Finite Group Databasebeta

← #10822209

Subgroups — #10822209

Order 768.

1980 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3449C211yesmaximal, characteristic, complemented
2#87268C211yesmaximal, characteristic, complemented
3C2×#5822C211yesmaximal, characteristic, complemented
4C2×#5236C211yesmaximal, characteristic, complemented
5#84074C211yesmaximal, characteristic, complemented
6C2×#5005C211yesmaximal, characteristic, complemented
7#71715C218yesmaximal, complemented
8C2×#4531C211yesmaximal, characteristic, complemented
9#23414—31nomaximal, Sylow
10C22×C3×#41C2211yescharacteristic
11C22×C3×#41C2211yescharacteristic
12C22×#235C2211yescharacteristic
13C3×#537—22no—
14C3×#536—21no—
15C3×#536—21no—
16C3×#535—21no—
17C3×#535—21no—
18C3×#534—22no—
19C3×#532—22no—
20C3×#525—22no—
21C3×#525C2214yescomplemented
22C2×C3×#117C2211yescharacteristic
23#5833—22no—
24#5832—22no—
25#5830—21no—
26#5828—22no—
27#5825—21no—
28C2×#951—21no—
29#5822—22no—
30#5822—22no—
31#5822—22no—
32#5822C2214yes—
33C2×#950—22no—
34C2×#949—21no—
35#5816—21no—
36C2×#942—21no—
37#5805—21no—
38#5804—22no—
39C2×#932—21no—
40#5791C2214yescomplemented
41C2×#926C2211yescharacteristic
42C22×#208C2211yescharacteristic
43C22×#208C2211yescharacteristic
44#5236—22no—
45#5236C2214yescomplemented
46C2×#837—22no—
47#5234—22no—
48#5234—22no—
49#5207C2214yescomplemented
50#5005—22no—
51#5005C2214yescomplemented
52C2×#805—22no—
53#4531C2214yescomplemented
54C2×#575—31no—
55#3449—31no—
56#3449D311yescharacteristic, complemented
57C2×#421—31no—
58C2×#421—31no—
59#2879—31no—
60#2010—38no—
61C2×H(3,ℤ/4)—31no—
62C2×C3×#41—21no—
63C2×C3×#41—21no—
64C2×C3×#41—21no—
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×#41D412yescomplemented
85C2×C3×#41C2312yes—
86C22×C3×Q8D411yescharacteristic
87C22×C3×Q8D411yescharacteristic, complemented
88C22×C3×D4—21no—
89C22×C3×D4D412yes—
90C22×C3×D4D411yescharacteristic
91C22×C3×D4D411yescharacteristic, complemented
92C23×C3×C4—21no—
93C23×C3×C4C2312yes—
94C23×C3×C4C2311yescharacteristic
95C22×#67—21no—
96C2×#235—21no—
97C2×#235—21no—
98C2×#235—21no—
99C2×#235—21no—
100C2×#235—21no—
101C2×#235—21no—
102C2×#235—21no—
103C2×#235—21no—
104C2×#235—21no—
105C2×#235—21no—
106C2×#235D412yescomplemented
107C2×#235C2312yes—
108C22×D12D411yescharacteristic, complemented
109C22×C4×D3—21no—
110C22×Dic6D411yescharacteristic, complemented
111C3×C4⋊Q8—22no—
112C3×#127—22no—
113C3×#124—22no—
114C3×#124—22no—
115C3×#123—24no—
116C3×#123—24no—
117C3×C22⋊Q8—24no—
118C3×C22⋊Q8—24no—
119C3×#121—24no—
120C3×#121—28no—
121C3×#121—24no—
122C3×#120—24no—
123C3×#120—24no—
124C3×C4×D4—28no—
125C3×#117—21no—
126C3×#117—21no—
127C3×#117D412yescomplemented
128C3×#117C2312yes—
129C2×C3×C4⋊C4—21no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C42D412yescomplemented
