Finite Group Databasebeta

← #11058571

Subgroups — #11058571

Order 768.

2998 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×D4×#67C211yesmaximal, characteristic
2C2×D3×#124C211yesmaximal, characteristic, complemented
3C3×#2435C211yesmaximal, characteristic, complemented
4#84050C211yesmaximal, characteristic, complemented
5#82969C211yesmaximal, characteristic, complemented
6#82962C211yesmaximal, characteristic, complemented
7#82961C211yesmaximal, characteristic, complemented
8#82756C211yesmaximal, characteristic, complemented
9#82751C211yesmaximal, characteristic, complemented
10#77125C212yesmaximal, complemented
11#77110C212yesmaximal, complemented
12#77009C212yesmaximal, complemented
13#77008C212yesmaximal, complemented
14#76475C211yesmaximal, characteristic, complemented
15#76431C211yesmaximal, characteristic, complemented
16#76350C211yesmaximal, characteristic, complemented
17#76319C211yesmaximal, characteristic, complemented
18#73859C212yesmaximal, complemented
19#73859C212yesmaximal, complemented
20#73853C212yesmaximal, complemented
21#73849C212yesmaximal, complemented
22C4×#883C211yesmaximal, characteristic, complemented
23#73486C211yesmaximal, characteristic, complemented
24#38906—31nomaximal, Sylow
25C23×C3×D4C2211yescharacteristic
26C23×#67C2212yes—
27C22×D3×Q8C2211yescharacteristic, complemented
28C22×D3×D4C2211yescharacteristic
29C2×C3×#124C2211yescharacteristic
30C2×C3×#124C2211yescharacteristic, complemented
31C2×C3×C22⋊Q8C2211yescharacteristic, complemented
32C2×#953C2212yes—
33C2×#947C2211yescharacteristic, complemented
34C2×#940C2211yescharacteristic
35C2×#939C2212yes—
36D4×#67—28no—
37C2×#938C2211yescharacteristic
38C2×#937C2212yes—
39C2×#936C2211yescharacteristic
40C2×#936C2211yescharacteristic, complemented
41C2×D4×Dic3C2211yescharacteristic
42C2×#930C2211yescharacteristic
43C2×C4×#67C2211yescharacteristic
44C2×#924C2211yescharacteristic, complemented
45D3×#124—28no—
46C2×#893C2211yescharacteristic, complemented
47C2×#885C2212yescomplemented
48C2×#885C2212yescomplemented
49C2×#883C2211yescharacteristic
50C2×#883C2212yescomplemented
51C2×D3×C22⋊C4C2212yescomplemented
52C2×D3×C22⋊C4C2212yescomplemented
53C2×D3×C22⋊C4C2212yescomplemented
54C2×#875C2211yescharacteristic, complemented
55C2×C4×D12C2211yescharacteristic, complemented
56C2×C42×D3C2211yescharacteristic, complemented
57C3×#394C2212yescomplemented
58C3×#394C2212yescomplemented
59C3×#390C2211yescharacteristic
60C3×#390C2211yescharacteristic, complemented
61C3×#379C2212yescomplemented
62C3×#379C2212yescomplemented
63C3×C4×C22⋊C4C2211yescharacteristic, complemented
64#5247C2212yescomplemented
65#5247C2212yescomplemented
66#5229C2211yescharacteristic, complemented
67#5229C2211yescharacteristic, complemented
68#5222C2212yescomplemented
69#5222C2212yescomplemented
70#5221C2211yescharacteristic
71#5221C2211yescharacteristic, complemented
72C4×#217C2211yescharacteristic, complemented
73#4992C2212yescomplemented
74#4989C2212yescomplemented
75#4987C2212yescomplemented
76#4987C2211yescharacteristic, complemented
77#4984C2211yescharacteristic, complemented
78#4979C2212yescomplemented
79#4973C2211yescharacteristic, complemented
80#4961C2212yescomplemented
81#4961C2212yescomplemented
82#4961C2212yescomplemented
83#4959C2212yescomplemented
84#4959C2212yescomplemented
85#4959C2212yescomplemented
86#4956C2212yes—
87#4956C2211yescharacteristic
88#4956C2212yescomplemented
89#4956C2212yescomplemented
90#4956C2212yescomplemented
91#4956C2212yescomplemented
92#4956C2212yescomplemented
