Finite Group Databasebeta

← #11670528

Subgroups — #11670528

Order 768.

2734 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
1C2×#5774C211yesmaximal, characteristic, complemented
2C22×#916C211yesmaximal, characteristic, complemented
3#86354C211yesmaximal, characteristic, complemented
4#85858C211yesmaximal, characteristic, complemented
5C3×#3042C211yesmaximal, characteristic, complemented
6#83945C211yesmaximal, characteristic, complemented
7#83859C211yesmaximal, characteristic, complemented
8#83403C211yesmaximal, characteristic, complemented
9#82538C211yesmaximal, characteristic, complemented
10#80567C214yesmaximal, complemented
11#80557C214yesmaximal, complemented
12#80449C214yesmaximal, complemented
13#80445C214yesmaximal, complemented
14#79087C211yesmaximal, characteristic, complemented
15#79073C211yesmaximal, characteristic, complemented
16#78964C211yesmaximal, characteristic, complemented
17#78959C211yesmaximal, characteristic, complemented
18#78838C211yesmaximal, characteristic, complemented
19#78835C211yesmaximal, characteristic, complemented
20#61051—31nomaximal, Sylow
21C2×#1009C2211yescharacteristic
22C22×#239C2211yescharacteristic, complemented
23C2×#1004C2211yescharacteristic
24C22×#237C2211yescharacteristic, complemented
25C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
26C22×C3×SD16C2211yescharacteristic, complemented
27C3×#536C2211yescharacteristic, complemented
28C3×#518C2211yescharacteristic, complemented
29#5828C2211yescharacteristic, complemented
30C2×#951C2211yescharacteristic, complemented
31C2×#950C2211yescharacteristic
32#5816C2211yescharacteristic
33C22×#216C2211yescharacteristic, complemented
34C2×#942C2211yescharacteristic, complemented
35C22×#213C2211yescharacteristic
36#5774—28no—
37C2×#916—28no—
38C2×#916C2214yescomplemented
39C2×#916C2212yescomplemented
40C2×#916C2214yescomplemented
41C2×#914C2212yescomplemented
42C2×#911C2212yescomplemented
43C2×D3×D8C2212yescomplemented
44C2×#908C2211yescharacteristic
45C2×#907C2211yescharacteristic
46C22×#204C2211yescharacteristic, complemented
47C22×D3×C8C2211yescharacteristic, complemented
48#5726C2214yescomplemented
49#5676C2214yescomplemented
50#5653—22no—
51D3×#123—22no—
52#5631—22no—
53#5630—22no—
54#5555—22no—
55#5555C2214yescomplemented
56#5554—22no—
57#5554C2214yescomplemented
58#5526C2211yescharacteristic
59#5526C2211yescharacteristic, complemented
60#5524C2211yescharacteristic
61#5524C2211yescharacteristic, complemented
62#5521C2211yescharacteristic, complemented
63#5493—22no—
64C2×#886—22no—
65C3×#463C2214yescomplemented
66C3×#461C2214yescomplemented
67C3×#424C2211yescharacteristic, complemented
68C3×#419C2211yescharacteristic, complemented
69C3×#416C2211yescharacteristic, complemented
70#5215C2211yescharacteristic, complemented
71#5173C2214yescomplemented
72#5173C2214yescomplemented
