Finite Group Databasebeta

← #11166141

Subgroups — #11166141

Order 768.

2816 conjugacy classes of subgroups.

The subgroup lattice has 1276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5599C211yesmaximal, characteristic, complemented
2C2×#5550C211yesmaximal, characteristic, complemented
3C3×#2416C211yesmaximal, characteristic, complemented
4#82714C212yesmaximal, complemented
5#82713C212yesmaximal, complemented
6#82701C211yesmaximal, characteristic, complemented
7#82676C211yesmaximal, characteristic, complemented
8#82653C211yesmaximal, characteristic, complemented
9#82345C211yesmaximal, characteristic, complemented
10#82193C211yesmaximal, characteristic, complemented
11#82186C211yesmaximal, characteristic, complemented
12#77448C212yesmaximal, complemented
13#77334C212yesmaximal, complemented
14#77123C212yesmaximal, complemented
15#77119C212yesmaximal, complemented
16#76316C211yesmaximal, characteristic, complemented
17#76313C211yesmaximal, characteristic, complemented
18#76213C211yesmaximal, characteristic, complemented
19#76007C211yesmaximal, characteristic, complemented
20#74922C212yesmaximal, complemented
21#74915C212yesmaximal, complemented
22#74016C211yesmaximal, characteristic, complemented
23#73892C211yesmaximal, characteristic, complemented
24#42951—31nomaximal, Sylow
25C22×#237C2211yescharacteristic, complemented
26C22×#235C2211yescharacteristic
27C23×D12C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2212yes—
30C2×C3×#121C2211yescharacteristic, complemented
31C2×C3×C4×D4C2211yescharacteristic
32C22×C3×C4⋊C4C2211yescharacteristic, complemented
33C2×#940C2211yescharacteristic
34C2×#940C2211yescharacteristic
35C2×#940C2212yescomplemented
36C2×#939C2212yescomplemented
37C2×#937C2212yes—
38C2×#937C2212yes—
39C2×#937C2212yes—
40C2×#930C2211yescharacteristic
41C2×#930C2212yescomplemented
42C2×C4×#67C2211yescharacteristic
43C2×C4×#67C2211yescharacteristic, complemented
44C2×#926C2211yescharacteristic, complemented
45C2×#924C2211yescharacteristic
46#5599—28no—
47#5550—28no—
48C2×#895C2211yescharacteristic
49C2×#895C2211yescharacteristic
50C2×#894C2212yes—
51C2×#887C2211yescharacteristic, complemented
52C2×#884C2212yes—
53C2×#884C2212yescomplemented
54C2×#883C2212yescomplemented
55C2×#882C2212yes—
56C2×#67⋊C4C2212yescomplemented
57C2×D3×C22⋊C4C2212yes—
58C2×#875C2211yescharacteristic
59C2×C4×D12C2211yescharacteristic
60C3×#396C2212yescomplemented
61C3×#394C2212yes—
62C3×#390C2211yescharacteristic, complemented
63C3×#389C2211yescharacteristic, complemented
64C3×#386C2212yescomplemented
65C3×#380C2211yescharacteristic
66#5223C2212yes—
67#5223C2211yescharacteristic
68#5223C2212yescomplemented
69#5223C2212yescomplemented
70#5222C2211yescharacteristic
71#5221C2211yescharacteristic, complemented
72#5220C2212yes—
73#5213C2212yescomplemented
74#5213C2212yescomplemented
75#5213C2212yescomplemented
76C4×#217C2211yescharacteristic
77#4994C2212yescomplemented
78#4994C2211yescharacteristic, complemented
79#4993C2212yescomplemented
80#4992C2212yescomplemented
81#4991C2212yescomplemented
82#4991C2212yescomplemented
83#4990C2212yescomplemented
84#4988C2211yescharacteristic
85#4988C2211yescharacteristic
86#4988C2211yescharacteristic
87#4988C2211yescharacteristic
88#4987C2212yescomplemented
89#4987C2212yescomplemented
90#4987C2211yescharacteristic, complemented
91#4984C2211yescharacteristic, complemented
92#4982C2211yescharacteristic, complemented
