Finite Group Databasebeta

← #10822197

Subgroups — #10822197

Order 768.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3449C211yesmaximal, characteristic, complemented
2C2×#5822C211yesmaximal, characteristic, complemented
3C2×#5822C211yesmaximal, characteristic, complemented
4C2×#5236C211yesmaximal, characteristic, complemented
5#84072C211yesmaximal, characteristic, complemented
6C2×#5006C211yesmaximal, characteristic, complemented
7#71869C214yesmaximal, complemented
8#71858C214yesmaximal, complemented
9C2×#4533C211yesmaximal, characteristic, complemented
10#23412—31nomaximal, Sylow
11C22×C3×#41C2211yescharacteristic
12C22×C3×#41C2211yescharacteristic
13C22×#235C2211yescharacteristic
14C3×#537—22no—
15C3×#536—21no—
16C3×#536C2212yescomplemented
17C3×#535—21no—
18C3×#535C2212yescomplemented
19C3×#534—22no—
20C3×#532—22no—
21C3×#525—22no—
22C3×#525—22no—
23C2×C3×#117C2211yescharacteristic
24C2×#951—21no—
25C2×#951—21no—
26#5822—22no—
27#5822—22no—
28#5822—22no—
29#5822—22no—
30#5822—22no—
31#5822—22no—
32#5822—22no—
33#5822C2214yes—
34C2×#950—22no—
35C2×#950—22no—
36C2×#949—21no—
37C2×#949—21no—
38C2×#942—21no—
39C2×#942C2212yescomplemented
40C2×#932—21no—
41C2×#932C2212yescomplemented
42C2×#926C2211yescharacteristic
43C22×#208C2211yescharacteristic
44C22×#208C2211yescharacteristic
45#5236—22no—
46#5236C2214yescomplemented
47C2×#837—22no—
48#5233—22no—
49#5232—22no—
50#5225C2212yescomplemented
51#5215C2212yescomplemented
52#5006—22no—
53#5006C2214yescomplemented
54C2×#806—22no—
55#4533C2214yescomplemented
56C2×#575—31no—
57C2×#575—31no—
58#3449D311yescharacteristic, complemented
59C2×#421—31no—
60#2896—31no—
61C2×#410—31no—
62#2009—34no—
63#2008—34no—
64C2×#344—31no—
65C2×C3×#41—21no—
66C2×C3×#41—21no—
67C2×C3×#41—21no—
68C2×C3×#41—21no—
69C2×C3×#41—21no—
70C2×C3×#41—21no—
71C2×C3×#41—21no—
72C2×C3×#41—21no—
73C2×C3×#41—21no—
74C2×C3×#41—21no—
75C2×C3×#41—21no—
76C2×C3×#41—21no—
77C2×C3×#41—21no—
78C2×C3×#41—21no—
79C2×C3×#41—21no—
80C2×C3×#41—21no—
81C2×C3×#41—21no—
82C2×C3×#41—21no—
83C2×C3×#41—21no—
84C2×C3×#41—21no—
85C2×C3×#41D412yes—
86C2×C3×#41D412yes—
87C2×C3×#41D412yes—
88C2×C3×#41C2312yes—
89C22×C3×Q8D411yescharacteristic
90C22×C3×Q8C2311yescharacteristic
91C22×C3×D4—21no—
92C22×C3×D4—21no—
93C22×C3×D4D411yescharacteristic
94C22×C3×D4C2311yescharacteristic
95C23×C3×C4—21no—
96C23×C3×C4—21no—
97C23×C3×C4C2311yescharacteristic
98C22×#67—21no—
99C2×#235—21no—
100C2×#235—21no—
101C2×#235—21no—
102C2×#235—21no—
103C2×#235—21no—
104C2×#235—21no—
105C2×#235—21no—
106C2×#235—21no—
107C2×#235—21no—
108C2×#235—21no—
109C2×#235D412yescomplemented
110C2×#235C2312yes—
111C22×D12D411yescharacteristic, complemented
112C22×C4×D3—21no—
113C22×Dic6D411yescharacteristic, complemented
114C3×C4⋊Q8—22no—
115C3×#127—22no—
116C3×#124—22no—
117C3×#124—22no—
118C3×#123—24no—
119C3×#123—24no—
