Finite Group Databasebeta

← #11661698

Subgroups — #11661698

Order 768.

4746 conjugacy classes of subgroups.

The subgroup lattice has 1358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5968C211yesmaximal, characteristic
2C2×D3×#137C211yesmaximal, characteristic, complemented
3C22×#918C211yesmaximal, characteristic, complemented
4D3×#536C211yesmaximal, characteristic, complemented
5C3×#3011C211yesmaximal, characteristic, complemented
6#84117C211yesmaximal, characteristic, complemented
7#83982C211yesmaximal, characteristic, complemented
8#83884C211yesmaximal, characteristic, complemented
9#83404C211yesmaximal, characteristic, complemented
10#80229C214yesmaximal, complemented
11#80228C214yesmaximal, complemented
12#80185C214yesmaximal, complemented
13#80184C214yesmaximal, complemented
14#78961C211yesmaximal, characteristic, complemented
15#78956C211yesmaximal, characteristic, complemented
16#78835C211yesmaximal, characteristic, complemented
17#78830C211yesmaximal, characteristic, complemented
18#78671C211yesmaximal, characteristic, complemented
19#78662C211yesmaximal, characteristic, complemented
20#60370—31nomaximal, Sylow
21C2×C3×2−1+4C2211yescharacteristic
22#5968—28no—
23#5968—28no—
24C2×#1009—22no—
25C2×#1009—21no—
26C2×#1009C2211yescharacteristic
27C2×#1009C2212yes—
28C2×#1009C2211yescharacteristic
29C2×D3×#41—22no—
30C2×D3×#41—21no—
31C2×D3×#41C2212yes—
32C2×D3×#41C2211yescharacteristic
33C2×D3×#41C2211yescharacteristic
34C2×#1007—21no—
35C2×#1007C2212yes—
36C2×#1007C2211yescharacteristic
37C22×#239—21no—
38C22×#239C2212yes—
39C22×#239C2211yescharacteristic
40C22×D3×Q8C2211yescharacteristic, complemented
41C2×C3×#137C2211yescharacteristic, complemented
42C22×C3×Q16C2211yescharacteristic, complemented
43C3×#536C2211yescharacteristic, complemented
44#5825C2211yescharacteristic, complemented
45C2×#951C2211yescharacteristic, complemented
46#5816C2211yescharacteristic, complemented
47C22×#216C2211yescharacteristic, complemented
48C2×#942C2211yescharacteristic, complemented
49C22×#215C2211yescharacteristic, complemented
50D3×#137—28no—
51C2×#918—28no—
52C2×#918C2212yescomplemented
53C2×#918C2214yescomplemented
54C2×#918C2214yescomplemented
55C2×D3×Q16C2212yescomplemented
56C2×#915C2212yescomplemented
57C2×D3×SD16C2212yescomplemented
58C2×#909C2211yescharacteristic, complemented
59C2×D3×M16C2211yescharacteristic, complemented
60C22×#204C2211yescharacteristic, complemented
61C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
62#5724—21no—
63D3×C4⋊Q8—21no—
64#5675—21no—
65D3×#124—21no—
66D3×#123—22no—
67#5648—22no—
68#5628C2214yescomplemented
69D3×C22⋊Q8C2214yescomplemented
70#5526C2211yescharacteristic, complemented
71D3×#117C2211yescharacteristic, complemented
72C3×#452C2214yescomplemented
73C3×#451C2214yescomplemented
74C3×#419C2211yescharacteristic, complemented
75C3×#416C2211yescharacteristic, complemented
76C3×#408C2211yescharacteristic, complemented
77#5239C2214yescomplemented
78#5234C2211yescharacteristic, complemented
79#5233C2211yescharacteristic, complemented
80#5228C2214yescomplemented
81#5225C2211yescharacteristic, complemented
82#5187C2214yescomplemented
83#5187C2214yescomplemented
84#5186C2214yescomplemented
85#5169C2214yescomplemented
86#5131C2211yescharacteristic, complemented
87#5129C2211yescharacteristic, complemented
88#5113C2211yescharacteristic, complemented
89#5110C2211yescharacteristic, complemented
90#5047C2214yescomplemented
91#5046C2214yescomplemented
92#5002C2211yescharacteristic, complemented
93#5001C2211yescharacteristic, complemented
