Finite Group Databasebeta

← #11883965

Subgroups — #11883965

Order 1152.

1241 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64141C211yesmaximal, characteristic, complemented
2C3×D4×#67C211yesmaximal, characteristic, complemented
3C2×D3×#214C211yesmaximal, characteristic, complemented
4#10594916C211yesmaximal, characteristic, complemented
5C3×#5218C211yesmaximal, characteristic, complemented
6#10591517C211yesmaximal, characteristic, complemented
7#10591472C211yesmaximal, characteristic, complemented
8#10591471C211yesmaximal, characteristic, complemented
9#10591449C211yesmaximal, characteristic, complemented
10#10591448C211yesmaximal, characteristic, complemented
11#10591439C211yesmaximal, characteristic, complemented
12#10591405C211yesmaximal, characteristic, complemented
13#10591182C211yesmaximal, characteristic, complemented
14#10591180C211yesmaximal, characteristic, complemented
15#10591151C211yesmaximal, characteristic, complemented
16#83491—31nomaximal
17#80156—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C2×#3828C2211yescharacteristic, complemented
20C22×C3×#67—21no—
21C2×C3×D3×D4C2211yescharacteristic
22C2×D3×Dic6C2211yescharacteristic, complemented
23C2×#3754C2211yescharacteristic
24C2×#3754C2211yescharacteristic, complemented
25#64141—24no—
26C2×#3753C2211yescharacteristic
27C2×#3753C2211yescharacteristic, complemented
28C2×#3748C2211yescharacteristic, complemented
29C3×#953—21no—
30C3×#940C2211yescharacteristic
31C3×#939—21no—
32C3×#938C2211yescharacteristic
33C3×#937—21no—
34C3×D4×Dic3C2211yescharacteristic
35C2×C3×#214C2211yescharacteristic
36C2×C3×#214C2211yescharacteristic, complemented
37C3×#930C2211yescharacteristic
38C3×C4×#67C2211yescharacteristic
39C3×#924C2211yescharacteristic, complemented
40#63971—21no—
41#63953—21no—
42D3×#214—24no—
43#63909C2211yescharacteristic, complemented
44#63881—21no—
45#63865—21no—
46#63864C2211yescharacteristic, complemented
47#63844C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic
53C3×#832C2211yescharacteristic, complemented
54C3×#830C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×D42—31no—
64D4×#67D311yescharacteristic, complemented
65C22×#214—31no—
66C2×#932—31no—
67C2×#932—31no—
68C2×#932—61no—
69C2×D3×SD16—31no—
70#5633—31no—
71#5552—31no—
72C3×#450—31no—
73#5218D311yescharacteristic, complemented
74#5217—31no—
75#5176—31no—
76#5170—31no—
77#5165—31no—
78#5075—31no—
79#5074—31no—
80#5049—31no—
81#5042—31no—
82#5040—31no—
83#5038—31no—
84#5037—31no—
85#5018—31no—
86#5016—31no—
87#5011—31no—
88#4775—31no—
89#4773—31no—
90#4762—31no—
91#4757—31no—
92#4734—31no—
93#4728—31no—
94C24×C32—21no—
95C23×C3×D3—21no—
96C2×C32×D4—22no—
97C2×C32×D4—21no—
98C2×C32×D4—41no—
99C2×C32×D4C2311yescharacteristic
100C2×C32×D4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C2×#638—21no—
103#3828—22no—
104#3828—41no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C2×C3×#67—21no—
113C2×C3×#67—44no—
114C2×C3×#67D411yescharacteristic
115C22×C3×Dic3—21no—
116C3×D3×D4—22no—
117C3×D3×D4—41no—
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×#627—21no—
122C2×#626—21no—
123C2×D3×Dic3—21no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126#3754—22no—
