Finite Group Databasebeta

← #11864212

Subgroups — #11864212

Order 1152.

1637 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic
2C2×#64160C211yesmaximal, characteristic, complemented
3C2×#63857C211yesmaximal, characteristic, complemented
4C2×#63831C211yesmaximal, characteristic, complemented
5C3×#5232C211yesmaximal, characteristic, complemented
6#10591599C212yesmaximal, complemented
7#10591595C212yesmaximal, complemented
8#10591463C212yesmaximal, complemented
9#10591459C212yesmaximal, complemented
10#10591087C211yesmaximal, characteristic, complemented
11#10591069C211yesmaximal, characteristic, complemented
12#84084—31nomaximal
13#78885—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C22×#634C2211yescharacteristic, complemented
16C3×D3×#41—24no—
17C3×D3×#41—24no—
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×#237—21no—
21C2×C3×#237C2211yescharacteristic
22C2×C3×D3×D4—21no—
23C2×C3×D3×D4C2211yescharacteristic
24C2×C3×#235—21no—
25C2×C3×#235C2211yescharacteristic
26C22×C3×C4×D3—21no—
27C22×C3×C4×D3C2211yescharacteristic
28#64160—24no—
29C2×#3756C2212yescomplemented
30C2×#3754C2212yescomplemented
31C2×#3748C2211yescharacteristic, complemented
32C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
33C2×C3×#208C2211yescharacteristic, complemented
34C2×Dic3⋊Dic3—21no—
35C2×(C2×D3)⋊Dic3—21no—
36#63857—21no—
37#63857—21no—
38#63857C2212yes—
39#63857C2212yescomplemented
40C2×#3719C2212yescomplemented
41#63831—24no—
42C2×#3716C2212yescomplemented
43C3×#835C2212yescomplemented
44C3×#832C2212yescomplemented
45#63565C2212yescomplemented
46#63562C2212yescomplemented
47(C2×D3)⋊(C3⋊C8)C2212yes—
48(C2×D3)⋊(C3⋊C8)C2212yescomplemented
49C22×C3×#41—31no—
50C2×D3×#41D311yescharacteristic
51C2×#951—31no—
52C2×#951—31no—
53C2×#951—31no—
54C2×#951—61no—
55C2×#924—31no—
56C2×#909—31no—
57C2×#897—31no—
58C3×#417—31no—
59#5239—32no—
60#5239—32no—
61#5232—31no—
62#5232D311yescharacteristic, complemented
63#5228—32no—
64#5218—32no—
65#5207—31no—
66#5126—31no—
67#4966—31no—
68#4809—32no—
69#4808—32no—
70#4783—32no—
71#4776—32no—
72C23×C3×D3—21no—
73C23×C3×D3D411yescharacteristic
74C32×#41—22no—
75C32×#41D414yes—
76C2×C32×Q8C2311yescharacteristic
77C2×C32×D4—21no—
78C2×C32×D4C2311yescharacteristic
79C22×C32×C4—21no—
80C22×C32×C4C2311yescharacteristic
81C22×C3⋊Dic3—21no—
82C2×#634—22no—
83C2×#634—22no—
84C2×#634—21no—
85C2×#634C2312yes—
86C2×C3×#67—21no—
87C2×C3×#67—21no—
88C2×C3×#67—21no—
89C22×C3×Dic3—21no—
90C22×C3×Dic3—21no—
91C22×C3×Dic3D411yescharacteristic
92C3×#239—22no—
93C3×#239—22no—
94C3×D3×Q8—22no—
95C3×D3×Q8—22no—
96C3×#237—28no—
97C3×#237—22no—
98C3×#237—22no—
99C3×D3×D4—28no—
100C3×D3×D4—22no—
101C3×D3×D4—22no—
102C3×#235—28no—
103C3×#235—22no—
104C3×#235D414yes—
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—28no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3D411yescharacteristic