132#953—24no—
133C2×#217—21no—
134#951—24no—
135#951—24no—
136#950—28no—
137#950—28no—
138#949—24no—
139#949—24no—
140#947—22no—
141#946—24no—
142#944—22no—
143C2×#216—22no—
144#942—24no—
145#942—24no—
146C2×#215—22no—
147#940—22no—
148#939—28no—
149#938—24no—
150#937—24no—
151#936—22no—
152#935—24no—
153C2×#214—22no—
154#932—24no—
155#932—24no—
156C2×#213—22no—
157#930—24no—
158#929—24no—
159C4×#67—28no—
160#926—21no—
161#926—21no—
162#926D412yescomplemented
163#926C2312yes—
164C2×C4⋊Dic3—21no—
165#924—24no—
166C2×C4×Dic3D412yescomplemented
167C2×#208—21no—
168C2×#208—21no—
169C2×#208—21no—
170C2×#208—21no—
171C2×#208—21no—
172C2×#208—21no—
173C2×#208—21no—
174C2×#208—21no—
175C2×#208—21no—
176C2×#208D412yescomplemented
177C2×#208C2312yes—
178C2×#208C2312yes—
179C22×C3⋊C8—21no—
180C22×C3⋊C8D412yescomplemented
181#837—28no—
182#830—28no—
183#805—28no—
184C22×#41—31no—
185C22×#41C2×D311yescharacteristic
186C22×#41C2×D311yescharacteristic
187#575—34no—
188#575—62no—
189#575—62no—
190#575—62no—
191C2×#137—61no—
192C2×#137—61no—
193C2×AGL(1,ℤ/8)—61no—
194C2×AGL(1,ℤ/8)—61no—
195C2×#135—62no—
196C22×M16—31no—
197C22×M16—31no—
198#537—22no—
199#537—62no—
200#536—21no—
201#536—21no—
202#536—61no—
203#536—61no—
204#535—21no—
205#535—21no—
206#535—61no—
207#535—61no—
208#534—22no—
209#534—62no—
210#532—22no—
211#532—62no—
212#525—22no—
213#525—34no—
214#525—62no—
215#525C2×D314yescomplemented
216C2×#117—31no—
217C2×#117C2×D311yescharacteristic
218#421—34no—
219#421—34no—
220#421—62no—
221#421—62no—
222C2×#104—62no—
223C2×#104—62no—
224#408—62no—
225#408—62no—
226#407—34no—
227H(3,ℤ/4)—34no—
228C24×C3—21no—
229C24×C3C2×D412yes—
230C24×C3C2×D411yescharacteristic
231C23×D3—21no—
232C3×#41—22no—
233C3×#41—22no—
234C3×#41—22no—
235C3×#41—22no—
236C3×#41—22no—
237C3×#41—22no—
238C3×#41—22no—
239C3×#41—22no—
240C3×#41—41no—
241C3×#41—41no—
242C3×#41—41no—
243C3×#41—41no—
244C3×#41—41no—
245C3×#41—41no—
246C3×#41—41no—
247C3×#41—41no—
248C3×#41—41no—
249C3×#41—41no—
250C3×#41—41no—
251C3×#41—41no—
252C3×#41—41no—
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—
264C2×C3×Q8—21no—
265C2×C3×Q8—21no—
266C2×C3×Q8—21no—
267C2×C3×Q8—21no—
268C2×C3×Q8—21no—
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×Q8C2×D412yes—
276C2×C3×D4—22no—
277C2×C3×D4—22no—
278C2×C3×D4—22no—
279C2×C3×D4—22no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—22no—
283C2×C3×D4—22no—
284C2×C3×D4—28no—
285C2×C3×D4—21no—
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×D4C2×D412yes—
301C22×C3×C4—21no—
302C22×C3×C4—22no—
303C22×C3×C4—22no—
304C22×C3×C4—22no—
305C22×C3×C4—22no—
306C22×C3×C4—22no—
307C22×C3×C4—22no—
308C22×C3×C4—22no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—41no—
312C22×C3×C4—41no—
313C22×C3×C4—41no—
