Finite Group Databasebeta

← #11024048

Subgroups — #11024048

Order 768.

3206 conjugacy classes of subgroups.

The subgroup lattice has 1284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#535C211yesmaximal, characteristic, complemented
2C2×#5824C211yesmaximal, characteristic, complemented
3C22×#935C211yesmaximal, characteristic, complemented
4C2×#5586C211yesmaximal, characteristic, complemented
5#84090C211yesmaximal, characteristic, complemented
6#84054C211yesmaximal, characteristic, complemented
7#83182C212yesmaximal, complemented
8#83176C212yesmaximal, complemented
9#82982C212yesmaximal, complemented
10#82964C212yesmaximal, complemented
11#82686C212yesmaximal, complemented
12#82685C212yesmaximal, complemented
13#82657C212yesmaximal, complemented
14#82655C212yesmaximal, complemented
15#82602C211yesmaximal, characteristic, complemented
16#82592C211yesmaximal, characteristic, complemented
17#82591C211yesmaximal, characteristic, complemented
18#82590C211yesmaximal, characteristic, complemented
19#82583C211yesmaximal, characteristic, complemented
20#82581C211yesmaximal, characteristic, complemented
21#82578C211yesmaximal, characteristic, complemented
22#82246C211yesmaximal, characteristic, complemented
23#82238C211yesmaximal, characteristic, complemented
24#37655—31nomaximal, Sylow
25C22×C3×#41C2211yescharacteristic
26C23×C3×D4C2211yescharacteristic
27C24×Dic3C2211yescharacteristic
28C22×#237C2211yescharacteristic
29C3×#535—28no—
30C2×C3×#127C2212yes—
31C2×C3×#124C2212yes—
32C2×C3×#121C2212yes—
33C2×C3×#121C2212yes—
34C2×C3×#120C2211yescharacteristic
35C2×C3×#120C2211yescharacteristic
36C2×C3×#120C2211yescharacteristic
37C2×C3×#120C2211yescharacteristic
38C2×C3×#117C2211yescharacteristic
39C2×#953C2211yescharacteristic
40C2×#953C2211yescharacteristic
41C22×#217C2211yescharacteristic
42C22×#217C2211yescharacteristic
43C22×#217C2211yescharacteristic
44#5824—28no—
45C2×#946C2211yescharacteristic, complemented
46C2×#944C2211yescharacteristic, complemented
47C2×#939C2211yescharacteristic
48C2×#939C2212yescomplemented
49C2×#939C2211yescharacteristic, complemented
50C2×#935—28no—
51C2×#935C2212yes—
52C2×#935C2212yes—
53C2×#935C2211yescharacteristic
54C2×#935C2211yescharacteristic
55C2×#935C2212yes—
56C2×#935C2212yes—
57C2×#935C2211yescharacteristic
58C2×#935C2211yescharacteristic, complemented
59C2×D4×Dic3C2211yescharacteristic
60C2×D4×Dic3C2212yescomplemented
61C2×#929C2211yescharacteristic
62C2×#929C2211yescharacteristic, complemented
63C2×C4×#67C2211yescharacteristic, complemented
64C2×#924C2211yescharacteristic, complemented
65C22×Dic3⋊C4C2211yescharacteristic
66C22×Dic3⋊C4C2211yescharacteristic
67C22×Dic3⋊C4C2211yescharacteristic, complemented
68#5586—28no—
69C2×#886C2211yescharacteristic
70C2×#67⋊C4C2212yescomplemented
71C2×#878C2212yescomplemented
72C2×#877C2211yescharacteristic
73#5247C2211yescharacteristic
74#5247C2211yescharacteristic
75#5230C2212yescomplemented
76#5223C2212yes—
77#5223C2212yes—
78#5223C2212yescomplemented
79#5223C2212yescomplemented
80#5223C2212yescomplemented
81#5222C2212yes—
82#5222C2212yes—
83#5222C2212yescomplemented
84#5222C2212yescomplemented
85#5222C2212yescomplemented
86#5222C2212yescomplemented
87#5221C2212yescomplemented
88#5221C2212yescomplemented
89#5221C2212yescomplemented
90#5220C2211yescharacteristic
91#5220C2211yescharacteristic
92#5220C2212yescomplemented
93#5220C2212yescomplemented
94#5220C2212yescomplemented
95#5220C2212yescomplemented
