Finite Group Databasebeta

← #11670698

Subgroups — #11670698

Order 768.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#918C211yesmaximal, characteristic, complemented
2C2×#5751C211yesmaximal, characteristic, complemented
3#86355C211yesmaximal, characteristic, complemented
4#86354C211yesmaximal, characteristic, complemented
5C3×#3059C211yesmaximal, characteristic, complemented
6#83881C211yesmaximal, characteristic, complemented
7#83795C211yesmaximal, characteristic, complemented
8#83411C211yesmaximal, characteristic, complemented
9#83404C211yesmaximal, characteristic, complemented
10#80923C214yesmaximal, complemented
11#80922C214yesmaximal, complemented
12#80772C214yesmaximal, complemented
13#80771C214yesmaximal, complemented
14#79181C211yesmaximal, characteristic, complemented
15#79168C211yesmaximal, characteristic, complemented
16#78977C211yesmaximal, characteristic, complemented
17#78976C211yesmaximal, characteristic, complemented
18#78959C211yesmaximal, characteristic, complemented
19#78958C211yesmaximal, characteristic, complemented
20#61060—31nomaximal, Sylow
21C2×#1010C2211yescharacteristic
22C2×#1009C2211yescharacteristic
23C22×#239C2211yescharacteristic
24C22×D3×Q8C2211yescharacteristic, complemented
25C22×C3×Q16C2211yescharacteristic, complemented
26C2×C3×#131C2211yescharacteristic
27C3×#536C2211yescharacteristic
28C3×#536C2211yescharacteristic
29#5828C2211yescharacteristic
30#5816C2211yescharacteristic
31#5816C2211yescharacteristic, complemented
32C22×#216C2211yescharacteristic, complemented
33C2×#942C2211yescharacteristic
34C2×#942C2211yescharacteristic, complemented
35C22×#215C2211yescharacteristic
36C2×#918—28no—
37C2×#918C2214yescomplemented
38C2×#918C2214yescomplemented
39#5751—28no—
40C2×#909C2211yescharacteristic
41C2×#909C2212yescomplemented
42C2×#908C2211yescharacteristic
43C2×#908C2212yescomplemented
44C2×#904C2211yescharacteristic
45C2×#904C2212yescomplemented
46C22×#204C2211yescharacteristic
47C22×#204C2212yescomplemented
48C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
49#5727—22no—
50#5726—22no—
51#5677—22no—
52#5676—22no—
53#5656—22no—
54#5653—22no—
55D3×#123—22no—
56#5648—22no—
57#5633C2214yescomplemented
58#5632C2214yescomplemented
59#5631C2214yes—
60#5630C2214yes—
61#5524C2211yescharacteristic
62#5524C2211yescharacteristic, complemented
63#5521C2211yescharacteristic
64#5516C2211yescharacteristic, complemented
65C3×#470C2214yescomplemented
66C3×#467C2214yescomplemented
67C3×#427C2211yescharacteristic, complemented
68C3×#419C2211yescharacteristic, complemented
69C3×#419C2211yescharacteristic, complemented
70#5234C2211yescharacteristic
71#5191C2212yescomplemented
72#5190C2212yescomplemented
73#5190C2212yescomplemented
74#5183C2212yescomplemented