127#3754D414yescomplemented
128#3753—22no—
129#3753—22no—
130#3748—22no—
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C3×#217—21no—
134C3×#217—21no—
135C3×#217—21no—
136C3×#217D411yescharacteristic
137C3×#214—22no—
138C3×#214—41no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×C4⋊Dic3C2311yescharacteristic
142C3×C4⋊Dic3C2311yescharacteristic
143C3×Dic3⋊C4—21no—
144C3×Dic3⋊C4D411yescharacteristic
145C3×C4×Dic3C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148#3724—21no—
149#3722—21no—
150#3722—21no—
151#3722—21no—
152Dic32—21no—
153#3716—22no—
154#3715—22no—
155#3714—41no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C22×C3×D4—21no—
159C22×C3×D4—31no—
160C22×C3×D4—61no—
161C22×C3×D4C2×D311yescharacteristic
162C22×C3×D4C2×D311yescharacteristic
163C22×#67—21no—
164C2×D3×Q8—31no—
165C2×D3×D4C2×D311yescharacteristic
166C2×#235—31no—
167C2×#235—31no—
168C2×#235—61no—
169C22×Dic6—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C3×#127—31no—
173C3×C22⋊Q8—31no—
174C3×#121—31no—
175C3×#121—31no—
176C3×#121—61no—
177C3×#120—61no—
178C3×#120—61no—
179C3×C4×D4—31no—
180C3×C4×D4—31no—
181#953—21no—
182#947—31no—
183C2×#215—31no—
184#940C2×D311yescharacteristic
185#939—21no—
186#939—61no—
187#938C2×D311yescharacteristic
188#937—21no—
189D4×Dic3C2×D311yescharacteristic
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—
199C2×#214C2×D311yescharacteristic
200C2×#214C2×D311yescharacteristic, complemented
201#932—64no—
202#932—64no—
203#932—68no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—31no—
208C2×#213—31no—
209C2×#213—61no—
210C2×#213—61no—
211#930—31no—
212#930C2×D311yescharacteristic
213C4×#67C2×D311yescharacteristic
214#924C2×D311yescharacteristic, complemented
215C2×#208—31no—
216C2×#208—31no—
217C2×#208—61no—
218C22×C3⋊C8—31no—
219D3×SD16—64no—
220C2×D24—31no—
221C2×#204—31no—
222C2×D3×C8—31no—
223#896—61no—
224#896—61no—
225#895—31no—
226#893—61no—
227#887—31no—
228#885—61no—
229#885—61no—
230#884—61no—
231#67⋊C4—61no—
232#875—31no—
233C4×Dic6—31no—
234C3×#102—31no—
235C3×#102—31no—
236C3×C22⋊C8—31no—
237#835—31no—
238#832—31no—
239#832C2×D311yescharacteristic
240#832C2×D311yescharacteristic, complemented
241#830—31no—
242#830C2×D311yescharacteristic, complemented
243#821—31no—
244(C2×D3)⋊C8—31no—
245#816—31no—
246#815—31no—
247Dic3⋊C8—31no—
248#810—31no—
249#810—31no—
250#809—31no—
251#809—31no—
252#807—31no—
253#807—31no—
254C4⋊(C3⋊C8)—31no—
255#803—31no—
256C23×C32—21no—
257C23×C32—21no—
258C23×C32—42no—
259C23×C32—42no—
260C23×C32—81no—
261C23×C32C2×D411yescharacteristic
262C22×C3⋊D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—42no—
265C22×C3×D3—42no—
266C22×C3×D3—81no—
267C22×C3×D3C2×D411yescharacteristic
268C32×D4—21no—
269C32×D4—21no—
270C32×D4—21no—
271C32×D4—42no—
272C32×D4C2×D412yes—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4C2×D411yescharacteristic
276C2×C32×C4C2411yescharacteristic
277#638—42no—
278C2×C3⋊Dic3—21no—
279C4⋊(C3⋊D3)—21no—
280C4⋊(C3⋊D3)—21no—
281C4×C3⋊D3—42no—
282#634—21no—
283#634C2×D412yescomplemented
284C3×#67—22no—
285C3×#67—42no—
286C3×#67—42no—
287C3×#67—42no—
288C3×#67—42no—
289C3×#67—81no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—42no—
