Finite Group Databasebeta

← #11223146

Subgroups — #11223146

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×#5607C211yesmaximal, characteristic, complemented
2C2×#5551C211yesmaximal, characteristic, complemented
3C3×#2420C211yesmaximal, characteristic, complemented
4#82666C211yesmaximal, characteristic, complemented
5D4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6#77696C212yesmaximal, complemented
7#77516C212yesmaximal, complemented
8#77151C212yesmaximal, complemented
9#77136C212yesmaximal, complemented
10#76436C211yesmaximal, characteristic, complemented
11#76304C211yesmaximal, characteristic, complemented
12#76223C211yesmaximal, characteristic, complemented
13#76209C211yesmaximal, characteristic, complemented
14#74728C212yesmaximal, complemented
15#74700C212yesmaximal, complemented
16#74229C211yesmaximal, characteristic, complemented
17#74168C211yesmaximal, characteristic, complemented
18#74125C212yesmaximal, complemented
19#74098C212yesmaximal, complemented
20#74003C211yesmaximal, characteristic, complemented
21#73887C211yesmaximal, characteristic, complemented
22#73580C211yesmaximal, characteristic, complemented
23#73507C211yesmaximal, characteristic, complemented
24#44871—31nomaximal, Sylow
25C22×D3×D4C2211yescharacteristic
26C22×#235C2211yescharacteristic
27C22×#235C2212yescomplemented
28C2×C3×#121C2211yescharacteristic
29C2×C3×C4×D4C2211yescharacteristic
30C2×#940C2212yes—
31C2×#938C2211yescharacteristic
32C2×#938C2211yescharacteristic
33C2×#937C2212yes—
34C2×D4×Dic3C2211yescharacteristic
35C2×#930C2211yescharacteristic
36C2×C4×#67C2211yescharacteristic, complemented
37C22×(C2×D3)⋊C4C2212yes—
38C2×#924C2212yescomplemented
39#5607—28no—
40#5551—28no—
41C2×#895C2211yescharacteristic
42C2×#895C2211yescharacteristic
43C2×#892C2211yescharacteristic
44C2×#892C2211yescharacteristic, complemented
45C2×D3×C4⋊C4C2211yescharacteristic, complemented
46C2×D3×C4⋊C4C2211yescharacteristic, complemented
47C2×#885C2212yes—
48C2×#885C2212yescomplemented
49C2×#884C2212yescomplemented
50C2×#883C2212yescomplemented
51C2×#883C2212yescomplemented
52C2×#882C2212yes—
53C2×#882C2212yes—
54C2×C4×D12C2211yescharacteristic
55C2×C4×D12C2211yescharacteristic, complemented
56C2×#869C2211yescharacteristic, complemented
57C3×#397C2212yescomplemented
58C3×#394C2212yescomplemented
59C3×#390C2211yescharacteristic
60C3×#389C2211yescharacteristic, complemented
61C3×#386C2212yescomplemented
62C3×#382C2211yescharacteristic, complemented
63C3×#381C2212yescomplemented
64C3×#380C2211yescharacteristic, complemented
65C3×C4×C22⋊C4C2211yescharacteristic, complemented
66#5223C2212yescomplemented
67#5220C2212yescomplemented
68#5213C2212yes—
69#5212C2211yescharacteristic, complemented
70#4994C2212yes—
71#4991C2212yescomplemented
72#4988C2211yescharacteristic
73#4988C2212yescomplemented
74#4987C2211yescharacteristic
75#4987C2211yescharacteristic
76#4987C2211yescharacteristic, complemented
77#4980C2212yescomplemented
78#4977C2211yescharacteristic, complemented
79#4972C2211yescharacteristic, complemented
80#4961C2212yes—
81#4961C2211yescharacteristic
82#4961C2212yescomplemented
83#4961C2211yescharacteristic, complemented
