Finite Group Databasebeta

← #72271513

Subgroups — #72271513

Order 1536.

3052 conjugacy classes of subgroups.

The subgroup lattice has 1420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10794351C211yesmaximal, characteristic
2#10717876C211yesmaximal, characteristic
3#10682467C214yesmaximal, complemented
4C3×#20591C211yesmaximal, characteristic
5#128059—31nomaximal, Sylow
6C23×C3×#41C2211yescharacteristic
7C2×C3×#413—21no—
8C2×C3×#413C412yescomplemented
9C2×C3×#407—21no—
10C2×#5237—21no—
11C2×#5237C412yescomplemented
12C2×#5220—21no—
13C2×#5220—21no—
14C2×#5211C411yescharacteristic
15C22×C3⋊#95C411yescharacteristic
16C2×#5207—21no—
17C3×#1785—21no—
18C3×#1785C412yescomplemented
19C3×#1784C2212yes—
20C3×#1783—21no—
21#72137—21no—
22#72137C412yescomplemented
23#72134C2212yes—
24#72133C2212yes—
25#72131C412yes—
26#72129—21no—
27#72127—21no—
28#72127—21no—
29#20591—31no—
30#20591D311yescharacteristic
31#13956—31no—
32#7308—34no—
33C22×C3×#41—41no—
34C22×C3×#41—41no—
35C22×C3×#41—41no—
36C22×C3×#41—41no—
37C22×C3×#41—44no—
38C22×C3×#41—44no—
39C22×C3×#41C2×C411yescharacteristic
40C22×C3×#41C2×C411yescharacteristic
41C22×C3×#41C2×C411yescharacteristic
42C22×C3×#41C2×C411yescharacteristic
43C22×C3×#41D411yescharacteristic
44C22×C3×#41D411yescharacteristic
45C22×C3×#41Q811yescharacteristic
46C22×C3×#41Q811yescharacteristic
47C23×C3×Q8C2311yescharacteristic
48C23×C3×D4C2×C411yescharacteristic
49C23×C3×D4D411yescharacteristic
50C23×C3×D4D411yescharacteristic
51C24×C3×C4C2×C411yescharacteristic
52C24×C3×C4D411yescharacteristic
53C24×C3×C4D411yescharacteristic
54C24×Dic3—21no—
55C22×C3×M16—22no—
56C22×#217—21no—
57C22×#217—22no—
58C22×#217—22no—
59C22×#208—22no—
60C3×#413—44no—
61C3×#413—44no—
62C2×C3×#101—22no—
63C2×C3×#101C2×C414yescomplemented
64C2×C3×#100—22no—
65C2×C3×#100—22no—
66C3×#407—22no—
67C3×#407—22no—
68C3×#407—41no—
69C3×#407—41no—
70C2×C3×C22⋊C8—41no—
71C2×C3×C22⋊C8—41no—
72#5237—44no—
73#5237—44no—
74C2×#836—22no—
75C2×#836C2×C414yescomplemented
76#5220—44no—
77#5220—44no—
78C2×#833—22no—
79C2×#833—22no—
80#5211—41no—
81#5211—41no—
82C2×C3⋊#95—21no—
83C2×C3⋊#95—21no—
84C2×C3⋊#95—22no—
85C2×C3⋊#95—22no—
86C2×C3⋊#95—41no—
87C2×C3⋊#95—41no—
88C2×C3⋊#95C2×C412yes—
89C2×C3⋊#95C2×C412yes—
90#5207—22no—
91#5207—22no—
92#5207—41no—
93#5207—41no—
94C2×#830—41no—
95C2×#830—41no—
96C23×#41C2×D311yescharacteristic
97C2×#413—21no—
98C2×#413—32no—
99C2×#413—61no—
100C2×#413Dic312yescomplemented
101C2×#407—21no—
102C2×#407—61no—
103C2×#386—61no—
104C2×#386—61no—
105C2×#381—31no—
106C22×#95—31no—
107#1785—21no—
108#1785—32no—
109#1785—61no—
110#1785Dic312yescomplemented
111#1784—32no—
112#1784C2×D312yes—
113#1783—21no—
114#1783—61no—
115#1446—32no—
116#1438—32no—
117C22⋊#95—61no—
118C22⋊#95—61no—
119C25×C3C22⋊C411yescharacteristic
120C25×C3C22⋊C411yescharacteristic
121C25×C3C22⋊C411yescharacteristic
122C2×C3×#41—24no—
123C2×C3×#41—24no—
124C2×C3×#41—24no—
125C2×C3×#41—24no—
126C2×C3×#41—41no—
127C2×C3×#41—41no—
128C2×C3×#41—41no—
129C2×C3×#41—41no—
130C2×C3×#41—41no—
131C2×C3×#41—41no—
132C2×C3×#41—41no—
133C2×C3×#41—41no—
134C2×C3×#41—41no—
135C2×C3×#41—41no—
136C2×C3×#41—41no—
137C2×C3×#41—41no—
138C2×C3×#41—41no—
139C2×C3×#41—41no—
140C2×C3×#41—41no—
141C2×C3×#41—41no—
142C2×C3×#41—42no—
143C2×C3×#41—42no—
144C2×C3×#41—42no—
145C2×C3×#41—42no—
146C2×C3×#41—42no—
147C2×C3×#41—42no—
148C2×C3×#41—42no—
149C2×C3×#41—42no—