96#5220C2212yescomplemented
97#5211C2211yescharacteristic
98#5210C2212yescomplemented
99#5210C2212yescomplemented
100#4994C2212yescomplemented
101#4981C2212yescomplemented
102#4978C2212yescomplemented
103#4976C2212yescomplemented
104#4959C2212yescomplemented
105#4958C2211yescharacteristic
106#4957C2212yescomplemented
107#4956C2212yescomplemented
108#4952C2212yescomplemented
109#4951C2212yescomplemented
110#4951C2212yescomplemented
111#4950C2211yescharacteristic
112#4949C2212yescomplemented
113#4948C2212yescomplemented
114#4948C2212yescomplemented
115#4947C2212yescomplemented
116#4946C2212yescomplemented
117#4946C2212yescomplemented
118#4945C2212yescomplemented
119#4944C2212yescomplemented
120#4943C2211yescharacteristic
121#4943C2211yescharacteristic
122#4942C2211yescharacteristic
123Dic3×C22⋊C4C2211yescharacteristic
124#4940C2212yescomplemented
125#4933C2212yescomplemented
126C4×Dic3⋊C4C2212yescomplemented
127#4928C2212yescomplemented
128C2×#547—31no—
129C2×#535D311yescharacteristic, complemented
130C2×#525—31no—
131C22×#123—31no—
132#2849—31no—
133#2682—32no—
134#2681—32no—
135#2674—32no—
136#2673—32no—
137#2617—31no—
138#2613—31no—
139#2539—31no—
140#2534—31no—
141#2461—32no—
142#2456—32no—
143#2445—32no—
144#2443—32no—
145#2413—31no—
146#2411—31no—
147#2406—31no—
148#2404—31no—
149#2344—31no—
150#2321—31no—
151C25×C3C2311yescharacteristic
152C25×C3C2311yescharacteristic
153C2×C3×#41—24no—
154C2×C3×#41—24no—
155C2×C3×#41—42no—
156C22×C3×Q8C2311yescharacteristic
157C22×C3×D4—24no—
158C22×C3×D4—24no—
159C22×C3×D4—42no—
160C22×C3×D4C2311yescharacteristic
161C22×C3×D4C2312yes—
162C22×C3×D4C2312yes—
163C22×C3×D4C2311yescharacteristic
164C22×C3×D4C2311yescharacteristic
165C22×C3×D4C2312yes—
166C22×C3×D4C2312yes—
167C22×C3×D4C2312yes—
168C22×C3×D4C2312yes—
169C23×C3×C4C2311yescharacteristic
170C23×C3×C4C2311yescharacteristic
171C23×C3×C4C2311yescharacteristic
172C22×#67C2311yescharacteristic
173C22×#67C2311yescharacteristic
174C22×#67C2312yes—
175C22×#67C2311yescharacteristic
176C22×#67C2312yes—
177C23×Dic3—24no—
178C23×Dic3—24no—
179C23×Dic3—42no—
180C23×Dic3C2311yescharacteristic
181C23×Dic3C2311yescharacteristic
182C23×Dic3C2312yes—
183C23×Dic3C2312yes—
184C23×Dic3C2311yescharacteristic
185C23×Dic3C2311yescharacteristic
186C23×Dic3C2311yescharacteristic
187C23×Dic3C2311yescharacteristic
188C2×#237—24no—
189C2×#237—24no—
190C2×#237—42no—
191C22×C4×D3C2311yescharacteristic
192C22×Dic6C2311yescharacteristic
193C3×#127—28no—
194C3×#124—28no—
195C3×#121—28no—
196C3×#121—28no—
197C3×#120—24no—
198C3×#120—24no—
199C3×#120—24no—
200C3×#120D418yescomplemented
201C3×#117—24no—
202C2×C3×C4⋊C4C2312yes—
203C2×C3×C22⋊C4C2311yescharacteristic
204C2×C3×C22⋊C4C2312yes—
205C2×C3×C22⋊C4C2312yes—
206C2×C3×C22⋊C4C2312yes—
207C2×C3×C22⋊C4C2311yescharacteristic
208C2×C3×C22⋊C4C2312yes—
209C2×C3×C42C2312yes—
210#953—24no—
211#953—42no—
212C2×#217—24no—
213C2×#217—24no—
214C2×#217—24no—
215C2×#217C2311yescharacteristic
216C2×#217C2311yescharacteristic
217C2×#217C2311yescharacteristic
218C2×#217C2312yes—
219C2×#217C2312yes—
220C2×#217C2312yes—
221C2×#217C2312yes—
222C2×#217C2312yes—
223C2×#217C2312yes—
224C2×#217C2312yes—
225C2×#217C2312yes—
226C2×#217C2311yescharacteristic
227C2×#217C2311yescharacteristic
228C2×#217C2311yescharacteristic
229C2×#217C2311yescharacteristic
230C2×#217C2312yes—
231C2×#217C2312yes—
232C2×#217C2312yes—
233C2×#217C2312yes—
234C2×#217C2312yes—
235C2×#217C2312yes—