120C3×C22⋊Q8—24no—
121C3×C22⋊Q8—24no—
122C3×#121—24no—
123C3×#121—28no—
124C3×#121—24no—
125C3×#120—24no—
126C3×#120—24no—
127C3×C4×D4—28no—
128C3×#117—21no—
129C3×#117—21no—
130C3×#117D412yes—
131C3×#117C2312yes—
132C2×C3×C4⋊C4—21no—
133C2×C3×C22⋊C4D412yes—
134C2×C3×C42—21no—
135C2×#217—21no—
136#951—24no—
137#951—24no—
138#951—24no—
139#951—24no—
140#950—28no—
141#950—28no—
142#950—28no—
143#950—28no—
144#949—24no—
145#949—24no—
146#949—24no—
147#949—24no—
148C2×#216—22no—
149C2×#216—22no—
150#942—24no—
151#942—24no—
152#942—24no—
153#942—24no—
154C2×#215—22no—
155C2×#215—22no—
156C2×#214—22no—
157C2×#214—22no—
158#932—24no—
159#932—24no—
160#932—24no—
161#932—24no—
162C2×#213—22no—
163C2×#213—22no—
164#926—21no—
165#926—21no—
166#926—21no—
167#926C2312yes—
168C2×C4⋊Dic3—21no—
169C2×C4×Dic3—21no—
170C2×#208—21no—
171C2×#208—21no—
172C2×#208—21no—
173C2×#208—21no—
174C2×#208—21no—
175C2×#208—21no—
176C2×#208—21no—
177C2×#208D412yescomplemented
178C2×#208D412yescomplemented
179C2×#208D412yescomplemented
180C2×#208C2312yes—
181C2×#208C2312yes—
182C22×C3⋊C8—21no—
183C22×C3⋊C8D412yescomplemented
184#837—28no—
185#835—24no—
186#832—24no—
187#806—28no—
188C22×#41—31no—
189C22×#41C2×D311yescharacteristic
190C22×#41C2×D311yescharacteristic
191#575—34no—
192#575—62no—
193#575—62no—
194#575—62no—
195#575—62no—
196#575—62no—
197#575—62no—
198#575—62no—
199C2×#137—32no—
200C2×#137—61no—
201C2×#137—61no—
202C2×#137—61no—
203C2×AGL(1,ℤ/8)—32no—
204C2×AGL(1,ℤ/8)—61no—
205C2×AGL(1,ℤ/8)—61no—
206C2×AGL(1,ℤ/8)—61no—
207C2×#135—62no—
208C2×#135—62no—
209C22×M16—31no—
210C22×M16—31no—
211#537—22no—
212#536—21no—
213#536C2×D312yescomplemented
214#535—21no—
215#535C2×D312yescomplemented
216#534—22no—
217#532—22no—
218#525—22no—
219#525—22no—
220C2×#117—31no—
221C2×#117C2×D311yescharacteristic
222#421—34no—
223#421—62no—
224C2×#104—62no—
225#419—32no—
226#418—32no—
227#417—62no—
228#416—62no—
229#410—34no—
230#410—62no—
231C2×#99—62no—
232#344—34no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3C2×D411yescharacteristic
236C23×D3—21no—
237C3×#41—22no—
238C3×#41—22no—
239C3×#41—22no—
240C3×#41—22no—
241C3×#41—22no—
242C3×#41—22no—
243C3×#41—22no—
244C3×#41—22no—
245C3×#41—22no—
246C3×#41—22no—
247C3×#41—22no—
248C3×#41—22no—
249C3×#41—22no—
250C3×#41—22no—
251C3×#41—22no—
252C3×#41—22no—
253C3×#41—41no—
254C3×#41—41no—
255C3×#41—41no—
256C3×#41—41no—
257C3×#41—41no—
258C3×#41—41no—
259C3×#41—41no—
260C3×#41—41no—
261C3×#41—41no—
262C3×#41—41no—
263C3×#41—41no—
264C3×#41—41no—
265C3×#41—41no—
266C3×#41—41no—
267C3×#41—41no—
268C3×#41—41no—
269C2×C3×Q8—21no—
270C2×C3×Q8—21no—
271C2×C3×Q8—21no—
272C2×C3×Q8—21no—
273C2×C3×Q8—21no—
274C2×C3×Q8—21no—
275C2×C3×Q8—21no—
276C2×C3×Q8—21no—
277C2×C3×Q8—21no—
278C2×C3×Q8—21no—
279C2×C3×Q8C2×D412yes—
280C2×C3×Q8C2×D412yes—
281C2×C3×D4—22no—
282C2×C3×D4—22no—