150C2×C3×#41—42no—
151C2×C3×#41—42no—
152C2×C3×#41—42no—
153C2×C3×#41—42no—
154C2×C3×#41—416no—
155C2×C3×#41—416no—
156C2×C3×#41—416no—
157C2×C3×#41—416no—
158C22×C3×Q8—41no—
159C22×C3×Q8—41no—
160C22×C3×Q8—42no—
161C22×C3×Q8—42no—
162C22×C3×Q8C22×C411yescharacteristic
163C22×C3×Q8C22×C411yescharacteristic
164C22×C3×Q8C2×D411yescharacteristic
165C22×C3×Q8C2×Q811yescharacteristic
166C22×C3×D4—24no—
167C22×C3×D4—24no—
168C22×C3×D4—41no—
169C22×C3×D4—41no—
170C22×C3×D4—41no—
171C22×C3×D4—41no—
172C22×C3×D4—41no—
173C22×C3×D4—41no—
174C22×C3×D4—42no—
175C22×C3×D4—42no—
176C22×C3×D4—42no—
177C22×C3×D4—42no—
178C22×C3×D4C4211yescharacteristic
179C22×C3×D4C4211yescharacteristic
180C22×C3×D4C22⋊C411yescharacteristic
181C22×C3×D4C22⋊C411yescharacteristic
182C22×C3×D4C22⋊C411yescharacteristic
183C22×C3×D4C22⋊C411yescharacteristic
184C22×C3×D4C4⋊C411yescharacteristic
185C22×C3×D4C4⋊C411yescharacteristic
186C22×C3×D4C4⋊C411yescharacteristic
187C22×C3×D4C4⋊C411yescharacteristic
188C22×C3×D4C4⋊C411yescharacteristic
189C22×C3×D4C4⋊C411yescharacteristic
190C23×C3×C4—21no—
191C23×C3×C4—21no—
192C23×C3×C4—21no—
193C23×C3×C4—21no—
194C23×C3×C4—21no—
195C23×C3×C4—21no—
196C23×C3×C4—21no—
197C23×C3×C4—21no—
198C23×C3×C4—21no—
199C23×C3×C4—21no—
200C23×C3×C4—21no—
201C23×C3×C4—21no—
202C23×C3×C4—42no—
203C23×C3×C4—42no—
204C23×C3×C4—42no—
205C23×C3×C4—42no—
206C23×C3×C4—42no—
207C23×C3×C4—42no—
208C23×C3×C4C4211yescharacteristic
209C23×C3×C4C4211yescharacteristic
210C23×C3×C4C22⋊C411yescharacteristic
211C23×C3×C4C22⋊C411yescharacteristic
212C23×C3×C4C22⋊C411yescharacteristic
213C23×C3×C4C22⋊C411yescharacteristic
214C23×C3×C4C22⋊C411yescharacteristic
215C23×C3×C4C4⋊C411yescharacteristic
216C23×C3×C4C4⋊C411yescharacteristic
217C23×C3×C4C4⋊C411yescharacteristic
218C23×C3×C4C4⋊C411yescharacteristic
219C23×C3×C4C4⋊C411yescharacteristic
220C23×C3×C4C4⋊C411yescharacteristic
221C23×C3×C4C22×C411yescharacteristic
222C23×C3×C4C2×D411yescharacteristic
223C23×C3×C4C2×D411yescharacteristic
224C23×Dic3—22no—
225C23×Dic3—22no—
226C23×Dic3—44no—
227C23×Dic3—42no—
228C23×Dic3—42no—
229C23×Dic3—42no—
230C23×Dic3—82no—
231C2×C3×M16—24no—
232C2×C3×M16—42no—
233C2×C3×M16—44no—
234C2×C3×M16—44no—
235C22×C3×C8—42no—
236C2×#217—44no—
237C2×#217—44no—
238C2×#217—42no—
239C2×#217—44no—
240C2×#217—44no—
241C2×#217—42no—
242C2×#217—42no—
243C2×#217—82no—
244C2×#217—82no—
245C2×#208—24no—
246C2×#208—42no—
247C2×#208—44no—
248C2×#208—44no—
249C22×C3⋊C8—42no—
250C3×#101—44no—
251C3×#101—44no—
252C3×#100—44no—
253C3×#100—44no—
254C3×C22⋊C8—42no—
255C3×C22⋊C8—42no—
256C3×C22⋊C8—42no—
257C3×C22⋊C8—42no—
258#836—44no—
259#836—44no—
260#833—44no—
261#833—44no—
262C3⋊#95—44no—
263C3⋊#95—44no—
264C3⋊#95—41no—
265C3⋊#95—41no—
266C3⋊#95—41no—
267C3⋊#95—41no—
268C3⋊#95—42no—
269C3⋊#95—42no—
270#830—42no—
271#830—42no—
272#830—42no—
273#830—42no—
274C22×#41—41no—
275C22×#41—41no—
276C22×#41—41no—
277C22×#41—41no—
278C22×#41—44no—
279C22×#41—44no—
280C22×#41Dic611yescharacteristic
281C22×#41Dic611yescharacteristic
282C22×#41C4×D311yescharacteristic
283C22×#41C4×D311yescharacteristic
284C22×#41C2×Dic311yescharacteristic
285C22×#41C2×Dic311yescharacteristic
286C22×#41#6711yescharacteristic
287C22×#41#6711yescharacteristic
288C23×Q8C22×D311yescharacteristic
289C23×D4C4×D311yescharacteristic
290C23×D4D1211yescharacteristic
291C23×D4#6711yescharacteristic
292C24×C4—61no—