236C2×#217C2312yes—
237C2×#217C2312yes—
238#946—24no—
239#944—24no—
240#939—28no—
241#939—24no—
242#939—24no—
243#935—24no—
244#935—24no—
245#935—28no—
246#935—28no—
247#935—28no—
248#935—28no—
249#935—24no—
250#935—42no—
251D4×Dic3—28no—
252D4×Dic3—24no—
253#929—24no—
254#929—24no—
255C4×#67—24no—
256C2×(C2×D3)⋊C4C2311yescharacteristic
257C2×(C2×D3)⋊C4C2312yes—
258C2×(C2×D3)⋊C4C2311yescharacteristic
259C2×(C2×D3)⋊C4C2311yescharacteristic
260C2×(C2×D3)⋊C4C2312yes—
261C2×C4⋊Dic3C2312yes—
262C2×C4⋊Dic3C2311yescharacteristic
263C2×C4⋊Dic3C2312yes—
264#924—24no—
265C2×Dic3⋊C4—24no—
266C2×Dic3⋊C4—24no—
267C2×Dic3⋊C4D418yescomplemented
268C2×Dic3⋊C4C2311yescharacteristic
269C2×Dic3⋊C4C2312yes—
270C2×Dic3⋊C4C2312yes—
271C2×Dic3⋊C4C2311yescharacteristic
272C2×Dic3⋊C4C2312yes—
273C2×Dic3⋊C4C2311yescharacteristic
274C2×Dic3⋊C4C2311yescharacteristic
275C2×Dic3⋊C4C2312yes—
276C2×Dic3⋊C4C2311yescharacteristic
277C2×Dic3⋊C4C2312yes—
278C2×Dic3⋊C4C2312yes—
279C2×Dic3⋊C4C2311yescharacteristic
280C2×Dic3⋊C4C2311yescharacteristic
281C2×Dic3⋊C4C2311yescharacteristic
282C2×Dic3⋊C4C2311yescharacteristic
283C2×C4×Dic3C2312yes—
284C2×C4×Dic3C2311yescharacteristic
285C2×C4×Dic3C2312yes—
286#886—24no—
287#67⋊C4—28no—
288#878—28no—
289#877—24no—
290C3⋊#95C2312yes—
291C3⋊#95C2312yes—
292C3⋊#95C2312yes—
293C3⋊#95C2312yes—
294C3⋊#95C2312yes—
295C3⋊#95C2312yes—
296C3⋊#95C2312yes—
297C3⋊#95C2312yes—
298C3⋊#95C2312yes—
299C3⋊#95C2312yes—
300C3⋊#95C2312yes—
301C3⋊#95C2312yes—
302C22×#41—31no—
303C22×#41C2×D311yescharacteristic
304C23×D4C2×D311yescharacteristic
305C24×C4—31no—
306#547—68no—
307#535—28no—
308C2×C4⋊Q8—31no—
309C2×#127C2×D312yes—
310C2×#124C2×D312yes—
311#525—68no—
312C2×#123—31no—
313C2×#123—31no—
314C2×#123—32no—
315C2×#123—32no—
316C2×#123—32no—
317C2×#123—32no—
318C2×#123—31no—
319C2×#123—31no—
320C2×#123—31no—
321C2×#123—31no—
322C2×#123—31no—
323C2×#123—68no—
324C2×C22⋊Q8—31no—
325C2×C22⋊Q8—31no—
326C2×C22⋊Q8—32no—
327C2×#121—31no—
328C2×#121—32no—
329C2×#121—31no—
330C2×#121C2×D312yes—
331C2×#121C2×D312yes—
332C2×#120—31no—
333C2×#120—31no—
334C2×#120C2×D311yescharacteristic
335C2×#120C2×D311yescharacteristic
336C2×#120C2×D311yescharacteristic
337C2×#120C2×D311yescharacteristic
338C2×C4×D4—31no—
339C2×C4×D4—32no—
340C2×C4×D4—31no—
341C2×C4×D4—32no—
342C2×#117—31no—
343C2×#117C2×D311yescharacteristic
344C22×C4⋊C4—31no—
345C22×C4⋊C4—31no—
346C22×C4⋊C4—31no—
347C22×C22⋊C4—31no—
348C22×C22⋊C4—31no—
349C22×C22⋊C4—31no—
350#399—32no—
351#398—32no—
352#397—32no—
353#396—32no—
354#396—32no—
355#396—32no—
356#395—32no—
357#394—32no—
358#394—32no—
359#394—32no—
360#394—32no—
361#394—32no—
362#394—32no—
363#394—32no—
364#393—32no—
365#392—32no—
366#392—32no—
367#392—32no—
368#392—32no—
369#392—32no—
370#390—32no—
371#390—32no—
372#390—32no—
373#390—32no—
374#389—32no—
375#389—32no—
376#388—32no—
377#388—32no—
378#388—32no—
379#388—32no—
380#388—32no—
381#387—32no—
382#387—32no—
383#386—31no—
384#386—32no—
385#386—32no—
386#386—32no—
387#386—31no—
388#386—32no—
389#386—32no—
390#386—31no—
391#386—32no—
392#385—32no—
393#385—32no—
394#385—31no—
395#385—32no—
396#385—32no—
397#381—31no—
398#381—31no—
399#381—31no—
400#380—31no—
401#379—31no—
402#379—31no—
403C4×C4⋊C4—32no—
404C4×C22⋊C4—31no—
405C24×C3—22no—
406C24×C3—22no—
407C24×C3—22no—
408C24×C3—22no—
409C24×C3—22no—
410C24×C3—42no—
411C24×C3—42no—
412C24×C3—42no—
413C24×C3—42no—
414C24×C3C2×D414yes—
415C24×C3C2412yes—
