Finite Group Databasebeta

← #11028664

Subgroups — #11028664

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×#5828C211yesmaximal, characteristic, complemented
2C2×#5507C211yesmaximal, characteristic, complemented
3C3×#2311C211yesmaximal, characteristic, complemented
4#84098C211yesmaximal, characteristic, complemented
5#82276C211yesmaximal, characteristic, complemented
6#82272C211yesmaximal, characteristic, complemented
7#82197C211yesmaximal, characteristic, complemented
8#76629C212yesmaximal, complemented
9#76564C212yesmaximal, complemented
10#76454C212yesmaximal, complemented
11#76384C212yesmaximal, complemented
12#74896C212yesmaximal, complemented
13#74886C212yesmaximal, complemented
14#74818C212yesmaximal, complemented
15#74815C212yesmaximal, complemented
16#74048C211yesmaximal, characteristic, complemented
17D3×#380C211yesmaximal, characteristic, complemented
18#73954C211yesmaximal, characteristic, complemented
19#73942C211yesmaximal, characteristic, complemented
20#73933C211yesmaximal, characteristic, complemented
21#73911C211yesmaximal, characteristic, complemented
22#73887C211yesmaximal, characteristic, complemented
23#73872C211yesmaximal, characteristic, complemented
24#37839—31nomaximal, Sylow
25C22×C3×#41C2211yescharacteristic
26C22×#235C2212yes—
27C23×C4×D3C2211yescharacteristic
28C2×C3×#117C2211yescharacteristic, complemented
29C22×C3×C4⋊C4C2211yescharacteristic, complemented
30#5828—28no—
31C2×#946C2211yescharacteristic
32C2×#946C2211yescharacteristic
33C2×#938C2211yescharacteristic
34C2×#938C2211yescharacteristic
35C2×#937C2211yescharacteristic
36C2×#937C2211yescharacteristic
37C2×#935C2211yescharacteristic
38C2×#935C2211yescharacteristic
39C2×#930C2211yescharacteristic
40C2×#930C2211yescharacteristic, complemented
41C2×#930C2211yescharacteristic, complemented
42C2×#929C2212yescomplemented
43C2×C4×#67C2211yescharacteristic
44C2×C4×#67C2211yescharacteristic
45C2×C4×#67C2211yescharacteristic
46C2×C4×#67C2211yescharacteristic
47C2×#926C2211yescharacteristic
48C2×#896C2212yescomplemented
49#5507—28no—
50C2×#895C2211yescharacteristic
51C2×#895C2211yescharacteristic
52C2×#894C2212yes—
53C2×#893C2211yescharacteristic, complemented
54C2×D3×C4⋊C4C2211yescharacteristic
55C2×D3×C4⋊C4C2211yescharacteristic
56C2×#888C2211yescharacteristic, complemented
57C2×#884C2212yes—
58C2×#883C2212yes—
59C2×#882C2212yes—
60C2×D3×C22⋊C4C2212yes—
61C3×#391C2212yescomplemented
62C3×#390C2212yes—
63C3×#386C2212yes—
64C3×#386C2212yescomplemented
65C3×#380C2211yescharacteristic
66C3×#380C2211yescharacteristic
67C3×#380C2211yescharacteristic, complemented
68C3×#380C2211yescharacteristic, complemented
69#5231C2212yescomplemented
70#5223C2212yes—
71#5223C2212yes—
72#5223C2212yescomplemented
73#5213C2212yes—
74#5212C2211yescharacteristic
75#5212C2211yescharacteristic, complemented
76#5212C2211yescharacteristic, complemented
77#5210C2212yescomplemented
78#4993C2212yes—
79#4988C2211yescharacteristic, complemented
80#4987C2211yescharacteristic
81#4987C2211yescharacteristic
82#4987C2211yescharacteristic