84#4960C2211yescharacteristic
85#4960C2212yes—
86#4960C2211yescharacteristic, complemented
87#4959C2212yescomplemented
88#4958C2212yes—
89#4958C2212yescomplemented
90#4958C2212yescomplemented
91#4957C2212yes—
92#4957C2212yescomplemented
93#4956C2212yescomplemented
94#4955C2212yes—
95#4955C2212yes—
96#4952C2212yescomplemented
97#4945C2212yescomplemented
98Dic3×C22⋊C4C2212yescomplemented
99#4939C2211yescharacteristic
100#4939C2211yescharacteristic
101C4×(C2×D3)⋊C4C2211yescharacteristic
102C4×(C2×D3)⋊C4C2211yescharacteristic, complemented
103C4×C4⋊Dic3C2211yescharacteristic, complemented
104#4676C2212yescomplemented
105#4675C2212yescomplemented
106#4675C2212yescomplemented
107#4673C2212yes—
108#4673C2212yescomplemented
109#4673C2211yescharacteristic, complemented
110#4672C2211yescharacteristic
111#4671C2211yescharacteristic
112#4671C2212yescomplemented
113#4670C2212yescomplemented
114#4670C2212yescomplemented
115#4669C2212yes—
116#4666C2212yescomplemented
117#4665C2212yes—
118#4665C2212yes—
119#4665C2212yescomplemented
120#4665C2212yescomplemented
121#4665C2212yescomplemented
122#4656C2211yescharacteristic, complemented
123#4654C2212yescomplemented
124#4646C2212yescomplemented
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#2491—31no—
136#2472—32no—
137#2439—31no—
138#2431—32no—
139#2420D311yescharacteristic, complemented
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×D4C2311yescharacteristic
151C22×C3×D4C2312yes—
152C23×C3×C4C2311yescharacteristic
153C23×C3×C4C2312yes—
154C22×#67C2311yescharacteristic
155C22×#67C2311yescharacteristic
156C22×#67C2312yes—
157C22×#67C2312yes—
158C22×#67C2312yes—
159C22×#67C2311yescharacteristic
160C22×#67C2312yes—
161C23×Dic3C2312yes—
162C2×D3×D4—24no—
163C2×D3×D4—24no—
164C2×D3×D4—42no—
165C2×#235—28no—
166C2×#235—24no—
167C2×#235—24no—
168C2×#235—44no—
169C2×#235—42no—
170C2×#235—44no—
171C22×D12C2311yescharacteristic
172C22×D12C2311yescharacteristic
173C22×D12C2311yescharacteristic
174C22×D12C2311yescharacteristic
175C22×D12C2312yes—
176C22×D12C2312yes—
177C22×C4×D3C2311yescharacteristic
178C22×C4×D3C2312yes—
179C22×C4×D3C2311yescharacteristic
180C22×C4×D3C2311yescharacteristic
181C22×C4×D3C2312yes—
182C22×Dic6C2311yescharacteristic
183C22×Dic6C2312yes—
184C3×#121—24no—
185C3×C4×D4—24no—
186C2×C3×C4⋊C4C2311yescharacteristic
187C2×C3×C4⋊C4C2311yescharacteristic
188C2×C3×C4⋊C4C2311yescharacteristic
189C2×C3×C4⋊C4C2312yes—
190C2×C3×C22⋊C4C2312yes—
191C2×C3×C22⋊C4C2312yes—
192C2×C3×C22⋊C4C2311yescharacteristic
193C2×C3×C22⋊C4C2312yes—
194C2×C3×C22⋊C4C2312yes—
195C2×C3×C22⋊C4C2312yes—
196C2×C3×C22⋊C4C2311yescharacteristic
197C2×C3×C42C2311yescharacteristic
198C2×C3×C42C2311yescharacteristic
199C2×#217C2312yes—
200C2×#217C2312yes—
201C2×#217C2312yes—
202C2×#217C2311yescharacteristic
203C2×#217C2312yes—
204#940—28no—
205#938—24no—
206#938D418yescomplemented
207#937—28no—
208D4×Dic3—42no—
209#930—24no—
210C4×#67—42no—
211C2×(C2×D3)⋊C4—44no—
212C2×(C2×D3)⋊C4C2312yes—
213C2×(C2×D3)⋊C4C2312yes—
214C2×(C2×D3)⋊C4C2311yescharacteristic
215C2×(C2×D3)⋊C4C2311yescharacteristic
216C2×(C2×D3)⋊C4C2312yes—
217C2×(C2×D3)⋊C4C2312yes—
218C2×(C2×D3)⋊C4C2311yescharacteristic
