Finite Group Databasebeta

← #11028681

Subgroups — #11028681

Order 768.

2822 conjugacy classes of subgroups.

The subgroup lattice has 1282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5611C211yesmaximal, characteristic, complemented
2C2×#5547C211yesmaximal, characteristic, complemented
3C3×#2416C211yesmaximal, characteristic, complemented
4#82723C211yesmaximal, characteristic, complemented
5#82709C211yesmaximal, characteristic, complemented
6#82708C212yesmaximal, complemented
7#82666C211yesmaximal, characteristic, complemented
8#82651C212yesmaximal, complemented
9#82373C211yesmaximal, characteristic, complemented
10C2×#4987C211yesmaximal, characteristic, complemented
11#82161C211yesmaximal, characteristic, complemented
12#77436C212yesmaximal, complemented
13#77355C212yesmaximal, complemented
14#77149C212yesmaximal, complemented
15#77017C212yesmaximal, complemented
16#76438C211yesmaximal, characteristic, complemented
17#76430C211yesmaximal, characteristic, complemented
18#76250C211yesmaximal, characteristic, complemented
19#76232C211yesmaximal, characteristic, complemented
20#74885C212yesmaximal, complemented
21#74739C212yesmaximal, complemented
22#74003C211yesmaximal, characteristic, complemented
23#73942C211yesmaximal, characteristic, complemented
24#37839—31nomaximal, Sylow
25C22×#237C2212yes—
26C22×#235C2211yescharacteristic
27C23×C4×D3C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2212yes—
30C2×C3×#121C2211yescharacteristic, complemented
31C2×C3×C4×D4C2211yescharacteristic
32C22×C3×C4⋊C4C2211yescharacteristic
33C2×#939C2211yescharacteristic
34C2×#938C2211yescharacteristic
35C2×#938C2211yescharacteristic
36C2×#938C2211yescharacteristic, complemented
37C2×#937C2211yescharacteristic
38C2×#937C2212yes—
39C2×#935C2212yes—
40C2×#935C2212yes—
41C2×D4×Dic3C2211yescharacteristic, complemented
42C2×C4×#67C2211yescharacteristic
43C2×C4×#67C2211yescharacteristic
44C22×(C2×D3)⋊C4C2212yes—
45C22×C4⋊Dic3C2211yescharacteristic
46#5611—28no—
47#5547—28no—
48C2×#896C2211yescharacteristic
49C2×#894C2211yescharacteristic
50C2×#892C2211yescharacteristic, complemented
51C2×D3×C4⋊C4C2211yescharacteristic, complemented
52C2×#888C2211yescharacteristic, complemented
53C2×#884C2211yescharacteristic
54C2×#883C2211yescharacteristic
55C2×#883C2212yescomplemented
56C2×#882C2211yescharacteristic
57C2×#878C2211yescharacteristic
58C2×#878C2212yescomplemented
59C2×C4×D12C2211yescharacteristic
60C2×#872C2211yescharacteristic
61C3×#396C2212yescomplemented
62C3×#394C2212yescomplemented
63C3×#390C2211yescharacteristic, complemented
64C3×#389C2211yescharacteristic, complemented
65C3×#386C2212yes—
66C3×#380C2211yescharacteristic, complemented
67#5223C2212yes—
68#5223C2212yes—
69#5223C2212yescomplemented
70#5220C2212yes—
71#5220C2212yescomplemented
72#5213C2212yes—
73#5212C2211yescharacteristic
74#5212C2211yescharacteristic, complemented
75#5212C2211yescharacteristic, complemented
76C4×#217C2212yes—
77C2×C3⋊#95C2212yes—
78#4993C2212yes—
79#4993C2212yes—
80#4990C2212yescomplemented
81#4989C2212yescomplemented
82#4987C2211yescharacteristic
83#4987C2211yescharacteristic
84#4987C2212yes—
85#4987C2212yes—
86#4987C2211yescharacteristic
87#4987C2211yescharacteristic
88#4987C2211yescharacteristic
89#4987C2211yescharacteristic
90#4987C2211yescharacteristic, complemented
91#4981C2212yescomplemented
92#4979C2212yescomplemented
93#4978C2212yescomplemented
94#4977C2211yescharacteristic, complemented