293C24×C4C4×D311yescharacteristic
294C24×C4D1211yescharacteristic
295C24×C4#6711yescharacteristic
296C22×M16—22no—
297C22×M16—62no—
298C22×C22⋊C4—61no—
299C22×C22⋊C4—62no—
300C22×C22⋊C4—62no—
301#413—44no—
302#413—44no—
303#413—124no—
304#413—124no—
305C2×#101—22no—
306C2×#101—34no—
307C2×#101—62no—
308C2×#101C2×Dic314yescomplemented
309C2×#100—22no—
310C2×#100—22no—
311C2×#100—62no—
312C2×#100—62no—
313#407—22no—
314#407—22no—
315#407—41no—
316#407—41no—
317#407—62no—
318#407—62no—
319#407—121no—
320#407—121no—
321C2×C22⋊C8—41no—
322C2×C22⋊C8—41no—
323C2×C22⋊C8—121no—
324C2×C22⋊C8—121no—
325#386—124no—
326#386—124no—
327#381—121no—
328#381—121no—
329C2×#95—32no—
330C2×#95—32no—
331C2×#95—61no—
332C2×#95—61no—
333C2×#95—62no—
334C2×#95—62no—
335C2×#95—121no—
336C2×#95—121no—
337C24×C3—22no—
338C24×C3—22no—
339C24×C3—21no—
340C24×C3—21no—
341C24×C3—22no—
342C24×C3—22no—
343C24×C3—21no—
344C24×C3—21no—
345C24×C3—21no—
346C24×C3—21no—
347C24×C3—41no—
348C24×C3—41no—
349C24×C3—41no—
350C24×C3—42no—
351C24×C3—41no—
352C24×C3—41no—
353C24×C3—41no—
354C24×C3—42no—
355C24×C3—42no—
356C24×C3—41no—
357C24×C3—41no—
358C24×C3#9511yescharacteristic
359C24×C3#9511yescharacteristic
360C24×C3#9511yescharacteristic
361C24×C3#9511yescharacteristic
362C24×C3#9511yescharacteristic
363C24×C3#9511yescharacteristic
364C24×C3C2×C22⋊C411yescharacteristic
365C3×#41—48no—
366C3×#41—48no—
367C3×#41—48no—
368C3×#41—48no—
369C3×#41—48no—
370C3×#41—48no—
371C3×#41—48no—
372C3×#41—48no—
373C3×#41—48no—
374C3×#41—48no—
375C3×#41—48no—
376C3×#41—48no—
377C3×#41—48no—
378C3×#41—48no—
379C3×#41—48no—
380C3×#41—48no—
381C2×C3×Q8—22no—
382C2×C3×Q8—22no—
383C2×C3×Q8—22no—
384C2×C3×Q8—22no—
385C2×C3×Q8—41no—
386C2×C3×Q8—41no—
387C2×C3×Q8—41no—
388C2×C3×Q8—41no—
389C2×C3×Q8—41no—
390C2×C3×Q8—41no—
391C2×C3×Q8—41no—
392C2×C3×Q8—41no—
393C2×C3×Q8—48no—
394C2×C3×Q8—48no—
395C2×C3×D4—22no—
396C2×C3×D4—22no—
397C2×C3×D4—22no—
398C2×C3×D4—22no—
399C2×C3×D4—22no—
400C2×C3×D4—22no—
401C2×C3×D4—22no—
402C2×C3×D4—22no—
403C2×C3×D4—22no—
404C2×C3×D4—22no—
405C2×C3×D4—22no—
406C2×C3×D4—22no—
407C2×C3×D4—22no—
408C2×C3×D4—22no—
409C2×C3×D4—41no—
410C2×C3×D4—41no—
411C2×C3×D4—41no—
412C2×C3×D4—41no—
413C2×C3×D4—41no—
414C2×C3×D4—41no—
415C2×C3×D4—41no—
416C2×C3×D4—41no—
417C2×C3×D4—41no—
418C2×C3×D4—41no—
419C2×C3×D4—41no—
420C2×C3×D4—41no—
421C2×C3×D4—41no—
422C2×C3×D4—41no—
423C2×C3×D4—41no—
424C2×C3×D4—41no—
425C2×C3×D4—41no—
426C2×C3×D4—41no—
427C2×C3×D4—41no—
428C2×C3×D4—41no—
429C2×C3×D4—48no—
430C2×C3×D4—48no—
431C2×C3×D4—48no—
432C2×C3×D4—48no—
433C2×C3×D4—48no—
434C2×C3×D4—48no—
435C2×C3×D4#9914yes—
436C2×C3×D4#9914yes—
437C22×C3×C4—22no—
438C22×C3×C4—22no—
439C22×C3×C4—21no—
440C22×C3×C4—21no—
441C22×C3×C4—21no—
442C22×C3×C4—21no—
443C22×C3×C4—22no—
444C22×C3×C4—22no—
445C22×C3×C4—22no—
446C22×C3×C4—22no—
447C22×C3×C4—22no—
448C22×C3×C4—22no—
449C22×C3×C4—22no—
450C22×C3×C4—22no—
451C22×C3×C4—21no—
452C22×C3×C4—21no—
453C22×C3×C4—21no—
454C22×C3×C4—21no—
455C22×C3×C4—21no—
456C22×C3×C4—21no—
457C22×C3×C4—21no—
458C22×C3×C4—21no—
459C22×C3×C4—21no—
460C22×C3×C4—21no—
461C22×C3×C4—21no—
462C22×C3×C4—21no—
463C22×C3×C4—21no—
464C22×C3×C4—21no—
465C22×C3×C4—21no—
466C22×C3×C4—21no—
467C22×C3×C4—21no—
468C22×C3×C4—21no—
469C22×C3×C4—21no—
470C22×C3×C4—21no—
471C22×C3×C4—21no—
472C22×C3×C4—21no—
473C22×C3×C4—21no—
474C22×C3×C4—21no—
475C22×C3×C4—21no—
476C22×C3×C4—21no—
477C22×C3×C4—22no—