73#5169C2214yescomplemented
74#5158C2214yescomplemented
75#5126C2211yescharacteristic, complemented
76#5120C2211yescharacteristic, complemented
77#5113C2211yescharacteristic, complemented
78#5110C2211yescharacteristic
79#5092C2212yescomplemented
80#5086C2212yescomplemented
81#5060C2212yescomplemented
82#5059C2212yescomplemented
83#5014C2214yescomplemented
84C4×#213C2214yescomplemented
85#5001C2211yescharacteristic, complemented
86#4998C2211yescharacteristic, complemented
87#4997C2211yescharacteristic, complemented
88#4844C2214yescomplemented
89#4841C2214yescomplemented
90#4836C2214yescomplemented
91#4834C2214yescomplemented
92#4816C2214yescomplemented
93#4813C2212yescomplemented
94#4813C2214yescomplemented
95#4810C2214yescomplemented
96#4808C2214yescomplemented
97#4808C2214yescomplemented
98#4807C2212yescomplemented
99#4778C2212yescomplemented
100#4776C2214yescomplemented
101#4775C2212yescomplemented
102C2×#576—31no—
103C22×#135—31no—
104#3485—31no—
105#3485—31no—
106#3283—34no—
107#3280—34no—
108#3267—34no—
109#3267—34no—
110#3156—31no—
111#3059—31no—
112#3050—31no—
113#3042—31no—
114#3042D311yescharacteristic, complemented
115#3009—31no—
116#3009—31no—
117#3005—31no—
118#3005—31no—
119#2948—31no—
120#2929—31no—
121C2×C3×#41C2311yescharacteristic
122C22×C3×Q8C2311yescharacteristic
123C22×C3×D4C2311yescharacteristic
124C22×#67—21no—
125C22×#67—22no—
126C23×Dic3—21no—
127#1009—24no—
128#1009—42no—
129C2×#239—22no—
130C2×#239—24no—
131C2×#239—42no—
132C2×#239C2314yes—
133C2×#239C2312yes—
134#1004—24no—
135#1004—42no—
136C2×#237—24no—
137C2×#237—22no—
138C2×#237—21no—
139C2×#237—42no—
140C2×#237C2314yes—
141C2×#237C2312yes—
142C2×D3×D4—22no—
143C2×D3×D4—21no—
144C2×D3×D4C2312yes—
145C2×D3×D4C2312yes—
146C2×#235—21no—
147C2×#235C2311yescharacteristic
148C2×#235C2311yescharacteristic
149C22×D12—21no—
150C22×D12—21no—
151C22×D12C2311yescharacteristic
152C22×C4×D3—21no—
153C22×C4×D3C2311yescharacteristic
154C22×Dic6C2311yescharacteristic
155C3×AGL(1,ℤ/8)—24no—
156C2×C3×SD16—24no—
157C2×C3×SD16C2314yes—
158C2×C3×SD16C2312yes—
159C2×C3×D8C2312yes—
160C2×C3×M16C2311yescharacteristic
161C22×C3×C8C2311yescharacteristic
162C3×C4⋊Q8C2312yes—
163C3×#124C2312yes—
164C3×#123—22no—
165C3×C22⋊Q8—22no—
166C3×C4×D4—22no—
167C3×C4×D4C2314yes—
168C3×#117C2311yescharacteristic
169C3×#117C2311yescharacteristic
170C2×C3×C22⋊C4—22no—
171#951—42no—
172#950—24no—
173#947—21no—
174#946C2314yes—
175#946C2312yes—
176#944—21no—
177C2×#216—24no—
178C2×#216C2312yes—
179C2×#216C2312yes—
180C2×#216C2311yescharacteristic
181C2×#216C2312yes—
182C2×#216C2312yes—
183#942—42no—
184C2×#215C2311yescharacteristic
185C2×#215C2312yes—
186#938C2312yes—
187#937—21no—
188#935—21no—
189C2×#214C2311yescharacteristic
190C2×#214C2312yes—
191C2×#213D418yescomplemented
192C2×#213C2311yescharacteristic
193C2×#213C2312yes—
194C2×#213C2312yes—
