Finite Group Databasebeta

← #11097535

Subgroups — #11097535

Order 768.

3000 conjugacy classes of subgroups.

The subgroup lattice has 1248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5678C211yesmaximal, characteristic, complemented
2C2×#5554C211yesmaximal, characteristic, complemented
3C3×#2540C211yesmaximal, characteristic, complemented
4#83007C211yesmaximal, characteristic, complemented
5#82827C212yesmaximal, complemented
6#82816C212yesmaximal, complemented
7#82718C212yesmaximal, complemented
8#82702C212yesmaximal, complemented
9#82423C211yesmaximal, characteristic, complemented
10#78125C211yesmaximal, characteristic, complemented
11#78111C211yesmaximal, characteristic, complemented
12#78110C211yesmaximal, characteristic, complemented
13#78108C211yesmaximal, characteristic, complemented
14#76757C211yesmaximal, characteristic, complemented
15D3×#392C211yesmaximal, characteristic, complemented
16#76697C211yesmaximal, characteristic, complemented
17#76669C211yesmaximal, characteristic, complemented
18#76442C212yesmaximal, complemented
19#76436C212yesmaximal, complemented
20#76388C212yesmaximal, complemented
21#76379C212yesmaximal, complemented
22#73816C211yesmaximal, characteristic, complemented
23#73770C211yesmaximal, characteristic, complemented
24#40488—31nomaximal, Sylow
25C22×#237C2211yescharacteristic, complemented
26C22×D3×D4C2211yescharacteristic
27C22×D3×D4C2212yes—
28C2×C3×#124C2211yescharacteristic, complemented
29C2×C3×C22⋊Q8C2212yescomplemented
30C2×C3×#121C2212yescomplemented
31C2×C3×C4×D4C2211yescharacteristic, complemented
32C2×#947C2211yescharacteristic, complemented
33C2×#946C2211yescharacteristic
34C2×#939C2211yescharacteristic, complemented
35C2×#939C2212yescomplemented
36C2×#939C2212yescomplemented
37C2×#938C2212yescomplemented
38C2×#937C2211yescharacteristic
39C2×#937C2212yes—
40C2×#930C2212yescomplemented
41C22×(C2×D3)⋊C4C2212yes—
42#5678—28no—
43#5554—28no—
44C2×#897C2211yescharacteristic
45C2×#895C2211yescharacteristic, complemented
46C2×#895C2212yescomplemented
47C2×#886C2212yescomplemented
48C2×#886C2211yescharacteristic, complemented
49C2×#884C2211yescharacteristic
50C2×#884C2211yescharacteristic, complemented
51C2×#884C2212yescomplemented
52C2×#883C2211yescharacteristic, complemented
53C2×#882C2212yes—
54C2×#882C2211yescharacteristic
55C2×#67⋊C4C2211yescharacteristic
56C2×D3×C22⋊C4C2211yescharacteristic
57C2×D3×C22⋊C4C2212yes—
58C2×#879C2211yescharacteristic, complemented
59C2×#876C2211yescharacteristic, complemented
60C2×#875C2211yescharacteristic, complemented
61C2×C4×D12C2212yes—
62C2×C4×D12C2211yescharacteristic
63C3×#399C2211yescharacteristic, complemented
64C3×#399C2211yescharacteristic, complemented
65C3×#392C2211yescharacteristic
66C3×#392C2211yescharacteristic, complemented
67C3×#390C2212yescomplemented
68C3×#390C2212yescomplemented
69C3×C4×C4⋊C4C2211yescharacteristic, complemented
70#5231C2212yescomplemented
71#5223C2212yes—
72#5223C2211yescharacteristic
73#5223C2212yescomplemented
74#5223C2212yescomplemented
75#5222C2211yescharacteristic, complemented
76#5220C2212yescomplemented
77#5213C2212yescomplemented
78#5210C2212yescomplemented
79#4994C2212yescomplemented
80#4994C2212yescomplemented
81#4994C2212yescomplemented
82#4993C2211yescharacteristic, complemented
83#4993C2212yescomplemented
84#4991C2212yescomplemented
85#4991C2212yescomplemented
86#4989C2212yes—
87#4989C2212yes—
88#4989C2212yescomplemented
89#4987C2212yes—