219C2×(C2×D3)⋊C4C2311yescharacteristic
220C2×(C2×D3)⋊C4C2311yescharacteristic
221C2×(C2×D3)⋊C4C2312yes—
222C2×(C2×D3)⋊C4C2312yes—
223C2×(C2×D3)⋊C4C2312yes—
224C2×(C2×D3)⋊C4C2312yes—
225C2×(C2×D3)⋊C4C2311yescharacteristic
226C2×(C2×D3)⋊C4C2311yescharacteristic
227C2×(C2×D3)⋊C4C2311yescharacteristic
228C2×(C2×D3)⋊C4C2312yes—
229C2×(C2×D3)⋊C4C2312yes—
230C2×(C2×D3)⋊C4C2312yes—
231C2×(C2×D3)⋊C4C2312yes—
232C2×(C2×D3)⋊C4C2312yes—
233C2×(C2×D3)⋊C4C2312yes—
234C2×(C2×D3)⋊C4C2311yescharacteristic
235C2×C4⋊Dic3C2311yescharacteristic
236C2×C4⋊Dic3C2311yescharacteristic
237C2×C4⋊Dic3C2312yes—
238C2×C4⋊Dic3C2311yescharacteristic
239C2×C4⋊Dic3C2311yescharacteristic
240C2×C4⋊Dic3C2311yescharacteristic
241#924—28no—
242C2×Dic3⋊C4C2312yes—
243C2×Dic3⋊C4C2312yes—
244C2×Dic3⋊C4C2312yes—
245C2×Dic3⋊C4C2311yescharacteristic
246C2×C4×Dic3C2312yes—
247C2×C4×Dic3C2311yescharacteristic
248C2×C4×Dic3C2312yes—
249C2×C4×Dic3C2312yes—
250#895—24no—
251#895—42no—
252#892—24no—
253#892—42no—
254D3×C4⋊C4—24no—
255D3×C4⋊C4—24no—
256#885—28no—
257#885—44no—
258#884—44no—
259#883—28no—
260#883—28no—
261#882—28no—
262#882—44no—
263C4×D12—24no—
264C4×D12—24no—
265#869—24no—
266C3×#95C2312yes—
267C3×#95C2312yes—
268C3×#95C2312yes—
269C3×#95C2311yescharacteristic
270C3×#95C2312yes—
271C3×#95C2311yescharacteristic
272C3⋊#95C2311yescharacteristic
273C3⋊#95C2312yes—
274C3⋊#95C2312yes—
275C3⋊#95C2312yes—
276C3⋊#95C2312yes—
277C3⋊#95C2312yes—
278C3⋊#95C2312yes—
279C3⋊#95C2311yescharacteristic
280C3⋊#95C2312yes—
281C3⋊#95C2312yes—
282C3⋊#95C2311yescharacteristic
283C3⋊#95C2311yescharacteristic
284C22×#41—31no—
285C22×#41—32no—
286C23×D4—31no—
287#547—68no—
288#535—68no—
289C2×C4⋊Q8—31no—
290C2×#127—32no—
291C2×#124—32no—
292C2×#124—32no—
293C2×#123—32no—
294C2×#123—32no—
295C2×C22⋊Q8—32no—
296C2×#121—31no—
297C2×#121—31no—
298C2×#121—31no—
299C2×#121—31no—
300C2×#121—31no—
301C2×#121—32no—
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×D4C2×D311yescharacteristic
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#397C2×D312yescomplemented
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#393—32no—
334#392—32no—
335#392—31no—
336#392—31no—
337#392—32no—
338#392—31no—
339#392—32no—
340#391—32no—
341#391—32no—
342#390—31no—
343#390—32no—
344#390—32no—
345#390—32no—
346#390—31no—
347#390—31no—
348#390C2×D311yescharacteristic
349#389—31no—
350#389C2×D311yescharacteristic, complemented
351#388—32no—
352#388—32no—
353#388—32no—
354#388—32no—
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#386C2×D312yescomplemented
369#382—31no—
370#382C2×D311yescharacteristic, complemented
371#381C2×D312yescomplemented
372#380—31no—
373#380—31no—
374#380—31no—
375#380—31no—
376#380C2×D311yescharacteristic, complemented
377#379—32no—
378#379—32no—
379C4×C4⋊C4—31no—
380C4×C22⋊C4—32no—
381C4×C22⋊C4—31no—
382C4×C22⋊C4—31no—
383C4×C22⋊C4—32no—
384C4×C22⋊C4C2×D311yescharacteristic, complemented
385C24×C3C2411yescharacteristic
386C24×C3C2412yes—
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×D4—24no—
399C2×C3×D4—22no—
400C2×C3×D4—22no—
401C2×C3×D4—42no—
402C2×C3×D4—42no—
403C2×C3×D4C2×D414yes—
404C22×C3×C4—24no—
405C22×C3×C4—22no—
406C22×C3×C4—22no—
407C22×C3×C4—24no—