75#5128C2214yescomplemented
76#5126C2211yescharacteristic, complemented
77#5119C2211yescharacteristic, complemented
78#5111C2214yescomplemented
79#5101C2211yescharacteristic, complemented
80#5050C2214yescomplemented
81#5047C2214yescomplemented
82#5047C2214yescomplemented
83#5046C2214yescomplemented
84#5004C2211yescharacteristic, complemented
85#5002C2211yescharacteristic
86#5002C2211yescharacteristic, complemented
87#5001C2211yescharacteristic
88#4889C2214yescomplemented
89#4886C2212yescomplemented
90#4886C2212yescomplemented
91#4867C2212yescomplemented
92#4865C2212yescomplemented
93#4852C2214yescomplemented
94#4819C2214yescomplemented
95#4818C2214yescomplemented
96#4810C2214yescomplemented
97#4809C2214yescomplemented
98#4808C2214yescomplemented
99#4806C2214yescomplemented
100#4798C2214yescomplemented
101#4795C2214yescomplemented
102C2×#577—31no—
103C22×#137—31no—
104#3486—31no—
105#3485—31no—
106#3276—34no—
107#3275—34no—
108#3269—34no—
109#3266—34no—
110#3156—31no—
111#3059D311yescharacteristic, complemented
112#3054—31no—
113#3044—31no—
114#3042—31no—
115#3011—31no—
116#3009—31no—
117#3005—31no—
118#3004—31no—
119#2949—31no—
120#2930—31no—
121C2×C3×#41C2311yescharacteristic
122C22×C3×Q8C2311yescharacteristic
123C22×C3×Q8C2311yescharacteristic
124#1010—24no—
125#1010—42no—
126#1009—24no—
127#1009—42no—
128C2×#239—21no—
129C2×#239—22no—
130C2×#239—24no—
131C2×#239—42no—
132C2×#239C2314yes—
133C2×D3×Q8—21no—
134C2×D3×Q8—22no—
135C2×D3×Q8—24no—
136C2×D3×Q8—42no—
137C2×D3×Q8C2314yes—
138C2×#237—22no—
139C2×#237—21no—
140C2×D3×D4—22no—
141C2×D3×D4—21no—
142C2×#235C2311yescharacteristic
143C2×#235C2311yescharacteristic
144C2×#235C2312yes—
145C2×#235C2312yes—
146C22×D12—21no—
147C22×D12C2312yes—
148C22×D12C2311yescharacteristic
149C22×C4×D3—21no—
150C22×C4×D3—21no—
151C22×C4×D3C2311yescharacteristic
152C22×Dic6—21no—
153C22×Dic6C2312yes—
154C22×Dic6C2311yescharacteristic
155C2×C3×Q16—24no—
156C2×C3×Q16C2312yes—
157C2×C3×Q16C2312yes—
158C3×#131—24no—
159C2×C3×M16C2311yescharacteristic
160C2×C3×M16C2312yes—
161C22×C3×C8C2312yes—
162C22×C3×C8C2311yescharacteristic
163C3×C4⋊Q8—21no—
164C3×C4⋊Q8—21no—
165C3×#124—21no—
166C3×#124—21no—
167C3×#123—22no—
168C3×#123—22no—
169C3×C22⋊Q8C2314yes—
170C3×C22⋊Q8C2314yes—
171C3×#117C2311yescharacteristic
172C3×#117C2311yescharacteristic
173#947C2312yes—
174#947C2312yes—
175#946—22no—
176#946—22no—
177#946D412yes—
178#944C2312yes—
179#944C2312yes—
180C2×#216—24no—
181C2×#216C2314yes—
182C2×#216C2312yes—
183C2×#216C2312yes—
184#942—42no—
185#942—42no—
186C2×#215—24no—
187C2×#215C2314yes—
188C2×#215C2312yes—
189C2×#215C2312yes—
190#938D412yes—
191#937D412yes—
192#935D412yes—
193#929—22no—
194#929—22no—
195C4×#67C2314yes—
196#926C2311yescharacteristic
197C2×#208C2311yescharacteristic
