Finite Group Databasebeta

← #11223129

Subgroups — #11223129

Order 768.

2844 conjugacy classes of subgroups.

The subgroup lattice has 1260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5726C211yesmaximal, characteristic, complemented
2C2×#5607C211yesmaximal, characteristic, complemented
3C3×#2491C211yesmaximal, characteristic, complemented
4#83256C211yesmaximal, characteristic, complemented
5#82965C212yesmaximal, complemented
6#82958C212yesmaximal, complemented
7#82641C211yesmaximal, characteristic, complemented
8#77152C212yesmaximal, complemented
9#77137C212yesmaximal, complemented
10#76879C212yesmaximal, complemented
11#76863C212yesmaximal, complemented
12#76438C211yesmaximal, characteristic, complemented
13#76436C211yesmaximal, characteristic, complemented
14#76431C211yesmaximal, characteristic, complemented
15#76336C211yesmaximal, characteristic, complemented
16#75923C212yesmaximal, complemented
17#75884C212yesmaximal, complemented
18#74003C211yesmaximal, characteristic, complemented
19#73933C211yesmaximal, characteristic, complemented
20#73771C211yesmaximal, characteristic, complemented
21#73649C211yesmaximal, characteristic, complemented
22#73584C211yesmaximal, characteristic, complemented
23#73580C211yesmaximal, characteristic, complemented
24#44871—31nomaximal, Sylow
25C22×#239C2212yescomplemented
26C22×D3×D4C2211yescharacteristic
27C22×#235C2211yescharacteristic
28C2×C3×C4⋊Q8C2211yescharacteristic, complemented
29C2×C3×#124C2212yescomplemented
30C2×C3×#121C2211yescharacteristic
31C2×#946C2212yescomplemented
32C2×#940C2212yes—
33C2×#938C2211yescharacteristic
34C2×#938C2211yescharacteristic
35C2×#938C2212yescomplemented
36C2×#937C2212yes—
37C2×#930C2211yescharacteristic
38C2×C4×#67C2211yescharacteristic, complemented
39#5726—28no—
40#5607—28no—
41C2×#895C2211yescharacteristic
42C2×#895C2211yescharacteristic
43C2×#894C2212yescomplemented
44C2×#894C2212yescomplemented
45C2×#893C2211yescharacteristic
46C2×#892C2211yescharacteristic
47C2×#892C2211yescharacteristic, complemented
48C2×D3×C4⋊C4C2211yescharacteristic, complemented
49C2×D3×C4⋊C4C2211yescharacteristic, complemented
50C2×#885C2212yes—
51C2×#882C2212yes—
52C2×#882C2212yes—
53C2×D3×C22⋊C4C2212yes—
54C2×C4×D12C2211yescharacteristic
55C2×C4×D12C2211yescharacteristic
56C2×C4×D12C2211yescharacteristic, complemented
57C3×#394C2212yescomplemented
58C3×#393C2212yescomplemented
59C3×#390C2211yescharacteristic
60C3×#390C2211yescharacteristic
61C3×#388C2212yescomplemented
62C3×#380C2211yescharacteristic, complemented
63C3×C4×C4⋊C4C2211yescharacteristic, complemented
64C3×C4×C22⋊C4C2211yescharacteristic, complemented
65#5231C2212yes—
66#5229C2212yescomplemented
67#5222C2212yescomplemented
68#5221C2211yescharacteristic
69#5212C2211yescharacteristic, complemented
70#4994C2212yes—
71#4987C2211yescharacteristic
72#4987C2211yescharacteristic
73#4987C2211yescharacteristic, complemented
74#4984C2211yescharacteristic, complemented
75#4978C2212yescomplemented
76#4977C2211yescharacteristic, complemented
77#4961C2211yescharacteristic
78#4961C2212yes—
79#4961C2211yescharacteristic, complemented
80#4960C2212yes—
81#4960C2211yescharacteristic
82#4960C2211yescharacteristic, complemented
83#4960C2212yescomplemented
84#4960C2212yescomplemented
85#4959C2212yescomplemented
86#4959C2212yescomplemented
87#4957C2212yes—
88#4957C2212yescomplemented
89#4956C2212yes—
90#4956C2212yes—
91#4956C2212yescomplemented
