Finite Group Databasebeta

← #11884019

Subgroups — #11884019

Order 1152.

1173 conjugacy classes of subgroups.

The subgroup lattice has 941 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5609C211yesmaximal, characteristic, complemented
2C2×D3×#214C211yesmaximal, characteristic, complemented
3#10594916C211yesmaximal, characteristic, complemented
4C2×#63830C211yesmaximal, characteristic, complemented
5#10592736C211yesmaximal, characteristic, complemented
6C3×#5042C211yesmaximal, characteristic, complemented
7#10591472C211yesmaximal, characteristic, complemented
8#10591448C211yesmaximal, characteristic, complemented
9#10591439C211yesmaximal, characteristic, complemented
10#10591169C211yesmaximal, characteristic, complemented
11#10591147C211yesmaximal, characteristic, complemented
12#10590603C211yesmaximal, characteristic, complemented
13#10590590C211yesmaximal, characteristic, complemented
14#10590576C211yesmaximal, characteristic, complemented
15#10590534C211yesmaximal, characteristic, complemented
16#83491—31nomaximal
17#80834—31nomaximal
18C2×#3828C2211yescharacteristic, complemented
19C2×C3×D3×D4—21no—
20C2×C3×D3×D4C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C2×D3×Dic6C2211yescharacteristic, complemented
23C32×#121C2211yescharacteristic
24C2×#3754C2211yescharacteristic, complemented
25C2×#3753C2211yescharacteristic, complemented
26C3×#940C2211yescharacteristic
27C3×#937—21no—
28C2×C3×#214C2211yescharacteristic, complemented
29C3×C4×#67C2211yescharacteristic
30C3×#924C2211yescharacteristic, complemented
31C2×C3×#208C2211yescharacteristic, complemented
32C3×#895C2211yescharacteristic
33C3×#893C2211yescharacteristic
34C3×#884—21no—
35C3×#882—21no—
36#63971—21no—
37#63953—21no—
38D3×#214—24no—
39#63909C2211yescharacteristic, complemented
40#63881—21no—
41#63865—21no—
42#63864C2211yescharacteristic, complemented
43#63844C2211yescharacteristic, complemented
44#63830—24no—
45C2×#3716C2211yescharacteristic
46C2×#3716C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63657C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#807C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×D42—31no—
64C22×#214—31no—
65C2×#932—31no—
66C2×D3×SD16—31no—
67C2×#908—31no—
68#5633—31no—
69#5609D311yescharacteristic, complemented
70#5552—31no—
71C3×#468—31no—
72#5218—31no—
73#5217—31no—
74#5176—31no—
75#5127—31no—
76#5075—31no—
77#5074—31no—
78#5046—31no—
79#5042D311yescharacteristic, complemented
80#5040—31no—
81#5038—31no—
82#5037—31no—
83#5037—31no—
84#5037—61no—
85#5018—31no—
86#5016—31no—
87#5011—31no—
88#4889—31no—
89#4883—31no—
90#4819—31no—
91#4806—31no—
92#4773—31no—
93#4762—31no—
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×#638—21no—
100#3828—22no—
101#3828—41no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3—21no—
104C2×#634C2311yescharacteristic
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67D411yescharacteristic
109C3×D3×D4—22no—
110C3×D3×D4—41no—
111C3×D3×D4—44no—
112C2×C3×D12—22no—
113C2×C3×D12—21no—
114C2×C3×D12—21no—
115C2×C3×D12—41no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×#627—21no—