198C22×C3⋊C8C2311yescharacteristic
199#918—216no—
200#918—216no—
201#909—24no—
202#909—28no—
203#908—24no—
204#908—28no—
205C2×Dic12C2311yescharacteristic
206C2×Dic12C2312yes—
207#904—24no—
208#904—28no—
209C2×D24C2311yescharacteristic
210C2×D24C2312yes—
211C2×#204—28no—
212C2×#204D418yescomplemented
213C2×#204C2311yescharacteristic
214C2×#204C2311yescharacteristic
215C2×#204C2312yes—
216C2×#204C2312yes—
217C2×#204C2312yes—
218C2×#204C2312yes—
219C2×ΓL(1,𝔽25)—24no—
220C2×ΓL(1,𝔽25)C2312yes—
221C2×ΓL(1,𝔽25)C2312yes—
222#897C2312yes—
223#897C2312yes—
224#896—24no—
225#896—24no—
226#895—24no—
227#895C2312yes—
228#895C2312yes—
229#894—24no—
230#894—24no—
231#893—24no—
232#893C2314yes—
233D3×C4⋊C4—24no—
234#888—24no—
235#887C2314yes—
236#886—21no—
237#886—21no—
238#885—24no—
239#884—24no—
240#884—24no—
241#883—24no—
242#882—21no—
243#882—21no—
244#882—24no—
245#67⋊C4—24no—
246D3×C22⋊C4—22no—
247D3×C22⋊C4—24no—
248#878—24no—
249#877—22no—
250C4×D12—22no—
251C4×D12—22no—
252C4×D12—22no—
253C4×Dic6—22no—
254C3×#107C2312yes—
255C3×#106C2312yes—
256C3×#103C2314yes—
257C3×#103C2314yes—
258#830C2314yes—
259(C2×D3)⋊C8C2314yes—
260#815C2312yes—
261Dic3⋊C8C2314yes—
262C8×Dic3C2312yes—
263#810C2312yes—
264#810C2312yes—
265#810C2314yes—
266#809C2312yes—
267#809C2312yes—
268#809C2314yes—
269C2×2−1+4—31no—
270C2×H(5,𝔽2)—31no—
271C22×#41—31no—
272C23×Q8—31no—
273#577—68no—
274C2×#137—31no—
275C2×#137—31no—
276C2×#137—34no—
277C2×#137—34no—
278C2×#137—31no—
279C2×#137—32no—
280C2×#137—68no—
281C2×AGL(1,ℤ/8)—31no—
282C2×AGL(1,ℤ/8)—32no—
283C2×#135—31no—
284C2×#135—32no—
285C22×Q16—31no—
286C22×Q16C2×D311yescharacteristic, complemented
287C22×SD16—31no—
288C22×SD16—31no—
289C22×SD16—32no—
290C2×#131C2×D311yescharacteristic
291C22×M16—31no—
292D4×Q8—34no—
293D4×Q8—62no—
294#548—34no—
295#548—62no—
296#547—34no—
297#547—62no—
298#546—34no—
299#546—62no—
300#536—31no—
301#536—31no—
302#536—62no—
303#536C2×D311yescharacteristic
304#536C2×D311yescharacteristic
305#534—62no—
306#525—31no—
307#525—31no—
308#525—31no—
309#525—62no—
310C2×#123—62no—
311#519—31no—
312#518—31no—
313#497—32no—
314#497—32no—
315#495—32no—
316#494—32no—
317#470—32no—
318#470C2×D314yescomplemented
319#469—32no—
320#468—32no—
321#468—32no—
322#467C2×D314yescomplemented
323#464—34no—
324#463—34no—
325#462—34no—
326#461—34no—
327#452—34no—
328#452—34no—
329#452—34no—
330#451—34no—
331#451—34no—
332#450—34no—
333#449—34no—
334#448—34no—
335#440—34no—
336C4×SD16—34no—
337#436—34no—
338#435—34no—
339#427C2×D311yescharacteristic, complemented
340#424—31no—
341#419—31no—
342#419C2×D311yescharacteristic, complemented
343#419C2×D311yescharacteristic, complemented
344#418—31no—
345#416—31no—
346#416—31no—
347#408—31no—
348#407—31no—
349#405—31no—
350C23×D3—21no—