94#4809C2214yescomplemented
95#4808C2214yescomplemented
96#4808C2214yescomplemented
97#4804C2214yescomplemented
98#4803C2212yescomplemented
99#4803C2214yescomplemented
100#4802C2212yescomplemented
101#4776C2214yescomplemented
102#4771C2212yescomplemented
103#4770C2212yescomplemented
104#4733C2214yescomplemented
105#4731C2214yescomplemented
106#4727C2214yescomplemented
107#4726C2214yescomplemented
108C2×#585—31no—
109C22×#137—31no—
110C22×#137—31no—
111C2×#536—31no—
112#3011—34no—
113#3011—31no—
114#3011—31no—
115#3011—31no—
116#3011D311yescharacteristic, complemented
117#3009—34no—
118#3009—31no—
119#3009—31no—
120#3009—31no—
121#3009—31no—
122#3007—34no—
123#3007—34no—
124#2896—31no—
125#2896—31no—
126#2879—31no—
127C3×2−1+4—24no—
128C3×2−1+4—24no—
129C2×C3×#41—22no—
130C2×C3×#41—21no—
131C2×C3×#41C2312yes—
132C2×C3×#41C2311yescharacteristic
133C2×C3×#41C2311yescharacteristic
134C22×C3×Q8—21no—
135C22×C3×Q8C2311yescharacteristic
136C22×C3×Q8C2312yes—
137C22×C3×Q8C2311yescharacteristic
138#1009—216no—
139#1009—232no—
140#1009—24no—
141#1009—28no—
142#1009—28no—
143#1009—24no—
144#1009—24no—
145#1009—24no—
146D3×#41—232no—
147D3×#41—216no—
148D3×#41—28no—
149D3×#41—28no—
150D3×#41—24no—
151D3×#41—24no—
152D3×#41—24no—
153D3×#41D418yes—
154#1007—216no—
155#1007—24no—
156#1007—28no—
157#1007—28no—
158#1007—24no—
159C2×#239—216no—
160C2×#239—21no—
161C2×#239—28no—
162C2×#239—28no—
163C2×#239—21no—
164C2×#239—22no—
165C2×#239—22no—
166C2×#239—21no—
167C2×#239—22no—
168C2×#239—21no—
169C2×#239—24no—
170C2×#239D418yes—
171C2×#239D411yescharacteristic
172C2×#239C2312yes—
173C2×#239C2312yes—
174C2×#239C2311yescharacteristic
175C2×#239C2312yes—
176C2×#239C2312yes—
177C2×D3×Q8—21no—
178C2×D3×Q8—21no—
179C2×D3×Q8—21no—
180C2×D3×Q8—22no—
181C2×D3×Q8—24no—
182C2×D3×Q8—24no—
183C2×D3×Q8D411yescharacteristic
184C2×D3×Q8C2312yes—
185C2×D3×Q8C2312yes—
186C2×D3×Q8C2312yes—
187C2×D3×Q8C2311yescharacteristic
188C2×#237—22no—
189C2×#237—21no—
190C2×#237D412yes—
191C2×#237D411yescharacteristic
192C2×#237C2311yescharacteristic
193C2×D3×D4—22no—
194C2×D3×D4—21no—
195C2×D3×D4—22no—
196C2×D3×D4—21no—
197C2×D3×D4—22no—
198C2×D3×D4—22no—
199C2×D3×D4—22no—
200C2×D3×D4D412yes—
201C2×D3×D4D411yescharacteristic
202C2×D3×D4C2312yes—
203C2×D3×D4C2311yescharacteristic
204C2×#235—22no—
205C2×#235—22no—
206C2×#235—22no—
207C2×#235—22no—
208C2×#235—21no—
209C2×#235—21no—
210C2×#235—22no—
211C2×#235C2311yescharacteristic
212C2×#235C2312yes—
213C2×#235C2312yes—
214C2×#235C2311yescharacteristic
215C22×D12—22no—
216C22×D12—21no—
217C22×D12—21no—
218C22×D12—22no—
219C22×D12C2312yes—
220C22×D12C2311yescharacteristic
221C22×C4×D3—22no—
222C22×C4×D3—21no—
223C22×C4×D3—22no—
224C22×C4×D3—21no—
225C22×C4×D3—21no—
226C22×C4×D3C2312yes—
227C22×C4×D3C2311yescharacteristic
228C22×Dic6—21no—
229C22×Dic6C2311yescharacteristic
230C3×#137—24no—
231C2×C3×Q16—24no—
232C2×C3×Q16C2314yes—
233C2×C3×Q16C2312yes—
234C2×C3×SD16C2312yes—
235C2×C3×M16C2311yescharacteristic
236C22×C3×C8C2311yescharacteristic
237C3×C4⋊Q8—21no—
238C3×#124—21no—
239C3×#123—22no—
240C3×C22⋊Q8C2314yes—
241C3×#117C2311yescharacteristic
242#951—24no—
243#947—21no—
244#946C2314yes—
245#944—21no—
246#944—21no—
247C2×#216—24no—
248C2×#216C2312yes—
249C2×#216C2312yes—
250C2×#216C2314yes—
251#942—24no—
252C2×#215—24no—
253C2×#215C2314yes—
254C2×#215C2312yes—
255#936—21no—
256#935—22no—
257C2×#214C2312yes—
258#929—22no—
259#926C2311yescharacteristic
260#924C2314yes—
261C2×#208C2311yescharacteristic
262C22×C3⋊C8C2311yescharacteristic
263#918—216no—
264#918—216no—