83#4987C2211yescharacteristic
84#4985C2212yescomplemented
85#4984C2211yescharacteristic, complemented
86#4977C2211yescharacteristic, complemented
87Dic3×C4⋊C4C2211yescharacteristic, complemented
88#4972C2211yescharacteristic, complemented
89#4972C2211yescharacteristic, complemented
90#4961C2212yescomplemented
91#4960C2212yes—
92#4960C2212yes—
93#4959C2212yescomplemented
94#4958C2212yes—
95#4957C2212yes—
96#4957C2212yes—
97#4956C2212yes—
98#4956C2212yes—
99#4956C2212yescomplemented
100#4952C2212yescomplemented
101#4949C2212yes—
102#4947C2212yes—
103#4947C2212yescomplemented
104#4945C2212yescomplemented
105#4942C2212yes—
106#4940C2212yescomplemented
107#4939C2212yes—
108C4×(C2×D3)⋊C4C2212yes—
109#4933C2212yescomplemented
110#4676C2212yescomplemented
111#4675C2212yescomplemented
112#4673C2212yes—
113#4670C2212yescomplemented
114#4668C2212yescomplemented
115#4667C2212yes—
116#4665C2212yes—
117#4665C2212yes—
118#4665C2212yes—
119#4665C2212yes—
120#4664C2212yes—
121D3×#95C2212yes—
122#4660C2212yescomplemented
123#4657C2212yescomplemented
124#4656C2212yescomplemented
125#4650C2212yescomplemented
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#2416—31no—
143#2414—31no—
144#2404—32no—
145#2352—31no—
146#2324—31no—
147#2311D311yescharacteristic, complemented
148C2×#380—31no—
149C24×D3C2311yescharacteristic
150C2×C3×#41—24no—
151C2×C3×#41—24no—
152C2×C3×#41—42no—
153C22×C3×Q8C2311yescharacteristic
154C22×C3×D4C2311yescharacteristic
155C22×C3×D4C2311yescharacteristic
156C22×C3×D4C2311yescharacteristic
157C23×C3×C4C2311yescharacteristic
158C23×C3×C4C2311yescharacteristic
159C23×C3×C4C2311yescharacteristic
160C23×C3×C4C2312yes—
161C22×#67C2311yescharacteristic
162C22×#67C2311yescharacteristic
163C22×#67C2311yescharacteristic
164C22×#67C2311yescharacteristic
165C22×#67C2312yes—
166C22×#67C2312yes—
167C22×#67C2312yes—
168C23×Dic3C2311yescharacteristic
169C2×#235—28no—
170C2×#235—44no—
171C2×#235—44no—
172C22×D12C2312yes—
173C22×D12C2311yescharacteristic
174C22×D12C2312yes—
175C22×C4×D3—24no—
176C22×C4×D3—24no—
177C22×C4×D3—42no—
178C22×C4×D3C2312yes—
179C22×C4×D3C2311yescharacteristic
180C22×C4×D3C2311yescharacteristic
181C22×C4×D3C2311yescharacteristic
182C22×C4×D3C2311yescharacteristic
183C22×C4×D3C2312yes—
184C22×C4×D3C2312yes—
185C22×Dic6C2312yes—
186C3×#117—42no—
187C2×C3×C4⋊C4—24no—
188C2×C3×C4⋊C4C2311yescharacteristic
189C2×C3×C4⋊C4C2311yescharacteristic
190C2×C3×C4⋊C4C2311yescharacteristic
191C2×C3×C4⋊C4C2311yescharacteristic
192C2×C3×C4⋊C4C2312yes—
193C2×C3×C22⋊C4C2312yes—
194C2×C3×C22⋊C4C2312yes—
195C2×C3×C22⋊C4C2312yes—
196C2×C3×C22⋊C4C2312yes—
197C2×C3×C22⋊C4C2312yes—
198C2×C3×C42C2312yes—
199C2×#217C2311yescharacteristic
200C2×#217C2311yescharacteristic
201C2×#217C2311yescharacteristic
202C2×#217C2311yescharacteristic
203C2×#217C2311yescharacteristic
204C2×#217C2312yes—
205C2×#217C2312yes—
206C2×#217C2312yes—
207C2×#217C2311yescharacteristic
208#946—24no—
209#946—24no—
210#938—24no—
211#938—24no—
212#937—24no—
213#937—24no—
214#935—24no—
215#935—24no—
216#930—24no—