93#4977C2211yescharacteristic, complemented
94#4973C2211yescharacteristic, complemented
95#4973C2211yescharacteristic, complemented
96#4961C2211yescharacteristic
97#4961C2212yescomplemented
98#4961C2212yescomplemented
99#4961C2212yescomplemented
100#4960C2212yes—
101#4960C2212yes—
102#4960C2212yescomplemented
103#4960C2212yescomplemented
104#4959C2212yescomplemented
105#4959C2212yescomplemented
106#4959C2211yescharacteristic, complemented
107#4958C2212yescomplemented
108#4958C2212yescomplemented
109#4956C2212yescomplemented
110#4955C2212yes—
111#4952C2212yes—
112#4952C2211yescharacteristic, complemented
113#4951C2212yes—
114#4948C2211yescharacteristic
115#4946C2212yescomplemented
116C4×(C2×D3)⋊C4C2211yescharacteristic, complemented
117C4×Dic3⋊C4C2211yescharacteristic, complemented
118#4675C2212yescomplemented
119#4672C2212yes—
120#4671C2212yes—
121#4669C2212yescomplemented
122#4665C2212yescomplemented
123#4664C2212yescomplemented
124#4658C2212yescomplemented
125#4654C2212yescomplemented
126C2×#550—31no—
127C2×#546—31no—
128#2813—32no—
129#2688—32no—
130#2673—32no—
131#2669—32no—
132#2668—32no—
133#2630—32no—
134#2619—31no—
135#2617—32no—
136#2534—32no—
137#2448—31no—
138#2445—31no—
139#2433—31no—
140#2431—31no—
141#2421—31no—
142#2420—31no—
143#2416—31no—
144#2416D311yescharacteristic, complemented
145#2408—31no—
146#2407—31no—
147#2392—31no—
148#2311—31no—
149C24×D3C2312yes—
150C22×C3×D4C2311yescharacteristic
151C22×C3×D4C2311yescharacteristic
152C22×C3×D4C2312yes—
153C22×C3×D4C2312yes—
154C23×C3×C4C2311yescharacteristic
155C23×C3×C4C2311yescharacteristic
156C23×C3×C4C2312yes—
157C22×#67C2311yescharacteristic
158C22×#67C2312yes—
159C22×#67C2312yes—
160C22×#67C2312yes—
161C22×#67C2312yes—
162C22×#67C2311yescharacteristic
163C22×#67C2312yes—
164C22×#67C2312yes—
165C22×#67C2312yes—
166C23×Dic3C2312yes—
167C2×#237—24no—
168C2×#237—42no—
169C2×#237—42no—
170C2×#235—42no—
171C2×#235—42no—
172C2×#235D418yescomplemented
173C22×D12—24no—
174C22×D12—42no—
175C22×D12—42no—
176C22×D12C2311yescharacteristic
177C22×D12C2311yescharacteristic
178C22×D12C2312yes—
179C22×D12C2312yes—
180C22×D12C2312yes—
181C22×C4×D3C2311yescharacteristic
182C22×C4×D3C2312yes—
183C22×C4×D3C2312yes—
184C22×Dic6C2311yescharacteristic
185C3×#121—24no—
186C3×#121—44no—
187C3×#121—42no—
188C3×C4×D4—24no—
189C2×C3×C4⋊C4—42no—
190C2×C3×C4⋊C4C2311yescharacteristic
191C2×C3×C4⋊C4C2311yescharacteristic
192C2×C3×C4⋊C4C2311yescharacteristic
193C2×C3×C4⋊C4C2311yescharacteristic
194C2×C3×C4⋊C4C2312yes—
195C2×C3×C4⋊C4C2312yes—
196C2×C3×C22⋊C4C2311yescharacteristic
197C2×C3×C22⋊C4C2312yes—
198C2×C3×C22⋊C4C2311yescharacteristic
199C2×C3×C22⋊C4C2312yes—
200C2×C3×C22⋊C4C2312yes—
201C2×C3×C22⋊C4C2312yes—
202C2×C3×C22⋊C4C2312yes—
203C2×C3×C42C2311yescharacteristic
204C2×#217C2311yescharacteristic
205C2×#217C2312yes—
206C2×#217C2311yescharacteristic
207C2×#217C2311yescharacteristic
208C2×#217C2312yes—
209C2×#217C2311yescharacteristic
210C2×#217C2311yescharacteristic
211C2×#217C2311yescharacteristic
212C2×#217C2312yes—
213#940—28no—
214#940—24no—
215#940—42no—
216#939—28no—
217#937—28no—
218#937—44no—
219#937—44no—
220#930—24no—
221#930—44no—
222C4×#67—24no—
223C4×#67—42no—
224C2×(C2×D3)⋊C4C2312yes—
225C2×(C2×D3)⋊C4C2312yes—
226C2×(C2×D3)⋊C4C2312yes—
227C2×(C2×D3)⋊C4C2312yes—
228C2×(C2×D3)⋊C4C2312yes—
229C2×(C2×D3)⋊C4C2311yescharacteristic
230C2×(C2×D3)⋊C4C2312yes—