92#4956C2212yescomplemented
93#4956C2212yescomplemented
94#4956C2212yescomplemented
95#4956C2212yescomplemented
96#4956C2212yescomplemented
97#4955C2212yes—
98#4955C2212yes—
99#4952C2212yescomplemented
100#4952C2212yescomplemented
101#4951C2212yescomplemented
102#4948C2212yescomplemented
103#4940C2212yes—
104#4939C2211yescharacteristic
105#4939C2212yescomplemented
106C4×(C2×D3)⋊C4C2211yescharacteristic
107C4×(C2×D3)⋊C4C2212yescomplemented
108C4×(C2×D3)⋊C4C2212yescomplemented
109C4×(C2×D3)⋊C4C2211yescharacteristic, complemented
110#4936C2211yescharacteristic, complemented
111#4928C2211yescharacteristic, complemented
112#4675C2212yescomplemented
113#4675C2212yescomplemented
114#4673C2211yescharacteristic, complemented
115#4672C2211yescharacteristic
116#4671C2211yescharacteristic
117#4670C2212yescomplemented
118#4665C2212yes—
119#4665C2212yes—
120#4665C2212yescomplemented
121#4665C2212yescomplemented
122#4664C2212yescomplemented
123#4656C2211yescharacteristic, complemented
124#4653C2212yescomplemented
125#4646C2212yescomplemented
126C2×#547—31no—
127C2×#535—31no—
128#2709—32no—
129#2700—32no—
130#2697—32no—
131#2678—32no—
132#2557—32no—
133#2535—31no—
134#2504—31no—
135#2491D311yescharacteristic, complemented
136#2472—32no—
137#2439—31no—
138#2431—32no—
139#2420—31no—
140#2416—31no—
141#2414—31no—
142#2408—31no—
143#2404—32no—
144#2388—31no—
145#2363—31no—
146#2352—31no—
147D4×C22⋊C4—31no—
148#2311—31no—
149C24×D3C2312yes—
150C22×C3×Q8C2312yes—
151C22×C3×D4C2311yescharacteristic
152C22×C3×D4C2312yes—
153C23×C3×C4C2311yescharacteristic
154C22×#67C2311yescharacteristic
155C22×#67C2311yescharacteristic
156C22×#67C2312yes—
157C22×#67C2312yes—
158C22×#67C2312yes—
159C22×#67C2312yes—
160C22×#67C2311yescharacteristic
161C2×#239—28no—
162C2×#239—44no—
163C2×#239—44no—
164C2×D3×D4—24no—
165C2×D3×D4—24no—
166C2×D3×D4—42no—
167C2×#235—24no—
168C2×#235—24no—
169C2×#235—42no—
170C22×D12C2311yescharacteristic
171C22×D12C2311yescharacteristic
172C22×D12C2311yescharacteristic
173C22×D12C2312yes—
174C22×D12C2311yescharacteristic
175C22×D12C2312yes—
176C22×C4×D3C2311yescharacteristic
177C22×C4×D3C2312yes—
178C22×C4×D3C2312yes—
179C22×C4×D3C2311yescharacteristic
180C22×C4×D3C2311yescharacteristic
181C22×C4×D3C2312yes—
182C22×C4×D3C2312yes—
183C22×Dic6C2311yescharacteristic
184C3×C4⋊Q8—24no—
185C3×#124—44no—
186C3×#121—24no—
187C2×C3×C4⋊C4C2311yescharacteristic
188C2×C3×C4⋊C4C2312yes—
189C2×C3×C4⋊C4C2311yescharacteristic
190C2×C3×C4⋊C4C2311yescharacteristic
191C2×C3×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
199C2×C3×C42C2311yescharacteristic
200C2×C3×C42C2311yescharacteristic
201C2×C3×C42C2312yes—
202C2×#217C2312yes—
203C2×#217C2312yes—
204C2×#217C2312yes—
205C2×#217C2312yes—
206C2×#217C2312yes—
207C2×#217C2311yescharacteristic
208#946—28no—
209#940—28no—
210#938—24no—
211#938—42no—
212#938—44no—
213#937—28no—
214#930—24no—
215C4×#67—42no—
216C2×(C2×D3)⋊C4C2312yes—
217C2×(C2×D3)⋊C4C2312yes—
218C2×(C2×D3)⋊C4C2311yescharacteristic
219C2×(C2×D3)⋊C4C2311yescharacteristic
220C2×(C2×D3)⋊C4C2311yescharacteristic
221C2×(C2×D3)⋊C4C2311yescharacteristic
222C2×(C2×D3)⋊C4C2311yescharacteristic
223C2×(C2×D3)⋊C4C2312yes—
224C2×(C2×D3)⋊C4C2312yes—
225C2×(C2×D3)⋊C4C2312yes—
226C2×(C2×D3)⋊C4C2312yes—
227C2×(C2×D3)⋊C4C2312yes—
228C2×(C2×D3)⋊C4C2312yes—
229C2×(C2×D3)⋊C4C2312yes—
230C2×(C2×D3)⋊C4C2311yescharacteristic
231C2×(C2×D3)⋊C4C2311yescharacteristic
232C2×(C2×D3)⋊C4C2312yes—