114C2×C3×C4×D3D411yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6—21no—
118C2×C3×Dic6C2311yescharacteristic
119#3756—24no—
120#3754—24no—
121#3748—22no—
122C2×C3⋊(C3⋊C8)C2312yes—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2312yes—
125C3×#208—22no—
126C2×C3×C3⋊C8C2312yes—
127Dic3⋊Dic3—22no—
128Dic3⋊Dic3—22no—
129(C2×D3)⋊Dic3—22no—
130(C2×D3)⋊Dic3—22no—
131#3719—24no—
132#3716—24no—
133#3007—91noSylow
134C2×C3×#41—21no—
135C2×C3×#41—31no—
136C2×C3×#41—31no—
137C2×C3×#41—31no—
138C2×C3×#41—61no—
139C2×C3×#41—61no—
140C2×C3×#41—64no—
141C2×C3×#41—64no—
142C2×C3×#41C2×D311yescharacteristic
143C2×C3×#41C2×D311yescharacteristic
144C22×C3×Q8—31no—
145C22×C3×D4—31no—
146C22×C3×D4—61no—
147C23×C3×C4—31no—
148C23×C3×C4—61no—
149D3×#41—24no—
150D3×#41—24no—
151C2×#239C2×D311yescharacteristic
152C2×D3×Q8C2×D311yescharacteristic
153C2×#237—21no—
154C2×#237C2×D311yescharacteristic
155C2×D3×D4—21no—
156C2×D3×D4C2×D311yescharacteristic
157C2×#235—21no—
158C2×#235C2×D311yescharacteristic
159C22×C4×D3—21no—
160C22×C4×D3C2×D311yescharacteristic
161C22×Dic6—31no—
162C22×Dic6—31no—
163C22×Dic6—61no—
164C2×C3×M16—31no—
165C2×C3×C4⋊C4—31no—
166C2×#217—61no—
167#951—64no—
168#951—68no—
169#951—64no—
170#951—64no—
171C2×#216—32no—
172C2×#216—32no—
173C2×#216—32no—
174C2×#216—62no—
175C2×#214—32no—
176C2×#214—32no—
177C2×#214—32no—
178C2×#214—62no—
179C2×(C2×D3)⋊C4—61no—
180C2×C4⋊Dic3—61no—
181C2×C4⋊Dic3C2×D311yescharacteristic, complemented
182#924—32no—
183#924—32no—
184#924—61no—
185#924—61no—
186C2×Dic3⋊C4—61no—
187C2×#208—31no—
188C2×#208—31no—
189C2×#208—61no—
190C2×#208C2×D311yescharacteristic, complemented
191#909—64no—
192C2×Dic12—32no—
193C2×#204—32no—
194#897—32no—
195#897—32no—
196#897—61no—
197#897—61no—
198C3×#103—32no—
199C3×#102—32no—
200#835—32no—
201#835C2×D312yescomplemented
202#832—32no—
203#832C2×D312yescomplemented
204#830—32no—
205#830—32no—
206(C2×D3)⋊C8—32no—
207(C2×D3)⋊C8—32no—
208#810—32no—
209#809—32no—
210C23×C32—21no—
211C23×C32C2×D411yescharacteristic
212C22×C3×D3—24no—
213C22×C3×D3—22no—
214C22×C3×D3—21no—
215C22×C3×D3—22no—
216C22×C3×D3—41no—
217C22×C3×D3—42no—
218C22×C3×D3—42no—
219C22×C3×D3C2×D411yescharacteristic
220C22×C3×D3C2×D411yescharacteristic
221C32×Q8—21no—
222C32×Q8C2×D412yes—
223C32×D4—24no—
224C32×D4—21no—
225C32×D4C2×D412yes—
226C2×C32×C4—21no—
227C2×C32×C4—24no—
228C2×C32×C4C2×D412yes—
229C2×C32×C4C2×D411yescharacteristic
230C2×C32×C4C2×D412yes—
231C2×C32×C4C2411yescharacteristic
232C2×C3⋊Dic3—22no—
233C2×C3⋊Dic3—42no—
234#634—22no—
235#634—22no—
236#634—42no—
237C3×#67—24no—
238C3×#67—24no—
239C3×#67—24no—
240C2×C3×Dic3—24no—
241C2×C3×Dic3—22no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—22no—
244C2×C3×Dic3—42no—
245C2×C3×Dic3C2×D411yescharacteristic
246C2×C3×Dic3C2×D411yescharacteristic
247C3×D12—24no—
248C3×D12—21no—
249C3×D12C2×D412yes—
250C3×C4×D3—24no—
251C3×C4×D3—24no—
252C3×C4×D3—22no—