95Dic3×C4⋊C4C2211yescharacteristic, complemented
96#4960C2212yes—
97#4960C2212yes—
98#4959C2212yescomplemented
99#4958C2212yes—
100#4958C2212yes—
101#4957C2212yes—
102#4957C2212yes—
103#4957C2212yes—
104#4957C2212yes—
105#4956C2212yes—
106#4956C2212yes—
107#4956C2212yescomplemented
108#4953C2212yescomplemented
109#4952C2212yescomplemented
110#4951C2212yescomplemented
111#4947C2212yescomplemented
112#4947C2212yescomplemented
113#4946C2212yescomplemented
114#4944C2212yescomplemented
115#4943C2212yes—
116#4928C2211yescharacteristic, complemented
117#4928C2211yescharacteristic, complemented
118#4673C2212yes—
119#4673C2212yes—
120#4665C2212yes—
121#4665C2212yes—
122#4660C2212yescomplemented
123#4658C2212yescomplemented
124#4650C2212yescomplemented
125#4646C2212yescomplemented
126C2×#547—31no—
127C2×#525—31no—
128#2847—31no—
129#2706—32no—
130#2703—32no—
131#2696—32no—
132#2692—32no—
133#2628—31no—
134#2615—31no—
135#2563—31no—
136#2539—32no—
137#2535—31no—
138#2488—32no—
139#2487—31no—
140#2486—31no—
141#2430—32no—
142#2416D311yescharacteristic, complemented
143#2414—31no—
144#2404—32no—
145#2352—31no—
146#2324—31no—
147#2311—31no—
148C2×#380—31no—
149C24×D3C2311yescharacteristic
150C22×C3×D4C2312yes—
151C22×C3×D4C2311yescharacteristic
152C22×C3×D4C2311yescharacteristic
153C22×C3×D4C2312yes—
154C23×C3×C4C2311yescharacteristic
155C23×C3×C4C2311yescharacteristic
156C23×C3×C4C2312yes—
157C22×#67C2311yescharacteristic
158C22×#67C2311yescharacteristic
159C22×#67C2311yescharacteristic
160C22×#67C2311yescharacteristic
161C22×#67C2312yes—
162C22×#67C2312yes—
163C22×#67C2312yes—
164C23×Dic3C2312yes—
165C23×Dic3C2311yescharacteristic
166C23×Dic3C2312yes—
167C2×#237—28no—
168C2×#237—44no—
169C2×#237—44no—
170C2×#235—24no—
171C2×#235—24no—
172C2×#235—42no—
173C22×D12C2311yescharacteristic
174C22×D12C2311yescharacteristic
175C22×C4×D3—24no—
176C22×C4×D3—24no—
177C22×C4×D3—42no—
178C22×C4×D3C2311yescharacteristic
179C22×C4×D3C2311yescharacteristic
180C22×C4×D3C2311yescharacteristic
181C22×C4×D3C2311yescharacteristic
182C22×C4×D3C2311yescharacteristic
183C22×C4×D3C2312yes—
184C22×Dic6C2311yescharacteristic
185C22×Dic6C2312yes—
186C3×#121—24no—
187C3×#121—42no—
188C3×#121—44no—
189C3×C4×D4—24no—
190C2×C3×C4⋊C4—42no—
191C2×C3×C4⋊C4C2311yescharacteristic
192C2×C3×C4⋊C4C2311yescharacteristic
193C2×C3×C4⋊C4C2311yescharacteristic
194C2×C3×C4⋊C4C2311yescharacteristic
195C2×C3×C4⋊C4C2312yes—
196C2×C3×C4⋊C4C2312yes—
197C2×C3×C22⋊C4C2311yescharacteristic
198C2×C3×C22⋊C4C2311yescharacteristic
199C2×C3×C22⋊C4C2312yes—
200C2×C3×C22⋊C4C2312yes—
201C2×C3×C22⋊C4C2312yes—
202C2×C3×C22⋊C4C2312yes—
203C2×C3×C22⋊C4C2312yes—
204C2×C3×C42C2311yescharacteristic
205C2×#217C2312yes—
206C2×#217C2312yes—
207C2×#217C2312yes—
208C2×#217C2311yescharacteristic
209C2×#217C2312yes—
210C2×#217C2312yes—
211C2×#217C2312yes—
212C2×#217C2312yes—
213C2×#217C2311yescharacteristic
214#939—24no—
215#938—24no—
216#938—24no—
217#938—42no—
218#937—24no—
219#937—44no—
220#935—28no—
221#935—44no—
222D4×Dic3—24no—
223C4×#67—24no—
224C4×#67D418yescomplemented
225C2×(C2×D3)⋊C4—44no—
226C2×(C2×D3)⋊C4C2311yescharacteristic
227C2×(C2×D3)⋊C4C2311yescharacteristic
228C2×(C2×D3)⋊C4C2311yescharacteristic
229C2×(C2×D3)⋊C4C2311yescharacteristic
230C2×(C2×D3)⋊C4C2311yescharacteristic
231C2×(C2×D3)⋊C4C2312yes—
232C2×(C2×D3)⋊C4C2312yes—
233C2×(C2×D3)⋊C4C2312yes—
234C2×(C2×D3)⋊C4C2312yes—
235C2×(C2×D3)⋊C4C2312yes—