314C22×C3×C4—41no—
315C22×C3×C4C2×D411yescharacteristic
316C22×C3×C4C2×D411yescharacteristic
317C22×C3×C4C2×D411yescharacteristic
318C22×C3×C4C2×D411yescharacteristic
319C22×C3×C4C2×D411yescharacteristic
320C22×C3×C4C2×D411yescharacteristic
321C22×C3×C4C2×D412yes—
322C22×C3×C4C2×D411yescharacteristic
323C22×C3×C4C2×D411yescharacteristic
324C22×C3×C4C2×D411yescharacteristic
325C22×C3×C4C2×D411yescharacteristic
326C22×C3×C4C2×D411yescharacteristic
327C22×C3×C4#4111yescharacteristic
328C22×C3×C4#4111yescharacteristic
329C22×C3×C4C2411yescharacteristic
330C2×#67—22no—
331C2×#67—22no—
332C2×#67—28no—
333C2×#67—41no—
334C2×#67—41no—
335C2×#67—41no—
336C2×#67—41no—
337C22×Dic3—21no—
338C22×Dic3—22no—
339#235—22no—
340#235—22no—
341#235—22no—
342#235—22no—
343#235—22no—
344#235—22no—
345#235—22no—
346#235—22no—
347#235—41no—
348#235—41no—
349#235—41no—
350#235—41no—
351#235—41no—
352#235—41no—
353#235—41no—
354#235—41no—
355C2×D12—21no—
356C2×D12—21no—
357C2×D12—21no—
358C2×D12—21no—
359C2×D12—21no—
360C2×D12C2×D412yes—
361C2×C4×D3—22no—
362C2×C4×D3—22no—
363C2×C4×D3—41no—
364C2×C4×D3—41no—
365C2×C4×D3—41no—
366C2×C4×D3—41no—
367C2×Dic6—21no—
368C2×Dic6—21no—
369C2×Dic6—21no—
370C2×Dic6—21no—
371C2×Dic6—21no—
372C2×Dic6C2×D412yes—
373C3×C4⋊C4—28no—
374C3×C4⋊C4—22no—
375C3×C4⋊C4—22no—
376C3×C22⋊C4—28no—
377C3×C22⋊C4—28no—
378C3×C22⋊C4—22no—
379C3×C22⋊C4—22no—
380C3×C42—22no—
381C3×C42C2×D414yes—
382#217—28no—
383#217—22no—
384#217—22no—
385#216—28no—
386#215—28no—
387#214—28no—
388#213—28no—
389(C2×D3)⋊C4—28no—
390C4⋊Dic3—22no—
391C4⋊Dic3—22no—
392Dic3⋊C4—28no—
393C4×Dic3—22no—
394C4×Dic3C2×D414yes—
395#208—22no—
396#208—22no—
397#208—22no—
398#208—22no—
399#208—22no—
400#208—22no—
401#208—41no—
402#208—41no—
403C2×C3⋊C8—22no—
404C2×C3⋊C8—22no—
405C2×C3⋊C8—22no—
406C2×C3⋊C8—41no—
407C2×C3⋊C8—41no—
408C2×C3⋊C8C2×D414yes—
409C2×#41—21no—
410C2×#41—21no—
411C2×#41—21no—
412C2×#41—21no—
413C2×#41—21no—
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—32no—
432C2×#41—32no—
433C2×#41—61no—
434C2×#41—61no—
435C2×#41—61no—
436C2×#41—61no—
437C2×#41—61no—
438C2×#41—61no—
439C2×#41—61no—
440C2×#41—61no—
441C2×#41—61no—
442C2×#41—61no—
443C2×#41#6712yescomplemented
444C2×#41C22×D312yes—
445C22×Q8—31no—
446C22×Q8#6711yescharacteristic
447C22×Q8#6711yescharacteristic, complemented
448C22×D4—21no—
449C22×D4—31no—
450C22×D4—61no—
451C22×D4#6712yes—
452C22×D4#6711yescharacteristic
453C22×D4#6711yescharacteristic, complemented
454C23×C4—21no—
455C23×C4—61no—
456C23×C4C22×D312yes—
457C23×C4C22×D311yescharacteristic
458#137—64no—
459#137—64no—
460#137—64no—
461#137—64no—
462AGL(1,ℤ/8)—64no—
463AGL(1,ℤ/8)—64no—
464AGL(1,ℤ/8)—64no—
465AGL(1,ℤ/8)—64no—
466#135—68no—
467#135—68no—
468C2×Q16—62no—
469C2×SD16—62no—
470C2×SD16—62no—
