Finite Group Databasebeta

← #11023863

Subgroups — #11023863

Order 768.

3130 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#546C211yesmaximal, characteristic
2C2×#5825C211yesmaximal, characteristic, complemented
3C22×#935C211yesmaximal, characteristic, complemented
4C22×#878C211yesmaximal, characteristic, complemented
5#84090C211yesmaximal, characteristic, complemented
6#84047C211yesmaximal, characteristic, complemented
7#82982C212yesmaximal, complemented
8#82871C212yesmaximal, complemented
9#82864C211yesmaximal, characteristic, complemented
10#82843C211yesmaximal, characteristic, complemented
11#82763C212yesmaximal, complemented
12#82685C212yesmaximal, complemented
13#82682C212yesmaximal, complemented
14#82675C211yesmaximal, characteristic, complemented
15#82664C211yesmaximal, characteristic, complemented
16#82602C211yesmaximal, characteristic, complemented
17#82589C212yesmaximal, complemented
18#82584C211yesmaximal, characteristic, complemented
19#82373C211yesmaximal, characteristic, complemented
20#82360C212yesmaximal, complemented
21#82326C211yesmaximal, characteristic, complemented
22#82110C212yesmaximal, complemented
23#82097C211yesmaximal, characteristic, complemented
24#37647—31nomaximal, Sylow
25C22×C3×#41C2211yescharacteristic
26C23×C3×D4C2211yescharacteristic
27C24×Dic3C2211yescharacteristic
28C23×Dic6C2211yescharacteristic, complemented
29C3×#546—28no—
30C2×C3×#124C2211yescharacteristic
31C2×C3×#123C2211yescharacteristic
32C2×C3×#123C2211yescharacteristic
33C2×C3×C22⋊Q8C2211yescharacteristic
34C2×C3×#121C2211yescharacteristic
35C2×C3×#121C2211yescharacteristic
36C2×C3×#121C2211yescharacteristic
37C2×C3×#120C2211yescharacteristic
38C2×C3×#120C2211yescharacteristic
39C2×C3×C4×D4C2211yescharacteristic
40C2×C3×C4×D4C2211yescharacteristic
41C22×C3×C22⋊C4C2211yescharacteristic
42C22×C3×C22⋊C4C2211yescharacteristic
43C22×#217C2211yescharacteristic
44C22×#217C2211yescharacteristic
45C22×#217C2212yes—
46#5825—28no—
47C2×#944C2212yescomplemented
48C2×#936C2212yescomplemented
49C2×#935—28no—
50C2×#935C2212yes—
51C2×#935C2211yescharacteristic
52C2×#935C2211yescharacteristic
53C2×#935C2211yescharacteristic
54C2×#935C2211yescharacteristic
55C2×#935C2212yes—
56C2×#935C2211yescharacteristic
57C2×#935C2211yescharacteristic
58C2×#935C2211yescharacteristic, complemented
59C2×#935C2211yescharacteristic, complemented
60C2×#935C2211yescharacteristic, complemented
61C2×#926C2211yescharacteristic, complemented
62C22×C4⋊Dic3C2211yescharacteristic, complemented
63C2×#924C2212yescomplemented
64C2×#924C2212yescomplemented
65C22×Dic3⋊C4C2212yes—
66C22×Dic3⋊C4C2211yescharacteristic, complemented
67C22×Dic3⋊C4C2211yescharacteristic, complemented
68C2×#878—28no—
69C2×#878C2212yes—
70C2×#878C2212yes—
71C2×#878C2212yescomplemented
72C2×#878C2212yescomplemented
73#5247C2212yes—
74#5247C2211yescharacteristic
75#5230C2212yescomplemented
76#5222C2212yes—
77#5222C2212yes—
78#5222C2212yescomplemented
79#5222C2212yescomplemented
80#5222C2212yescomplemented
81#5221C2212yescomplemented
82#5220C2211yescharacteristic
83#5220C2211yescharacteristic
84#5220C2212yes—
85#5220C2212yes—
86#5220C2211yescharacteristic, complemented
87#5220C2212yescomplemented
88#5212C2211yescharacteristic, complemented
89#5212C2212yescomplemented
90#5211C2211yescharacteristic, complemented
91#5210C2212yes—
92#5210C2212yescomplemented