217#930—24no—
218#930—42no—
219#929—28no—
220C4×#67—24no—
221C4×#67—24no—
222C4×#67—24no—
223C4×#67D418yescomplemented
224C2×(C2×D3)⋊C4C2311yescharacteristic
225C2×(C2×D3)⋊C4C2312yes—
226C2×(C2×D3)⋊C4C2312yes—
227C2×(C2×D3)⋊C4C2311yescharacteristic
228C2×(C2×D3)⋊C4C2312yes—
229C2×(C2×D3)⋊C4C2312yes—
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
240#926—24no—
241C2×C4⋊Dic3C2311yescharacteristic
242C2×C4⋊Dic3C2311yescharacteristic
243C2×C4⋊Dic3C2311yescharacteristic
244C2×C4⋊Dic3C2311yescharacteristic
245C2×C4⋊Dic3C2311yescharacteristic
246C2×C4⋊Dic3C2312yes—
247C2×Dic3⋊C4C2311yescharacteristic
248C2×Dic3⋊C4C2312yes—
249C2×Dic3⋊C4C2311yescharacteristic
250C2×Dic3⋊C4C2312yes—
251C2×Dic3⋊C4C2311yescharacteristic
252C2×Dic3⋊C4C2312yes—
253C2×Dic3⋊C4C2312yes—
254C2×Dic3⋊C4C2312yes—
255C2×Dic3⋊C4C2311yescharacteristic
256C2×C4×Dic3C2311yescharacteristic
257C2×C4×Dic3C2312yes—
258C2×C4×Dic3C2311yescharacteristic
259#896—28no—
260#895—24no—
261#895—42no—
262#894—28no—
263#893—24no—
264D3×C4⋊C4—24no—
265D3×C4⋊C4—42no—
266#888—24no—
267#884—44no—
268#883—44no—
269#882—44no—
270D3×C22⋊C4—44no—
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×#41C2×D311yescharacteristic
290C24×C4—31no—
291#547—68no—
292C2×C4⋊Q8—31no—
293#525—68no—
294C2×#123—31no—
295C2×#123—31no—
296C2×#123—32no—
297C2×#123—32no—
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×#121—31no—
308C2×#121—31no—
309C2×#121—32no—
310C2×#120—31no—
311C2×#120—31no—
312C2×#120—32no—
313C2×C4×D4—31no—
314C2×C4×D4—31no—
315C2×C4×D4—31no—
316C2×C4×D4—31no—
317C2×C4×D4—31no—
318C2×#117—31no—
319C2×#117C2×D311yescharacteristic, complemented
320C22×C4⋊C4—31no—
321C22×C4⋊C4—31no—
322C22×C4⋊C4C2×D311yescharacteristic, complemented
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#396—32no—
332#395—32no—
333#394—32no—
334#394—32no—
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#391C2×D312yescomplemented
345#390—31no—
346#390—32no—
347#390—32no—
348#390—32no—
349#390C2×D312yes—
350#389—31no—
351#389—31no—
352#389—31no—
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#386C2×D312yes—
367#386C2×D312yescomplemented
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—32no—
381#380—32no—
382#380C2×D311yescharacteristic
383#380C2×D311yescharacteristic
384#380C2×D311yescharacteristic, complemented
385#380C2×D311yescharacteristic, complemented
386C4×C4⋊C4—31no—
387C4×C22⋊C4—32no—
388C2×#95—32no—
389C24×C3C2411yescharacteristic
390C24×C3C2411yescharacteristic
391C24×C3C2411yescharacteristic
392C23×D3—22no—
393C23×D3—22no—
394C23×D3—22no—
395C23×D3—22no—
396C23×D3—22no—
397C23×D3—41no—
398C23×D3—41no—
399C23×D3C2412yes—
400C23×D3C2411yescharacteristic
401C23×D3C2411yescharacteristic
402C3×#41—416no—
403C2×C3×Q8—22no—
404C2×C3×Q8—22no—
405C2×C3×Q8—41no—
406C2×C3×D4—22no—
407C2×C3×D4—22no—
408C2×C3×D4—22no—
409C2×C3×D4—22no—
410C2×C3×D4—22no—
411C2×C3×D4—22no—
412C2×C3×D4—41no—
413C2×C3×D4—41no—
414C2×C3×D4—41no—
415C22×C3×C4—22no—
416C22×C3×C4—22no—
417C22×C3×C4—22no—
418C22×C3×C4—22no—
419C22×C3×C4—24no—
420C22×C3×C4—22no—