93#4956C2212yescomplemented
94#4956C2212yescomplemented
95#4956C2212yescomplemented
96#4956C2212yescomplemented
97#4956C2212yescomplemented
98#4956C2212yescomplemented
99#4955C2212yescomplemented
100#4953C2212yescomplemented
101#4953C2212yescomplemented
102#4952C2212yescomplemented
103#4952C2212yescomplemented
104#4951C2211yescharacteristic, complemented
105#4951C2212yescomplemented
106#4950C2212yescomplemented
107#4947C2212yescomplemented
108#4947C2212yescomplemented
109#4947C2212yescomplemented
110#4946C2212yescomplemented
111#4945C2211yescharacteristic, complemented
112#4945C2212yescomplemented
113#4943C2212yescomplemented
114#4943C2212yescomplemented
115C4×(C2×D3)⋊C4C2211yescharacteristic, complemented
116C4×C4⋊Dic3C2211yescharacteristic, complemented
117C4×Dic3⋊C4C2211yescharacteristic, complemented
118#4929C2211yescharacteristic, complemented
119#4928C2211yescharacteristic, complemented
120#4675C2212yescomplemented
121#4668C2211yescharacteristic, complemented
122#4667C2212yescomplemented
123#4664C2211yescharacteristic, complemented
124#4654C2211yescharacteristic, complemented
125#4652C2211yescharacteristic, complemented
126C2×D42—31no—
127C22×#124—31no—
128#2854—31no—
129#2686—32no—
130#2686—32no—
131#2684—32no—
132#2684—32no—
133#2622—32no—
134#2544—31no—
135#2544—31no—
136#2447—31no—
137#2447—31no—
138#2436—31no—
139#2435—31no—
140#2435D311yescharacteristic, complemented
141#2427—31no—
142#2427—31no—
143#2412—32no—
144#2409—31no—
145#2405—32no—
146D4×C22⋊C4—31no—
147#2308—32no—
148C4×#123—31no—
149C25×C3C2312yes—
150C24×D3C2312yes—
151C22×C3×Q8C2311yescharacteristic
152C22×C3×D4—24no—
153C22×C3×D4—42no—
154C22×C3×D4—42no—
155C22×C3×D4C2311yescharacteristic
156C22×C3×D4C2311yescharacteristic
157C22×C3×D4C2312yes—
158C23×C3×C4C2311yescharacteristic
159C22×#67—28no—
160C22×#67—28no—
161C22×#67—44no—
162C22×#67C2312yes—
163C22×#67C2312yes—
164C22×#67C2312yes—
165C22×#67C2311yescharacteristic
166C22×#67C2312yes—
167C22×#67C2312yes—
168C23×Dic3C2312yes—
169C2×D3×Q8—24no—
170C2×D3×Q8—42no—
171C2×D3×Q8—42no—
172C2×D3×D4—42no—
173C2×D3×D4—42no—
174C2×D3×D4D418yes—
175C22×D12C2311yescharacteristic
176C22×C4×D3C2311yescharacteristic
177C22×C4×D3C2311yescharacteristic
178C22×C4×D3C2311yescharacteristic
179C22×C4×D3C2312yes—
180C22×C4×D3C2312yes—
181C22×C4×D3C2312yes—
182C22×Dic6C2311yescharacteristic
183C22×Dic6C2312yes—
184C3×#124—24no—
185C3×#124—42no—
186C3×C22⋊Q8—42no—
187C2×C3×C4⋊C4C2311yescharacteristic
188C2×C3×C4⋊C4C2312yes—
189C2×C3×C22⋊C4C2312yes—
190C2×C3×C22⋊C4C2312yes—
191C2×C3×C22⋊C4C2311yescharacteristic
192C2×C3×C22⋊C4C2312yes—
193C2×C3×C22⋊C4C2311yescharacteristic
194C2×C3×C22⋊C4C2312yes—
195C2×C3×C22⋊C4C2312yes—
196C2×C3×C22⋊C4C2312yes—
197C2×C3×C22⋊C4C2312yes—
198C2×C3×C22⋊C4C2312yes—
199C2×C3×C22⋊C4C2312yes—
200C2×C3×C42C2311yescharacteristic
201C2×C3×C42C2311yescharacteristic
202#953—28no—
203C2×#217C2312yes—
204C2×#217C2311yescharacteristic
205C2×#217C2312yes—
206C2×#217C2311yescharacteristic
207C2×#217C2312yes—
208C2×#217C2312yes—
209C2×#217C2312yes—
210C2×#217C2312yes—
211C2×#217C2312yes—
212C2×#217C2312yes—
213C2×#217C2312yes—
214C2×#217C2312yes—
215C2×#217C2311yescharacteristic
216C2×#217C2312yes—
217#947—24no—
218#940—24no—
219#939—28no—
220#938—24no—
221#937—28no—
222#936—24no—
223#936—42no—
224D4×Dic3—24no—
225#930—24no—
226C4×#67—24no—
227C2×(C2×D3)⋊C4C2311yescharacteristic
228C2×(C2×D3)⋊C4C2311yescharacteristic
229C2×(C2×D3)⋊C4C2312yes—
230C2×(C2×D3)⋊C4C2312yes—
231C2×(C2×D3)⋊C4C2311yescharacteristic
232C2×(C2×D3)⋊C4C2312yes—