93#5210C2212yescomplemented
94#5210C2212yescomplemented
95C4×#217C2211yescharacteristic, complemented
96#4983C2212yescomplemented
97#4982C2212yescomplemented
98#4981C2212yescomplemented
99#4979C2212yescomplemented
100#4979C2212yescomplemented
101#4976C2212yescomplemented
102#4976C2212yescomplemented
103#4975C2212yescomplemented
104#4953C2212yescomplemented
105#4952C2212yescomplemented
106#4951C2212yescomplemented
107#4951C2212yescomplemented
108#4950C2212yes—
109#4949C2212yescomplemented
110#4949C2212yescomplemented
111#4948C2212yescomplemented
112#4948C2212yescomplemented
113#4948C2212yescomplemented
114#4947C2212yescomplemented
115#4947C2212yescomplemented
116#4946C2212yes—
117#4946C2212yescomplemented
118#4946C2211yescharacteristic, complemented
119#4945C2212yescomplemented
120#4945C2212yescomplemented
121#4943C2211yescharacteristic, complemented
122#4943C2211yescharacteristic, complemented
123#4943C2211yescharacteristic, complemented
124#4942C2212yes—
125Dic3×C22⋊C4C2212yes—
126#4933C2212yescomplemented
127#4928C2212yescomplemented
128C2×#546D311yescharacteristic
129C2×#536—31no—
130C22×#123—31no—
131C22×C22⋊Q8—31no—
132#2849—31no—
133#2681—32no—
134#2680—32no—
135#2674—32no—
136#2672—32no—
137#2618—31no—
138#2614—31no—
139#2501—31no—
140#2486—31no—
141#2472—32no—
142#2449—32no—
143#2440—32no—
144#2437—32no—
145#2413—31no—
146#2412—31no—
147#2406—31no—
148#2405—31no—
149#2342—31no—
150#2322—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×D4C2311yescharacteristic
162C22×C3×D4C2311yescharacteristic
163C22×C3×D4C2311yescharacteristic
164C22×C3×D4C2311yescharacteristic
165C22×C3×D4C2311yescharacteristic
166C22×C3×D4C2311yescharacteristic
167C22×C3×D4C2311yescharacteristic
168C22×C3×D4C2311yescharacteristic
169C23×C3×C4C2311yescharacteristic
170C23×C3×C4C2311yescharacteristic
171C23×C3×C4C2311yescharacteristic
172C23×C3×C4C2311yescharacteristic
173C23×C3×C4C2311yescharacteristic
174C23×C3×C4C2311yescharacteristic
175C23×Dic3—24no—
176C23×Dic3—24no—
177C23×Dic3—42no—
178C23×Dic3C2311yescharacteristic
179C23×Dic3C2311yescharacteristic
180C23×Dic3C2312yes—
181C23×Dic3C2312yes—
182C23×Dic3C2312yes—
183C23×Dic3C2311yescharacteristic
184C23×Dic3C2311yescharacteristic
185C22×Dic6—24no—
186C22×Dic6—24no—
187C22×Dic6—42no—
188C22×Dic6C2312yes—
189C22×Dic6C2312yes—
190C3×#124—24no—
191C3×#123—24no—
192C3×#123—24no—
193C3×C22⋊Q8—24no—
194C3×#121—24no—
195C3×#121—24no—
196C3×#121—24no—
197C3×#120—24no—
198C3×#120—24no—
199C3×C4×D4—24no—
200C3×C4×D4—24no—
201C2×C3×C4⋊C4C2311yescharacteristic
202C2×C3×C4⋊C4C2311yescharacteristic
203C2×C3×C4⋊C4C2311yescharacteristic
204C2×C3×C4⋊C4C2311yescharacteristic
205C2×C3×C22⋊C4—24no—
206C2×C3×C22⋊C4D418yes—
207C2×C3×C22⋊C4C2311yescharacteristic
208C2×C3×C22⋊C4C2311yescharacteristic
209C2×C3×C22⋊C4C2311yescharacteristic
210C2×C3×C22⋊C4C2311yescharacteristic
211C2×C3×C22⋊C4C2311yescharacteristic
212C2×C3×C22⋊C4C2311yescharacteristic
213C2×C3×C22⋊C4C2311yescharacteristic
214C2×C3×C22⋊C4C2311yescharacteristic
215C2×C3×C22⋊C4C2311yescharacteristic
216C2×C3×C22⋊C4C2311yescharacteristic
217C2×C3×C22⋊C4C2311yescharacteristic
218C2×C3×C22⋊C4C2311yescharacteristic
219C2×C3×C42C2311yescharacteristic
220C2×#217—24no—
221C2×#217—28no—
222C2×#217—24no—
223C2×#217C2312yes—
224C2×#217C2312yes—
225C2×#217C2311yescharacteristic
226C2×#217C2311yescharacteristic