478C22×C3×C4—22no—
479C22×C3×C4—22no—
480C22×C3×C4—22no—
481C22×C3×C4—41no—
482C22×C3×C4—41no—
483C22×C3×C4—41no—
484C22×C3×C4—41no—
485C22×C3×C4—41no—
486C22×C3×C4—41no—
487C22×C3×C4—41no—
488C22×C3×C4—41no—
489C22×C3×C4—41no—
490C22×C3×C4—41no—
491C22×C3×C4—41no—
492C22×C3×C4—41no—
493C22×C3×C4—41no—
494C22×C3×C4—41no—
495C22×C3×C4—41no—
496C22×C3×C4—41no—
497C22×C3×C4—41no—
498C22×C3×C4—41no—
499C22×C3×C4—44no—
500C22×C3×C4—44no—
501C22×C3×C4—44no—
502C22×C3×C4—44no—
503C22×C3×C4—44no—
504C22×C3×C4—44no—
505C22×C3×C4—44no—
506C22×C3×C4—44no—
507C22×C3×C4—44no—
508C22×C3×C4—44no—
509C22×C3×C4—44no—
510C22×C3×C4—44no—
511C22×C3×C4#9511yescharacteristic
512C22×C3×C4#9511yescharacteristic
513C22×C3×C4#9911yescharacteristic
514C22×C3×C4#9911yescharacteristic
515C22×C3×C4#9911yescharacteristic
516C22×C3×C4#9911yescharacteristic
517C22×C3×C4C2×C4211yescharacteristic
518C22×C3×C4C2×C22⋊C411yescharacteristic
519C22×C3×C4C2×C22⋊C411yescharacteristic
520C22×C3×C4C2×C4⋊C411yescharacteristic
521C22×C3×C4C2×C4⋊C411yescharacteristic
522C22×C3×C4C2×C4⋊C411yescharacteristic
523C22×Dic3—24no—
524C22×Dic3—42no—
525C22×Dic3—42no—
526C22×Dic3—42no—
527C22×Dic3—42no—
528C22×Dic3—42no—
529C22×Dic3—48no—
530C22×Dic3—42no—
531C22×Dic3—42no—
532C22×Dic3—42no—
533C22×Dic3—42no—
534C22×Dic3—42no—
535C22×Dic3—42no—
536C22×Dic3—42no—
537C22×Dic3—42no—
538C22×Dic3—88no—
539C22×Dic3—88no—
540C22×Dic3—84no—
541C22×Dic3—84no—
542C3×M16—44no—
543C3×M16—44no—
544C3×M16—84no—
545C2×C3×C8—44no—
546C2×C3×C8—84no—
547#217—88no—
548#217—88no—
549#217—84no—
550#208—44no—
551#208—44no—
552#208—84no—
553C2×C3⋊C8—44no—
554C2×C3⋊C8—84no—
555C25(C2×D3)⋊C411yescharacteristic
556C25(C2×D3)⋊C411yescharacteristic
557C25(C2×D3)⋊C411yescharacteristic
558C2×#41—24no—
559C2×#41—24no—
560C2×#41—24no—
561C2×#41—24no—
562C2×#41—41no—
563C2×#41—41no—
564C2×#41—41no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—41no—
568C2×#41—41no—
569C2×#41—41no—
570C2×#41—41no—
571C2×#41—41no—
572C2×#41—41no—
573C2×#41—41no—
574C2×#41—41no—
575C2×#41—41no—
576C2×#41—41no—
577C2×#41—41no—
578C2×#41—42no—
579C2×#41—42no—
580C2×#41—42no—
581C2×#41—42no—
582C2×#41—42no—
583C2×#41—42no—
584C2×#41—42no—
585C2×#41—42no—
586C2×#41—42no—
587C2×#41—42no—
588C2×#41—42no—
589C2×#41—42no—
590C2×#41—416no—
591C2×#41—416no—
592C2×#41—416no—
593C2×#41—416no—
594C22×Q8—41no—
595C22×Q8—41no—
596C22×Q8—42no—
597C22×Q8—42no—
598C22×Q8C2×Dic611yescharacteristic
599C22×Q8C2×C4×D311yescharacteristic
600C22×Q8C22×Dic311yescharacteristic
601C22×Q8C2×#6711yescharacteristic
602C22×D4—24no—
603C22×D4—24no—
604C22×D4—41no—
605C22×D4—41no—
606C22×D4—41no—
607C22×D4—41no—
608C22×D4—41no—
609C22×D4—41no—
610C22×D4—42no—
611C22×D4—42no—
612C22×D4—42no—
613C22×D4—42no—
614C22×D4C4×Dic311yescharacteristic
615C22×D4C4×Dic311yescharacteristic
616C22×D4Dic3⋊C411yescharacteristic
617C22×D4Dic3⋊C411yescharacteristic
618C22×D4Dic3⋊C411yescharacteristic
619C22×D4Dic3⋊C411yescharacteristic
620C22×D4C4⋊Dic311yescharacteristic
621C22×D4C4⋊Dic311yescharacteristic
622C22×D4(C2×D3)⋊C411yescharacteristic
623C22×D4(C2×D3)⋊C411yescharacteristic
624C22×D4#21711yescharacteristic
625C22×D4#21711yescharacteristic
626C23×C4—21no—
627C23×C4—21no—
628C23×C4—21no—
629C23×C4—21no—
630C23×C4—21no—
631C23×C4—21no—
632C23×C4—21no—
633C23×C4—21no—
634C23×C4—21no—
635C23×C4—21no—
636C23×C4—21no—
637C23×C4—21no—
638C23×C4—42no—
639C23×C4—42no—