294C2×C3×Dic3C2×D411yescharacteristic
295C2×C3×Dic3C2×D411yescharacteristic
296C2×C3×Dic3C2×D411yescharacteristic
297C3×D12—21no—
298C3×D12—21no—
299C3×C4×D3—21no—
300C3×C4×D3—21no—
301C3×Dic6—21no—
302C3×Dic6—21no—
303#627—42no—
304#626—42no—
305D3×Dic3—42no—
306C3⋊(C3⋊C8)—21no—
307C3⋊(C3⋊C8)C2×D412yescomplemented
308C3×C3⋊C8—21no—
309C3×C3⋊C8—21no—
310C2×AGL(1,ℤ/8)—91no—
311C22×SD16—91no—
312#548—91no—
313D42—31no—
314#496—91no—
315#468—91no—
316#466—91no—
317#463—91no—
318#460—91no—
319#450—31no—
320#449—91no—
321#448—91no—
322#447—91no—
323#440—91no—
324#435—91no—
325C24×C3—21no—
326C24×C3—21no—
327C24×C3—41no—
328C24×C3—61no—
329C23×D3—21no—
330C2×C3×Q8—31no—
331C2×C3×D4—24no—
332C2×C3×D4—22no—
333C2×C3×D4—22no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4—21no—
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—41no—
341C2×C3×D4—41no—
342C2×C3×D4—41no—
343C2×C3×D4—42no—
344C2×C3×D4—61no—
345C2×C3×D4—61no—
346C2×C3×D4—61no—
347C2×C3×D4—62no—
348C2×C3×D4—61no—
349C2×C3×D4—61no—
350C2×C3×D4—121no—
351C2×C3×D4—124no—
352C2×C3×D4C22×D311yescharacteristic
353C2×C3×D4C22×D311yescharacteristic
354C2×C3×D4C22×D311yescharacteristic
355C2×C3×D4C22×D311yescharacteristic
356C22×C3×C4—21no—
357C22×C3×C4—31no—
358C22×C3×C4—61no—
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C2×#67—21no—
362C2×#67—21no—
363C2×#67—21no—
364C2×#67—21no—
365C2×#67—21no—
366C2×#67—44no—
367C2×#67—61no—
368C2×#67—61no—
369C2×#67—61no—
370C2×#67—121no—
371C2×#67#6711yescharacteristic
372C22×Dic3—21no—
373C22×Dic3—61no—
374D3×Q8—62no—
375D3×Q8—121no—
376D3×D4—22no—
377D3×D4—41no—
378#235—62no—
379#235—62no—
380#235—64no—
381#235—121no—
382#235—121no—
383#235—122no—
384C2×D12—31no—
385C2×D12—31no—
386C2×D12—61no—
387C2×D12—61no—
388C2×D12C22×D311yescharacteristic
389C2×C4×D3—61no—
390C2×C4×D3—61no—
391C2×C4×D3—61no—
392C2×C4×D3—121no—
393C2×C4×D3C22×D311yescharacteristic
394C2×Dic6—31no—
395C2×Dic6—31no—
396C2×Dic6—61no—
397C2×Dic6—62no—
398C2×Dic6—61no—
399C2×Dic6—61no—
400C2×Dic6—121no—
401C2×Dic6C22×D311yescharacteristic
402C3×SD16—62no—
403C3×SD16—121no—
404C2×C3×C8—31no—
405C2×C3×C8—31no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—31no—
408C3×C4⋊C4—31no—
409C3×C4⋊C4—61no—
410C3×C22⋊C4—31no—
411C3×C22⋊C4—31no—
412C3×C22⋊C4—61no—
413C3×C22⋊C4—61no—
414C3×C22⋊C4—61no—
415C3×C22⋊C4—61no—
416C3×C42—31no—
417#217—21no—
418#217—21no—
419#217—21no—
420#217#6711yescharacteristic
421#215—62no—
422#214—22no—
423#214—34no—
424#214—34no—
425#214—41no—
426#214—64no—
427#214—62no—
428#214—62no—
429#214—62no—
430#214—62no—
431#214—64no—
432#213—62no—
433#213—62no—
434#213—64no—
435#213—64no—
436#213—62no—
437#213—62no—
438#213—121no—
439(C2×D3)⋊C4—21no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4—61no—
442(C2×D3)⋊C4—61no—
443(C2×D3)⋊C4—61no—
444(C2×D3)⋊C4—61no—
445(C2×D3)⋊C4—61no—
446(C2×D3)⋊C4#6711yescharacteristic
447C4⋊Dic3C22×D311yescharacteristic
448C4⋊Dic3C22×D311yescharacteristic
449Dic3⋊C4—21no—
450Dic3⋊C4—61no—
451Dic3⋊C4—61no—
452Dic3⋊C4#6711yescharacteristic
453C4×Dic3—61no—
454C4×Dic3—61no—
455C4×Dic3C22×D311yescharacteristic
456#208—62no—
457#208—62no—
458#208—64no—
459C2×C3⋊C8—31no—
460C2×C3⋊C8—31no—
461C2×C3⋊C8—31no—
462C2×C3⋊C8—31no—
463C2×C3⋊C8—61no—