122C2×#626—21no—
123C2×D3×Dic3—21no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C32×C4⋊C4C2311yescharacteristic
127C32×C22⋊C4—21no—
128#3754—22no—
129#3753—41no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#217—21no—
133C3×#217D411yescharacteristic
134C3×#214—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4D411yescharacteristic
141C3×C4×Dic3C2311yescharacteristic
142C3×#208—22no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145#3724—21no—
146#3722—21no—
147#3722—21no—
148#3722—21no—
149Dic32—21no—
150#3716—22no—
151#3716D414yescomplemented
152#3715—22no—
153#3715—41no—
154#3714—22no—
155#3714—22no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C22×C3×D4—31no—
159C22×C3×D4—31no—
160C22×C3×D4—61no—
161C2×D3×Q8—31no—
162C2×D3×D4—21no—
163C2×D3×D4C2×D311yescharacteristic
164C2×#235—31no—
165C2×#235—31no—
166C2×#235—61no—
167C22×D12C2×D311yescharacteristic
168C22×Dic6—31no—
169C2×C3×SD16—31no—
170C2×C3×M16—31no—
171C3×#127—31no—
172C3×C22⋊Q8—31no—
173C3×#121—21no—
174C3×#121—31no—
175C3×#121—61no—
176C3×#121C2×D311yescharacteristic
177C3×#121C2×D311yescharacteristic
178C3×#120—61no—
179C3×#120—61no—
180C3×C4×D4—31no—
181C3×C4×D4—31no—
182#947—31no—
183C2×#215—31no—
184C2×#215—31no—
185#940C2×D311yescharacteristic
186#939—61no—
187#937—21no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#214—31no—
191C2×#214—31no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214—61no—
195C2×#214—64no—
196C2×#214C2×D311yescharacteristic, complemented
197#932—64no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—61no—
203#930—31no—
204C4×#67C2×D311yescharacteristic
205#924C2×D311yescharacteristic, complemented
206C2×#208C2×D311yescharacteristic, complemented
207C22×C3⋊C8—31no—
208D3×SD16—64no—
209#908—64no—
210C2×D24—31no—
211C2×D24—31no—
212C2×#204—31no—
213C2×#204—31no—
214C2×D3×C8—31no—
215#896—61no—
216#896—61no—
217#895—31no—
218#895C2×D311yescharacteristic
219#893—61no—
220#893C2×D311yescharacteristic
221#887—31no—
222#885—61no—
223#885—61no—
224#884—21no—
225#884—61no—
226#882—21no—
227#67⋊C4—61no—
228#875—31no—
229C4×Dic6—31no—
230C3×#107—31no—
231C3×#103—31no—
232C3×#102—31no—
233#832—31no—
234#832—31no—
235#832C2×D311yescharacteristic, complemented
236#830—31no—
237#830—31no—
238#830—31no—
239#830—61no—
240(C2×D3)⋊C8—31no—
241#815—31no—
242Dic3⋊C8—31no—
243#810—31no—
244#810—31no—
245#810—61no—
246#810C2×D311yescharacteristic, complemented
247#809—31no—
248#809—31no—
249#809—31no—
250#809—31no—
251#809—61no—
252#807C2×D311yescharacteristic, complemented
253C4⋊(C3⋊C8)—31no—
254#803—31no—
255C23×C32—21no—
256C23×C32C2×D411yescharacteristic
257C22×C3⋊D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—42no—
263C22×C3×D3—42no—
264C22×C3×D3—81no—
265C22×C3×D3—81no—
266C22×C3×D3C2×D411yescharacteristic
267C32×D4—21no—
268C32×D4—21no—
269C32×D4—42no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2411yescharacteristic
275#638—42no—
276C2×C3⋊Dic3—21no—
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—21no—
279C4×C3⋊D3—42no—
280#634—21no—