236C2×(C2×D3)⋊C4C2312yes—
237C2×(C2×D3)⋊C4C2312yes—
238C2×(C2×D3)⋊C4C2312yes—
239C2×(C2×D3)⋊C4C2311yescharacteristic
240C2×C4⋊Dic3—24no—
241C2×C4⋊Dic3C2311yescharacteristic
242C2×C4⋊Dic3C2311yescharacteristic
243C2×C4⋊Dic3C2311yescharacteristic
244C2×C4⋊Dic3C2311yescharacteristic
245C2×C4⋊Dic3C2311yescharacteristic
246C2×C4⋊Dic3C2312yes—
247C2×Dic3⋊C4C2312yes—
248C2×Dic3⋊C4C2311yescharacteristic
249C2×Dic3⋊C4C2312yes—
250C2×Dic3⋊C4C2311yescharacteristic
251C2×Dic3⋊C4C2311yescharacteristic
252C2×Dic3⋊C4C2312yes—
253C2×Dic3⋊C4C2312yes—
254C2×Dic3⋊C4C2311yescharacteristic
255C2×C4×Dic3C2312yes—
256C2×C4×Dic3C2312yes—
257C2×C4×Dic3C2311yescharacteristic
258#896—24no—
259#894—24no—
260#892—42no—
261D3×C4⋊C4—24no—
262#888—24no—
263#884—24no—
264#883—28no—
265#883—24no—
266#882—24no—
267#878—24no—
268#878—28no—
269C4×D12—24no—
270#872—24no—
271C3×#95C2312yes—
272C3×#95C2312yes—
273C3⋊#95C2312yes—
274C3⋊#95C2312yes—
275C3⋊#95C2312yes—
276C3⋊#95C2312yes—
277C3⋊#95C2312yes—
278C3⋊#95C2312yes—
279C3⋊#95C2312yes—
280C3⋊#95C2312yes—
281C3⋊#95C2312yes—
282C3⋊#95C2312yes—
283C3⋊#95C2312yes—
284C3⋊#95C2312yes—
285C3⋊#95C2312yes—
286C3⋊#95C2312yes—
287C3⋊#95C2312yes—
288C22×#41—32no—
289C22×#41—31no—
290C24×C4—31no—
291#547—68no—
292C2×C4⋊Q8—31no—
293#525—68no—
294C2×#123—32no—
295C2×#123—32no—
296C2×#123—31no—
297C2×#123—31no—
298C2×#123—32no—
299C2×C22⋊Q8—31no—
300C2×C22⋊Q8—31no—
301C2×C22⋊Q8—32no—
302C2×#121—31no—
303C2×#121—31no—
304C2×#121—31no—
305C2×#121—31no—
306C2×#121—31no—
307C2×#121C2×D311yescharacteristic
308C2×#121C2×D312yes—
309C2×#121C2×D311yescharacteristic, complemented
310C2×#120—31no—
311C2×#120—32no—
312C2×#120—31no—
313C2×C4×D4—31no—
314C2×C4×D4—31no—
315C2×C4×D4—31no—
316C2×C4×D4—31no—
317C2×C4×D4C2×D311yescharacteristic
318C2×#117—31no—
319C2×#117—31no—
320C22×C4⋊C4—31no—
321C22×C4⋊C4—31no—
322C22×C4⋊C4C2×D311yescharacteristic
323C22×C22⋊C4—32no—
324#400—32no—
325#400—32no—
326#399—32no—
327#399—32no—
328#398—32no—
329#397—32no—
330#397—32no—
331#396C2×D312yescomplemented
332#395—32no—
333#394—32no—
334#394C2×D312yescomplemented
335#393—32no—
336#393—32no—
337#393—32no—
338#393—32no—
339#392—32no—
340#392—32no—
341#392—32no—
342#392—32no—
343#392—32no—
344#391—32no—
345#390—32no—
346#390—32no—
347#390—32no—
348#390—32no—
349#390C2×D311yescharacteristic, complemented
350#389—31no—
351#389—31no—
352#389C2×D311yescharacteristic, complemented
353#388—32no—
354#388—32no—
355#388—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#386C2×D312yes—
368#385—32no—
369#385—32no—
370#382—31no—
371#382—32no—
372#381—32no—
373#380—31no—
374#380—31no—
375#380—31no—
376#380—31no—
377#380—31no—
378#380—31no—
379#380—31no—
380#380—31no—
381#380—31no—
382#380—32no—
383#380—32no—
384#380—31no—
385#380C2×D311yescharacteristic, complemented
386C4×C4⋊C4—31no—
387C4×C22⋊C4—32no—
388C2×#95—32no—
389C24×C3C2411yescharacteristic
390C24×C3C2412yes—
391C24×C3C2411yescharacteristic
392C23×D3—22no—
393C23×D3—22no—
394C23×D3—22no—
395C23×D3—22no—
396C23×D3—22no—
397C23×D3—41no—
398C23×D3—41no—
399C23×D3C2411yescharacteristic
400C23×D3C2411yescharacteristic
401C23×D3C2411yescharacteristic
402C2×C3×D4—24no—
403C2×C3×D4—22no—
404C2×C3×D4—22no—
405C2×C3×D4—24no—
406C2×C3×D4—22no—
407C2×C3×D4—24no—
408C2×C3×D4—22no—
409C2×C3×D4—22no—
410C2×C3×D4—22no—
411C2×C3×D4—42no—
412C2×C3×D4—42no—
413C2×C3×D4—42no—
414C22×C3×C4—22no—
415C22×C3×C4—22no—
416C22×C3×C4—24no—
417C22×C3×C4—22no—