90#4985C2211yescharacteristic, complemented
91#4980C2212yescomplemented
92#4961C2212yescomplemented
93#4961C2212yescomplemented
94#4961C2212yescomplemented
95#4960C2211yescharacteristic
96#4960C2212yes—
97#4960C2212yescomplemented
98#4960C2212yescomplemented
99#4960C2211yescharacteristic, complemented
100#4960C2212yescomplemented
101#4959C2212yescomplemented
102#4957C2212yescomplemented
103#4956C2212yes—
104#4956C2212yescomplemented
105#4955C2212yes—
106#4955C2212yes—
107#4950C2212yescomplemented
108#4950C2212yescomplemented
109#4948C2212yescomplemented
110#4948C2212yescomplemented
111#4947C2211yescharacteristic, complemented
112#4947C2211yescharacteristic, complemented
113#4942C2212yescomplemented
114#4940C2212yescomplemented
115#4939C2212yescomplemented
116#4936C2211yescharacteristic, complemented
117#4928C2212yescomplemented
118#4673C2211yescharacteristic, complemented
119#4672C2211yescharacteristic, complemented
120#4671C2211yescharacteristic
121#4667C2211yescharacteristic
122#4667C2211yescharacteristic, complemented
123D3×#95C2211yescharacteristic
124D3×#95C2211yescharacteristic, complemented
125#4656C2211yescharacteristic, complemented
126C2×#546—31no—
127C2×#538—31no—
128#2819—31no—
129#2813—31no—
130#2705—32no—
131#2682—32no—
132#2676—32no—
133#2675—32no—
134#2662—31no—
135#2656—31no—
136#2636—31no—
137#2626—31no—
138#2615—31no—
139#2564—31no—
140#2540D311yescharacteristic, complemented
141#2437—32no—
142#2430—31no—
143#2424—32no—
144#2410—32no—
145#2408—31no—
146#2408—32no—
147C2×#392—31no—
148#2349—31no—
149C24×D3C2312yes—
150C24×D3C2311yescharacteristic
151C22×C3×Q8C2311yescharacteristic
152C22×C3×D4C2311yescharacteristic
153C22×C3×D4C2312yes—
154C22×C3×D4C2311yescharacteristic
155C22×C3×D4C2312yes—
156C23×C3×C4C2312yes—
157C22×#67C2311yescharacteristic
158C22×#67C2312yes—
159C22×#67C2312yes—
160C22×#67C2312yes—
161C22×#67C2311yescharacteristic
162C22×#67C2311yescharacteristic
163C22×#67C2311yescharacteristic
164C22×#67C2312yes—
165C22×#67C2312yes—
166C23×Dic3C2312yes—
167C23×Dic3C2311yescharacteristic
168C2×#237—24no—
169C2×#237—44no—
170C2×D3×D4—24no—
171C2×D3×D4—44no—
172C2×D3×D4—44no—
173C2×D3×D4—44no—
174C2×D3×D4—44no—
175C22×D12C2311yescharacteristic
176C22×D12C2311yescharacteristic
177C22×D12C2312yes—
178C22×D12C2311yescharacteristic
179C22×D12C2312yes—
180C22×C4×D3C2312yes—
181C22×C4×D3C2312yes—
182C22×C4×D3C2311yescharacteristic
183C22×C4×D3C2311yescharacteristic
184C22×C4×D3C2311yescharacteristic
185C22×Dic6C2311yescharacteristic
186C3×#124—24no—
187C3×C22⋊Q8—44no—
188C3×#121—44no—
189C3×C4×D4—24no—
190C2×C3×C4⋊C4C2312yes—
191C2×C3×C4⋊C4C2311yescharacteristic
192C2×C3×C4⋊C4C2312yes—
193C2×C3×C4⋊C4C2312yes—
194C2×C3×C22⋊C4C2311yescharacteristic
195C2×C3×C22⋊C4C2311yescharacteristic
196C2×C3×C22⋊C4C2312yes—
197C2×C3×C22⋊C4C2312yes—
198C2×C3×C22⋊C4C2312yes—
199C2×C3×C22⋊C4C2311yescharacteristic
200C2×C3×C22⋊C4C2311yescharacteristic
201C2×C3×C22⋊C4C2312yes—
202C2×C3×C22⋊C4C2312yes—
203C2×C3×C42C2312yes—
204C2×C3×C42C2311yescharacteristic
205C2×#217C2311yescharacteristic
206C2×#217C2312yes—
207C2×#217C2311yescharacteristic
208C2×#217C2312yes—
209C2×#217C2312yes—
210C2×#217C2312yes—
211C2×#217C2312yes—
212#947—24no—
213#946—24no—
214#939—24no—
215#939—44no—
216#939—44no—
217#938—44no—
218#937—24no—
219#937—44no—
220#930—28no—
221C2×(C2×D3)⋊C4—28no—
222C2×(C2×D3)⋊C4C2312yes—
223C2×(C2×D3)⋊C4C2311yescharacteristic
224C2×(C2×D3)⋊C4C2312yes—
225C2×(C2×D3)⋊C4C2311yescharacteristic
226C2×(C2×D3)⋊C4C2312yes—
