Finite Group Databasebeta

← #11867148

Subgroups — #11867148

Order 1152.

1158 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#121C211yesmaximal, characteristic, complemented
2C2×#63932C211yesmaximal, characteristic, complemented
3#10594892C211yesmaximal, characteristic, complemented
4C22×#3711C211yesmaximal, characteristic, complemented
5#10592740C211yesmaximal, characteristic, complemented
6C3×#5038C211yesmaximal, characteristic, complemented
7#10591462C211yesmaximal, characteristic, complemented
8#10591451C211yesmaximal, characteristic, complemented
9#10591421C211yesmaximal, characteristic, complemented
10#10591175C211yesmaximal, characteristic, complemented
11#10591166C211yesmaximal, characteristic, complemented
12#10590607C211yesmaximal, characteristic, complemented
13#10590588C211yesmaximal, characteristic, complemented
14#10590580C211yesmaximal, characteristic, complemented
15#10590504C211yesmaximal, characteristic, complemented
16#82621—31nomaximal
17#80715—31nomaximal
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C32×#121C2211yescharacteristic
23C2×#3754C2211yescharacteristic, complemented
24#64133C2211yescharacteristic, complemented
25C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C3×#939—21no—
27C3×#938C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic, complemented
29C3×#930C2211yescharacteristic
30C3×#930C2211yescharacteristic, complemented
31C22×C3×C3⋊C8C2211yescharacteristic, complemented
32C3×#895C2211yescharacteristic
33C3×D3×C4⋊C4C2211yescharacteristic
34C3×#884—21no—
35C3×D3×C22⋊C4—21no—
36#63976—21no—
37Dic3×#67—21no—
38#63932—24no—
39#63908C2211yescharacteristic, complemented
40#63905—21no—
41#63879—21no—
42#63857C2211yescharacteristic, complemented
43#63841C2211yescharacteristic
44C2×#3716C2211yescharacteristic, complemented
45C2×#3713C2211yescharacteristic, complemented
46C2×#3711—24no—
47C2×#3711C2211yescharacteristic
48C2×#3711C2211yescharacteristic
49C2×#3711C2211yescharacteristic, complemented
50C2×#3711C2211yescharacteristic, complemented
51#63659C2211yescharacteristic, complemented
52#63637C2211yescharacteristic, complemented
53#63635C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic, complemented
56C3×#807C2211yescharacteristic, complemented
57#63576C2211yescharacteristic, complemented
58#63573C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63562C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×C3×#121—31no—
64C2×#932—31no—
65#5791—31no—
66C22×#208—31no—
67C2×#911—31no—
68C22×ΓL(1,𝔽25)—31no—
69#5606—31no—
70D3×#121D311yescharacteristic, complemented
71C3×#466—31no—
72#5215—31no—
73#5159—31no—
74#5114—31no—
75#5042—31no—
76#5042—31no—
77#5041—31no—
78#5041—31no—
79#5041—31no—
80#5041—61no—
81#5039—31no—
82#5039—31no—
83#5038—31no—
84#5038—31no—
85#5038D311yescharacteristic, complemented
86#4966—31no—
87#4964—31no—
88#4886—31no—
89#4881—31no—
90#4782—31no—
91#4780—31no—
92#4771—31no—
93#4770—31no—
94C23×C3×D3—21no—
95C23×C3×D3D411yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C22×C3×Dic3D411yescharacteristic
105C3×D3×D4—22no—
106C3×D3×D4—22no—
107C3×D3×D4—44no—
108C2×C3×D12—21no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3D411yescharacteristic
115C2×C3×C4×D3D411yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×#625—21no—
119C2×#625—21no—
120C2×D3×Dic3—21no—
121#3795—22no—
122#3795—22no—
123C32×C4⋊C4C2311yescharacteristic
124C32×C22⋊C4—21no—
125#3757—21no—
126#3754—22no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128#3750—21no—
129C2×C3⋊(C3⋊C8)—22no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#217—21no—