233C2×(C2×D3)⋊C4C2312yes—
234C2×(C2×D3)⋊C4C2312yes—
235C2×(C2×D3)⋊C4C2312yes—
236C2×(C2×D3)⋊C4C2312yes—
237C2×(C2×D3)⋊C4C2312yes—
238C2×C4⋊Dic3C2311yescharacteristic
239C2×C4⋊Dic3C2311yescharacteristic
240C2×C4⋊Dic3C2311yescharacteristic
241C2×C4⋊Dic3C2311yescharacteristic
242C2×C4⋊Dic3C2312yes—
243#924—42no—
244C2×Dic3⋊C4C2311yescharacteristic
245C2×Dic3⋊C4C2311yescharacteristic
246C2×Dic3⋊C4C2312yes—
247C2×Dic3⋊C4C2312yes—
248C2×Dic3⋊C4C2311yescharacteristic
249C2×C4×Dic3C2311yescharacteristic
250C2×C4×Dic3C2311yescharacteristic
251C2×C4×Dic3C2311yescharacteristic
252C2×C4×Dic3C2311yescharacteristic
253C2×C4×Dic3C2311yescharacteristic
254#893—42no—
255#885—28no—
256#885—28no—
257#883—24no—
258#883—44no—
259D3×C22⋊C4—28no—
260D3×C22⋊C4—28no—
261D3×C22⋊C4—44no—
262#875—24no—
263C4×D12—42no—
264C42×D3—24no—
265C3×#95C2311yescharacteristic
266C3×#95C2311yescharacteristic
267C3⋊#95C2311yescharacteristic
268C3⋊#95C2311yescharacteristic
269C3⋊#95C2311yescharacteristic
270C3⋊#95C2311yescharacteristic
271C3⋊#95C2311yescharacteristic
272C3⋊#95C2311yescharacteristic
273C3⋊#95C2311yescharacteristic
274C3⋊#95C2311yescharacteristic
275C3⋊#95C2312yes—
276C3⋊#95C2312yes—
277C3⋊#95C2312yes—
278C3⋊#95C2312yes—
279C3⋊#95C2312yes—
280C3⋊#95C2312yes—
281C3⋊#95C2312yes—
282C3⋊#95C2312yes—
283C3⋊#95C2312yes—
284C3⋊#95C2312yes—
285C3⋊#95C2312yes—
286C23×Q8—31no—
287C23×D4—31no—
288C23×D4—32no—
289C23×D4C2×D311yescharacteristic
290D42—68no—
291C2×#127—31no—
292C2×#124—31no—
293C2×#124—31no—
294C2×#124—31no—
295C2×#124—32no—
296C2×#124—32no—
297C2×#124—31no—
298C2×#124—68no—
299C2×#124C2×D311yescharacteristic
300C2×#124C2×D311yescharacteristic, complemented
301C2×#123—31no—
302C2×#123—32no—
303C2×C22⋊Q8—31no—
304C2×C22⋊Q8C2×D311yescharacteristic, complemented
305C2×#121—31no—
306C2×#121—32no—
307C2×#121—31no—
308C2×#120—32no—
309C2×#120—32no—
310C2×C4×D4—31no—
311C2×C4×D4—31no—
312C2×C4×D4—31no—
313C2×C4×D4—31no—
314C22×C22⋊C4—32no—
315C22×C22⋊C4—32no—
316C22×C22⋊C4—32no—
317C22×C42—31no—
318#397—32no—
319#397—32no—
320#397—32no—
321#397—32no—
322#397—32no—
323#397—32no—
324#395—32no—
325#394—32no—
326#394—32no—
327#394—32no—
328#394—32no—
329#394—32no—
330#394—32no—
331#394—32no—
332#394—32no—
333#394C2×D312yescomplemented
334#394C2×D312yescomplemented
335#393—32no—
336#393—32no—
337#393—32no—
338#391—31no—
339#391—31no—
340#391—31no—
341#391—31no—
342#390—31no—
343#390—31no—
344#390C2×D311yescharacteristic
345#390C2×D311yescharacteristic, complemented
346#389—31no—
347#389—31no—
348#388—32no—
349#388—32no—
350#388—31no—
351#388—31no—
352#387—31no—
353#387—31no—
354#386—31no—
355#386—32no—
356#386—32no—
357#386—32no—
358#386—32no—
359#386—32no—
360#386—32no—
361#386—32no—
362#386—32no—
363#386—32no—
364#386—32no—
365#386—32no—
366#386—32no—
367#385—32no—
368#385—32no—
369#385—32no—
370#385—31no—
371#381—32no—
372#381—32no—
373#381—31no—
374#380—31no—
375#380—32no—
376#380—32no—
377#379—32no—
378#379—32no—
379#379—32no—
380#379C2×D312yescomplemented
381#379C2×D312yescomplemented
382C4×C4⋊C4—31no—
383C4×C4⋊C4—31no—
384C4×C22⋊C4—31no—
385C4×C22⋊C4—31no—
386C4×C22⋊C4C2×D311yescharacteristic, complemented
387C24×C3—24no—
388C24×C3—24no—
389C24×C3—42no—
390C24×C3—42no—
391C24×C3—42no—
392C24×C3—42no—
393C24×C3—42no—
394C24×C3C2412yes—
395C24×C3C2412yes—
396C24×C3C2411yescharacteristic
397C23×D3—24no—
398C23×D3—24no—
399C23×D3—42no—
400C23×D3—42no—
401C23×D3—42no—
402C23×D3—42no—
403C23×D3C2×D418yes—
404C23×D3C2412yes—
405C23×D3C2411yescharacteristic
406C2×C3×Q8—22no—
407C2×C3×Q8—22no—