227C2×#217C2311yescharacteristic
228C2×#217C2312yes—
229C2×#217C2312yes—
230C2×#217C2312yes—
231C2×#217C2312yes—
232C2×#217C2312yes—
233C2×#217C2312yes—
234C2×#217C2312yes—
235C2×#217C2312yes—
236C2×#217C2312yes—
237C2×#217C2312yes—
238C2×#217C2312yes—
239C2×#217C2312yes—
240C2×#217C2312yes—
241C2×#217C2312yes—
242C2×#217C2312yes—
243C2×#217C2311yescharacteristic
244#944—28no—
245#936—28no—
246#935—24no—
247#935—24no—
248#935—24no—
249#935—24no—
250#935—28no—
251#935—24no—
252#935—24no—
253#935—28no—
254#935—42no—
255#935—42no—
256#935D418yescomplemented
257#926—24no—
258C2×C4⋊Dic3—24no—
259C2×C4⋊Dic3C2312yes—
260C2×C4⋊Dic3C2312yes—
261C2×C4⋊Dic3C2312yes—
262C2×C4⋊Dic3C2312yes—
263#924—28no—
264#924—28no—
265C2×Dic3⋊C4—24no—
266C2×Dic3⋊C4—24no—
267C2×Dic3⋊C4—28no—
268C2×Dic3⋊C4C2312yes—
269C2×Dic3⋊C4C2312yes—
270C2×Dic3⋊C4C2312yes—
271C2×Dic3⋊C4C2312yes—
272C2×Dic3⋊C4C2312yes—
273C2×Dic3⋊C4C2312yes—
274C2×Dic3⋊C4C2312yes—
275C2×Dic3⋊C4C2312yes—
276C2×Dic3⋊C4C2312yes—
277C2×Dic3⋊C4C2312yes—
278C2×Dic3⋊C4C2312yes—
279C2×Dic3⋊C4C2312yes—
280C2×Dic3⋊C4C2312yes—
281C2×Dic3⋊C4C2312yes—
282C2×C4×Dic3C2312yes—
283C2×C4×Dic3C2312yes—
284#878—28no—
285#878—28no—
286#878—28no—
287#878—28no—
288C3⋊#95C2312yes—
289C3⋊#95C2312yes—
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×#41C2×D311yescharacteristic
303C23×Q8—31no—
304C23×D4C2×D311yescharacteristic
305C24×C4—31no—
306#546—28no—
307#536—68no—
308C2×C4⋊Q8—32no—
309C2×#124—32no—
310C2×#124C2×D311yescharacteristic
311C2×#123—31no—
312C2×#123—31no—
313C2×#123—31no—
314C2×#123—31no—
315C2×#123—31no—
316C2×#123—31no—
317C2×#123—32no—
318C2×#123—32no—
319C2×#123—31no—
320C2×#123—31no—
321C2×#123—31no—
322C2×#123—68no—
323C2×#123C2×D311yescharacteristic
324C2×#123C2×D311yescharacteristic
325C2×C22⋊Q8—32no—
326C2×C22⋊Q8—32no—
327C2×C22⋊Q8—32no—
328C2×C22⋊Q8—32no—
329C2×C22⋊Q8—32no—
330C2×C22⋊Q8—32no—
331C2×C22⋊Q8—68no—
332C2×C22⋊Q8C2×D311yescharacteristic
333C2×#121C2×D311yescharacteristic
334C2×#121C2×D311yescharacteristic
335C2×#121C2×D311yescharacteristic
336C2×#120C2×D311yescharacteristic
337C2×#120C2×D311yescharacteristic
338C2×C4×D4C2×D311yescharacteristic
339C2×C4×D4C2×D311yescharacteristic
340C2×#117—31no—
341C22×C4⋊C4—31no—
342C22×C4⋊C4—31no—
343C22×C4⋊C4—31no—
344C22×C4⋊C4—32no—
345C22×C22⋊C4—31no—
346C22×C22⋊C4—31no—
347C22×C22⋊C4—32no—
348C22×C22⋊C4C2×D311yescharacteristic
349C22×C22⋊C4C2×D311yescharacteristic
350#399—32no—
351#399—32no—
352#398—32no—
353#398—32no—
354#398—32no—
355#397—32no—
356#397—32no—
357#396—32no—
358#396—32no—
359#396—32no—
360#395—32no—
361#395—32no—
362#395—32no—
363#394—32no—
364#394—32no—
365#394—32no—
366#394—32no—
367#394—32no—
368#393—32no—
369#393—32no—
370#390—32no—
371#389—32no—
372#389—32no—
373#389—32no—
374#388—32no—
375#388—32no—
376#388—32no—
377#388—32no—
378#387—32no—
379#386—31no—
380#386—32no—
381#386—32no—
382#386—31no—
383#386—31no—
384#386—32no—
385#385—32no—
386#385—32no—
387#385—32no—
388#385—32no—
389#385—31no—
390#385—32no—
391#385—32no—
392#385—32no—
393#384—32no—
394#381—31no—
395#381—31no—
396#381—31no—
397#381—31no—
398#380—31no—
399#380—32no—
400#380—32no—
401#379—31no—
402#379—32no—
403C4×C22⋊C4—31no—
404C4×C22⋊C4—32no—
405C24×C3—22no—
406C24×C3—22no—
407C24×C3—24no—
408C24×C3—22no—
409C24×C3—22no—
410C24×C3—24no—
411C24×C3—42no—
412C24×C3—42no—