418C22×C3×C4—22no—
419C22×C3×C4—22no—
420C22×C3×C4—42no—
421C22×C3×C4—42no—
422C22×C3×C4C2×D414yes—
423C22×C3×C4C2412yes—
424C22×C3×C4C2411yescharacteristic
425C22×C3×C4C2411yescharacteristic
426C22×C3×C4C2412yes—
427C22×C3×C4C2412yes—
428C22×C3×C4C2411yescharacteristic
429C22×C3×C4C2411yescharacteristic
430C22×C3×C4C2411yescharacteristic
431C2×#67—22no—
432C2×#67—22no—
433C2×#67—24no—
434C2×#67—22no—
435C2×#67—22no—
436C2×#67—22no—
437C2×#67—24no—
438C2×#67—24no—
439C2×#67—22no—
440C2×#67—22no—
441C2×#67—22no—
442C2×#67—41no—
443C2×#67—41no—
444C2×#67—42no—
445C2×#67—42no—
446C2×#67—41no—
447C2×#67—42no—
448C2×#67—42no—
449C2×#67—42no—
450C2×#67—42no—
451C2×#67C2×D414yes—
452C22×Dic3—22no—
453C22×Dic3—24no—
454C22×Dic3—24no—
455C22×Dic3—24no—
456C22×Dic3—24no—
457C22×Dic3—22no—
458C22×Dic3—41no—
459C22×Dic3—42no—
460C22×Dic3—42no—
461C22×Dic3C2412yes—
462C22×Dic3C2412yes—
463C22×Dic3C2411yescharacteristic
464C22×Dic3C2412yes—
465C22×Dic3C2412yes—
466C22×Dic3C2411yescharacteristic
467C22×Dic3C2411yescharacteristic
468C22×Dic3C2411yescharacteristic
469C22×Dic3C2411yescharacteristic
470#237—432no—
471#235—416no—
472C2×D12—22no—
473C2×D12—22no—
474C2×D12—22no—
475C2×D12—22no—
476C2×D12—41no—
477C2×D12—41no—
478C2×C4×D3—22no—
479C2×C4×D3—22no—
480C2×C4×D3—22no—
481C2×C4×D3—22no—
482C2×C4×D3—24no—
483C2×C4×D3—22no—
484C2×C4×D3—22no—
485C2×C4×D3—22no—
486C2×C4×D3—22no—
487C2×C4×D3—22no—
488C2×C4×D3—22no—
489C2×C4×D3—22no—
490C2×C4×D3—416no—
491C2×C4×D3—41no—
492C2×C4×D3—41no—
493C2×C4×D3—42no—
494C2×C4×D3—42no—
495C2×C4×D3C2×D414yes—
496C2×C4×D3#4114yescomplemented
497C2×Dic6—24no—
498C2×Dic6—22no—
499C2×Dic6—22no—
500C2×Dic6—41no—
501C2×Dic6—42no—
502C2×Dic6—42no—
503C3×C4⋊C4—22no—
504C3×C4⋊C4—22no—
505C3×C4⋊C4—22no—
506C3×C4⋊C4—22no—
507C3×C4⋊C4—42no—
508C3×C4⋊C4—42no—
509C3×C22⋊C4—22no—
510C3×C22⋊C4—24no—
511C3×C22⋊C4—22no—
512C3×C22⋊C4—42no—
513C3×C22⋊C4—42no—
514C3×C22⋊C4—42no—
515C3×C22⋊C4—42no—
516C3×C42—22no—
517#217—24no—
518#217—24no—
519#217—22no—
520#217—24no—
521#217—24no—
522#217—42no—
523#217—42no—
524#217—42no—
525#217C2×D414yes—
526(C2×D3)⋊C4—22no—
527(C2×D3)⋊C4—22no—
528(C2×D3)⋊C4—22no—
529(C2×D3)⋊C4—22no—
530(C2×D3)⋊C4—22no—
531(C2×D3)⋊C4—42no—
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—
540C4⋊Dic3—24no—
541C4⋊Dic3—22no—
542C4⋊Dic3—22no—
543C4⋊Dic3—22no—
544C4⋊Dic3—22no—
545C4⋊Dic3—22no—
546Dic3⋊C4—22no—
547Dic3⋊C4—22no—
548Dic3⋊C4—24no—
549Dic3⋊C4—22no—
550Dic3⋊C4—24no—
551Dic3⋊C4—42no—
552Dic3⋊C4—42no—
553Dic3⋊C4C2×D414yes—
554C4×Dic3—42no—
555C4×Dic3—42no—
556C4×Dic3C2×D414yes—
557C25—31no—
558C2×#41—64no—
559C2×#41—64no—
560C2×#41—68no—
561C2×#41—122no—
562C2×#41—124no—
563C2×#41—124no—
564C22×Q8—31no—
565C22×Q8—32no—
566C22×D4—31no—
567C22×D4—31no—
568C22×D4—31no—
569C22×D4—31no—
570C22×D4—32no—
571C22×D4—32no—
572C22×D4—32no—
573C22×D4—31no—
574C22×D4—31no—
575C22×D4C22×D311yescharacteristic
576C22×D4C22×D311yescharacteristic
577C22×D4C22×D312yes—
578C22×D4C22×D312yes—
579C23×C4—31no—
580C23×C4—31no—
581C23×C4—32no—
582C23×C4—31no—
583C23×C4—32no—
584C23×C4—31no—
585C23×C4—31no—
586C23×C4—31no—
587C23×C4—32no—
588C23×C4—64no—
589C23×C4—64no—
590C23×C4—122no—
591C23×C4C22×D311yescharacteristic
592C23×C4C22×D311yescharacteristic
593C23×C4C22×D312yes—
594C4⋊Q8—64no—
595#123—68no—
596#123—64no—
597#123—64no—
598#123—68no—
599#123—124no—
600C22⋊Q8—64no—
601C22⋊Q8—68no—
602C22⋊Q8—64no—
603#121—24no—
604#121—42no—