265#918—28no—
266D3×Q16—28no—
267#915—28no—
268D3×SD16—28no—
269#909—24no—
270D3×M16—24no—
271C2×Dic12C2312yes—
272C2×#204—24no—
273C2×#204C2314yes—
274C2×#204C2312yes—
275C2×ΓL(1,𝔽25)—24no—
276C2×ΓL(1,𝔽25)C2312yes—
277C2×ΓL(1,𝔽25)C2312yes—
278C2×ΓL(1,𝔽25)C2312yes—
279C2×D3×C8C2312yes—
280#897C2314yes—
281#896—24no—
282#894—24no—
283#892C2312yes—
284D3×C4⋊C4—24no—
285D3×C4⋊C4C2312yes—
286#888—24no—
287#886—22no—
288#885—24no—
289#883—24no—
290D3×C22⋊C4—21no—
291D3×C22⋊C4—24no—
292#878—24no—
293#877—21no—
294#875—21no—
295#872—21no—
296C42×D3—21no—
297#869—21no—
298C3×#103C2312yes—
299C3×#103C2314yes—
300C3×#102C2312yes—
301C3×C22⋊C8C2314yes—
302#835C2314yes—
303#835C2312yes—
304#832C2312yes—
305#830C2314yes—
306#821C2314yes—
307#821C2312yes—
308(C2×D3)⋊C8C2314yes—
309(C2×D3)⋊C8C2314yes—
310#816C2312yes—
311#810C2312yes—
312#809C2314yes—
313#809C2312yes—
314#585—68no—
315#585—68no—
316C2×2−1+4—32no—
317C2×2−1+4—31no—
318C2×2−1+4—61no—
319C2×2−1+4C2×D311yescharacteristic
320C2×H(5,𝔽2)—32no—
321C2×H(5,𝔽2)—31no—
322C2×H(5,𝔽2)—31no—
323C2×H(5,𝔽2)—62no—
324C2×H(5,𝔽2)—61no—
325C22×#41—31no—
326C22×#41—31no—
327C22×#41—32no—
328C22×#41—31no—
329C22×#41—32no—
330C22×#41—61no—
331C22×#41—62no—
332C22×#41—61no—
333C23×Q8—31no—
334C2×#137—31no—
335C2×#137—31no—
336C2×#137—32no—
337C2×#137—34no—
338C2×#137—34no—
339C2×#137—32no—
340C2×#137—31no—
341C2×#137—68no—
342C2×#137—68no—
343C2×#137C2×D311yescharacteristic, complemented
344C22×Q16—31no—
345C22×Q16—32no—
346C22×Q16C2×D311yescharacteristic, complemented
347C22×SD16—31no—
348C22×SD16—32no—
349C22×SD16—31no—
350C22×M16—31no—
351C22×M16—31no—
352#536—31no—
353#536—31no—
354#536—34no—
355#536—31no—
356#536—62no—
357#536—61no—
358#536—61no—
359#536C2×D311yescharacteristic, complemented
360C2×C4⋊Q8—61no—
361C2×#124—61no—
362C2×#123—62no—
363C2×C22⋊Q8—34no—
364C2×#117—31no—
365#452—34no—
366#452—34no—
367#452—34no—
368#452—34no—
369#452—34no—
370#452—34no—
371#452—34no—
372#452C2×D314yescomplemented
373#451—34no—
374#451—34no—
375#451—34no—
376#451C2×D314yescomplemented
377#450—34no—
378#450—34no—
379#450—34no—
380#450—34no—
381#419—31no—
382#419—32no—
383#419C2×D311yescharacteristic, complemented
384#418—31no—
385#418—31no—
386#418—32no—
387#417—34no—
388#417—32no—
389#417—32no—
390#416—31no—
391#416—31no—
392#416—31no—
393#416—34no—
394#416C2×D311yescharacteristic, complemented
395#408—31no—
396#408—31no—
397#408—31no—
398#408—34no—
399#408C2×D311yescharacteristic, complemented
400#407—34no—
401C23×D3—22no—
402C23×D3—21no—
403C23×D3—22no—
404C23×D3—21no—
405C23×D3C2×D412yes—
406C23×D3C2×D411yescharacteristic
407C3×#41—216no—
408C3×#41—28no—
409C3×#41—24no—
410C3×#41—24no—
411C3×#41—22no—
412C3×#41—22no—
413C3×#41—22no—
414C3×#41C2×D414yes—
415C2×C3×Q8—28no—
416C2×C3×Q8—24no—
417C2×C3×Q8—24no—
418C2×C3×Q8—22no—
419C2×C3×Q8—21no—
420C2×C3×Q8—22no—
421C2×C3×Q8—21no—
422C2×C3×Q8—22no—
423C2×C3×Q8—22no—
424C2×C3×Q8C2×D414yes—
425C2×C3×Q8C2×D411yescharacteristic
426C2×C3×Q8C2412yes—
427C2×C3×Q8C2412yes—
428C2×C3×Q8C2411yescharacteristic
429C2×C3×D4—22no—
430C2×C3×D4—21no—
431C2×C3×D4C2×D412yes—
432C2×C3×D4C2×D411yescharacteristic
433C2×C3×D4C2411yescharacteristic
434C22×C3×C4—22no—
435C22×C3×C4—21no—
436C22×C3×C4—22no—
437C22×C3×C4—21no—
438C22×C3×C4—21no—
439C22×C3×C4C2412yes—
440C22×C3×C4C2411yescharacteristic
441C2×#67—22no—
442C2×#67—21no—
443C2×#67—21no—
444C2×#67—22no—
445C2×#67—21no—
446C2×#67C2×D412yes—
447C2×#67C2×D412yes—
448C2×#67C2×D412yes—
449C22×Dic3—21no—
450C22×Dic3—21no—
451C22×Dic3C2×D412yes—
452C22×Dic3C2×D411yescharacteristic