227C2×(C2×D3)⋊C4C2311yescharacteristic
228C2×(C2×D3)⋊C4C2312yes—
229C2×(C2×D3)⋊C4C2311yescharacteristic
230C2×(C2×D3)⋊C4C2311yescharacteristic
231C2×(C2×D3)⋊C4C2312yes—
232C2×(C2×D3)⋊C4C2311yescharacteristic
233C2×(C2×D3)⋊C4C2312yes—
234C2×(C2×D3)⋊C4C2312yes—
235C2×(C2×D3)⋊C4C2312yes—
236C2×(C2×D3)⋊C4C2312yes—
237C2×(C2×D3)⋊C4C2312yes—
238C2×(C2×D3)⋊C4C2312yes—
239C2×(C2×D3)⋊C4C2312yes—
240C2×(C2×D3)⋊C4C2312yes—
241C2×(C2×D3)⋊C4C2311yescharacteristic
242C2×(C2×D3)⋊C4C2311yescharacteristic
243C2×C4⋊Dic3C2312yes—
244C2×C4⋊Dic3C2311yescharacteristic
245C2×C4⋊Dic3C2312yes—
246C2×C4⋊Dic3C2312yes—
247C2×C4⋊Dic3C2311yescharacteristic
248C2×Dic3⋊C4C2311yescharacteristic
249C2×Dic3⋊C4C2311yescharacteristic
250C2×Dic3⋊C4C2311yescharacteristic
251C2×Dic3⋊C4C2311yescharacteristic
252C2×Dic3⋊C4C2312yes—
253C2×Dic3⋊C4C2312yes—
254C2×Dic3⋊C4C2312yes—
255C2×C4×Dic3C2311yescharacteristic
256#897—24no—
257#895—24no—
258#895—44no—
259#886—24no—
260#886—28no—
261#884—24no—
262#884—24no—
263#884—44no—
264#883—24no—
265#882—24no—
266#882—28no—
267#67⋊C4—24no—
268D3×C22⋊C4—24no—
269D3×C22⋊C4—44no—
270#879—24no—
271#876—24no—
272#875—24no—
273C4×D12—44no—
274C4×D12D418yescomplemented
275C3×#95C2311yescharacteristic
276C3×#95C2311yescharacteristic
277C3⋊#95C2312yes—
278C3⋊#95C2311yescharacteristic
279C3⋊#95C2312yes—
280C3⋊#95C2311yescharacteristic
281C3⋊#95C2312yes—
282C3⋊#95C2312yes—
283C3⋊#95C2312yes—
284C3⋊#95C2312yes—
285C3⋊#95C2312yes—
286C3⋊#95C2312yes—
287C3⋊#95C2312yes—
288C22×#41—31no—
289C23×D4—31no—
290C23×D4—32no—
291#546—68no—
292#538—68no—
293C2×#126—31no—
294C2×#126—31no—
295C2×#124—31no—
296C2×#124—31no—
297C2×#124C2×D311yescharacteristic, complemented
298C2×#123—31no—
299C2×#123—31no—
300C2×#123—32no—
301C2×C22⋊Q8—31no—
302C2×C22⋊Q8—31no—
303C2×C22⋊Q8C2×D312yescomplemented
304C2×#121—31no—
305C2×#121—32no—
306C2×#121—32no—
307C2×#121—32no—
308C2×#121—32no—
309C2×#121—31no—
310C2×#121—32no—
311C2×#121—31no—
312C2×#121—31no—
313C2×#121—32no—
314C2×#121C2×D312yescomplemented
315C2×#120—31no—
316C2×#120—32no—
317C2×#120—31no—
318C2×#120—32no—
319C2×C4×D4—31no—
320C2×C4×D4—31no—
321C2×C4×D4—32no—
322C2×C4×D4C2×D311yescharacteristic, complemented
323C22×C22⋊C4—32no—
324C22×C22⋊C4—31no—
325C22×C22⋊C4—32no—
326#400—31no—
327#399—31no—
328#399—32no—
329#399C2×D311yescharacteristic, complemented
330#399C2×D311yescharacteristic, complemented
331#396—32no—
332#396—32no—
333#396—32no—
334#396—32no—
335#396—32no—
336#395—31no—
337#394—31no—
338#394—32no—
339#394—32no—
340#394—32no—
341#394—32no—
342#394—32no—
343#394—32no—
344#394—31no—
345#393—32no—
346#393—31no—
347#393—31no—
348#393—31no—
349#392—32no—
350#392—31no—
351#392—32no—
352#392—32no—
353#392—31no—
354#392—31no—
355#392—32no—
356#392—32no—
357#392—32no—
358#392—32no—
359#392—31no—
360#392C2×D311yescharacteristic
361#392C2×D311yescharacteristic, complemented
362#390—32no—
363#390—32no—
364#390C2×D312yescomplemented
365#390C2×D312yescomplemented
366#389—32no—
367#388—32no—
368#387—32no—
369#386—32no—
370#386—32no—
371#386—32no—
372#386—32no—
373#385—32no—
374#385—32no—
375#385—32no—
376#385—32no—
377#385—32no—
378#385—32no—
379#382—31no—
380#380—32no—
381#380—32no—
382#380—31no—
383#380—31no—
384#379—32no—
385#379—32no—
386C4×C4⋊C4C2×D311yescharacteristic, complemented
387C2×#95—31no—
388C2×#95—31no—
389C24×C3C2411yescharacteristic
390C24×C3C2411yescharacteristic
391C24×C3C2412yes—
392C23×D3—24no—
393C23×D3—22no—
394C23×D3—24no—
395C23×D3—24no—