253C3×C4×D3—24no—
254C3×C4×D3—22no—
255C3×C4×D3—21no—
256C3×C4×D3—21no—
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×Dic6—24no—
260C3×Dic6—21no—
261C3×Dic6C2×D412yes—
262C3⋊(C3⋊C8)—22no—
263C3×C3⋊C8—22no—
264C22×#41—31no—
265C2×#137—91no—
266C2×#137—91no—
267C2×C22⋊Q8—91no—
268#452—92no—
269#452—92no—
270#451—92no—
271#450—92no—
272#417—31no—
273#417—91no—
274#407—91no—
275C24×C3—31no—
276C24×C3—61no—
277C23×D3—21no—
278C23×D3#6711yescharacteristic
279C3×#41—22no—
280C3×#41—22no—
281C3×#41—24no—
282C3×#41—34no—
283C3×#41—42no—
284C3×#41—68no—
285C3×#41—62no—
286C3×#41—68no—
287C3×#41—62no—
288C3×#41—62no—
289C3×#41—62no—
290C3×#41—62no—
291C3×#41D1214yes—
292C3×#41#6714yes—
293C2×C3×Q8—21no—
294C2×C3×Q8—31no—
295C2×C3×Q8—61no—
296C2×C3×Q8—62no—
297C2×C3×Q8—62no—
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—21no—
303C2×C3×D4—31no—
304C2×C3×D4—41no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—62no—
308C2×C3×D4—68no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4—62no—
312C2×C3×D4C22×D311yescharacteristic
313C2×C3×D4C22×D311yescharacteristic
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—41no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4—68no—
326C22×C3×C4—61no—
327C22×C3×C4—62no—
328C22×C3×C4—62no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C2×#67—21no—
334C2×#67—21no—
335C2×#67—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—121no—
341C22×Dic3#6711yescharacteristic
342#239—22no—
343#239—22no—
344D3×Q8—22no—
345D3×Q8—22no—
346#237—28no—
347#237—22no—
348#237—22no—
349D3×D4—28no—
350D3×D4—22no—
351D3×D4—22no—
352#235—28no—
353#235—22no—
354#235#6714yes—
355C2×D12—21no—
356C2×D12C22×D311yescharacteristic
357C2×C4×D3—28no—
358C2×C4×D3—21no—
359C2×C4×D3—21no—
360C2×C4×D3—22no—
361C2×C4×D3—22no—
362C2×C4×D3—21no—
363C2×C4×D3#6711yescharacteristic
364C2×C4×D3#6711yescharacteristic
365C2×C4×D3C22×D311yescharacteristic
366C2×C4×D3C22×D311yescharacteristic
367C2×Dic6—21no—
368C2×Dic6—32no—
369C2×Dic6—32no—
370C2×Dic6—62no—
371C2×Dic6—64no—
372C2×Dic6—62no—
373C2×Dic6—62no—
374C2×Dic6—62no—
375C2×Dic6—62no—
376C2×Dic6—61no—
377C2×Dic6—61no—
378C2×Dic6—121no—
379C2×Dic6—122no—
380C2×Dic6C22×D311yescharacteristic
381C3×M16—62no—
382C2×C3×C8—32no—
383C3×C4⋊C4—32no—
384C3×C4⋊C4—61no—
385#217—62no—
386#217—62no—
387#216—64no—
388#216—68no—
389#216—64no—
390#216—64no—
391#214—64no—
392#214—68no—
393#214—64no—
394#214—64no—
395(C2×D3)⋊C4—62no—
396(C2×D3)⋊C4—62no—
397C4⋊Dic3—21no—
398C4⋊Dic3—62no—
399C4⋊Dic3—62no—
400C4⋊Dic3C22×D312yes—
401Dic3⋊C4—62no—
402Dic3⋊C4—62no—
403#208—22no—
404#208—64no—
405#208—62no—
406#208—62no—
407C2×C3⋊C8—32no—
408C2×C3⋊C8—32no—
409C2×C3⋊C8—62no—
410C2×C3⋊C8C22×D312yes—
411Dic12—64no—
412#204—64no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—22no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32#12012yes—
419C22×C32C22×D411yescharacteristic