453#239—216no—
454#239—216no—
455#239—216no—
456#239—28no—
457#239—28no—
458#239—24no—
459#239—24no—
460#239—24no—
461#239—24no—
462#239—28no—
463#239—24no—
464#239—28no—
465#239—22no—
466#239—24no—
467#239—24no—
468#239C2×D414yes—
469#239C2×D418yes—
470#239C2×D418yes—
471D3×Q8—28no—
472D3×Q8—216no—
473D3×Q8—24no—
474D3×Q8—24no—
475D3×Q8—22no—
476D3×Q8—24no—
477D3×Q8—24no—
478D3×Q8—24no—
479D3×Q8—24no—
480D3×Q8—24no—
481D3×Q8—44no—
482D3×Q8—44no—
483D3×Q8C2×D414yes—
484#237—216no—
485#237—28no—
486#237—28no—
487#237—24no—
488#237—22no—
489#237C2×D414yes—
490D3×D4—216no—
491D3×D4—216no—
492D3×D4—216no—
493D3×D4—216no—
494D3×D4—28no—
495D3×D4—216no—
496D3×D4—28no—
497D3×D4—28no—
498D3×D4—24no—
499D3×D4—24no—
500D3×D4—24no—
501D3×D4—22no—
502D3×D4C2×D414yes—
503#235—216no—
504#235—216no—
505#235—216no—
506#235—28no—
507#235—216no—
508#235—216no—
509#235—22no—
510#235—22no—
511#235—22no—
512#235—24no—
513#235—28no—
514#235—24no—
515#235—24no—
516#235—24no—
517#235C2×D414yes—
518C2×D12—216no—
519C2×D12—216no—
520C2×D12—28no—
521C2×D12—28no—
522C2×D12—22no—
523C2×D12—22no—
524C2×D12—22no—
525C2×D12—21no—
526C2×D12—22no—
527C2×D12—22no—
528C2×D12—21no—
529C2×D12—22no—
530C2×D12—24no—
531C2×D12—24no—
532C2×D12C2×D411yescharacteristic
533C2×D12C2×D412yes—
534C2×D12C2×D414yes—
535C2×D12C2411yescharacteristic
536C2×D12C2412yes—
537C2×C4×D3—216no—
538C2×C4×D3—216no—
539C2×C4×D3—22no—
540C2×C4×D3—21no—
541C2×C4×D3—22no—
542C2×C4×D3—21no—
543C2×C4×D3—28no—
544C2×C4×D3—22no—
545C2×C4×D3—21no—
546C2×C4×D3—22no—
547C2×C4×D3—22no—
548C2×C4×D3—22no—
549C2×C4×D3—28no—
550C2×C4×D3—24no—
551C2×C4×D3—24no—
552C2×C4×D3—22no—
553C2×C4×D3—22no—
554C2×C4×D3—22no—
555C2×C4×D3—44no—
556C2×C4×D3C2×D412yes—
557C2×C4×D3C2×D412yes—
558C2×C4×D3C2×D411yescharacteristic
559C2×C4×D3C2×D411yescharacteristic
560C2×C4×D3C2×D414yes—
561C2×C4×D3C2×D414yes—
562C2×C4×D3C2412yes—
563C2×C4×D3C2411yescharacteristic
564C2×C4×D3C2411yescharacteristic
565C2×Dic6—22no—
566C2×Dic6—21no—
567C2×Dic6—22no—
568C2×Dic6—22no—
569C2×Dic6—21no—
570C2×Dic6—22no—
571C2×Dic6—22no—
572C2×Dic6—44no—
573C2×Dic6C2×D411yescharacteristic
574C2×Dic6C2×D412yes—
575C2×Dic6C2412yes—
576C2×Dic6C2411yescharacteristic
577C3×Q16—24no—
578C3×Q16—28no—
579C3×SD16—24no—
580C3×M16—22no—
581C2×C3×C8—22no—
582C2×C3×C8C2412yes—
583C2×C3×C8C2412yes—
584C3×C4⋊C4—24no—
585C3×C4⋊C4C2412yes—
586C3×C22⋊C4—21no—
587C3×C22⋊C4—24no—
588C3×C42—21no—
589#217—21no—
590#217—24no—
591#216—24no—
592#216—28no—
593#216—24no—
594#215—24no—
595#215—28no—
596#214—24no—
597(C2×D3)⋊C4—22no—
598(C2×D3)⋊C4—24no—
599(C2×D3)⋊C4—24no—
600C4⋊Dic3—24no—
601C4⋊Dic3C2412yes—
602Dic3⋊C4—24no—
603Dic3⋊C4—22no—
604Dic3⋊C4—24no—
605C4×Dic3—21no—
606C4×Dic3—22no—
607#208—22no—
608C2×C3⋊C8—22no—
609C2×C3⋊C8C2412yes—
610C2×C3⋊C8C2412yes—
611Dic12—24no—
612#204—28no—
613#204—24no—
614ΓL(1,𝔽25)—24no—
615ΓL(1,𝔽25)—24no—
616ΓL(1,𝔽25)—24no—
617D3×C8—24no—
6182−1+4—24no—
6192−1+4—24no—
6202−1+4—68no—
6212−1+4—68no—
6222−1+4—64no—
6232−1+4—616no—
6242−1+4—64no—
625H(5,𝔽2)—68no—
626H(5,𝔽2)—64no—
627H(5,𝔽2)—64no—
628H(5,𝔽2)—64no—
629H(5,𝔽2)—68no—
630H(5,𝔽2)—632no—
631H(5,𝔽2)—616no—
632H(5,𝔽2)—64no—
633C2×#41—22no—
634C2×#41—21no—
635C2×#41—31no—
636C2×#41—32no—
637C2×#41—31no—
638C2×#41—32no—
639C2×#41—31no—
640C2×#41—38no—
641C2×#41—38no—
642C2×#41—31no—
643C2×#41—32no—
644C2×#41—32no—
645C2×#41—32no—
646C2×#41—32no—
647C2×#41—31no—
648C2×#41—31no—
649C2×#41—32no—
650C2×#41—61no—
651C2×#41—62no—
652C2×#41—62no—
653C2×#41—62no—
654C2×#41—62no—
655C2×#41—62no—
656C2×#41—61no—
657C2×#41—61no—
