Finite Group Databasebeta

← #11864221

Subgroups — #11864221

Order 1152.

1589 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic
2C2×C3×#897C211yesmaximal, characteristic, complemented
3C2×#63833C211yesmaximal, characteristic, complemented
4C2×#63827C211yesmaximal, characteristic, complemented
5#10592665C211yesmaximal, characteristic, complemented
6C3×#4966C211yesmaximal, characteristic, complemented
7#10591069C211yesmaximal, characteristic, complemented
8#10590616C212yesmaximal, complemented
9#10590614C212yesmaximal, complemented
10#10590604C212yesmaximal, complemented
11#10590596C212yesmaximal, complemented
12#82735—31nomaximal
13#78885—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×C3×Dic6C2211yescharacteristic, complemented
18C2×D3×#67—21no—
19C2×#3804—21no—
20D3×#235—24no—
21D3×#235—24no—
22C2×D3×D12C2211yescharacteristic
23C2×C4×D32—21no—
24C2×#3799C2211yescharacteristic
25C2×#3798—21no—
26C2×#3795C2211yescharacteristic
27C2×D3×Dic6C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic, complemented
29C2×#3748C2211yescharacteristic, complemented
30C2×C3×(C2×D3)⋊C4—21no—
31C2×C3×C4⋊Dic3—21no—
32C2×C3×#208C2211yescharacteristic, complemented
33C3×#897—21no—
34C3×#897—21no—
35C3×#897C2212yes—
36C3×#897C2212yescomplemented
37C2×#3719C2212yescomplemented
38C2×#3718C2212yescomplemented
39#63833—24no—
40C2×#3717C2212yescomplemented
41#63827—24no—
42C2×#3715C2212yescomplemented
43#63637C2212yescomplemented
44#63636C2212yescomplemented
45C3×#810C2212yescomplemented
46C3×#809C2212yescomplemented
47(C2×D3)⋊(C3⋊C8)C2212yes—
48(C2×D3)⋊(C3⋊C8)C2212yescomplemented
49C2×D3×#41—31no—
50C22×#235—31no—
51C2×C3×C22⋊Q8—31no—
52C2×#951—31no—
53C2×#942—31no—
54C2×#942—31no—
55C2×#909—31no—
56C2×#897D311yescharacteristic, complemented
57C3×#417—31no—
58#5207—31no—
59#5126—31no—
60#5050—32no—
61#5047—32no—
62#5047—32no—
63#5046—32no—
64#4966—31no—
65#4966—31no—
66#4966—61no—
67#4966D311yescharacteristic, complemented
68#4809—32no—
69#4808—32no—
70#4783—32no—
71#4776—32no—
72C23×C3×D3D411yescharacteristic
73C22×D32—21no—
74C22×C32×C4—21no—
75C22×C32×C4C2311yescharacteristic
76C2×#638—21no—
77#3828—22no—
78#3828D414yes—
79C2×C4⋊(C3⋊D3)C2311yescharacteristic
80C2×C4×C3⋊D3—21no—
81C2×#634C2311yescharacteristic
82C2×C3×#67—21no—
83C22×C3×Dic3—21no—
84C22×C3×Dic3D411yescharacteristic
85C3×#235—22no—
86C3×#235D414yes—
87C2×C3×D12C2311yescharacteristic
88C2×C3×C4×D3—21no—
89C2×C3×C4×D3—22no—
90C2×C3×C4×D3—22no—
91C2×C3×C4×D3D411yescharacteristic
92C2×C3×C4×D3D411yescharacteristic
93C2×C3×C4×D3C2311yescharacteristic
94C2×C3×C4×D3C2311yescharacteristic
95C2×C3×Dic6—22no—
96C2×C3×Dic6—22no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6C2312yes—
99C2×C3×Dic6C2311yescharacteristic
100D3×#67—28no—
101C2×#627—21no—
102C2×#626—21no—
103C2×#626—21no—
104C2×#625—21no—
105C2×#624—21no—