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—22no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—44no—
427C2×C3×D3—48no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3#13712yescomplemented
431C32×C4—22no—
432C32×C4#12012yes—
433C32×C4C22×D411yescharacteristic
434C32×C4C22×D411yescharacteristic
435C3⋊Dic3—42no—
436C3×Dic3—21no—
437C3×Dic3—22no—
438C3×Dic3—21no—
439C3×Dic3—42no—
440C2×#41—31no—
441C2×#41—31no—
442C2×#41—31no—
443C2×#41—61no—
444C2×#41—61no—
445C2×#41—64no—
446C2×#41—64no—
447C2×#41D3211yescharacteristic
448C22×Q8—31no—
449C22×Q8—91no—
450C22×D4—31no—
451C22×D4—61no—
452C23×C4—31no—
453C23×C4—61no—
454#137—184no—
455#137—184no—
456C2×Q16—92no—
457C2×Q16—92no—
458C2×SD16—92no—
459C2×SD16—92no—
460C2×M16—31no—
461C2×M16—91no—
462C22⋊Q8—92no—
463C22⋊Q8—92no—
464C22⋊Q8—181no—
465C22⋊Q8—181no—
466C2×C4⋊C4—31no—
467C2×C4⋊C4—181no—
468C2×C22⋊C4—181no—
469#103—32no—
470#103—92no—
471#102—32no—
472#102—92no—
473C22⋊C8—92no—
474C22⋊C8—92no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—31no—
479C23×C3—31no—
480C23×C3—41no—
481C23×C3—62no—
482C23×C3—64no—
483C23×C3—62no—
484C23×C3—61no—
485C23×C3—121no—
486C23×C3—122no—
487C23×C3—122no—
488C23×C3D3×D411yescharacteristic
489C23×C3C2×#6711yescharacteristic
490C22×D3—24no—
491C22×D3—22no—
492C22×D3—21no—
493C22×D3—22no—
494C22×D3—41no—
495C22×D3—42no—
496C22×D3—42no—
497C22×D3C2×#6711yescharacteristic
498C22×D3C2×#6711yescharacteristic
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—22no—
502C3×Q8—32no—
503C3×Q8—41no—
504C3×Q8—64no—
505C3×Q8—61no—
506C3×Q8C2×D1212yes—
507C3×Q8C2×#6712yes—
508C3×D4—24no—
509C3×D4—24no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—22no—
513C3×D4—32no—
514C3×D4—41no—
515C3×D4—44no—
516C3×D4—64no—
517C3×D4—64no—
518C3×D4—64no—
519C3×D4—64no—
520C3×D4—61no—
521C3×D4C2×D1212yes—
522C3×D4C2×#6712yes—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—24no—
526C2×C3×C4—24no—
527C2×C3×C4—21no—
528C2×C3×C4—22no—
529C2×C3×C4—21no—
530C2×C3×C4—22no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—44no—
534C2×C3×C4—41no—
535C2×C3×C4—64no—
536C2×C3×C4—64no—
537C2×C3×C4—64no—
538C2×C3×C4—62no—
539C2×C3×C4—61no—
540C2×C3×C4—62no—
541C2×C3×C4—62no—
542C2×C3×C4—64no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—62no—
548C2×C3×C4—122no—
549C2×C3×C4C2×D1212yes—
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4D3×D412yes—
552C2×C3×C4C2×#6712yes—
553C2×C3×C4C2×#6711yescharacteristic
554C2×C3×C4C2×#6712yes—
555C2×C3×C4C23×D311yescharacteristic
556C2×C3×C4C23×D311yescharacteristic
557#67—24no—
558#67—24no—
559#67—24no—
560C2×Dic3—24no—
561C2×Dic3—22no—
562C2×Dic3—21no—
563C2×Dic3—22no—
564C2×Dic3—42no—
565C2×Dic3—62no—
566C2×Dic3—62no—
567C2×Dic3—122no—
568C2×Dic3—124no—
569C2×Dic3—122no—
570C2×Dic3—122no—
571C2×Dic3C2×#6711yescharacteristic
572C2×Dic3C2×#6711yescharacteristic
573D12—24no—
574D12—21no—
575D12C2×#6712yes—