231C2×(C2×D3)⋊C4C2312yes—
232C2×(C2×D3)⋊C4C2311yescharacteristic
233C2×(C2×D3)⋊C4C2312yes—
234C2×(C2×D3)⋊C4C2312yes—
235C2×(C2×D3)⋊C4C2312yes—
236C2×(C2×D3)⋊C4C2311yescharacteristic
237C2×(C2×D3)⋊C4C2312yes—
238C2×(C2×D3)⋊C4C2312yes—
239C2×(C2×D3)⋊C4C2312yes—
240C2×(C2×D3)⋊C4C2312yes—
241C2×(C2×D3)⋊C4C2312yes—
242C2×(C2×D3)⋊C4C2311yescharacteristic
243#926—42no—
244C2×C4⋊Dic3C2312yes—
245C2×C4⋊Dic3C2311yescharacteristic
246C2×C4⋊Dic3C2311yescharacteristic
247C2×C4⋊Dic3C2311yescharacteristic
248#924—24no—
249C2×Dic3⋊C4C2312yes—
250C2×Dic3⋊C4C2312yes—
251C2×Dic3⋊C4C2311yescharacteristic
252C2×Dic3⋊C4C2311yescharacteristic
253C2×Dic3⋊C4C2311yescharacteristic
254C2×Dic3⋊C4C2311yescharacteristic
255C2×C4×Dic3C2312yes—
256C2×C4×Dic3C2311yescharacteristic
257C2×C4×Dic3C2311yescharacteristic
258C2×C4×Dic3C2311yescharacteristic
259#895—24no—
260#895—42no—
261#894—28no—
262#887—24no—
263#884—28no—
264#884—28no—
265#883—44no—
266#882—44no—
267#67⋊C4—28no—
268D3×C22⋊C4—28no—
269#875—24no—
270C4×D12—24no—
271C3×#95C2312yes—
272C3×#95C2312yes—
273C3⋊#95C2311yescharacteristic
274C3⋊#95C2312yes—
275C3⋊#95C2312yes—
276C3⋊#95C2311yescharacteristic
277C3⋊#95C2312yes—
278C3⋊#95C2312yes—
279C3⋊#95C2312yes—
280C3⋊#95C2311yescharacteristic
281C3⋊#95C2312yes—
282C3⋊#95C2312yes—
283C3⋊#95C2311yescharacteristic
284C3⋊#95C2312yes—
285C3⋊#95C2311yescharacteristic
286C3⋊#95C2311yescharacteristic
287C22×#41—31no—
288C22×#41—31no—
289C23×D4—31no—
290#550—68no—
291#546—68no—
292C2×#127—32no—
293C2×#127—31no—
294C2×#127—31no—
295C2×#124—31no—
296C2×#123—32no—
297C2×#123—32no—
298C2×C22⋊Q8—31no—
299C2×#121—32no—
300C2×#121—31no—
301C2×#121—32no—
302C2×#121—31no—
303C2×#121—31no—
304C2×#121—32no—
305C2×#121—32no—
306C2×#121C2×D311yescharacteristic
307C2×#121C2×D312yes—
308C2×#121C2×D311yescharacteristic, complemented
309C2×#120—32no—
310C2×#120—32no—
311C2×#120—32no—
312C2×#120—32no—
313C2×C4×Q8—31no—
314C2×C4×D4—31no—
315C2×C4×D4—31no—
316C2×C4×D4—32no—
317C2×C4×D4—31no—
318C2×C4×D4C2×D311yescharacteristic
319C2×#117—31no—
320C22×C4⋊C4C2×D311yescharacteristic, complemented
321C22×C22⋊C4—32no—
322#400—32no—
323#399—32no—
324#398—31no—
325#397—32no—
326#397—32no—
327#397—31no—
328#397—32no—
329#396—32no—
330#396—31no—
331#396—31no—
332#396C2×D312yescomplemented
333#394—31no—
334#394—32no—
335#394—32no—
336#394—31no—
337#394—32no—
338#394—32no—
339#394—32no—
340#394—31no—
341#394—32no—
342#394—32no—
343#394—32no—
344#394C2×D312yes—
345#392—32no—
346#392—32no—
347#392—32no—
348#392—31no—
349#392—32no—
350#392—32no—
351#392—32no—
352#392—32no—
353#392—32no—
354#391—31no—
355#391—31no—
356#390—31no—
357#390—31no—
358#390—31no—
359#390—31no—
360#390—31no—
361#390C2×D311yescharacteristic, complemented
362#389—31no—
363#389C2×D311yescharacteristic, complemented
364#388—32no—
365#388—32no—
366#388—32no—
367#387—32no—
368#386—32no—
369#386—32no—
370#386—32no—
371#386—32no—
372#386—32no—
373#386—32no—
374#386—32no—
375#386—32no—
376#386C2×D312yescomplemented
377#385—32no—
378#382—31no—
379#381—32no—
380#380—32no—
381#380—32no—
382#380—31no—
383#380C2×D311yescharacteristic
384#379—32no—
385C4×C4⋊C4—31no—
386C4×C22⋊C4—31no—
387C4×C22⋊C4—31no—
388C24×C3C2412yes—
389C24×C3C2411yescharacteristic
390C24×C3C2411yescharacteristic
391C23×D3—24no—
392C23×D3—24no—
393C23×D3—42no—
394C23×D3—42no—
395C23×D3—42no—
396C23×D3—42no—
397C23×D3—42no—
398C23×D3C2412yes—
399C23×D3C2411yescharacteristic
