Finite Group Databasebeta

← #11883947

Subgroups — #11883947

Order 1152.

1171 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5609C211yesmaximal, characteristic, complemented
2C2×#63932C211yesmaximal, characteristic, complemented
3#10594918C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5#10592739C211yesmaximal, characteristic, complemented
6C3×#5038C211yesmaximal, characteristic, complemented
7#10591469C211yesmaximal, characteristic, complemented
8#10591459C211yesmaximal, characteristic, complemented
9#10591439C211yesmaximal, characteristic, complemented
10#10591160C211yesmaximal, characteristic, complemented
11#10591155C211yesmaximal, characteristic, complemented
12#10590613C211yesmaximal, characteristic, complemented
13#10590590C211yesmaximal, characteristic, complemented
14#10590588C211yesmaximal, characteristic, complemented
15#10590530C211yesmaximal, characteristic, complemented
16#83491—31nomaximal
17#80727—31nomaximal
18C22×#634C2211yescharacteristic, complemented
19C2×C3×D3×D4—21no—
20C2×C3×D3×D4C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C2×#3795C2211yescharacteristic, complemented
23C32×#121C2211yescharacteristic
24C2×#3754C2211yescharacteristic, complemented
25C2×#3754C2211yescharacteristic, complemented
26C3×#940C2211yescharacteristic
27C3×#937—21no—
28C2×C3×#213C2211yescharacteristic, complemented
29C3×#930C2211yescharacteristic, complemented
30C3×C4×#67C2211yescharacteristic
31C22×C3×C3⋊C8C2211yescharacteristic, complemented
32C3×#895C2211yescharacteristic
33C3×#893C2211yescharacteristic
34C3×#884—21no—
35C3×#882—21no—
36#63980—21no—
37#67⋊Dic3—21no—
38#63932—24no—
39#63913—21no—
40#63896—21no—
41#63860C2211yescharacteristic, complemented
42#63857C2211yescharacteristic, complemented
43#63844C2211yescharacteristic, complemented
44C2×#3716—24no—
45C2×#3716C2211yescharacteristic
46C2×#3716C2211yescharacteristic
47C2×#3716C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic
50C2×#3713C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52#63657C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, 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×#911—31no—
67C22×#204—31no—
68#5609D311yescharacteristic, complemented
69#5598—31no—
70#5552—31no—
71C3×#466—31no—
72#5218—31no—
73#5217—31no—
74#5154—31no—
75#5111—31no—
76#5075—31no—
77#5074—31no—
78#5042—31no—
79#5040—31no—
80#5040—31no—
81#5040—61no—
82#5038D311yescharacteristic, complemented
83#5037—31no—
84#5036—31no—
85#5018—31no—
86#5016—31no—
87#5011—31no—
88#4889—31no—
89#4886—31no—
90#4787—31no—
91#4781—31no—
92#4776—31no—
93#4762—31no—
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C3⋊Dic3—21no—
100C2×#634—22no—
101C2×#634—21no—
102C2×#634—41no—
103C2×#634C2311yescharacteristic
104C2×#634C2311yescharacteristic
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67D411yescharacteristic
110C3×D3×D4—22no—
111C3×D3×D4—41no—
112C3×D3×D4—44no—
113C2×C3×D12—22no—
114C2×C3×D12—21no—
115C2×C3×D12—21no—
116C2×C3×D12—41no—
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×D12C2311yescharacteristic
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3C2311yescharacteristic
122C2×#625—21no—
123C2×D3×Dic3—21no—
124#3795—22no—
125#3795—41no—
126C32×C4⋊C4C2311yescharacteristic
127C32×C22⋊C4—21no—
128#3754—22no—
129#3754—41no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#217D411yescharacteristic