195#930—24no—
196#930—24no—
197#929—22no—
198C4×#67—22no—
199C2×(C2×D3)⋊C4—24no—
200#926C2311yescharacteristic
201C2×C4⋊Dic3—24no—
202C2×#208C2311yescharacteristic
203C22×C3⋊C8C2311yescharacteristic
204#916—216no—
205#916—216no—
206#916—28no—
207#914—28no—
208#911—28no—
209D3×D8—28no—
210#908—24no—
211#907—24no—
212C2×D24C2312yes—
213C2×#204—24no—
214C2×#204C2314yes—
215C2×#204C2312yes—
216C2×ΓL(1,𝔽25)C2312yes—
217C2×D3×C8—24no—
218C2×D3×C8C2312yes—
219C2×D3×C8C2312yes—
220C2×D3×C8C2312yes—
221#897—22no—
222#897D412yes—
223#897C2312yes—
224#897C2314yes—
225#895—24no—
226#895D412yes—
227#895C2312yes—
228#894—24no—
229#894—24no—
230#893—22no—
231D3×C4⋊C4—24no—
232#886—22no—
233#886—21no—
234#886—22no—
235#886—24no—
236#886—24no—
237#886—24no—
238#886D412yes—
239#884—24no—
240#883—24no—
241#882—21no—
242#882—24no—
243#882—24no—
244#882D412yes—
245D3×C22⋊C4—22no—
246D3×C22⋊C4—24no—
247#875—21no—
248#875C2312yes—
249C4×D12—22no—
250C4×D12C2314yes—
251C4×D12C2314yes—
252#869—21no—
253#869C2312yes—
254C3×C4⋊C8C2314yes—
255C3×#103C2312yes—
256C3×#103C2314yes—
257C3×#102C2312yes—
258#832C2314yes—
259#821C2312yes—
260(C2×D3)⋊C8C2314yes—
261(C2×D3)⋊C8C2314yes—
262#816C2314yes—
263#816C2312yes—
264#809C2314yes—
265#808C2312yes—
266#807C2312yes—
267#803C2312yes—
268C4×C3⋊C8C2312yes—
269C2×H(5,𝔽2)—31no—
270C2×H(5,𝔽2)—31no—
271C22×#41—31no—
272C22×#41—31no—
273#576—68no—
274C2×#137—31no—
275C2×#137—31no—
276C2×AGL(1,ℤ/8)—32no—
277C2×AGL(1,ℤ/8)—32no—
278C2×AGL(1,ℤ/8)—31no—
279C2×AGL(1,ℤ/8)C2×D311yescharacteristic
280C2×#135—31no—
281C2×#135—34no—
282C2×#135—34no—
283C2×#135—32no—
284C2×#135—68no—
285C22×Q16—31no—
286C22×SD16—31no—
287C22×SD16C2×D311yescharacteristic, complemented
288C22×D8—31no—
289C22×D8—32no—
290C2×#131—31no—
291C23×C8—31no—
292#547—34no—
293#547—34no—
294#547—62no—
295#547—62no—
296#546—34no—
297#546—34no—
298#546—62no—
299#546—62no—
300#536—31no—
301#536—31no—
302#536—31no—
303#536C2×D311yescharacteristic, complemented
304#534—62no—
305#534—62no—
306#525—31no—
307#525—31no—
308#525—31no—
309C2×#123—62no—
310C2×#123—62no—
311#518—31no—
312#518C2×D311yescharacteristic, complemented
313#497—32no—
314#497—32no—
315#495—32no—
316#494—32no—
317#470—34no—
318#467—34no—
319#467—32no—
320#466—32no—
321#465—32no—
322#465—32no—
323#463—34no—
324#463C2×D314yescomplemented
325#461—34no—
326#461C2×D314yescomplemented
327#452—34no—
328#452—34no—
329#452—34no—
330#452—34no—
331#450—34no—
332#450—34no—
333#449—34no—
334#449—34no—
335#442—34no—
336C4×D8—34no—
337#435—34no—
338C8×D4—34no—
339#427—31no—
340#424C2×D311yescharacteristic, complemented
341#419—31no—
342#419C2×D311yescharacteristic, complemented
343#418—31no—
344#418—31no—
345#416—31no—
346#416C2×D311yescharacteristic, complemented
347#408—31no—
348#407—31no—
349#405—31no—
350C24×C3—21no—
351C23×D3—21no—
352C23×D3—22no—
353C23×D3—22no—
