharacteristic
852C2×C3#583511yescharacteristic
853D3—22no—
854D3—42no—
855D3—81no—
856D3—81no—
857D3—241no—
858D3—241no—
859D3—481no—
860C22—22no—
861C22—32no—
862C22—41no—
863C22—41no—
864C22—61no—
865C22—61no—
866C22—62no—
867C22—121no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—121no—
872C22—121no—
873C22—121no—
874C22—121no—
875C22—244no—
876C22—361no—
877C22—361no—
878C22—361no—
879C22—724no—
880C22C2×D3×#6711yescharacteristic
881C4—21no—
882C4—21no—
883C4—32no—
884C4—41no—
885C4—61no—
886C4—61no—
887C4—121no—
888C4—361no—
889C4C2×D3×D1211yescharacteristic
890C4D3×#23511yescharacteristic
891C3—21no—
892C3#8033411yescharacteristic, complemented
893C3#8254011yescharacteristic, complemented
894C2—42no—
895C2—62no—
896C2—122no—
897C2—241no—
898C2—241no—
899C2—721no—
900C2D3×#93011yescharacteristic
901C2#1059509611yescharacteristic
902C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5545C2semidirect
2. C2×#63932C2semidirect
3. C2×D3×#213C2semidirect
4. #10594000C2semidirect
5. #10592715C2semidirect
6. C3×#5015C2semidirect
7. #10591481C2semidirect
8. #10591468C2semidirect
9. #10590608C2semidirect
10. #10590592C2semidirect
11. #10590547C2semidirect
12. #10590530C2semidirect
13. #10590366C2semidirect
14. #10590347C2semidirect
15. #10590324C2semidirect
21. C32×C4×D4C22semidirect
22. C2×#3754C22semidirect
24. #64084C22semidirect
25. C3×D4×Dic3C22semidirect
27. C2×C3×#213C22semidirect
30. C3×#893C22semidirect
34. C3×#874C22semidirect
35. C3×C4×D12C22semidirect
41. #63911C22semidirect
44. #63860C22semidirect
45. C2×#3716C22semidirect
48. C2×#3713C22semidirect
51. #63637C22semidirect
52. #63636C22semidirect
53. C4⋊(C3⋊(C3⋊C8))C22semidirect
54. C3×#809C22semidirect
55. C3×#809C22semidirect
56. C3×C4⋊(C3⋊C8)C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
60. #63564C22semidirect
61. #63562C22semidirect
62. #63562C22semidirect
69. #5545D3semidirect
84. #5015D3semidirect
103. C3×D3×D4D4semidirect
169. C3×C4×D4C2×D3semidirect
170. C3×C4×D4C2×D3semidirect
181. D4×Dic3C2×D3semidirect
197. C2×#213C2×D3semidirect
210. #893C2×D3semidirect
221. #874C2×D3semidirect
222. C4×D12C2×D3semidirect
243. #809C2×D3semidirect
244. #809C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
352. D3×D4D12semidirect
507. C4×D4D32semidirect
785. C32#3041semidirect
892. C3#80334semidirect
893. C3#82540semidirect

Maximal subgroups

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

subgroupindex
C3×#55452
C2×#639322
C2×D3×#2132
#105940002
#105927152
C3×#50152
#105914812
#105914682
#105906082
#105905922
#105905472
#105905302
#105903662
#105903472
#105903242
#825403
#803343