351C23×D3—22no—
352C23×D3C2×D411yescharacteristic
353C3×#41—22no—
354C3×#41—22no—
355C2×C3×Q8—21no—
356C2×C3×Q8—21no—
357C2×C3×Q8—22no—
358C2×C3×Q8—22no—
359C2×C3×Q8—22no—
360C2×C3×Q8—22no—
361C2×C3×Q8C2×D411yescharacteristic
362C2×C3×Q8C2412yes—
363C2×C3×Q8C2412yes—
364C2×C3×D4C2×D412yes—
365C2×C3×D4C2×D411yescharacteristic
366C22×C3×C4—21no—
367C22×C3×C4—21no—
368C22×C3×C4C2412yes—
369C22×C3×C4C2411yescharacteristic
370C2×#67—21no—
371C2×#67—21no—
372C2×#67—22no—
373C2×#67—22no—
374C2×#67C2×D414yes—
375C22×Dic3—21no—
376C22×Dic3—22no—
377C22×Dic3C2×D411yescharacteristic
378#239—28no—
379#239—44no—
380#239—48no—
381#239—44no—
382D3×Q8—28no—
383D3×Q8—44no—
384D3×Q8—48no—
385D3×Q8—44no—
386#237—44no—
387#237—48no—
388D3×D4—44no—
389D3×D4—48no—
390#235—22no—
391#235—22no—
392#235—22no—
393#235—22no—
394#235—24no—
395#235—24no—
396#235—42no—
397#235—42no—
398C2×D12—21no—
399C2×D12—22no—
400C2×D12—24no—
401C2×D12—22no—
402C2×D12—24no—
403C2×D12—22no—
404C2×D12—22no—
405C2×D12—42no—
406C2×D12—44no—
407C2×D12C2×D414yes—
408C2×D12C2411yescharacteristic
409C2×D12C2411yescharacteristic
410C2×D12C2412yes—
411C2×C4×D3—22no—
412C2×C4×D3—22no—
413C2×C4×D3—24no—
414C2×C4×D3—21no—
415C2×C4×D3—21no—
416C2×C4×D3—22no—
417C2×C4×D3—22no—
418C2×C4×D3—24no—
419C2×C4×D3—24no—
420C2×C4×D3—44no—
421C2×C4×D3—44no—
422C2×C4×D3C2×D412yes—
423C2×C4×D3C2412yes—
424C2×Dic6—21no—
425C2×Dic6—22no—
426C2×Dic6—24no—
427C2×Dic6—22no—
428C2×Dic6—24no—
429C2×Dic6—42no—
430C2×Dic6—44no—
431C2×Dic6C2×D414yes—
432C2×Dic6C2411yescharacteristic
433C2×Dic6C2411yescharacteristic
434C2×Dic6C2412yes—
435C3×Q16—24no—
436C3×Q16—24no—
437C3×M16—22no—
438C3×M16—24no—
439C2×C3×C8—24no—
440C2×C3×C8C2×D414yes—
441C2×C3×C8C2412yes—
442C2×C3×C8C2411yescharacteristic
443C2×C3×C8C2411yescharacteristic
444C3×C4⋊C4—24no—
445C3×C4⋊C4—24no—
446C3×C4⋊C4C2412yes—
447C3×C4⋊C4C2412yes—
448C3×C22⋊C4—21no—
449C3×C22⋊C4—24no—
450C3×C22⋊C4—21no—
451C3×C22⋊C4—24no—
452C3×C42—21no—
453C3×C42—21no—
454#217C2×D412yes—
455#217C2×D414yes—
456#216—28no—
457#216—42no—
458#216—42no—
459#215—28no—
460#215—42no—
461#215—42no—
462(C2×D3)⋊C4—22no—
463(C2×D3)⋊C4—22no—
464(C2×D3)⋊C4—22no—
465(C2×D3)⋊C4—24no—
466(C2×D3)⋊C4—22no—
467(C2×D3)⋊C4—24no—
468(C2×D3)⋊C4—24no—
469(C2×D3)⋊C4C2×D414yes—
470C4⋊Dic3—22no—
471C4⋊Dic3—22no—
472C4⋊Dic3C2×D412yes—
473Dic3⋊C4—24no—
474Dic3⋊C4—24no—
475Dic3⋊C4—24no—
476Dic3⋊C4C2×D414yes—
477C4×Dic3—24no—
478C4×Dic3C2412yes—
479#208—22no—
480C2×C3⋊C8—22no—
481C2×C3⋊C8C2412yes—
482C2×C3⋊C8C2412yes—
483Dic12—24no—
484Dic12—22no—
485D24—24no—
486D24—22no—
487#204—24no—
488#204—24no—
489#204—22no—
490#204—22no—
491#204C2×D418yes—
492#204C2×D418yes—
493ΓL(1,𝔽25)—24no—
494ΓL(1,𝔽25)—24no—
4952−1+4—64no—
4962−1+4—122no—
497H(5,𝔽2)—64no—
498H(5,𝔽2)—122no—