658C2×#41—62no—
659C2×#41—61no—
660C2×#41—62no—
661C2×#41—61no—
662C2×#41—62no—
663C2×#41—64no—
664C2×#41—64no—
665C2×#41—64no—
666C2×#41—64no—
667C2×#41—62no—
668C2×#41—61no—
669C2×#41—68no—
670C2×#41—68no—
671C2×#41—616no—
672C2×#41—68no—
673C2×#41—68no—
674C2×#41—632no—
675C2×#41—616no—
676C2×#41—61no—
677C2×#41C22×D312yes—
678C2×#41C22×D311yescharacteristic
679C2×#41C22×D311yescharacteristic
680C22×Q8—21no—
681C22×Q8—31no—
682C22×Q8—31no—
683C22×Q8—32no—
684C22×Q8—32no—
685C22×Q8—32no—
686C22×Q8—31no—
687C22×Q8—61no—
688C22×Q8—61no—
689C22×Q8—61no—
690C22×Q8—64no—
691C22×Q8—64no—
692C22×Q8—62no—
693C22×Q8—61no—
694C22×Q8C22×D311yescharacteristic
695C22×Q8C22×D312yes—
696C22×Q8C22×D311yescharacteristic
697C22×D4—31no—
698C22×D4—32no—
699C22×D4—31no—
700C22×D4—32no—
701C22×D4—31no—
702C22×D4—32no—
703C22×D4—62no—
704C22×D4—61no—
705C22×D4—61no—
706C22×D4—62no—
707C22×D4—62no—
708C22×D4—62no—
709C22×D4—62no—
710C22×D4—61no—
711C22×D4—62no—
712C22×D4—62no—
713C22×D4—61no—
714C23×C4—31no—
715C23×C4—32no—
716C23×C4—61no—
717C23×C4—62no—
718C23×C4—61no—
719C23×C4—62no—
720C23×C4—61no—
721#137—24no—
722#137—64no—
723#137—68no—
724#137—616no—
725#137—616no—
726#137—68no—
727#137—64no—
728#137—64no—
729C2×Q16—24no—
730C2×Q16—32no—
731C2×Q16—34no—
732C2×Q16—32no—
733C2×Q16—32no—
734C2×Q16—68no—
735C2×Q16—64no—
736C2×Q16C22×D312yes—
737C2×Q16C22×D314yes—
738C2×SD16—34no—
739C2×SD16—32no—
740C2×SD16—32no—
741C2×SD16—32no—
742C2×SD16—34no—
743C2×SD16—64no—
744C2×SD16—68no—
745C2×SD16—64no—
746C2×SD16C22×D312yes—
747C2×M16—31no—
748C2×M16—32no—
749C2×M16—32no—
750C2×M16—32no—
751C2×M16—64no—
752C2×M16—64no—
753C2×M16C22×D311yescharacteristic
754C22×C8—31no—
755C22×C8—32no—
756C22×C8C22×D311yescharacteristic
757C4⋊Q8—21no—
758C4⋊Q8—61no—
759C4⋊Q8—64no—
760C4⋊Q8—61no—
761C4⋊Q8—61no—
762#124—21no—
763#124—61no—
764#124—64no—
765#124—61no—
766#124—61no—
767#123—22no—
768#123—64no—
769#123—62no—
770#123—64no—
771#123—62no—
772#123—62no—
773C22⋊Q8—34no—
774C22⋊Q8—34no—
775C22⋊Q8—34no—
776C22⋊Q8—64no—
777C22⋊Q8—64no—
778C22⋊Q8C22×D314yes—
779#117—31no—
780#117—32no—
781#117—61no—
782#117—61no—
783#117C22×D311yescharacteristic
784C2×C4⋊C4—32no—
785C2×C4⋊C4—64no—
786C2×C22⋊C4—61no—
787C2×C22⋊C4—64no—
788C2×C42—61no—
789#103—34no—
790#103—32no—
791#103—32no—
792#103—32no—
793#103C22×D314yes—
794#103C22×D312yes—
795#102—32no—
796#102—34no—
797#102—32no—
798#102—34no—
799#102—32no—
800#102C22×D312yes—
801C22⋊C8—34no—
802C22⋊C8—34no—
803C22⋊C8—34no—
804C22⋊C8C22×D314yes—
805C23×C3—21no—
806C23×C3C22×D412yes—
807C23×C3C22×D411yescharacteristic
808C22×D3—21no—
809C22×D3—22no—
810C22×D3—28no—
811C22×D3—28no—
812C22×D3—24no—
813C22×D3—24no—
814C22×D3—24no—
815C22×D3—42no—
816C22×D3—44no—
817C22×D3—82no—
818C22×D3—84no—
819C22×D3—82no—
820C22×D3—84no—
821C22×D3#12014yes—
822C22×D3C22×D412yes—
823C22×D3C22×D411yescharacteristic
824C22×D3C22×D411yescharacteristic
825C3×Q8—28no—
826C3×Q8—24no—
827C3×Q8—22no—
828C3×Q8—21no—
829C3×Q8—22no—
830C3×Q8—22no—
831C3×Q8—22no—
832C3×Q8—42no—
833C3×Q8C22×D414yes—
834C3×Q8C22×D412yes—
835C3×D4—28no—
836C3×D4—24no—
837C3×D4—24no—
838C3×D4—22no—
839C3×D4—21no—
840C3×D4C22×D412yes—
841C2×C3×C4—28no—
842C2×C3×C4—28no—
843C2×C3×C4—24no—
844C2×C3×C4—22no—
845C2×C3×C4—21no—
846C2×C3×C4—24no—
847C2×C3×C4—22no—
848C2×C3×C4—22no—
849C2×C3×C4—22no—
850C2×C3×C4—22no—
851C2×C3×C4—42no—
852C2×C3×C4C22×D412yes—
853C2×C3×C4C22×D411yescharacteristic
854C2×C3×C4C22×D412yes—
855C2×C3×C4C22×D412yes—
856C2×C3×C4C2511yescharacteristic
857#67—28no—
858#67—28no—
859#67—24no—
860#67—24no—
861#67—24no—