354C23×D3C2×D411yescharacteristic
355C3×#41—22no—
356C3×#41—22no—
357C2×C3×Q8—21no—
358C2×C3×Q8—22no—
359C2×C3×Q8—22no—
360C2×C3×Q8C2412yes—
361C2×C3×Q8C2411yescharacteristic
362C2×C3×D4—21no—
363C2×C3×D4—21no—
364C2×C3×D4—22no—
365C2×C3×D4C2×D414yes—
366C2×C3×D4C2411yescharacteristic
367C2×C3×D4C2412yes—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—24no—
371C22×C3×C4C2411yescharacteristic
372C2×#67—21no—
373C2×#67—24no—
374C2×#67—22no—
375C2×#67—22no—
376C2×#67—22no—
377C2×#67—22no—
378C2×#67—48no—
379C2×#67—44no—
380C2×#67C2×D412yes—
381C22×Dic3—21no—
382C22×Dic3—22no—
383C22×Dic3—24no—
384C22×Dic3—44no—
385C22×Dic3C2×D411yescharacteristic
386#239—24no—
387#239—28no—
388#239—44no—
389#239—42no—
390#239—48no—
391#237—24no—
392#237—28no—
393#237—44no—
394#237—42no—
395#237—44no—
396#237—48no—
397D3×D4—24no—
398D3×D4—24no—
399D3×D4—42no—
400D3×D4—42no—
401D3×D4—44no—
402D3×D4—48no—
403#235—22no—
404#235—22no—
405#235—22no—
406#235—22no—
407#235—44no—
408C2×D12—21no—
409C2×D12—22no—
410C2×D12—24no—
411C2×D12—22no—
412C2×D12—22no—
413C2×D12—44no—
414C2×D12—44no—
415C2×D12C2×D411yescharacteristic
416C2×D12C2×D414yes—
417C2×D12C2×D414yes—
418C2×D12C2411yescharacteristic
419C2×D12C2412yes—
420C2×C4×D3—22no—
421C2×C4×D3—22no—
422C2×C4×D3—21no—
423C2×C4×D3—24no—
424C2×C4×D3—22no—
425C2×C4×D3—24no—
426C2×C4×D3—44no—
427C2×C4×D3C2×D412yes—
428C2×C4×D3C2412yes—
429C2×C4×D3C2412yes—
430C2×Dic6—22no—
431C2×Dic6—22no—
432C2×Dic6—21no—
433C2×Dic6C2×D411yescharacteristic
434C2×Dic6C2411yescharacteristic
435C2×Dic6C2412yes—
436C3×SD16—24no—
437C3×SD16—28no—
438C3×D8—24no—
439C3×M16—22no—
440C2×C3×C8—22no—
441C2×C3×C8C2412yes—
442C2×C3×C8C2412yes—
443C3×C4⋊C4—24no—
444C3×C4⋊C4C2×D412yes—
445C3×C4⋊C4C2412yes—
446C3×C22⋊C4—21no—
447C3×C22⋊C4—24no—
448C3×C22⋊C4—24no—
449C3×C22⋊C4C2×D412yes—
450C3×C42—21no—
451C3×C42C2412yes—
452#217—21no—
453#217—22no—
454#216—24no—
455#216—24no—
456#216—22no—
457#216—42no—
458#216—42no—
459#215—22no—
460#215—42no—
461#214—22no—
462#214—42no—
463#213—22no—
464#213C2×D418yes—
465#213C2×D418yes—
466(C2×D3)⋊C4—22no—
467(C2×D3)⋊C4—24no—
468(C2×D3)⋊C4—24no—
469(C2×D3)⋊C4—22no—
470(C2×D3)⋊C4—24no—
471(C2×D3)⋊C4—24no—
472(C2×D3)⋊C4—22no—
473(C2×D3)⋊C4C2×D414yes—
474(C2×D3)⋊C4C2×D414yes—
475C4⋊Dic3—24no—
476C4⋊Dic3—24no—
477C4⋊Dic3—22no—
478C4⋊Dic3C2×D414yes—
479C4⋊Dic3C2412yes—
480Dic3⋊C4—24no—
481Dic3⋊C4—22no—
482C4×Dic3—21no—
483#208—22no—
484C2×C3⋊C8C2×D414yes—
485C2×C3⋊C8C2412yes—
486C2×C3⋊C8C2411yescharacteristic
487C2×C3⋊C8C2411yescharacteristic
488D24—24no—
489#204—28no—
490#204—24no—
491ΓL(1,𝔽25)—24no—
492D3×C8—24no—
493D3×C8—24no—
494D3×C8—24no—
495H(5,𝔽2)—64no—
496H(5,𝔽2)—64no—
497H(5,𝔽2)—122no—
498H(5,𝔽2)—122no—
499C2×#41—31no—
500C2×#41—34no—
501C2×#41—32no—
502C2×#41—34no—
503C2×#41—32no—
504C2×#41—31no—
505C2×#41—61no—
506C2×#41—62no—
507C2×#41—62no—
508C2×#41—61no—