133C3×#213—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4D411yescharacteristic
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8—22no—
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144#3724—21no—
145Dic3⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149Dic32—21no—
150#3716—22no—
151#3716—22no—
152#3716—22no—
153#3716D414yescomplemented
154#3713—22no—
155#3713—41no—
156#3711—22no—
157#3265—91noSylow
158C22×C3×D4—31no—
159C22×C3×D4—31no—
160C22×C3×D4—61no—
161C2×#237—31no—
162C2×D3×D4—21no—
163C2×D3×D4C2×D311yescharacteristic
164C2×#235—31no—
165C22×D12C2×D311yescharacteristic
166C22×Dic6—31no—
167C22×Dic6—31no—
168C22×Dic6—61no—
169C2×C3×D8—31no—
170C22×C3×C8—31no—
171C3×#127—31no—
172C3×#121—21no—
173C3×#121—31no—
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#940C2×D311yescharacteristic
183#939—61no—
184#939—61no—
185#937—21no—
186#936—31no—
187D4×Dic3—61no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#214—31no—
191C2×#214—31no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214—31no—
195C2×#214—31no—
196C2×#214—61no—
197C2×#214—61no—
198C2×#214—64no—
199#932—64no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213C2×D311yescharacteristic, complemented
205#930C2×D311yescharacteristic, complemented
206C4×#67C2×D311yescharacteristic
207#924—31no—
208C2×#208—31no—
209C22×C3⋊C8C2×D311yescharacteristic, complemented
210#911—64no—
211C2×#204—31no—
212C2×#204—31no—
213C2×#204—31no—
214C2×#204—31no—
215C2×#204—64no—
216C2×ΓL(1,𝔽25)—31no—
217#897—31no—
218#896—61no—
219#895C2×D311yescharacteristic
220#893C2×D311yescharacteristic
221#887—31no—
222#885—61no—
223#885—61no—
224#884—21no—
225#882—21no—
226#67⋊C4—61no—
227#878—61no—
228#875—31no—
229C4×Dic6—31no—
230C3×#107—31no—
231C3×#102—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—31no—
246#810—31no—
247#810—61no—
248#810—61no—
249#809—31no—
250#809—31no—
251#809C2×D311yescharacteristic, complemented
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
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—42no—
278#634—21no—
279#634—21no—
280#634—21no—
281#634—42no—
282#634C2×D412yescomplemented
283C3×#67—22no—
284C3×#67—42no—
285C3×#67—42no—
286C3×#67—42no—
287C3×#67—81no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D411yescharacteristic
292C3×D12—21no—
293C3×D12—21no—
294C3×D12—21no—
295C3×D12—21no—
296C3×D12—21no—
297C3×D12—42no—
298C3×D12—42no—
299C3×D12C2×D412yes—
300C3×C4×D3—21no—
301C3×C4×D3—21no—
302C3×C4×D3—42no—
303#625—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—91no—
315#466—31no—
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×D4—21no—
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—31no—
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—61no—
344C2×C3×D4—121no—
345C2×C3×D4—121no—
346C2×C3×D4—124no—
347C2×C3×D4C22×D311yescharacteristic
348C2×C3×D4C22×D311yescharacteristic
349C22×C3×C4—21no—
350C22×C3×C4—31no—
351C22×C3×C4—61no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C2×#67—21no—
355C2×#67—21no—
356C2×#67—21no—
357C2×#67—21no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67#6711yescharacteristic
361C22×Dic3—61no—
362C22×Dic3—61no—
363C22×Dic3—61no—
364C22×Dic3—121no—
365#237—62no—
366#237—121no—
367D3×D4—22no—
368D3×D4—41no—
369D3×D4—44no—
370#235—62no—
371#235—121no—
372C2×D12—22no—