640C23×C4—42no—
641C23×C4—42no—
642C23×C4—42no—
643C23×C4—42no—
644C23×C4—62no—
645C23×C4—62no—
646C23×C4—124no—
647C23×C4—122no—
648C23×C4—122no—
649C23×C4—122no—
650C23×C4—242no—
651C23×C4C4×Dic311yescharacteristic
652C23×C4C4×Dic311yescharacteristic
653C23×C4Dic3⋊C411yescharacteristic
654C23×C4Dic3⋊C411yescharacteristic
655C23×C4Dic3⋊C411yescharacteristic
656C23×C4Dic3⋊C411yescharacteristic
657C23×C4C4⋊Dic311yescharacteristic
658C23×C4C4⋊Dic311yescharacteristic
659C23×C4(C2×D3)⋊C411yescharacteristic
660C23×C4(C2×D3)⋊C411yescharacteristic
661C23×C4(C2×D3)⋊C411yescharacteristic
662C23×C4#21711yescharacteristic
663C23×C4#21711yescharacteristic
664C23×C4C2×C4×D311yescharacteristic
665C23×C4C2×D1211yescharacteristic
666C23×C4C2×#6711yescharacteristic
667C2×M16—24no—
668C2×M16—42no—
669C2×M16—44no—
670C2×M16—44no—
671C2×M16—64no—
672C2×M16—122no—
673C2×M16—124no—
674C2×M16—124no—
675C22×C8—42no—
676C22×C8—122no—
677C2×C22⋊C4—124no—
678C2×C22⋊C4—124no—
679C2×C22⋊C4—122no—
680C2×C22⋊C4—124no—
681C2×C22⋊C4—124no—
682C2×C22⋊C4—122no—
683C2×C22⋊C4—122no—
684C2×C22⋊C4—242no—
685C2×C22⋊C4—242no—
686#101—44no—
687#101—44no—
688#101—124no—
689#101—124no—
690#100—44no—
691#100—44no—
692#100—124no—
693#100—124no—
694C22⋊C8—42no—
695C22⋊C8—42no—
696C22⋊C8—42no—
697C22⋊C8—42no—
698C22⋊C8—122no—
699C22⋊C8—122no—
700C22⋊C8—122no—
701C22⋊C8—122no—
702#95—122no—
703#95—122no—
704#95—124no—
705#95—124no—
706#95—121no—
707#95—121no—
708#95—121no—
709#95—121no—
710C23×C3—22no—
711C23×C3—21no—
712C23×C3—21no—
713C23×C3—21no—
714C23×C3—21no—
715C23×C3—24no—
716C23×C3—24no—
717C23×C3—21no—
718C23×C3—21no—
719C23×C3—21no—
720C23×C3—21no—
721C23×C3—21no—
722C23×C3—21no—
723C23×C3—21no—
724C23×C3—21no—
725C23×C3—21no—
726C23×C3—21no—
727C23×C3—21no—
728C23×C3—21no—
729C23×C3—21no—
730C23×C3—21no—
731C23×C3—42no—
732C23×C3—42no—
733C23×C3—42no—
734C23×C3—42no—
735C23×C3—41no—
736C23×C3—41no—
737C23×C3—41no—
738C23×C3—41no—
739C23×C3—42no—
740C23×C3—44no—
741C23×C3—44no—
742C23×C3—44no—
743C23×C3—44no—
744C23×C3—42no—
745C23×C3—41no—
746C23×C3—41no—
747C23×C3—41no—
748C23×C3—41no—
749C23×C3—41no—
750C23×C3—41no—
751C23×C3—41no—
752C23×C3—41no—
753C23×C3—44no—
754C23×C3—44no—
755C23×C3—44no—
756C23×C3—44no—
757C23×C3—42no—
758C23×C3—41no—
759C23×C3—41no—
760C23×C3—42no—
761C23×C3—42no—
762C23×C3—41no—
763C23×C3—41no—
764C23×C3—41no—
765C23×C3—41no—
766C23×C3—81no—
767C23×C3—81no—
768C23×C3—81no—
769C23×C3—81no—
770C23×C3—82no—
771C23×C3—82no—
772C23×C3—82no—
773C23×C3—82no—
774C23×C3#34212yes—
775C23×C3#34212yes—
776C23×C3#34212yes—
777C23×C3#34212yes—
778C23×C3C2×#9511yescharacteristic
779C23×C3C2×#9911yescharacteristic
780C23×C3C2×#9911yescharacteristic
781C3×Q8—44no—
782C3×Q8—44no—
783C3×Q8—44no—
784C3×Q8—44no—
785C3×D4—44no—
786C3×D4—44no—
787C3×D4—44no—
788C3×D4—44no—
789C3×D4—44no—
790C3×D4—44no—
791C3×D4—44no—
792C3×D4—44no—
793C3×D4—44no—
794C3×D4—44no—
795C3×D4—44no—
796C3×D4—44no—
797C2×C3×C4—24no—
798C2×C3×C4—24no—
799C2×C3×C4—24no—
800C2×C3×C4—24no—
801C2×C3×C4—21no—
802C2×C3×C4—21no—
803C2×C3×C4—21no—
804C2×C3×C4—21no—
805C2×C3×C4—21no—
806C2×C3×C4—21no—
807C2×C3×C4—21no—
808C2×C3×C4—21no—
809C2×C3×C4—21no—
810C2×C3×C4—21no—
811C2×C3×C4—21no—
812C2×C3×C4—21no—
813C2×C3×C4—21no—
814C2×C3×C4—21no—
815C2×C3×C4—21no—
816C2×C3×C4—21no—
817C2×C3×C4—21no—
818C2×C3×C4—21no—
819C2×C3×C4—21no—
820C2×C3×C4—21no—
821C2×C3×C4—41no—
822C2×C3×C4—41no—