509C2×#41—64no—
510C2×#41—64no—
511C2×#41—122no—
512C2×#41—122no—
513C2×#41C22×D311yescharacteristic
514C22×Q8—31no—
515C22×Q8C22×D311yescharacteristic
516C22×D4—32no—
517C22×D4—32no—
518C22×D4—31no—
519C22×D4—61no—
520C22×D4—61no—
521C22×D4—62no—
522C22×D4—61no—
523C22×D4—62no—
524C22×D4—61no—
525C22×D4C22×D311yescharacteristic
526C23×C4—31no—
527C23×C4—61no—
528C23×C4—61no—
529#137—122no—
530#137—122no—
531AGL(1,ℤ/8)—24no—
532AGL(1,ℤ/8)—64no—
533AGL(1,ℤ/8)—68no—
534AGL(1,ℤ/8)—68no—
535#135—64no—
536#135—616no—
537#135—616no—
538#135—68no—
539C2×Q16—32no—
540C2×Q16—32no—
541C2×Q16—31no—
542C2×Q16—32no—
543C2×Q16—32no—
544C2×Q16—64no—
545C2×SD16—24no—
546C2×SD16—31no—
547C2×SD16—31no—
548C2×SD16—32no—
549C2×SD16—32no—
550C2×SD16—34no—
551C2×SD16—32no—
552C2×SD16—64no—
553C2×SD16C22×D314yes—
554C2×SD16C22×D312yes—
555C2×D8—38no—
556C2×D8—32no—
557C2×D8—32no—
558C2×D8—31no—
559C2×D8—32no—
560C2×D8—68no—
561C2×D8C22×D312yes—
562#131—64no—
563C2×M16—31no—
564C2×M16—32no—
565C2×M16C22×D311yescharacteristic
566C22×C8—31no—
567C22×C8—32no—
568C22×C8—32no—
569C22×C8—32no—
570C22×C8—64no—
571C22×C8C22×D311yescharacteristic
572C4⋊Q8—32no—
573C4⋊Q8—61no—
574C4⋊Q8—61no—
575C4⋊Q8C22×D312yes—
576#124—32no—
577#124—61no—
578#124—61no—
579#124C22×D312yes—
580#123—22no—
581#123—32no—
582#123—64no—
583#123—64no—
584#123—64no—
585#123—64no—
586#123—61no—
587#123—62no—
588#123—64no—
589#123—64no—
590#123—62no—
591#123—61no—
592#123—62no—
593C22⋊Q8—22no—
594C22⋊Q8—32no—
595C22⋊Q8—32no—
596C22⋊Q8—34no—
597C22⋊Q8—32no—
598C22⋊Q8—34no—
599C22⋊Q8—62no—
600#121—32no—
601#121—32no—
602#121—32no—
603#121—64no—
604#121—64no—
605#121—64no—
606#121—64no—
607#120—32no—
608#120—64no—
609#120—64no—
610#120—61no—
611#120—61no—
612C4×D4—22no—
613C4×D4—34no—
614C4×D4—34no—
615C4×D4—62no—
616C4×D4—62no—
617C4×D4—62no—
618C4×D4C22×D314yes—
619#117—31no—
620#117C22×D311yescharacteristic
621#117C22×D311yescharacteristic
622C2×C4⋊C4—64no—
623C2×C4⋊C4—64no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—64no—
626C2×C22⋊C4—64no—
627C2×C22⋊C4—62no—
628#107—32no—
629#106—32no—
630C4⋊C8C22×D314yes—
631#103—32no—
632#103—34no—
633#103C22×D312yes—
634#103C22×D314yes—
635#102—34no—
636#102—32no—
637#102—34no—
638#102C22×D312yes—
639C22⋊C8—34no—
640C22⋊C8—34no—
641#97—32no—
642C4×C8—32no—
643C23×C3—22no—
644C23×C3—24no—
645C23×C3—21no—
646C23×C3—82no—
647C23×C3C22×D411yescharacteristic
648C22×D3—22no—
649C22×D3—22no—
650C22×D3—24no—
651C22×D3—21no—
652C22×D3—42no—
653C22×D3—44no—
654C22×D3—44no—
655C22×D3—84no—
656C22×D3—84no—
657C22×D3—82no—
658C22×D3C22×D412yes—
659C22×D3C22×D412yes—
660C3×Q8—21no—
661C3×Q8—22no—
662C3×Q8—22no—
663C3×Q8—21no—
664C3×Q8—42no—
665C3×D4—24no—
666C3×D4—21no—
667C3×D4—22no—
668C3×D4—21no—
669C3×D4—42no—
670C3×D4C22×D414yes—
671C2×C3×C4—22no—
672C2×C3×C4—21no—
673C2×C3×C4—22no—
674C2×C3×C4—42no—