421C22×C3×C4—22no—
422C22×C3×C4—22no—
423C22×C3×C4—42no—
424C22×C3×C4—42no—
425C22×C3×C4C2×D414yes—
426C22×C3×C4#4114yescomplemented
427C22×C3×C4C2412yes—
428C22×C3×C4C2411yescharacteristic
429C22×C3×C4C2412yes—
430C22×C3×C4C2412yes—
431C22×C3×C4C2412yes—
432C22×C3×C4C2411yescharacteristic
433C22×C3×C4C2411yescharacteristic
434C22×C3×C4C2411yescharacteristic
435C2×#67—22no—
436C2×#67—22no—
437C2×#67—22no—
438C2×#67—24no—
439C2×#67—22no—
440C2×#67—22no—
441C2×#67—22no—
442C2×#67—22no—
443C2×#67—22no—
444C2×#67—24no—
445C2×#67—22no—
446C2×#67—42no—
447C2×#67—42no—
448C2×#67—41no—
449C2×#67—41no—
450C2×#67—42no—
451C2×#67—42no—
452C2×#67—42no—
453C2×#67—42no—
454C2×#67—42no—
455C2×#67C2×D414yes—
456C22×Dic3—22no—
457C22×Dic3—22no—
458C22×Dic3—41no—
459C22×Dic3C2411yescharacteristic
460C22×Dic3C2412yes—
461C22×Dic3C2412yes—
462C22×Dic3C2411yescharacteristic
463C22×Dic3C2412yes—
464C22×Dic3C2411yescharacteristic
465C22×Dic3C2411yescharacteristic
466C22×Dic3C2411yescharacteristic
467C22×Dic3C2411yescharacteristic
468#235—432no—
469C2×D12—24no—
470C2×D12—24no—
471C2×D12—24no—
472C2×D12—22no—
473C2×D12—22no—
474C2×D12—22no—
475C2×D12—24no—
476C2×D12—42no—
477C2×D12—42no—
478C2×C4×D3—22no—
479C2×C4×D3—22no—
480C2×C4×D3—24no—
481C2×C4×D3—22no—
482C2×C4×D3—24no—
483C2×C4×D3—24no—
484C2×C4×D3—22no—
485C2×C4×D3—22no—
486C2×C4×D3—22no—
487C2×C4×D3—22no—
488C2×C4×D3—22no—
489C2×C4×D3—24no—
490C2×C4×D3—22no—
491C2×C4×D3—24no—
492C2×C4×D3—416no—
493C2×C4×D3—41no—
494C2×C4×D3—41no—
495C2×C4×D3—42no—
496C2×C4×D3—42no—
497C2×C4×D3—42no—
498C2×C4×D3—42no—
499C2×C4×D3C2×D414yes—
500C2×Dic6—24no—
501C2×Dic6—42no—
502C2×Dic6—42no—
503C3×C4⋊C4—22no—
504C3×C4⋊C4—22no—
505C3×C4⋊C4—24no—
506C3×C4⋊C4—22no—
507C3×C4⋊C4—22no—
508C3×C22⋊C4—42no—
509C3×C22⋊C4—42no—
510C3×C22⋊C4—42no—
511C3×C22⋊C4—42no—
512C3×C22⋊C4—42no—
513C3×C42—42no—
514#217—22no—
515#217—22no—
516#217—22no—
517#217—22no—
518#217—22no—
519#217—42no—
520#217—42no—
521#217—42no—
522#217C2×D414yes—
523(C2×D3)⋊C4—22no—
524(C2×D3)⋊C4—24no—
525(C2×D3)⋊C4—24no—
526(C2×D3)⋊C4—22no—
527(C2×D3)⋊C4—24no—
528(C2×D3)⋊C4—24no—
529(C2×D3)⋊C4—24no—
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)⋊C4C2×D414yes—
539C4⋊Dic3—22no—
540C4⋊Dic3—22no—
541C4⋊Dic3—22no—
542C4⋊Dic3—22no—
543C4⋊Dic3—22no—
544C4⋊Dic3—42no—
545Dic3⋊C4—22no—
546Dic3⋊C4—24no—
547Dic3⋊C4—24no—
548Dic3⋊C4—22no—
549Dic3⋊C4—22no—
550Dic3⋊C4—42no—
551Dic3⋊C4—42no—
552Dic3⋊C4—42no—
553Dic3⋊C4C2×D414yes—
554C4×Dic3—22no—
555C4×Dic3—42no—
556C4×Dic3C2×D414yes—
557C25—31no—
558C2×#41—24no—
559C2×#41—24no—
560C2×#41—42no—
561C2×#41—68no—
562C2×#41—124no—
563C2×#41—124no—
564C22×Q8—32no—
565C22×Q8C22×D311yescharacteristic
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—32no—
575C22×D4—32no—
576C22×D4C22×D311yescharacteristic
577C22×D4C22×D311yescharacteristic
578C22×D4C22×D311yescharacteristic
579C23×C4—31no—
580C23×C4—31no—
581C23×C4—32no—
582C23×C4—31no—
583C23×C4—31no—
584C23×C4—31no—
585C23×C4—32no—
586C23×C4—32no—
587C23×C4—64no—
588C23×C4—64no—
589C23×C4—122no—