464C2×C3⋊C8—61no—
465C2×C3⋊C8—62no—
466C2×C3⋊C8C22×D311yescharacteristic
467C2×C3⋊C8C22×D311yescharacteristic
468D24—121no—
469#204—62no—
470D3×C8—62no—
471C22×C32—21no—
472C22×C32—22no—
473C22×C32—21no—
474C22×C32—21no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32—41no—
480C22×C32—84no—
481C22×C32C22×D411yescharacteristic
482C2×C3⋊D3—41no—
483C2×C3⋊D3—41no—
484C2×C3⋊D3—41no—
485C2×C3×D3—21no—
486C2×C3×D3—21no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—84no—
491C2×C3×D3AGL(1,ℤ/8)12yescomplemented
492C32×C4—21no—
493C32×C4C22×D411yescharacteristic
494C32×C4H(5,𝔽2)11yescharacteristic
495C3⋊Dic3—22no—
496C3×Dic3—21no—
497C3×Dic3—21no—
498C3×Dic3—21no—
499C3×Dic3—41no—
500C3×Dic3—41no—
501C3×Dic3—41no—
502C2×#41—91no—
503C22×Q8—91no—
504C22×D4—31no—
505C22×D4—61no—
506C22×D4D3211yescharacteristic
507AGL(1,ℤ/8)—184no—
508C2×SD16—31no—
509C2×SD16—31no—
510C2×SD16—91no—
511C2×SD16—91no—
512C2×SD16—91no—
513C2×SD16—91no—
514C2×SD16—184no—
515C2×D8—91no—
516C2×D8—91no—
517C2×D8—91no—
518C2×M16—91no—
519C22×C8—91no—
520#127—31no—
521#124—91no—
522#124—181no—
523C22⋊Q8—31no—
524C22⋊Q8—181no—
525#121—31no—
526#121—31no—
527#121—61no—
528#121—91no—
529#121—181no—
530#120—61no—
531#120—61no—
532C4×Q8—91no—
533C4×D4—31no—
534C4×D4—31no—
535C4×D4—181no—
536#107—91no—
537C4⋊C8—91no—
538#103—91no—
539#103—91no—
540#102—31no—
541#102—31no—
542#102—91no—
543#102—91no—
544C22⋊C8—31no—
545C22⋊C8—91no—
546#97—91no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—31no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—42no—
556C23×C3—42no—
557C23×C3—42no—
558C23×C3—44no—
559C23×C3—42no—
560C23×C3—61no—
561C23×C3—82no—
562C23×C3—81no—
563C23×C3—81no—
564C23×C3—82no—
565C23×C3—122no—
566C23×C3—122no—
567C23×C3—241no—
568C23×C3D3×D411yescharacteristic
569C23×C3C2×#6711yescharacteristic
570C22×D3—21no—
571C22×D3—42no—
572C22×D3—42no—
573C22×D3—61no—
574C22×D3—61no—
575C22×D3—81no—
576C22×D3—121no—
577C22×D3C2×#6711yescharacteristic
578C3×Q8—61no—
579C3×Q8—61no—
580C3×D4—22no—
581C3×D4—21no—
582C3×D4—21no—
583C3×D4—21no—
584C3×D4—21no—
585C3×D4—21no—
586C3×D4—21no—
587C3×D4—22no—
588C3×D4—41no—
589C3×D4—41no—
590C3×D4—42no—
591C3×D4—42no—
592C3×D4—44no—
593C3×D4—62no—
594C3×D4—61no—
595C3×D4—61no—
596C3×D4—122no—
597C3×D4—122no—
598C3×D4—122no—
599C3×D4—122no—
600C3×D4—241no—
601C3×D4D3×D412yes—
602C3×D4D3×D412yes—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—31no—
612C2×C3×C4—31no—
613C2×C3×C4—31no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—122no—
620C2×C3×C4D3×D411yescharacteristic
621C2×C3×C4C2×#6711yescharacteristic
622C2×C3×C4C23×D311yescharacteristic
623C2×C3×C4C23×D311yescharacteristic
624#67—22no—
625#67—42no—
626#67—42no—
627#67—42no—
628#67—42no—
629#67—81no—
630#67—122no—
631#67—122no—
632#67—122no—
633#67—124no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—42no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—121no—
641C2×Dic3—122no—
642C2×Dic3C2×#6711yescharacteristic
643C2×Dic3C2×#6711yescharacteristic
644C2×Dic3C2×#6711yescharacteristic
645D12—21no—
646D12—21no—
647D12—62no—
648D12—61no—
649D12—61no—
650D12—61no—
651D12—61no—
652D12—121no—
653D12—122no—
654C4×D3—21no—
655C4×D3—21no—