133C3×#213—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C2×C3×C3⋊C8—22no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143Dic3⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147Dic32—21no—
148#3716—22no—
149#3713—22no—
150#3711—22no—
151#3711—22no—
152#3711—22no—
153#3711D414yescomplemented
154#3055—91noSylow
155C22×C3×D4—31no—
156C22×C3×D4—61no—
157C23×C3×C4—31no—
158C2×#237—31no—
159C2×D3×D4—21no—
160C2×D3×D4C2×D311yescharacteristic
161C2×#235—31no—
162C22×C4×D3C2×D311yescharacteristic
163C2×C3×D8—31no—
164C22×C3×C8—31no—
165C3×#121—21no—
166C3×#121—31no—
167C3×#121—31no—
168C3×#121—31no—
169C3×#121—31no—
170C3×#121—61no—
171C3×#121—61no—
172C3×#121C2×D311yescharacteristic
173C3×#121C2×D311yescharacteristic
174C2×C3×C4⋊C4—31no—
175C2×C3×C22⋊C4—61no—
176#953—61no—
177#939—21no—
178#938—31no—
179#938C2×D311yescharacteristic
180#937—61no—
181D4×Dic3—61no—
182C2×#214—31no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—61no—
186#932—64no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213C2×D311yescharacteristic, complemented
190#930—31no—
191#930C2×D311yescharacteristic
192#930C2×D311yescharacteristic, complemented
193#929—61no—
194C4×#67—61no—
195C4×#67—61no—
196#926—31no—
197#924—31no—
198#924—31no—
199#924—31no—
200#924—61no—
201C2×#208—31no—
202C2×#208—31no—
203C2×#208—31no—
204C2×#208—31no—
205C2×#208—64no—
206C22×C3⋊C8—31no—
207C22×C3⋊C8—31no—
208C22×C3⋊C8—61no—
209C22×C3⋊C8C2×D311yescharacteristic, complemented
210#911—64no—
211C2×#204—31no—
212C2×ΓL(1,𝔽25)—31no—
213C2×ΓL(1,𝔽25)—31no—
214C2×ΓL(1,𝔽25)—31no—
215C2×ΓL(1,𝔽25)—31no—
216C2×ΓL(1,𝔽25)—64no—
217#897—31no—
218#895C2×D311yescharacteristic
219#892—31no—
220D3×C4⋊C4C2×D311yescharacteristic
221#884—21no—
222#883—61no—
223#67⋊C4—61no—
224D3×C22⋊C4—21no—
225C3×#107—31no—
226C3×#102—31no—
227C3×#102—31no—
228#832—31no—
229#832—31no—
230#832—31no—
231#832—31no—
232#832—31no—
233#832—61no—
234#832C2×D311yescharacteristic, complemented
235#821—31no—
236#817—31no—
237#816—31no—
238#810—31no—
239#810—31no—
240#810—31no—
241#810—61no—
242#809—31no—
243#809—31no—
244#809C2×D311yescharacteristic, complemented
245#808—31no—
246#808—31no—
247#808—31no—
248#808—61no—
249#807—31no—
250#807—31no—
251#807C2×D311yescharacteristic, complemented
252C23×C32—21no—
253C23×C32C2×D411yescharacteristic
254C22×C3×D3—22no—
255C22×C3×D3—22no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—41no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3C2×D411yescharacteristic
263C22×C3×D3C2×D411yescharacteristic
264C32×D4—21no—
265C32×D4—21no—
266C32×D4—42no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2411yescharacteristic
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274#634—21no—
275#634—21no—
276C3×#67—42no—
277C3×#67—42no—
278C3×#67—42no—
279C3×#67—42no—
280C2×C3×Dic3—22no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—42no—
290C3×C4×D3—22no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—22no—
294C3×C4×D3—42no—
295C3×C4×D3C2×D412yes—
296C3×C4×D3#4112yes—
297#625—42no—
298#625—42no—
299D3×Dic3—42no—
300C3⋊(C3⋊C8)—21no—
301C3⋊(C3⋊C8)C2×D412yescomplemented
302C3×C3⋊C8—21no—
303C3×C3⋊C8C2×D412yescomplemented
304C2×AGL(1,ℤ/8)—91no—
305C22×M16—91no—
306#525—91no—
307C2×#121—31no—
308#469—91no—
309#469—91no—
310#468—91no—
311#468—91no—
312#466—31no—
313#466—91no—
314#465—91no—
315#465—91no—
316#428—91no—
317#418—91no—
318#417—91no—
319C24×C3—31no—
320C24×C3—61no—
321C23×D3—21no—
322C23×D3#6711yescharacteristic
323C2×C3×D4—21no—
324C2×C3×D4—21no—
325C2×C3×D4—21no—
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—41no—
329C2×C3×D4—61no—
330C2×C3×D4—62no—
331C2×C3×D4—62no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—124no—
337C2×C3×D4C22×D311yescharacteristic