471C2×D8—62no—
472C2×M16—32no—
473C2×M16—32no—
474C2×M16—32no—
475C2×M16—61no—
476C2×M16—61no—
477C2×M16—61no—
478C2×M16—61no—
479C2×M16—61no—
480C2×M16—61no—
481C2×M16—61no—
482C2×M16—61no—
483C2×M16—61no—
484C22×C8—32no—
485C22×C8—61no—
486C4⋊Q8—22no—
487C4⋊Q8—62no—
488#127—22no—
489#127—62no—
490#124—22no—
491#124—22no—
492#124—62no—
493#124—62no—
494#123—24no—
495#123—24no—
496#123—64no—
497#123—64no—
498C22⋊Q8—24no—
499C22⋊Q8—24no—
500C22⋊Q8—64no—
501C22⋊Q8—64no—
502#121—24no—
503#121—28no—
504#121—24no—
505#121—64no—
506#121—64no—
507#121—68no—
508#120—24no—
509#120—24no—
510#120—64no—
511#120—64no—
512C4×D4—28no—
513C4×D4—68no—
514#117—21no—
515#117—21no—
516#117—32no—
517#117—32no—
518#117—61no—
519#117—61no—
520#117#6712yescomplemented
521#117C22×D312yes—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—61no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—61no—
526C2×C42—32no—
527C2×C42#6712yescomplemented
528#104—68no—
529#104—68no—
530C22⋊C8—68no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—81no—
538C23×C3—82no—
539C23×C3—82no—
540C23×C3#12011yescharacteristic
541C23×C3#12011yescharacteristic
542C23×C3#12011yescharacteristic
543C23×C3#12011yescharacteristic
544C23×C3#12111yescharacteristic
545C23×C3#12111yescharacteristic
546C23×C3C22×D411yescharacteristic
547C22×D3—22no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—82no—
551C3×Q8—22no—
552C3×Q8—22no—
553C3×Q8—41no—
554C3×Q8—41no—
555C3×Q8—41no—
556C3×Q8—41no—
557C3×Q8—41no—
558C3×Q8—41no—
559C3×D4—22no—
560C3×D4—22no—
561C3×D4—42no—
562C3×D4—42no—
563C3×D4—42no—
564C3×D4—42no—
565C3×D4—42no—
566C3×D4—42no—
567C3×D4—42no—
568C3×D4—42no—
569C3×D4—41no—
570C3×D4—41no—
571C3×D4—41no—
572C3×D4—41no—
573C3×D4—41no—
574C3×D4—41no—
575C3×D4—88no—
576C2×C3×C4—22no—
577C2×C3×C4—24no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—42no—
584C2×C3×C4—42no—
585C2×C3×C4—42no—
586C2×C3×C4—42no—
587C2×C3×C4—42no—
588C2×C3×C4—42no—
589C2×C3×C4—42no—
590C2×C3×C4—42no—
591C2×C3×C4—82no—
592C2×C3×C4#12011yescharacteristic
593C2×C3×C4#12011yescharacteristic
594C2×C3×C4#12011yescharacteristic
595C2×C3×C4#12011yescharacteristic
596C2×C3×C4#12011yescharacteristic
597C2×C3×C4#12011yescharacteristic
598C2×C3×C4#12011yescharacteristic
599C2×C3×C4#12011yescharacteristic
600C2×C3×C4#12111yescharacteristic
601C2×C3×C4#12111yescharacteristic
602C2×C3×C4#12111yescharacteristic
603C2×C3×C4#12111yescharacteristic
604C2×C3×C4#12111yescharacteristic
605C2×C3×C4#12111yescharacteristic
606C2×C3×C4#12111yescharacteristic
607C2×C3×C4#12111yescharacteristic
608C2×C3×C4#12111yescharacteristic
609C2×C3×C4#12111yescharacteristic
610C2×C3×C4#12711yescharacteristic
611C2×C3×C4#12711yescharacteristic
612C2×C3×C4#12711yescharacteristic
613C2×C3×C4#12711yescharacteristic