675C2×C3×C4—42no—
676C2×C3×C4—84no—
677C2×C3×C4C22×D414yes—
678C2×C3×C4C22×D411yescharacteristic
679C2×C3×C4C22×D412yes—
680C2×C3×C4H(5,𝔽2)12yes—
681C2×C3×C4C2511yescharacteristic
682#67—24no—
683#67—44no—
684#67—44no—
685#67—44no—
686#67—48no—
687#67—42no—
688#67—82no—
689C2×Dic3—22no—
690C2×Dic3—22no—
691C2×Dic3—21no—
692C2×Dic3—22no—
693C2×Dic3—48no—
694C2×Dic3—44no—
695C2×Dic3—42no—
696C2×Dic3C22×D412yes—
697C2×Dic3C22×D412yes—
698D12—24no—
699D12—22no—
700D12—21no—
701D12—22no—
702D12—21no—
703D12—44no—
704D12—44no—
705D12—48no—
706D12—82no—
707D12C22×D414yes—
708C4×D3—24no—
709C4×D3—22no—
710C4×D3—22no—
711C4×D3—22no—
712C4×D3—22no—
713C4×D3—48no—
714C4×D3—44no—
715C4×D3—42no—
716C4×D3—84no—
717Dic6—22no—
718Dic6—21no—
719Dic6—22no—
720Dic6—22no—
721Dic6—21no—
722Dic6—42no—
723C3×C8—22no—
724C3×C8—22no—
725C3⋊C8—22no—
726C3⋊C8C22×D412yes—
727C3⋊C8C22×D412yes—
728C24—21no—
729C24—31no—
730C24—62no—
731C24—62no—
732C24—61no—
733#41—22no—
734#41—22no—
735#41—62no—
736#41—62no—
737#41—68no—
738#41—64no—
739#41—68no—
740#41—64no—
741#41—62no—
742#41—62no—
743#41—124no—
744#41—124no—
745#41—122no—
746#41—128no—
747#41—124no—
748#41—122no—
749#41—128no—
750#41—124no—
751C2×Q8—21no—
752C2×Q8—22no—
753C2×Q8—22no—
754C2×Q8—31no—
755C2×Q8—32no—
756C2×Q8—31no—
757C2×Q8—61no—
758C2×Q8—62no—
759C2×Q8—62no—
760C2×Q8C23×D312yes—
761C2×Q8C23×D311yescharacteristic
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—22no—
765C2×D4—32no—
766C2×D4—34no—
767C2×D4—31no—
768C2×D4—34no—
769C2×D4—32no—
770C2×D4—31no—
771C2×D4—64no—
772C2×D4—62no—
773C2×D4—62no—
774C2×D4—62no—
775C2×D4—62no—
776C2×D4—64no—
777C2×D4—64no—
778C2×D4—64no—
779C2×D4—62no—
780C2×D4—61no—
781C2×D4—62no—
782C2×D4—61no—
783C2×D4—62no—
784C2×D4—124no—
785C2×D4—124no—
786C2×D4—122no—
787C2×D4—122no—
788C2×D4—124no—
789C2×D4—128no—
790C2×D4—128no—
791C2×D4—124no—
792C2×D4D3×D414yes—
793C2×D4C23×D311yescharacteristic
794C2×D4C23×D312yes—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—24no—
798C22×C4—31no—
799C22×C4—32no—
800C22×C4—32no—
801C22×C4—32no—
802C22×C4—64no—
803C22×C4—62no—
804C22×C4—64no—
805C22×C4—62no—
806C22×C4—62no—
807C22×C4—62no—
808C22×C4—61no—
809C22×C4—61no—
810C22×C4—64no—
811C22×C4—124no—
812C22×C4—124no—
813C22×C4C23×D311yescharacteristic
814Q16—64no—
815Q16—64no—
816Q16—62no—
817Q16—122no—
818Q16—122no—
819SD16—28no—
820SD16—24no—
821SD16—68no—
822SD16—64no—
823SD16—62no—
824SD16—62no—
825SD16—122no—
826SD16—122no—
827D8—24no—
828D8—38no—
829D8—38no—
830D8—64no—
831D8—62no—
832M16—22no—
833M16—64no—
834M16—62no—
835C2×C8—22no—
836C2×C8—34no—
837C2×C8—31no—
838C2×C8—31no—
839C2×C8—32no—
840C2×C8—64no—
841C2×C8—64no—
842C2×C8—64no—
843C2×C8C23×D312yes—
844C2×C8C23×D312yes—
845C4⋊C4—24no—
846C4⋊C4—34no—
847C4⋊C4—32no—
848C4⋊C4—62no—
849C4⋊C4—62no—
850C4⋊C4—64no—
851C4⋊C4—64no—
852C4⋊C4—64no—
853C4⋊C4D3×D412yes—