413C24×C3—41no—
414C24×C3C2×D414yes—
415C24×C3C2411yescharacteristic
416C24×C3C2411yescharacteristic
417C24×C3C2411yescharacteristic
418C24×C3C2411yescharacteristic
419C24×C3C2411yescharacteristic
420C24×C3C2411yescharacteristic
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—22no—
430C2×C3×D4—22no—
431C2×C3×D4—22no—
432C2×C3×D4—22no—
433C2×C3×D4—22no—
434C2×C3×D4—22no—
435C2×C3×D4—22no—
436C2×C3×D4—22no—
437C2×C3×D4—22no—
438C2×C3×D4—24no—
439C2×C3×D4—22no—
440C2×C3×D4—22no—
441C2×C3×D4—22no—
442C2×C3×D4—22no—
443C2×C3×D4—41no—
444C2×C3×D4—41no—
445C2×C3×D4—41no—
446C2×C3×D4—42no—
447C2×C3×D4—42no—
448C2×C3×D4—416no—
449C2×C3×D4C2×D414yes—
450C22×C3×C4—22no—
451C22×C3×C4—22no—
452C22×C3×C4—22no—
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—42no—
460C22×C3×C4—41no—
461C22×C3×C4—41no—
462C22×C3×C4—41no—
463C22×C3×C4—42no—
464C22×C3×C4C2×D414yes—
465C22×C3×C4C2×D414yes—
466C22×C3×C4C2411yescharacteristic
467C22×C3×C4C2411yescharacteristic
468C22×C3×C4C2411yescharacteristic
469C22×C3×C4C2411yescharacteristic
470C22×C3×C4C2411yescharacteristic
471C22×C3×C4C2411yescharacteristic
472C22×C3×C4C2411yescharacteristic
473C22×C3×C4C2411yescharacteristic
474C22×C3×C4C2411yescharacteristic
475C22×Dic3—22no—
476C22×Dic3—22no—
477C22×Dic3—24no—
478C22×Dic3—24no—
479C22×Dic3—22no—
480C22×Dic3—22no—
481C22×Dic3—22no—
482C22×Dic3—22no—
483C22×Dic3—22no—
484C22×Dic3—22no—
485C22×Dic3—22no—
486C22×Dic3—24no—
487C22×Dic3—24no—
488C22×Dic3—24no—
489C22×Dic3—24no—
490C22×Dic3—42no—
491C22×Dic3—42no—
492C22×Dic3—42no—
493C22×Dic3—42no—
494C22×Dic3—416no—
495C22×Dic3C2×D414yes—
496C22×Dic3C2412yes—
497C22×Dic3C2412yes—
498C22×Dic3C2412yes—
499C22×Dic3C2412yes—
500C22×Dic3C2412yes—
501C22×Dic3C2412yes—
502C22×Dic3C2412yes—
503C22×Dic3C2412yes—
504C2×Dic6—24no—
505C2×Dic6—24no—
506C2×Dic6—24no—
507C2×Dic6—24no—
508C2×Dic6—42no—
509C2×Dic6—42no—
510C2×Dic6—416no—
511C3×C4⋊C4—22no—
512C3×C4⋊C4—22no—
513C3×C4⋊C4—22no—
514C3×C4⋊C4—22no—
515C3×C22⋊C4—22no—
516C3×C22⋊C4—22no—
517C3×C22⋊C4—22no—
518C3×C22⋊C4—22no—
519C3×C22⋊C4—22no—
520C3×C22⋊C4—22no—
521C3×C22⋊C4—22no—
522C3×C22⋊C4—22no—
523C3×C22⋊C4C2×D414yes—
524C3×C22⋊C4C2×D414yes—
525C3×C22⋊C4C2×D414yes—
526C3×C22⋊C4C2×D414yes—
527C3×C42—22no—
528#217—24no—
529#217—24no—
530#217—24no—
531#217—22no—
532#217—22no—
533#217—24no—
534#217—22no—
535#217—24no—
536#217—24no—
537#217—24no—
538#217—24no—
539#217—24no—
540#217—24no—
541#217—42no—
542#217—42no—
543#217—42no—
544#217—42no—
545#217—42no—
546#217—42no—
547#217C2×D418yes—
548#217C2×D414yes—
549C4⋊Dic3—24no—
550C4⋊Dic3—24no—
551C4⋊Dic3—24no—
552C4⋊Dic3—42no—
553Dic3⋊C4—24no—
554Dic3⋊C4—24no—
555Dic3⋊C4—24no—
556Dic3⋊C4—24no—
557Dic3⋊C4—24no—
558Dic3⋊C4—24no—
559Dic3⋊C4—24no—
560Dic3⋊C4—24no—
561Dic3⋊C4—24no—
562Dic3⋊C4—24no—
563Dic3⋊C4—42no—
564Dic3⋊C4—42no—
565Dic3⋊C4—42no—
566Dic3⋊C4C2×D418yes—
567C4×Dic3—24no—
568C4×Dic3—42no—
569C25C22×D311yescharacteristic
570C25C22×D311yescharacteristic
571C2×#41—24no—
572C2×#41—24no—
573C2×#41—42no—
574C22×Q8—32no—
575C22×Q8—32no—
576C22×Q8—64no—
577C22×Q8—64no—
578C22×Q8—122no—
579C22×Q8C22×D311yescharacteristic
580C22×D4—24no—
581C22×D4—24no—
582C22×D4—42no—
583C22×D4C22×D311yescharacteristic
584C22×D4C22×D311yescharacteristic
585C22×D4C22×D311yescharacteristic
586C22×D4C22×D311yescharacteristic
587C22×D4C22×D311yescharacteristic
588C22×D4C22×D311yescharacteristic