605#121—44no—
606#121—64no—
607#121—64no—
608#121—64no—
609#121—64no—
610#121—122no—
611#120—64no—
612#120—64no—
613#120—124no—
614C4×D4—24no—
615C4×D4—38no—
616C4×D4—64no—
617C4×D4—64no—
618C4×D4—64no—
619#117—64no—
620#117—122no—
621C2×C4⋊C4—31no—
622C2×C4⋊C4—31no—
623C2×C4⋊C4—31no—
624C2×C4⋊C4—32no—
625C2×C4⋊C4—32no—
626C2×C4⋊C4—31no—
627C2×C4⋊C4—31no—
628C2×C4⋊C4—31no—
629C2×C4⋊C4—31no—
630C2×C4⋊C4—31no—
631C2×C4⋊C4—31no—
632C2×C4⋊C4—32no—
633C2×C4⋊C4—32no—
634C2×C4⋊C4—32no—
635C2×C4⋊C4—42no—
636C2×C4⋊C4—64no—
637C2×C4⋊C4—64no—
638C2×C4⋊C4C22×D311yescharacteristic
639C2×C4⋊C4C22×D311yescharacteristic
640C2×C4⋊C4C22×D311yescharacteristic
641C2×C4⋊C4C22×D311yescharacteristic
642C2×C4⋊C4C22×D312yes—
643C2×C4⋊C4C22×D312yes—
644C2×C22⋊C4—31no—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—31no—
647C2×C22⋊C4—32no—
648C2×C22⋊C4—32no—
649C2×C22⋊C4—32no—
650C2×C22⋊C4—32no—
651C2×C22⋊C4—31no—
652C2×C22⋊C4—31no—
653C2×C22⋊C4—31no—
654C2×C22⋊C4—31no—
655C2×C22⋊C4—31no—
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—32no—
666C2×C22⋊C4—32no—
667C2×C22⋊C4—124no—
668C2×C22⋊C4C22×D311yescharacteristic
669C2×C22⋊C4C22×D311yescharacteristic
670C2×C22⋊C4C22×D312yes—
671C2×C22⋊C4C22×D312yes—
672C2×C22⋊C4C22×D312yes—
673C2×C22⋊C4C22×D312yes—
674C2×C22⋊C4C22×D312yes—
675C2×C42—31no—
676C2×C42—32no—
677C2×C42—32no—
678C2×C42C22×D311yescharacteristic
679#95—32no—
680#95—32no—
681#95—32no—
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#95—32no—
692#95—32no—
693#95—32no—
694#95C22×D312yes—
695#95C22×D312yes—
696C23×C3—21no—
697C23×C3—21no—
698C23×C3—21no—
699C23×C3—21no—
700C23×C3—22no—
701C23×C3—21no—
702C23×C3—22no—
703C23×C3—21no—
704C23×C3—21no—
705C23×C3—22no—
706C23×C3—21no—
707C23×C3—22no—
708C23×C3—22no—
709C23×C3—21no—
710C23×C3—21no—
711C23×C3—22no—
712C23×C3—22no—
713C23×C3—21no—
714C23×C3C22×D412yes—
715C23×C3H(5,𝔽2)12yes—
716C23×C3H(5,𝔽2)12yes—
717C23×C3C2511yescharacteristic
718C22×D3—28no—
719C22×D3—21no—
720C22×D3—21no—
721C22×D3—21no—
722C22×D3—21no—
723C22×D3—21no—
724C22×D3—21no—
725C22×D3—21no—
726C22×D3—21no—
727C22×D3—21no—
728C22×D3—21no—
729C22×D3—21no—
730C22×D3—21no—
731C22×D3—21no—
732C22×D3—21no—
733C22×D3—21no—
734C22×D3—21no—
735C22×D3—21no—
736C22×D3—21no—
737C22×D3—44no—
738C22×D3—44no—
739C22×D3—44no—
740C22×D3—44no—
741C22×D3—44no—
742C22×D3—44no—
743C22×D3C22×D412yes—
744C22×D3C2×#4112yes—
745C22×D32−1+412yes—
746C3×D4—48no—
747C3×D4—44no—
748C3×D4—44no—
749C3×D4—84no—
750C2×C3×C4—21no—
751C2×C3×C4—21no—
752C2×C3×C4—28no—
753C2×C3×C4—22no—
754C2×C3×C4—21no—
755C2×C3×C4—21no—
756C2×C3×C4—21no—
757C2×C3×C4—21no—
758C2×C3×C4—22no—
759C2×C3×C4—21no—
760C2×C3×C4—22no—
761C2×C3×C4—22no—
762C2×C3×C4—22no—
763C2×C3×C4—21no—
764C2×C3×C4—21no—
765C2×C3×C4—22no—
766C2×C3×C4—22no—
767C2×C3×C4—21no—
768C2×C3×C4—22no—
769C2×C3×C4—22no—
770C2×C3×C4—21no—
771C2×C3×C4—44no—
772C2×C3×C4—84no—
773C2×C3×C4C22×D412yes—
774C2×C3×C4C22×D412yes—
775C2×C3×C4C2×#4112yes—
776C2×C3×C4H(5,𝔽2)12yes—
777#67—28no—
778#67—44no—
779#67—44no—
780#67—44no—
781#67—48no—
782#67—84no—
783#67—84no—
784C2×Dic3—21no—
785C2×Dic3—21no—
786C2×Dic3—21no—
787C2×Dic3—21no—
788C2×Dic3—21no—
789C2×Dic3—21no—
790C2×Dic3—21no—
791C2×Dic3—21no—
792C2×Dic3—22no—
793C2×Dic3—22no—
794C2×Dic3—21no—
795C2×Dic3—22no—
796C2×Dic3—21no—
797C2×Dic3—22no—
798C2×Dic3—22no—
799C2×Dic3—22no—
800C2×Dic3—22no—
801C2×Dic3—22no—
802C2×Dic3—22no—
803C2×Dic3—22no—
804C2×Dic3—21no—
805C2×Dic3—22no—