373C2×D12—21no—
374C2×D12—21no—
375C2×D12—41no—
376C2×D12C22×D311yescharacteristic
377C2×D12C22×D311yescharacteristic
378C2×D12C22×D311yescharacteristic
379C2×C4×D3—21no—
380C2×C4×D3—61no—
381C2×C4×D3C22×D311yescharacteristic
382C2×Dic6—31no—
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—31no—
386C2×Dic6—61no—
387C2×Dic6—61no—
388C2×Dic6—62no—
389C2×Dic6—62no—
390C2×Dic6—61no—
391C2×Dic6—61no—
392C2×Dic6—122no—
393C2×Dic6—121no—
394C2×Dic6—121no—
395C2×Dic6—121no—
396C2×Dic6—122no—
397C3×D8—62no—
398C2×C3×C8—31no—
399C2×C3×C8—31no—
400C2×C3×C8—62no—
401C3×C4⋊C4—21no—
402C3×C4⋊C4—31no—
403C3×C4⋊C4—31no—
404C3×C4⋊C4C22×D311yescharacteristic
405C3×C4⋊C4C22×D311yescharacteristic
406C3×C22⋊C4—21no—
407C3×C22⋊C4—21no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—31no—
410C3×C22⋊C4—41no—
411C3×C22⋊C4—61no—
412C3×C22⋊C4—61no—
413C3×C22⋊C4—61no—
414C3×C42—31no—
415#217—61no—
416#217—61no—
417#217—61no—
418#217#6711yescharacteristic
419#214—34no—
420#214—62no—
421#214—62no—
422#214—62no—
423#214—62no—
424#214—62no—
425#214—122no—
426#214—121no—
427#214—121no—
428#214—122no—
429#213—22no—
430#213—62no—
431#213—62no—
432#213—121no—
433#213—121no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4#6711yescharacteristic
441C4⋊Dic3—61no—
442C4⋊Dic3C22×D311yescharacteristic
443Dic3⋊C4—61no—
444Dic3⋊C4—61no—
445Dic3⋊C4—61no—
446Dic3⋊C4#6711yescharacteristic
447C4×Dic3—61no—
448C4×Dic3—61no—
449C4×Dic3C22×D311yescharacteristic
450#208—62no—
451C2×C3⋊C8—22no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—31no—
456C2×C3⋊C8—61no—
457C2×C3⋊C8—61no—
458C2×C3⋊C8C22×D311yescharacteristic
459C2×C3⋊C8C22×D311yescharacteristic
460#204—34no—
461#204—62no—
462#204—62no—
463#204—62no—
464ΓL(1,𝔽25)—62no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32AGL(1,ℤ/8)12yescomplemented
471C22×C32C22×D411yescharacteristic
472C2×C3×D3—21no—
473C2×C3×D3—22no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—84no—
485C2×C3×D3—84no—
486C32×C4—21no—
487C32×C4—41no—
488C32×C4C22×D411yescharacteristic
489C32×C4H(5,𝔽2)11yescharacteristic
490C3⋊Dic3—22no—
491C3⋊Dic3—41no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—21no—
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—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—184no—
509C2×D8—31no—
510C2×D8—91no—
511C2×D8—91no—
512C2×M16—91no—
513C22×C8—31no—
514#127—31no—
515#124—91no—
516#124—181no—
517C22⋊Q8—91no—
518C22⋊Q8—181no—
519#121—31no—
520#121—31no—
521#121—61no—
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—91no—
533#103—91no—
534#102—31no—
535#102—31no—
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—61no—
549C23×C3—122no—
550C23×C3—122no—
551C23×C3—122no—
552C23×C3—122no—
553C23×C3—241no—
554C23×C3—241no—
555C23×C3D3×D411yescharacteristic
556C23×C3C2×#6711yescharacteristic
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—21no—
560C22×D3—42no—
561C22×D3—42no—
562C22×D3—42no—
563C22×D3—42no—
564C22×D3—81no—
565C22×D3—81no—
566C22×D3C2×#6711yescharacteristic
567C3×D4—21no—
568C3×D4—21no—
569C3×D4—21no—
570C3×D4—21no—
571C3×D4—32no—
572C3×D4—41no—
573C3×D4—41no—
574C3×D4—42no—
575C3×D4—42no—
576C3×D4—62no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—61no—
581C3×D4—61no—
582C3×D4—82no—
583C3×D4—122no—
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—122no—
607C2×C3×C4D3×D411yescharacteristic