408C22×C3×C4—22no—
409C22×C3×C4—42no—
410C22×C3×C4C2412yes—
411C22×C3×C4C2411yescharacteristic
412C22×C3×C4C2411yescharacteristic
413C22×C3×C4C2412yes—
414C22×C3×C4C2411yescharacteristic
415C22×C3×C4C2412yes—
416C22×C3×C4C2411yescharacteristic
417C22×C3×C4C2411yescharacteristic
418C22×C3×C4C2411yescharacteristic
419C2×#67—24no—
420C2×#67—24no—
421C2×#67—22no—
422C2×#67—22no—
423C2×#67—24no—
424C2×#67—22no—
425C2×#67—22no—
426C2×#67—24no—
427C2×#67—22no—
428C2×#67—24no—
429C2×#67—41no—
430C2×#67—41no—
431C2×#67—42no—
432C2×#67—42no—
433C2×#67—41no—
434C2×#67—42no—
435C2×#67—42no—
436C2×#67—41no—
437C2×#67—42no—
438C2×#67—42no—
439C2×#67C2×D418yes—
440C22×Dic3—42no—
441C22×Dic3—42no—
442C22×Dic3—42no—
443C22×Dic3C2411yescharacteristic
444C22×Dic3C2412yes—
445C22×Dic3C2411yescharacteristic
446C22×Dic3C2412yes—
447C22×Dic3C2411yescharacteristic
448C22×Dic3C2412yes—
449C22×Dic3C2411yescharacteristic
450C22×Dic3C2411yescharacteristic
451D3×D4—416no—
452#235—416no—
453#235—432no—
454C2×D12—22no—
455C2×D12—22no—
456C2×D12—22no—
457C2×D12—22no—
458C2×D12—22no—
459C2×D12—22no—
460C2×D12—22no—
461C2×D12—22no—
462C2×D12—22no—
463C2×D12—22no—
464C2×D12—24no—
465C2×D12—24no—
466C2×D12—41no—
467C2×D12—41no—
468C2×D12—42no—
469C2×D12—42no—
470C2×D12—42no—
471C2×D12—42no—
472C2×C4×D3—22no—
473C2×C4×D3—22no—
474C2×C4×D3—22no—
475C2×C4×D3—22no—
476C2×C4×D3—24no—
477C2×C4×D3—24no—
478C2×C4×D3—22no—
479C2×C4×D3—22no—
480C2×C4×D3—22no—
481C2×C4×D3—24no—
482C2×C4×D3—42no—
483C2×C4×D3—42no—
484C2×C4×D3—42no—
485C2×C4×D3C2×D414yes—
486C2×C4×D3#4114yescomplemented
487C2×Dic6—24no—
488C2×Dic6—24no—
489C2×Dic6—22no—
490C2×Dic6—22no—
491C2×Dic6—41no—
492C2×Dic6—42no—
493C3×C4⋊C4—22no—
494C3×C4⋊C4—22no—
495C3×C4⋊C4—22no—
496C3×C4⋊C4—42no—
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×C42—22no—
505C3×C42—22no—
506#217—24no—
507#217—42no—
508#217—41no—
509#217—42no—
510#217C2×D418yes—
511(C2×D3)⋊C4—22no—
512(C2×D3)⋊C4—22no—
513(C2×D3)⋊C4—24no—
514(C2×D3)⋊C4—22no—
515(C2×D3)⋊C4—22no—
516(C2×D3)⋊C4—24no—
517(C2×D3)⋊C4—24no—
518(C2×D3)⋊C4—24no—
519(C2×D3)⋊C4—22no—
520(C2×D3)⋊C4—42no—
521(C2×D3)⋊C4—42no—
522(C2×D3)⋊C4—42no—
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—42no—
530(C2×D3)⋊C4—41no—
531(C2×D3)⋊C4—41no—
532(C2×D3)⋊C4—41no—
533(C2×D3)⋊C4—41no—
534C4⋊Dic3—22no—
535C4⋊Dic3—22no—
536C4⋊Dic3—24no—
537C4⋊Dic3—22no—
538C4⋊Dic3—22no—
539C4⋊Dic3C2×D414yes—
540Dic3⋊C4—24no—
541Dic3⋊C4—24no—
542Dic3⋊C4—42no—
543Dic3⋊C4—41no—
544C4×Dic3—22no—
545C4×Dic3—24no—
546C4×Dic3—42no—
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—32no—
556C22×Q8—31no—
557C22×D4—32no—
558C22×D4—31no—
559C22×D4—32no—
560C22×D4—32no—
561C22×D4—31no—
562C22×D4—31no—
563C22×D4—32no—
564C22×D4—31no—
565C22×D4—31no—
566C22×D4—31no—
567C22×D4—31no—
568C22×D4—32no—
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—32no—
578C23×C4—31no—
579C23×C4—32no—
580C23×C4—32no—
581C23×C4C22×D311yescharacteristic
582C23×C4C22×D312yes—
583C4⋊Q8—64no—
584#127—68no—
585#124—68no—
586#124—124no—
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—124no—
596#121—122no—
597#120—68no—
598#120—68no—
599#120—124no—
600C4×D4—24no—