862#67—24no—
863#67—24no—
864#67—24no—
865C2×Dic3—21no—
866C2×Dic3—24no—
867C2×Dic3—24no—
868C2×Dic3—22no—
869C2×Dic3—22no—
870C2×Dic3—42no—
871C2×Dic3#12014yes—
872C2×Dic3C22×D412yes—
873C2×Dic3C22×D411yescharacteristic
874C2×Dic3C22×D411yescharacteristic
875D12—28no—
876D12—28no—
877D12—28no—
878D12—24no—
879D12—28no—
880D12—28no—
881D12—24no—
882D12—22no—
883D12—24no—
884D12—21no—
885D12—22no—
886D12C22×D412yes—
887D12C22×D414yes—
888C4×D3—28no—
889C4×D3—28no—
890C4×D3—28no—
891C4×D3—28no—
892C4×D3—24no—
893C4×D3—24no—
894C4×D3—24no—
895C4×D3—22no—
896C4×D3—22no—
897C4×D3—28no—
898C4×D3—24no—
899C4×D3—24no—
900C4×D3—28no—
901C4×D3—44no—
902C4×D3—44no—
903C4×D3—44no—
904C4×D3#12014yes—
905C4×D3#12014yes—
906C4×D3C22×D412yes—
907C4×D3C22×D412yes—
908C4×D3C22×D412yes—
909C4×D3C22×D412yes—
910Dic6—28no—
911Dic6—22no—
912Dic6—21no—
913Dic6—24no—
914Dic6—24no—
915Dic6—22no—
916Dic6—22no—
917Dic6—42no—
918Dic6—44no—
919Dic6—44no—
920Dic6C22×D412yes—
921C3×C8—22no—
922C3×C8—22no—
923C3⋊C8—22no—
924C3⋊C8—22no—
925C24—31no—
926C24—32no—
927C24—61no—
928C24—62no—
929C24—62no—
930C24—61no—
931#41—216no—
932#41—28no—
933#41—24no—
934#41—24no—
935#41—22no—
936#41—22no—
937#41—22no—
938#41—34no—
939#41—38no—
940#41—38no—
941#41—34no—
942#41—34no—
943#41—64no—
944#41—64no—
945#41—68no—
946#41—64no—
947#41—64no—
948#41—616no—
949#41—616no—
950#41—616no—
951#41—616no—
952#41—616no—
953#41—68no—
954#41—68no—
955#41—68no—
956#41—62no—
957#41—64no—
958#41—64no—
959#41—62no—
960#41—64no—
961#41—68no—
962#41—64no—
963#41—68no—
964#41—616no—
965#41—64no—
966#41—64no—
967#41—616no—
968#41—616no—
969#41—616no—
970#41—68no—
971#41—68no—
972#41—64no—
973#41—64no—
974#41—62no—
975#41—62no—
976#41—62no—
977#41D3×D414yes—
978C2×Q8—28no—
979C2×Q8—24no—
980C2×Q8—24no—
981C2×Q8—22no—
982C2×Q8—21no—
983C2×Q8—22no—
984C2×Q8—21no—
985C2×Q8—22no—
986C2×Q8—22no—
987C2×Q8—32no—
988C2×Q8—31no—
989C2×Q8—34no—
990C2×Q8—31no—
991C2×Q8—32no—
992C2×Q8—61no—
993C2×Q8—62no—
994C2×Q8—62no—
995C2×Q8—62no—
996C2×Q8—62no—
997C2×Q8—64no—
998C2×Q8—64no—
999C2×Q8—64no—
1000C2×Q8—64no—
1001C2×Q8—64no—
1002C2×Q8—64no—
1003C2×Q8—616no—
1004C2×Q8—68no—
1005C2×Q8—64no—
1006C2×Q8—61no—
1007C2×Q8—62no—
1008C2×Q8—62no—
1009C2×Q8—124no—
1010C2×Q8—124no—
1011C2×Q8—124no—
1012C2×Q8D3×D414yes—
1013C2×Q8D3×D411yescharacteristic
1014C2×Q8C23×D312yes—
1015C2×Q8C23×D311yescharacteristic
1016C2×Q8C23×D312yes—
1017C2×D4—22no—
1018C2×D4—21no—
1019C2×D4—34no—
1020C2×D4—32no—
1021C2×D4—32no—
1022C2×D4—32no—
1023C2×D4—34no—
1024C2×D4—32no—
1025C2×D4—31no—
1026C2×D4—31no—
1027C2×D4—32no—
1028C2×D4—64no—
1029C2×D4—64no—
1030C2×D4—62no—
1031C2×D4—62no—
1032C2×D4—61no—
1033C2×D4—62no—
1034C2×D4—62no—
1035C2×D4—68no—
1036C2×D4—616no—
1037C2×D4—616no—
1038C2×D4—68no—
1039C2×D4—62no—
1040C2×D4—64no—
1041C2×D4—61no—
1042C2×D4—62no—
1043C2×D4—64no—
1044C2×D4—68no—
1045C2×D4—68no—
1046C2×D4—616no—
1047C2×D4—616no—
1048C2×D4—616no—
1049C2×D4—616no—
1050C2×D4—616no—
1051C2×D4—68no—
1052C2×D4—61no—
1053C2×D4—62no—
1054C2×D4—61no—
1055C2×D4—64no—
1056C2×D4—62no—
1057C2×D4—61no—
1058C2×D4—62no—
1059C2×D4D3×D412yes—
1060C2×D4D3×D411yescharacteristic
1061C2×D4C23×D311yescharacteristic
1062C22×C4—22no—
1063C22×C4—21no—
1064C22×C4—22no—
1065C22×C4—21no—
1066C22×C4—21no—
1067C22×C4—31no—
1068C22×C4—31no—
1069C22×C4—31no—
1070C22×C4—34no—
1071C22×C4—34no—
1072C22×C4—31no—
1073C22×C4—31no—
1074C22×C4—32no—
1075C22×C4—32no—
1076C22×C4—32no—
1077C22×C4—32no—
1078C22×C4—64no—
1079C22×C4—64no—
1080C22×C4—61no—
1081C22×C4—62no—
1082C22×C4—62no—
1083C22×C4—62no—