614C2×C3×C4C22×D411yescharacteristic
615C2×C3×C4C22×D411yescharacteristic
616C2×C3×C4C22×D411yescharacteristic
617C2×C3×C4C22×D411yescharacteristic
618C2×C3×C4C22×D411yescharacteristic
619C2×C3×C4C2×#4111yescharacteristic
620#67—42no—
621#67—42no—
622#67—42no—
623#67—42no—
624#67—88no—
625C2×Dic3—24no—
626C2×Dic3—22no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—82no—
630D12—22no—
631D12—22no—
632D12—41no—
633D12—41no—
634C4×D3—42no—
635C4×D3—42no—
636C4×D3—42no—
637C4×D3—42no—
638Dic6—22no—
639Dic6—22no—
640Dic6—41no—
641Dic6—41no—
642C3⋊C8—24no—
643C3⋊C8—42no—
644C24—21no—
645C24—61no—
646C24C2×#6712yes—
647C24C2×#6711yescharacteristic
648#41—22no—
649#41—22no—
650#41—22no—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—41no—
657#41—41no—
658#41—41no—
659#41—41no—
660#41—41no—
661#41—41no—
662#41—41no—
663#41—41no—
664#41—41no—
665#41—41no—
666#41—41no—
667#41—41no—
668#41—41no—
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—62no—
681#41—62no—
682#41—62no—
683#41—62no—
684#41—62no—
685#41—62no—
686#41—62no—
687#41—62no—
688#41—121no—
689#41—121no—
690#41—121no—
691#41—121no—
692#41—121no—
693#41—121no—
694#41—121no—
695#41—121no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—21no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—32no—
708C2×Q8—61no—
709C2×Q8—61no—
710C2×Q8—61no—
711C2×Q8—61no—
712C2×Q8—61no—
713C2×Q8C2×#6712yes—
714C2×D4—22no—
715C2×D4—22no—
716C2×D4—22no—
717C2×D4—22no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—28no—
723C2×D4—21no—
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—62no—
740C2×D4—62no—
741C2×D4—68no—
742C2×D4—61no—
743C2×D4—61no—
744C2×D4—61no—
745C2×D4—61no—
746C2×D4—61no—
747C2×D4—121no—
748C2×D4—121no—
749C2×D4—121no—
750C2×D4—121no—
751C2×D4C2×#6712yes—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—41no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—61no—
767C22×C4—62no—
768C22×C4—62no—
769C22×C4—62no—
770C22×C4—121no—
771C22×C4—121no—
772C22×C4—121no—
773C22×C4—121no—
774C22×C4D3×D411yescharacteristic
775C22×C4D3×D411yescharacteristic
776C22×C4D3×D411yescharacteristic
777C22×C4D3×D411yescharacteristic
778C22×C4D3×D411yescharacteristic
779C22×C4D3×D411yescharacteristic
780C22×C4#23711yescharacteristic
781C22×C4#23711yescharacteristic
782C22×C4C2×#6712yes—
783C22×C4C2×#6711yescharacteristic
784C22×C4C2×#6711yescharacteristic
785C22×C4C2×#6711yescharacteristic
786C22×C4C2×#6711yescharacteristic
787C22×C4C2×#6711yescharacteristic
788C22×C4C23×D311yescharacteristic
789Q16—68no—
790SD16—68no—
791SD16—68no—
792D8—68no—
793M16—62no—
794M16—62no—
795M16—62no—
796M16—62no—
797M16—62no—
798M16—62no—
799M16—121no—
800M16—121no—
801C2×C8—34no—
802C2×C8—62no—
803C2×C8—62no—
804C2×C8—62no—
805C2×C8—121no—
806C2×C8—121no—