416C24×C3C2411yescharacteristic
417C24×C3C2412yes—
418C24×C3C2411yescharacteristic
419C24×C3C2411yescharacteristic
420C23×D3C2411yescharacteristic
421C3×#41—416no—
422C2×C3×Q8—22no—
423C2×C3×Q8—22no—
424C2×C3×Q8—41no—
425C2×C3×D4—22no—
426C2×C3×D4—22no—
427C2×C3×D4—22no—
428C2×C3×D4—22no—
429C2×C3×D4—24no—
430C2×C3×D4—24no—
431C2×C3×D4—22no—
432C2×C3×D4—22no—
433C2×C3×D4—24no—
434C2×C3×D4—24no—
435C2×C3×D4—24no—
436C2×C3×D4—24no—
437C2×C3×D4—22no—
438C2×C3×D4—24no—
439C2×C3×D4—42no—
440C2×C3×D4—42no—
441C2×C3×D4—42no—
442C2×C3×D4—42no—
443C2×C3×D4—41no—
444C2×C3×D4—416no—
445C2×C3×D4—42no—
446C2×C3×D4—42no—
447C2×C3×D4—42no—
448C2×C3×D4—42no—
449C2×C3×D4—42no—
450C2×C3×D4—42no—
451C2×C3×D4C2×D414yes—
452C2×C3×D4C2×D418yes—
453C22×C3×C4—22no—
454C22×C3×C4—22no—
455C22×C3×C4—22no—
456C22×C3×C4—22no—
457C22×C3×C4—22no—
458C22×C3×C4—22no—
459C22×C3×C4—41no—
460C22×C3×C4—41no—
461C22×C3×C4C2×D414yes—
462C22×C3×C4C2412yes—
463C22×C3×C4C2411yescharacteristic
464C22×C3×C4C2412yes—
465C22×C3×C4C2411yescharacteristic
466C22×C3×C4C2411yescharacteristic
467C22×C3×C4C2411yescharacteristic
468C2×#67—24no—
469C2×#67—22no—
470C2×#67—22no—
471C2×#67—22no—
472C2×#67—22no—
473C2×#67—22no—
474C2×#67—22no—
475C2×#67—41no—
476C2×#67—42no—
477C2×#67—42no—
478C2×#67—42no—
479C2×#67—42no—
480C2×#67—42no—
481C2×#67—42no—
482C22×Dic3—22no—
483C22×Dic3—22no—
484C22×Dic3—24no—
485C22×Dic3—24no—
486C22×Dic3—22no—
487C22×Dic3—22no—
488C22×Dic3—22no—
489C22×Dic3—22no—
490C22×Dic3—22no—
491C22×Dic3—22no—
492C22×Dic3—22no—
493C22×Dic3—24no—
494C22×Dic3—24no—
495C22×Dic3—41no—
496C22×Dic3—42no—
497C22×Dic3—42no—
498C22×Dic3—42no—
499C22×Dic3—42no—
500C22×Dic3—42no—
501C22×Dic3—416no—
502C22×Dic3C2×D414yes—
503C22×Dic3C2×D414yes—
504C22×Dic3C2412yes—
505C22×Dic3C2412yes—
506C22×Dic3C2411yescharacteristic
507C22×Dic3C2412yes—
508C22×Dic3C2411yescharacteristic
509C22×Dic3C2412yes—
510C22×Dic3C2411yescharacteristic
511C22×Dic3C2411yescharacteristic
512C22×Dic3C2411yescharacteristic
513C22×Dic3C2411yescharacteristic
514C22×Dic3C2411yescharacteristic
515#237—416no—
516C2×C4×D3—22no—
517C2×C4×D3—22no—
518C2×C4×D3—41no—
519C2×Dic6—22no—
520C2×Dic6—22no—
521C2×Dic6—41no—
522C3×C4⋊C4—24no—
523C3×C22⋊C4—22no—
524C3×C22⋊C4—24no—
525C3×C22⋊C4—24no—
526C3×C22⋊C4—24no—
527C3×C22⋊C4C2×D414yes—
528C3×C22⋊C4C2×D418yes—
529C3×C42—24no—
530#217—22no—
531#217—24no—
532#217—22no—
533#217—24no—
534#217—22no—
535#217—22no—
536#217—22no—
537#217—22no—
538#217—22no—
539#217—24no—
540#217—24no—
541#217—24no—
542#217—24no—
543#217—24no—
544#217—24no—
545#217—42no—
546#217—42no—
547#217—42no—
548#217—42no—
549#217—42no—
550#217—42no—
551#217—42no—
552#217—42no—
553(C2×D3)⋊C4—24no—
554(C2×D3)⋊C4—22no—
555(C2×D3)⋊C4—22no—
556(C2×D3)⋊C4—22no—
557(C2×D3)⋊C4—42no—
558C4⋊Dic3—24no—
559C4⋊Dic3—22no—
560C4⋊Dic3—42no—
561Dic3⋊C4—24no—
562Dic3⋊C4—24no—
563Dic3⋊C4—22no—
564Dic3⋊C4—24no—
565Dic3⋊C4—24no—
566Dic3⋊C4—22no—
567Dic3⋊C4—22no—
568Dic3⋊C4—22no—
569Dic3⋊C4—22no—
570Dic3⋊C4—42no—
571Dic3⋊C4—42no—
572Dic3⋊C4C2×D414yes—
573Dic3⋊C4C2×D414yes—
574Dic3⋊C4C2×D414yes—
575Dic3⋊C4C2×D414yes—
576C4×Dic3—24no—
577C4×Dic3—22no—
578C4×Dic3—42no—
579C25C22×D311yescharacteristic
580C25C22×D311yescharacteristic
581C2×#41—24no—
582C2×#41—24no—
583C2×#41—42no—
584C2×#41—64no—
585C2×#41—64no—
586C2×#41—122no—
587C22×Q8—31no—
588C22×Q8C22×D311yescharacteristic
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—31no—
592C22×D4—31no—
593C22×D4—32no—
594C22×D4—31no—