408C2×C3×Q8—22no—
409C2×C3×D4—24no—
410C2×C3×D4—22no—
411C2×C3×D4—22no—
412C2×C3×D4—22no—
413C2×C3×D4—22no—
414C2×C3×D4—22no—
415C2×C3×D4—42no—
416C2×C3×D4—42no—
417C2×C3×D4—416no—
418C2×C3×D4C2×D414yes—
419C22×C3×C4—22no—
420C22×C3×C4—22no—
421C22×C3×C4—22no—
422C22×C3×C4C2411yescharacteristic
423C22×C3×C4C2412yes—
424C22×C3×C4C2412yes—
425C22×C3×C4C2411yescharacteristic
426C22×C3×C4C2411yescharacteristic
427C22×C3×C4C2411yescharacteristic
428C22×C3×C4C2411yescharacteristic
429C22×C3×C4C2411yescharacteristic
430C2×#67—22no—
431C2×#67—22no—
432C2×#67—24no—
433C2×#67—24no—
434C2×#67—24no—
435C2×#67—24no—
436C2×#67—24no—
437C2×#67—24no—
438C2×#67—24no—
439C2×#67—24no—
440C2×#67—42no—
441C2×#67—42no—
442C2×#67—42no—
443C2×#67—42no—
444C2×#67—42no—
445C2×#67—42no—
446C2×#67—432no—
447C2×#67C2×D418yes—
448C2×#67#4114yes—
449C22×Dic3—24no—
450C22×Dic3—24no—
451C22×Dic3—42no—
452C22×Dic3C2411yescharacteristic
453C22×Dic3C2411yescharacteristic
454C22×Dic3C2412yes—
455C22×Dic3C2411yescharacteristic
456C22×Dic3C2411yescharacteristic
457C22×Dic3C2412yes—
458C22×Dic3C2412yes—
459C22×Dic3C2411yescharacteristic
460C22×Dic3C2411yescharacteristic
461C22×Dic3C2411yescharacteristic
462D3×Q8—416no—
463D3×D4—416no—
464C2×D12—22no—
465C2×D12—22no—
466C2×D12C2×D414yes—
467C2×C4×D3—22no—
468C2×C4×D3—22no—
469C2×C4×D3—22no—
470C2×C4×D3—22no—
471C2×C4×D3—24no—
472C2×C4×D3—22no—
473C2×C4×D3—22no—
474C2×C4×D3—41no—
475C2×C4×D3—41no—
476C2×C4×D3—42no—
477C2×C4×D3—42no—
478C2×C4×D3—42no—
479C2×C4×D3—42no—
480C2×C4×D3—42no—
481C2×C4×D3—42no—
482C2×C4×D3—42no—
483C2×C4×D3—42no—
484C2×C4×D3C2×D414yes—
485C2×Dic6—22no—
486C2×Dic6—22no—
487C2×Dic6—22no—
488C2×Dic6—24no—
489C2×Dic6—42no—
490C2×Dic6—42no—
491C3×C4⋊C4—22no—
492C3×C4⋊C4—42no—
493C3×C22⋊C4—24no—
494C3×C22⋊C4—24no—
495C3×C22⋊C4—22no—
496C3×C22⋊C4—42no—
497C3×C22⋊C4—42no—
498C3×C22⋊C4—41no—
499C3×C22⋊C4—42no—
500C3×C22⋊C4—42no—
501C3×C22⋊C4—42no—
502C3×C22⋊C4—42no—
503C3×C22⋊C4—42no—
504C3×C42—22no—
505C3×C42—22no—
506#217—24no—
507#217—24no—
508#217—24no—
509#217—22no—
510#217—22no—
511#217—24no—
512#217—42no—
513#217—42no—
514#217—42no—
515#217—42no—
516#217—42no—
517#217—42no—
518#217—41no—
519#217—42no—
520(C2×D3)⋊C4—24no—
521(C2×D3)⋊C4—24no—
522(C2×D3)⋊C4—24no—
523(C2×D3)⋊C4—24no—
524(C2×D3)⋊C4—22no—
525(C2×D3)⋊C4—24no—
526(C2×D3)⋊C4—22no—
527(C2×D3)⋊C4—22no—
528(C2×D3)⋊C4—24no—
529(C2×D3)⋊C4—42no—
530(C2×D3)⋊C4—42no—
531C4⋊Dic3—22no—
532C4⋊Dic3—22no—
533C4⋊Dic3—22no—
534C4⋊Dic3—42no—
535C4⋊Dic3—41no—
536Dic3⋊C4—22no—
537Dic3⋊C4—22no—
538Dic3⋊C4—42no—
539Dic3⋊C4—41no—
540Dic3⋊C4—42no—
541C4×Dic3—22no—
542C4×Dic3—22no—
543C4×Dic3—22no—
544C4×Dic3—22no—
545C4×Dic3—22no—
546C25—32no—
547C25C22×D312yes—
548C22×Q8—31no—
549C22×Q8—32no—
550C22×Q8—64no—
551C22×Q8—122no—
552C22×Q8—122no—
553C22×Q8C22×D311yescharacteristic
554C22×D4—24no—
555C22×D4—31no—
556C22×D4—32no—
557C22×D4—38no—
558C22×D4—32no—
559C22×D4—32no—
560C22×D4—32no—
561C22×D4—32no—
562C22×D4—31no—
563C22×D4—42no—
564C22×D4—42no—
565C22×D4—68no—
566C22×D4—68no—
567C22×D4—122no—
568C22×D4—122no—
569C22×D4—124no—
570C22×D4C22×D311yescharacteristic
571C22×D4C22×D311yescharacteristic
572C22×D4C22×D312yes—
573C23×C4—31no—
574C23×C4—32no—
575C23×C4—31no—
576C23×C4—32no—
577C23×C4—31no—
578C23×C4—32no—
579C23×C4—32no—
580C23×C4C22×D311yescharacteristic
581#127—64no—
582#124—24no—
583#124—42no—
584#124—64no—
585#124—68no—
586#124—68no—
587#124—64no—
588#124—64no—
589#124—122no—
590#123—64no—
591#123—124no—
592C22⋊Q8—42no—
593C22⋊Q8—122no—
594#121—64no—
595#121—64no—