656C4×D3—122no—
657C4×D3—122no—
658C4×D3—122no—
659C4×D3—124no—
660Dic6—21no—
661Dic6—21no—
662Dic6—32no—
663Dic6—32no—
664Dic6—62no—
665Dic6—61no—
666Dic6—61no—
667Dic6—121no—
668Dic6—122no—
669Dic6—122no—
670C3×C8—61no—
671C3×C8—61no—
672C3⋊C8—21no—
673C3⋊C8—21no—
674C3⋊C8—32no—
675C3⋊C8—32no—
676C3⋊C8—62no—
677C3⋊C8—62no—
678C3⋊C8—61no—
679C3⋊C8—61no—
680C2×C32—41no—
681C2×C32—42no—
682C2×C32—81no—
683C2×C32D4211yescharacteristic
684C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
685C2×C32#57711yescharacteristic
686C3⋊D3—81no—
687C3×D3—22no—
688C3×D3—81no—
689C24—21no—
690C24—61no—
691#41—182no—
692#41—361no—
693C2×Q8—31no—
694C2×Q8—91no—
695C2×Q8—181no—
696C2×Q8—182no—
697C2×Q8—361no—
698C2×D4—22no—
699C2×D4—21no—
700C2×D4—31no—
701C2×D4—31no—
702C2×D4—41no—
703C2×D4—61no—
704C2×D4—61no—
705C2×D4—61no—
706C2×D4—62no—
707C2×D4—61no—
708C2×D4—61no—
709C2×D4—91no—
710C2×D4—121no—
711C2×D4—124no—
712C2×D4—181no—
713C2×D4—181no—
714C2×D4C2×D3211yescharacteristic
715C2×D4C2×D3211yescharacteristic
716C22×C4—31no—
717C22×C4—61no—
718C22×C4—181no—
719C22×C4—181no—
720C22×C4C2×D3211yescharacteristic
721SD16—62no—
722SD16—94no—
723SD16—121no—
724SD16—182no—
725SD16—182no—
726SD16—182no—
727D8—182no—
728D8—182no—
729D8—361no—
730M16—182no—
731C2×C8—31no—
732C2×C8—31no—
733C2×C8—91no—
734C2×C8—91no—
735C2×C8—182no—
736C4⋊C4—31no—
737C4⋊C4—31no—
738C4⋊C4—31no—
739C4⋊C4—61no—
740C4⋊C4—181no—
741C22⋊C4—31no—
742C22⋊C4—31no—
743C22⋊C4—61no—
744C22⋊C4—61no—
745C22⋊C4—61no—
746C22⋊C4—61no—
747C22⋊C4—181no—
748C22⋊C4—181no—
749C22⋊C4—181no—
750C42—31no—
751C42—181no—
752C22×C3—22no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—22no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—22no—
761C22×C3—21no—
762C22×C3—32no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—61no—
778C22×C3—61no—
779C22×C3—81no—
780C22×C3—81no—
781C22×C3—81no—
782C22×C3—81no—
783C22×C3—84no—
784C22×C3—84no—
785C22×C3—88no—
786C22×C3—121no—
787C22×C3—121no—
788C22×C3—121no—
789C22×C3—244no—
790C22×C3C2×D3×D411yescharacteristic
791C22×C3C22×#6711yescharacteristic
792C2×D3—21no—
793C2×D3—21no—
794C2×D3—41no—
795C2×D3—41no—
796C2×D3—41no—
797C2×D3—84no—
798C2×D3—122no—
799C2×D3—121no—
800C2×D3—121no—
801C2×D3—121no—
802C2×D3—121no—
803C2×D3—121no—
804C2×D3—121no—
805C2×D3—241no—
806C2×D3—241no—
807C2×D3#93212yescomplemented
808C3×C4—22no—
809C3×C4—21no—
810C3×C4—21no—
811C3×C4—21no—
812C3×C4—21no—
813C3×C4—61no—
814C3×C4—61no—
815C3×C4—61no—
816C3×C4—121no—
817C3×C4—121no—
818C3×C4—121no—
819C3×C4C2×D3×D411yescharacteristic
820C3×C4C2×D3×D411yescharacteristic
821C3×C4#100411yescharacteristic
822C3×C4#100411yescharacteristic
823Dic3—21no—
824Dic3—21no—
825Dic3—21no—
826Dic3—41no—
827Dic3—41no—
828Dic3—41no—
829Dic3—62no—
830Dic3—62no—
831Dic3—122no—
832C32#326511yescharacteristic, complemented, Sylow
833C23—21no—
834C23—21no—
835C23—31no—
836C23—42no—
837C23—42no—
838C23—61no—
839C23—81no—
840C23—122no—
841C23—122no—
842C23—181no—
843C23—241no—
844C23D3×#6711yescharacteristic
845Q8—61no—
846Q8—61no—
847Q8—92no—
848Q8—181no—
849Q8—362no—
850D4—21no—
851D4—21no—
852D4—21no—
853D4—42no—
854D4—62no—
855D4—61no—
856D4—61no—
857D4—122no—
858D4—122no—
859D4—122no—
860D4—122no—