595C22×D4—32no—
596C22×D4—42no—
597C22×D4C22×D311yescharacteristic
598C22×D4C22×D311yescharacteristic
599C22×D4C22×D312yes—
600C22×D4C22×D312yes—
601C22×D4C22×D311yescharacteristic
602C22×D4C22×D312yes—
603C22×D4C22×D312yes—
604C22×D4C22×D312yes—
605C22×D4C22×D312yes—
606C23×C4—31no—
607C23×C4—31no—
608C23×C4—31no—
609C23×C4—31no—
610C23×C4—32no—
611C23×C4—32no—
612C23×C4—31no—
613C23×C4—31no—
614C23×C4—31no—
615C23×C4—64no—
616C23×C4—64no—
617C23×C4—122no—
618C23×C4C22×D311yescharacteristic
619C23×C4C22×D311yescharacteristic
620C23×C4C22×D311yescharacteristic
621C4⋊Q8—64no—
622#127—28no—
623#124—28no—
624#123—64no—
625#123—68no—
626#123—68no—
627#123—68no—
628#123—68no—
629#123—64no—
630#123—64no—
631#123—64no—
632#123—64no—
633#123—64no—
634#123—122no—
635C22⋊Q8—64no—
636C22⋊Q8—64no—
637C22⋊Q8—68no—
638#121—28no—
639#121—28no—
640#121—64no—
641#121—64no—
642#121—68no—
643#120—24no—
644#120—24no—
645#120—24no—
646#120—64no—
647#120—122no—
648#120#6718yescomplemented
649C4×D4—64no—
650C4×D4—64no—
651C4×D4—68no—
652C4×D4—68no—
653#117—24no—
654#117—64no—
655C2×C4⋊C4—38no—
656C2×C4⋊C4—31no—
657C2×C4⋊C4—31no—
658C2×C4⋊C4—31no—
659C2×C4⋊C4—31no—
660C2×C4⋊C4—31no—
661C2×C4⋊C4—31no—
662C2×C4⋊C4—31no—
663C2×C4⋊C4—32no—
664C2×C4⋊C4—32no—
665C2×C4⋊C4—32no—
666C2×C4⋊C4—31no—
667C2×C4⋊C4—32no—
668C2×C4⋊C4—32no—
669C2×C4⋊C4—31no—
670C2×C4⋊C4—31no—
671C2×C4⋊C4—32no—
672C2×C4⋊C4—32no—
673C2×C4⋊C4—32no—
674C2×C4⋊C4—64no—
675C2×C4⋊C4—64no—
676C2×C4⋊C4C22×D312yes—
677C2×C22⋊C4—32no—
678C2×C22⋊C4—32no—
679C2×C22⋊C4—32no—
680C2×C22⋊C4—32no—
681C2×C22⋊C4—32no—
682C2×C22⋊C4—32no—
683C2×C22⋊C4—31no—
684C2×C22⋊C4—32no—
685C2×C22⋊C4—32no—
686C2×C22⋊C4—31no—
687C2×C22⋊C4—31no—
688C2×C22⋊C4—31no—
689C2×C22⋊C4—31no—
690C2×C22⋊C4—31no—
691C2×C22⋊C4—31no—
692C2×C22⋊C4—32no—
693C2×C22⋊C4—31no—
694C2×C22⋊C4—31no—
695C2×C22⋊C4—31no—
696C2×C22⋊C4—32no—
697C2×C22⋊C4—32no—
698C2×C22⋊C4—32no—
699C2×C22⋊C4—32no—
700C2×C22⋊C4—32no—
701C2×C22⋊C4—32no—
702C2×C22⋊C4—32no—
703C2×C22⋊C4—32no—
704C2×C22⋊C4—32no—
705C2×C22⋊C4—64no—
706C2×C22⋊C4—64no—
707C2×C22⋊C4—64no—
708C2×C22⋊C4C22×D311yescharacteristic
709C2×C22⋊C4C22×D312yes—
710C2×C22⋊C4C22×D312yes—
711C2×C22⋊C4C22×D312yes—
712C2×C22⋊C4C22×D311yescharacteristic
713C2×C22⋊C4C22×D312yes—
714C2×C42—32no—
715C2×C42—31no—
716C2×C42—32no—
717C2×C42C22×D312yes—
718#95—32no—
719#95—32no—
720#95—32no—
721#95—32no—
722#95—32no—
723#95—32no—
724#95—32no—
725#95—32no—
726#95—32no—
727#95—32no—
728#95—32no—
729#95—32no—
730C23×C3—22no—
731C23×C3—22no—
732C23×C3—28no—
733C23×C3—22no—
734C23×C3—21no—
735C23×C3—22no—
736C23×C3—21no—
737C23×C3—22no—
738C23×C3—22no—
739C23×C3—22no—
740C23×C3—22no—
741C23×C3—22no—
742C23×C3—22no—
743C23×C3—22no—
744C23×C3—21no—
745C23×C3—22no—
746C23×C3—21no—
747C23×C3—21no—
748C23×C3—22no—
749C23×C3—22no—
750C23×C3—22no—
751C23×C3—22no—
752C23×C3—22no—
753C23×C3—22no—
754C23×C3—22no—
755C23×C3—48no—
756C23×C3—44no—
757C23×C3—44no—
758C23×C3—48no—
759C23×C3—44no—
760C23×C3—44no—
761C23×C3—44no—
762C23×C3—84no—
763C23×C3—84no—
764C23×C3C22×D412yes—
765C23×C3C22×D412yes—
766C23×C3C22×D414yes—
767C23×C3C22×D412yes—
768C23×C3H(5,𝔽2)12yes—
769C23×C3C2511yescharacteristic
770C22×D3—21no—
771C22×D3—21no—
772C22×D3—21no—
773C22×D3—22no—
774C22×D3—22no—
775C3×Q8—44no—
776C3×D4—28no—
777C3×D4—48no—
778C3×D4—48no—
779C3×D4—48no—
780C3×D4—44no—
781C3×D4—44no—
782C3×D4—84no—
783C3×D4—84no—
784C3×D4—84no—
785C2×C3×C4—28no—
786C2×C3×C4—21no—
787C2×C3×C4—21no—