596#121—68no—
597#120—68no—
598#120—68no—
599C4×D4—64no—
600C4×D4—64no—
601C4×D4—122no—
602C4×D4—122no—
603C2×C4⋊C4—31no—
604C2×C4⋊C4—31no—
605C2×C4⋊C4—31no—
606C2×C4⋊C4—31no—
607C2×C4⋊C4—31no—
608C2×C4⋊C4—32no—
609C2×C4⋊C4—32no—
610C2×C4⋊C4—32no—
611C2×C4⋊C4—31no—
612C2×C4⋊C4—31no—
613C2×C4⋊C4C22×D311yescharacteristic
614C2×C4⋊C4C22×D312yes—
615C2×C22⋊C4—32no—
616C2×C22⋊C4—32no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—32no—
619C2×C22⋊C4—32no—
620C2×C22⋊C4—31no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—32no—
623C2×C22⋊C4—32no—
624C2×C22⋊C4—32no—
625C2×C22⋊C4—32no—
626C2×C22⋊C4—32no—
627C2×C22⋊C4—31no—
628C2×C22⋊C4—32no—
629C2×C22⋊C4—31no—
630C2×C22⋊C4—32no—
631C2×C22⋊C4—32no—
632C2×C22⋊C4—32no—
633C2×C22⋊C4—32no—
634C2×C22⋊C4—32no—
635C2×C22⋊C4—31no—
636C2×C22⋊C4—32no—
637C2×C22⋊C4—32no—
638C2×C22⋊C4—32no—
639C2×C22⋊C4—32no—
640C2×C22⋊C4—68no—
641C2×C22⋊C4—68no—
642C2×C22⋊C4—124no—
643C2×C22⋊C4C22×D312yes—
644C2×C22⋊C4C22×D312yes—
645C2×C22⋊C4C22×D311yescharacteristic
646C2×C22⋊C4C22×D312yes—
647C2×C22⋊C4C22×D312yes—
648C2×C22⋊C4C22×D312yes—
649C2×C22⋊C4C22×D312yes—
650C2×C22⋊C4C22×D312yes—
651C2×C22⋊C4C22×D311yescharacteristic
652C2×C22⋊C4C22×D312yes—
653C2×C22⋊C4C22×D312yes—
654C2×C42—31no—
655C2×C42—31no—
656C2×C42—31no—
657C2×C42—31no—
658C2×C42—31no—
659C2×C42—64no—
660C2×C42C22×D311yescharacteristic
661C2×C42C22×D311yescharacteristic
662#95—31no—
663#95—31no—
664#95—31no—
665#95—31no—
666#95—31no—
667#95—31no—
668#95—31no—
669#95—31no—
670#95—32no—
671#95—32no—
672#95—32no—
673#95—32no—
674#95—32no—
675#95—32no—
676#95—32no—
677#95—32no—
678#95—32no—
679#95—32no—
680#95—32no—
681#95C22×D311yescharacteristic
682#95C22×D311yescharacteristic
683C23×C3—21no—
684C23×C3—22no—
685C23×C3—21no—
686C23×C3—22no—
687C23×C3—21no—
688C23×C3—21no—
689C23×C3—22no—
690C23×C3—22no—
691C23×C3—22no—
692C23×C3—21no—
693C23×C3—22no—
694C23×C3—21no—
695C23×C3—22no—
696C23×C3—22no—
697C23×C3—22no—
698C23×C3—22no—
699C23×C3—22no—
700C23×C3—22no—
701C23×C3—22no—
702C23×C3—48no—
703C23×C3—48no—
704C23×C3—84no—
705C23×C3—84no—
706C23×C3—84no—
707C23×C3—84no—
708C23×C3—84no—
709C23×C3C22×D414yes—
710C23×C3C2×#4112yes—
711C23×C3C2511yescharacteristic
712C22×D3—21no—
713C22×D3—21no—
714C22×D3—21no—
715C22×D3—21no—
716C22×D3—22no—
717C22×D3—22no—
718C22×D3—22no—
719C22×D3—22no—
720C22×D3—22no—
721C22×D3—22no—
722C22×D3—216no—
723C22×D3—48no—
724C22×D3—48no—
725C22×D3—84no—
726C22×D3—84no—
727C22×D3—84no—
728C22×D3—84no—
729C22×D3C22×D414yes—
730C22×D3C22×D412yes—
731C22×D3C2×#4112yes—
732C22×D3H(5,𝔽2)12yes—
733C3×Q8—44no—
734C3×D4—28no—
735C3×D4—48no—
736C3×D4—44no—
737C2×C3×C4—21no—
738C2×C3×C4—21no—
739C2×C3×C4—21no—
740C2×C3×C4—22no—
741C2×C3×C4—21no—
742C2×C3×C4—21no—
743C2×C3×C4—21no—
744C2×C3×C4—21no—
745C2×C3×C4—22no—
746C2×C3×C4—21no—
747C2×C3×C4—21no—
748C2×C3×C4—22no—
749C2×C3×C4—21no—
750C2×C3×C4—22no—
751C2×C3×C4—22no—
752C2×C3×C4—21no—
753C2×C3×C4—21no—
754C2×C3×C4—21no—
755C2×C3×C4—21no—
756C2×C3×C4—22no—
757C2×C3×C4—21no—
758C2×C3×C4—44no—
759C2×C3×C4C22×D412yes—
760C2×C3×C4H(5,𝔽2)12yes—
761C2×C3×C4H(5,𝔽2)12yes—
762#67—28no—
763#67—48no—
764#67—48no—
765#67—48no—
766#67—48no—
767#67—84no—
768C2×Dic3—21no—
769C2×Dic3—21no—
770C2×Dic3—21no—
771C2×Dic3—21no—
772C2×Dic3—21no—
773C2×Dic3—21no—
774C2×Dic3—21no—
775C2×Dic3—22no—
776C2×Dic3—22no—
777C2×Dic3—21no—
778C2×Dic3—21no—
779C2×Dic3—22no—
780C2×Dic3—21no—
781C2×Dic3—21no—
782C2×Dic3—22no—
783C2×Dic3—22no—
784C2×Dic3—22no—
785C2×Dic3—22no—
786C2×Dic3—21no—
787C2×Dic3—21no—
788C2×Dic3—22no—