400C23×D3C2412yes—
401C2×C3×D4—22no—
402C2×C3×D4—22no—
403C2×C3×D4—24no—
404C2×C3×D4—24no—
405C2×C3×D4—22no—
406C2×C3×D4—22no—
407C2×C3×D4—22no—
408C2×C3×D4—41no—
409C2×C3×D4—42no—
410C2×C3×D4—42no—
411C2×C3×D4—42no—
412C2×C3×D4—42no—
413C22×C3×C4—22no—
414C22×C3×C4—22no—
415C22×C3×C4—22no—
416C22×C3×C4—22no—
417C22×C3×C4—22no—
418C22×C3×C4—42no—
419C22×C3×C4—42no—
420C22×C3×C4—42no—
421C22×C3×C4C2×D414yes—
422C22×C3×C4C2412yes—
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—22no—
438C2×#67—41no—
439C2×#67—42no—
440C2×#67—42no—
441C2×#67—42no—
442C2×#67—42no—
443C2×#67—42no—
444C2×#67—41no—
445C2×#67—41no—
446C2×#67—42no—
447C2×#67—42no—
448C2×#67—42no—
449C2×#67—42no—
450C2×#67—42no—
451C2×#67—42no—
452C2×#67—42no—
453C2×#67—42no—
454C2×#67—42no—
455C2×#67—42no—
456C2×#67C2×D418yes—
457C22×Dic3—24no—
458C22×Dic3—42no—
459C22×Dic3—42no—
460C22×Dic3C2411yescharacteristic
461C22×Dic3C2411yescharacteristic
462C22×Dic3C2411yescharacteristic
463C22×Dic3C2411yescharacteristic
464C22×Dic3C2411yescharacteristic
465C22×Dic3C2412yes—
466C22×Dic3C2411yescharacteristic
467C22×Dic3C2412yes—
468C22×Dic3C2411yescharacteristic
469#237—416no—
470#235—416no—
471C2×D12—22no—
472C2×D12—22no—
473C2×D12—24no—
474C2×D12—22no—
475C2×D12—22no—
476C2×D12—22no—
477C2×D12—24no—
478C2×D12—416no—
479C2×D12—42no—
480C2×D12—42no—
481C2×D12—42no—
482C2×D12—42no—
483C2×D12—42no—
484C2×D12—42no—
485C2×D12—42no—
486C2×D12C2×D414yes—
487C2×C4×D3—22no—
488C2×C4×D3—22no—
489C2×C4×D3—22no—
490C2×C4×D3—24no—
491C2×C4×D3—42no—
492C2×C4×D3—42no—
493C2×C4×D3—42no—
494C2×C4×D3—42no—
495C2×C4×D3C2×D418yes—
496C2×Dic6—22no—
497C2×Dic6—22no—
498C2×Dic6C2×D414yes—
499C3×C4⋊C4—22no—
500C3×C4⋊C4—22no—
501C3×C4⋊C4—22no—
502C3×C4⋊C4—22no—
503C3×C4⋊C4—42no—
504C3×C4⋊C4—42no—
505C3×C22⋊C4—22no—
506C3×C22⋊C4—24no—
507C3×C22⋊C4—22no—
508C3×C22⋊C4—24no—
509C3×C22⋊C4—42no—
510C3×C22⋊C4—42no—
511C3×C22⋊C4—42no—
512C3×C42—22no—
513#217—22no—
514#217—22no—
515#217—24no—
516#217—22no—
517#217—42no—
518#217—41no—
519#217—41no—
520#217—41no—
521#217—42no—
522(C2×D3)⋊C4—24no—
523(C2×D3)⋊C4—24no—
524(C2×D3)⋊C4—24no—
525(C2×D3)⋊C4—22no—
526(C2×D3)⋊C4—24no—
527(C2×D3)⋊C4—24no—
528(C2×D3)⋊C4—24no—
529(C2×D3)⋊C4—42no—
530(C2×D3)⋊C4—42no—
531(C2×D3)⋊C4—42no—
532(C2×D3)⋊C4—42no—
533(C2×D3)⋊C4—42no—
534(C2×D3)⋊C4—41no—
535(C2×D3)⋊C4—41no—
536(C2×D3)⋊C4—41no—
537(C2×D3)⋊C4—42no—
538(C2×D3)⋊C4—42no—
539(C2×D3)⋊C4—42no—
540(C2×D3)⋊C4—42no—
541C4⋊Dic3—22no—
542C4⋊Dic3—24no—
543C4⋊Dic3—41no—
544C4⋊Dic3—41no—
545Dic3⋊C4—22no—
546Dic3⋊C4—24no—
547Dic3⋊C4—24no—
548Dic3⋊C4—22no—
549Dic3⋊C4—41no—
550Dic3⋊C4—41no—
551C4×Dic3—22no—
552C4×Dic3—22no—
553C4×Dic3—22no—
554C4×Dic3—24no—
555C25—32no—
556C2×#41—38no—
557C2×#41—64no—
558C2×#41—122no—
559C2×#41—122no—
560C2×#41—122no—
561C2×#41—122no—
562C22×Q8—31no—
563C22×D4—32no—
564C22×D4—32no—
565C22×D4—31no—
566C22×D4—31no—
567C22×D4—32no—
568C22×D4—32no—
569C22×D4—32no—
570C22×D4—32no—
571C22×D4—32no—
572C22×D4—31no—
573C22×D4—31no—
574C22×D4—32no—
575C22×D4—32no—
576C22×D4—32no—
577C22×D4—64no—
578C22×D4—122no—
579C22×D4—122no—
580C22×D4C22×D311yescharacteristic
581C22×D4C22×D311yescharacteristic
582C22×D4C22×D312yes—
583C22×D4C22×D312yes—
584C23×C4—32no—
585C23×C4—32no—
586C23×C4—31no—
587C23×C4—32no—
588C23×C4C22×D311yescharacteristic
589C23×C4C22×D311yescharacteristic
590C23×C4C22×D312yes—
591#127—68no—
592#127—64no—
593#127—122no—
594#124—64no—
595#123—68no—