576C4×D3—24no—
577C4×D3—24no—
578C4×D3—22no—
579C4×D3—24no—
580C4×D3—22no—
581C4×D3—21no—
582C4×D3—21no—
583C4×D3—21no—
584C4×D3—21no—
585Dic6—24no—
586Dic6—21no—
587Dic6—64no—
588Dic6—62no—
589Dic6—62no—
590Dic6—62no—
591Dic6—62no—
592Dic6—122no—
593Dic6—124no—
594Dic6—122no—
595Dic6—122no—
596Dic6C2×#6712yes—
597C3×C8—62no—
598C3⋊C8—22no—
599C3⋊C8—64no—
600C3⋊C8—62no—
601C3⋊C8—62no—
602C2×C32—22no—
603C2×C32—42no—
604C2×C32C2×#12011yescharacteristic
605C2×C32C2×#13711yescharacteristic
606C2×C32#57511yescharacteristic
607C3×D3—22no—
608C3×D3—41no—
609C3×D3—42no—
610C24—31no—
611C24—61no—
612#41—22no—
613#41—34no—
614#41—68no—
615#41—62no—
616#41—68no—
617#41—62no—
618#41—62no—
619#41—62no—
620#41—62no—
621#41#62614yes—
622C2×Q8—31no—
623C2×Q8—61no—
624C2×Q8—62no—
625C2×Q8—62no—
626C2×Q8—92no—
627C2×Q8—181no—
628C2×Q8—182no—
629C2×Q8—182no—
630C2×Q8C2×D3211yescharacteristic
631C2×D4—21no—
632C2×D4—31no—
633C2×D4—61no—
634C2×D4—61no—
635C2×D4—62no—
636C2×D4—68no—
637C2×D4—61no—
638C2×D4—61no—
639C2×D4—62no—
640C2×D4C2×D3211yescharacteristic
641C22×C4—21no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—68no—
650C22×C4—61no—
651C22×C4—62no—
652C22×C4—62no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—181no—
656C22×C4C2×D3211yescharacteristic
657Q16—184no—
658Q16—184no—
659SD16—184no—
660SD16—184no—
661M16—62no—
662M16—182no—
663C2×C8—32no—
664C2×C8—92no—
665C4⋊C4—32no—
666C4⋊C4—61no—
667C4⋊C4—182no—
668C4⋊C4—182no—
669C22⋊C4—182no—
670C22⋊C4—182no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—21no—
678C22×C3—22no—
679C22×C3—32no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—42no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—61no—
688C22×C3—61no—
689C22×C3—62no—
690C22×C3—61no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—81no—
694C22×C3—81no—
695C22×C3—124no—
696C22×C3—128no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3#88212yes—
700C22×C3#95312yes—
701C22×C3C2×D3×D411yescharacteristic
702C22×C3C22×#6711yescharacteristic
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—22no—
709C2×D3—44no—
710C2×D3—48no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3#95112yescomplemented
714C3×C4—22no—
715C3×C4—22no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—22no—
719C3×C4—42no—
720C3×C4—61no—
721C3×C4—61no—
722C3×C4—62no—
723C3×C4—122no—
724C3×C4#88212yes—
725C3×C4#95312yes—
726C3×C4C22×D1211yescharacteristic
727C3×C4C2×D3×D411yescharacteristic
728C3×C4C22×#6711yescharacteristic
729C3×C4C22×#6711yescharacteristic
730Dic3—21no—
731Dic3—22no—
732Dic3—21no—
733Dic3—42no—
734Dic3—124no—
735Dic3—122no—
736Dic3—122no—
737C32#300711yescharacteristic, complemented, Sylow
738C23—21no—
739C23—31no—
740C23—31no—
741C23—62no—
742C23—64no—
743C23—61no—
744C23—62no—
745C23—121no—
746C23—122no—
747C23—122no—
748C23D3×#6711yescharacteristic
749Q8—21no—
750Q8—32no—
751Q8—64no—
752Q8—61no—