1084C22×C4—62no—
1085C22×C4—68no—
1086C22×C4—68no—
1087C22×C4—61no—
1088C22×C4—62no—
1089C22×C4—616no—
1090C22×C4—616no—
1091C22×C4—62no—
1092C22×C4—62no—
1093C22×C4—62no—
1094C22×C4—61no—
1095C22×C4—62no—
1096C22×C4—61no—
1097C22×C4—61no—
1098C22×C4—124no—
1099C22×C4C23×D312yes—
1100C22×C4C23×D311yescharacteristic
1101Q16—28no—
1102Q16—24no—
1103Q16—64no—
1104Q16—64no—
1105Q16—64no—
1106Q16—68no—
1107SD16—24no—
1108SD16—68no—
1109SD16—64no—
1110SD16—64no—
1111SD16—68no—
1112SD16—64no—
1113M16—22no—
1114M16—64no—
1115M16—64no—
1116M16—64no—
1117M16—62no—
1118C2×C8—22no—
1119C2×C8—32no—
1120C2×C8—32no—
1121C2×C8—64no—
1122C2×C8—62no—
1123C2×C8C23×D312yes—
1124C2×C8C23×D312yes—
1125C4⋊C4—24no—
1126C4⋊C4—32no—
1127C4⋊C4—62no—
1128C4⋊C4—64no—
1129C4⋊C4—64no—
1130C4⋊C4—64no—
1131C4⋊C4C23×D312yes—
1132C22⋊C4—21no—
1133C22⋊C4—24no—
1134C22⋊C4—62no—
1135C22⋊C4—64no—
1136C22⋊C4—64no—
1137C22⋊C4—61no—
1138C22⋊C4—64no—
1139C42—21no—
1140C42—62no—
1141C42—61no—
1142C22×C3—22no—
1143C22×C3—24no—
1144C22×C3—22no—
1145C22×C3—22no—
1146C22×C3—42no—
1147C22×C3C2×#12012yes—
1148C22×C3C23×D411yescharacteristic
1149C2×D3—22no—
1150C2×D3—22no—
1151C2×D3—24no—
1152C2×D3—22no—
1153C2×D3—22no—
1154C2×D3—24no—
1155C2×D3—44no—
1156C2×D3—42no—
1157C2×D3—44no—
1158C2×D3—84no—
1159C2×D3—84no—
1160C2×D3—84no—
1161C2×D3—88no—
1162C2×D3—88no—
1163C2×D3C2×#12012yes—
1164C2×D3C2×#12012yes—
1165C3×C4—24no—
1166C3×C4—22no—
1167C3×C4—22no—
1168C3×C4—42no—
1169C3×C4—42no—
1170C3×C4C2×#12012yes—
1171C3×C4C23×D411yescharacteristic
1172C3×C4C23×D411yescharacteristic
1173Dic3—22no—
1174Dic3—22no—
1175Dic3—42no—
1176Dic3—42no—
1177Dic3C2×#12012yes—
1178Dic3C2×#12012yes—
1179C23—21no—
1180C23—31no—
1181C23—31no—
1182C23—34no—
1183C23—32no—
1184C23—64no—
1185C23—64no—
1186C23—68no—
1187C23—68no—
1188C23—62no—
1189C23—61no—
1190C23—64no—
1191C23—122no—
1192C23—124no—
1193C23—242no—
1194C23—244no—
1195C23—242no—
1196C23—244no—
1197C23C2×D3×D412yes—
1198C23C2×D3×D411yescharacteristic
1199Q8—28no—
1200Q8—21no—
1201Q8—22no—
1202Q8—24no—
1203Q8—22no—
1204Q8—22no—
1205Q8—22no—
1206Q8—32no—
1207Q8—42no—
1208Q8—64no—
1209Q8—64no—
1210Q8—68no—
1211Q8—61no—
1212Q8—62no—
1213Q8—62no—
1214Q8—62no—
1215Q8—124no—
1216Q8—124no—
1217Q8—122no—
1218Q8C2×D3×D412yes—
1219Q8C2×D3×D414yes—
1220D4—28no—
1221D4—24no—
1222D4—24no—
1223D4—21no—
1224D4—22no—
1225D4—34no—
1226D4—32no—
1227D4—64no—
1228D4—68no—
1229D4—68no—
1230D4—64no—
1231D4—68no—
1232D4—68no—
1233D4—68no—
1234D4—64no—
1235D4—64no—
1236D4—64no—
1237D4—64no—
1238D4—68no—
1239D4—68no—
1240D4—64no—
1241D4—64no—
1242D4—61no—
1243D4—62no—
1244D4—64no—
1245D4—62no—
1246D4C2×D3×D412yes—
1247C2×C4—28no—
1248C2×C4—28no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—31no—
1258C2×C4—31no—
1259C2×C4—34no—
1260C2×C4—32no—
1261C2×C4—32no—
1262C2×C4—32no—
1263C2×C4—32no—
1264C2×C4—34no—
1265C2×C4—34no—
1266C2×C4—32no—
1267C2×C4—42no—
1268C2×C4—64no—
1269C2×C4—64no—
1270C2×C4—68no—
1271C2×C4—68no—
1272C2×C4—64no—
1273C2×C4—64no—
1274C2×C4—68no—
1275C2×C4—68no—
1276C2×C4—68no—
1277C2×C4—68no—
1278C2×C4—64no—
1279C2×C4—64no—
1280C2×C4—61no—
1281C2×C4—62no—
1282C2×C4—62no—
1283C2×C4—64no—
1284C2×C4—62no—
1285C2×C4—62no—
1286C2×C4—124no—
1287C2×C4—124no—
1288C2×C4—124no—
1289C2×C4—122no—
1290C2×C4C2×D3×D412yes—
1291C2×C4C2×D3×D412yes—
1292C2×C4C2×D3×D412yes—
1293C2×C4C2×D3×D411yescharacteristic
1294C2×C4C24×D311yescharacteristic
1295C8—22no—
1296C8—22no—
1297C8—62no—
1298C8—62no—
1299C2×C3—22no—
1300C2×C3—42no—
1301C2×C3—42no—
1302C2×C3C22×#12011yescharacteristic
1303C2×C3#358612yes—
1304D3—22no—