281#634C2×D412yescomplemented
282C3×#67—22no—
283C3×#67—42no—
284C3×#67—42no—
285C3×#67—81no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C3×D12—21no—
292C3×D12—21no—
293C3×D12—21no—
294C3×D12—42no—
295C3×D12—42no—
296C3×D12C2×D412yes—
297C3×C4×D3—21no—
298C3×C4×D3—21no—
299C3×C4×D3—42no—
300C3×Dic6—21no—
301C3×Dic6—21no—
302#627—42no—
303#626—42no—
304D3×Dic3—42no—
305C3⋊(C3⋊C8)—21no—
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—31no—
313#496—91no—
314#468—31no—
315#466—91no—
316#463—91no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C24×C3—61no—
325C24×C3—61no—
326C23×D3—21no—
327C23×D3—21no—
328C2×C3×Q8—31no—
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—41no—
336C2×C3×D4—62no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—62no—
342C2×C3×D4—61no—
343C2×C3×D4—121no—
344C2×C3×D4—121no—
345C2×C3×D4—124no—
346C2×C3×D4C22×D311yescharacteristic
347C2×C3×D4C22×D311yescharacteristic
348C22×C3×C4—21no—
349C22×C3×C4—31no—
350C22×C3×C4—61no—
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C2×#67—21no—
354C2×#67—21no—
355C2×#67—21no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—121no—
360C2×#67#6711yescharacteristic
361C22×Dic3—61no—
362D3×Q8—62no—
363D3×Q8—121no—
364D3×D4—22no—
365D3×D4—41no—
366D3×D4—44no—
367#235—62no—
368#235—62no—
369#235—122no—
370#235—121no—
371#235—121no—
372#235—122no—
373C2×D12—22no—
374C2×D12—21no—
375C2×D12—21no—
376C2×D12—31no—
377C2×D12—31no—
378C2×D12—41no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12C22×D311yescharacteristic
382C2×D12C22×D311yescharacteristic
383C2×C4×D3—21no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3—121no—
388C2×C4×D3C22×D311yescharacteristic
389C2×Dic6—31no—
390C2×Dic6—31no—
391C2×Dic6—61no—
392C2×Dic6—62no—
393C2×Dic6—61no—
394C2×Dic6—61no—
395C2×Dic6—121no—
396C2×Dic6C22×D311yescharacteristic
397C3×SD16—62no—
398C3×M16—62no—
399C2×C3×C8—31no—
400C2×C3×C8—31no—
401C3×C4⋊C4—21no—
402C3×C4⋊C4—31no—
403C3×C4⋊C4—31no—
404C3×C4⋊C4—61no—
405C3×C4⋊C4C22×D311yescharacteristic
406C3×C4⋊C4C22×D311yescharacteristic
407C3×C22⋊C4—21no—
408C3×C22⋊C4—21no—
409C3×C22⋊C4—31no—
410C3×C22⋊C4—31no—
411C3×C22⋊C4—41no—
412C3×C22⋊C4—61no—
413C3×C22⋊C4—61no—
414C3×C22⋊C4—61no—
415C3×C42—31no—
416#217—21no—
417#217#6711yescharacteristic
418#215—62no—
419#215—121no—
420#214—22no—
421#214—34no—
422#214—62no—
423#214—62no—
424#214—62no—
425#214—62no—
426#214—122no—
427#214—121no—
428#213—62no—
429#213—62no—
430#213—121no—
431#213—121no—
432#213—122no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4#6711yescharacteristic
442C4⋊Dic3C22×D311yescharacteristic
443Dic3⋊C4—21no—
444Dic3⋊C4—61no—
445Dic3⋊C4—61no—
446Dic3⋊C4#6711yescharacteristic
447C4×Dic3—61no—
448C4×Dic3—61no—
449C4×Dic3C22×D311yescharacteristic
450#208—22no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—61no—
456C2×C3⋊C8—61no—
457C2×C3⋊C8—62no—
458C2×C3⋊C8C22×D311yescharacteristic
459C2×C3⋊C8C22×D311yescharacteristic
460D24—62no—
461D24—62no—
462#204—34no—
463#204—62no—
464D3×C8—62no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—21no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32—41no—