823C2×C3×C4—41no—
824C2×C3×C4—41no—
825C2×C3×C4—42no—
826C2×C3×C4—42no—
827C2×C3×C4—42no—
828C2×C3×C4—42no—
829C2×C3×C4—42no—
830C2×C3×C4—42no—
831C2×C3×C4—42no—
832C2×C3×C4—42no—
833C2×C3×C4—42no—
834C2×C3×C4—42no—
835C2×C3×C4—42no—
836C2×C3×C4—42no—
837C2×C3×C4—42no—
838C2×C3×C4—42no—
839C2×C3×C4—42no—
840C2×C3×C4—42no—
841C2×C3×C4—42no—
842C2×C3×C4—42no—
843C2×C3×C4—42no—
844C2×C3×C4—42no—
845C2×C3×C4—42no—
846C2×C3×C4—42no—
847C2×C3×C4—42no—
848C2×C3×C4—42no—
849C2×C3×C4—42no—
850C2×C3×C4—42no—
851C2×C3×C4#34211yescharacteristic
852C2×C3×C4#34211yescharacteristic
853C2×C3×C4#34211yescharacteristic
854C2×C3×C4#34211yescharacteristic
855C2×C3×C4C2×#9912yes—
856C2×C3×C4C2×#9912yes—
857C2×Dic3—44no—
858C2×Dic3—44no—
859C2×Dic3—44no—
860C2×Dic3—82no—
861C2×Dic3—82no—
862C2×Dic3—82no—
863C2×Dic3—816no—
864C2×Dic3—82no—
865C2×Dic3—82no—
866C2×Dic3—82no—
867C2×Dic3—82no—
868C2×Dic3—82no—
869C2×Dic3—82no—
870C2×Dic3—82no—
871C2×Dic3—82no—
872C3×C8—84no—
873C3⋊C8—84no—
874C24—21no—
875C24—21no—
876C24—22no—
877C24—22no—
878C24—22no—
879C24—22no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—41no—
885C24—41no—
886C24—42no—
887C24—41no—
888C24—41no—
889C24—42no—
890C24—42no—
891C24—41no—
892C24—41no—
893C24—41no—
894C24—41no—
895C24C3⋊#9511yescharacteristic
896C24C3⋊#9511yescharacteristic
897C24C3⋊#9511yescharacteristic
898C24C3⋊#9511yescharacteristic
899C24C3⋊#9511yescharacteristic
900C24C3⋊#9511yescharacteristic
901C24C2×(C2×D3)⋊C411yescharacteristic
902#41—48no—
903#41—48no—
904#41—48no—
905#41—48no—
906#41—48no—
907#41—48no—
908#41—48no—
909#41—48no—
910#41—48no—
911#41—48no—
912#41—48no—
913#41—48no—
914#41—48no—
915#41—48no—
916#41—48no—
917#41—48no—
918C2×Q8—22no—
919C2×Q8—22no—
920C2×Q8—22no—
921C2×Q8—22no—
922C2×Q8—41no—
923C2×Q8—41no—
924C2×Q8—41no—
925C2×Q8—41no—
926C2×Q8—41no—
927C2×Q8—41no—
928C2×Q8—41no—
929C2×Q8—41no—
930C2×Q8—48no—
931C2×Q8—48no—
932C2×D4—22no—
933C2×D4—22no—
934C2×D4—22no—
935C2×D4—22no—
936C2×D4—22no—
937C2×D4—22no—
938C2×D4—22no—
939C2×D4—22no—
940C2×D4—22no—
941C2×D4—22no—
942C2×D4—22no—
943C2×D4—22no—
944C2×D4—22no—
945C2×D4—22no—
946C2×D4—41no—
947C2×D4—41no—
948C2×D4—41no—
949C2×D4—41no—
950C2×D4—41no—
951C2×D4—41no—
952C2×D4—41no—
953C2×D4—41no—
954C2×D4—41no—
955C2×D4—41no—
956C2×D4—41no—
957C2×D4—41no—
958C2×D4—41no—
959C2×D4—41no—
960C2×D4—41no—
961C2×D4—41no—
962C2×D4—41no—
963C2×D4—41no—
964C2×D4—41no—
965C2×D4—41no—
966C2×D4—48no—
967C2×D4—48no—
968C2×D4—48no—
969C2×D4—48no—
970C2×D4—48no—
971C2×D4—48no—
972C2×D4#80614yes—
973C2×D4#83414yes—
974C22×C4—22no—
975C22×C4—22no—
976C22×C4—22no—
977C22×C4—22no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—22no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—22no—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—21no—
1001C22×C4—21no—
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—21no—
1005C22×C4—21no—
1006C22×C4—21no—
1007C22×C4—21no—
1008C22×C4—21no—
1009C22×C4—21no—
1010C22×C4—21no—
1011C22×C4—21no—
1012C22×C4—21no—
1013C22×C4—21no—
1014C22×C4—21no—
1015C22×C4—21no—
1016C22×C4—21no—
1017C22×C4—21no—
1018C22×C4—41no—
1019C22×C4—41no—
1020C22×C4—41no—
1021C22×C4—41no—
1022C22×C4—41no—
1023C22×C4—41no—
1024C22×C4—41no—
1025C22×C4—41no—
1026C22×C4—41no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—41no—
1030C22×C4—41no—
1031C22×C4—41no—
1032C22×C4—41no—
1033C22×C4—41no—
1034C22×C4—41no—