233C2×(C2×D3)⋊C4C2311yescharacteristic
234C2×(C2×D3)⋊C4C2311yescharacteristic
235C2×(C2×D3)⋊C4C2312yes—
236C2×(C2×D3)⋊C4C2312yes—
237C2×C4⋊Dic3C2311yescharacteristic
238C2×C4⋊Dic3C2311yescharacteristic
239C2×C4⋊Dic3C2311yescharacteristic
240C2×C4⋊Dic3C2311yescharacteristic
241C2×C4⋊Dic3C2311yescharacteristic
242C2×C4⋊Dic3C2312yes—
243C2×Dic3⋊C4C2312yes—
244C2×Dic3⋊C4C2312yes—
245C2×Dic3⋊C4C2311yescharacteristic
246C2×Dic3⋊C4C2312yes—
247C2×C4×Dic3C2312yes—
248C2×C4×Dic3C2311yescharacteristic
249C2×C4×Dic3C2312yes—
250#895—24no—
251#895D418yescomplemented
252#894—28no—
253#894—28no—
254#893—42no—
255#892—24no—
256#892—42no—
257D3×C4⋊C4—24no—
258D3×C4⋊C4—24no—
259#885—28no—
260#882—28no—
261#882—44no—
262D3×C22⋊C4—44no—
263C4×D12—24no—
264C4×D12—24no—
265C4×D12—24no—
266C3×#95C2312yes—
267C3×#95C2312yes—
268C3×#95C2311yescharacteristic
269C3×#95C2311yescharacteristic
270C3⋊#95C2312yes—
271C3⋊#95C2312yes—
272C3⋊#95C2312yes—
273C3⋊#95C2312yes—
274C3⋊#95C2312yes—
275C3⋊#95C2311yescharacteristic
276C3⋊#95C2311yescharacteristic
277C3⋊#95C2312yes—
278C3⋊#95C2312yes—
279C3⋊#95C2312yes—
280C3⋊#95C2311yescharacteristic
281C3⋊#95C2311yescharacteristic
282C3⋊#95C2312yes—
283C3⋊#95C2312yes—
284C22×#41—32no—
285C22×#41—31no—
286C23×D4—31no—
287#547—68no—
288#535—68no—
289C2×C4⋊Q8C2×D311yescharacteristic, complemented
290C2×#127—32no—
291C2×#124—32no—
292C2×#124C2×D312yescomplemented
293C2×#123—32no—
294C2×#123—32no—
295C2×C22⋊Q8—32no—
296C2×#121—31no—
297C2×#121—31no—
298C2×#121—31no—
299C2×#121—32no—
300C2×#121—31no—
301C2×#121—31no—
302C2×#121C2×D311yescharacteristic
303C2×#120—32no—
304C2×#120—32no—
305C2×#120—32no—
306C2×C4×D4—31no—
307C2×C4×D4—31no—
308C2×C4×D4—31no—
309C2×C4×D4—31no—
310C2×C4×D4—31no—
311C2×#117—31no—
312C2×#117—31no—
313C22×C4⋊C4—31no—
314C22×C4⋊C4—31no—
315C22×C22⋊C4—32no—
316#397—32no—
317#397—32no—
318#397—32no—
319#397—32no—
320#396—32no—
321#396—32no—
322#395—31no—
323#394—32no—
324#394—31no—
325#394—31no—
326#394—32no—
327#394—32no—
328#394—32no—
329#394—31no—
330#394C2×D312yescomplemented
331#393—32no—
332#393—31no—
333#393C2×D312yescomplemented
334#392—31no—
335#392—31no—
336#392—32no—
337#392—32no—
338#392—32no—
339#392—31no—
340#391—32no—
341#391—32no—
342#390—31no—
343#390—32no—
344#390—32no—
345#390—31no—
346#390—32no—
347#390C2×D311yescharacteristic
348#390C2×D311yescharacteristic
349#389—31no—
350#389—31no—
351#388—32no—
352#388—32no—
353#388—32no—
354#388C2×D312yescomplemented
355#387—32no—
356#387—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#386—32no—
368#386—32no—
369#382—31no—
370#382—31no—
371#381—32no—
372#380—31no—
373#380—31no—
374#380—31no—
375#380—31no—
376#380C2×D311yescharacteristic, complemented
377#379—32no—
378#379—32no—
379C4×C4⋊C4C2×D311yescharacteristic, complemented
380C4×C22⋊C4—31no—
381C4×C22⋊C4—32no—
382C4×C22⋊C4—31no—
383C4×C22⋊C4—32no—
384C4×C22⋊C4C2×D311yescharacteristic, complemented
385C24×C3C2412yes—
386C24×C3C2411yescharacteristic
387C23×D3—24no—
388C23×D3—24no—
389C23×D3—42no—
390C23×D3—42no—
391C23×D3—42no—
392C23×D3—42no—
393C23×D3—42no—
394C23×D3C2412yes—
395C23×D3C2411yescharacteristic
396C23×D3C2411yescharacteristic
397C23×D3C2411yescharacteristic
398C2×C3×Q8—24no—
399C2×C3×Q8—24no—
400C2×C3×Q8—42no—
401C2×C3×D4—22no—
402C2×C3×D4—24no—
403C2×C3×D4—22no—
404C2×C3×D4—22no—
405C2×C3×D4—42no—
406C2×C3×D4—42no—
407C22×C3×C4—22no—
408C22×C3×C4—22no—
409C22×C3×C4—22no—
410C22×C3×C4C2411yescharacteristic