471C22×C32C22×D411yescharacteristic
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—22no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—84no—
484C2×C3×D3—84no—
485C2×C3×D3AGL(1,ℤ/8)12yescomplemented
486C32×C4—21no—
487C32×C4—41no—
488C32×C4C22×D411yescharacteristic
489C32×C4H(5,𝔽2)11yescharacteristic
490C3⋊Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41—91no—
497C22×Q8—91no—
498C22×D4—31no—
499C22×D4—31no—
500C22×D4—61no—
501AGL(1,ℤ/8)—184no—
502C2×SD16—31no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—184no—
509C2×D8—91no—
510C2×D8—91no—
511C2×D8—91no—
512C2×M16—31no—
513C22×C8—91no—
514#127—31no—
515#124—91no—
516#124—181no—
517C22⋊Q8—31no—
518C22⋊Q8—181no—
519#121—31no—
520#121—61no—
521#121—91no—
522#121—181no—
523#121D3211yescharacteristic
524#120—61no—
525#120—61no—
526C4×Q8—91no—
527C4×D4—31no—
528C4×D4—31no—
529C4×D4—181no—
530#107—31no—
531C4⋊C8—91no—
532#103—31no—
533#103—91no—
534#102—31no—
535#102—91no—
536#102—91no—
537#102—91no—
538C22⋊C8—91no—
539C22⋊C8—91no—
540#97—91no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—31no—
545C23×C3—41no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—122no—
549C23×C3—122no—
550C23×C3—122no—
551C23×C3—122no—
552C23×C3—241no—
553C23×C3—241no—
554C23×C3D3×D411yescharacteristic
555C23×C3C2×#6711yescharacteristic
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—42no—
559C22×D3—42no—
560C22×D3—42no—
561C22×D3—42no—
562C22×D3—61no—
563C22×D3—61no—
564C22×D3—81no—
565C22×D3—81no—
566C22×D3—121no—
567C22×D3C2×#6711yescharacteristic
568C3×Q8—61no—
569C3×Q8—61no—
570C3×D4—21no—
571C3×D4—21no—
572C3×D4—21no—
573C3×D4—21no—
574C3×D4—32no—
575C3×D4—41no—
576C3×D4—41no—
577C3×D4—42no—
578C3×D4—42no—
579C3×D4—62no—
580C3×D4—61no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—82no—
584C3×D4—122no—
585C3×D4—122no—
586C3×D4—122no—
587C3×D4—122no—
588C3×D4—241no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—31no—
598C2×C3×C4—31no—
599C2×C3×C4—31no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—122no—
608C2×C3×C4D3×D411yescharacteristic
609C2×C3×C4C2×#6711yescharacteristic
610C2×C3×C4C23×D311yescharacteristic
611C2×C3×C4C23×D311yescharacteristic
612#67—22no—
613#67—42no—
614#67—42no—
615#67—81no—
616#67—122no—
617#67—122no—
618#67—122no—
619#67—124no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—121no—
625C2×Dic3—122no—
626C2×Dic3C2×#6711yescharacteristic
627C2×Dic3C2×#6711yescharacteristic
628C2×Dic3C2×#6711yescharacteristic
629D12—21no—
630D12—21no—
631D12—21no—
632D12—42no—
633D12—42no—
634D12—62no—
635D12—61no—
636D12—61no—
637D12—61no—
638D12—61no—
639D12—121no—
640D12—122no—
641D12D3×D412yes—
642C4×D3—21no—
643C4×D3—21no—
644C4×D3—42no—
645C4×D3—122no—
646C4×D3—122no—
647C4×D3—122no—
648C4×D3—124no—
649Dic6—21no—
650Dic6—21no—
651Dic6—32no—
652Dic6—32no—
653Dic6—62no—
654Dic6—61no—
655Dic6—61no—
656Dic6—121no—
657Dic6—122no—
658Dic6—122no—
659C3×C8—32no—
660C3×C8—61no—
661C3⋊C8—21no—
662C3⋊C8—61no—
663C3⋊C8—61no—
664C3⋊C8—61no—
665C3⋊C8—61no—