1035C22×C4—41no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—64no—
1049C22×C4—122no—
1050C22×C4—122no—
1051C22×C4—122no—
1052C22×C4—122no—
1053C22×C4—122no—
1054C22×C4—128no—
1055C22×C4—122no—
1056C22×C4—122no—
1057C22×C4—122no—
1058C22×C4—122no—
1059C22×C4—122no—
1060C22×C4—122no—
1061C22×C4—122no—
1062C22×C4—122no—
1063C22×C4—248no—
1064C22×C4—248no—
1065C22×C4—244no—
1066C22×C4—244no—
1067C22×C4#80611yescharacteristic
1068C22×C4#80611yescharacteristic
1069C22×C4#80611yescharacteristic
1070C22×C4#80611yescharacteristic
1071C22×C4C3⋊#9511yescharacteristic
1072C22×C4C3⋊#9511yescharacteristic
1073C22×C4C2×C4×Dic311yescharacteristic
1074C22×C4C2×Dic3⋊C411yescharacteristic
1075C22×C4C2×Dic3⋊C411yescharacteristic
1076C22×C4C2×C4⋊Dic311yescharacteristic
1077C22×C4C2×(C2×D3)⋊C411yescharacteristic
1078C22×C4C2×#21711yescharacteristic
1079M16—44no—
1080M16—44no—
1081M16—84no—
1082M16—124no—
1083M16—124no—
1084M16—244no—
1085C2×C8—44no—
1086C2×C8—84no—
1087C2×C8—124no—
1088C2×C8—244no—
1089C22⋊C4—248no—
1090C22⋊C4—248no—
1091C22⋊C4—244no—
1092C22×C3—22no—
1093C22×C3—22no—
1094C22×C3—22no—
1095C22×C3—22no—
1096C22×C3—21no—
1097C22×C3—21no—
1098C22×C3—21no—
1099C22×C3—21no—
1100C22×C3—21no—
1101C22×C3—21no—
1102C22×C3—22no—
1103C22×C3—22no—
1104C22×C3—22no—
1105C22×C3—22no—
1106C22×C3—42no—
1107C22×C3—42no—
1108C22×C3—42no—
1109C22×C3—42no—
1110C22×C3—44no—
1111C22×C3—48no—
1112C22×C3—42no—
1113C22×C3—42no—
1114C22×C3—44no—
1115C22×C3—42no—
1116C22×C3—42no—
1117C22×C3—41no—
1118C22×C3—41no—
1119C22×C3—41no—
1120C22×C3—41no—
1121C22×C3—41no—
1122C22×C3—41no—
1123C22×C3—41no—
1124C22×C3—41no—
1125C22×C3—41no—
1126C22×C3—41no—
1127C22×C3—41no—
1128C22×C3—41no—
1129C22×C3—41no—
1130C22×C3—41no—
1131C22×C3—81no—
1132C22×C3—81no—
1133C22×C3—82no—
1134C22×C3—82no—
1135C22×C3—84no—
1136C22×C3—84no—
1137C22×C3—82no—
1138C22×C3—82no—
1139C22×C3—81no—
1140C22×C3—81no—
1141C22×C3C2×#34211yescharacteristic
1142C22×C3C2×#34211yescharacteristic
1143C22×C3C2×#34211yescharacteristic
1144C22×C3#213212yes—
1145C22×C3#213411yescharacteristic
1146C22×C3#213511yescharacteristic
1147C3×C4—22no—
1148C3×C4—22no—
1149C3×C4—21no—
1150C3×C4—21no—
1151C3×C4—21no—
1152C3×C4—21no—
1153C3×C4—41no—
1154C3×C4—41no—
1155C3×C4—41no—
1156C3×C4—41no—
1157Dic3—84no—
1158Dic3—162no—
1159C23—22no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—24no—
1165C23—24no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—21no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—42no—
1181C23—42no—
1182C23—42no—
1183C23—42no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—42no—
1189C23—44no—
1190C23—44no—
1191C23—44no—
1192C23—44no—
1193C23—42no—
1194C23—41no—
1195C23—41no—
1196C23—41no—
1197C23—41no—
1198C23—41no—
1199C23—41no—
1200C23—41no—
1201C23—41no—
1202C23—44no—
1203C23—44no—
1204C23—44no—
1205C23—44no—
1206C23—42no—
1207C23—41no—
1208C23—41no—
1209C23—42no—
1210C23—42no—
1211C23—41no—
1212C23—41no—
1213C23—41no—
1214C23—41no—
1215C23—81no—
1216C23—81no—
1217C23—81no—
1218C23—81no—
1219C23—82no—
1220C23—82no—
1221C23—82no—
1222C23—82no—
1223C23#452612yes—
1224C23#452612yes—
1225C23#452712yes—
1226C23#452712yes—
1227C23C2×#80611yescharacteristic
1228C23C2×#80611yescharacteristic
1229C23C2×C3⋊#9511yescharacteristic
1230Q8—44no—
1231Q8—44no—
1232Q8—44no—
1233Q8—44no—
1234D4—44no—
1235D4—44no—
1236D4—44no—
1237D4—44no—
1238D4—44no—
1239D4—44no—
1240D4—44no—