283C2×C3×D4—22no—
284C2×C3×D4—22no—
285C2×C3×D4—28no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4—21no—
289C2×C3×D4—21no—
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—41no—
297C2×C3×D4—41no—
298C2×C3×D4—41no—
299C2×C3×D4—41no—
300C2×C3×D4—41no—
301C2×C3×D4—41no—
302C2×C3×D4—41no—
303C2×C3×D4—41no—
304C2×C3×D4C2×D412yes—
305C2×C3×D4C2×D412yes—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—22no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—41no—
314C22×C3×C4—41no—
315C22×C3×C4—41no—
316C22×C3×C4—41no—
317C22×C3×C4—41no—
318C22×C3×C4—41no—
319C22×C3×C4—41no—
320C22×C3×C4—41no—
321C22×C3×C4C2×D411yescharacteristic
322C22×C3×C4C2×D411yescharacteristic
323C22×C3×C4C2×D411yescharacteristic
324C22×C3×C4C2×D411yescharacteristic
325C22×C3×C4C2×D411yescharacteristic
326C22×C3×C4C2×D411yescharacteristic
327C22×C3×C4C2×D411yescharacteristic
328C22×C3×C4C2×D411yescharacteristic
329C22×C3×C4C2×D411yescharacteristic
330C22×C3×C4C2×D411yescharacteristic
331C22×C3×C4C2×D411yescharacteristic
332C22×C3×C4#4111yescharacteristic
333C22×C3×C4#4111yescharacteristic
334C22×C3×C4C2411yescharacteristic
335C2×#67—22no—
336C2×#67—22no—
337C2×#67—41no—
338C2×#67—41no—
339C2×#67—41no—
340C2×#67—41no—
341C22×Dic3—21no—
342C22×Dic3—41no—
343#235—22no—
344#235—22no—
345#235—22no—
346#235—22no—
347#235—22no—
348#235—22no—
349#235—22no—
350#235—22no—
351#235—41no—
352#235—41no—
353#235—41no—
354#235—41no—
355#235—41no—
356#235—41no—
357#235—41no—
358#235—41no—
359C2×D12—21no—
360C2×D12—21no—
361C2×D12—21no—
362C2×D12—21no—
363C2×D12—21no—
364C2×D12C2×D412yes—
365C2×C4×D3—22no—
366C2×C4×D3—22no—
367C2×C4×D3—41no—
368C2×C4×D3—41no—
369C2×C4×D3—41no—
370C2×C4×D3—41no—
371C2×Dic6—21no—
372C2×Dic6—21no—
373C2×Dic6—21no—
374C2×Dic6—21no—
375C2×Dic6—21no—
376C2×Dic6C2×D412yes—
377C3×C4⋊C4—28no—
378C3×C4⋊C4—22no—
379C3×C4⋊C4—22no—
380C3×C22⋊C4—28no—
381C3×C22⋊C4—28no—
382C3×C22⋊C4—22no—
383C3×C22⋊C4C2×D414yes—
384C3×C42—22no—
385C3×C42—22no—
386#217—22no—
387#217—41no—
388#216—28no—
389#216—28no—
390#215—28no—
391#215—28no—
392#214—28no—
393#214—28no—
394#213—28no—
395#213—28no—
396C4⋊Dic3—22no—
397C4⋊Dic3—41no—
398C4×Dic3—22no—
399C4×Dic3—41no—
400#208—22no—
401#208—22no—
402#208—22no—
403#208—22no—
404#208—22no—
405#208—22no—
406#208—22no—
407#208C2×D414yes—
408C2×C3⋊C8—22no—
409C2×C3⋊C8—22no—
410C2×C3⋊C8—22no—
411C2×C3⋊C8—22no—
412C2×C3⋊C8—22no—
413C2×C3⋊C8C2×D414yes—
414C2×#41—21no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—32no—
435C2×#41—32no—
436C2×#41—61no—
437C2×#41—61no—
438C2×#41—61no—
439C2×#41—61no—
440C2×#41—61no—
441C2×#41—61no—
442C2×#41—61no—
443C2×#41—61no—
444C2×#41—61no—
445C2×#41—61no—
446C2×#41#6712yes—
447C2×#41#6712yes—
448C2×#41#6712yes—
449C2×#41C22×D312yes—
450C22×Q8—31no—
451C22×Q8#6711yescharacteristic
452C22×Q8C22×D311yescharacteristic