806C2×Dic3—22no—
807C2×Dic3—44no—
808C2×Dic3—48no—
809C2×Dic3—48no—
810C2×Dic3C22×D412yes—
811C2×Dic3C22×D412yes—
812C2×Dic3C22×D412yes—
813C2×Dic3C2×#4112yes—
814D12—44no—
815D12—44no—
816C4×D3—28no—
817C4×D3—28no—
818C4×D3—44no—
819C4×D3—44no—
820C4×D3—48no—
821C4×D3—44no—
822Dic6—44no—
823Dic6—48no—
824C24—31no—
825C24—31no—
826C24—31no—
827C24—62no—
828C24—62no—
829C24—62no—
830C24—62no—
831C24—62no—
832C24—121no—
833C24—121no—
834C24C23×D311yescharacteristic
835C24C23×D312yes—
836C24C23×D311yescharacteristic
837#41—1216no—
838#41—1232no—
839C2×Q8—62no—
840C2×Q8—64no—
841C2×Q8—62no—
842C2×Q8—121no—
843C2×Q8—122no—
844C2×Q8—122no—
845C2×D4—22no—
846C2×D4—24no—
847C2×D4—22no—
848C2×D4—24no—
849C2×D4—24no—
850C2×D4—22no—
851C2×D4—22no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—34no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—62no—
859C2×D4—62no—
860C2×D4—62no—
861C2×D4—62no—
862C2×D4—62no—
863C2×D4—62no—
864C2×D4—62no—
865C2×D4—62no—
866C2×D4—62no—
867C2×D4—62no—
868C2×D4—64no—
869C2×D4—62no—
870C2×D4—62no—
871C2×D4—64no—
872C2×D4—64no—
873C2×D4—121no—
874C2×D4—121no—
875C2×D4—121no—
876C2×D4—121no—
877C2×D4—122no—
878C2×D4—122no—
879C2×D4—121no—
880C2×D4—122no—
881C2×D4—122no—
882C2×D4—122no—
883C2×D4—122no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—24no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—31no—
891C22×C4—31no—
892C22×C4—31no—
893C22×C4—31no—
894C22×C4—34no—
895C22×C4—34no—
896C22×C4—32no—
897C22×C4—32no—
898C22×C4—31no—
899C22×C4—32no—
900C22×C4—32no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—62no—
904C22×C4—64no—
905C22×C4—62no—
906C22×C4—64no—
907C22×C4—62no—
908C22×C4—62no—
909C22×C4—62no—
910C22×C4—62no—
911C22×C4—62no—
912C22×C4—64no—
913C22×C4—62no—
914C22×C4—64no—
915C22×C4—64no—
916C22×C4—62no—
917C22×C4—62no—
918C22×C4—62no—
919C22×C4—62no—
920C22×C4—62no—
921C22×C4—121no—
922C22×C4—121no—
923C22×C4—122no—
924C22×C4—122no—
925C22×C4—1216no—
926C22×C4—121no—
927C22×C4—122no—
928C22×C4—122no—
929C22×C4D3×D414yes—
930C22×C4C23×D312yes—
931C22×C4C23×D311yescharacteristic
932C22×C4C23×D311yescharacteristic
933C22×C4C23×D312yes—
934C22×C4C23×D312yes—
935C22×C4C23×D311yescharacteristic
936C22×C4C23×D311yescharacteristic
937C22×C4C23×D311yescharacteristic
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—34no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—64no—
946C4⋊C4—62no—
947C4⋊C4—62no—
948C4⋊C4—62no—
949C4⋊C4—62no—
950C4⋊C4—64no—
951C4⋊C4—62no—
952C4⋊C4—62no—
953C4⋊C4—64no—
954C4⋊C4—62no—
955C4⋊C4—62no—
956C4⋊C4—122no—
957C4⋊C4—122no—
958C22⋊C4—22no—
959C22⋊C4—22no—
960C22⋊C4—24no—
961C22⋊C4—34no—
962C22⋊C4—34no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—62no—
968C22⋊C4—62no—
969C22⋊C4—62no—
970C22⋊C4—62no—
971C22⋊C4—62no—
972C22⋊C4—62no—
973C22⋊C4—64no—
974C22⋊C4—64no—
975C22⋊C4—64no—
976C22⋊C4—64no—
977C22⋊C4—122no—
978C22⋊C4—122no—
979C22⋊C4—122no—
980C22⋊C4—122no—
981C22⋊C4—122no—
982C22⋊C4—122no—
983C22⋊C4—122no—
984C22⋊C4—122no—
985C22⋊C4—122no—
986C22⋊C4—122no—
987C22⋊C4—122no—
988C42—22no—
989C42—34no—
990C42—122no—
991C42—122no—
992C22×C3—22no—
993C22×C3—22no—
994C22×C3—22no—
995C22×C3—22no—
996C22×C3—22no—
997C22×C3—22no—
998C22×C3—42no—
999C22×C3—41no—
1000C22×C3—41no—
1001C22×C3—42no—
1002C22×C3—41no—
1003C22×C3—42no—
1004C22×C3—42no—
1005C22×C3—41no—
1006C22×C3—42no—
1007C22×C3—41no—
1008C22×C3—42no—
1009C22×C3—41no—
1010C22×C3—41no—
1011C22×C3—42no—