589C22×D4C22×D311yescharacteristic
590C22×D4C22×D311yescharacteristic
591C22×D4C22×D311yescharacteristic
592C23×C4—31no—
593C23×C4—31no—
594C23×C4—31no—
595C23×C4—32no—
596C23×C4—32no—
597C23×C4—32no—
598C23×C4—31no—
599C23×C4—64no—
600C23×C4—64no—
601C23×C4—122no—
602C23×C4C22×D311yescharacteristic
603C23×C4C22×D311yescharacteristic
604C23×C4C22×D311yescharacteristic
605C23×C4C22×D311yescharacteristic
606C23×C4C22×D311yescharacteristic
607C23×C4C22×D311yescharacteristic
608C4⋊Q8—68no—
609#124—24no—
610#124—68no—
611#123—24no—
612#123—24no—
613#123—38no—
614#123—64no—
615#123—68no—
616#123—64no—
617#123—68no—
618#123—64no—
619#123—64no—
620#123—64no—
621#123—64no—
622#123—122no—
623#123—122no—
624C22⋊Q8—24no—
625C22⋊Q8—68no—
626C22⋊Q8—68no—
627C22⋊Q8—68no—
628C22⋊Q8—68no—
629C22⋊Q8—68no—
630C22⋊Q8—68no—
631#121—24no—
632#121—24no—
633#121—24no—
634#120—24no—
635#120—24no—
636C4×D4—24no—
637C4×D4—24no—
638#117—64no—
639C2×C4⋊C4—32no—
640C2×C4⋊C4—32no—
641C2×C4⋊C4—32no—
642C2×C4⋊C4—32no—
643C2×C4⋊C4—32no—
644C2×C4⋊C4—32no—
645C2×C4⋊C4—32no—
646C2×C4⋊C4—32no—
647C2×C4⋊C4—32no—
648C2×C4⋊C4—32no—
649C2×C4⋊C4—32no—
650C2×C4⋊C4—32no—
651C2×C4⋊C4—32no—
652C2×C4⋊C4—32no—
653C2×C4⋊C4—32no—
654C2×C4⋊C4—32no—
655C2×C4⋊C4—32no—
656C2×C4⋊C4—32no—
657C2×C4⋊C4—68no—
658C2×C4⋊C4—64no—
659C2×C4⋊C4—64no—
660C2×C4⋊C4—64no—
661C2×C4⋊C4C22×D311yescharacteristic
662C2×C4⋊C4C22×D311yescharacteristic
663C2×C4⋊C4C22×D311yescharacteristic
664C2×C4⋊C4C22×D311yescharacteristic
665C2×C22⋊C4—24no—
666C2×C22⋊C4—31no—
667C2×C22⋊C4—32no—
668C2×C22⋊C4—32no—
669C2×C22⋊C4—32no—
670C2×C22⋊C4—31no—
671C2×C22⋊C4—32no—
672C2×C22⋊C4—32no—
673C2×C22⋊C4—32no—
674C2×C22⋊C4—32no—
675C2×C22⋊C4—31no—
676C2×C22⋊C4—32no—
677C2×C22⋊C4—32no—
678C2×C22⋊C4—32no—
679C2×C22⋊C4—31no—
680C2×C22⋊C4—32no—
681C2×C22⋊C4—32no—
682C2×C22⋊C4—32no—
683C2×C22⋊C4—32no—
684C2×C22⋊C4—32no—
685C2×C22⋊C4—32no—
686C2×C22⋊C4—32no—
687C2×C22⋊C4—64no—
688C2×C22⋊C4—68no—
689C2×C22⋊C4—64no—
690C2×C22⋊C4#6718yes—
691C2×C22⋊C4C22×D311yescharacteristic
692C2×C22⋊C4C22×D311yescharacteristic
693C2×C22⋊C4C22×D311yescharacteristic
694C2×C22⋊C4C22×D311yescharacteristic
695C2×C22⋊C4C22×D311yescharacteristic
696C2×C22⋊C4C22×D311yescharacteristic
697C2×C22⋊C4C22×D311yescharacteristic
698C2×C22⋊C4C22×D311yescharacteristic
699C2×C22⋊C4C22×D311yescharacteristic
700C2×C22⋊C4C22×D311yescharacteristic
701C2×C22⋊C4C22×D311yescharacteristic
702C2×C22⋊C4C22×D311yescharacteristic
703C2×C42—32no—
704C2×C42—32no—
705C2×C42C22×D311yescharacteristic
706#95—32no—
707#95—32no—
708#95—32no—
709#95—32no—
710#95—32no—
711#95—32no—
712#95—32no—
713#95—32no—
714#95—32no—
715#95—32no—
716#95—32no—
717#95—32no—
718#95—32no—
719#95—32no—
720C23×C3—21no—
721C23×C3—21no—
722C23×C3—22no—
723C23×C3—22no—
724C23×C3—22no—
725C23×C3—28no—
726C23×C3—28no—
727C23×C3—21no—
728C23×C3—21no—
729C23×C3—21no—
730C23×C3—21no—
731C23×C3—22no—
732C23×C3—22no—
733C23×C3—22no—
734C23×C3—22no—
735C23×C3—21no—
736C23×C3—21no—
737C23×C3—21no—
738C23×C3—21no—
739C23×C3—21no—
740C23×C3—21no—
741C23×C3—22no—
742C23×C3—22no—
743C23×C3—22no—
744C23×C3—22no—
745C23×C3—44no—
746C23×C3—48no—
747C23×C3—48no—
748C23×C3—44no—
749C23×C3—48no—
750C23×C3—44no—
751C23×C3—82no—
752C23×C3—84no—
753C23×C3C22×D412yes—
754C23×C3C22×D412yes—
755C23×C3C22×D412yes—
756C23×C3C22×D412yes—
757C23×C3C22×D412yes—
