Finite Group Databasebeta

← #11028602

Subgroups — #11028602

Order 768.

2710 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5547C211yesmaximal, characteristic, complemented
2C2×#5514C211yesmaximal, characteristic, complemented
3C3×#2487C211yesmaximal, characteristic, complemented
4#82352C211yesmaximal, characteristic, complemented
5C2×#4987C211yesmaximal, characteristic, complemented
6#78370C212yesmaximal, complemented
7#78238C212yesmaximal, complemented
8#78113C212yesmaximal, complemented
9#78065C212yesmaximal, complemented
10#76251C211yesmaximal, characteristic, complemented
11#76229C211yesmaximal, characteristic, complemented
12#76211C211yesmaximal, characteristic, complemented
13#76198C211yesmaximal, characteristic, complemented
14#74893C212yesmaximal, complemented
15#74752C212yesmaximal, complemented
16#74605C212yesmaximal, complemented
17#74423C212yesmaximal, complemented
18#74048C211yesmaximal, characteristic, complemented
19#74030C211yesmaximal, characteristic, complemented
20#74010C211yesmaximal, characteristic, complemented
21#74003C211yesmaximal, characteristic, complemented
22#73940C211yesmaximal, characteristic, complemented
23#73935C211yesmaximal, characteristic, complemented
24#37836—31nomaximal, Sylow
25C22×#235C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C22×C3×C4⋊C4C2211yescharacteristic
29C2×#939C2211yescharacteristic
30C2×#939C2212yes—
31C2×#937C2211yescharacteristic
32C2×#930C2212yes—
33C2×#930C2211yescharacteristic
34C2×#930C2211yescharacteristic, complemented
35C2×C4×#67C2211yescharacteristic
36C2×C4×#67C2212yes—
37C2×C4×#67C2211yescharacteristic
38C22×(C2×D3)⋊C4C2212yes—
39C22×C4⋊Dic3C2211yescharacteristic
40#5547—28no—
41#5514—28no—
42C2×#898C2212yescomplemented
43C2×#896C2211yescharacteristic
44C2×#895C2211yescharacteristic
45C2×#895C2212yes—
46C2×#895C2211yescharacteristic
47C2×#895C2211yescharacteristic, complemented
48C2×#894C2211yescharacteristic
49C2×#894C2212yescomplemented
50C2×#893C2211yescharacteristic, complemented
51C2×#892C2211yescharacteristic, complemented
52C2×D3×C4⋊C4C2211yescharacteristic, complemented
53C2×#890C2211yescharacteristic, complemented
54C2×#884C2211yescharacteristic
55C2×#884C2212yes—
56C2×#883C2211yescharacteristic
57C2×#882C2211yescharacteristic
58C2×#882C2212yes—
59C2×#67⋊C4C2212yes—
60C2×#878C2211yescharacteristic
61C2×C4×D12C2211yescharacteristic
62C2×#872C2211yescharacteristic
63C3×#400C2212yescomplemented
64C3×#399C2212yescomplemented
65C3×#389C2211yescharacteristic, complemented
66C3×#389C2211yescharacteristic, complemented
67C3×#386C2212yes—
68C3×#385C2212yes—
69C3×#380C2211yescharacteristic
70C3×#380C2211yescharacteristic, complemented
71C3×#380C2211yescharacteristic, complemented
72#5212C2211yescharacteristic, complemented
73C2×C3⋊#95C2212yes—
74#4994C2212yes—
75#4994C2212yescomplemented
76#4994C2212yescomplemented
77#4991C2212yes—
78#4989C2212yescomplemented
79#4988C2212yes—
80#4987C2211yescharacteristic
81#4987C2212yes—
82#4987C2211yescharacteristic
83#4987C2212yes—