106#3804—28no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109D3×D12—22no—
110D3×D12—22no—
111C4×D32—28no—
112#3799—22no—
113#3799—22no—
114#3798—28no—
115#3795—22no—
116#3795—22no—
117D3×Dic6—22no—
118D3×Dic6—22no—
119C32×C4⋊C4—21no—
120C32×C4⋊C4C2312yes—
121#3748—22no—
122C2×C3⋊(C3⋊C8)C2312yes—
123C3×(C2×D3)⋊C4—22no—
124C3×(C2×D3)⋊C4—22no—
125C3×C4⋊Dic3—22no—
126C3×C4⋊Dic3—22no—
127C3×#208—22no—
128C2×C3×C3⋊C8C2312yes—
129#3719—24no—
130#3718—24no—
131#3717—24no—
132#3715—24no—
133#3007—91noSylow
134C2×C3×#41—31no—
135C22×C3×Q8—31no—
136C23×C3×C4—31no—
137C22×#67—61no—
138D3×#41—64no—
139D3×#41—64no—
140C2×#239—31no—
141C2×D3×Q8—31no—
142C2×#237—31no—
143C2×#237—61no—
144C2×D3×D4—31no—
145C2×D3×D4—61no—
146C2×#235—31no—
147C2×#235—31no—
148C2×#235—31no—
149C2×#235—31no—
150C2×#235—61no—
151C2×#235—61no—
152C2×#235—64no—
153C2×#235—61no—
154C2×#235—64no—
155C2×#235—61no—
156C2×#235C2×D311yescharacteristic
157C22×D12—31no—
158C22×C4×D3—61no—
159C22×C4×D3—61no—
160C22×C4×D3C2×D311yescharacteristic
161C22×Dic6—31no—
162C22×Dic6C2×D311yescharacteristic, complemented
163C2×C3×M16—31no—
164C3×C22⋊Q8—32no—
165C3×C22⋊Q8—32no—
166C3×C22⋊Q8—61no—
167C3×C22⋊Q8—61no—
168C2×C3×C4⋊C4—21no—
169C2×C3×C4⋊C4—61no—
170C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
171C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
172C2×C3×C22⋊C4—61no—
173#951—64no—
174C2×#216—32no—
175C2×#216—32no—
176C2×#216—32no—
177#942—64no—
178#942—64no—
179C2×#215—32no—
180C2×#215—32no—
181C2×#214—32no—
182C2×(C2×D3)⋊C4—21no—
183C2×C4⋊Dic3—21no—
184C2×#208—31no—
185C2×#208—31no—
186C2×#208—61no—
187C2×#208C2×D311yescharacteristic, complemented
188#909—64no—
189C2×Dic12—32no—
190C2×#204—32no—
191#897—21no—
192#897—21no—
193#897C2×D312yes—
194#897C2×D312yescomplemented
195C3×#103—32no—
196C3×#102—32no—
197#830—32no—
198#830—32no—
199(C2×D3)⋊C8—32no—
200(C2×D3)⋊C8—32no—
201#810—32no—
202#810—32no—
203#810—62no—
204#810C2×D312yescomplemented
205#809—32no—
206#809—32no—
207#809—62no—
208#809C2×D312yescomplemented
209C23×C32C2×D411yescharacteristic
210C22×C3⋊D3—21no—
211C22×C3×D3—22no—
212C22×C3×D3—21no—
213C22×C3×D3—22no—
214C22×C3×D3—41no—
215C22×C3×D3C2×D411yescharacteristic
216C22×C3×D3C2×D411yescharacteristic
217C2×D32—24no—
218C2×D32—42no—
219C2×D32—42no—
220C2×C32×C4—22no—
221C2×C32×C4—42no—
222C2×C32×C4C2×D412yes—
223C2×C32×C4C2×D412yes—
224C2×C32×C4C2×D411yescharacteristic
225C2×C32×C4C2411yescharacteristic
226#638—24no—
227C2×C3⋊Dic3—21no—
228C4⋊(C3⋊D3)—21no—
229C4⋊(C3⋊D3)C2×D412yes—
230C4×C3⋊D3—24no—
231#634—21no—
232#634C2×D412yes—
233C3×#67—24no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—42no—
238C2×C3×Dic3C2×D411yescharacteristic
239C2×C3×Dic3C2×D411yescharacteristic
240C3×D12—21no—
241C3×D12C2×D412yes—
242C3×C4×D3—22no—
243C3×C4×D3—24no—
244C3×C4×D3—22no—
245C3×C4×D3—21no—
246C3×C4×D3—21no—