338C2×C3×D4C22×D311yescharacteristic
339C22×C3×C4—21no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—62no—
346C22×C3×C4—62no—
347C22×C3×C4—61no—
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C2×#67—21no—
351C2×#67—21no—
352C2×#67—21no—
353C2×#67—21no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C22×Dic3—61no—
359C22×Dic3#6711yescharacteristic
360#237—62no—
361#237—62no—
362D3×D4—22no—
363D3×D4—22no—
364D3×D4—44no—
365#235—62no—
366#235—62no—
367C2×D12—21no—
368C2×D12C22×D311yescharacteristic
369C2×D12C22×D311yescharacteristic
370C2×C4×D3—22no—
371C2×C4×D3—22no—
372C2×C4×D3—21no—
373C2×C4×D3—61no—
374C2×C4×D3#6711yescharacteristic
375C2×C4×D3#6711yescharacteristic
376C2×C4×D3C22×D311yescharacteristic
377C2×C4×D3C22×D311yescharacteristic
378C2×Dic6—31no—
379C2×Dic6—31no—
380C2×Dic6—61no—
381C3×D8—62no—
382C2×C3×C8—31no—
383C2×C3×C8—31no—
384C2×C3×C8—62no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—61no—
389C3×C4⋊C4C22×D311yescharacteristic
390C3×C4⋊C4C22×D311yescharacteristic
391C3×C22⋊C4—21no—
392C3×C22⋊C4—21no—
393C3×C22⋊C4—41no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398#217—21no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—121no—
405#214—62no—
406#214—62no—
407#214—62no—
408#214—122no—
409#213—22no—
410#213—62no—
411#213—62no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—21no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418C4⋊Dic3—31no—
419C4⋊Dic3—31no—
420C4⋊Dic3—61no—
421C4⋊Dic3—61no—
422C4⋊Dic3C22×D311yescharacteristic
423C4⋊Dic3C22×D311yescharacteristic
424Dic3⋊C4—21no—
425Dic3⋊C4—61no—
426Dic3⋊C4—61no—
427Dic3⋊C4—61no—
428Dic3⋊C4—121no—
429C4×Dic3—61no—
430C4×Dic3—61no—
431#208—34no—
432#208—62no—
433#208—62no—
434#208—62no—
435C2×C3⋊C8—22no—
436C2×C3⋊C8—31no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—61no—
441C2×C3⋊C8—61no—
442C2×C3⋊C8—62no—
443C2×C3⋊C8—62no—
444C2×C3⋊C8—122no—
445C2×C3⋊C8C22×D311yescharacteristic
446C2×C3⋊C8C22×D311yescharacteristic
447#204—62no—
448ΓL(1,𝔽25)—34no—
449ΓL(1,𝔽25)—62no—
450ΓL(1,𝔽25)—62no—
451ΓL(1,𝔽25)—62no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32—41no—
457C22×C32AGL(1,ℤ/8)12yescomplemented
458C22×C32C22×D411yescharacteristic
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—44no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—84no—
472C2×C3×D3#12112yes—
473C32×C4—21no—
474C32×C4—41no—
475C32×C4C22×D411yescharacteristic
476C32×C4C2×#4111yescharacteristic
477C3⋊Dic3—41no—
478C3⋊Dic3—41no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3#12112yes—
483C2×#41—91no—
484C22×D4—31no—
485C22×D4—61no—
486C23×C4—31no—
487AGL(1,ℤ/8)—184no—
488C2×SD16—91no—
489C2×SD16—91no—
490C2×D8—31no—
491C2×D8—91no—
492C2×M16—91no—
493C2×M16—91no—
494C2×M16—91no—
495C2×M16—91no—
496C2×M16—184no—
497C22×C8—31no—
498C22×C8—91no—
499#123—181no—
500C22⋊Q8—91no—
501C22⋊Q8—91no—
502#121—31no—
503#121—31no—
504#121—31no—
505#121—31no—
506#121—61no—
507#121—61no—
508#121—91no—
509#121D3211yescharacteristic
510#120—181no—
511C4×D4—181no—
512C4×D4—181no—
513#117—91no—
514C2×C4⋊C4—31no—
515C2×C22⋊C4—61no—
516#107—31no—
517#107—91no—
518#106—91no—
519#106—91no—
520#103—91no—
521#103—91no—
522#102—31no—
523#102—31no—
524#102—91no—
525#102—91no—
526#102—91no—
527#102—91no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—31no—
532C23×C3—31no—
533C23×C3—41no—
534C23×C3—62no—
535C23×C3—62no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—121no—
539C23×C3—122no—
540C23×C3—122no—
541C23×C3—122no—
542C23×C3D3×D411yescharacteristic
543C23×C3C2×#6711yescharacteristic
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—41no—
549C22×D3—42no—
550C22×D3—42no—
551C22×D3—42no—