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—31no—
609C2×C4⋊C4—32no—
610C2×C4⋊C4—32no—
611C2×C4⋊C4—31no—
612C2×C4⋊C4—31no—
613C2×C4⋊C4—31no—
614C2×C4⋊C4—32no—
615C2×C4⋊C4—31no—
616C2×C4⋊C4—32no—
617C2×C4⋊C4—64no—
618C2×C4⋊C4—64no—
619C2×C4⋊C4C22×D311yescharacteristic
620C2×C4⋊C4C22×D311yescharacteristic
621C2×C4⋊C4C22×D311yescharacteristic
622C2×C4⋊C4C22×D312yes—
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—31no—
641C2×C22⋊C4—32no—
642C2×C22⋊C4—32no—
643C2×C22⋊C4—32no—
644C2×C22⋊C4—32no—
645C2×C22⋊C4—32no—
646C2×C22⋊C4—31no—
647C2×C22⋊C4—32no—
648C2×C22⋊C4—31no—
649C2×C22⋊C4—31no—
650C2×C22⋊C4—32no—
651C2×C22⋊C4—124no—
652C2×C22⋊C4C22×D312yes—
653C2×C22⋊C4C22×D312yes—
654C2×C22⋊C4C22×D311yescharacteristic
655C2×C22⋊C4C22×D312yes—
656C2×C22⋊C4C22×D312yes—
657C2×C22⋊C4C22×D312yes—
658C2×C22⋊C4C22×D311yescharacteristic
659C2×C42—32no—
660C2×C42—31no—
661C2×C42—32no—
662C2×C42—32no—
663C2×C42C22×D311yescharacteristic
664C2×C42C22×D311yescharacteristic
665#95—31no—
666#95—32no—
667#95—31no—
668#95—32no—
669#95—31no—
670#95—31no—
671#95—32no—
672#95—32no—
673#95—32no—
674#95—32no—
675#95—32no—
676#95—32no—
677#95C22×D312yes—
678#95C22×D311yescharacteristic
679#95C22×D311yescharacteristic
680#95C22×D312yes—
681#95C22×D312yes—
682#95C22×D312yes—
683C23×C3—22no—
684C23×C3—22no—
685C23×C3—22no—
686C23×C3—22no—
687C23×C3—22no—
688C23×C3—22no—
689C23×C3—21no—
690C23×C3—21no—
691C23×C3—21no—
692C23×C3—21no—
693C23×C3—21no—
694C23×C3—21no—
695C23×C3—21no—
696C23×C3C22×D414yes—
697C23×C3C2511yescharacteristic
698C22×D3—21no—
699C22×D3—21no—
700C22×D3—21no—
701C22×D3—21no—
702C22×D3—21no—
703C22×D3—21no—
704C22×D3—21no—
705C22×D3—21no—
706C22×D3—21no—
707C22×D3—21no—
708C22×D3—21no—
709C22×D3—21no—
710C22×D3—21no—
711C22×D3—21no—
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—22no—
723C22×D3—48no—
724C22×D3—48no—
725C22×D3—84no—
726C22×D3—84no—
727C22×D3—84no—
728C22×D3—84no—
729C22×D3—84no—
730C22×D3C22×D412yes—
731C22×D3C2×#4112yes—
732C22×D3H(5,𝔽2)12yes—
733C3×D4—28no—
734C3×D4—84no—
735C2×C3×C4—21no—
736C2×C3×C4—21no—
737C2×C3×C4—22no—
738C2×C3×C4—22no—
739C2×C3×C4—21no—
740C2×C3×C4—21no—
741C2×C3×C4—21no—
742C2×C3×C4—21no—
743C2×C3×C4—21no—
744C2×C3×C4—21no—
745C2×C3×C4—22no—
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—21no—
753C2×C3×C4—21no—
754C2×C3×C4—21no—
755C2×C3×C4—22no—
756C2×C3×C4—22no—
757C2×C3×C4—22no—
758C2×C3×C4—48no—
759C2×C3×C4—44no—
760C2×C3×C4C22×D412yes—
761C2×C3×C4C2×#4112yes—
762C2×C3×C4H(5,𝔽2)12yes—
763C2×C3×C4H(5,𝔽2)12yes—
764#67—48no—
765#67—44no—
766#67—44no—
767#67—48no—
768#67—48no—
769#67—44no—
770#67—84no—
771C2×Dic3—21no—
772C2×Dic3—21no—
773C2×Dic3—21no—
774C2×Dic3—22no—
775C2×Dic3—22no—
776C2×Dic3—21no—
777C2×Dic3—21no—
778C2×Dic3—22no—
779C2×Dic3—21no—
780C2×Dic3—21no—
781C2×Dic3—21no—
782C2×Dic3—22no—
783C2×Dic3—22no—
784C2×Dic3—21no—
785C2×Dic3—21no—
786C2×Dic3—21no—
787C2×Dic3—22no—
788C2×Dic3—22no—
789C2×Dic3—22no—
790C2×Dic3—21no—
791C2×Dic3—21no—
792C2×Dic3—84no—
793C2×Dic3C22×D414yes—
794C2×Dic3C22×D412yes—
795C2×Dic3C2×#4112yes—
796D12—28no—
797D12—44no—
798D12—44no—
799D12—44no—
800D12—84no—
801D12—84no—
802C4×D3—28no—
803C4×D3—28no—
804C4×D3—48no—
805C4×D3—48no—