854C4⋊C4C23×D312yes—
855C22⋊C4—21no—
856C22⋊C4—24no—
857C22⋊C4—24no—
858C22⋊C4—34no—
859C22⋊C4—34no—
860C22⋊C4—62no—
861C22⋊C4—64no—
862C22⋊C4—64no—
863C22⋊C4—62no—
864C22⋊C4—62no—
865C22⋊C4—62no—
866C22⋊C4—61no—
867C22⋊C4—64no—
868C22⋊C4—64no—
869C22⋊C4D3×D412yes—
870C42—21no—
871C42—61no—
872C42C23×D312yes—
873C22×C3—22no—
874C22×C3—24no—
875C22×C3—44no—
876C22×C3—42no—
877C22×C3—41no—
878C22×C3—84no—
879C22×C3D4212yes—
880C22×C3C23×D411yescharacteristic
881C2×D3—22no—
882C2×D3—24no—
883C2×D3—22no—
884C2×D3—22no—
885C2×D3—22no—
886C2×D3—24no—
887C2×D3—44no—
888C2×D3—44no—
889C2×D3—42no—
890C2×D3—41no—
891C2×D3—84no—
892C2×D3—164no—
893C2×D3—164no—
894C3×C4—24no—
895C3×C4—42no—
896C3×C4—41no—
897C3×C4—42no—
898C3×C4D4212yes—
899C3×C4C23×D411yescharacteristic
900C3×C4C2×H(5,𝔽2)11yescharacteristic
901Dic3—22no—
902Dic3—22no—
903Dic3—42no—
904Dic3—42no—
905Dic3—41no—
906C23—22no—
907C23—24no—
908C23—21no—
909C23—32no—
910C23—32no—
911C23—62no—
912C23—62no—
913C23—64no—
914C23—61no—
915C23—82no—
916C23—122no—
917C23—124no—
918C23—124no—
919C23—242no—
920C23—244no—
921C23—244no—
922C23C2×D3×D411yescharacteristic
923Q8—21no—
924Q8—22no—
925Q8—22no—
926Q8—21no—
927Q8—42no—
928Q8—62no—
929Q8—61no—
930Q8—62no—
931Q8—62no—
932Q8—61no—
933Q8—122no—
934D4—21no—
935D4—22no—
936D4—21no—
937D4—24no—
938D4—34no—
939D4—42no—
940D4—64no—
941D4—61no—
942D4—62no—
943D4—61no—
944D4—64no—
945D4—62no—
946D4—124no—
947D4—124no—
948D4—128no—
949D4—124no—
950D4—124no—
951D4—124no—
952D4—128no—
953D4—122no—
954D4—242no—
955D4—242no—
956D4C2×D3×D414yes—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—32no—
961C2×C4—32no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—62no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—64no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—61no—
973C2×C4—84no—
974C2×C4—128no—
975C2×C4—124no—
976C2×C4—128no—
977C2×C4—124no—
978C2×C4—122no—
979C2×C4—122no—
980C2×C4—244no—
981C2×C4C2×D3×D414yes—
982C2×C4C2×D3×D412yes—
983C2×C4C2×D3×D411yescharacteristic
984C2×C4#100912yes—
985C2×C4C24×D311yescharacteristic
986C8—22no—
987C8—22no—
988C8—32no—
989C8—32no—
990C8—62no—
991C2×C3—22no—
992C2×C3—44no—
993C2×C3—81no—
994C2×C3C2×D4211yescharacteristic
995C2×C3#358412yes—
996D3—42no—
997D3—42no—
998D3—44no—
999D3—81no—
1000C22—22no—
1001C22—24no—
1002C22—44no—
1003C22—42no—
1004C22—41no—
1005C22—62no—
1006C22—64no—
1007C22—62no—
1008C22—62no—
1009C22—62no—
1010C22—64no—
1011C22—84no—
1012C22—124no—
1013C22—124no—
1014C22—122no—
1015C22—121no—
1016C22—244no—
1017C22—484no—
1018C22—484no—
1019C22#560912yes—
1020C22C22×D3×D411yescharacteristic
1021C4—24no—
1022C4—42no—
1023C4—41no—
1024C4—42no—
1025C4—62no—
1026C4—62no—
1027C4—122no—
1028C4—121no—
1029C4—122no—
1030C4#560912yes—
1031C4C22×D3×D411yescharacteristic
1032C4C2×#100911yescharacteristic