789C2×Dic3—21no—
790C2×Dic3—21no—
791C2×Dic3—21no—
792C2×Dic3—21no—
793C2×Dic3—21no—
794C2×Dic3—22no—
795C2×Dic3—21no—
796C2×Dic3—48no—
797C2×Dic3C22×D412yes—
798C2×Dic3C2×#4112yes—
799D12—28no—
800C4×D3—28no—
801C4×D3—44no—
802C4×D3—48no—
803C4×D3—44no—
804C4×D3—84no—
805C4×D3—84no—
806Dic6—48no—
807Dic6—44no—
808C24—24no—
809C24—24no—
810C24—31no—
811C24—32no—
812C24—38no—
813C24—42no—
814C24—42no—
815C24—42no—
816C24—42no—
817C24—42no—
818C24—64no—
819C24—64no—
820C24—122no—
821C24—122no—
822C24—122no—
823C24—122no—
824C24C23×D312yes—
825C24C23×D312yes—
826C24C23×D311yescharacteristic
827C2×Q8—22no—
828C2×Q8—22no—
829C2×Q8—22no—
830C2×Q8—64no—
831C2×Q8—62no—
832C2×Q8—62no—
833C2×Q8—62no—
834C2×Q8—122no—
835C2×Q8—122no—
836C2×Q8—1216no—
837C2×D4—24no—
838C2×D4—22no—
839C2×D4—22no—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—34no—
844C2×D4—38no—
845C2×D4—34no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—416no—
849C2×D4—64no—
850C2×D4—62no—
851C2×D4—62no—
852C2×D4—64no—
853C2×D4—64no—
854C2×D4—64no—
855C2×D4—64no—
856C2×D4—64no—
857C2×D4—64no—
858C2×D4—64no—
859C2×D4—62no—
860C2×D4—62no—
861C2×D4—1216no—
862C2×D4—122no—
863C2×D4—122no—
864C2×D4—122no—
865C2×D4—122no—
866C2×D4—122no—
867C2×D4—122no—
868C2×D4—1232no—
869C2×D4D3×D414yes—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—31no—
874C22×C4—31no—
875C22×C4—34no—
876C22×C4—31no—
877C22×C4—31no—
878C22×C4—32no—
879C22×C4—31no—
880C22×C4—31no—
881C22×C4—32no—
882C22×C4—32no—
883C22×C4—31no—
884C22×C4—62no—
885C22×C4—62no—
886C22×C4—64no—
887C22×C4—62no—
888C22×C4—62no—
889C22×C4—64no—
890C22×C4—62no—
891C22×C4—62no—
892C22×C4—64no—
893C22×C4—122no—
894C22×C4—122no—
895C22×C4—121no—
896C22×C4—121no—
897C22×C4—122no—
898C22×C4—122no—
899C22×C4—122no—
900C22×C4—122no—
901C22×C4—122no—
902C22×C4—122no—
903C22×C4—122no—
904C22×C4C23×D311yescharacteristic
905C22×C4C23×D312yes—
906C22×C4C23×D312yes—
907C22×C4C23×D311yescharacteristic
908C22×C4C23×D311yescharacteristic
909C22×C4C23×D311yescharacteristic
910C22×C4C23×D311yescharacteristic
911C22×C4C23×D311yescharacteristic
912C4⋊C4—22no—
913C4⋊C4—42no—
914C4⋊C4—62no—
915C4⋊C4—62no—
916C4⋊C4—62no—
917C4⋊C4—62no—
918C4⋊C4—62no—
919C4⋊C4—122no—
920C4⋊C4—122no—
921C4⋊C4—122no—
922C4⋊C4—121no—
923C4⋊C4—121no—
924C22⋊C4—24no—
925C22⋊C4—24no—
926C22⋊C4—22no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—41no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—64no—
936C22⋊C4—64no—
937C22⋊C4—64no—
938C22⋊C4—64no—
939C22⋊C4—62no—
940C22⋊C4—64no—
941C22⋊C4—62no—
942C22⋊C4—64no—
943C22⋊C4—62no—
944C22⋊C4—62no—
945C22⋊C4—64no—
946C22⋊C4—64no—
947C22⋊C4—64no—
948C22⋊C4—64no—
949C22⋊C4—62no—
950C22⋊C4—122no—
951C22⋊C4—122no—
952C22⋊C4—122no—
953C22⋊C4—122no—
954C22⋊C4—122no—
955C22⋊C4—122no—
956C22⋊C4—122no—
957C22⋊C4—122no—
958C22⋊C4—122no—
959C22⋊C4—121no—
960C42—22no—
961C42—22no—
962C42—62no—
963C42—62no—
964C42—62no—
965C42—62no—
966C42—62no—
967C22×C3—24no—
968C22×C3—24no—
969C22×C3—22no—
970C22×C3—24no—
971C22×C3—22no—
972C22×C3—22no—
973C22×C3—41no—
974C22×C3—41no—
975C22×C3—42no—
976C22×C3—42no—
977C22×C3—42no—
978C22×C3—42no—
979C22×C3—41no—
980C22×C3—41no—
981C22×C3—42no—
982C22×C3—42no—
983C22×C3—42no—
984C22×C3—42no—
985C22×C3—42no—
986C22×C3—42no—
987C22×C3—42no—
988C22×C3—816no—
989C22×C3C23×D411yescharacteristic
990C22×C3C22×#4111yescharacteristic
991C22×C3C2×H(5,𝔽2)11yescharacteristic
992C22×C3C2×H(5,𝔽2)11yescharacteristic
993C22×C3C2×H(5,𝔽2)11yescharacteristic
994C22×C3#58511yescharacteristic
995C22×C3#58511yescharacteristic