608C2×C3×C4C2×#6711yescharacteristic
609C2×C3×C4C23×D311yescharacteristic
610C2×C3×C4C23×D311yescharacteristic
611#67—22no—
612#67—42no—
613#67—42no—
614#67—42no—
615#67—81no—
616#67—122no—
617#67—122no—
618C2×Dic3—21no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—121no—
624C2×Dic3—121no—
625C2×Dic3—122no—
626C2×Dic3—122no—
627C2×Dic3—122no—
628C2×Dic3—124no—
629C2×Dic3C2×#6711yescharacteristic
630C2×Dic3C2×#6711yescharacteristic
631C2×Dic3C2×#6711yescharacteristic
632D12—21no—
633D12—21no—
634D12—21no—
635D12—21no—
636D12—21no—
637D12—42no—
638D12—42no—
639D12D3×D412yes—
640C4×D3—21no—
641C4×D3—21no—
642C4×D3—42no—
643C4×D3—122no—
644Dic6—32no—
645Dic6—32no—
646Dic6—62no—
647Dic6—61no—
648Dic6—61no—
649Dic6—62no—
650Dic6—61no—
651Dic6—61no—
652Dic6—61no—
653Dic6—61no—
654Dic6—121no—
655Dic6—121no—
656Dic6—122no—
657Dic6—122no—
658Dic6—124no—
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—22no—
670C2×C32—81no—
671C2×C32D4211yescharacteristic
672C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
673C2×C32#57711yescharacteristic
674C3×D3—41no—
675C3×D3—42no—
676C3×D3—81no—
677C3×D3—81no—
678C24—61no—
679C24—61no—
680#41—182no—
681#41—361no—
682C2×Q8—91no—
683C2×Q8—91no—
684C2×Q8—182no—
685C2×Q8—181no—
686C2×Q8—361no—
687C2×D4—21no—
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—31no—
691C2×D4—31no—
692C2×D4—62no—
693C2×D4—61no—
694C2×D4—61no—
695C2×D4—61no—
696C2×D4—61no—
697C2×D4—62no—
698C2×D4—61no—
699C2×D4—61no—
700C2×D4—121no—
701C2×D4—121no—
702C2×D4—124no—
703C2×D4—181no—
704C2×D4C2×D3211yescharacteristic
705C22×C4—31no—
706C22×C4—61no—
707C22×C4—181no—
708C22×C4—181no—
709C22×C4C2×D3211yescharacteristic
710SD16—94no—
711SD16—182no—
712SD16—182no—
713SD16—182no—
714SD16—182no—
715SD16—361no—
716D8—62no—
717D8—182no—
718D8—361no—
719M16—182no—
720C2×C8—31no—
721C2×C8—31no—
722C2×C8—62no—
723C2×C8—91no—
724C2×C8—91no—
725C4⋊C4—31no—
726C4⋊C4—31no—
727C4⋊C4—181no—
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—22no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—61no—
756C22×C3—61no—
757C22×C3—61no—
758C22×C3—62no—
759C22×C3—81no—
760C22×C3—81no—
761C22×C3—81no—
762C22×C3—121no—
763C22×C3—121no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3—121no—
770C22×C3—244no—
771C22×C3—244no—
772C22×C3#91112yescomplemented
773C22×C3#93212yescomplemented
774C22×C3C2×D3×D411yescharacteristic
775C22×C3C22×#6711yescharacteristic
776C2×D3—21no—
777C2×D3—21no—
778C2×D3—22no—
779C2×D3—21no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C2×D3—84no—
789C2×D3—84no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—41no—
795C3×C4—41no—
796C3×C4—41no—
797C3×C4—61no—
798C3×C4—61no—
799C3×C4—61no—
800C3×C4—81no—
801C3×C4—121no—
802C3×C4C2×D3×D411yescharacteristic
803C3×C4C2×D3×D411yescharacteristic
804C3×C4#100411yescharacteristic
805C3×C4#100911yescharacteristic
806Dic3—21no—
807Dic3—21no—
808Dic3—21no—
809Dic3—41no—
810Dic3—62no—
811Dic3—62no—
812Dic3—122no—
813Dic3—122no—
814Dic3—121no—
815Dic3—121no—
816C32#326511yescharacteristic, complemented, Sylow
817C23—21no—
818C23—31no—
819C23—61no—
820C23—61no—
821C23—61no—
822C23—122no—
823C23—122no—
824C23—122no—
825C23—122no—
826C23—241no—
827C23—241no—
828C23D3×#6711yescharacteristic
829Q8—92no—
830Q8—181no—
831Q8—181no—
832Q8—181no—
833Q8—362no—
834D4—21no—
835D4—21no—