396C23×D3—24no—
397C23×D3—22no—
398C23×D3—22no—
399C23×D3—42no—
400C23×D3—42no—
401C23×D3—42no—
402C23×D3—42no—
403C23×D3—42no—
404C23×D3C2411yescharacteristic
405C23×D3C2412yes—
406C23×D3C2411yescharacteristic
407C23×D3C2411yescharacteristic
408C2×C3×Q8—22no—
409C2×C3×Q8—42no—
410C2×C3×D4—24no—
411C2×C3×D4—24no—
412C2×C3×D4—24no—
413C2×C3×D4—22no—
414C2×C3×D4—22no—
415C2×C3×D4—24no—
416C2×C3×D4—42no—
417C2×C3×D4—42no—
418C2×C3×D4—42no—
419C2×C3×D4—42no—
420C22×C3×C4—24no—
421C22×C3×C4—42no—
422C22×C3×C4—42no—
423C22×C3×C4C2411yescharacteristic
424C22×C3×C4C2412yes—
425C22×C3×C4C2411yescharacteristic
426C22×C3×C4C2412yes—
427C22×C3×C4C2411yescharacteristic
428C22×C3×C4C2411yescharacteristic
429C22×C3×C4C2411yescharacteristic
430C22×C3×C4C2412yes—
431C2×#67—24no—
432C2×#67—24no—
433C2×#67—24no—
434C2×#67—22no—
435C2×#67—24no—
436C2×#67—22no—
437C2×#67—22no—
438C2×#67—22no—
439C2×#67—22no—
440C2×#67—24no—
441C2×#67—22no—
442C2×#67—42no—
443C2×#67—42no—
444C2×#67—42no—
445C2×#67—42no—
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—
455C22×Dic3—24no—
456C22×Dic3—24no—
457C22×Dic3—22no—
458C22×Dic3—42no—
459C22×Dic3—42no—
460C22×Dic3C2412yes—
461C22×Dic3C2411yescharacteristic
462C22×Dic3C2412yes—
463C22×Dic3C2412yes—
464C22×Dic3C2411yescharacteristic
465C22×Dic3C2411yescharacteristic
466C22×Dic3C2411yescharacteristic
467C22×Dic3C2411yescharacteristic
468#237—416no—
469D3×D4—416no—
470D3×D4—432no—
471C2×D12—22no—
472C2×D12—22no—
473C2×D12—22no—
474C2×D12—24no—
475C2×D12—22no—
476C2×D12—24no—
477C2×D12—42no—
478C2×D12—42no—
479C2×D12—42no—
480C2×D12—42no—
481C2×D12—42no—
482C2×D12—42no—
483C2×D12C2×D414yes—
484C2×C4×D3—24no—
485C2×C4×D3—24no—
486C2×C4×D3—22no—
487C2×C4×D3—24no—
488C2×C4×D3—42no—
489C2×C4×D3—42no—
490C2×C4×D3—42no—
491C2×C4×D3—42no—
492C2×C4×D3—42no—
493C2×C4×D3—42no—
494C2×C4×D3C2×D414yes—
495C2×C4×D3C2×D414yescomplemented
496C2×Dic6—22no—
497C2×Dic6—42no—
498C3×C4⋊C4—22no—
499C3×C4⋊C4—24no—
500C3×C4⋊C4—24no—
501C3×C4⋊C4—42no—
502C3×C22⋊C4—22no—
503C3×C22⋊C4—22no—
504C3×C22⋊C4—22no—
505C3×C22⋊C4—24no—
506C3×C22⋊C4—22no—
507C3×C22⋊C4—24no—
508C3×C22⋊C4—24no—
509C3×C22⋊C4—42no—
510C3×C22⋊C4—42no—
511C3×C42—42no—
512C3×C42C2×D414yescomplemented
513#217—24no—
514#217—22no—
515#217—22no—
516#217—42no—
517#217—42no—
518#217—42no—
519#217—42no—
520(C2×D3)⋊C4—22no—
521(C2×D3)⋊C4—24no—
522(C2×D3)⋊C4—22no—
523(C2×D3)⋊C4—24no—
524(C2×D3)⋊C4—24no—
525(C2×D3)⋊C4—24no—
526(C2×D3)⋊C4—22no—
527(C2×D3)⋊C4—22no—
528(C2×D3)⋊C4—22no—
529(C2×D3)⋊C4—24no—
530(C2×D3)⋊C4—22no—
531(C2×D3)⋊C4—24no—
532(C2×D3)⋊C4—42no—
533(C2×D3)⋊C4—42no—
534(C2×D3)⋊C4—42no—
535(C2×D3)⋊C4—42no—
536(C2×D3)⋊C4—42no—
537(C2×D3)⋊C4—42no—
538(C2×D3)⋊C4—42no—
539(C2×D3)⋊C4C2×D414yes—
540(C2×D3)⋊C4C2×D414yescomplemented
541C4⋊Dic3—22no—
542C4⋊Dic3—24no—
543C4⋊Dic3—42no—
544C4⋊Dic3—42no—
545C4⋊Dic3C2×D414yescomplemented
546Dic3⋊C4—22no—
547Dic3⋊C4—22no—
548Dic3⋊C4—22no—
549Dic3⋊C4—22no—
550Dic3⋊C4—42no—
551Dic3⋊C4—42no—
552Dic3⋊C4—42no—
553C4×Dic3—22no—
554C25—32no—
555C25—31no—
556C2×#41—64no—
557C2×#41—124no—
558C22×Q8—31no—
559C22×Q8C22×D311yescharacteristic
560C22×D4—31no—
561C22×D4—32no—
562C22×D4—32no—
563C22×D4—31no—
564C22×D4—31no—
565C22×D4—31no—
566C22×D4—32no—
567C22×D4—32no—
568C22×D4—32no—
569C22×D4—31no—
570C22×D4—32no—
571C22×D4—31no—
572C22×D4—31no—
573C22×D4—32no—
574C22×D4—64no—
575C22×D4—124no—
576C22×D4—124no—
577C22×D4—124no—
578C22×D4—124no—
579C22×D4C22×D311yescharacteristic
580C22×D4C22×D312yes—