411C22×C3×C4C2412yes—
412C22×C3×C4C2411yescharacteristic
413C22×C3×C4C2411yescharacteristic
414C22×C3×C4C2412yes—
415C22×C3×C4C2411yescharacteristic
416C22×C3×C4C2412yes—
417C22×C3×C4C2411yescharacteristic
418C22×C3×C4C2411yescharacteristic
419C2×#67—24no—
420C2×#67—22no—
421C2×#67—22no—
422C2×#67—22no—
423C2×#67—24no—
424C2×#67—24no—
425C2×#67—24no—
426C2×#67—22no—
427C2×#67—22no—
428C2×#67—24no—
429C2×#67—41no—
430C2×#67—41no—
431C2×#67—41no—
432C2×#67—42no—
433C2×#67—41no—
434C2×#67—42no—
435C2×#67—42no—
436C2×#67—42no—
437C2×#67—42no—
438C2×#67—42no—
439C2×#67—42no—
440C22×Dic3C2412yes—
441C22×Dic3C2411yescharacteristic
442C22×Dic3C2411yescharacteristic
443C22×Dic3C2412yes—
444C22×Dic3C2412yes—
445C22×Dic3C2411yescharacteristic
446C22×Dic3C2411yescharacteristic
447C22×Dic3C2411yescharacteristic
448#239—432no—
449D3×D4—416no—
450#235—416no—
451C2×D12—22no—
452C2×D12—22no—
453C2×D12—22no—
454C2×D12—22no—
455C2×D12—22no—
456C2×D12—22no—
457C2×D12—24no—
458C2×D12—22no—
459C2×D12—22no—
460C2×D12—22no—
461C2×D12—24no—
462C2×D12—41no—
463C2×D12—41no—
464C2×D12—42no—
465C2×D12—42no—
466C2×D12—42no—
467C2×D12C2×D414yes—
468C2×D12C2×D418yes—
469C2×C4×D3—22no—
470C2×C4×D3—22no—
471C2×C4×D3—22no—
472C2×C4×D3—22no—
473C2×C4×D3—24no—
474C2×C4×D3—24no—
475C2×C4×D3—24no—
476C2×C4×D3—22no—
477C2×C4×D3—24no—
478C2×C4×D3—22no—
479C2×C4×D3—24no—
480C2×C4×D3—22no—
481C2×C4×D3—42no—
482C2×C4×D3—42no—
483C2×C4×D3—42no—
484C2×C4×D3—42no—
485C2×C4×D3—42no—
486C2×C4×D3—42no—
487C2×C4×D3—42no—
488C2×C4×D3C2×D414yes—
489C2×C4×D3#4114yescomplemented
490C2×Dic6—22no—
491C2×Dic6—22no—
492C2×Dic6—41no—
493C3×C4⋊C4—22no—
494C3×C4⋊C4—24no—
495C3×C4⋊C4—22no—
496C3×C4⋊C4C2×D414yes—
497C3×C22⋊C4—24no—
498C3×C22⋊C4—24no—
499C3×C22⋊C4—22no—
500C3×C22⋊C4—42no—
501C3×C22⋊C4—42no—
502C3×C22⋊C4—41no—
503C3×C22⋊C4—42no—
504C3×C22⋊C4—42no—
505C3×C42—22no—
506C3×C42—22no—
507C3×C42—42no—
508#217—24no—
509#217—42no—
510#217—41no—
511#217—42no—
512#217—42no—
513#217—42no—
514(C2×D3)⋊C4—22no—
515(C2×D3)⋊C4—24no—
516(C2×D3)⋊C4—24no—
517(C2×D3)⋊C4—24no—
518(C2×D3)⋊C4—22no—
519(C2×D3)⋊C4—24no—
520(C2×D3)⋊C4—22no—
521(C2×D3)⋊C4—22no—
522(C2×D3)⋊C4—22no—
523(C2×D3)⋊C4—42no—
524(C2×D3)⋊C4—42no—
525(C2×D3)⋊C4—42no—
526(C2×D3)⋊C4—42no—
527(C2×D3)⋊C4—42no—
528(C2×D3)⋊C4—42no—
529(C2×D3)⋊C4—41no—
530(C2×D3)⋊C4—41no—
531(C2×D3)⋊C4—41no—
532(C2×D3)⋊C4—42no—
533(C2×D3)⋊C4—41no—
534(C2×D3)⋊C4C2×D418yes—
535C4⋊Dic3—22no—
536C4⋊Dic3—22no—
537C4⋊Dic3—22no—
538C4⋊Dic3—22no—
539C4⋊Dic3—22no—
540C4⋊Dic3—42no—
541Dic3⋊C4—24no—
542Dic3⋊C4—24no—
543Dic3⋊C4—42no—
544Dic3⋊C4—41no—
545C4×Dic3—24no—
546C4×Dic3—22no—
547C4×Dic3—42no—
548C25—32no—
549C2×#41—64no—
550C2×#41—64no—
551C2×#41—68no—
552C2×#41—122no—
553C2×#41—124no—
554C2×#41—124no—
555C22×Q8—31no—
556C22×Q8C22×D312yes—
557C22×D4—31no—
558C22×D4—32no—
559C22×D4—31no—
560C22×D4—31no—
561C22×D4—32no—
562C22×D4—32no—
563C22×D4—32no—
564C22×D4—31no—
565C22×D4—32no—
566C22×D4—31no—
567C22×D4—31no—
568C22×D4—31no—
569C22×D4—32no—
570C22×D4—64no—
571C22×D4—64no—
572C22×D4—122no—
573C22×D4C22×D311yescharacteristic
574C22×D4C22×D312yes—
575C23×C4—31no—
576C23×C4—31no—
577C23×C4—31no—
578C23×C4—32no—
579C23×C4—32no—
580C23×C4—32no—
581C23×C4—32no—
582C23×C4C22×D311yescharacteristic
583C4⋊Q8—24no—
584#127—68no—
585#124—44no—
586#124—68no—
587#123—68no—
588#123—68no—
589C22⋊Q8—68no—
590#121—24no—
591#121—38no—
592#121—64no—
593#121—64no—
594#121—64no—
595#121—122no—
596#121—124no—