499C2×#41—34no—
500C2×#41—31no—
501C2×#41—31no—
502C2×#41—32no—
503C2×#41—32no—
504C2×#41—62no—
505C2×#41—61no—
506C2×#41—62no—
507C2×#41—61no—
508C2×#41—64no—
509C2×#41—122no—
510C2×#41C22×D311yescharacteristic
511C22×Q8—34no—
512C22×Q8—31no—
513C22×Q8—32no—
514C22×Q8—61no—
515C22×Q8—62no—
516C22×Q8—61no—
517C22×Q8—64no—
518C22×Q8—122no—
519C22×Q8C22×D311yescharacteristic
520C22×Q8C22×D311yescharacteristic
521C22×D4—31no—
522C22×D4—32no—
523C22×D4—61no—
524C22×D4—62no—
525C22×D4—61no—
526C23×C4—31no—
527C23×C4—61no—
528C23×C4—61no—
529#137—68no—
530#137—64no—
531#137—616no—
532#137—616no—
533#137—122no—
534#137—122no—
535AGL(1,ℤ/8)—68no—
536AGL(1,ℤ/8)—64no—
537#135—68no—
538#135—64no—
539C2×Q16—24no—
540C2×Q16—34no—
541C2×Q16—32no—
542C2×Q16—32no—
543C2×Q16—32no—
544C2×Q16—31no—
545C2×Q16—64no—
546C2×Q16C22×D312yes—
547C2×Q16C22×D312yes—
548C2×SD16—34no—
549C2×SD16—32no—
550C2×SD16—32no—
551C2×SD16—38no—
552C2×SD16—32no—
553C2×SD16—32no—
554C2×SD16—31no—
555C2×SD16—32no—
556C2×SD16—32no—
557C2×SD16—31no—
558C2×SD16—68no—
559C2×SD16—64no—
560C2×D8—32no—
561C2×D8—31no—
562#131—24no—
563C2×M16—31no—
564C2×M16—32no—
565C2×M16—32no—
566C2×M16—64no—
567C2×M16C22×D311yescharacteristic
568C2×M16C22×D312yes—
569C22×C8—31no—
570C22×C8C22×D312yes—
571C22×C8C22×D311yescharacteristic
572C4⋊Q8—21no—
573C4⋊Q8—21no—
574C4⋊Q8—32no—
575C4⋊Q8—32no—
576C4⋊Q8—64no—
577#124—21no—
578#124—21no—
579#124—32no—
580#124—32no—
581#124—64no—
582#123—22no—
583#123—22no—
584#123—32no—
585#123—64no—
586#123—61no—
587#123—61no—
588#123—64no—
589#123—62no—
590#123—62no—
591#123—64no—
592C22⋊Q8—32no—
593C22⋊Q8—32no—
594C22⋊Q8—32no—
595C22⋊Q8—64no—
596C22⋊Q8—64no—
597C22⋊Q8—64no—
598C22⋊Q8—62no—
599C22⋊Q8—62no—
600C22⋊Q8C22×D314yes—
601C22⋊Q8C22×D314yes—
602#121—32no—
603#121—32no—
604#121—32no—
605#121—64no—
606#121—64no—
607#121—64no—
608#120—32no—
609#120—64no—
610#120—61no—
611#120—61no—
612C4×Q8—34no—
613C4×Q8—62no—
614C4×D4—34no—
615C4×D4—34no—
616C4×D4—62no—
617C4×D4—62no—
618C4×D4—62no—
619C4×D4—64no—
620C4×D4—64no—
621#117—31no—
622#117—62no—
623#117C22×D311yescharacteristic
624#117C22×D311yescharacteristic
625C2×C4⋊C4—64no—
626C2×C22⋊C4—62no—
627C2×C22⋊C4—64no—
628#107C22×D312yes—
629#106C22×D312yes—
630C4⋊C8—34no—
631#103—32no—
632#103—32no—
633#103—34no—
634#103C22×D314yes—
635#103C22×D314yes—
636#102—32no—
637#102—32no—
638#102—34no—
639C22⋊C8—34no—
640C22⋊C8—34no—
641#97—32no—
642C4×C8—32no—
643C23×C3C22×D412yes—
644C23×C3C22×D411yescharacteristic
645C22×D3—22no—
646C22×D3—22no—
647C22×D3—24no—
648C22×D3—21no—
649C22×D3—21no—
650C22×D3—42no—
651C22×D3—44no—
652C22×D3—82no—
653C22×D3—84no—
654C22×D3C22×D412yes—
655C3×Q8—22no—
656C3×Q8—22no—
657C3×Q8—22no—
658C3×Q8—22no—
659C3×Q8—22no—
660C3×Q8—42no—
661C3×Q8—42no—