596#123—124no—
597C22⋊Q8—64no—
598#121—24no—
599#121—44no—
600#121—42no—
601#121—68no—
602#121—68no—
603#121—64no—
604#121—68no—
605#121—64no—
606#121—124no—
607#121—122no—
608#120—68no—
609#120—124no—
610#120—124no—
611#120—124no—
612C4×Q8—64no—
613C4×D4—24no—
614C4×D4—64no—
615C4×D4—68no—
616C4×D4—64no—
617C4×D4—122no—
618#117—122no—
619C2×C4⋊C4—31no—
620C2×C4⋊C4—31no—
621C2×C4⋊C4—32no—
622C2×C4⋊C4—32no—
623C2×C4⋊C4—32no—
624C2×C4⋊C4—31no—
625C2×C4⋊C4—31no—
626C2×C4⋊C4—31no—
627C2×C4⋊C4—31no—
628C2×C4⋊C4—31no—
629C2×C4⋊C4—42no—
630C2×C4⋊C4C22×D311yescharacteristic
631C2×C4⋊C4C22×D311yescharacteristic
632C2×C4⋊C4C22×D311yescharacteristic
633C2×C4⋊C4C22×D311yescharacteristic
634C2×C4⋊C4C22×D312yes—
635C2×C4⋊C4C22×D312yes—
636C2×C22⋊C4—32no—
637C2×C22⋊C4—31no—
638C2×C22⋊C4—31no—
639C2×C22⋊C4—31no—
640C2×C22⋊C4—32no—
641C2×C22⋊C4—32no—
642C2×C22⋊C4—32no—
643C2×C22⋊C4—32no—
644C2×C22⋊C4—31no—
645C2×C22⋊C4—32no—
646C2×C22⋊C4—32no—
647C2×C22⋊C4—31no—
648C2×C22⋊C4—31no—
649C2×C22⋊C4—31no—
650C2×C22⋊C4—32no—
651C2×C22⋊C4—32no—
652C2×C22⋊C4—31no—
653C2×C22⋊C4—32no—
654C2×C22⋊C4—32no—
655C2×C22⋊C4—32no—
656C2×C22⋊C4—32no—
657C2×C22⋊C4—32no—
658C2×C22⋊C4—32no—
659C2×C22⋊C4—32no—
660C2×C22⋊C4—32no—
661C2×C22⋊C4—31no—
662C2×C22⋊C4—31no—
663C2×C22⋊C4—32no—
664C2×C22⋊C4—68no—
665C2×C22⋊C4C22×D311yescharacteristic
666C2×C22⋊C4C22×D312yes—
667C2×C22⋊C4C22×D311yescharacteristic
668C2×C22⋊C4C22×D312yes—
669C2×C22⋊C4C22×D312yes—
670C2×C22⋊C4C22×D312yes—
671C2×C22⋊C4C22×D312yes—
672C2×C42—31no—
673C2×C42—31no—
674C2×C42—31no—
675C2×C42—32no—
676C2×C42C22×D311yescharacteristic
677#95—31no—
678#95—31no—
679#95—31no—
680#95—31no—
681#95—31no—
682#95—31no—
683#95—32no—
684#95—32no—
685#95—32no—
686#95—32no—
687#95—32no—
688#95—32no—
689#95—32no—
690#95—32no—
691#95C22×D312yes—
692#95C22×D312yes—
693C23×C3—21no—
694C23×C3—21no—
695C23×C3—21no—
696C23×C3—21no—
697C23×C3—21no—
698C23×C3—21no—
699C23×C3—21no—
700C23×C3—21no—
701C23×C3—21no—
702C23×C3—21no—
703C23×C3—21no—
704C23×C3—21no—
705C23×C3—22no—
706C23×C3—22no—
707C23×C3—22no—
708C23×C3—22no—
709C23×C3—22no—
710C23×C3—22no—
711C23×C3—22no—
712C23×C3C22×D412yes—
713C23×C3H(5,𝔽2)12yes—
714C23×C3C2511yescharacteristic
715C22×D3—22no—
716C22×D3—22no—
717C22×D3—22no—
718C22×D3—22no—
719C22×D3—22no—
720C22×D3—22no—
721C22×D3—22no—
722C22×D3—21no—
723C22×D3—22no—
724C22×D3—21no—
725C22×D3—22no—
726C22×D3—21no—
727C22×D3—22no—
728C22×D3—21no—
729C22×D3—22no—
730C22×D3—21no—
731C22×D3—21no—
732C22×D3—21no—
733C22×D3—22no—
734C22×D3—22no—
735C22×D3—48no—
736C22×D3—48no—
737C22×D3—84no—
738C22×D3—84no—
739C22×D3—84no—
740C22×D3—84no—
741C22×D3—84no—
742C22×D3C22×D414yes—
743C3×D4—44no—
744C3×D4—44no—
745C3×D4—84no—
746C3×D4—84no—
747C2×C3×C4—21no—
748C2×C3×C4—21no—
749C2×C3×C4—28no—
750C2×C3×C4—22no—
751C2×C3×C4—21no—
752C2×C3×C4—21no—
753C2×C3×C4—21no—
754C2×C3×C4—21no—
755C2×C3×C4—21no—
756C2×C3×C4—22no—
757C2×C3×C4—22no—
758C2×C3×C4—22no—
759C2×C3×C4—22no—
760C2×C3×C4—22no—
761C2×C3×C4—22no—
762C2×C3×C4—21no—
763C2×C3×C4—21no—
764C2×C3×C4—22no—
765C2×C3×C4—21no—
766C2×C3×C4—21no—
767C2×C3×C4—22no—
768C2×C3×C4—44no—
769C2×C3×C4—84no—
770C2×C3×C4C22×D412yes—
771C2×C3×C4C22×D412yes—
772C2×C3×C4H(5,𝔽2)12yes—
773C2×C3×C4H(5,𝔽2)12yes—
774#67—48no—
775#67—48no—
776#67—44no—
777#67—48no—
778#67—44no—
779#67—84no—
780#67—84no—
781#67—84no—
782#67—84no—
783C2×Dic3—21no—
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—21no—