597#120—68no—
598#120—68no—
599#120—124no—
600C4×D4—64no—
601C4×D4—64no—
602C4×D4—64no—
603C4×D4—122no—
604C4×D4—122no—
605#117—64no—
606#117—122no—
607C2×C4⋊C4—31no—
608C2×C4⋊C4—32no—
609C2×C4⋊C4—32no—
610C2×C4⋊C4—31no—
611C2×C4⋊C4—31no—
612C2×C4⋊C4—31no—
613C2×C4⋊C4—31no—
614C2×C4⋊C4—31no—
615C2×C4⋊C4—32no—
616C2×C4⋊C4—32no—
617C2×C4⋊C4—64no—
618C2×C4⋊C4—64no—
619C2×C4⋊C4C22×D311yescharacteristic
620C2×C4⋊C4C22×D311yescharacteristic
621C2×C4⋊C4C22×D312yes—
622C2×C4⋊C4C22×D311yescharacteristic
623C2×C22⋊C4—32no—
624C2×C22⋊C4—32no—
625C2×C22⋊C4—31no—
626C2×C22⋊C4—32no—
627C2×C22⋊C4—32no—
628C2×C22⋊C4—31no—
629C2×C22⋊C4—31no—
630C2×C22⋊C4—31no—
631C2×C22⋊C4—31no—
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—32no—
641C2×C22⋊C4—32no—
642C2×C22⋊C4—31no—
643C2×C22⋊C4—32no—
644C2×C22⋊C4—32no—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—32no—
647C2×C22⋊C4—32no—
648C2×C22⋊C4—31no—
649C2×C22⋊C4—31no—
650C2×C22⋊C4—124no—
651C2×C22⋊C4C22×D312yes—
652C2×C22⋊C4C22×D312yes—
653C2×C22⋊C4C22×D311yescharacteristic
654C2×C22⋊C4C22×D312yes—
655C2×C22⋊C4C22×D312yes—
656C2×C22⋊C4C22×D312yes—
657C2×C22⋊C4C22×D311yescharacteristic
658C2×C22⋊C4C22×D312yes—
659C2×C42—32no—
660C2×C42—31no—
661C2×C42—32no—
662C2×C42C22×D311yescharacteristic
663C2×C42C22×D311yescharacteristic
664C2×C42C22×D312yes—
665#95—31no—
666#95—32no—
667#95—32no—
668#95—31no—
669#95—32no—
670#95—31no—
671#95—31no—
672#95—32no—
673#95—32no—
674#95—32no—
675#95—32no—
676#95—32no—
677#95—32no—
678#95—32no—
679#95C22×D311yescharacteristic
680#95C22×D311yescharacteristic
681#95C22×D312yes—
682#95C22×D312yes—
683C23×C3—22no—
684C23×C3—21no—
685C23×C3—21no—
686C23×C3—22no—
687C23×C3—21no—
688C23×C3—22no—
689C23×C3—22no—
690C23×C3—21no—
691C23×C3—22no—
692C23×C3—21no—
693C23×C3—21no—
694C23×C3—22no—
695C23×C3—21no—
696C23×C3—22no—
697C23×C3C2511yescharacteristic
698C22×D3—21no—
699C22×D3—21no—
700C22×D3—21no—
701C22×D3—21no—
702C22×D3—22no—
703C22×D3—21no—
704C22×D3—21no—
705C22×D3—21no—
706C22×D3—21no—
707C22×D3—22no—
708C22×D3—22no—
709C22×D3—22no—
710C22×D3—21no—
711C22×D3—21no—
712C22×D3—21no—
713C22×D3—21no—
714C22×D3—21no—
715C22×D3—21no—
716C22×D3—21no—
717C22×D3—22no—
718C22×D3—21no—
719C22×D3—22no—
720C22×D3—21no—
721C22×D3—21no—
722C22×D3—48no—
723C22×D3—48no—
724C22×D3—84no—
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—48no—
734C3×D4—44no—
735C3×D4—84no—
736C2×C3×C4—21no—
737C2×C3×C4—22no—
738C2×C3×C4—22no—
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—21no—
746C2×C3×C4—22no—
747C2×C3×C4—21no—
748C2×C3×C4—21no—
749C2×C3×C4—22no—
750C2×C3×C4—22no—
751C2×C3×C4—21no—
752C2×C3×C4—22no—
753C2×C3×C4—21no—
754C2×C3×C4—21no—
755C2×C3×C4—22no—
756C2×C3×C4—21no—
757C2×C3×C4—21no—
758C2×C3×C4—44no—
759C2×C3×C4C22×D414yes—
760C2×C3×C4C22×D412yes—
761C2×C3×C4C2×#4112yes—
762C2×C3×C4H(5,𝔽2)12yes—
763C2×C3×C4H(5,𝔽2)12yes—
764#67—44no—
765#67—44no—
766#67—48no—
767#67—44no—
768#67—84no—
769#67—84no—
770#67—84no—
771C2×Dic3—21no—
772C2×Dic3—21no—
773C2×Dic3—21no—
774C2×Dic3—21no—
775C2×Dic3—22no—
776C2×Dic3—21no—
777C2×Dic3—22no—
778C2×Dic3—21no—
779C2×Dic3—21no—
780C2×Dic3—21no—
781C2×Dic3—22no—
782C2×Dic3—21no—
783C2×Dic3—21no—
784C2×Dic3—22no—
785C2×Dic3—21no—
786C2×Dic3—22no—
787C2×Dic3—22no—
788C2×Dic3—22no—
789C2×Dic3—22no—
790C2×Dic3—21no—
791C2×Dic3—21no—
792C2×Dic3—22no—
793C2×Dic3C22×D412yes—
794C2×Dic3C2×#4112yes—
795D12—28no—
796D12—28no—
797D12—48no—
798D12—44no—
799D12—44no—