788C2×C3×C4—21no—
789C2×C3×C4—21no—
790C2×C3×C4—21no—
791C2×C3×C4—21no—
792C2×C3×C4—22no—
793C2×C3×C4—22no—
794C2×C3×C4—21no—
795C2×C3×C4—22no—
796C2×C3×C4—21no—
797C2×C3×C4—21no—
798C2×C3×C4—22no—
799C2×C3×C4—22no—
800C2×C3×C4—44no—
801C2×C3×C4—44no—
802C2×C3×C4C22×D412yes—
803C2×C3×C4C22×D412yes—
804C2×C3×C4C22×D414yes—
805C2×C3×C4C22×D412yes—
806#67—44no—
807#67—44no—
808#67—48no—
809#67—44no—
810#67—84no—
811C2×Dic3—28no—
812C2×Dic3—21no—
813C2×Dic3—21no—
814C2×Dic3—21no—
815C2×Dic3—21no—
816C2×Dic3—22no—
817C2×Dic3—22no—
818C2×Dic3—21no—
819C2×Dic3—22no—
820C2×Dic3—21no—
821C2×Dic3—21no—
822C2×Dic3—22no—
823C2×Dic3—22no—
824C2×Dic3—22no—
825C2×Dic3—21no—
826C2×Dic3—22no—
827C2×Dic3—22no—
828C2×Dic3—21no—
829C2×Dic3—22no—
830C2×Dic3—22no—
831C2×Dic3—22no—
832C2×Dic3—22no—
833C2×Dic3—22no—
834C2×Dic3—22no—
835C2×Dic3—22no—
836C2×Dic3—22no—
837C2×Dic3—44no—
838C2×Dic3—44no—
839C2×Dic3—48no—
840C2×Dic3—48no—
841C2×Dic3—44no—
842C2×Dic3—44no—
843C2×Dic3—44no—
844C2×Dic3C22×D412yes—
845C2×Dic3C22×D412yes—
846C2×Dic3C22×D412yes—
847C2×Dic3C22×D412yes—
848C4×D3—44no—
849Dic6—44no—
850C24—22no—
851C24—22no—
852C24—22no—
853C24—22no—
854C24—22no—
855C24—31no—
856C24—42no—
857C24—42no—
858C24—42no—
859C24—42no—
860C24C2×#6714yes—
861C24C23×D312yes—
862C24C23×D311yescharacteristic
863C24C23×D312yes—
864C24C23×D311yescharacteristic
865C24C23×D311yescharacteristic
866#41—416no—
867#41—1216no—
868C2×Q8—22no—
869C2×Q8—22no—
870C2×Q8—41no—
871C2×Q8—62no—
872C2×Q8—62no—
873C2×Q8—121no—
874C2×D4—22no—
875C2×D4—22no—
876C2×D4—22no—
877C2×D4—22no—
878C2×D4—22no—
879C2×D4—24no—
880C2×D4—24no—
881C2×D4—22no—
882C2×D4—24no—
883C2×D4—24no—
884C2×D4—22no—
885C2×D4—24no—
886C2×D4—24no—
887C2×D4—24no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—41no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—416no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—62no—
901C2×D4—62no—
902C2×D4—62no—
903C2×D4—62no—
904C2×D4—64no—
905C2×D4—62no—
906C2×D4—62no—
907C2×D4—121no—
908C2×D4—122no—
909C2×D4—122no—
910C2×D4—122no—
911C2×D4—122no—
912C2×D4—122no—
913C2×D4—122no—
914C2×D4C2×#6714yes—
915C2×D4C2×#6718yes—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4—22no—
922C22×C4—34no—
923C22×C4—31no—
924C22×C4—31no—
925C22×C4—31no—
926C22×C4—31no—
927C22×C4—34no—
928C22×C4—32no—
929C22×C4—32no—
930C22×C4—32no—
931C22×C4—31no—
932C22×C4—31no—
933C22×C4—32no—
934C22×C4—31no—
935C22×C4—41no—
936C22×C4—41no—
937C22×C4—62no—
938C22×C4—62no—
939C22×C4—62no—
940C22×C4—64no—
941C22×C4—64no—
942C22×C4—62no—
943C22×C4—62no—
944C22×C4—62no—
945C22×C4—62no—
946C22×C4—62no—
947C22×C4—64no—
948C22×C4—62no—
949C22×C4—64no—
950C22×C4—62no—
951C22×C4—62no—
952C22×C4—121no—
953C22×C4—122no—
954C22×C4—122no—
955C22×C4—121no—
956C22×C4—122no—
957C22×C4—122no—
958C22×C4—122no—
959C22×C4—1216no—
960C22×C4D3×D414yes—
961C22×C4C23×D312yes—
962C22×C4C23×D311yescharacteristic
963C22×C4C23×D311yescharacteristic
964C22×C4C23×D311yescharacteristic
965C22×C4C23×D312yes—
966C22×C4C23×D311yescharacteristic
967C4⋊C4—24no—
968C4⋊C4—34no—
969C4⋊C4—34no—
970C4⋊C4—34no—
971C4⋊C4—34no—
972C4⋊C4—62no—
973C4⋊C4—62no—
974C4⋊C4—62no—
975C4⋊C4—62no—
976C4⋊C4—62no—
977C4⋊C4—64no—
978C4⋊C4—64no—
979C4⋊C4—62no—
980C4⋊C4—64no—
981C4⋊C4—64no—
982C4⋊C4—64no—
983C4⋊C4—122no—
984C4⋊C4—122no—
985C4⋊C4—122no—
986C22⋊C4—22no—
987C22⋊C4—24no—
988C22⋊C4—24no—
989C22⋊C4—24no—
990C22⋊C4—62no—
991C22⋊C4—64no—
992C22⋊C4—64no—
993C22⋊C4—64no—