795C2×Dic3—21no—
796C2×Dic3—22no—
797C2×Dic3—21no—
798C2×Dic3—21no—
799C2×Dic3—21no—
800C2×Dic3—21no—
801C2×Dic3—21no—
802C2×Dic3—21no—
803C2×Dic3—21no—
804C2×Dic3—21no—
805C2×Dic3—21no—
806C2×Dic3—21no—
807C2×Dic3—22no—
808C2×Dic3—48no—
809C2×Dic3C22×D414yes—
810C2×Dic3H(5,𝔽2)12yes—
811D12—28no—
812D12—48no—
813D12—44no—
814D12—84no—
815D12—84no—
816C4×D3—48no—
817C4×D3—44no—
818C4×D3—84no—
819Dic6—28no—
820C24—32no—
821C24—32no—
822C24—31no—
823C24—64no—
824C24—64no—
825C24—122no—
826C24—122no—
827C24—122no—
828C24—122no—
829C24—122no—
830C24C23×D312yes—
831C24C23×D311yescharacteristic
832C24C23×D311yescharacteristic
833#41—1216no—
834#41—1216no—
835C2×Q8—34no—
836C2×Q8—62no—
837C2×Q8—62no—
838C2×D4—22no—
839C2×D4—22no—
840C2×D4—24no—
841C2×D4—24no—
842C2×D4—22no—
843C2×D4—22no—
844C2×D4—22no—
845C2×D4—38no—
846C2×D4—34no—
847C2×D4—41no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—64no—
853C2×D4—64no—
854C2×D4—64no—
855C2×D4—64no—
856C2×D4—62no—
857C2×D4—64no—
858C2×D4—62no—
859C2×D4—62no—
860C2×D4—64no—
861C2×D4—64no—
862C2×D4—62no—
863C2×D4—62no—
864C2×D4—62no—
865C2×D4—62no—
866C2×D4—62no—
867C2×D4—122no—
868C2×D4—122no—
869C2×D4—122no—
870C2×D4—122no—
871C2×D4—122no—
872C2×D4—122no—
873C2×D4—122no—
874C2×D4—1216no—
875C2×D4—121no—
876C2×D4—122no—
877C2×D4—122no—
878C2×D4—122no—
879C2×D4—122no—
880C2×D4—121no—
881C2×D4—122no—
882C2×D4—121no—
883C2×D4—122no—
884C2×D4—122no—
885C2×D4—122no—
886C2×D4—122no—
887C2×D4—122no—
888C2×D4—122no—
889C2×D4—122no—
890C2×D4—122no—
891C2×D4—122no—
892C2×D4—122no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—32no—
899C22×C4—31no—
900C22×C4—38no—
901C22×C4—31no—
902C22×C4—31no—
903C22×C4—31no—
904C22×C4—31no—
905C22×C4—32no—
906C22×C4—31no—
907C22×C4—31no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—64no—
912C22×C4—64no—
913C22×C4—62no—
914C22×C4—62no—
915C22×C4—62no—
916C22×C4—122no—
917C22×C4—122no—
918C22×C4—122no—
919C22×C4—122no—
920C22×C4—122no—
921C22×C4—122no—
922C22×C4D3×D414yes—
923C22×C4C23×D312yes—
924C22×C4C23×D312yes—
925C22×C4C23×D312yes—
926C22×C4C23×D311yescharacteristic
927C22×C4C23×D311yescharacteristic
928C22×C4C23×D311yescharacteristic
929C22×C4C23×D311yescharacteristic
930C22×C4C23×D311yescharacteristic
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—64no—
938C4⋊C4—64no—
939C4⋊C4—64no—
940C4⋊C4—62no—
941C4⋊C4—62no—
942C4⋊C4—62no—
943C4⋊C4—121no—
944C4⋊C4—121no—
945C4⋊C4—121no—
946C4⋊C4—121no—
947C22⋊C4—22no—
948C22⋊C4—24no—
949C22⋊C4—22no—
950C22⋊C4—24no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—64no—
955C22⋊C4—64no—
956C22⋊C4—64no—
957C22⋊C4—64no—
958C22⋊C4—64no—
959C22⋊C4—64no—
960C22⋊C4—62no—
961C22⋊C4—62no—
962C22⋊C4—62no—
963C22⋊C4—64no—
964C22⋊C4—62no—
965C22⋊C4—121no—
966C22⋊C4—122no—
967C22⋊C4—122no—
968C22⋊C4—122no—
969C22⋊C4—122no—
970C22⋊C4—122no—
971C22⋊C4—122no—
972C22⋊C4—122no—
973C22⋊C4—122no—
974C22⋊C4—121no—
975C22⋊C4—122no—
976C22⋊C4—121no—
977C22⋊C4—121no—
978C22⋊C4—121no—
979C22⋊C4—121no—
980C22⋊C4—122no—
981C22⋊C4—122no—
982C42—22no—
983C42—64no—
984C42—62no—
985C42—62no—
986C42—62no—
987C22×C3—22no—
988C22×C3—22no—
989C22×C3—22no—
990C22×C3—22no—
991C22×C3—22no—
992C22×C3—22no—
993C22×C3—41no—
994C22×C3—41no—
995C22×C3—41no—
996C22×C3—41no—
997C22×C3—41no—
998C22×C3—41no—
999C22×C3—41no—
1000C22×C3—41no—
1001C22×C3—42no—
1002C22×C3—42no—
1003C22×C3—42no—
1004C22×C3—42no—
1005C22×C3—42no—