581C22×D4C22×D312yes—
582C22×D4C22×D311yescharacteristic
583C23×C4—31no—
584C23×C4—31no—
585C23×C4—32no—
586C23×C4—31no—
587C23×C4—32no—
588C23×C4—31no—
589C23×C4—32no—
590C23×C4C22×D312yes—
591#126—64no—
592#126—64no—
593#124—24no—
594#124—64no—
595#124—64no—
596#123—64no—
597#123—68no—
598#123—64no—
599C22⋊Q8—44no—
600C22⋊Q8—64no—
601C22⋊Q8—64no—
602#121—44no—
603#121—64no—
604#121—64no—
605#121—68no—
606#121—64no—
607#121—64no—
608#121—124no—
609#121—124no—
610#121—124no—
611#121—124no—
612#121—124no—
613#120—64no—
614#120—68no—
615#120—64no—
616#120—124no—
617C4×D4—24no—
618C4×D4—38no—
619C4×D4—64no—
620C4×D4—124no—
621C2×C4⋊C4—31no—
622C2×C4⋊C4—31no—
623C2×C4⋊C4—32no—
624C2×C4⋊C4—31no—
625C2×C4⋊C4—31no—
626C2×C4⋊C4—31no—
627C2×C4⋊C4—31no—
628C2×C4⋊C4—32no—
629C2×C4⋊C4—32no—
630C2×C4⋊C4—32no—
631C2×C4⋊C4—32no—
632C2×C4⋊C4—32no—
633C2×C4⋊C4C22×D311yescharacteristic
634C2×C4⋊C4C22×D312yes—
635C2×C4⋊C4C22×D312yes—
636C2×C4⋊C4C22×D312yes—
637C2×C22⋊C4—31no—
638C2×C22⋊C4—31no—
639C2×C22⋊C4—31no—
640C2×C22⋊C4—31no—
641C2×C22⋊C4—32no—
642C2×C22⋊C4—32no—
643C2×C22⋊C4—32no—
644C2×C22⋊C4—32no—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—32no—
647C2×C22⋊C4—31no—
648C2×C22⋊C4—31no—
649C2×C22⋊C4—32no—
650C2×C22⋊C4—32no—
651C2×C22⋊C4—31no—
652C2×C22⋊C4—31no—
653C2×C22⋊C4—31no—
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—32no—
662C2×C22⋊C4—32no—
663C2×C22⋊C4—32no—
664C2×C22⋊C4—32no—
665C2×C22⋊C4—64no—
666C2×C22⋊C4—68no—
667C2×C22⋊C4—124no—
668C2×C22⋊C4C22×D312yes—
669C2×C22⋊C4C22×D311yescharacteristic
670C2×C22⋊C4C22×D311yescharacteristic
671C2×C22⋊C4C22×D312yes—
672C2×C22⋊C4C22×D311yescharacteristic
673C2×C22⋊C4C22×D312yes—
674C2×C22⋊C4C22×D311yescharacteristic
675C2×C22⋊C4C22×D312yes—
676C2×C22⋊C4C22×D312yes—
677C2×C42—31no—
678C2×C42C22×D312yes—
679C2×C42C22×D311yescharacteristic
680#95—31no—
681#95—31no—
682#95—32no—
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×D311yescharacteristic
692#95C22×D311yescharacteristic
693C23×C3—22no—
694C23×C3—22no—
695C23×C3—22no—
696C23×C3—22no—
697C23×C3—22no—
698C23×C3—22no—
699C23×C3—21no—
700C23×C3—21no—
701C23×C3—22no—
702C23×C3—22no—
703C23×C3—22no—
704C23×C3—22no—
705C23×C3—21no—
706C23×C3—21no—
707C23×C3—21no—
708C23×C3—21no—
709C23×C3H(5,𝔽2)14yes—
710C23×C3C2511yescharacteristic
711C22×D3—22no—
712C22×D3—22no—
713C22×D3—21no—
714C22×D3—22no—
715C22×D3—22no—
716C22×D3—21no—
717C22×D3—21no—
718C22×D3—22no—
719C22×D3—22no—
720C22×D3—22no—
721C22×D3—22no—
722C22×D3—22no—
723C22×D3—22no—
724C22×D3—22no—
725C22×D3—22no—
726C22×D3—21no—
727C22×D3—22no—
728C22×D3—21no—
729C22×D3—48no—
730C22×D3—48no—
731C22×D3—48no—
732C22×D3—48no—
733C22×D3—48no—
734C22×D3—44no—
735C22×D3—82no—
736C22×D3—84no—
737C22×D3—82no—
738C22×D3—84no—
739C22×D3—84no—
740C22×D3—84no—
741C22×D3C22×D412yes—
742C22×D3C22×D412yes—
743C22×D3H(5,𝔽2)12yes—
744C22×D32−1+412yes—
745C3×Q8—82no—
746C3×D4—28no—
747C3×D4—48no—
748C3×D4—82no—
749C3×D4—84no—
750C2×C3×C4—21no—
751C2×C3×C4—22no—
752C2×C3×C4—22no—
753C2×C3×C4—22no—
754C2×C3×C4—22no—
755C2×C3×C4—21no—
756C2×C3×C4—21no—
757C2×C3×C4—21no—
758C2×C3×C4—22no—
759C2×C3×C4—22no—
760C2×C3×C4—22no—
761C2×C3×C4—22no—
762C2×C3×C4—22no—
763C2×C3×C4—22no—
764C2×C3×C4—22no—
765C2×C3×C4—22no—
766C2×C3×C4—84no—
767C2×C3×C4C22×D412yes—
768C2×C3×C4C22×D412yes—
769C2×C3×C4C22×D412yes—
770C2×C3×C4H(5,𝔽2)14yes—
771#67—48no—
772#67—48no—
773#67—48no—
774#67—48no—
775#67—44no—
776#67—82no—
777#67—82no—
778#67—82no—
779#67—84no—