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—31no—
456C22×D4—61no—
457C22×D4#6711yescharacteristic
458C22×D4C22×D311yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—61no—
462C23×C4C22×D311yescharacteristic
463#137—64no—
464#137—64no—
465#137—64no—
466#137—64no—
467#137—64no—
468#137—64no—
469#137—64no—
470#137—64no—
471AGL(1,ℤ/8)—64no—
472AGL(1,ℤ/8)—64no—
473AGL(1,ℤ/8)—64no—
474AGL(1,ℤ/8)—64no—
475AGL(1,ℤ/8)—64no—
476AGL(1,ℤ/8)—64no—
477AGL(1,ℤ/8)—64no—
478AGL(1,ℤ/8)—64no—
479#135—68no—
480#135—68no—
481#135—68no—
482#135—68no—
483C2×Q16—62no—
484C2×Q16—62no—
485C2×SD16—62no—
486C2×SD16—62no—
487C2×SD16—62no—
488C2×SD16—62no—
489C2×D8—62no—
490C2×D8—62no—
491C2×M16—32no—
492C2×M16—32no—
493C2×M16—32no—
494C2×M16—32no—
495C2×M16—32no—
496C2×M16—61no—
497C2×M16—61no—
498C2×M16—61no—
499C2×M16—61no—
500C2×M16—61no—
501C2×M16—61no—
502C2×M16—61no—
503C22×C8—32no—
504C22×C8—61no—
505C4⋊Q8—22no—
506#127—22no—
507#124—22no—
508#124—22no—
509#123—24no—
510#123—24no—
511C22⋊Q8—24no—
512C22⋊Q8—24no—
513#121—24no—
514#121—28no—
515#121—24no—
516#120—24no—
517#120—24no—
518C4×D4—28no—
519#117—21no—
520#117—21no—
521#117—32no—
522#117—61no—
523#117—61no—
524#117—61no—
525#117#6712yes—
526#117C22×D312yes—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—61no—
529C2×C22⋊C4—61no—
530C2×C22⋊C4#6712yes—
531C2×C42—21no—
532C2×C42—61no—
533#104—68no—
534#103—64no—
535#102—64no—
536#99—68no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—81no—
544C23×C3—82no—
545C23×C3—82no—
546C23×C3#12011yescharacteristic
547C23×C3#12011yescharacteristic
548C23×C3#12111yescharacteristic
549C23×C3#12111yescharacteristic
550C23×C3#12711yescharacteristic
551C23×C3#12711yescharacteristic
552C23×C3C22×D411yescharacteristic
553C22×D3—22no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—82no—
557C3×Q8—22no—
558C3×Q8—22no—
559C3×Q8—22no—
560C3×Q8—22no—
561C3×Q8—41no—
562C3×Q8—41no—
563C3×Q8—41no—
564C3×Q8—41no—
565C3×D4—22no—
566C3×D4—22no—
567C3×D4—22no—
568C3×D4—22no—
569C3×D4—42no—
570C3×D4—42no—
571C3×D4—42no—
572C3×D4—42no—
573C3×D4—42no—
574C3×D4—42no—
575C3×D4—42no—
576C3×D4—42no—
577C3×D4—41no—
578C3×D4—41no—
579C3×D4—41no—
580C3×D4—41no—
581C3×D4—88no—
582C2×C3×C4—24no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—42no—
590C2×C3×C4—42no—
591C2×C3×C4—42no—
592C2×C3×C4—42no—
593C2×C3×C4—42no—
594C2×C3×C4—42no—
595C2×C3×C4—42no—
596C2×C3×C4—42no—
597C2×C3×C4—82no—
598C2×C3×C4#12011yescharacteristic
599C2×C3×C4#12011yescharacteristic
600C2×C3×C4#12011yescharacteristic
601C2×C3×C4#12011yescharacteristic
602C2×C3×C4#12011yescharacteristic
603C2×C3×C4#12011yescharacteristic
604C2×C3×C4#12011yescharacteristic
605C2×C3×C4#12011yescharacteristic
606C2×C3×C4#12011yescharacteristic
607C2×C3×C4#12011yescharacteristic
608C2×C3×C4#12111yescharacteristic
609C2×C3×C4#12111yescharacteristic
610C2×C3×C4#12111yescharacteristic