800D12—48no—
801C4×D3—28no—
802C4×D3—28no—
803C4×D3—48no—
804C4×D3—48no—
805C4×D3—48no—
806C4×D3—44no—
807C4×D3—84no—
808Dic6—44no—
809C24—31no—
810C24—32no—
811C24—31no—
812C24—31no—
813C24—64no—
814C24—64no—
815C24—122no—
816C24—122no—
817C24—122no—
818C24—122no—
819C24—122no—
820C24C23×D312yes—
821C24C23×D311yescharacteristic
822#41—1216no—
823#41—1232no—
824C2×Q8—24no—
825C2×Q8—24no—
826C2×Q8—42no—
827C2×Q8—62no—
828C2×Q8—62no—
829C2×Q8—121no—
830C2×D4—22no—
831C2×D4—24no—
832C2×D4—22no—
833C2×D4—22no—
834C2×D4—34no—
835C2×D4—38no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—62no—
839C2×D4—62no—
840C2×D4—62no—
841C2×D4—62no—
842C2×D4—62no—
843C2×D4—64no—
844C2×D4—64no—
845C2×D4—62no—
846C2×D4—62no—
847C2×D4—64no—
848C2×D4—62no—
849C2×D4—62no—
850C2×D4—64no—
851C2×D4—62no—
852C2×D4—62no—
853C2×D4—64no—
854C2×D4—64no—
855C2×D4—64no—
856C2×D4—62no—
857C2×D4—62no—
858C2×D4—62no—
859C2×D4—122no—
860C2×D4—122no—
861C2×D4—122no—
862C2×D4—121no—
863C2×D4—121no—
864C2×D4—1216no—
865C2×D4—121no—
866C2×D4—122no—
867C2×D4—121no—
868C2×D4—121no—
869C2×D4—121no—
870C2×D4—122no—
871C2×D4—122no—
872C2×D4—122no—
873C2×D4—122no—
874C2×D4—122no—
875C2×D4—122no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—31no—
880C22×C4—31no—
881C22×C4—34no—
882C22×C4—34no—
883C22×C4—31no—
884C22×C4—32no—
885C22×C4—31no—
886C22×C4—32no—
887C22×C4—32no—
888C22×C4—31no—
889C22×C4—64no—
890C22×C4—64no—
891C22×C4—64no—
892C22×C4—62no—
893C22×C4—62no—
894C22×C4—62no—
895C22×C4—62no—
896C22×C4—62no—
897C22×C4—64no—
898C22×C4—64no—
899C22×C4—62no—
900C22×C4—62no—
901C22×C4—122no—
902C22×C4—122no—
903C22×C4—122no—
904C22×C4—122no—
905C22×C4—122no—
906C22×C4—122no—
907C22×C4—122no—
908C22×C4C23×D311yescharacteristic
909C22×C4C23×D311yescharacteristic
910C22×C4C23×D312yes—
911C22×C4C23×D311yescharacteristic
912C22×C4C23×D312yes—
913C22×C4C23×D311yescharacteristic
914C22×C4C23×D312yes—
915C22×C4C23×D311yescharacteristic
916C22×C4C23×D311yescharacteristic
917C4⋊C4—22no—
918C4⋊C4—24no—
919C4⋊C4—22no—
920C4⋊C4—64no—
921C4⋊C4—62no—
922C4⋊C4—62no—
923C4⋊C4—62no—
924C4⋊C4—64no—
925C4⋊C4—62no—
926C4⋊C4—62no—
927C4⋊C4—121no—
928C4⋊C4—122no—
929C4⋊C4—122no—
930C4⋊C4D3×D414yes—
931C22⋊C4—24no—
932C22⋊C4—24no—
933C22⋊C4—22no—
934C22⋊C4—38no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—41no—
940C22⋊C4—62no—
941C22⋊C4—62no—
942C22⋊C4—62no—
943C22⋊C4—64no—
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—121no—
954C22⋊C4—122no—
955C22⋊C4—122no—
956C22⋊C4—122no—
957C22⋊C4—121no—
958C22⋊C4—121no—
959C22⋊C4—122no—
960C22⋊C4—121no—
961C22⋊C4—122no—
962C22⋊C4—121no—
963C22⋊C4—122no—
964C22⋊C4—122no—
965C22⋊C4—122no—
966C42—22no—
967C42—22no—
968C42—42no—
969C42—64no—
970C42—62no—
971C42—122no—
972C22×C3—41no—
973C22×C3—42no—
974C22×C3—41no—
975C22×C3—42no—
976C22×C3—42no—
977C22×C3—41no—
978C22×C3—41no—
979C22×C3—42no—
980C22×C3—42no—
981C22×C3—41no—
982C22×C3—41no—
983C22×C3—42no—
984C22×C3—42no—
985C22×C3—41no—
986C22×C3C23×D411yescharacteristic
987C22×C3C22×#4111yescharacteristic
988C22×C3C2×H(5,𝔽2)11yescharacteristic
989C22×C3C2×H(5,𝔽2)11yescharacteristic
990C22×C3C2×H(5,𝔽2)11yescharacteristic
991C22×C3#58511yescharacteristic
992C22×C3#58511yescharacteristic
993C2×D3—22no—
994C2×D3—22no—
995C2×D3—24no—
996C2×D3—22no—
997C2×D3—22no—
998C2×D3—24no—
999C2×D3—22no—
1000C2×D3—22no—
1001C2×D3—22no—
1002C2×D3—24no—
1003C2×D3—22no—
1004C2×D3—22no—
1005C2×D3—41no—
1006C2×D3—41no—
1007C2×D3—41no—