247C3×C4×D3—21no—
248C3×C4×D3—21no—
249C3×Dic6—21no—
250C3×Dic6—22no—
251C3×Dic6—22no—
252C3×Dic6—42no—
253C3×Dic6C2×D412yes—
254#627—24no—
255#626—24no—
256#626—24no—
257#625—24no—
258#624—24no—
259D3×Dic3—24no—
260D3×Dic3—24no—
261C3⋊(C3⋊C8)—22no—
262C3×C3⋊C8—22no—
263C22×#41—91no—
264C2×#137—91no—
265C2×#137—91no—
266C2×C22⋊Q8—31no—
267#452—92no—
268#452—92no—
269#451—92no—
270#450—92no—
271#417—31no—
272#417—91no—
273#407—91no—
274C24×C3—31no—
275C23×D3—61no—
276C23×D3—61no—
277C23×D3#6711yescharacteristic
278C3×#41—34no—
279C3×#41—62no—
280C2×C3×Q8—31no—
281C2×C3×Q8—32no—
282C2×C3×Q8—61no—
283C2×C3×Q8—62no—
284C2×C3×Q8—62no—
285C2×C3×D4—31no—
286C2×C3×D4—61no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—41no—
296C22×C3×C4—62no—
297C22×C3×C4—62no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C2×#67—21no—
303C2×#67—61no—
304C2×#67—68no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—121no—
311C22×Dic3—21no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3#6711yescharacteristic
315#239—62no—
316#239—62no—
317D3×Q8—62no—
318D3×Q8—62no—
319#237—62no—
320#237—62no—
321#237—68no—
322D3×D4—62no—
323D3×D4—62no—
324D3×D4—68no—
325#235—22no—
326#235—34no—
327#235—34no—
328#235—64no—
329#235—62no—
330#235—62no—
331#235—68no—
332#235—68no—
333#235—68no—
334#235—62no—
335#235—62no—
336#235—62no—
337#235—62no—
338#235—122no—
339#235D1214yes—
340C2×D12—31no—
341C2×D12—31no—
342C2×D12—61no—
343C2×D12—62no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—62no—
347C2×D12C22×D311yescharacteristic
348C2×C4×D3—21no—
349C2×C4×D3—22no—
350C2×C4×D3—22no—
351C2×C4×D3—68no—
352C2×C4×D3—68no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—61no—
357C2×C4×D3—61no—
358C2×C4×D3—61no—
359C2×C4×D3—121no—
360C2×C4×D3#6711yescharacteristic
361C2×C4×D3#6711yescharacteristic
362C2×C4×D3C22×D311yescharacteristic
363C2×C4×D3C22×D311yescharacteristic
364C2×Dic6—22no—
365C2×Dic6—22no—
366C2×Dic6—21no—
367C2×Dic6—31no—
368C2×Dic6—31no—
369C2×Dic6—61no—
370C2×Dic6—62no—
371C2×Dic6—61no—
372C2×Dic6—61no—
373C2×Dic6—62no—
374C2×Dic6C22×D312yes—
375C2×Dic6C22×D311yescharacteristic
376C3×M16—62no—
377C2×C3×C8—32no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—22no—
381C3×C4⋊C4—41no—
382C3×C4⋊C4—62no—
383C3×C4⋊C4—62no—
384C3×C4⋊C4C22×D312yes—
385C3×C4⋊C4C22×D312yes—
386C3×C22⋊C4—62no—
387C3×C22⋊C4—62no—
388#216—64no—
389#216—64no—
390#216—64no—
391#215—64no—
392#215—64no—
393#214—64no—
394(C2×D3)⋊C4—22no—
395(C2×D3)⋊C4—22no—
396C4⋊Dic3—22no—
397C4⋊Dic3—22no—
398#208—22no—
399#208—62no—
400#208—62no—
401#208—122no—
402C2×C3⋊C8—32no—
403C2×C3⋊C8—32no—
404C2×C3⋊C8—62no—
405C2×C3⋊C8C22×D312yes—
406Dic12—64no—
407#204—64no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32#12012yes—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—22no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—22no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—44no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3#13712yescomplemented