611C2×C3×C4#12111yescharacteristic
612C2×C3×C4#12111yescharacteristic
613C2×C3×C4#12111yescharacteristic
614C2×C3×C4#12111yescharacteristic
615C2×C3×C4#12111yescharacteristic
616C2×C3×C4#12111yescharacteristic
617C2×C3×C4#12111yescharacteristic
618C2×C3×C4#12711yescharacteristic
619C2×C3×C4#12711yescharacteristic
620C2×C3×C4C22×D411yescharacteristic
621C2×C3×C4C22×D411yescharacteristic
622C2×C3×C4C22×D411yescharacteristic
623C2×C3×C4C22×D411yescharacteristic
624C2×C3×C4C22×D411yescharacteristic
625C2×C3×C4C2×#4111yescharacteristic
626#67—42no—
627#67—42no—
628#67—42no—
629#67—42no—
630C2×Dic3—22no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—42no—
634C2×Dic3—82no—
635D12—22no—
636D12—22no—
637D12—41no—
638D12—41no—
639C4×D3—42no—
640C4×D3—42no—
641C4×D3—42no—
642C4×D3—42no—
643Dic6—22no—
644Dic6—22no—
645Dic6—41no—
646Dic6—41no—
647C3⋊C8—24no—
648C3⋊C8—24no—
649C24—21no—
650C24—21no—
651C24—61no—
652C24C2×#6711yescharacteristic
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—22no—
659#41—22no—
660#41—22no—
661#41—22no—
662#41—22no—
663#41—22no—
664#41—22no—
665#41—22no—
666#41—22no—
667#41—22no—
668#41—22no—
669#41—41no—
670#41—41no—
671#41—41no—
672#41—41no—
673#41—41no—
674#41—41no—
675#41—41no—
676#41—41no—
677#41—41no—
678#41—41no—
679#41—41no—
680#41—41no—
681#41—41no—
682#41—41no—
683#41—41no—
684#41—41no—
685#41—62no—
686#41—62no—
687#41—62no—
688#41—62no—
689#41—62no—
690#41—62no—
691#41—62no—
692#41—62no—
693#41—121no—
694#41—121no—
695#41—121no—
696#41—121no—
697#41—121no—
698#41—121no—
699#41—121no—
700#41—121no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—21no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—32no—
712C2×Q8—61no—
713C2×Q8—61no—
714C2×Q8—61no—
715C2×Q8—61no—
716C2×Q8—61no—
717C2×Q8C2×#6712yes—
718C2×Q8C2×#6712yes—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—28no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—32no—
735C2×D4—41no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—62no—
744C2×D4—62no—
745C2×D4—61no—
746C2×D4—61no—
747C2×D4—61no—
748C2×D4—61no—
749C2×D4—61no—
750C2×D4—121no—
751C2×D4—121no—
752C2×D4—121no—
753C2×D4—121no—
754C2×D4C2×#6712yes—
755C2×D4C2×#6712yes—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—41no—
769C22×C4—41no—
770C22×C4—41no—
771C22×C4—61no—
772C22×C4—62no—
773C22×C4—62no—
774C22×C4—121no—
775C22×C4—121no—
776C22×C4—121no—
777C22×C4—121no—
778C22×C4—121no—
779C22×C4D3×D411yescharacteristic
780C22×C4D3×D411yescharacteristic
781C22×C4D3×D411yescharacteristic
782C22×C4D3×D411yescharacteristic
783C22×C4D3×D411yescharacteristic
784C22×C4D3×D411yescharacteristic
785C22×C4#23711yescharacteristic
786C22×C4#23711yescharacteristic
787C22×C4C2×#6711yescharacteristic
788C22×C4C2×#6711yescharacteristic
789C22×C4C2×#6711yescharacteristic
790C22×C4C2×#6711yescharacteristic