1008C2×D3—42no—
1009C2×D3—41no—
1010C2×D3—41no—
1011C2×D3—41no—
1012C2×D3—41no—
1013C2×D3—42no—
1014C2×D3—41no—
1015C2×D3—42no—
1016C2×D3—41no—
1017C2×D3—42no—
1018C2×D3—41no—
1019C2×D3—41no—
1020C2×D3—41no—
1021C2×D3—816no—
1022C3×C4—22no—
1023C3×C4—24no—
1024C3×C4—41no—
1025C3×C4—42no—
1026C3×C4—41no—
1027C3×C4—41no—
1028C3×C4—41no—
1029C3×C4—42no—
1030C3×C4#54614yes—
1031Dic3—22no—
1032Dic3—22no—
1033Dic3—41no—
1034Dic3—42no—
1035Dic3—42no—
1036Dic3—41no—
1037Dic3—42no—
1038Dic3—41no—
1039C23—22no—
1040C23—21no—
1041C23—21no—
1042C23—22no—
1043C23—21no—
1044C23—22no—
1045C23—21no—
1046C23—22no—
1047C23—21no—
1048C23—22no—
1049C23—22no—
1050C23—21no—
1051C23—21no—
1052C23—22no—
1053C23—34no—
1054C23—32no—
1055C23—32no—
1056C23—32no—
1057C23—61no—
1058C23—61no—
1059C23—61no—
1060C23—62no—
1061C23—61no—
1062C23—61no—
1063C23—61no—
1064C23—61no—
1065C23—62no—
1066C23—61no—
1067C23—61no—
1068C23—62no—
1069C23—61no—
1070C23—61no—
1071C23—61no—
1072C23—62no—
1073C23—61no—
1074C23—61no—
1075C23—62no—
1076C23—61no—
1077C23—61no—
1078C23—62no—
1079C23—61no—
1080C23—61no—
1081C23—128no—
1082C23—128no—
1083C23—244no—
1084C23—244no—
1085C23—244no—
1086C23—244no—
1087C23—244no—
1088C23C24×D311yescharacteristic
1089Q8—48no—
1090Q8—124no—
1091D4—44no—
1092D4—68no—
1093D4—68no—
1094D4—84no—
1095D4—128no—
1096D4—124no—
1097D4—128no—
1098D4—124no—
1099D4—128no—
1100D4—124no—
1101D4—124no—
1102D4—124no—
1103D4—244no—
1104D4—244no—
1105D4—244no—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—22no—
1113C2×C4—21no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—22no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—32no—
1129C2×C4—32no—
1130C2×C4—44no—
1131C2×C4—61no—
1132C2×C4—61no—
1133C2×C4—61no—
1134C2×C4—61no—
1135C2×C4—68no—
1136C2×C4—68no—
1137C2×C4—62no—
1138C2×C4—61no—
1139C2×C4—62no—
1140C2×C4—61no—
1141C2×C4—62no—
1142C2×C4—61no—
1143C2×C4—61no—
1144C2×C4—61no—
1145C2×C4—62no—
1146C2×C4—61no—
1147C2×C4—61no—
1148C2×C4—62no—
1149C2×C4—62no—
1150C2×C4—61no—
1151C2×C4—62no—
1152C2×C4—61no—
1153C2×C4—62no—
1154C2×C4—62no—
1155C2×C4—128no—
1156C2×C4—128no—
1157C2×C4—128no—
1158C2×C4—124no—
1159C2×C4—244no—
1160C2×C4C2×D3×D414yes—
1161C2×C4C2×D3×D412yes—
1162C2×C4#100412yes—
1163C2×C4D3×#4112yes—
1164C2×C4#100912yes—
1165C2×C3—82no—
1166C2×C3—81no—
1167C2×C3C2×#54611yescharacteristic
1168C2×C3#348411yescharacteristic
1169C2×C3#349411yescharacteristic
1170C2×C3#350011yescharacteristic
1171C2×C3#350611yescharacteristic
1172C2×C3#354211yescharacteristic
1173C2×C3#354611yescharacteristic
1174D3—42no—
1175D3—42no—
1176D3—44no—
1177D3—42no—
1178C22—41no—
1179C22—42no—
1180C22—41no—
1181C22—42no—
1182C22—41no—
1183C22—42no—
1184C22—42no—
1185C22—41no—
1186C22—42no—
1187C22—41no—
1188C22—41no—
1189C22—42no—
1190C22—42no—
1191C22—41no—
1192C22—62no—
1193C22—62no—
1194C22—62no—
1195C22—64no—
1196C22—62no—
1197C22—62no—
1198C22—64no—
1199C22—62no—
1200C22—62no—
1201C22—62no—
1202C22—62no—
1203C22—64no—
1204C22—121no—
1205C22—122no—
1206C22—121no—
1207C22—121no—
1208C22—121no—
1209C22—122no—
1210C22—121no—
1211C22—121no—
1212C22—122no—
1213C22—121no—
1214C22—121no—
1215C22—121no—
1216C22—122no—
1217C22—121no—
1218C22—121no—
1219C22—121no—
1220C22—2416no—
1221C22C22×D3×D411yescharacteristic
1222C22C2×#100411yescharacteristic
1223C22C2×D3×#4111yescharacteristic
1224C22C2×#100911yescharacteristic
1225C22#596411yescharacteristic
1226C22D3×H(5,𝔽2)11yescharacteristic