758C23×C3H(5,𝔽2)12yes—
759C23×C32−1+414yes—
760C23×C3C2511yescharacteristic
761C3×Q8—44no—
762C3×D4—28no—
763C3×D4—44no—
764C3×D4—44no—
765C3×D4—44no—
766C3×D4—44no—
767C3×D4—44no—
768C3×D4—44no—
769C3×D4—82no—
770C3×D4—82no—
771C2×C3×C4—28no—
772C2×C3×C4—21no—
773C2×C3×C4—21no—
774C2×C3×C4—21no—
775C2×C3×C4—21no—
776C2×C3×C4—21no—
777C2×C3×C4—21no—
778C2×C3×C4—22no—
779C2×C3×C4—22no—
780C2×C3×C4—21no—
781C2×C3×C4—21no—
782C2×C3×C4—21no—
783C2×C3×C4—21no—
784C2×C3×C4—21no—
785C2×C3×C4—21no—
786C2×C3×C4—21no—
787C2×C3×C4—21no—
788C2×C3×C4—22no—
789C2×C3×C4—22no—
790C2×C3×C4—44no—
791C2×C3×C4—44no—
792C2×C3×C4—44no—
793C2×C3×C4—44no—
794C2×C3×C4—82no—
795C2×C3×C4C22×D412yes—
796C2×C3×C4C22×D412yes—
797C2×C3×C4C22×D412yes—
798C2×C3×C4C22×D412yes—
799C2×C3×C4C22×D412yes—
800C2×Dic3—28no—
801C2×Dic3—22no—
802C2×Dic3—22no—
803C2×Dic3—22no—
804C2×Dic3—22no—
805C2×Dic3—22no—
806C2×Dic3—22no—
807C2×Dic3—22no—
808C2×Dic3—22no—
809C2×Dic3—22no—
810C2×Dic3—22no—
811C2×Dic3—22no—
812C2×Dic3—22no—
813C2×Dic3—22no—
814C2×Dic3—22no—
815C2×Dic3—22no—
816C2×Dic3—22no—
817C2×Dic3—22no—
818C2×Dic3—22no—
819C2×Dic3—22no—
820C2×Dic3—22no—
821C2×Dic3—22no—
822C2×Dic3—22no—
823C2×Dic3—48no—
824C2×Dic3—48no—
825C2×Dic3—48no—
826C2×Dic3—44no—
827C2×Dic3—44no—
828C2×Dic3—44no—
829C2×Dic3C22×D414yes—
830C2×Dic3C22×D414yes—
831Dic6—48no—
832Dic6—48no—
833C24—22no—
834C24—22no—
835C24—24no—
836C24—22no—
837C24—24no—
838C24—22no—
839C24—42no—
840C24—41no—
841C24—42no—
842C24C2×#6714yes—
843C24C23×D311yescharacteristic
844C24C23×D311yescharacteristic
845C24C23×D311yescharacteristic
846C24C23×D311yescharacteristic
847C24C23×D311yescharacteristic
848C24C23×D311yescharacteristic
849#41—416no—
850C2×Q8—22no—
851C2×Q8—22no—
852C2×Q8—41no—
853C2×Q8—64no—
854C2×Q8—64no—
855C2×Q8—64no—
856C2×Q8—64no—
857C2×Q8—122no—
858C2×Q8—122no—
859C2×Q8—1216no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—22no—
865C2×D4—22no—
866C2×D4—22no—
867C2×D4—22no—
868C2×D4—24no—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—22no—
875C2×D4—22no—
876C2×D4—22no—
877C2×D4—22no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—416no—
884C2×D4D3×D414yes—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—34no—
895C22×C4—32no—
896C22×C4—32no—
897C22×C4—32no—
898C22×C4—32no—
899C22×C4—32no—
900C22×C4—32no—
901C22×C4—32no—
902C22×C4—32no—
903C22×C4—41no—
904C22×C4—41no—
905C22×C4—41no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—64no—
909C22×C4—64no—
910C22×C4—64no—
911C22×C4—62no—
912C22×C4—62no—
913C22×C4—62no—
914C22×C4—62no—
915C22×C4—62no—
916C22×C4—62no—
917C22×C4—64no—
918C22×C4—62no—
919C22×C4—62no—
920C22×C4—62no—
921C22×C4—64no—
922C22×C4—64no—
923C22×C4—122no—
924C22×C4—122no—
925C22×C4—122no—
926C22×C4—122no—
927C22×C4—1216no—
928C22×C4C2×#6714yes—
929C22×C4C2×#6714yes—
930C22×C4C23×D311yescharacteristic
931C22×C4C23×D311yescharacteristic
932C22×C4C23×D311yescharacteristic
933C22×C4C23×D311yescharacteristic
934C22×C4C23×D311yescharacteristic
935C22×C4C23×D311yescharacteristic
936C22×C4C23×D311yescharacteristic
937C22×C4C23×D311yescharacteristic
938C22×C4C23×D311yescharacteristic
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—38no—
944C4⋊C4—64no—
945C4⋊C4—64no—
946C4⋊C4—64no—
947C4⋊C4—64no—
948C4⋊C4—64no—
949C4⋊C4—64no—
950C4⋊C4—64no—
951C4⋊C4—64no—
952C4⋊C4—64no—
953C4⋊C4—64no—
954C4⋊C4—64no—
955C4⋊C4—64no—