425D32—48no—
426C32×C4—42no—
427C32×C4#12012yes—
428C32×C4C22×D411yescharacteristic
429C32×C4C22×D411yescharacteristic
430C3⋊Dic3—22no—
431C3×Dic3—21no—
432C3×Dic3—22no—
433C3×Dic3—21no—
434C3×Dic3—42no—
435C2×#41—31no—
436C2×#41—91no—
437C2×#41—91no—
438C2×#41—91no—
439C2×#41—181no—
440C2×#41—181no—
441C2×#41—184no—
442C2×#41—184no—
443C22×Q8—31no—
444C22×Q8—91no—
445C22×D4—91no—
446C22×D4—181no—
447C23×C4—31no—
448C23×C4—181no—
449#137—184no—
450#137—184no—
451C2×Q16—92no—
452C2×Q16—92no—
453C2×SD16—92no—
454C2×SD16—92no—
455C2×M16—31no—
456C2×M16—91no—
457C22⋊Q8—32no—
458C22⋊Q8—32no—
459C22⋊Q8—61no—
460C22⋊Q8—61no—
461C2×C4⋊C4—61no—
462C2×C4⋊C4D3211yescharacteristic, complemented
463C2×C22⋊C4—61no—
464#103—32no—
465#103—92no—
466#102—32no—
467#102—92no—
468C22⋊C8—92no—
469C22⋊C8—92no—
470C23×C3—21no—
471C23×C3—31no—
472C23×C3—31no—
473C23×C3—62no—
474C23×C3—62no—
475C23×C3—61no—
476C23×C3—121no—
477C23×C3D3×D411yescharacteristic
478C23×C3C2×#6711yescharacteristic
479C22×D3—22no—
480C22×D3—21no—
481C22×D3—22no—
482C22×D3—41no—
483C22×D3—64no—
484C22×D3—64no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—121no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3C2×#6711yescharacteristic
493C22×D3C2×#6711yescharacteristic
494C3×Q8—32no—
495C3×Q8—61no—
496C3×Q8—62no—
497C3×Q8—62no—
498C3×Q8—122no—
499C3×D4—32no—
500C3×D4—64no—
501C3×D4—61no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—21no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—42no—
511C2×C3×C4—42no—
512C2×C3×C4—42no—
513C2×C3×C4—62no—
514C2×C3×C4—61no—
515C2×C3×C4—62no—
516C2×C3×C4—62no—
517C2×C3×C4—64no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—62no—
523C2×C3×C4—82no—
524C2×C3×C4—122no—
525C2×C3×C4C2×D1212yes—
526C2×C3×C4D3×D412yes—
527C2×C3×C4D3×D412yes—
528C2×C3×C4D3×D412yes—
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C2×#6711yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533#67—24no—
534#67—64no—
535#67—64no—
536#67—64no—
537#67—64no—
538#67—64no—
539#67—64no—
540#67—124no—
541C2×Dic3—22no—
542C2×Dic3—21no—
543C2×Dic3—22no—
544C2×Dic3—42no—
545C2×Dic3—64no—
546C2×Dic3—64no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—121no—
550C2×Dic3C2×#6711yescharacteristic
551C2×Dic3C2×#6711yescharacteristic
552D12—21no—
553D12—32no—
554D12—32no—
555D12—62no—
556D12—64no—
557D12—64no—
558D12—61no—
559D12—61no—
560D12—121no—
561D12C2×D1212yes—
562C4×D3—24no—
563C4×D3—22no—
564C4×D3—22no—
565C4×D3—21no—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—64no—
570C4×D3—64no—
571C4×D3—64no—
572C4×D3—64no—
573C4×D3—64no—
574C4×D3—64no—
575C4×D3—124no—
576Dic6—21no—
577Dic6—22no—
578Dic6—22no—
579Dic6—32no—
580Dic6—32no—
581Dic6—42no—