1305D3—22no—
1306D3—42no—
1307D3—42no—
1308D3—44no—
1309C22—22no—
1310C22—22no—
1311C22—22no—
1312C22—24no—
1313C22—32no—
1314C22—32no—
1315C22—42no—
1316C22—62no—
1317C22—62no—
1318C22—64no—
1319C22—62no—
1320C22—62no—
1321C22—64no—
1322C22—124no—
1323C22—124no—
1324C22—122no—
1325C22—244no—
1326C22—244no—
1327C22—244no—
1328C22—248no—
1329C22—248no—
1330C22D3×#12012yes—
1331C22C22×D3×D411yescharacteristic
1332C4—24no—
1333C4—22no—
1334C4—22no—
1335C4—32no—
1336C4—32no—
1337C4—42no—
1338C4—42no—
1339C4—62no—
1340C4—62no—
1341C4—122no—
1342C4—122no—
1343C4D3×#12012yes—
1344C4C22×D3×D411yescharacteristic
1345C4C22×D3×D411yescharacteristic
1346C3#6037011yescharacteristic, complemented, Sylow
1347C2—22no—
1348C2—42no—
1349C2—42no—
1350C2—62no—
1351C2—62no—
1352C2—122no—
1353C2—124no—
1354C2—122no—
1355C2C2×D3×#12011yescharacteristic
1356C2#8721112yes—
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3011C2
socleC22×C3C23×D4
prime radicalC2×#5968C2
hypercenter#3011D3
hypocenterC3#60370
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3011

Complements

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

NH ≅ G/Ntype
2. C2×D3×#137C2semidirect
3. C22×#918C2semidirect
4. D3×#536C2semidirect
5. C3×#3011C2semidirect
6. #84117C2semidirect
7. #83982C2semidirect
8. #83884C2semidirect
9. #83404C2semidirect
10. #80229C2semidirect
11. #80228C2semidirect
12. #80185C2semidirect
13. #80184C2semidirect
14. #78961C2semidirect
15. #78956C2semidirect
16. #78835C2semidirect
17. #78830C2semidirect
18. #78671C2semidirect
19. #78662C2semidirect
40. C22×D3×Q8C22semidirect
41. C2×C3×#137C22semidirect
42. C22×C3×Q16C22semidirect
43. C3×#536C22semidirect
44. #5825C22semidirect
45. C2×#951C22semidirect
46. #5816C22semidirect
47. C22×#216C22semidirect
48. C2×#942C22semidirect
49. C22×#215C22semidirect
52. C2×#918C22semidirect
53. C2×#918C22semidirect
54. C2×#918C22semidirect
55. C2×D3×Q16C22semidirect
56. C2×#915C22semidirect
57. C2×D3×SD16C22semidirect
58. C2×#909C22semidirect
59. C2×D3×M16C22semidirect
60. C22×#204C22semidirect
61. C22×ΓL(1,𝔽25)C22semidirect
68. #5628C22semidirect
69. D3×C22⋊Q8C22semidirect
70. #5526C22semidirect
71. D3×#117C22semidirect
72. C3×#452C22semidirect
73. C3×#451C22semidirect
74. C3×#419C22semidirect
75. C3×#416C22semidirect
76. C3×#408C22semidirect
77. #5239C22semidirect
78. #5234C22semidirect
79. #5233C22semidirect
80. #5228C22semidirect
81. #5225C22semidirect
82. #5187C22semidirect
83. #5187C22semidirect
84. #5186C22semidirect
85. #5169C22semidirect
86. #5131C22semidirect
87. #5129C22semidirect
88. #5113C22semidirect
89. #5110C22semidirect
90. #5047C22semidirect
91. #5046C22semidirect
92. #5002C22semidirect
93. #5001C22semidirect
94. #4809C22semidirect
95. #4808C22semidirect
96. #4808C22semidirect
97. #4804C22semidirect
98. #4803C22semidirect
99. #4803C22semidirect
100. #4802C22semidirect
101. #4776C22semidirect
102. #4771C22semidirect
103. #4770C22semidirect
104. #4733C22semidirect
105. #4731C22semidirect
106. #4727C22semidirect
107. #4726C22semidirect
116. #3011D3semidirect
343. C2×#137C2×D3semidirect
346. C22×Q16C2×D3semidirect
359. #536C2×D3semidirect
372. #452C2×D3semidirect
376. #451C2×D3semidirect
383. #419C2×D3semidirect
394. #416C2×D3semidirect
399. #408C2×D3semidirect
1346. C3#60370semidirect

Maximal subgroups

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

subgroupindex
C2×#59682
C2×D3×#1372
C22×#9182
D3×#5362
C3×#30112
#841172
#839822
#838842
#834042
#802292
#802282
#801852
#801842
#789612
#789562
#788352
#788302
#786712
#786622
#603703