552C22×D3C2×#6711yescharacteristic
553C22×D3C2×#6711yescharacteristic
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—41no—
559C3×D4—41no—
560C3×D4—42no—
561C3×D4—42no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—82no—
567C3×D4—122no—
568C3×D4—122no—
569C3×D4—122no—
570C3×D4—122no—
571C3×D4—122no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—31no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—31no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—62no—
588C2×C3×C4—62no—
589C2×C3×C4—62no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—122no—
595C2×C3×C4D3×D411yescharacteristic
596C2×C3×C4C2×#6711yescharacteristic
597C2×C3×C4C23×D311yescharacteristic
598C2×C3×C4C23×D311yescharacteristic
599#67—42no—
600#67—42no—
601#67—42no—
602#67—42no—
603#67—122no—
604#67—122no—
605#67—122no—
606#67—122no—
607C2×Dic3—22no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—121no—
615C2×Dic3—121no—
616C2×Dic3—122no—
617C2×Dic3C2×#6711yescharacteristic
618C2×Dic3C2×#6711yescharacteristic
619D12—21no—
620D12—21no—
621D12—21no—
622D12—21no—
623D12—42no—
624C4×D3—22no—
625C4×D3—21no—
626C4×D3—21no—
627C4×D3—22no—
628C4×D3—42no—
629C4×D3—122no—
630C4×D3D3×D412yes—
631C4×D3#23712yes—
632Dic6—61no—
633Dic6—61no—
634Dic6—61no—
635Dic6—61no—
636Dic6—121no—
637Dic6—121no—
638C3×C8—32no—
639C3×C8—61no—
640C3⋊C8—21no—
641C3⋊C8—32no—
642C3⋊C8—32no—
643C3⋊C8—62no—
644C3⋊C8—61no—
645C3⋊C8—61no—
646C3⋊C8—121no—
647C3⋊C8D3×D412yescomplemented
648C2×C32—22no—
649C2×C32—81no—
650C2×C32C2×#12111yescharacteristic
651C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
652C2×C32#57511yescharacteristic
653C3×D3—22no—
654C3×D3—41no—
655C3×D3—81no—
656C3×D3—81no—
657C24—31no—
658C24—61no—
659#41—182no—
660#41—182no—
661C2×Q8—91no—
662C2×D4—21no—
663C2×D4—31no—
664C2×D4—31no—
665C2×D4—61no—
666C2×D4—62no—
667C2×D4—62no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4—61no—
671C2×D4—61no—
672C2×D4—124no—
673C2×D4—181no—
674C2×D4—181no—
675C2×D4C2×D3211yescharacteristic
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—61no—
684C22×C4—181no—
685C22×C4C2×D3211yescharacteristic
686SD16—182no—
687SD16—182no—
688D8—62no—
689D8—182no—
690M16—94no—
691M16—182no—
692M16—182no—
693M16—182no—
694C2×C8—31no—
695C2×C8—31no—
696C2×C8—62no—
697C2×C8—91no—
698C2×C8—91no—
699C2×C8—182no—
700C4⋊C4—31no—
701C4⋊C4—31no—
702C4⋊C4—61no—
703C4⋊C4—91no—
704C4⋊C4—181no—
705C4⋊C4—181no—
706C4⋊C4C2×D3211yescharacteristic
707C22⋊C4—21no—
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C22⋊C4—61no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C42—181no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—22no—
723C22×C3—32no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—81no—
738C22×C3—81no—
739C22×C3—81no—
740C22×C3—124no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—244no—
748C22×C3#91112yescomplemented
749C22×C3#93212yescomplemented
750C22×C3C2×D3×D411yescharacteristic
751C22×C3C22×#6711yescharacteristic
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—21no—
757C2×D3—44no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—84no—
765C2×D3#93912yes—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—32no—
771C3×C4—41no—
772C3×C4—41no—
773C3×C4—41no—
774C3×C4—61no—
775C3×C4—81no—
776C3×C4—121no—
777C3×C4—121no—
778C3×C4C2×D3×D411yescharacteristic
779C3×C4C2×D3×D411yescharacteristic
780C3×C4C2×#23711yescharacteristic
781C3×C4D3×#4111yescharacteristic
782Dic3—21no—
783Dic3—41no—
784Dic3—41no—
785Dic3—121no—
786Dic3—121no—
787Dic3—121no—
788Dic3—121no—
789Dic3—241no—
790Dic3—241no—
791Dic3#93912yes—
792C32#305511yescharacteristic, complemented, Sylow
793C23—21no—
794C23—31no—