1241D4—44no—
1242D4—44no—
1243D4—44no—
1244D4—44no—
1245D4—44no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—42no—
1275C2×C4—42no—
1276C2×C4—42no—
1277C2×C4—42no—
1278C2×C4—42no—
1279C2×C4—42no—
1280C2×C4—42no—
1281C2×C4—42no—
1282C2×C4—42no—
1283C2×C4—42no—
1284C2×C4—42no—
1285C2×C4—42no—
1286C2×C4—42no—
1287C2×C4—42no—
1288C2×C4—42no—
1289C2×C4—42no—
1290C2×C4—42no—
1291C2×C4—42no—
1292C2×C4—42no—
1293C2×C4—42no—
1294C2×C4—42no—
1295C2×C4—42no—
1296C2×C4—42no—
1297C2×C4—42no—
1298C2×C4—42no—
1299C2×C4—42no—
1300C2×C4—124no—
1301C2×C4—124no—
1302C2×C4—124no—
1303C2×C4—242no—
1304C2×C4—242no—
1305C2×C4—242no—
1306C2×C4—2416no—
1307C2×C4—242no—
1308C2×C4—242no—
1309C2×C4—242no—
1310C2×C4—242no—
1311C2×C4—242no—
1312C2×C4—242no—
1313C2×C4—242no—
1314C2×C4—242no—
1315C2×C4#452711yescharacteristic
1316C2×C4#452711yescharacteristic
1317C2×C4#452711yescharacteristic
1318C2×C4#452711yescharacteristic
1319C2×C4C2×#80612yes—
1320C2×C4C2×#83412yes—
1321C8—84no—
1322C8—244no—
1323C2×C3—21no—
1324C2×C3—22no—
1325C2×C3—21no—
1326C2×C3—21no—
1327C2×C3—21no—
1328C2×C3—42no—
1329C2×C3—42no—
1330C2×C3—42no—
1331C2×C3—42no—
1332C2×C3—81no—
1333C2×C3—81no—
1334C2×C3#810111yescharacteristic
1335C2×C3#1258511yescharacteristic
1336C2×C3#1258711yescharacteristic
1337C22—22no—
1338C22—22no—
1339C22—22no—
1340C22—22no—
1341C22—21no—
1342C22—21no—
1343C22—21no—
1344C22—21no—
1345C22—21no—
1346C22—21no—
1347C22—22no—
1348C22—22no—
1349C22—22no—
1350C22—22no—
1351C22—42no—
1352C22—42no—
1353C22—42no—
1354C22—42no—
1355C22—44no—
1356C22—48no—
1357C22—42no—
1358C22—42no—
1359C22—44no—
1360C22—42no—
1361C22—42no—
1362C22—41no—
1363C22—41no—
1364C22—41no—
1365C22—41no—
1366C22—41no—
1367C22—41no—
1368C22—41no—
1369C22—41no—
1370C22—41no—
1371C22—41no—
1372C22—41no—
1373C22—41no—
1374C22—41no—
1375C22—41no—
1376C22—81no—
1377C22—81no—
1378C22—82no—
1379C22—82no—
1380C22—84no—
1381C22—84no—
1382C22—82no—
1383C22—82no—
1384C22—81no—
1385C22—81no—
1386C22#7014812yes—
1387C22#7014911yescharacteristic
1388C22#7015011yescharacteristic
1389C22C2×#452611yescharacteristic
1390C22C2×#452711yescharacteristic
1391C22C2×#452711yescharacteristic
1392C4—22no—
1393C4—22no—
1394C4—21no—
1395C4—21no—
1396C4—21no—
1397C4—21no—
1398C4—41no—
1399C4—41no—
1400C4—41no—
1401C4—41no—
1402C4—244no—
1403C4—482no—
1404C3#12805911yescharacteristic, complemented, Sylow
1405C2—21no—
1406C2—22no—
1407C2—21no—
1408C2—21no—
1409C2—21no—
1410C2—42no—
1411C2—42no—
1412C2—42no—
1413C2—42no—
1414C2—81no—
1415C2—81no—
1416C2#1068551111yescharacteristic
1417C2#1071016811yescharacteristic
1418C2#1071017411yescharacteristic
subgroupG/H
centerC22C2×#4527
commutatorC22×C3×C4C2×C42
FrattiniC23×Q8C22×D3
FittingC3×#20591C2
socleC22×C3C2×#342
prime radicalC23×C3×#41C22
cosocleC23×C3×Q8C23
hypercenter#20591D3
hypocenterC3#128059
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×#41 ◁ #20591

Complements

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

NH ≅ G/Ntype
3. #10682467C2semidirect
8. C2×C3×#413C4semidirect
11. C2×#5237C4semidirect
18. C3×#1785C4semidirect
22. #72137C4semidirect
63. C2×C3×#101C2×C4semidirect
75. C2×#836C2×C4semidirect
100. C2×#413Dic3semidirect
110. #1785Dic3semidirect
308. C2×#101C2×Dic3semidirect
1404. C3#128059semidirect

Maximal subgroups

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

subgroupindex
#107943512
#107178762
#106824672
C3×#205912
#1280593