806C4×D3—44no—
807Dic6—44no—
808Dic6—48no—
809C24—31no—
810C24—31no—
811C24—31no—
812C24—32no—
813C24—64no—
814C24—64no—
815C24—122no—
816C24—122no—
817C24—122no—
818C24—122no—
819C24—122no—
820C24C23×D311yescharacteristic
821C24C23×D312yes—
822#41—1216no—
823#41—1232no—
824C2×Q8—64no—
825C2×Q8—62no—
826C2×Q8—62no—
827C2×Q8—64no—
828C2×Q8—122no—
829C2×Q8—121no—
830C2×D4—24no—
831C2×D4—22no—
832C2×D4—22no—
833C2×D4—38no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—62no—
837C2×D4—62no—
838C2×D4—62no—
839C2×D4—62no—
840C2×D4—62no—
841C2×D4—62no—
842C2×D4—64no—
843C2×D4—64no—
844C2×D4—62no—
845C2×D4—64no—
846C2×D4—62no—
847C2×D4—64no—
848C2×D4—64no—
849C2×D4—62no—
850C2×D4—62no—
851C2×D4—62no—
852C2×D4—64no—
853C2×D4—64no—
854C2×D4—62no—
855C2×D4—62no—
856C2×D4—62no—
857C2×D4—62no—
858C2×D4—121no—
859C2×D4—121no—
860C2×D4—122no—
861C2×D4—122no—
862C2×D4—122no—
863C2×D4—122no—
864C2×D4—1216no—
865C2×D4—121no—
866C2×D4—122no—
867C2×D4—121no—
868C2×D4—122no—
869C2×D4—121no—
870C2×D4—122no—
871C2×D4—122no—
872C2×D4—121no—
873C2×D4—122no—
874C2×D4—122no—
875C2×D4D3×D414yes—
876C22×C4—24no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—24no—
880C22×C4—22no—
881C22×C4—31no—
882C22×C4—31no—
883C22×C4—32no—
884C22×C4—34no—
885C22×C4—34no—
886C22×C4—31no—
887C22×C4—32no—
888C22×C4—31no—
889C22×C4—32no—
890C22×C4—31no—
891C22×C4—42no—
892C22×C4—64no—
893C22×C4—64no—
894C22×C4—64no—
895C22×C4—62no—
896C22×C4—62no—
897C22×C4—62no—
898C22×C4—62no—
899C22×C4—62no—
900C22×C4—62no—
901C22×C4—62no—
902C22×C4—122no—
903C22×C4—122no—
904C22×C4—122no—
905C22×C4—122no—
906C22×C4—122no—
907C22×C4—122no—
908C22×C4C23×D312yes—
909C22×C4C23×D311yescharacteristic
910C22×C4C23×D311yescharacteristic
911C22×C4C23×D312yes—
912C22×C4C23×D311yescharacteristic
913C22×C4C23×D312yes—
914C22×C4C23×D311yescharacteristic
915C22×C4C23×D311yescharacteristic
916C22×C4C23×D311yescharacteristic
917C4⋊C4—22no—
918C4⋊C4—22no—
919C4⋊C4—22no—
920C4⋊C4—34no—
921C4⋊C4—42no—
922C4⋊C4—64no—
923C4⋊C4—64no—
924C4⋊C4—62no—
925C4⋊C4—62no—
926C4⋊C4—64no—
927C4⋊C4—62no—
928C4⋊C4—62no—
929C4⋊C4—121no—
930C4⋊C4—122no—
931C22⋊C4—24no—
932C22⋊C4—24no—
933C22⋊C4—22no—
934C22⋊C4—38no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C22⋊C4—41no—
938C22⋊C4—42no—
939C22⋊C4—64no—
940C22⋊C4—62no—
941C22⋊C4—62no—
942C22⋊C4—64no—
943C22⋊C4—64no—
944C22⋊C4—62no—
945C22⋊C4—62no—
946C22⋊C4—64no—
947C22⋊C4—62no—
948C22⋊C4—64no—
949C22⋊C4—122no—
950C22⋊C4—122no—
951C22⋊C4—122no—
952C22⋊C4—121no—
953C22⋊C4—122no—
954C22⋊C4—122no—
955C22⋊C4—122no—
956C22⋊C4—122no—
957C22⋊C4—122no—
958C22⋊C4—122no—
959C22⋊C4—121no—
960C22⋊C4—122no—
961C22⋊C4—121no—
962C22⋊C4—121no—
963C22⋊C4—122no—
964C22⋊C4—121no—
965C22⋊C4—122no—
966C42—22no—
967C42—22no—
968C42—64no—
969C42—62no—
970C42—122no—
971C42—122no—
972C22×C3—24no—
973C22×C3—24no—
974C22×C3—24no—
975C22×C3—42no—
976C22×C3—42no—
977C22×C3—42no—
978C22×C3—42no—
979C22×C3—41no—
980C22×C3—41no—
981C22×C3—41no—
982C22×C3—41no—
983C22×C3—41no—
984C22×C3—41no—
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—22no—
996C2×D3—22no—
997C2×D3—22no—
998C2×D3—22no—
999C2×D3—22no—
1000C2×D3—22no—
1001C2×D3—22no—
1002C2×D3—41no—