807C4⋊C4—28no—
808C4⋊C4—22no—
809C4⋊C4—22no—
810C4⋊C4—68no—
811C4⋊C4—62no—
812C4⋊C4—62no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—68no—
818C22⋊C4—68no—
819C22⋊C4—62no—
820C22⋊C4—62no—
821C42—22no—
822C42—34no—
823C42—62no—
824C42C2×#6714yes—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—44no—
833C22×C3—44no—
834C22×C3—44no—
835C22×C3—44no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—82no—
839C22×C3—82no—
840C22×C3#39211yescharacteristic
841C22×C3#39211yescharacteristic
842C22×C3#39211yescharacteristic
843C22×C3#39211yescharacteristic
844C22×C3C2×#12011yescharacteristic
845C22×C3C2×#12011yescharacteristic
846C22×C3C2×#12111yescharacteristic
847C2×D3—44no—
848C2×D3—42no—
849C2×D3—82no—
850C2×D3—82no—
851C3×C4—44no—
852C3×C4—42no—
853C3×C4—42no—
854C3×C4#39211yescharacteristic
855C3×C4#39211yescharacteristic
856C3×C4#39211yescharacteristic
857C3×C4#39211yescharacteristic
858C3×C4C2×#12011yescharacteristic
859C3×C4C2×#12111yescharacteristic
860C3×C4C2×#12111yescharacteristic
861C3×C4C2×#12711yescharacteristic
862Dic3—44no—
863Dic3—42no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—41no—
869C23—41no—
870C23—62no—
871C23—81no—
872C23—82no—
873C23—82no—
874C23—121no—
875C23—121no—
876C23—242no—
877C23#93711yescharacteristic
878C23#93711yescharacteristic
879C23#93911yescharacteristic
880C23#93911yescharacteristic
881C23#95311yescharacteristic
882C23#95311yescharacteristic
883C23C22×#6711yescharacteristic
884Q8—22no—
885Q8—22no—
886Q8—41no—
887Q8—41no—
888Q8—41no—
889Q8—41no—
890Q8—41no—
891Q8—41no—
892Q8—62no—
893Q8—62no—
894Q8—121no—
895Q8—121no—
896D4—22no—
897D4—22no—
898D4—42no—
899D4—42no—
900D4—42no—
901D4—42no—
902D4—42no—
903D4—42no—
904D4—42no—
905D4—42no—
906D4—41no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—41no—
912D4—62no—
913D4—62no—
914D4—88no—
915D4—122no—
916D4—122no—
917D4—122no—
918D4—122no—
919D4—121no—
920D4—121no—
921D4—248no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—24no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—64no—
938C2×C4—62no—
939C2×C4—82no—
940C2×C4—121no—
941C2×C4—121no—
942C2×C4—122no—
943C2×C4—122no—
944C2×C4—122no—
945C2×C4—122no—
946C2×C4—242no—
947C2×C4#93711yescharacteristic
948C2×C4#93711yescharacteristic
949C2×C4#93711yescharacteristic
950C2×C4#93711yescharacteristic
951C2×C4#93711yescharacteristic
952C2×C4#93711yescharacteristic
953C2×C4#93811yescharacteristic
954C2×C4#93811yescharacteristic
955C2×C4#93811yescharacteristic
956C2×C4#93811yescharacteristic
957C2×C4#93911yescharacteristic
958C2×C4#93911yescharacteristic
959C2×C4#93911yescharacteristic
960C2×C4#93911yescharacteristic
961C2×C4#93911yescharacteristic
962C2×C4#93911yescharacteristic
963C2×C4#94011yescharacteristic
964C2×C4#94011yescharacteristic