1033C3#6105111yescharacteristic, complemented, Sylow
1034C2—22no—
1035C2—44no—
1036C2—81no—
1037C2—122no—
1038C2—122no—
1039C2—124no—
1040C2—241no—
1041C2C2×#560911yescharacteristic
1042C2#8720612yes—
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3042C2
socleC22×C3C23×D4
hypercenter#3042D3
hypocenterC3#61051
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #3042

Complements

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

NH ≅ G/Ntype
1. C2×#5774C2semidirect
2. C22×#916C2semidirect
3. #86354C2semidirect
4. #85858C2semidirect
5. C3×#3042C2semidirect
6. #83945C2semidirect
7. #83859C2semidirect
8. #83403C2semidirect
9. #82538C2semidirect
10. #80567C2semidirect
11. #80557C2semidirect
12. #80449C2semidirect
13. #80445C2semidirect
14. #79087C2semidirect
15. #79073C2semidirect
16. #78964C2semidirect
17. #78959C2semidirect
18. #78838C2semidirect
19. #78835C2semidirect
22. C22×#239C22semidirect
24. C22×#237C22semidirect
26. C22×C3×SD16C22semidirect
27. C3×#536C22semidirect
28. C3×#518C22semidirect
29. #5828C22semidirect
30. C2×#951C22semidirect
33. C22×#216C22semidirect
34. C2×#942C22semidirect
38. C2×#916C22semidirect
39. C2×#916C22semidirect
40. C2×#916C22semidirect
41. C2×#914C22semidirect
42. C2×#911C22semidirect
43. C2×D3×D8C22semidirect
46. C22×#204C22semidirect
47. C22×D3×C8C22semidirect
48. #5726C22semidirect
49. #5676C22semidirect
55. #5555C22semidirect
57. #5554C22semidirect
59. #5526C22semidirect
61. #5524C22semidirect
62. #5521C22semidirect
65. C3×#463C22semidirect
66. C3×#461C22semidirect
67. C3×#424C22semidirect
68. C3×#419C22semidirect
69. C3×#416C22semidirect
70. #5215C22semidirect
71. #5173C22semidirect
72. #5173C22semidirect
73. #5169C22semidirect
74. #5158C22semidirect
75. #5126C22semidirect
76. #5120C22semidirect
77. #5113C22semidirect
79. #5092C22semidirect
80. #5086C22semidirect
81. #5060C22semidirect
82. #5059C22semidirect
83. #5014C22semidirect
84. C4×#213C22semidirect
85. #5001C22semidirect
86. #4998C22semidirect
87. #4997C22semidirect
88. #4844C22semidirect
89. #4841C22semidirect
90. #4836C22semidirect
91. #4834C22semidirect
92. #4816C22semidirect
93. #4813C22semidirect
94. #4813C22semidirect
95. #4810C22semidirect
96. #4808C22semidirect
97. #4808C22semidirect
98. #4807C22semidirect
99. #4778C22semidirect
100. #4776C22semidirect
101. #4775C22semidirect
114. #3042D3semidirect
191. C2×#213D4semidirect
287. C22×SD16C2×D3semidirect
303. #536C2×D3semidirect
312. #518C2×D3semidirect
324. #463C2×D3semidirect
326. #461C2×D3semidirect
340. #424C2×D3semidirect
342. #419C2×D3semidirect
346. #416C2×D3semidirect
1033. C3#61051semidirect

Maximal subgroups

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

subgroupindex
C2×#57742
C22×#9162
#863542
#858582
C3×#30422
#839452
#838592
#834032
#825382
#805672
#805572
#804492
#804452
#790872
#790732
#789642
#789592
#788382
#788352
#610513