780C2×Dic3—22no—
781C2×Dic3—22no—
782C2×Dic3—21no—
783C2×Dic3—21no—
784C2×Dic3—21no—
785C2×Dic3—22no—
786C2×Dic3—22no—
787C2×Dic3—22no—
788C2×Dic3—22no—
789C2×Dic3—22no—
790C2×Dic3—22no—
791C2×Dic3—22no—
792C2×Dic3—22no—
793C2×Dic3—22no—
794C2×Dic3—21no—
795C2×Dic3—22no—
796C2×Dic3—22no—
797C2×Dic3—21no—
798C2×Dic3—48no—
799C2×Dic3—82no—
800C2×Dic3C22×D412yes—
801C2×Dic3C22×D412yes—
802D12—28no—
803D12—44no—
804D12—48no—
805D12—84no—
806D12—82no—
807C4×D3—44no—
808C4×D3—44no—
809C4×D3—48no—
810C4×D3—84no—
811C4×D3—82no—
812Dic6—44no—
813C24—31no—
814C24—31no—
815C24—31no—
816C24—32no—
817C24—62no—
818C24—64no—
819C24—64no—
820C24—64no—
821C24—62no—
822C24—62no—
823C24—64no—
824C24—122no—
825C24—122no—
826C24—122no—
827C24—122no—
828C24—122no—
829C24C23×D311yescharacteristic
830C24C23×D311yescharacteristic
831C24C23×D312yes—
832#41—1216no—
833C2×Q8—22no—
834C2×Q8—42no—
835C2×Q8—62no—
836C2×Q8—122no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—24no—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—24no—
843C2×D4—34no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—62no—
849C2×D4—62no—
850C2×D4—64no—
851C2×D4—62no—
852C2×D4—64no—
853C2×D4—62no—
854C2×D4—62no—
855C2×D4—64no—
856C2×D4—62no—
857C2×D4—62no—
858C2×D4—64no—
859C2×D4—64no—
860C2×D4—64no—
861C2×D4—62no—
862C2×D4—62no—
863C2×D4—62no—
864C2×D4—64no—
865C2×D4—122no—
866C2×D4—122no—
867C2×D4—122no—
868C2×D4—122no—
869C2×D4—122no—
870C2×D4—122no—
871C2×D4—122no—
872C2×D4—122no—
873C2×D4—122no—
874C2×D4—122no—
875C2×D4—122no—
876C2×D4—122no—
877C2×D4—122no—
878C2×D4—122no—
879C2×D4—122no—
880C2×D4—122no—
881C2×D4—122no—
882C2×D4—122no—
883C2×D4—122no—
884C2×D4—1216no—
885C2×D4—1232no—
886C22×C4—24no—
887C22×C4—31no—
888C22×C4—31no—
889C22×C4—34no—
890C22×C4—34no—
891C22×C4—32no—
892C22×C4—31no—
893C22×C4—32no—
894C22×C4—32no—
895C22×C4—31no—
896C22×C4—31no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—64no—
900C22×C4—62no—
901C22×C4—64no—
902C22×C4—62no—
903C22×C4—64no—
904C22×C4—64no—
905C22×C4—64no—
906C22×C4—122no—
907C22×C4—122no—
908C22×C4—122no—
909C22×C4—122no—
910C22×C4—122no—
911C22×C4—122no—
912C22×C4—122no—
913C22×C4—122no—
914C22×C4C23×D311yescharacteristic
915C22×C4C23×D311yescharacteristic
916C22×C4C23×D312yes—
917C22×C4C23×D312yes—
918C22×C4C23×D311yescharacteristic
919C22×C4C23×D311yescharacteristic
920C22×C4C23×D311yescharacteristic
921C22×C4C23×D312yes—
922C4⋊C4—22no—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—34no—
926C4⋊C4—42no—
927C4⋊C4—64no—
928C4⋊C4—62no—
929C4⋊C4—62no—
930C4⋊C4—62no—
931C4⋊C4—62no—
932C4⋊C4—62no—
933C4⋊C4—122no—
934C4⋊C4—122no—
935C4⋊C4—122no—
936C4⋊C4—122no—
937C4⋊C4—122no—
938C22⋊C4—22no—
939C22⋊C4—24no—
940C22⋊C4—22no—
941C22⋊C4—22no—
942C22⋊C4—22no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—34no—
946C22⋊C4—34no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—64no—
950C22⋊C4—62no—
951C22⋊C4—64no—
952C22⋊C4—62no—
953C22⋊C4—64no—
954C22⋊C4—62no—
955C22⋊C4—62no—
956C22⋊C4—62no—
957C22⋊C4—64no—
958C22⋊C4—64no—
959C22⋊C4—62no—
960C22⋊C4—64no—
961C22⋊C4—62no—
962C22⋊C4—62no—
963C22⋊C4—64no—
964C22⋊C4—122no—
965C22⋊C4—122no—
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—122no—
975C42—42no—
976C42—62no—
977C42D3×D414yescomplemented
978C22×C3—24no—
979C22×C3—24no—
980C22×C3—24no—
981C22×C3—42no—
982C22×C3—42no—
983C22×C3—42no—
984C22×C3—42no—
985C22×C3—41no—
986C22×C3—41no—
987C22×C3—41no—
988C22×C3—41no—
989C22×C3—41no—
990C22×C3—41no—
991C22×C3—42no—