795C23—31no—
796C23—62no—
797C23—62no—
798C23—61no—
799C23—61no—
800C23—121no—
801C23—122no—
802C23—122no—
803C23—122no—
804C23D3×#6711yescharacteristic
805Q8—181no—
806Q8—181no—
807D4—21no—
808D4—21no—
809D4—42no—
810D4—61no—
811D4—61no—
812D4—61no—
813D4—61no—
814D4—122no—
815D4—122no—
816D4—122no—
817D4—122no—
818D4—122no—
819D4—362no—
820D4—362no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—31no—
825C2×C4—32no—
826C2×C4—32no—
827C2×C4—31no—
828C2×C4—62no—
829C2×C4—62no—
830C2×C4—62no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—122no—
836C2×C4—181no—
837C2×C4—181no—
838C2×C4—362no—
839C2×C4D3×#6711yescharacteristic
840C2×C4C22×D3211yescharacteristic
841C8—32no—
842C8—61no—
843C8—92no—
844C8—181no—
845C2×C3—22no—
846C2×C3—22no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—42no—
851C2×C3—62no—
852C2×C3—81no—
853C2×C3—81no—
854C2×C3—121no—
855C2×C3—161no—
856C2×C3—241no—
857C2×C3—241no—
858C2×C3D3×#12111yescharacteristic
859C2×C3C2×#91111yescharacteristic
860C2×C3#576811yescharacteristic
861C2×C3C2×#93211yescharacteristic
862C2×C3C2×#93911yescharacteristic
863C2×C3#582211yescharacteristic
864D3—22no—
865D3—41no—
866D3—81no—
867D3—81no—
868C22—21no—
869C22—21no—
870C22—32no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—61no—
875C22—61no—
876C22—61no—
877C22—61no—
878C22—61no—
879C22—124no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—121no—
886C22—244no—
887C22#6393212yescomplemented
888C22C2×D3×#6711yescharacteristic
889C4—21no—
890C4—32no—
891C4—41no—
892C4—61no—
893C4—121no—
894C4—121no—
895C4—361no—
896C4—361no—
897C4D32×D411yescharacteristic
898C4D3×#23711yescharacteristic
899C3—21no—
900C3#8071511yescharacteristic, complemented
901C3#8262111yescharacteristic, complemented
902C2—22no—
903C2—62no—
904C2—81no—
905C2—121no—
906C2—241no—
907C2—241no—
908C2C2×#6393211yescharacteristic
909C2D3×#93911yescharacteristic
910C2#1059545311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×D3×#121C2semidirect
2. C2×#63932C2semidirect
3. #10594892C2semidirect
4. C22×#3711C2semidirect
5. #10592740C2semidirect
6. C3×#5038C2semidirect
7. #10591462C2semidirect
8. #10591451C2semidirect
9. #10591421C2semidirect
10. #10591175C2semidirect
11. #10591166C2semidirect
12. #10590607C2semidirect
13. #10590588C2semidirect
14. #10590580C2semidirect
15. #10590504C2semidirect
23. C2×#3754C22semidirect
24. #64133C22semidirect
25. C22×C3⋊(C3⋊C8)C22semidirect
28. C2×C3×#213C22semidirect
30. C3×#930C22semidirect
31. C22×C3×C3⋊C8C22semidirect
39. #63908C22semidirect
42. #63857C22semidirect
44. C2×#3716C22semidirect
45. C2×#3713C22semidirect
49. C2×#3711C22semidirect
50. C2×#3711C22semidirect
51. #63659C22semidirect
52. #63637C22semidirect
53. #63635C22semidirect
54. C3×#832C22semidirect
55. C3×#809C22semidirect
56. C3×#807C22semidirect
57. #63576C22semidirect
58. #63573C22semidirect
59. #63567C22semidirect
60. #63563C22semidirect
61. #63562C22semidirect
62. #63562C22semidirect
70. D3×#121D3semidirect
85. #5038D3semidirect
153. #3711D4semidirect
189. C2×#213C2×D3semidirect
192. #930C2×D3semidirect
209. C22×C3⋊C8C2×D3semidirect
234. #832C2×D3semidirect
244. #809C2×D3semidirect
251. #807C2×D3semidirect
301. C3⋊(C3⋊C8)C2×D4semidirect
303. C3×C3⋊C8C2×D4semidirect
457. C22×C32AGL(1,ℤ/8)semidirect
647. C3⋊C8D3×D4semidirect
748. C22×C3#911semidirect
749. C22×C3#932semidirect
792. C32#3055semidirect
887. C22#63932semidirect
900. C3#80715semidirect
901. C3#82621semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1212
C2×#639322
#105948922
C22×#37112
#105927402
C3×#50382
#105914622
#105914512
#105914212
#105911752
#105911662
#105906072
#105905882
#105905802
#105905042
#826213
#807153