590C23×C4C22×D311yescharacteristic
591C23×C4C22×D311yescharacteristic
592C23×C4C22×D311yescharacteristic
593C23×C4C22×D312yes—
594C4⋊Q8—64no—
595#123—68no—
596#123—68no—
597#123—64no—
598#123—64no—
599#123—124no—
600C22⋊Q8—64no—
601C22⋊Q8—68no—
602C22⋊Q8—64no—
603#121—64no—
604#121—64no—
605#121—64no—
606#121—64no—
607#121—64no—
608#121—124no—
609#121—122no—
610#121—122no—
611#120—64no—
612#120—64no—
613#120—124no—
614C4×D4—38no—
615C4×D4—64no—
616C4×D4—64no—
617C4×D4—64no—
618C4×D4—64no—
619#117—42no—
620#117—64no—
621C2×C4⋊C4—24no—
622C2×C4⋊C4—31no—
623C2×C4⋊C4—31no—
624C2×C4⋊C4—31no—
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—32no—
636C2×C4⋊C4—32no—
637C2×C4⋊C4—64no—
638C2×C4⋊C4—122no—
639C2×C4⋊C4C22×D311yescharacteristic
640C2×C4⋊C4C22×D311yescharacteristic
641C2×C4⋊C4C22×D311yescharacteristic
642C2×C4⋊C4C22×D312yes—
643C2×C4⋊C4C22×D311yescharacteristic
644C2×C22⋊C4—31no—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—31no—
647C2×C22⋊C4—31no—
648C2×C22⋊C4—31no—
649C2×C22⋊C4—31no—
650C2×C22⋊C4—31no—
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—32no—
666C2×C22⋊C4—32no—
667C2×C22⋊C4—32no—
668C2×C22⋊C4—32no—
669C2×C22⋊C4—124no—
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—31no—
677C2×C42—32no—
678C2×C42C22×D312yes—
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#95C22×D312yes—
693#95C22×D312yes—
694#95C22×D312yes—
695#95C22×D312yes—
696C23×C3—21no—
697C23×C3—21no—
698C23×C3—21no—
699C23×C3—21no—
700C23×C3—21no—
701C23×C3—21no—
702C23×C3—21no—
703C23×C3—21no—
704C23×C3—21no—
705C23×C3—21no—
706C23×C3—21no—
707C23×C3—21no—
708C23×C3—21no—
709C23×C3—21no—
710C23×C3—21no—
711C23×C3—21no—
712C23×C3—21no—
713C23×C3—21no—
714C23×C3—21no—
715C23×C3C22×D412yes—
716C23×C3C2×#4112yes—
717C23×C3C2511yescharacteristic
718C22×D3—21no—
719C22×D3—21no—
720C22×D3—21no—
721C22×D3—21no—
722C22×D3—28no—
723C22×D3—21no—
724C22×D3—21no—
725C22×D3—21no—
726C22×D3—21no—
727C22×D3—21no—
728C22×D3—21no—
729C22×D3—22no—
730C22×D3—22no—
731C22×D3—22no—
732C22×D3—22no—
733C22×D3—22no—
734C22×D3—22no—
735C22×D3—22no—
736C22×D3—44no—
737C22×D3—44no—
738C22×D3—44no—
739C22×D3—44no—
740C22×D3—44no—
741C22×D3—44no—
742C22×D3C22×D412yes—
743C22×D3H(5,𝔽2)12yes—
744C22×D3H(5,𝔽2)12yes—
745C22×D32−1+412yes—
746C3×Q8—44no—
747C3×D4—44no—
748C3×D4—44no—
749C3×D4—44no—
750C2×C3×C4—21no—
751C2×C3×C4—21no—
752C2×C3×C4—21no—
753C2×C3×C4—21no—
754C2×C3×C4—28no—
755C2×C3×C4—28no—
756C2×C3×C4—21no—
757C2×C3×C4—22no—
758C2×C3×C4—22no—
759C2×C3×C4—21no—
760C2×C3×C4—22no—
761C2×C3×C4—22no—
762C2×C3×C4—22no—
763C2×C3×C4—22no—
764C2×C3×C4—22no—
765C2×C3×C4—21no—
766C2×C3×C4—22no—
767C2×C3×C4—22no—
768C2×C3×C4—22no—
769C2×C3×C4—22no—
770C2×C3×C4—22no—
771C2×C3×C4—48no—
772C2×C3×C4—44no—
773C2×C3×C4C22×D412yes—
774C2×C3×C4C22×D412yes—
775C2×C3×C4C2×#4112yes—
776C2×C3×C4C2×#4112yes—
777C2×C3×C4H(5,𝔽2)12yes—
778#67—28no—
779#67—44no—
780#67—44no—
781#67—48no—
782#67—44no—
783#67—84no—
784#67—84no—
785C2×Dic3—21no—
786C2×Dic3—21no—
787C2×Dic3—21no—
788C2×Dic3—21no—
789C2×Dic3—21no—
790C2×Dic3—21no—