996C2×D3—22no—
997C2×D3—22no—
998C2×D3—22no—
999C2×D3—22no—
1000C2×D3—22no—
1001C2×D3—22no—
1002C2×D3—24no—
1003C2×D3—24no—
1004C2×D3—24no—
1005C2×D3—42no—
1006C2×D3—42no—
1007C2×D3—42no—
1008C2×D3—42no—
1009C2×D3—816no—
1010C2×D3#54614yes—
1011C3×C4—42no—
1012C3×C4—41no—
1013C3×C4—41no—
1014C3×C4—41no—
1015C3×C4—41no—
1016C3×C4—41no—
1017C3×C4—42no—
1018C3×C4#53414yes—
1019Dic3—22no—
1020Dic3—22no—
1021Dic3—42no—
1022Dic3—41no—
1023Dic3—42no—
1024Dic3—41no—
1025Dic3—41no—
1026Dic3—41no—
1027Dic3—41no—
1028Dic3—42no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—21no—
1036C23—22no—
1037C23—22no—
1038C23—21no—
1039C23—22no—
1040C23—21no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—32no—
1049C23—32no—
1050C23—32no—
1051C23—34no—
1052C23—48no—
1053C23—48no—
1054C23—616no—
1055C23—61no—
1056C23—61no—
1057C23—61no—
1058C23—61no—
1059C23—62no—
1060C23—62no—
1061C23—62no—
1062C23—62no—
1063C23—62no—
1064C23—62no—
1065C23—84no—
1066C23—84no—
1067C23—84no—
1068C23—84no—
1069C23—84no—
1070C23—128no—
1071C23—128no—
1072C23—244no—
1073C23—244no—
1074C23—244no—
1075C23—244no—
1076C23C2×D3×D414yes—
1077C23D3×#4112yes—
1078C23C24×D311yescharacteristic
1079Q8—44no—
1080Q8—128no—
1081Q8—124no—
1082D4—28no—
1083D4—48no—
1084D4—44no—
1085D4—68no—
1086D4—68no—
1087D4—128no—
1088D4—128no—
1089D4—128no—
1090D4—128no—
1091D4—244no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—22no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—22no—
1112C2×C4—21no—
1113C2×C4—32no—
1114C2×C4—32no—
1115C2×C4—44no—
1116C2×C4—61no—
1117C2×C4—61no—
1118C2×C4—61no—
1119C2×C4—61no—
1120C2×C4—68no—
1121C2×C4—61no—
1122C2×C4—61no—
1123C2×C4—61no—
1124C2×C4—62no—
1125C2×C4—62no—
1126C2×C4—61no—
1127C2×C4—61no—
1128C2×C4—62no—
1129C2×C4—62no—
1130C2×C4—62no—
1131C2×C4—61no—
1132C2×C4—61no—
1133C2×C4—62no—
1134C2×C4—61no—
1135C2×C4—61no—
1136C2×C4—62no—
1137C2×C4—61no—
1138C2×C4—62no—
1139C2×C4—61no—
1140C2×C4—61no—
1141C2×C4—62no—
1142C2×C4—61no—
1143C2×C4—61no—
1144C2×C4—61no—
1145C2×C4—124no—
1146C2×C4—128no—
1147C2×C4—124no—
1148C2×C4—128no—
1149C2×C4—244no—
1150C2×C4—244no—
1151C2×C4C2×D3×D412yes—
1152C2×C4#100412yes—
1153C2×C4#100412yes—
1154C2×C3—44no—
1155C2×C3—42no—
1156C2×C3—82no—
1157C2×C3C2×#53411yescharacteristic
1158C2×C3C2×#54611yescharacteristic
1159C2×C3#348511yescharacteristic
1160C2×C3#351411yescharacteristic
1161C2×C3#351411yescharacteristic
1162C2×C3#355811yescharacteristic
1163C2×C3#355811yescharacteristic
1164D3—24no—
1165D3—44no—
1166C22—22no—
1167C22—22no—
1168C22—24no—
1169C22—22no—
1170C22—24no—
1171C22—24no—
1172C22—34no—
1173C22—42no—
1174C22—41no—
1175C22—42no—
1176C22—42no—
1177C22—41no—
1178C22—41no—
1179C22—42no—
1180C22—41no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—42no—
1188C22—62no—
1189C22—62no—
1190C22—62no—
1191C22—62no—
1192C22—62no—
1193C22—62no—
1194C22—64no—
1195C22—64no—
1196C22—64no—
1197C22—816no—
1198C22—122no—
1199C22—122no—
1200C22—122no—
1201C22—122no—
1202C22—2416no—
1203C22C22×D3×D411yescharacteristic
1204C22C2×#100411yescharacteristic
1205C22C2×#100411yescharacteristic
1206C22C2×D3×#4111yescharacteristic
1207C22#596411yescharacteristic
1208C22D3×H(5,𝔽2)11yescharacteristic
1209C22#596611yescharacteristic
1210C4—42no—
1211C4—41no—
1212C4—41no—
1213C4—41no—
1214C4—41no—
1215C4—41no—
1216C4—42no—
1217C4—62no—
1218C4—62no—
1219C4—121no—
1220C4—121no—
1221C4—122no—
1222C4—121no—
1223C4—121no—
1224C4—121no—
1225C4—122no—
1226C4—122no—
1227C4#558914yes—
1228C3#3890611yescharacteristic, complemented, Sylow
1229C2—42no—