666C3⋊C8—121no—
667C3⋊C8—121no—
668C3⋊C8D3×D412yescomplemented
669C2×C32—41no—
670C2×C32—81no—
671C2×C32D4211yescharacteristic
672C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
673C2×C32#57711yescharacteristic
674C3⋊D3—81no—
675C3×D3—22no—
676C3×D3—42no—
677C3×D3—81no—
678C24—61no—
679C24—61no—
680#41—182no—
681#41—361no—
682C2×Q8—31no—
683C2×Q8—91no—
684C2×Q8—181no—
685C2×Q8—182no—
686C2×Q8—361no—
687C2×D4—21no—
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—31no—
691C2×D4—62no—
692C2×D4—61no—
693C2×D4—61no—
694C2×D4—61no—
695C2×D4—61no—
696C2×D4—62no—
697C2×D4—61no—
698C2×D4—91no—
699C2×D4—121no—
700C2×D4—121no—
701C2×D4—124no—
702C2×D4—181no—
703C2×D4—181no—
704C2×D4C2×D3211yescharacteristic
705C22×C4—31no—
706C22×C4—61no—
707C22×C4—181no—
708C22×C4—181no—
709C22×C4C2×D3211yescharacteristic
710SD16—62no—
711SD16—94no—
712SD16—182no—
713SD16—182no—
714SD16—182no—
715SD16—361no—
716D8—182no—
717D8—182no—
718D8—361no—
719M16—62no—
720C2×C8—31no—
721C2×C8—31no—
722C2×C8—91no—
723C2×C8—91no—
724C2×C8—182no—
725C4⋊C4—31no—
726C4⋊C4—31no—
727C4⋊C4—61no—
728C4⋊C4—181no—
729C4⋊C4C2×D3211yescharacteristic
730C22⋊C4—21no—
731C22⋊C4—31no—
732C22⋊C4—31no—
733C22⋊C4—61no—
734C22⋊C4—61no—
735C22⋊C4—61no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C42—31no—
740C42—181no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—32no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—61no—
759C22×C3—61no—
760C22×C3—62no—
761C22×C3—81no—
762C22×C3—81no—
763C22×C3—81no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3—244no—
770C22×C3—244no—
771C22×C3C2×D3×D411yescharacteristic
772C22×C3C22×#6711yescharacteristic
773C2×D3—21no—
774C2×D3—21no—
775C2×D3—22no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—84no—
782C2×D3—84no—
783C2×D3—122no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—121no—
790C2×D3—241no—
791C2×D3—241no—
792C2×D3#93212yescomplemented
793C3×C4—21no—
794C3×C4—21no—
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—41no—
800C3×C4—61no—
801C3×C4—61no—
802C3×C4—61no—
803C3×C4—81no—
804C3×C4—121no—
805C3×C4—121no—
806C3×C4C2×D3×D411yescharacteristic
807C3×C4C2×D3×D411yescharacteristic
808C3×C4#100411yescharacteristic
809C3×C4#100911yescharacteristic
810Dic3—21no—
811Dic3—21no—
812Dic3—21no—
813Dic3—41no—
814Dic3—41no—
815Dic3—62no—
816Dic3—62no—
817Dic3—122no—
818C32#326511yescharacteristic, complemented, Sylow
819C23—21no—
820C23—31no—
821C23—61no—
822C23—61no—
823C23—122no—
824C23—122no—
825C23—122no—
826C23—122no—
827C23—181no—
828C23—241no—
829C23—241no—
830C23D3×#6711yescharacteristic
831Q8—61no—
832Q8—61no—
833Q8—92no—
834Q8—181no—
835Q8—362no—
836D4—21no—
837D4—21no—
838D4—32no—
839D4—42no—
840D4—62no—
841D4—61no—
842D4—61no—
843D4—61no—
844D4—122no—
845D4—122no—
846D4—122no—
847D4—122no—
848D4—181no—
849D4—181no—
850D4—241no—
851D4—362no—
852D4—362no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—31no—
857C2×C4—31no—
858C2×C4—31no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—122no—
864C2×C4—181no—
865C2×C4—362no—
866C2×C4—362no—
867C2×C4D3×#6711yescharacteristic