992C22×C3—42no—
993C22×C3—42no—
994C22×C3—42no—
995C22×C3C23×D411yescharacteristic
996C22×C3C2×H(5,𝔽2)12yes—
997C22×C3C2×H(5,𝔽2)12yes—
998C22×C3C2×H(5,𝔽2)11yescharacteristic
999C22×C3C2×2−1+411yescharacteristic
1000C2×D3—22no—
1001C2×D3—22no—
1002C2×D3—24no—
1003C2×D3—24no—
1004C2×D3—22no—
1005C2×D3—22no—
1006C2×D3—22no—
1007C2×D3—42no—
1008C2×D3—42no—
1009C2×D3—41no—
1010C2×D3—42no—
1011C2×D3—42no—
1012C2×D3—41no—
1013C2×D3—41no—
1014C2×D3—42no—
1015C2×D3—42no—
1016C2×D3—42no—
1017C2×D3—42no—
1018C2×D3—42no—
1019C2×D3—42no—
1020C2×D3—42no—
1021C2×D3—816no—
1022C2×D3—88no—
1023C2×D3#53714yes—
1024C3×C4—22no—
1025C3×C4—22no—
1026C3×C4—22no—
1027C3×C4—24no—
1028C3×C4—41no—
1029C3×C4—42no—
1030C3×C4—41no—
1031C3×C4—42no—
1032Dic3—22no—
1033Dic3—22no—
1034Dic3—41no—
1035Dic3—42no—
1036Dic3—41no—
1037Dic3—41no—
1038Dic3—42no—
1039Dic3—42no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—21no—
1047C23—21no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—32no—
1057C23—32no—
1058C23—32no—
1059C23—32no—
1060C23—62no—
1061C23—62no—
1062C23—62no—
1063C23—62no—
1064C23—61no—
1065C23—61no—
1066C23—61no—
1067C23—62no—
1068C23—62no—
1069C23—62no—
1070C23—62no—
1071C23—62no—
1072C23—62no—
1073C23—62no—
1074C23—62no—
1075C23—61no—
1076C23—62no—
1077C23—61no—
1078C23—128no—
1079C23—128no—
1080C23—128no—
1081C23—128no—
1082C23—124no—
1083C23—128no—
1084C23—244no—
1085C23—244no—
1086C23—244no—
1087C23—242no—
1088C23—242no—
1089C23—244no—
1090C23#100914yes—
1091C23C24×D311yescharacteristic
1092Q8—82no—
1093Q8—124no—
1094D4—28no—
1095D4—48no—
1096D4—68no—
1097D4—82no—
1098D4—84no—
1099D4—124no—
1100D4—128no—
1101D4—128no—
1102D4—128no—
1103D4—128no—
1104D4—124no—
1105D4—128no—
1106D4—244no—
1107D4—242no—
1108D4—242no—
1109D4—242no—
1110D4—242no—
1111D4—244no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—32no—
1129C2×C4—32no—
1130C2×C4—62no—
1131C2×C4—62no—
1132C2×C4—61no—
1133C2×C4—62no—
1134C2×C4—61no—
1135C2×C4—61no—
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—61no—
1146C2×C4—62no—
1147C2×C4—61no—
1148C2×C4—84no—
1149C2×C4—124no—
1150C2×C4—124no—
1151C2×C4—128no—
1152C2×C4—128no—
1153C2×C4—244no—
1154C2×C4—242no—
1155C2×C4—242no—
1156C2×C4C2×D3×D412yes—
1157C2×C4C2×D3×D412yes—
1158C2×C4C2×D3×D412yes—
1159C2×C4#100414yes—
1160C2×C3—44no—
1161C2×C3—81no—
1162C2×C3—81no—
1163C2×C3C2×#53711yescharacteristic
1164C2×C3#348411yescharacteristic
1165C2×C3#349811yescharacteristic
1166C2×C3#353212yes—
1167C2×C3#353612yes—
1168D3—24no—
1169D3—42no—
1170D3—82no—
1171D3—81no—
1172C22—24no—
1173C22—24no—
1174C22—24no—
1175C22—34no—
1176C22—42no—
1177C22—42no—
1178C22—42no—
1179C22—42no—
1180C22—41no—
1181C22—41no—
1182C22—41no—
1183C22—41no—
1184C22—42no—
1185C22—42no—
1186C22—41no—
1187C22—41no—
1188C22—42no—
1189C22—42no—
1190C22—62no—
1191C22—64no—
1192C22—62no—
1193C22—64no—
1194C22—62no—
1195C22—62no—
1196C22—62no—
1197C22—122no—
1198C22—122no—
1199C22—122no—
1200C22—121no—
1201C22—121no—
1202C22—122no—
1203C22—122no—
1204C22—122no—
1205C22—122no—
1206C22—121no—
1207C22—122no—
1208C22—122no—
1209C22—122no—
1210C22—122no—
1211C22—2416no—
1212C22—248no—
1213C22C22×D3×D411yescharacteristic
1214C22C2×#100412yes—
1215C22C2×#100912yes—
1216C22D3×H(5,𝔽2)11yescharacteristic
1217C22D3×2−1+411yescharacteristic
1218C4—22no—
1219C4—22no—
1220C4—24no—
1221C4—22no—
1222C4—42no—
1223C4—42no—
1224C4—41no—
1225C4—41no—
1226C4—62no—
1227C4—62no—
1228C4—122no—
1229C4—121no—
1230C4—121no—
1231C4—122no—