1012C22×C3#53514yes—
1013C22×C3C23×D411yescharacteristic
1014C22×C3C22×#4111yescharacteristic
1015C22×C3C2×H(5,𝔽2)11yescharacteristic
1016C22×C3C2×H(5,𝔽2)11yescharacteristic
1017C22×C3C2×H(5,𝔽2)11yescharacteristic
1018C22×C3C2×2−1+411yescharacteristic
1019C22×C3#58511yescharacteristic
1020C2×D3—22no—
1021C2×D3—22no—
1022C2×D3—22no—
1023C2×D3—22no—
1024C2×D3—22no—
1025C2×D3—22no—
1026C2×D3—22no—
1027C2×D3—22no—
1028C2×D3—22no—
1029C2×D3—416no—
1030C2×D3—41no—
1031C2×D3—41no—
1032C2×D3—41no—
1033C2×D3—41no—
1034C2×D3—41no—
1035C2×D3—41no—
1036C2×D3—41no—
1037C2×D3—41no—
1038C2×D3—41no—
1039C2×D3—41no—
1040C2×D3—41no—
1041C2×D3—41no—
1042C3×C4—22no—
1043C3×C4—42no—
1044C3×C4—41no—
1045C3×C4—41no—
1046C3×C4—41no—
1047C3×C4—42no—
1048C3×C4—42no—
1049C3×C4#54614yes—
1050Dic3—22no—
1051Dic3—22no—
1052Dic3—22no—
1053Dic3—22no—
1054Dic3—42no—
1055Dic3—42no—
1056Dic3—41no—
1057Dic3—42no—
1058Dic3—42no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—22no—
1064C23—21no—
1065C23—21no—
1066C23—22no—
1067C23—22no—
1068C23—21no—
1069C23—22no—
1070C23—21no—
1071C23—21no—
1072C23—22no—
1073C23—22no—
1074C23—21no—
1075C23—21no—
1076C23—22no—
1077C23—32no—
1078C23—32no—
1079C23—32no—
1080C23—68no—
1081C23—61no—
1082C23—61no—
1083C23—61no—
1084C23—61no—
1085C23—61no—
1086C23—61no—
1087C23—61no—
1088C23—61no—
1089C23—61no—
1090C23—61no—
1091C23—61no—
1092C23—61no—
1093C23—61no—
1094C23—61no—
1095C23—61no—
1096C23—61no—
1097C23—61no—
1098C23—61no—
1099C23—124no—
1100C23—124no—
1101C23—124no—
1102C23—124no—
1103C23—124no—
1104C23—124no—
1105C23C2×D3×D412yes—
1106C23#100412yes—
1107C23#100912yes—
1108C23C24×D311yescharacteristic
1109Q8—124no—
1110Q8—128no—
1111D4—48no—
1112D4—44no—
1113D4—44no—
1114D4—68no—
1115D4—84no—
1116D4—124no—
1117D4—124no—
1118D4—124no—
1119D4—124no—
1120D4—124no—
1121D4—128no—
1122D4—244no—
1123D4—244no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—28no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—22no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—21no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—32no—
1146C2×C4—32no—
1147C2×C4—32no—
1148C2×C4—32no—
1149C2×C4—44no—
1150C2×C4—61no—
1151C2×C4—61no—
1152C2×C4—61no—
1153C2×C4—61no—
1154C2×C4—61no—
1155C2×C4—61no—
1156C2×C4—61no—
1157C2×C4—61no—
1158C2×C4—68no—
1159C2×C4—68no—
1160C2×C4—61no—
1161C2×C4—62no—
1162C2×C4—62no—
1163C2×C4—62no—
1164C2×C4—62no—
1165C2×C4—61no—
1166C2×C4—62no—
1167C2×C4—62no—
1168C2×C4—61no—
1169C2×C4—62no—
1170C2×C4—62no—
1171C2×C4—62no—
1172C2×C4—62no—
1173C2×C4—62no—
1174C2×C4—62no—
1175C2×C4—84no—
1176C2×C4—124no—
1177C2×C4—124no—
1178C2×C4—128no—
1179C2×C4—124no—
1180C2×C4—128no—
1181C2×C4—128no—
1182C2×C4—124no—
1183C2×C4C2×D3×D412yes—
1184C2×C4C2×D3×D412yes—
1185C2×C4#100412yes—
1186C2×C4D3×#4112yes—
1187C2×C3—24no—
1188C2×C3—82no—
1189C2×C3—81no—
1190C2×C3C2×#53511yescharacteristic
1191C2×C3C2×#54611yescharacteristic
1192C2×C3#348911yescharacteristic
1193C2×C3#349211yescharacteristic
1194C2×C3#349411yescharacteristic
1195C2×C3#353611yescharacteristic
1196C2×C3#354211yescharacteristic
1197D3—42no—
1198D3—42no—
1199D3—42no—
1200C22—22no—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—22no—
1205C22—22no—
1206C22—41no—
1207C22—42no—
1208C22—42no—
1209C22—41no—
1210C22—41no—
1211C22—42no—
1212C22—41no—
1213C22—42no—
1214C22—42no—
1215C22—41no—
1216C22—41no—
1217C22—42no—
1218C22—42no—
1219C22—41no—
1220C22—62no—
1221C22—62no—