1006C22×C3—42no—
1007C22×C3—42no—
1008C22×C3C23×D411yescharacteristic
1009C22×C3C2×H(5,𝔽2)11yescharacteristic
1010C22×C3C2×H(5,𝔽2)11yescharacteristic
1011C22×C3C2×H(5,𝔽2)11yescharacteristic
1012C22×C3C2×H(5,𝔽2)11yescharacteristic
1013C22×C3#58511yescharacteristic
1014C22×C3#58511yescharacteristic
1015C2×D3—24no—
1016C2×D3—24no—
1017C2×D3—24no—
1018C2×D3—42no—
1019C2×D3—42no—
1020C2×D3—42no—
1021C2×D3—42no—
1022C2×D3—41no—
1023C2×D3—42no—
1024C2×D3—41no—
1025C2×D3—41no—
1026C2×D3—42no—
1027C2×D3—42no—
1028C2×D3—41no—
1029C2×D3—42no—
1030C2×D3—41no—
1031C2×D3—42no—
1032C2×D3—42no—
1033C2×D3—41no—
1034C2×D3—41no—
1035C2×D3—42no—
1036C2×D3—816no—
1037C3×C4—22no—
1038C3×C4—41no—
1039C3×C4—41no—
1040C3×C4—42no—
1041C3×C4—41no—
1042C3×C4—42no—
1043C3×C4—42no—
1044C3×C4#53414yes—
1045Dic3—24no—
1046Dic3—22no—
1047Dic3—41no—
1048Dic3—42no—
1049Dic3—41no—
1050Dic3—41no—
1051Dic3—41no—
1052Dic3—41no—
1053Dic3—41no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—34no—
1074C23—62no—
1075C23—62no—
1076C23—62no—
1077C23—62no—
1078C23—62no—
1079C23—62no—
1080C23—62no—
1081C23—61no—
1082C23—62no—
1083C23—62no—
1084C23—61no—
1085C23—61no—
1086C23—61no—
1087C23—62no—
1088C23—61no—
1089C23—62no—
1090C23—62no—
1091C23—61no—
1092C23—61no—
1093C23—62no—
1094C23—128no—
1095C23—128no—
1096C23—244no—
1097C23—244no—
1098C23—244no—
1099C23—244no—
1100C23—244no—
1101C23C2×D3×D412yes—
1102C23#100412yes—
1103C23C24×D311yescharacteristic
1104Q8—68no—
1105D4—44no—
1106D4—44no—
1107D4—68no—
1108D4—84no—
1109D4—84no—
1110D4—128no—
1111D4—128no—
1112D4—124no—
1113D4—128no—
1114D4—128no—
1115D4—124no—
1116D4—124no—
1117D4—244no—
1118D4—244no—
1119D4—244no—
1120D4—244no—
1121D4—244no—
1122D4—244no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—28no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—22no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—21no—
1144C2×C4—34no—
1145C2×C4—32no—
1146C2×C4—44no—
1147C2×C4—61no—
1148C2×C4—62no—
1149C2×C4—62no—
1150C2×C4—61no—
1151C2×C4—61no—
1152C2×C4—62no—
1153C2×C4—61no—
1154C2×C4—61no—
1155C2×C4—61no—
1156C2×C4—61no—
1157C2×C4—61no—
1158C2×C4—61no—
1159C2×C4—61no—
1160C2×C4—61no—
1161C2×C4—61no—
1162C2×C4—61no—
1163C2×C4—61no—
1164C2×C4—61no—
1165C2×C4—61no—
1166C2×C4—61no—
1167C2×C4—61no—
1168C2×C4—62no—
1169C2×C4—61no—
1170C2×C4—62no—
1171C2×C4—61no—
1172C2×C4—84no—
1173C2×C4—128no—
1174C2×C4—128no—
1175C2×C4—124no—
1176C2×C4—244no—
1177C2×C4C2×D3×D412yes—
1178C2×C4C2×D3×D412yes—
1179C2×C4#100412yes—
1180C2×C4#100912yes—
1181C2×C3—42no—
1182C2×C3—42no—
1183C2×C3—82no—
1184C2×C3C2×#53411yescharacteristic
1185C2×C3#348811yescharacteristic
1186C2×C3#348811yescharacteristic
1187C2×C3#354211yescharacteristic
1188C2×C3#354311yescharacteristic
1189C2×C3#354611yescharacteristic
1190C2×C3#356211yescharacteristic
1191D3—44no—
1192D3—81no—
1193D3—82no—
1194C22—22no—
1195C22—22no—
1196C22—22no—
1197C22—22no—
1198C22—22no—
1199C22—22no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—64no—
1216C22—64no—
1217C22—64no—
1218C22—122no—
1219C22—122no—
1220C22—122no—
1221C22—122no—
1222C22—121no—
1223C22—122no—
1224C22—121no—
1225C22—122no—
1226C22—122no—
1227C22—121no—
1228C22—121no—
1229C22—122no—
1230C22—121no—
1231C22—122no—
1232C22—121no—
1233C22—122no—
1234C22—122no—
1235C22—121no—
1236C22—2416no—
1237C22C22×D3×D411yescharacteristic
1238C22C2×#100411yescharacteristic
1239C22C2×#100411yescharacteristic