956C4⋊C4—64no—
957C4⋊C4—122no—
958C4⋊C4—122no—
959C4⋊C4—122no—
960C4⋊C4—122no—
961C22⋊C4—22no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—34no—
970C22⋊C4—38no—
971C22⋊C4—64no—
972C22⋊C4—64no—
973C22⋊C4—64no—
974C22⋊C4—64no—
975C22⋊C4—64no—
976C22⋊C4—62no—
977C22⋊C4—64no—
978C22⋊C4—62no—
979C22⋊C4—64no—
980C22⋊C4—62no—
981C22⋊C4—64no—
982C22⋊C4—64no—
983C22⋊C4—64no—
984C22⋊C4—122no—
985C22⋊C4—122no—
986C22⋊C4—122no—
987C22⋊C4—122no—
988C22⋊C4—122no—
989C22⋊C4—122no—
990C22⋊C4C2×#6714yes—
991C22⋊C4C2×#6714yes—
992C22⋊C4C2×#6714yes—
993C22⋊C4C2×#6714yes—
994C42—22no—
995C42—64no—
996C42—122no—
997C22×C3—22no—
998C22×C3—22no—
999C22×C3—22no—
1000C22×C3—22no—
1001C22×C3—24no—
1002C22×C3—24no—
1003C22×C3—24no—
1004C22×C3—24no—
1005C22×C3—22no—
1006C22×C3—22no—
1007C22×C3—22no—
1008C22×C3—22no—
1009C22×C3—24no—
1010C22×C3—416no—
1011C22×C3—41no—
1012C22×C3—41no—
1013C22×C3—42no—
1014C22×C3—42no—
1015C22×C3—42no—
1016C22×C3—41no—
1017C22×C3—41no—
1018C22×C3—41no—
1019C22×C3—41no—
1020C22×C3—41no—
1021C22×C3—41no—
1022C22×C3—42no—
1023C22×C3—42no—
1024C22×C3—42no—
1025C22×C3—42no—
1026C22×C3—88no—
1027C22×C3#53614yescomplemented
1028C22×C3D4214yes—
1029C22×C3C23×D411yescharacteristic
1030C22×C3C23×D411yescharacteristic
1031C22×C3C2×H(5,𝔽2)11yescharacteristic
1032C22×C3C2×2−1+412yes—
1033C22×C3#58512yes—
1034C3×C4—22no—
1035C3×C4—22no—
1036C3×C4—22no—
1037C3×C4—22no—
1038C3×C4—22no—
1039C3×C4—41no—
1040C3×C4—41no—
1041C3×C4—41no—
1042C3×C4—41no—
1043Dic3—24no—
1044Dic3—24no—
1045Dic3—42no—
1046Dic3—42no—
1047Dic3—42no—
1048Dic3—42no—
1049Dic3—42no—
1050Dic3—42no—
1051C23—21no—
1052C23—21no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—21no—
1064C23—28no—
1065C23—28no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—21no—
1075C23—21no—
1076C23—44no—
1077C23—48no—
1078C23—48no—
1079C23—44no—
1080C23—48no—
1081C23—44no—
1082C23—84no—
1083C23—82no—
1084C23C2×D3×D412yes—
1085C23C2×D3×D412yes—
1086C23#100412yes—
1087C23#101014yes—
1088C23C22×#6712yes—
1089C23C22×#6712yes—
1090C23C22×#6712yes—
1091C23C24×D311yescharacteristic
1092Q8—44no—
1093Q8—128no—
1094Q8—128no—
1095D4—28no—
1096D4—44no—
1097D4—44no—
1098D4—44no—
1099D4—44no—
1100D4—44no—
1101D4—44no—
1102D4—82no—
1103D4—82no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—21no—
1112C2×C4—28no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—34no—
1124C2×C4—34no—
1125C2×C4—44no—
1126C2×C4—44no—
1127C2×C4—44no—
1128C2×C4—44no—
1129C2×C4—62no—
1130C2×C4—62no—
1131C2×C4—62no—
1132C2×C4—62no—
1133C2×C4—68no—
1134C2×C4—62no—
1135C2×C4—62no—
1136C2×C4—62no—
1137C2×C4—62no—
1138C2×C4—62no—
1139C2×C4—62no—
1140C2×C4—62no—
1141C2×C4—62no—
1142C2×C4—62no—
1143C2×C4—62no—
1144C2×C4—62no—
1145C2×C4—62no—
1146C2×C4—62no—
1147C2×C4—62no—
1148C2×C4—62no—
1149C2×C4—62no—
1150C2×C4—62no—
1151C2×C4—62no—
1152C2×C4—82no—
1153C2×C4—128no—
1154C2×C4—128no—
1155C2×C4—128no—
1156C2×C4—124no—
1157C2×C4—124no—
1158C2×C4—124no—
1159C2×C4C2×D3×D412yes—
1160C2×C4C22×#6712yes—
1161C2×C4C22×#6712yes—
1162C2×C4C22×#6712yes—
1163C2×C4C22×#6712yes—
1164C2×C3—24no—
1165C2×C3—24no—
1166C2×C3—42no—
1167C2×C3—42no—
1168C2×C3—81no—
1169C2×C3—81no—
1170C2×C3C2×#53611yescharacteristic
1171C2×C3C2×D4211yescharacteristic
1172C2×C3#348511yescharacteristic
1173C2×C3#348912yes—
1174C2×C3#353512yes—
1175C22—24no—
1176C22—24no—
1177C22—24no—