994C22⋊C4—64no—
995C22⋊C4—64no—
996C22⋊C4—64no—
997C22⋊C4—62no—
998C22⋊C4—62no—
999C22⋊C4—62no—
1000C22⋊C4—62no—
1001C22⋊C4—62no—
1002C22⋊C4—62no—
1003C22⋊C4—62no—
1004C22⋊C4—64no—
1005C22⋊C4—64no—
1006C22⋊C4—62no—
1007C22⋊C4—62no—
1008C22⋊C4—64no—
1009C22⋊C4—122no—
1010C22⋊C4—122no—
1011C22⋊C4—122no—
1012C22⋊C4—122no—
1013C22⋊C4—122no—
1014C22⋊C4—122no—
1015C22⋊C4—122no—
1016C22⋊C4—122no—
1017C22⋊C4—122no—
1018C22⋊C4C2×#6714yes—
1019C22⋊C4C2×#6718yes—
1020C42—24no—
1021C42—62no—
1022C42—64no—
1023C42—122no—
1024C22×C3—22no—
1025C22×C3—24no—
1026C22×C3—22no—
1027C22×C3—24no—
1028C22×C3—24no—
1029C22×C3—22no—
1030C22×C3—24no—
1031C22×C3—24no—
1032C22×C3—24no—
1033C22×C3—416no—
1034C22×C3—41no—
1035C22×C3—42no—
1036C22×C3—41no—
1037C22×C3—42no—
1038C22×C3—42no—
1039C22×C3—42no—
1040C22×C3—42no—
1041C22×C3—41no—
1042C22×C3—42no—
1043C22×C3—41no—
1044C22×C3—42no—
1045C22×C3—42no—
1046C22×C3—42no—
1047C22×C3—42no—
1048C22×C3—41no—
1049C22×C3—42no—
1050C22×C3—42no—
1051C22×C3—42no—
1052C22×C3—42no—
1053C22×C3—88no—
1054C22×C3D4214yes—
1055C22×C3C23×D411yescharacteristic
1056C22×C3C23×D411yescharacteristic
1057C22×C3C2×H(5,𝔽2)11yescharacteristic
1058C22×C3#58512yes—
1059C22×C3#58512yes—
1060C2×D3—41no—
1061C2×D3—41no—
1062C2×D3—42no—
1063C2×D3—41no—
1064C2×D3—42no—
1065C3×C4—22no—
1066C3×C4—22no—
1067C3×C4—22no—
1068C3×C4—24no—
1069C3×C4—41no—
1070C3×C4—42no—
1071Dic3—22no—
1072Dic3—22no—
1073Dic3—22no—
1074Dic3—22no—
1075Dic3—41no—
1076Dic3—41no—
1077Dic3—42no—
1078Dic3—42no—
1079Dic3—41no—
1080Dic3—42no—
1081Dic3—42no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—21no—
1086C23—21no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—28no—
1095C23—22no—
1096C23—21no—
1097C23—21no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—21no—
1107C23—48no—
1108C23—44no—
1109C23—44no—
1110C23—48no—
1111C23—44no—
1112C23—44no—
1113C23—44no—
1114C23—61no—
1115C23—61no—
1116C23—62no—
1117C23—62no—
1118C23—61no—
1119C23—84no—
1120C23—84no—
1121C23C2×D3×D412yes—
1122C23#100412yes—
1123C23C22×#6714yes—
1124C23C22×#6712yes—
1125C23C22×#6712yes—
1126C23C24×D311yescharacteristic
1127Q8—44no—
1128Q8—124no—
1129D4—28no—
1130D4—48no—
1131D4—48no—
1132D4—48no—
1133D4—44no—
1134D4—44no—
1135D4—84no—
1136D4—84no—
1137D4—84no—
1138D4—124no—
1139D4—124no—
1140D4—128no—
1141D4—124no—
1142D4—244no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—28no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—21no—
1158C2×C4—32no—
1159C2×C4—32no—
1160C2×C4—32no—
1161C2×C4—32no—
1162C2×C4—44no—
1163C2×C4—44no—
1164C2×C4—61no—
1165C2×C4—61no—
1166C2×C4—62no—
1167C2×C4—62no—
1168C2×C4—61no—
1169C2×C4—61no—
1170C2×C4—68no—
1171C2×C4—61no—
1172C2×C4—62no—
1173C2×C4—61no—
1174C2×C4—62no—
1175C2×C4—61no—
1176C2×C4—62no—
1177C2×C4—61no—
1178C2×C4—62no—
1179C2×C4—62no—
1180C2×C4—62no—
1181C2×C4—62no—
1182C2×C4—62no—
1183C2×C4—62no—
1184C2×C4—62no—
1185C2×C4—62no—
1186C2×C4—62no—
1187C2×C4—62no—
1188C2×C4—62no—
1189C2×C4—61no—
1190C2×C4—124no—
1191C2×C4—124no—
1192C2×C4—128no—
1193C2×C4—128no—
1194C2×C4—124no—
1195C2×C4—124no—
1196C2×C4—124no—
1197C2×C4—124no—
1198C2×C4C2×D3×D412yes—
1199C2×C4C2×D3×D412yes—
1200C2×C4C22×#6714yes—
1201C2×C4C22×#6712yes—
1202C2×C3—24no—
1203C2×C3—42no—
1204C2×C3—44no—
1205C2×C3—81no—
1206C2×C3—82no—
1207C2×C3#344911yescharacteristic
1208C2×C3C2×D4211yescharacteristic
1209C2×C3#348512yes—
1210C2×C3#348711yescharacteristic
1211C2×C3#353312yes—
1212D3—81no—
1213C22—22no—