1227C22#596811yescharacteristic
1228C4—22no—
1229C4—24no—
1230C4—41no—
1231C4—42no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—42no—
1236C4—62no—
1237C4—62no—
1238C4—121no—
1239C4—122no—
1240C4—121no—
1241C4—122no—
1242C4—122no—
1243C4—121no—
1244C4#567614yes—
1245C3#4487111yescharacteristic, complemented, Sylow
1246C2—82no—
1247C2—81no—
1248C2—122no—
1249C2—124no—
1250C2—122no—
1251C2—122no—
1252C2C2×#567611yescharacteristic
1253C2#8625011yescharacteristic
1254C2#8656311yescharacteristic
1255C2#8662011yescharacteristic
1256C2#8670311yescharacteristic
1257C2#8671511yescharacteristic
1258C2#8696011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2491C2
hypercenter#2491D3
hypocenterC3#44871
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2491

Complements

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

NH ≅ G/Ntype
1. C2×#5726C2semidirect
2. C2×#5607C2semidirect
3. C3×#2491C2semidirect
4. #83256C2semidirect
5. #82965C2semidirect
6. #82958C2semidirect
7. #82641C2semidirect
8. #77152C2semidirect
9. #77137C2semidirect
10. #76879C2semidirect
11. #76863C2semidirect
12. #76438C2semidirect
13. #76436C2semidirect
14. #76431C2semidirect
15. #76336C2semidirect
16. #75923C2semidirect
17. #75884C2semidirect
18. #74003C2semidirect
19. #73933C2semidirect
20. #73771C2semidirect
21. #73649C2semidirect
22. #73584C2semidirect
23. #73580C2semidirect
25. C22×#239C22semidirect
28. C2×C3×C4⋊Q8C22semidirect
29. C2×C3×#124C22semidirect
31. C2×#946C22semidirect
35. C2×#938C22semidirect
38. C2×C4×#67C22semidirect
43. C2×#894C22semidirect
44. C2×#894C22semidirect
47. C2×#892C22semidirect
48. C2×D3×C4⋊C4C22semidirect
49. C2×D3×C4⋊C4C22semidirect
56. C2×C4×D12C22semidirect
57. C3×#394C22semidirect
58. C3×#393C22semidirect
61. C3×#388C22semidirect
62. C3×#380C22semidirect
63. C3×C4×C4⋊C4C22semidirect
64. C3×C4×C22⋊C4C22semidirect
66. #5229C22semidirect
67. #5222C22semidirect
69. #5212C22semidirect
73. #4987C22semidirect
74. #4984C22semidirect
75. #4978C22semidirect
76. #4977C22semidirect
79. #4961C22semidirect
82. #4960C22semidirect
83. #4960C22semidirect
84. #4960C22semidirect
85. #4959C22semidirect
86. #4959C22semidirect
88. #4957C22semidirect
91. #4956C22semidirect
92. #4956C22semidirect
93. #4956C22semidirect
94. #4956C22semidirect
95. #4956C22semidirect
96. #4956C22semidirect
99. #4952C22semidirect
100. #4952C22semidirect
101. #4951C22semidirect
102. #4948C22semidirect
105. #4939C22semidirect
107. C4×(C2×D3)⋊C4C22semidirect
108. C4×(C2×D3)⋊C4C22semidirect
109. C4×(C2×D3)⋊C4C22semidirect
110. #4936C22semidirect
111. #4928C22semidirect
112. #4675C22semidirect
113. #4675C22semidirect
114. #4673C22semidirect
117. #4670C22semidirect
120. #4665C22semidirect
121. #4665C22semidirect
122. #4664C22semidirect
123. #4656C22semidirect
124. #4653C22semidirect
125. #4646C22semidirect
135. #2491D3semidirect
251. #895D4semidirect
289. C2×C4⋊Q8C2×D3semidirect
292. C2×#124C2×D3semidirect
330. #394C2×D3semidirect
333. #393C2×D3semidirect
354. #388C2×D3semidirect
376. #380C2×D3semidirect
379. C4×C4⋊C4C2×D3semidirect
384. C4×C22⋊C4C2×D3semidirect
489. C2×C4×D3#41semidirect
1245. C3#44871semidirect

Maximal subgroups

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

subgroupindex
C2×#57262
C2×#56072
C3×#24912
#832562
#829652
#829582
#826412
#771522
#771372
#768792
#768632
#764382
#764362
#764312
#763362
#759232
#758842
#740032
#739332
#737712
#736492
#735842
#735802
#448713