965C2×C4#94011yescharacteristic
966C2×C4#94011yescharacteristic
967C2×C4#95311yescharacteristic
968C2×C4#95311yescharacteristic
969C2×C4C2×D3×D411yescharacteristic
970C2×C4C2×D3×D411yescharacteristic
971C2×C4C2×D3×D411yescharacteristic
972C2×C4C2×#23711yescharacteristic
973C2×C4C22×#6711yescharacteristic
974C2×C4C22×#6711yescharacteristic
975C8—64no—
976C8—122no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—21no—
980C2×C3—21no—
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—82no—
985C2×C3—82no—
986C2×C3C2×#39211yescharacteristic
987D3—82no—
988C22—41no—
989C22—41no—
990C22—41no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—41no—
995C22—44no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—42no—
1000C22—42no—
1001C22—82no—
1002C22—82no—
1003C22—124no—
1004C22—122no—
1005C22—242no—
1006C22—242no—
1007C22#522311yescharacteristic
1008C22#522311yescharacteristic
1009C22#522311yescharacteristic
1010C22#522311yescharacteristic
1011C22C2×#93711yescharacteristic
1012C22C2×#93911yescharacteristic
1013C22C2×#95311yescharacteristic
1014C4—44no—
1015C4—42no—
1016C4—42no—
1017C4—124no—
1018C4—122no—
1019C4#522311yescharacteristic
1020C4#522311yescharacteristic
1021C4#522311yescharacteristic
1022C4#522311yescharacteristic
1023C4C2×#93711yescharacteristic
1024C4C2×#93811yescharacteristic
1025C4C2×#93911yescharacteristic
1026C4C2×#94011yescharacteristic
1027C3#2341411yescharacteristic, complemented, Sylow
1028C2—21no—
1029C2—21no—
1030C2—21no—
1031C2—21no—
1032C2—21no—
1033C2—21no—
1034C2—21no—
1035C2—82no—
1036C2—82no—
1037C2—242no—
1038C2C2×#522311yescharacteristic
subgroupG/H
centerC4C2×#940
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#3449C2
socleC2×C3C2×#392
hypercenter#3449D3
hypocenterC3#23414
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. #87268C2semidirect
3. C2×#5822C2semidirect
4. C2×#5236C2semidirect
5. #84074C2semidirect
6. C2×#5005C2semidirect
7. #71715C2semidirect
8. C2×#4531C2semidirect
21. C3×#525C22semidirect
40. #5791C22semidirect
45. #5236C22semidirect
49. #5207C22semidirect
51. #5005C22semidirect
53. #4531C22semidirect
56. #3449D3semidirect
84. C2×C3×#41D4semidirect
87. C22×C3×Q8D4semidirect
91. C22×C3×D4D4semidirect
106. C2×#235D4semidirect
108. C22×D12D4semidirect
110. C22×Dic6D4semidirect
127. C3×#117D4semidirect
131. C2×C3×C42D4semidirect
162. #926D4semidirect
166. C2×C4×Dic3D4semidirect
176. C2×#208D4semidirect
180. C22×C3⋊C8D4semidirect
215. #525C2×D3semidirect
443. C2×#41#67semidirect
447. C22×Q8#67semidirect
453. C22×D4#67semidirect
520. #117#67semidirect
527. C2×C42#67semidirect
1027. C3#23414semidirect

Maximal subgroups

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

subgroupindex
C3×#34492
#872682
C2×#58222
C2×#52362
#840742
C2×#50052
#717152
C2×#45312
#234143