791C2×Dic3—21no—
792C2×Dic3—21no—
793C2×Dic3—22no—
794C2×Dic3—21no—
795C2×Dic3—22no—
796C2×Dic3—21no—
797C2×Dic3—21no—
798C2×Dic3—21no—
799C2×Dic3—22no—
800C2×Dic3—22no—
801C2×Dic3—22no—
802C2×Dic3—22no—
803C2×Dic3—21no—
804C2×Dic3—22no—
805C2×Dic3—21no—
806C2×Dic3—22no—
807C2×Dic3—21no—
808C2×Dic3—22no—
809C2×Dic3—44no—
810C2×Dic3C22×D412yes—
811C2×Dic3C22×D412yes—
812C2×Dic3C22×D412yes—
813D12—48no—
814D12—44no—
815D12—84no—
816C4×D3—28no—
817C4×D3—44no—
818C4×D3—48no—
819C4×D3—44no—
820C4×D3—48no—
821C4×D3—44no—
822C4×D3—84no—
823Dic6—48no—
824C24—31no—
825C24—31no—
826C24—32no—
827C24—62no—
828C24—62no—
829C24—62no—
830C24—62no—
831C24—62no—
832C24—121no—
833C24—121no—
834C24C23×D311yescharacteristic
835C24C23×D311yescharacteristic
836C24C23×D311yescharacteristic
837#41—416no—
838#41—1232no—
839C2×Q8—22no—
840C2×Q8—22no—
841C2×Q8—41no—
842C2×Q8—64no—
843C2×Q8—122no—
844C2×Q8—122no—
845C2×D4—22no—
846C2×D4—22no—
847C2×D4—22no—
848C2×D4—22no—
849C2×D4—22no—
850C2×D4—22no—
851C2×D4—34no—
852C2×D4—41no—
853C2×D4—41no—
854C2×D4—41no—
855C2×D4—64no—
856C2×D4—64no—
857C2×D4—64no—
858C2×D4—64no—
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—64no—
870C2×D4—62no—
871C2×D4—62no—
872C2×D4—62no—
873C2×D4—122no—
874C2×D4—122no—
875C2×D4—122no—
876C2×D4—122no—
877C2×D4—121no—
878C2×D4—121no—
879C2×D4—122no—
880C2×D4—122no—
881C2×D4—122no—
882C2×D4—122no—
883C2×D4—122no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—24no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—31no—
893C22×C4—31no—
894C22×C4—31no—
895C22×C4—34no—
896C22×C4—32no—
897C22×C4—31no—
898C22×C4—32no—
899C22×C4—31no—
900C22×C4—32no—
901C22×C4—31no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—64no—
905C22×C4—62no—
906C22×C4—64no—
907C22×C4—64no—
908C22×C4—62no—
909C22×C4—64no—
910C22×C4—64no—
911C22×C4—62no—
912C22×C4—62no—
913C22×C4—62no—
914C22×C4—62no—
915C22×C4—62no—
916C22×C4—62no—
917C22×C4—62no—
918C22×C4—62no—
919C22×C4—62no—
920C22×C4—121no—
921C22×C4—121no—
922C22×C4—122no—
923C22×C4—122no—
924C22×C4—1216no—
925C22×C4—122no—
926C22×C4—122no—
927C22×C4—121no—
928C22×C4#23514yescomplemented
929C22×C4D3×D414yes—
930C22×C4C23×D312yes—
931C22×C4C23×D311yescharacteristic
932C22×C4C23×D312yes—
933C22×C4C23×D312yes—
934C22×C4C23×D312yes—
935C22×C4C23×D311yescharacteristic
936C22×C4C23×D311yescharacteristic
937C22×C4C23×D311yescharacteristic
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—24no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—34no—
944C4⋊C4—64no—
945C4⋊C4—62no—
946C4⋊C4—62no—
947C4⋊C4—62no—
948C4⋊C4—62no—
949C4⋊C4—64no—
950C4⋊C4—62no—
951C4⋊C4—62no—
952C4⋊C4—62no—
953C4⋊C4—62no—
954C4⋊C4—122no—
955C4⋊C4—122no—
956C4⋊C4—122no—
957C4⋊C4—122no—
958C22⋊C4—34no—
959C22⋊C4—34no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—62no—
966C22⋊C4—64no—
967C22⋊C4—64no—
968C22⋊C4—62no—
969C22⋊C4—64no—
970C22⋊C4—62no—
971C22⋊C4—62no—
972C22⋊C4—62no—
973C22⋊C4—62no—
974C22⋊C4—62no—
975C22⋊C4—64no—
976C22⋊C4—62no—
977C22⋊C4—64no—
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—34no—