662C3×D4—24no—
663C3×D4—22no—
664C2×C3×C4—22no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—42no—
671C2×C3×C4—42no—
672C2×C3×C4C22×D412yes—
673C2×C3×C4C22×D411yescharacteristic
674C2×C3×C4C22×D412yes—
675C2×C3×C4H(5,𝔽2)12yes—
676C2×C3×C4C2511yescharacteristic
677#67—44no—
678#67—44no—
679#67—44no—
680#67—42no—
681#67—42no—
682C2×Dic3—24no—
683C2×Dic3—22no—
684C2×Dic3—22no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—44no—
688C2×Dic3C22×D414yes—
689C2×Dic3C22×D412yes—
690D12—24no—
691D12—21no—
692D12—21no—
693D12—22no—
694D12—21no—
695D12—21no—
696D12—44no—
697D12—48no—
698D12—44no—
699D12—82no—
700D12C22×D414yes—
701C4×D3—24no—
702C4×D3—22no—
703C4×D3—22no—
704C4×D3—44no—
705C4×D3—48no—
706C4×D3—48no—
707C4×D3—44no—
708C4×D3—42no—
709C4×D3—42no—
710C4×D3—84no—
711Dic6—24no—
712Dic6—22no—
713Dic6—21no—
714Dic6—21no—
715Dic6—21no—
716Dic6—21no—
717Dic6—48no—
718Dic6—44no—
719Dic6C22×D414yes—
720C3×C8—22no—
721C3×C8C22×D412yes—
722C3×C8C22×D412yes—
723C3⋊C8—22no—
724C3⋊C8—22no—
725C24—31no—
726C24—61no—
727C24—62no—
728#41—22no—
729#41—22no—
730#41—64no—
731#41—64no—
732#41—68no—
733#41—62no—
734#41—62no—
735#41—62no—
736#41—62no—
737#41—122no—
738#41—122no—
739#41—128no—
740#41—124no—
741#41—128no—
742#41—124no—
743#41—124no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—22no—
747C2×Q8—22no—
748C2×Q8—22no—
749C2×Q8—22no—
750C2×Q8—34no—
751C2×Q8—32no—
752C2×Q8—31no—
753C2×Q8—31no—
754C2×Q8—64no—
755C2×Q8—64no—
756C2×Q8—61no—
757C2×Q8—62no—
758C2×Q8—62no—
759C2×Q8—68no—
760C2×Q8—122no—
761C2×Q8—124no—
762C2×Q8—124no—
763C2×Q8—128no—
764C2×Q8—124no—
765C2×Q8D3×D411yescharacteristic
766C2×Q8C23×D312yes—
767C2×Q8C23×D312yes—
768C2×D4—34no—
769C2×D4—34no—
770C2×D4—32no—
771C2×D4—31no—
772C2×D4—31no—
773C2×D4—64no—
774C2×D4—62no—
775C2×D4—64no—
776C2×D4—62no—
777C2×D4—61no—
778C2×D4—61no—
779C2×D4—62no—
780C2×D4—62no—
781C2×D4—61no—
782C2×D4—62no—
783C2×D4—62no—
784C2×D4—122no—
785C2×D4—124no—
786C2×D4—124no—
787C2×D4—128no—
788C2×D4D3×D412yes—
789C2×D4D3×D411yescharacteristic
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—31no—
793C22×C4—32no—
794C22×C4—32no—
795C22×C4—64no—
796C22×C4—64no—
797C22×C4—64no—
798C22×C4—61no—
799C22×C4—62no—
800C22×C4—62no—
801C22×C4—62no—
802C22×C4—62no—
803C22×C4—61no—
804C22×C4—62no—
805C22×C4—61no—
806C22×C4—124no—
807C22×C4—124no—
808C22×C4C23×D312yes—
809C22×C4C23×D311yescharacteristic
810Q16—24no—
811Q16—24no—
812Q16—64no—
813Q16—68no—
814Q16—62no—
815Q16—122no—
816Q16—122no—
817SD16—38no—
818SD16—38no—
819SD16—64no—
820SD16—64no—
821SD16—68no—
822SD16—62no—
823SD16—62no—
824SD16—122no—
825SD16—122no—
826D8—64no—
827D8—62no—
828M16—22no—
829M16—24no—
830M16—62no—
831M16—64no—
832M16—64no—
833C2×C8—24no—
834C2×C8—32no—
835C2×C8—32no—