1232C4—122no—
1233C4—121no—
1234C3#4048811yescharacteristic, complemented, Sylow
1235C2—44no—
1236C2—64no—
1237C2—81no—
1238C2—81no—
1239C2—122no—
1240C2—242no—
1241C2—241no—
1242C2#8603911yescharacteristic
1243C2#8619511yescharacteristic
1244C2D3×#53711yescharacteristic
1245C2#8666712yes—
1246C2#8673912yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2540C2
hypercenter#2540D3
hypocenterC3#40488
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. C2×#5678C2semidirect
2. C2×#5554C2semidirect
3. C3×#2540C2semidirect
4. #83007C2semidirect
5. #82827C2semidirect
6. #82816C2semidirect
7. #82718C2semidirect
8. #82702C2semidirect
9. #82423C2semidirect
10. #78125C2semidirect
11. #78111C2semidirect
12. #78110C2semidirect
13. #78108C2semidirect
14. #76757C2semidirect
15. D3×#392C2semidirect
16. #76697C2semidirect
17. #76669C2semidirect
18. #76442C2semidirect
19. #76436C2semidirect
20. #76388C2semidirect
21. #76379C2semidirect
22. #73816C2semidirect
23. #73770C2semidirect
25. C22×#237C22semidirect
28. C2×C3×#124C22semidirect
29. C2×C3×C22⋊Q8C22semidirect
30. C2×C3×#121C22semidirect
31. C2×C3×C4×D4C22semidirect
32. C2×#947C22semidirect
34. C2×#939C22semidirect
35. C2×#939C22semidirect
36. C2×#939C22semidirect
37. C2×#938C22semidirect
40. C2×#930C22semidirect
45. C2×#895C22semidirect
46. C2×#895C22semidirect
47. C2×#886C22semidirect
48. C2×#886C22semidirect
50. C2×#884C22semidirect
51. C2×#884C22semidirect
52. C2×#883C22semidirect
58. C2×#879C22semidirect
59. C2×#876C22semidirect
60. C2×#875C22semidirect
63. C3×#399C22semidirect
64. C3×#399C22semidirect
66. C3×#392C22semidirect
67. C3×#390C22semidirect
68. C3×#390C22semidirect
69. C3×C4×C4⋊C4C22semidirect
70. #5231C22semidirect
73. #5223C22semidirect
74. #5223C22semidirect
75. #5222C22semidirect
76. #5220C22semidirect
77. #5213C22semidirect
78. #5210C22semidirect
79. #4994C22semidirect
80. #4994C22semidirect
81. #4994C22semidirect
82. #4993C22semidirect
83. #4993C22semidirect
84. #4991C22semidirect
85. #4991C22semidirect
88. #4989C22semidirect
90. #4985C22semidirect
91. #4980C22semidirect
92. #4961C22semidirect
93. #4961C22semidirect
94. #4961C22semidirect
97. #4960C22semidirect
98. #4960C22semidirect
99. #4960C22semidirect
100. #4960C22semidirect
101. #4959C22semidirect
102. #4957C22semidirect
104. #4956C22semidirect
107. #4950C22semidirect
108. #4950C22semidirect
109. #4948C22semidirect
110. #4948C22semidirect
111. #4947C22semidirect
112. #4947C22semidirect
113. #4942C22semidirect
114. #4940C22semidirect
115. #4939C22semidirect
116. #4936C22semidirect
117. #4928C22semidirect
118. #4673C22semidirect
119. #4672C22semidirect
122. #4667C22semidirect
124. D3×#95C22semidirect
125. #4656C22semidirect
140. #2540D3semidirect
274. C4×D12D4semidirect
297. C2×#124C2×D3semidirect
303. C2×C22⋊Q8C2×D3semidirect
314. C2×#121C2×D3semidirect
322. C2×C4×D4C2×D3semidirect
329. #399C2×D3semidirect
330. #399C2×D3semidirect
361. #392C2×D3semidirect
364. #390C2×D3semidirect
365. #390C2×D3semidirect
386. C4×C4⋊C4C2×D3semidirect
495. C2×C4×D3C2×D4semidirect
512. C3×C42C2×D4semidirect
540. (C2×D3)⋊C4C2×D4semidirect
545. C4⋊Dic3C2×D4semidirect
977. C42D3×D4semidirect
1234. C3#40488semidirect

Maximal subgroups

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

subgroupindex
C2×#56782
C2×#55542
C3×#25402
#830072
#828272
#828162
#827182
#827022
#824232
#781252
#781112
#781102
#781082
#767572
D3×#3922
#766972
#766692
#764422
#764362
#763882
#763792
#738162
#737702
#404883