1230C2—44no—
1231C2—64no—
1232C2—82no—
1233C2—124no—
1234C2C2×#558911yescharacteristic
1235C2#8607711yescharacteristic
1236C2#8633711yescharacteristic
1237C2#8663811yescharacteristic
1238C2D3×#54611yescharacteristic
1239C2#8666311yescharacteristic
1240C2#8667311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2435C2
prime radicalC2×D4×#67C2
hypercenter#2435D3
hypocenterC3#38906
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2435

Complements

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

NH ≅ G/Ntype
2. C2×D3×#124C2semidirect
3. C3×#2435C2semidirect
4. #84050C2semidirect
5. #82969C2semidirect
6. #82962C2semidirect
7. #82961C2semidirect
8. #82756C2semidirect
9. #82751C2semidirect
10. #77125C2semidirect
11. #77110C2semidirect
12. #77009C2semidirect
13. #77008C2semidirect
14. #76475C2semidirect
15. #76431C2semidirect
16. #76350C2semidirect
17. #76319C2semidirect
18. #73859C2semidirect
19. #73859C2semidirect
20. #73853C2semidirect
21. #73849C2semidirect
22. C4×#883C2semidirect
23. #73486C2semidirect
27. C22×D3×Q8C22semidirect
30. C2×C3×#124C22semidirect
31. C2×C3×C22⋊Q8C22semidirect
33. C2×#947C22semidirect
40. C2×#936C22semidirect
44. C2×#924C22semidirect
46. C2×#893C22semidirect
47. C2×#885C22semidirect
48. C2×#885C22semidirect
50. C2×#883C22semidirect
51. C2×D3×C22⋊C4C22semidirect
52. C2×D3×C22⋊C4C22semidirect
53. C2×D3×C22⋊C4C22semidirect
54. C2×#875C22semidirect
55. C2×C4×D12C22semidirect
56. C2×C42×D3C22semidirect
57. C3×#394C22semidirect
58. C3×#394C22semidirect
60. C3×#390C22semidirect
61. C3×#379C22semidirect
62. C3×#379C22semidirect
63. C3×C4×C22⋊C4C22semidirect
64. #5247C22semidirect
65. #5247C22semidirect
66. #5229C22semidirect
67. #5229C22semidirect
68. #5222C22semidirect
69. #5222C22semidirect
71. #5221C22semidirect
72. C4×#217C22semidirect
73. #4992C22semidirect
74. #4989C22semidirect
75. #4987C22semidirect
76. #4987C22semidirect
77. #4984C22semidirect
78. #4979C22semidirect
79. #4973C22semidirect
80. #4961C22semidirect
81. #4961C22semidirect
82. #4961C22semidirect
83. #4959C22semidirect
84. #4959C22semidirect
85. #4959C22semidirect
88. #4956C22semidirect
89. #4956C22semidirect
90. #4956C22semidirect
91. #4956C22semidirect
92. #4956C22semidirect
93. #4956C22semidirect
94. #4956C22semidirect
95. #4956C22semidirect
96. #4956C22semidirect
97. #4956C22semidirect
98. #4956C22semidirect
99. #4955C22semidirect
100. #4953C22semidirect
101. #4953C22semidirect
102. #4952C22semidirect
103. #4952C22semidirect
104. #4951C22semidirect
105. #4951C22semidirect
106. #4950C22semidirect
107. #4947C22semidirect
108. #4947C22semidirect
109. #4947C22semidirect
110. #4946C22semidirect
111. #4945C22semidirect
112. #4945C22semidirect
113. #4943C22semidirect
114. #4943C22semidirect
115. C4×(C2×D3)⋊C4C22semidirect
116. C4×C4⋊Dic3C22semidirect
117. C4×Dic3⋊C4C22semidirect
118. #4929C22semidirect
119. #4928C22semidirect
120. #4675C22semidirect
121. #4668C22semidirect
122. #4667C22semidirect
123. #4664C22semidirect
124. #4654C22semidirect
125. #4652C22semidirect
140. #2435D3semidirect
300. C2×#124C2×D3semidirect
304. C2×C22⋊Q8C2×D3semidirect
333. #394C2×D3semidirect
334. #394C2×D3semidirect
345. #390C2×D3semidirect
380. #379C2×D3semidirect
381. #379C2×D3semidirect
386. C4×C22⋊C4C2×D3semidirect
1228. C3#38906semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#672
C2×D3×#1242
C3×#24352
#840502
#829692
#829622
#829612
#827562
#827512
#771252
#771102
#770092
#770082
#764752
#764312
#763502
#763192
#738592
#738532
#738492
C4×#8832
#734862
#389063