836C2×C8—62no—
837C2×C8D3×D414yes—
838C2×C8C23×D312yes—
839C2×C8C23×D311yescharacteristic
840C2×C8C23×D311yescharacteristic
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—34no—
844C4⋊C4—32no—
845C4⋊C4—62no—
846C4⋊C4—64no—
847C4⋊C4—64no—
848C4⋊C4—62no—
849C4⋊C4—64no—
850C4⋊C4C23×D312yes—
851C4⋊C4C23×D312yes—
852C22⋊C4—21no—
853C22⋊C4—24no—
854C22⋊C4—21no—
855C22⋊C4—24no—
856C22⋊C4—32no—
857C22⋊C4—34no—
858C22⋊C4—34no—
859C22⋊C4—62no—
860C22⋊C4—64no—
861C22⋊C4—64no—
862C22⋊C4—62no—
863C22⋊C4—64no—
864C22⋊C4—62no—
865C22⋊C4—62no—
866C42—21no—
867C42—21no—
868C42—32no—
869C42—64no—
870C22×C3—22no—
871C22×C3—24no—
872C22×C3—22no—
873C22×C3D4212yes—
874C22×C3C23×D411yescharacteristic
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—22no—
878C2×D3—24no—
879C2×D3—44no—
880C2×D3—44no—
881C2×D3—42no—
882C2×D3—42no—
883C2×D3—41no—
884C2×D3—41no—
885C2×D3—84no—
886C2×D3—164no—
887C3×C4—22no—
888C3×C4—42no—
889C3×C4—42no—
890C3×C4—42no—
891C3×C4—42no—
892C3×C4D4212yes—
893C3×C4C23×D411yescharacteristic
894C3×C4C2×H(5,𝔽2)11yescharacteristic
895Dic3—24no—
896Dic3—24no—
897Dic3—22no—
898Dic3—41no—
899Dic3—41no—
900C23—32no—
901C23—62no—
902C23—62no—
903C23—64no—
904C23—61no—
905C23—61no—
906C23—122no—
907C23—124no—
908C23—242no—
909C23—244no—
910C23C2×D3×D412yes—
911C23C2×D3×D411yescharacteristic
912Q8—22no—
913Q8—22no—
914Q8—22no—
915Q8—22no—
916Q8—22no—
917Q8—34no—
918Q8—42no—
919Q8—42no—
920Q8—62no—
921Q8—64no—
922Q8—61no—
923Q8—61no—
924Q8—61no—
925Q8—61no—
926Q8—124no—
927Q8—128no—
928D4—24no—
929D4—22no—
930D4—34no—
931D4—61no—
932D4—61no—
933D4—62no—
934D4—61no—
935D4—61no—
936D4—64no—
937D4—124no—
938D4—128no—
939D4—124no—
940D4—124no—
941D4—124no—
942D4—124no—
943D4—122no—
944D4—122no—
945D4—242no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—34no—
953C2×C4—32no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—62no—
957C2×C4—62no—
958C2×C4—64no—
959C2×C4—62no—
960C2×C4—62no—
961C2×C4—64no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—124no—
965C2×C4—124no—
966C2×C4—128no—
967C2×C4—128no—
968C2×C4—124no—
969C2×C4—122no—
970C2×C4—122no—
971C2×C4—244no—
972C2×C4C2×D3×D412yes—
973C2×C4C2×D3×D412yes—
974C2×C4C2×D3×D411yescharacteristic
975C2×C4#100912yes—
976C2×C4C24×D311yescharacteristic
977C8—22no—
978C8—62no—
979C8—62no—
980C8C2×D3×D412yes—
981C8C2×D3×D412yes—
982C2×C3—22no—
983C2×C3—42no—
984C2×C3C2×D4211yescharacteristic
985C2×C3#358612yes—
986D3—42no—
987D3—44no—
988D3—81no—
989D3—81no—
990C22—22no—
991C22—24no—
992C22—22no—
993C22—62no—
994C22—62no—
995C22—62no—
996C22—64no—
997C22—124no—
998C22—124no—
999C22—122no—
1000C22—122no—
1001C22—121no—
1002C22—121no—
1003C22—244no—
1004C22—484no—
1005C22#560912yes—
1006C22C22×D3×D411yescharacteristic
1007C4—22no—