791C22×C4C2×#6711yescharacteristic
792C22×C4C23×D311yescharacteristic
793Q16—68no—
794Q16—68no—
795SD16—68no—
796SD16—68no—
797SD16—68no—
798SD16—68no—
799D8—68no—
800D8—68no—
801M16—34no—
802M16—62no—
803M16—62no—
804M16—62no—
805M16—62no—
806M16—62no—
807M16—62no—
808M16—62no—
809C2×C8—34no—
810C2×C8—62no—
811C2×C8—62no—
812C2×C8—62no—
813C2×C8—62no—
814C2×C8—62no—
815C4⋊C4—28no—
816C4⋊C4—22no—
817C4⋊C4—22no—
818C4⋊C4—62no—
819C4⋊C4—121no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—22no—
823C22⋊C4—62no—
824C22⋊C4—121no—
825C22⋊C4C2×#6714yes—
826C42—22no—
827C42—22no—
828C42—62no—
829C42—121no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—44no—
838C22×C3—44no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—82no—
842C22×C3—82no—
843C22×C3—82no—
844C22×C3—82no—
845C22×C3#39211yescharacteristic
846C22×C3#39211yescharacteristic
847C22×C3#39211yescharacteristic
848C22×C3#39211yescharacteristic
849C22×C3C2×#12011yescharacteristic
850C22×C3C2×#12111yescharacteristic
851C22×C3C2×#12711yescharacteristic
852C2×D3—42no—
853C2×D3—82no—
854C2×D3—82no—
855C2×D3—82no—
856C3×C4—44no—
857C3×C4—42no—
858C3×C4—42no—
859C3×C4#39211yescharacteristic
860C3×C4#39211yescharacteristic
861C3×C4#39211yescharacteristic
862C3×C4#39211yescharacteristic
863C3×C4C2×#12011yescharacteristic
864C3×C4C2×#12011yescharacteristic
865C3×C4C2×#12111yescharacteristic
866C3×C4C2×#12111yescharacteristic
867Dic3—42no—
868Dic3—82no—
869C23—22no—
870C23—22no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—62no—
876C23—81no—
877C23—82no—
878C23—82no—
879C23—121no—
880C23—121no—
881C23—242no—
882C23#93811yescharacteristic
883C23#93811yescharacteristic
884C23#94011yescharacteristic
885C23#94011yescharacteristic
886C23#95311yescharacteristic
887C23#95311yescharacteristic
888C23C22×#6711yescharacteristic
889Q8—22no—
890Q8—22no—
891Q8—22no—
892Q8—22no—
893Q8—41no—
894Q8—41no—
895Q8—41no—
896Q8—41no—
897Q8—62no—
898Q8—62no—
899Q8—121no—
900Q8—121no—
901D4—22no—
902D4—22no—
903D4—22no—
904D4—22no—
905D4—42no—
906D4—42no—
907D4—42no—
908D4—42no—
909D4—42no—
910D4—42no—
911D4—42no—
912D4—42no—
913D4—41no—
914D4—41no—
915D4—41no—
916D4—41no—
917D4—62no—
918D4—62no—
919D4—88no—
920D4—122no—
921D4—122no—
922D4—122no—
923D4—122no—
924D4—121no—
925D4—121no—
926C2×C4—24no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—62no—
942C2×C4—82no—
943C2×C4—121no—
944C2×C4—121no—
945C2×C4—122no—
946C2×C4—122no—
947C2×C4—122no—
948C2×C4—122no—
949C2×C4—122no—
950C2×C4—242no—
951C2×C4#93711yescharacteristic
952C2×C4#93711yescharacteristic
953C2×C4#93711yescharacteristic
954C2×C4#93711yescharacteristic
955C2×C4#93711yescharacteristic
956C2×C4#93711yescharacteristic
957C2×C4#93711yescharacteristic
958C2×C4#93711yescharacteristic
959C2×C4#93811yescharacteristic
960C2×C4#93811yescharacteristic
961C2×C4#93911yescharacteristic