1003C2×D3—41no—
1004C2×D3—41no—
1005C2×D3—41no—
1006C2×D3—41no—
1007C2×D3—41no—
1008C2×D3—41no—
1009C2×D3—41no—
1010C2×D3—41no—
1011C2×D3—41no—
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—
1022C3×C4—22no—
1023C3×C4—41no—
1024C3×C4—42no—
1025C3×C4—41no—
1026C3×C4—42no—
1027C3×C4—41no—
1028C3×C4—41no—
1029C3×C4—42no—
1030C3×C4#54614yes—
1031Dic3—22no—
1032Dic3—22no—
1033Dic3—24no—
1034Dic3—41no—
1035Dic3—42no—
1036Dic3—41no—
1037Dic3—42no—
1038Dic3—41no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—32no—
1053C23—32no—
1054C23—32no—
1055C23—61no—
1056C23—61no—
1057C23—61no—
1058C23—61no—
1059C23—61no—
1060C23—61no—
1061C23—61no—
1062C23—61no—
1063C23—61no—
1064C23—61no—
1065C23—61no—
1066C23—61no—
1067C23—61no—
1068C23—61no—
1069C23—61no—
1070C23—61no—
1071C23—61no—
1072C23—61no—
1073C23—62no—
1074C23—62no—
1075C23—62no—
1076C23—62no—
1077C23—62no—
1078C23—62no—
1079C23—62no—
1080C23—128no—
1081C23—128no—
1082C23—244no—
1083C23—244no—
1084C23—244no—
1085C23—244no—
1086C23—244no—
1087C23C2×D3×D414yes—
1088C23C24×D311yescharacteristic
1089Q8—128no—
1090Q8—124no—
1091D4—28no—
1092D4—68no—
1093D4—84no—
1094D4—124no—
1095D4—124no—
1096D4—128no—
1097D4—128no—
1098D4—124no—
1099D4—124no—
1100D4—128no—
1101D4—124no—
1102D4—124no—
1103D4—244no—
1104D4—244no—
1105D4—244no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—22no—
1110C2×C4—21no—
1111C2×C4—22no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—22no—
1122C2×C4—21no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—21no—
1126C2×C4—22no—
1127C2×C4—21no—
1128C2×C4—22no—
1129C2×C4—34no—
1130C2×C4—32no—
1131C2×C4—32no—
1132C2×C4—48no—
1133C2×C4—44no—
1134C2×C4—61no—
1135C2×C4—61no—
1136C2×C4—61no—
1137C2×C4—62no—
1138C2×C4—61no—
1139C2×C4—62no—
1140C2×C4—68no—
1141C2×C4—68no—
1142C2×C4—61no—
1143C2×C4—62no—
1144C2×C4—61no—
1145C2×C4—61no—
1146C2×C4—61no—
1147C2×C4—62no—
1148C2×C4—62no—
1149C2×C4—61no—
1150C2×C4—61no—
1151C2×C4—62no—
1152C2×C4—62no—
1153C2×C4—61no—
1154C2×C4—61no—
1155C2×C4—62no—
1156C2×C4—61no—
1157C2×C4—128no—
1158C2×C4—128no—
1159C2×C4—124no—
1160C2×C4—244no—
1161C2×C4C2×D3×D412yes—
1162C2×C4D3×#4112yes—
1163C2×C4#100912yes—
1164C2×C4#100912yes—
1165C2×C3—44no—
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—42no—
1177D3—82no—
1178C22—24no—
1179C22—24no—
1180C22—24no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—41no—
1192C22—62no—
1193C22—62no—
1194C22—62no—
1195C22—62no—
1196C22—62no—
1197C22—62no—
1198C22—62no—
1199C22—62no—
1200C22—62no—
1201C22—121no—
1202C22—121no—
1203C22—121no—
1204C22—121no—
1205C22—121no—
1206C22—121no—
1207C22—121no—
1208C22—121no—
1209C22—121no—
1210C22—121no—
1211C22—121no—
1212C22—121no—
1213C22—122no—
1214C22—122no—
1215C22—122no—
1216C22—122no—
1217C22—122no—
1218C22—122no—
1219C22—122no—
1220C22—2416no—
1221C22C22×D3×D411yescharacteristic
1222C22C2×D3×#4111yescharacteristic
1223C22C2×#100911yescharacteristic
1224C22C2×#100911yescharacteristic
1225C22#596411yescharacteristic
1226C22D3×H(5,𝔽2)11yescharacteristic
1227C22#596611yescharacteristic
1228C4—22no—
1229C4—41no—
1230C4—42no—
1231C4—41no—
1232C4—42no—
1233C4—41no—
1234C4—42no—
1235C4—41no—
1236C4—64no—
1237C4—62no—