582Dic6—62no—
583Dic6—64no—
584Dic6—64no—
585Dic6—61no—
586Dic6—61no—
587Dic6—121no—
588Dic6C2×D1212yes—
589C3×C8—62no—
590C3⋊C8—22no—
591C3⋊C8—62no—
592C3⋊C8—62no—
593C3⋊C8—122no—
594C2×C32—22no—
595C2×C32C2×#12011yescharacteristic
596C2×C32C2×#13711yescharacteristic
597C2×C32#57511yescharacteristic
598C3⋊D3—42no—
599C3×D3—22no—
600C3×D3—42no—
601C3×D3—41no—
602C24—31no—
603C24—181no—
604#41—34no—
605#41—62no—
606#41—94no—
607#41—188no—
608#41—182no—
609#41—182no—
610#41—188no—
611#41—182no—
612#41—182no—
613#41—182no—
614C2×Q8—31no—
615C2×Q8—32no—
616C2×Q8—61no—
617C2×Q8—62no—
618C2×Q8—62no—
619C2×Q8—91no—
620C2×Q8—181no—
621C2×Q8—182no—
622C2×Q8—182no—
623C2×D4—31no—
624C2×D4—61no—
625C2×D4—91no—
626C2×D4—181no—
627C2×D4—182no—
628C2×D4—182no—
629C2×D4—181no—
630C2×D4—188no—
631C2×D4—181no—
632C2×D4—181no—
633C22×C4—21no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—62no—
640C22×C4—62no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—181no—
644C22×C4—181no—
645C22×C4—188no—
646C22×C4—181no—
647C22×C4—181no—
648C22×C4C2×D3211yescharacteristic
649Q16—184no—
650Q16—184no—
651SD16—184no—
652SD16—184no—
653M16—62no—
654M16—182no—
655C2×C8—32no—
656C2×C8—92no—
657C4⋊C4—21no—
658C4⋊C4—62no—
659C4⋊C4—62no—
660C4⋊C4C2×D3212yes—
661C22⋊C4—62no—
662C22⋊C4—62no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—22no—
669C22×C3—32no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—61no—
676C22×C3—61no—
677C22×C3—62no—
678C22×C3—124no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3#88212yes—
682C22×C3#93712yes—
683C22×C3C2×D3×D411yescharacteristic
684C22×C3C22×#6711yescharacteristic
685C2×D3—21no—
686C2×D3—21no—
687C2×D3—22no—
688C2×D3—21no—
689C2×D3—21no—
690C2×D3—21no—
691C2×D3—44no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—62no—
695C2×D3—62no—
696C2×D3—122no—
697C2×D3—128no—
698C2×D3—128no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—241no—
704C2×D3—241no—
705C2×D3#94212yescomplemented
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—22no—
709C3×C4—42no—
710C3×C4—42no—
711C3×C4—61no—
712C3×C4—61no—
713C3×C4—62no—
714C3×C4—82no—
715C3×C4—122no—
716C3×C4#88212yes—
717C3×C4#93712yes—
718C3×C4C22×D1211yescharacteristic
719C3×C4C2×D3×D411yescharacteristic
720C3×C4C2×D3×D411yescharacteristic
721C3×C4C2×D3×D411yescharacteristic
722Dic3—22no—
723Dic3—21no—
724Dic3—21no—
725Dic3—42no—
726Dic3—62no—
727Dic3—62no—
728Dic3—122no—
729C32#300711yescharacteristic, complemented, Sylow
730C23—31no—
731C23—31no—
732C23—62no—
733C23—61no—
734C23—62no—
735C23—121no—
736C23—184no—
737C23—181no—
738C23—362no—
739C23—362no—
740C23D3×#6711yescharacteristic
741Q8—32no—
742Q8—61no—
743Q8—62no—
744Q8—62no—
745Q8—92no—
746Q8—122no—
747Q8—184no—
748Q8—181no—
749D4—32no—
750D4—64no—
751D4—61no—
752D4—92no—
753D4—184no—
754D4—184no—
755D4—184no—
756D4—184no—
757D4—181no—