753Q8—182no—
754Q8—182no—
755Q8—362no—
756Q8C2×#62612yes—
757D4—24no—
758D4—21no—
759D4—32no—
760D4—64no—
761D4—64no—
762D4—64no—
763D4—64no—
764D4—61no—
765D4C2×#62612yes—
766C2×C4—21no—
767C2×C4—24no—
768C2×C4—31no—
769C2×C4—31no—
770C2×C4—64no—
771C2×C4—64no—
772C2×C4—64no—
773C2×C4—61no—
774C2×C4—62no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—64no—
782C2×C4—62no—
783C2×C4—122no—
784C2×C4—182no—
785C2×C4—362no—
786C2×C4C2×#62612yes—
787C2×C4D3×#6712yes—
788C2×C4D3×#6711yescharacteristic
789C2×C4C22×D3211yescharacteristic
790C8—62no—
791C8—182no—
792C2×C3—22no—
793C2×C3—22no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—42no—
798C2×C3—42no—
799C2×C3—42no—
800C2×C3—62no—
801C2×C3—82no—
802C2×C3—121no—
803C2×C3—122no—
804C2×C3C2×#88211yescharacteristic
805C2×C3#577311yescharacteristic
806C2×C3D3×#13711yescharacteristic
807C2×C3#582211yescharacteristic
808C2×C3C2×#95111yescharacteristic
809C2×C3C2×#95311yescharacteristic
810D3—22no—
811D3—41no—
812D3—42no—
813C22—21no—
814C22—21no—
815C22—22no—
816C22—32no—
817C22—41no—
818C22—41no—
819C22—61no—
820C22—61no—
821C22—61no—
822C22—61no—
823C22—62no—
824C22—61no—
825C22—124no—
826C22—128no—
827C22—121no—
828C22—121no—
829C22#6397712yes—
830C22C2×D3×#6711yescharacteristic
831C4—22no—
832C4—61no—
833C4—61no—
834C4—62no—
835C4—122no—
836C4—362no—
837C4#6397712yes—
838C4C22×#62611yescharacteristic
839C4C2×D3×#6711yescharacteristic
840C3—21no—
841C3#7888511yescharacteristic, complemented
842C3#8408411yescharacteristic, complemented
843C2—22no—
844C2—42no—
845C2—62no—
846C2—121no—
847C2—122no—
848C2D3×#95111yescharacteristic
849C2#1059546911yescharacteristic
850C2C2×#6397711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×#41C2
hypercenterC2×#41D32
hypocenterC32#3007
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#64160C2semidirect
3. C2×#63857C2semidirect
4. C2×#63831C2semidirect
5. C3×#5232C2semidirect
6. #10591599C2semidirect
7. #10591595C2semidirect
8. #10591463C2semidirect
9. #10591459C2semidirect
10. #10591087C2semidirect
11. #10591069C2semidirect
15. C22×#634C22semidirect
29. C2×#3756C22semidirect
30. C2×#3754C22semidirect
31. C2×#3748C22semidirect
32. C2×C3×C4⋊Dic3C22semidirect
33. C2×C3×#208C22semidirect
39. #63857C22semidirect
40. C2×#3719C22semidirect
42. C2×#3716C22semidirect
43. C3×#835C22semidirect
44. C3×#832C22semidirect
45. #63565C22semidirect
46. #63562C22semidirect
48. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #5232D3semidirect
181. C2×C4⋊Dic3C2×D3semidirect
190. C2×#208C2×D3semidirect
201. #835C2×D3semidirect
203. #832C2×D3semidirect
430. C2×C3×D3#137semidirect
713. C2×D3#951semidirect
737. C32#3007semidirect
841. C3#78885semidirect
842. C3#84084semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C2×#641602
C2×#638572
C2×#638312
C3×#52322
#105915992
#105915952
#105914632
#105914592
#105910872
#105910692
#840843
#788853