1222C22—62no—
1223C22—62no—
1224C22—62no—
1225C22—62no—
1226C22—62no—
1227C22—62no—
1228C22—62no—
1229C22—1216no—
1230C22—121no—
1231C22—121no—
1232C22—121no—
1233C22—121no—
1234C22—121no—
1235C22—121no—
1236C22—121no—
1237C22—121no—
1238C22—121no—
1239C22—121no—
1240C22—121no—
1241C22—121no—
1242C22#560714yes—
1243C22C22×D3×D411yescharacteristic
1244C22C2×#100411yescharacteristic
1245C22C2×#100411yescharacteristic
1246C22C2×D3×#4111yescharacteristic
1247C22C2×#100911yescharacteristic
1248C22#596611yescharacteristic
1249C22D3×2−1+411yescharacteristic
1250C4—22no—
1251C4—42no—
1252C4—42no—
1253C4—41no—
1254C4—42no—
1255C4—41no—
1256C4—41no—
1257C4—62no—
1258C4—62no—
1259C4—62no—
1260C4—62no—
1261C4—122no—
1262C4—122no—
1263C4—122no—
1264C4—121no—
1265C4—122no—
1266C4#561014yes—
1267C3#3783911yescharacteristic, complemented, Sylow
1268C2—24no—
1269C2—81no—
1270C2—82no—
1271C2—122no—
1272C2—122no—
1273C2—122no—
1274C2C2×#560711yescharacteristic
1275C2C2×#561011yescharacteristic
1276C2#8638011yescharacteristic
1277C2#8661511yescharacteristic
1278C2#8670111yescharacteristic
1279C2#8673911yescharacteristic
1280C2#8687711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2416C2
hypercenter#2416D3
hypocenterC3#37839
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2416

Complements

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

NH ≅ G/Ntype
1. C2×#5611C2semidirect
2. C2×#5547C2semidirect
3. C3×#2416C2semidirect
4. #82723C2semidirect
5. #82709C2semidirect
6. #82708C2semidirect
7. #82666C2semidirect
8. #82651C2semidirect
9. #82373C2semidirect
10. C2×#4987C2semidirect
11. #82161C2semidirect
12. #77436C2semidirect
13. #77355C2semidirect
14. #77149C2semidirect
15. #77017C2semidirect
16. #76438C2semidirect
17. #76430C2semidirect
18. #76250C2semidirect
19. #76232C2semidirect
20. #74885C2semidirect
21. #74739C2semidirect
22. #74003C2semidirect
23. #73942C2semidirect
30. C2×C3×#121C22semidirect
36. C2×#938C22semidirect
41. C2×D4×Dic3C22semidirect
50. C2×#892C22semidirect
51. C2×D3×C4⋊C4C22semidirect
52. C2×#888C22semidirect
55. C2×#883C22semidirect
58. C2×#878C22semidirect
61. C3×#396C22semidirect
62. C3×#394C22semidirect
63. C3×#390C22semidirect
64. C3×#389C22semidirect
66. C3×#380C22semidirect
69. #5223C22semidirect
71. #5220C22semidirect
74. #5212C22semidirect
75. #5212C22semidirect
80. #4990C22semidirect
81. #4989C22semidirect
90. #4987C22semidirect
91. #4981C22semidirect
92. #4979C22semidirect
93. #4978C22semidirect
94. #4977C22semidirect
95. Dic3×C4⋊C4C22semidirect
98. #4959C22semidirect
107. #4956C22semidirect
108. #4953C22semidirect
109. #4952C22semidirect
110. #4951C22semidirect
111. #4947C22semidirect
112. #4947C22semidirect
113. #4946C22semidirect
114. #4944C22semidirect
116. #4928C22semidirect
117. #4928C22semidirect
122. #4660C22semidirect
123. #4658C22semidirect
124. #4650C22semidirect
125. #4646C22semidirect
142. #2416D3semidirect
224. C4×#67D4semidirect
309. C2×#121C2×D3semidirect
331. #396C2×D3semidirect
334. #394C2×D3semidirect
349. #390C2×D3semidirect
352. #389C2×D3semidirect
385. #380C2×D3semidirect
496. C2×C4×D3#41semidirect
1267. C3#37839semidirect

Maximal subgroups

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

subgroupindex
C2×#56112
C2×#55472
C3×#24162
#827232
#827092
#827082
#826662
#826512
#823732
C2×#49872
#821612
#774362
#773552
#771492
#770172
#764382
#764302
#762502
#762322
#748852
#747392
#740032
#739422
#378393