758C2×C4—22no—
759C2×C4—31no—
760C2×C4—31no—
761C2×C4—42no—
762C2×C4—61no—
763C2×C4—62no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—64no—
771C2×C4—62no—
772C2×C4—122no—
773C2×C4—184no—
774C2×C4—184no—
775C2×C4—184no—
776C2×C4—181no—
777C2×C4—184no—
778C2×C4D3×D1212yes—
779C2×C4#380212yes—
780C2×C4D3×#6711yescharacteristic
781C2×C4C22×D3211yescharacteristic
782C8—62no—
783C8—182no—
784C2×C3—22no—
785C2×C3—22no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—42no—
790C2×C3—62no—
791C2×C3—121no—
792C2×C3—122no—
793C2×C3C2×#88211yescharacteristic
794C2×C3#577311yescharacteristic
795C2×C3D3×#13711yescharacteristic
796C2×C3C2×#93711yescharacteristic
797C2×C3C2×#94211yescharacteristic
798C2×C3#582211yescharacteristic
799D3—22no—
800D3—42no—
801D3—41no—
802D3—122no—
803D3—122no—
804D3—242no—
805C22—21no—
806C22—21no—
807C22—32no—
808C22—61no—
809C22—61no—
810C22—61no—
811C22—61no—
812C22—62no—
813C22—61no—
814C22—124no—
815C22—121no—
816C22—121no—
817C22—182no—
818C22—368no—
819C22—361no—
820C22—361no—
821C22#6392212yes—
822C22C2×D3×#6711yescharacteristic
823C4—42no—
824C4—61no—
825C4—61no—
826C4—62no—
827C4—122no—
828C4—182no—
829C4#6392212yes—
830C4C2×D3×D1211yescharacteristic
831C4C2×#380211yescharacteristic
832C3—21no—
833C3#7888511yescharacteristic, complemented
834C3#8273511yescharacteristic, complemented
835C2—22no—
836C2—62no—
837C2—121no—
838C2—122no—
839C2—362no—
840C2C2×#6392211yescharacteristic
841C2#1059509511yescharacteristic
842C2D3×#94211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×D3×#235C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3007
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#897C2semidirect
3. C2×#63833C2semidirect
4. C2×#63827C2semidirect
5. #10592665C2semidirect
6. C3×#4966C2semidirect
7. #10591069C2semidirect
8. #10590616C2semidirect
9. #10590614C2semidirect
10. #10590604C2semidirect
11. #10590596C2semidirect
17. C22×C3×Dic6C22semidirect
28. C2×C32×C4⋊C4C22semidirect
29. C2×#3748C22semidirect
32. C2×C3×#208C22semidirect
36. C3×#897C22semidirect
37. C2×#3719C22semidirect
38. C2×#3718C22semidirect
40. C2×#3717C22semidirect
42. C2×#3715C22semidirect
43. #63637C22semidirect
44. #63636C22semidirect
45. C3×#810C22semidirect
46. C3×#809C22semidirect
48. (C2×D3)⋊(C3⋊C8)C22semidirect
56. C2×#897D3semidirect
67. #4966D3semidirect
162. C22×Dic6C2×D3semidirect
170. C2×C3×C4⋊C4C2×D3semidirect
171. C2×C3×C4⋊C4C2×D3semidirect
187. C2×#208C2×D3semidirect
194. #897C2×D3semidirect
204. #810C2×D3semidirect
208. #809C2×D3semidirect
424. C2×C3×D3#137semidirect
462. C2×C4⋊C4D32semidirect
705. C2×D3#942semidirect
729. C32#3007semidirect
833. C3#78885semidirect
834. C3#82735semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C2×C3×#8972
C2×#638332
C2×#638272
#105926652
C3×#49662
#105910692
#105906162
#105906142
#105906042
#105905962
#827353
#788853