836D4—32no—
837D4—42no—
838D4—62no—
839D4—61no—
840D4—61no—
841D4—61no—
842D4—61no—
843D4—61no—
844D4—122no—
845D4—122no—
846D4—122no—
847D4—122no—
848D4—122no—
849D4—241no—
850D4—362no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—31no—
855C2×C4—31no—
856C2×C4—31no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—122no—
861C2×C4—181no—
862C2×C4—181no—
863C2×C4—362no—
864C2×C4—362no—
865C2×C4D3×#6711yescharacteristic
866C2×C4C22×D3211yescharacteristic
867C8—32no—
868C8—61no—
869C8—181no—
870C8—181no—
871C2×C3—22no—
872C2×C3—22no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—42no—
877C2×C3—81no—
878C2×C3—81no—
879C2×C3—121no—
880C2×C3—122no—
881C2×C3—161no—
882C2×C3—241no—
883C2×C3—241no—
884C2×C3#560911yescharacteristic
885C2×C3C2×#91111yescharacteristic
886C2×C3#577011yescharacteristic
887C2×C3C2×#93211yescharacteristic
888C2×C3D4×#6711yescharacteristic
889C2×C3#583611yescharacteristic
890D3—41no—
891D3—42no—
892D3—81no—
893D3—81no—
894C22—21no—
895C22—21no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—61no—
900C22—61no—
901C22—61no—
902C22—62no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—121no—
911C22—244no—
912C22—244no—
913C22#6393212yescomplemented
914C22C2×D3×#6711yescharacteristic
915C4—21no—
916C4—41no—
917C4—61no—
918C4—61no—
919C4—61no—
920C4—121no—
921C4—182no—
922C4—361no—
923C4D32×D411yescharacteristic
924C4#6431411yescharacteristic
925C3—21no—
926C3#8072711yescharacteristic, complemented
927C3#8349111yescharacteristic, complemented
928C2—22no—
929C2—81no—
930C2—121no—
931C2—122no—
932C2—241no—
933C2—241no—
934C2C2×#6393211yescharacteristic
935C2#1059529111yescharacteristic
936C2#1059546611yescharacteristic
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×#63932C2semidirect
3. #10594918C2semidirect
4. C22×#3716C2semidirect
5. #10592739C2semidirect
6. C3×#5038C2semidirect
7. #10591469C2semidirect
8. #10591459C2semidirect
9. #10591439C2semidirect
10. #10591160C2semidirect
11. #10591155C2semidirect
12. #10590613C2semidirect
13. #10590590C2semidirect
14. #10590588C2semidirect
15. #10590530C2semidirect
18. C22×#634C22semidirect
22. C2×#3795C22semidirect
24. C2×#3754C22semidirect
25. C2×#3754C22semidirect
28. C2×C3×#213C22semidirect
29. C3×#930C22semidirect
31. C22×C3×C3⋊C8C22semidirect
41. #63860C22semidirect
42. #63857C22semidirect
43. #63844C22semidirect
47. C2×#3716C22semidirect
48. C2×#3716C22semidirect
50. C2×#3713C22semidirect
51. C2×#3711C22semidirect
52. #63657C22semidirect
53. #63637C22semidirect
54. #63637C22semidirect
55. C3×#832C22semidirect
56. C3×#809C22semidirect
57. C3×#807C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
68. #5609D3semidirect
82. #5038D3semidirect
153. #3716D4semidirect
204. C2×#213C2×D3semidirect
205. #930C2×D3semidirect
209. C22×C3⋊C8C2×D3semidirect
235. #832C2×D3semidirect
251. #809C2×D3semidirect
252. #807C2×D3semidirect
282. #634C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
470. C22×C32AGL(1,ℤ/8)semidirect
668. C3⋊C8D3×D4semidirect
772. C22×C3#911semidirect
773. C22×C3#932semidirect
816. C32#3265semidirect
913. C22#63932semidirect
926. C3#80727semidirect
927. 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×#639322
#105949182
C22×#37162
#105927392
C3×#50382
#105914692
#105914592
#105914392
#105911602
#105911552
#105906132
#105905902
#105905882
#105905302
#834913
#807273