989C42—42no—
990C42—62no—
991C42—122no—
992C22×C3—22no—
993C22×C3—22no—
994C22×C3—22no—
995C22×C3—22no—
996C22×C3—22no—
997C22×C3—22no—
998C22×C3—41no—
999C22×C3—41no—
1000C22×C3—41no—
1001C22×C3—41no—
1002C22×C3—41no—
1003C22×C3—41no—
1004C22×C3—41no—
1005C22×C3—41no—
1006C22×C3—41no—
1007C22×C3—41no—
1008C22×C3—41no—
1009C22×C3—41no—
1010C22×C3—41no—
1011C22×C3—41no—
1012C22×C3—41no—
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—42no—
1035C2×D3—42no—
1036C2×D3—42no—
1037C2×D3—42no—
1038C2×D3—42no—
1039C2×D3—42no—
1040C2×D3—42no—
1041C2×D3#53514yes—
1042C3×C4—22no—
1043C3×C4—22no—
1044C3×C4—42no—
1045C3×C4—42no—
1046C3×C4—41no—
1047C3×C4—42no—
1048C3×C4—42no—
1049C3×C4#54614yes—
1050Dic3—22no—
1051Dic3—22no—
1052Dic3—22no—
1053Dic3—42no—
1054Dic3—41no—
1055Dic3—41no—
1056Dic3—41no—
1057Dic3—42no—
1058Dic3—42no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—32no—
1079C23—32no—
1080C23—32no—
1081C23—32no—
1082C23—68no—
1083C23—61no—
1084C23—61no—
1085C23—61no—
1086C23—61no—
1087C23—61no—
1088C23—61no—
1089C23—61no—
1090C23—61no—
1091C23—61no—
1092C23—61no—
1093C23—62no—
1094C23—62no—
1095C23—62no—
1096C23—62no—
1097C23—62no—
1098C23—62no—
1099C23—62no—
1100C23—124no—
1101C23—124no—
1102C23—124no—
1103C23—124no—
1104C23—124no—
1105C23—124no—
1106C23C2×#23512yes—
1107C23C2×D3×D412yes—
1108C23C24×D311yescharacteristic
1109Q8—44no—
1110Q8—128no—
1111D4—44no—
1112D4—44no—
1113D4—44no—
1114D4—68no—
1115D4—128no—
1116D4—124no—
1117D4—124no—
1118D4—128no—
1119D4—124no—
1120D4—124no—
1121D4—244no—
1122D4—244no—
1123D4—244no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—28no—
1129C2×C4—28no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—21no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—32no—
1146C2×C4—32no—
1147C2×C4—32no—
1148C2×C4—48no—
1149C2×C4—44no—
1150C2×C4—61no—
1151C2×C4—61no—
1152C2×C4—61no—
1153C2×C4—61no—
1154C2×C4—61no—
1155C2×C4—61no—
1156C2×C4—68no—
1157C2×C4—62no—
1158C2×C4—61no—
1159C2×C4—61no—
1160C2×C4—61no—
1161C2×C4—61no—
1162C2×C4—62no—
1163C2×C4—61no—
1164C2×C4—62no—
1165C2×C4—62no—
1166C2×C4—61no—
1167C2×C4—62no—
1168C2×C4—62no—
1169C2×C4—62no—
1170C2×C4—61no—
1171C2×C4—61no—
1172C2×C4—62no—
1173C2×C4—61no—
1174C2×C4—62no—
1175C2×C4—124no—
1176C2×C4—124no—
1177C2×C4—128no—
1178C2×C4—128no—
1179C2×C4—124no—
1180C2×C4—124no—
1181C2×C4—244no—
1182C2×C4C2×#23512yes—
1183C2×C4C2×#23512yes—
1184C2×C4C2×D3×D412yes—
1185C2×C4C2×D3×D412yes—
1186C2×C4#100412yes—
1187C2×C3—42no—
1188C2×C3—42no—
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—24no—
1198D3—42no—
1199D3—82no—
1200C22—22no—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—22no—
1205C22—22no—
1206C22—34no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22—62no—
1223C22—62no—
1224C22—62no—
1225C22—62no—
1226C22—62no—
1227C22—62no—
1228C22—62no—
1229C22—62no—
1230C22—62no—
1231C22—1216no—
1232C22—121no—
1233C22—121no—
1234C22—121no—
1235C22—121no—
1236C22—122no—
1237C22—122no—
1238C22—122no—
1239C22—122no—
1240C22—122no—
1241C22—122no—
1242C22—122no—