1008C4—42no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—64no—
1013C4—62no—
1014C4—64no—
1015C4—121no—
1016C4—121no—
1017C4#560912yes—
1018C4C22×D3×D411yescharacteristic
1019C4C2×#100911yescharacteristic
1020C3#6106011yescharacteristic, complemented, Sylow
1021C2—22no—
1022C2—42no—
1023C2—122no—
1024C2—124no—
1025C2—241no—
1026C2—241no—
1027C2C2×#560911yescharacteristic
1028C2#8721112yes—
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3059C2
socleC22×C3C23×D4
hypercenter#3059D3
hypocenterC3#61060
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3059

Complements

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

NH ≅ G/Ntype
1. C22×#918C2semidirect
2. C2×#5751C2semidirect
3. #86355C2semidirect
4. #86354C2semidirect
5. C3×#3059C2semidirect
6. #83881C2semidirect
7. #83795C2semidirect
8. #83411C2semidirect
9. #83404C2semidirect
10. #80923C2semidirect
11. #80922C2semidirect
12. #80772C2semidirect
13. #80771C2semidirect
14. #79181C2semidirect
15. #79168C2semidirect
16. #78977C2semidirect
17. #78976C2semidirect
18. #78959C2semidirect
19. #78958C2semidirect
24. C22×D3×Q8C22semidirect
25. C22×C3×Q16C22semidirect
31. #5816C22semidirect
32. C22×#216C22semidirect
34. C2×#942C22semidirect
37. C2×#918C22semidirect
38. C2×#918C22semidirect
41. C2×#909C22semidirect
43. C2×#908C22semidirect
45. C2×#904C22semidirect
47. C22×#204C22semidirect
48. C22×ΓL(1,𝔽25)C22semidirect
57. #5633C22semidirect
58. #5632C22semidirect
62. #5524C22semidirect
64. #5516C22semidirect
65. C3×#470C22semidirect
66. C3×#467C22semidirect
67. C3×#427C22semidirect
68. C3×#419C22semidirect
69. C3×#419C22semidirect
71. #5191C22semidirect
72. #5190C22semidirect
73. #5190C22semidirect
74. #5183C22semidirect
75. #5128C22semidirect
76. #5126C22semidirect
77. #5119C22semidirect
78. #5111C22semidirect
79. #5101C22semidirect
80. #5050C22semidirect
81. #5047C22semidirect
82. #5047C22semidirect
83. #5046C22semidirect
84. #5004C22semidirect
86. #5002C22semidirect
88. #4889C22semidirect
89. #4886C22semidirect
90. #4886C22semidirect
91. #4867C22semidirect
92. #4865C22semidirect
93. #4852C22semidirect
94. #4819C22semidirect
95. #4818C22semidirect
96. #4810C22semidirect
97. #4809C22semidirect
98. #4808C22semidirect
99. #4806C22semidirect
100. #4798C22semidirect
101. #4795C22semidirect
111. #3059D3semidirect
212. C2×#204D4semidirect
286. C22×Q16C2×D3semidirect
318. #470C2×D3semidirect
322. #467C2×D3semidirect
339. #427C2×D3semidirect
342. #419C2×D3semidirect
343. #419C2×D3semidirect
1020. C3#61060semidirect

Maximal subgroups

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

subgroupindex
C22×#9182
C2×#57512
#863552
#863542
C3×#30592
#838812
#837952
#834112
#834042
#809232
#809222
#807722
#807712
#791812
#791682
#789772
#789762
#789592
#789582
#610603