868C2×C4C22×D3211yescharacteristic
869C8—32no—
870C8—61no—
871C8—181no—
872C8—181no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—41no—
877C2×C3—41no—
878C2×C3—62no—
879C2×C3—81no—
880C2×C3—81no—
881C2×C3—81no—
882C2×C3—122no—
883C2×C3—161no—
884C2×C3—241no—
885C2×C3#560911yescharacteristic
886C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
887C2×C3#577811yescharacteristic
888C2×C3C2×#93211yescharacteristic
889C2×C3D4×#6711yescharacteristic
890C2×C3#583611yescharacteristic
891D3—22no—
892D3—42no—
893D3—81no—
894D3—242no—
895D3—241no—
896D3—241no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—32no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—61no—
905C22—61no—
906C22—62no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—121no—
911C22—121no—
912C22—244no—
913C22—244no—
914C22—361no—
915C22—361no—
916C22—361no—
917C22C2×D3×#6711yescharacteristic
918C4—21no—
919C4—41no—
920C4—61no—
921C4—61no—
922C4—61no—
923C4—121no—
924C4—121no—
925C4—182no—
926C4D32×D411yescharacteristic
927C4#6431411yescharacteristic
928C3—21no—
929C3#8083411yescharacteristic, complemented
930C3#8349111yescharacteristic, complemented
931C2—41no—
932C2—62no—
933C2—81no—
934C2—122no—
935C2—241no—
936C2—721no—
937C2D3×#93211yescharacteristic
938C2#1059529111yescharacteristic
939C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3265
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×#5609C2semidirect
2. C2×D3×#214C2semidirect
3. #10594916C2semidirect
4. C2×#63830C2semidirect
5. #10592736C2semidirect
6. C3×#5042C2semidirect
7. #10591472C2semidirect
8. #10591448C2semidirect
9. #10591439C2semidirect
10. #10591169C2semidirect
11. #10591147C2semidirect
12. #10590603C2semidirect
13. #10590590C2semidirect
14. #10590576C2semidirect
15. #10590534C2semidirect
18. C2×#3828C22semidirect
22. C2×D3×Dic6C22semidirect
24. C2×#3754C22semidirect
25. C2×#3753C22semidirect
28. C2×C3×#214C22semidirect
30. C3×#924C22semidirect
31. C2×C3×#208C22semidirect
39. #63909C22semidirect
42. #63864C22semidirect
43. #63844C22semidirect
46. C2×#3716C22semidirect
48. C2×#3715C22semidirect
50. C2×#3714C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63657C22semidirect
53. #63637C22semidirect
54. #63636C22semidirect
55. C3×#832C22semidirect
56. C3×#810C22semidirect
57. C3×#807C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
69. #5609D3semidirect
79. #5042D3semidirect
151. #3716D4semidirect
196. C2×#214C2×D3semidirect
205. #924C2×D3semidirect
206. C2×#208C2×D3semidirect
235. #832C2×D3semidirect
246. #810C2×D3semidirect
252. #807C2×D3semidirect
281. #634C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
485. C2×C3×D3AGL(1,ℤ/8)semidirect
668. C3⋊C8D3×D4semidirect
792. C2×D3#932semidirect
818. C32#3265semidirect
929. C3#80834semidirect
930. C3#83491semidirect

Maximal subgroups

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

subgroupindex
C3×#56092
C2×D3×#2142
#105949162
C2×#638302
#105927362
C3×#50422
#105914722
#105914482
#105914392
#105911692
#105911472
#105906032
#105905902
#105905762
#105905342
#834913
#808343