1243C22C22×#23511yescharacteristic
1244C22C22×D3×D411yescharacteristic
1245C22C2×#100411yescharacteristic
1246C22D3×H(5,𝔽2)11yescharacteristic
1247C22D3×H(5,𝔽2)11yescharacteristic
1248C22D3×2−1+411yescharacteristic
1249C22#596811yescharacteristic
1250C4—22no—
1251C4—22no—
1252C4—42no—
1253C4—42no—
1254C4—42no—
1255C4—42no—
1256C4—41no—
1257C4—62no—
1258C4—62no—
1259C4—62no—
1260C4—122no—
1261C4—121no—
1262C4—121no—
1263C4—122no—
1264C4—122no—
1265C4—121no—
1266C4#549014yes—
1267C3#3783911yescharacteristic, complemented, Sylow
1268C2—42no—
1269C2—42no—
1270C2—64no—
1271C2—81no—
1272C2—122no—
1273C2—242no—
1274C2C2×#549011yescharacteristic
1275C2#8590211yescharacteristic
1276C2#8590311yescharacteristic
1277C2D3×#53511yescharacteristic
1278C2#8635611yescharacteristic
1279C2#8638411yescharacteristic
1280C2#8638611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2311C2
hypercenter#2311D3
hypocenterC3#37839
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
1. C2×#5828C2semidirect
2. C2×#5507C2semidirect
3. C3×#2311C2semidirect
4. #84098C2semidirect
5. #82276C2semidirect
6. #82272C2semidirect
7. #82197C2semidirect
8. #76629C2semidirect
9. #76564C2semidirect
10. #76454C2semidirect
11. #76384C2semidirect
12. #74896C2semidirect
13. #74886C2semidirect
14. #74818C2semidirect
15. #74815C2semidirect
16. #74048C2semidirect
17. D3×#380C2semidirect
18. #73954C2semidirect
19. #73942C2semidirect
20. #73933C2semidirect
21. #73911C2semidirect
22. #73887C2semidirect
23. #73872C2semidirect
28. C2×C3×#117C22semidirect
29. C22×C3×C4⋊C4C22semidirect
40. C2×#930C22semidirect
41. C2×#930C22semidirect
42. C2×#929C22semidirect
48. C2×#896C22semidirect
53. C2×#893C22semidirect
56. C2×#888C22semidirect
61. C3×#391C22semidirect
64. C3×#386C22semidirect
67. C3×#380C22semidirect
68. C3×#380C22semidirect
69. #5231C22semidirect
72. #5223C22semidirect
75. #5212C22semidirect
76. #5212C22semidirect
77. #5210C22semidirect
79. #4988C22semidirect
84. #4985C22semidirect
85. #4984C22semidirect
86. #4977C22semidirect
87. Dic3×C4⋊C4C22semidirect
88. #4972C22semidirect
89. #4972C22semidirect
90. #4961C22semidirect
93. #4959C22semidirect
99. #4956C22semidirect
100. #4952C22semidirect
103. #4947C22semidirect
104. #4945C22semidirect
106. #4940C22semidirect
109. #4933C22semidirect
110. #4676C22semidirect
111. #4675C22semidirect
113. #4670C22semidirect
114. #4668C22semidirect
122. #4660C22semidirect
123. #4657C22semidirect
124. #4656C22semidirect
125. #4650C22semidirect
147. #2311D3semidirect
223. C4×#67D4semidirect
319. C2×#117C2×D3semidirect
322. C22×C4⋊C4C2×D3semidirect
344. #391C2×D3semidirect
367. #386C2×D3semidirect
384. #380C2×D3semidirect
385. #380C2×D3semidirect
426. C22×C3×C4#41semidirect
928. C22×C4#235semidirect
1267. C3#37839semidirect

Maximal subgroups

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

subgroupindex
C2×#58282
C2×#55072
C3×#23112
#840982
#822762
#822722
#821972
#766292
#765642
#764542
#763842
#748962
#748862
#748182
#748152
#740482
D3×#3802
#739542
#739422
#739332
#739112
#738872
#738722
#378393