1214C22—22no—
1215C22—24no—
1216C22—24no—
1217C22—22no—
1218C22—24no—
1219C22—24no—
1220C22—24no—
1221C22—24no—
1222C22—416no—
1223C22—41no—
1224C22—42no—
1225C22—42no—
1226C22—41no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—41no—
1231C22—42no—
1232C22—42no—
1233C22—41no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—41no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—88no—
1243C22—121no—
1244C22—121no—
1245C22—122no—
1246C22—121no—
1247C22—122no—
1248C22D4×#6714yes—
1249C22C22×D3×D411yescharacteristic
1250C22C2×#100411yescharacteristic
1251C22#596612yes—
1252C22#596612yes—
1253C22C23×#6711yescharacteristic
1254C4—22no—
1255C4—22no—
1256C4—22no—
1257C4—24no—
1258C4—41no—
1259C4—42no—
1260C4—62no—
1261C4—62no—
1262C4—62no—
1263C4—62no—
1264C4—121no—
1265C4—122no—
1266C4—121no—
1267C4—122no—
1268C4—122no—
1269C4—121no—
1270C4—122no—
1271C3#3765511yescharacteristic, complemented, Sylow
1272C2—24no—
1273C2—44no—
1274C2—42no—
1275C2—82no—
1276C2—81no—
1277C2—241no—
1278C2#8631311yescharacteristic
1279C2#8631511yescharacteristic
1280C2#8632112yes—
1281C2C2×D4×#6711yescharacteristic
1282C2#8728012yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#535C2
hypercenterC2×#535D3
hypocenterC3#37655
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×C3×#535C2semidirect
2. C2×#5824C2semidirect
3. C22×#935C2semidirect
4. C2×#5586C2semidirect
5. #84090C2semidirect
6. #84054C2semidirect
7. #83182C2semidirect
8. #83176C2semidirect
9. #82982C2semidirect
10. #82964C2semidirect
11. #82686C2semidirect
12. #82685C2semidirect
13. #82657C2semidirect
14. #82655C2semidirect
15. #82602C2semidirect
16. #82592C2semidirect
17. #82591C2semidirect
18. #82590C2semidirect
19. #82583C2semidirect
20. #82581C2semidirect
21. #82578C2semidirect
22. #82246C2semidirect
23. #82238C2semidirect
45. C2×#946C22semidirect
46. C2×#944C22semidirect
48. C2×#939C22semidirect
49. C2×#939C22semidirect
58. C2×#935C22semidirect
60. C2×D4×Dic3C22semidirect
62. C2×#929C22semidirect
63. C2×C4×#67C22semidirect
64. C2×#924C22semidirect
67. C22×Dic3⋊C4C22semidirect
70. C2×#67⋊C4C22semidirect
71. C2×#878C22semidirect
75. #5230C22semidirect
78. #5223C22semidirect
79. #5223C22semidirect
80. #5223C22semidirect
83. #5222C22semidirect
84. #5222C22semidirect
85. #5222C22semidirect
86. #5222C22semidirect
87. #5221C22semidirect
88. #5221C22semidirect
89. #5221C22semidirect
92. #5220C22semidirect
93. #5220C22semidirect
94. #5220C22semidirect
95. #5220C22semidirect
96. #5220C22semidirect
98. #5210C22semidirect
99. #5210C22semidirect
100. #4994C22semidirect
101. #4981C22semidirect
102. #4978C22semidirect
103. #4976C22semidirect
104. #4959C22semidirect
106. #4957C22semidirect
107. #4956C22semidirect
108. #4952C22semidirect
109. #4951C22semidirect
110. #4951C22semidirect
112. #4949C22semidirect
113. #4948C22semidirect
114. #4948C22semidirect
115. #4947C22semidirect
116. #4946C22semidirect
117. #4946C22semidirect
118. #4945C22semidirect
119. #4944C22semidirect
124. #4940C22semidirect
125. #4933C22semidirect
126. C4×Dic3⋊C4C22semidirect
127. #4928C22semidirect
129. C2×#535D3semidirect
200. C3×#120D4semidirect
267. C2×Dic3⋊C4D4semidirect
648. #120#67semidirect
1271. C3#37655semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5352
C2×#58242
C22×#9352
C2×#55862
#840902
#840542
#831822
#831762
#829822
#829642
#826862
#826852
#826572
#826552
#826022
#825922
#825912
#825902
#825832
#825812
#825782
#822462
#822382
#376553