962C2×C4#93911yescharacteristic
963C2×C4#93911yescharacteristic
964C2×C4#93911yescharacteristic
965C2×C4#93911yescharacteristic
966C2×C4#93911yescharacteristic
967C2×C4#93911yescharacteristic
968C2×C4#93911yescharacteristic
969C2×C4#94011yescharacteristic
970C2×C4#94011yescharacteristic
971C2×C4#95311yescharacteristic
972C2×C4#95311yescharacteristic
973C2×C4C2×D3×D411yescharacteristic
974C2×C4C2×D3×D411yescharacteristic
975C2×C4C2×D3×D411yescharacteristic
976C2×C4C2×#23711yescharacteristic
977C2×C4C22×#6711yescharacteristic
978C2×C4C22×#6711yescharacteristic
979C8—64no—
980C8—64no—
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—82no—
989C2×C3—82no—
990C2×C3C2×#39211yescharacteristic
991D3—82no—
992C22—41no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—44no—
1000C22—44no—
1001C22—42no—
1002C22—42no—
1003C22—82no—
1004C22—82no—
1005C22—82no—
1006C22—82no—
1007C22—122no—
1008C22—242no—
1009C22—242no—
1010C22—242no—
1011C22#522311yescharacteristic
1012C22#522311yescharacteristic
1013C22#522311yescharacteristic
1014C22#522311yescharacteristic
1015C22C2×#93811yescharacteristic
1016C22C2×#94011yescharacteristic
1017C22C2×#95311yescharacteristic
1018C4—44no—
1019C4—42no—
1020C4—42no—
1021C4—122no—
1022C4—242no—
1023C4#522311yescharacteristic
1024C4#522311yescharacteristic
1025C4#522311yescharacteristic
1026C4#522311yescharacteristic
1027C4C2×#93711yescharacteristic
1028C4C2×#93711yescharacteristic
1029C4C2×#93911yescharacteristic
1030C4C2×#93911yescharacteristic
1031C3#2341211yescharacteristic, complemented, Sylow
1032C2—21no—
1033C2—21no—
1034C2—21no—
1035C2—21no—
1036C2—21no—
1037C2—21no—
1038C2—21no—
1039C2—82no—
1040C2—82no—
1041C2—242no—
1042C2C2×#522311yescharacteristic
subgroupG/H
centerC4#5223
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#3449C2
socleC2×C3C2×#392
hypercenter#3449D3
hypocenterC3#23412
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4 ◁ C23×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C3×#3449C2semidirect
2. C2×#5822C2semidirect
3. C2×#5822C2semidirect
4. C2×#5236C2semidirect
5. #84072C2semidirect
6. C2×#5006C2semidirect
7. #71869C2semidirect
8. #71858C2semidirect
9. C2×#4533C2semidirect
16. C3×#536C22semidirect
18. C3×#535C22semidirect
39. C2×#942C22semidirect
41. C2×#932C22semidirect
46. #5236C22semidirect
50. #5225C22semidirect
51. #5215C22semidirect
53. #5006C22semidirect
55. #4533C22semidirect
58. #3449D3semidirect
109. C2×#235D4semidirect
111. C22×D12D4semidirect
113. C22×Dic6D4semidirect
177. C2×#208D4semidirect
178. C2×#208D4semidirect
179. C2×#208D4semidirect
183. C22×C3⋊C8D4semidirect
213. #536C2×D3semidirect
215. #535C2×D3semidirect
1031. C3#23412semidirect

Maximal subgroups

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

subgroupindex
C3×#34492
C2×#58222
C2×#52362
#840722
C2×#50062
#718692
#718582
C2×#45332
#234123