1178C22—24no—
1179C22—22no—
1180C22—22no—
1181C22—22no—
1182C22—22no—
1183C22—24no—
1184C22—22no—
1185C22—22no—
1186C22—22no—
1187C22—22no—
1188C22—416no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—41no—
1193C22—41no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—88no—
1205C22D4×#6714yes—
1206C22#582514yescomplemented
1207C22C22×D3×D411yescharacteristic
1208C22C2×#100411yescharacteristic
1209C22C2×#101012yes—
1210C22#596612yes—
1211C22C23×#6711yescharacteristic
1212C4—22no—
1213C4—22no—
1214C4—22no—
1215C4—22no—
1216C4—22no—
1217C4—41no—
1218C4—41no—
1219C4—41no—
1220C4—41no—
1221C4—64no—
1222C4—64no—
1223C4—122no—
1224C4—122no—
1225C4—122no—
1226C4—122no—
1227C4—122no—
1228C4—122no—
1229C3#3764711yescharacteristic, complemented, Sylow
1230C2—24no—
1231C2—24no—
1232C2—42no—
1233C2—42no—
1234C2—81no—
1235C2—81no—
1236C2#8663012yes—
1237C2#8664612yes—
1238C2C2×D4×#6711yescharacteristic
1239C2C2×#582511yescharacteristic
1240C2#8728011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
Fitting, prime radicalC2×C3×#546C2
hypercenterC2×#546D3
hypocenterC3#37647
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
2. C2×#5825C2semidirect
3. C22×#935C2semidirect
4. C22×#878C2semidirect
5. #84090C2semidirect
6. #84047C2semidirect
7. #82982C2semidirect
8. #82871C2semidirect
9. #82864C2semidirect
10. #82843C2semidirect
11. #82763C2semidirect
12. #82685C2semidirect
13. #82682C2semidirect
14. #82675C2semidirect
15. #82664C2semidirect
16. #82602C2semidirect
17. #82589C2semidirect
18. #82584C2semidirect
19. #82373C2semidirect
20. #82360C2semidirect
21. #82326C2semidirect
22. #82110C2semidirect
23. #82097C2semidirect
28. C23×Dic6C22semidirect
47. C2×#944C22semidirect
48. C2×#936C22semidirect
58. C2×#935C22semidirect
59. C2×#935C22semidirect
60. C2×#935C22semidirect
61. C2×#926C22semidirect
62. C22×C4⋊Dic3C22semidirect
63. C2×#924C22semidirect
64. C2×#924C22semidirect
66. C22×Dic3⋊C4C22semidirect
67. C22×Dic3⋊C4C22semidirect
71. C2×#878C22semidirect
72. C2×#878C22semidirect
75. #5230C22semidirect
78. #5222C22semidirect
79. #5222C22semidirect
80. #5222C22semidirect
81. #5221C22semidirect
86. #5220C22semidirect
87. #5220C22semidirect
88. #5212C22semidirect
89. #5212C22semidirect
90. #5211C22semidirect
92. #5210C22semidirect
93. #5210C22semidirect
94. #5210C22semidirect
95. C4×#217C22semidirect
96. #4983C22semidirect
97. #4982C22semidirect
98. #4981C22semidirect
99. #4979C22semidirect
100. #4979C22semidirect
101. #4976C22semidirect
102. #4976C22semidirect
103. #4975C22semidirect
104. #4953C22semidirect
105. #4952C22semidirect
106. #4951C22semidirect
107. #4951C22semidirect
109. #4949C22semidirect
110. #4949C22semidirect
111. #4948C22semidirect
112. #4948C22semidirect
113. #4948C22semidirect
114. #4947C22semidirect
115. #4947C22semidirect
117. #4946C22semidirect
118. #4946C22semidirect
119. #4945C22semidirect
120. #4945C22semidirect
121. #4943C22semidirect
122. #4943C22semidirect
123. #4943C22semidirect
126. #4933C22semidirect
127. #4928C22semidirect
256. #935D4semidirect
1027. C22×C3#536semidirect
1206. C22#5825semidirect
1229. C3#37647semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5462
C2×#58252
C22×#9352
C22×#8782
#840902
#840472
#829822
#828712
#828642
#828432
#827632
#826852
#826822
#826752
#826642
#826022
#825892
#825842
#823732
#823602
#823262
#821102
#820972
#376473