1240C22C2×#100911yescharacteristic
1241C22#596411yescharacteristic
1242C22D3×H(5,𝔽2)11yescharacteristic
1243C22#596811yescharacteristic
1244C4—22no—
1245C4—42no—
1246C4—42no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—42no—
1251C4—62no—
1252C4—64no—
1253C4—122no—
1254C4—121no—
1255C4—121no—
1256C4—121no—
1257C4—121no—
1258C4—121no—
1259C4—121no—
1260C4#560514yes—
1261C3#4295111yescharacteristic, complemented, Sylow
1262C2—42no—
1263C2—42no—
1264C2—82no—
1265C2—124no—
1266C2—242no—
1267C2—241no—
1268C2C2×#560511yescharacteristic
1269C2#8594911yescharacteristic
1270C2#8637911yescharacteristic
1271C2#8661611yescharacteristic
1272C2#8669111yescharacteristic
1273C2#8673311yescharacteristic
1274C2#8691811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2416C2
hypercenter#2416D3
hypocenterC3#42951
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2416

Complements

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

NH ≅ G/Ntype
1. C2×#5599C2semidirect
2. C2×#5550C2semidirect
3. C3×#2416C2semidirect
4. #82714C2semidirect
5. #82713C2semidirect
6. #82701C2semidirect
7. #82676C2semidirect
8. #82653C2semidirect
9. #82345C2semidirect
10. #82193C2semidirect
11. #82186C2semidirect
12. #77448C2semidirect
13. #77334C2semidirect
14. #77123C2semidirect
15. #77119C2semidirect
16. #76316C2semidirect
17. #76313C2semidirect
18. #76213C2semidirect
19. #76007C2semidirect
20. #74922C2semidirect
21. #74915C2semidirect
22. #74016C2semidirect
23. #73892C2semidirect
25. C22×#237C22semidirect
30. C2×C3×#121C22semidirect
32. C22×C3×C4⋊C4C22semidirect
35. C2×#940C22semidirect
36. C2×#939C22semidirect
41. C2×#930C22semidirect
43. C2×C4×#67C22semidirect
44. C2×#926C22semidirect
51. C2×#887C22semidirect
53. C2×#884C22semidirect
54. C2×#883C22semidirect
56. C2×#67⋊C4C22semidirect
60. C3×#396C22semidirect
62. C3×#390C22semidirect
63. C3×#389C22semidirect
64. C3×#386C22semidirect
68. #5223C22semidirect
69. #5223C22semidirect
71. #5221C22semidirect
73. #5213C22semidirect
74. #5213C22semidirect
75. #5213C22semidirect
77. #4994C22semidirect
78. #4994C22semidirect
79. #4993C22semidirect
80. #4992C22semidirect
81. #4991C22semidirect
82. #4991C22semidirect
83. #4990C22semidirect
88. #4987C22semidirect
89. #4987C22semidirect
90. #4987C22semidirect
91. #4984C22semidirect
92. #4982C22semidirect
93. #4977C22semidirect
94. #4973C22semidirect
95. #4973C22semidirect
97. #4961C22semidirect
98. #4961C22semidirect
99. #4961C22semidirect
102. #4960C22semidirect
103. #4960C22semidirect
104. #4959C22semidirect
105. #4959C22semidirect
106. #4959C22semidirect
107. #4958C22semidirect
108. #4958C22semidirect
109. #4956C22semidirect
112. #4952C22semidirect
115. #4946C22semidirect
116. C4×(C2×D3)⋊C4C22semidirect
117. C4×Dic3⋊C4C22semidirect
118. #4675C22semidirect
121. #4669C22semidirect
122. #4665C22semidirect
123. #4664C22semidirect
124. #4658C22semidirect
125. #4654C22semidirect
144. #2416D3semidirect
172. C2×#235D4semidirect
308. C2×#121C2×D3semidirect
320. C22×C4⋊C4C2×D3semidirect
332. #396C2×D3semidirect
361. #390C2×D3semidirect
363. #389C2×D3semidirect
376. #386C2×D3semidirect
1261. C3#42951semidirect

Maximal subgroups

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

subgroupindex
C2×#55992
C2×#55502
C3×#24162
#827142
#827132
#827012
#826762
#826532
#823452
#821932
#821862
#774482
#773342
#771232
#771192
#763162
#763132
#762132
#760072
#749222
#749152
#740162
#738922
#429513