861D4—181no—
862D4—181no—
863D4—241no—
864D4—362no—
865D4—362no—
866D4#381112yes—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—31no—
870C2×C4—31no—
871C2×C4—31no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—122no—
878C2×C4—181no—
879C2×C4—362no—
880C2×C4—362no—
881C2×C4D3×#6711yescharacteristic
882C2×C4C22×D3211yescharacteristic
883C8—61no—
884C8—61no—
885C8—92no—
886C8—181no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—42no—
891C2×C3—41no—
892C2×C3—42no—
893C2×C3—42no—
894C2×C3—41no—
895C2×C3—62no—
896C2×C3—82no—
897C2×C3—82no—
898C2×C3—81no—
899C2×C3—81no—
900C2×C3—241no—
901C2×C3#559011yescharacteristic
902C2×C3#576211yescharacteristic
903C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
904C2×C3C2×#93211yescharacteristic
905C2×C3D4×#6711yescharacteristic
906C2×C3#583611yescharacteristic
907D3—22no—
908D3—81no—
909D3—242no—
910D3—241no—
911D3—241no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—22no—
916C22—32no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—61no—
923C22—61no—
924C22—84no—
925C22—121no—
926C22—121no—
927C22—121no—
928C22—244no—
929C22—361no—
930C22—361no—
931C22—361no—
932C22C2×D3×#6711yescharacteristic
933C4—21no—
934C4—61no—
935C4—61no—
936C4—61no—
937C4—121no—
938C4—121no—
939C4—121no—
940C4—182no—
941C4C2×#381111yescharacteristic
942C4#6433011yescharacteristic
943C3—21no—
944C3#8015611yescharacteristic, complemented
945C3#8349111yescharacteristic, complemented
946C2—41no—
947C2—42no—
948C2—62no—
949C2—81no—
950C2—241no—
951C2—721no—
952C2D3×#93211yescharacteristic
953C2#1059510511yescharacteristic
954C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64141C2semidirect
2. C3×D4×#67C2semidirect
3. C2×D3×#214C2semidirect
4. #10594916C2semidirect
5. C3×#5218C2semidirect
6. #10591517C2semidirect
7. #10591472C2semidirect
8. #10591471C2semidirect
9. #10591449C2semidirect
10. #10591448C2semidirect
11. #10591439C2semidirect
12. #10591405C2semidirect
13. #10591182C2semidirect
14. #10591180C2semidirect
15. #10591151C2semidirect
19. C2×#3828C22semidirect
22. C2×D3×Dic6C22semidirect
24. C2×#3754C22semidirect
27. C2×#3753C22semidirect
28. C2×#3748C22semidirect
36. C2×C3×#214C22semidirect
39. C3×#924C22semidirect
43. #63909C22semidirect
46. #63864C22semidirect
47. #63844C22semidirect
48. C2×#3716C22semidirect
49. C2×#3715C22semidirect
50. C2×#3714C22semidirect
51. C2×D3×C3⋊C8C22semidirect
53. C3×#832C22semidirect
54. C3×#830C22semidirect
55. #63576C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
59. #63564C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
64. D4×#67D3semidirect
73. #5218D3semidirect
127. #3754D4semidirect
200. C2×#214C2×D3semidirect
214. #924C2×D3semidirect
240. #832C2×D3semidirect
242. #830C2×D3semidirect
283. #634C2×D4semidirect
307. C3⋊(C3⋊C8)C2×D4semidirect
491. C2×C3×D3AGL(1,ℤ/8)semidirect
807. C2×D3#932semidirect
832. C32#3265semidirect
944. C3#80156semidirect
945. C3#83491semidirect

Maximal subgroups

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

subgroupindex
C2×#641412
C3×D4×#672
C2×D3×#2142
#105949162
C3×#52182
#105915172
#105914722
#105914712
#105914492
#105914482
#105914392
#105914052
#105911822
#105911802
#105911512
#834913
#801563