1238C4—62no—
1239C4—122no—
1240C4—121no—
1241C4—122no—
1242C4—121no—
1243C4—121no—
1244C4#565414yes—
1245C3#4487111yescharacteristic, complemented, Sylow
1246C2—44no—
1247C2—81no—
1248C2—122no—
1249C2—122no—
1250C2—122no—
1251C2—242no—
1252C2C2×#565411yescharacteristic
1253C2#8617411yescharacteristic
1254C2#8649211yescharacteristic
1255C2#8663211yescharacteristic
1256C2#8666211yescharacteristic
1257C2#8687811yescharacteristic
1258C2#8697311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2420C2
hypercenter#2420D3
hypocenterC3#44871
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2420

Complements

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

NH ≅ G/Ntype
1. C2×#5607C2semidirect
2. C2×#5551C2semidirect
3. C3×#2420C2semidirect
4. #82666C2semidirect
5. D4×(C2×D3)⋊C4C2semidirect
6. #77696C2semidirect
7. #77516C2semidirect
8. #77151C2semidirect
9. #77136C2semidirect
10. #76436C2semidirect
11. #76304C2semidirect
12. #76223C2semidirect
13. #76209C2semidirect
14. #74728C2semidirect
15. #74700C2semidirect
16. #74229C2semidirect
17. #74168C2semidirect
18. #74125C2semidirect
19. #74098C2semidirect
20. #74003C2semidirect
21. #73887C2semidirect
22. #73580C2semidirect
23. #73507C2semidirect
27. C22×#235C22semidirect
36. C2×C4×#67C22semidirect
38. C2×#924C22semidirect
44. C2×#892C22semidirect
45. C2×D3×C4⋊C4C22semidirect
46. C2×D3×C4⋊C4C22semidirect
48. C2×#885C22semidirect
49. C2×#884C22semidirect
50. C2×#883C22semidirect
51. C2×#883C22semidirect
55. C2×C4×D12C22semidirect
56. C2×#869C22semidirect
57. C3×#397C22semidirect
58. C3×#394C22semidirect
60. C3×#389C22semidirect
61. C3×#386C22semidirect
62. C3×#382C22semidirect
63. C3×#381C22semidirect
64. C3×#380C22semidirect
65. C3×C4×C22⋊C4C22semidirect
66. #5223C22semidirect
67. #5220C22semidirect
69. #5212C22semidirect
71. #4991C22semidirect
73. #4988C22semidirect
76. #4987C22semidirect
77. #4980C22semidirect
78. #4977C22semidirect
79. #4972C22semidirect
82. #4961C22semidirect
83. #4961C22semidirect
86. #4960C22semidirect
87. #4959C22semidirect
89. #4958C22semidirect
90. #4958C22semidirect
92. #4957C22semidirect
93. #4956C22semidirect
96. #4952C22semidirect
97. #4945C22semidirect
98. Dic3×C22⋊C4C22semidirect
102. C4×(C2×D3)⋊C4C22semidirect
103. C4×C4⋊Dic3C22semidirect
104. #4676C22semidirect
105. #4675C22semidirect
106. #4675C22semidirect
108. #4673C22semidirect
109. #4673C22semidirect
112. #4671C22semidirect
113. #4670C22semidirect
114. #4670C22semidirect
116. #4666C22semidirect
119. #4665C22semidirect
120. #4665C22semidirect
121. #4665C22semidirect
122. #4656C22semidirect
123. #4654C22semidirect
124. #4646C22semidirect
125. #4646C22semidirect
139. #2420D3semidirect
206. #938D4semidirect
319. #397C2×D3semidirect
330. #394C2×D3semidirect
350. #389C2×D3semidirect
368. #386C2×D3semidirect
370. #382C2×D3semidirect
371. #381C2×D3semidirect
376. #380C2×D3semidirect
384. C4×C22⋊C4C2×D3semidirect
486. 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×#56072
C2×#55512
C3×#24202
#826662
D4×(C2×D3)⋊C42
#776962
#775162
#771512
#771362
#764362
#763042
#762232
#762092
#747282
#747002
#742292
#741682
#741252
#740982
#740032
#738872
#735802
#735072
#448713