84#4987C2211yescharacteristic
85#4987C2211yescharacteristic
86#4987C2211yescharacteristic
87#4987C2211yescharacteristic
88#4987C2211yescharacteristic, complemented
89#4983C2212yescomplemented
90#4980C2212yescomplemented
91#4975C2211yescharacteristic, complemented
92Dic3×C4⋊C4C2211yescharacteristic, complemented
93#4961C2212yescomplemented
94#4960C2212yes—
95#4960C2212yescomplemented
96#4959C2212yes—
97#4959C2212yescomplemented
98#4958C2212yes—
99#4958C2212yes—
100#4957C2212yes—
101#4956C2212yescomplemented
102#4951C2212yescomplemented
103#4946C2212yes—
104#4939C2211yescharacteristic, complemented
105#4928C2211yescharacteristic, complemented
106#4676C2212yes—
107#4675C2212yescomplemented
108#4673C2212yescomplemented
109#4672C2212yes—
110#4672C2212yes—
111#4671C2212yes—
112#4670C2212yes—
113#4669C2212yes—
114#4669C2212yescomplemented
115#4668C2212yescomplemented
116#4667C2212yescomplemented
117#4665C2212yes—
118#4665C2212yes—
119#4665C2212yes—
120#4665C2212yes—
121#4665C2212yescomplemented
122#4658C2212yescomplemented
123#4657C2212yescomplemented
124#4647C2212yescomplemented
125#4646C2212yescomplemented
126C2×#553—31no—
127C2×#525—31no—
128#2847—31no—
129#2705—32no—
130#2702—32no—
131#2693—32no—
132#2671—32no—
133#2629—31no—
134#2615—31no—
135#2562—31no—
136#2543—32no—
137#2537—31no—
138#2487D311yescharacteristic, complemented
139#2485—31no—
140#2450—32no—
141#2424—32no—
142#2424—32no—
143#2416—31no—
144#2416—31no—
145D4×C4⋊C4—31no—
146#2324—31no—
147#2311—31no—
148C2×#380—31no—
149C24×D3C2311yescharacteristic
150C22×C3×D4C2311yescharacteristic
151C23×C3×C4C2311yescharacteristic
152C23×C3×C4C2311yescharacteristic
153C23×C3×C4C2312yes—
154C22×#67C2312yes—
155C22×#67C2311yescharacteristic
156C22×#67C2311yescharacteristic
157C22×#67C2311yescharacteristic
158C22×#67C2311yescharacteristic
159C22×#67C2312yes—
160C23×Dic3C2311yescharacteristic
161C23×Dic3C2312yes—
162C2×#235—24no—
163C2×#235—24no—
164C2×#235—42no—
165C22×D12C2311yescharacteristic
166C22×D12C2311yescharacteristic
167C22×D12C2311yescharacteristic
168C22×D12C2312yes—
169C22×D12C2312yes—
170C22×D12C2312yes—
171C22×C4×D3—24no—
172C22×C4×D3—24no—
173C22×C4×D3—42no—
174C22×C4×D3C2311yescharacteristic
175C22×C4×D3C2311yescharacteristic
176C22×C4×D3C2311yescharacteristic
177C22×C4×D3C2311yescharacteristic
178C22×C4×D3C2311yescharacteristic
179C22×C4×D3C2312yes—
180C22×C4×D3C2312yes—
181C22×Dic6C2311yescharacteristic
182C3×C4×D4—24no—
183C2×C3×C4⋊C4—24no—
184C2×C3×C4⋊C4C2311yescharacteristic
185C2×C3×C4⋊C4C2311yescharacteristic
186C2×C3×C4⋊C4C2311yescharacteristic
187C2×C3×C4⋊C4C2311yescharacteristic
188C2×C3×C4⋊C4C2312yes—
189C2×C3×C4⋊C4C2311yescharacteristic
190C2×C3×C4⋊C4C2312yes—
191C2×C3×C4⋊C4C2312yes—
192C2×C3×C22⋊C4C2312yes—
193C2×C3×C22⋊C4C2311yescharacteristic
194C2×C3×C22⋊C4C2311yescharacteristic
195C2×C3×C22⋊C4C2312yes—
196C2×C3×C22⋊C4C2312yes—
197C2×C3×C42C2311yescharacteristic
198C2×#217C2311yescharacteristic
199C2×#217C2312yes—
200C2×#217C2311yescharacteristic
201#939—24no—
202#939—44no—
203#937—24no—
204#930—24no—
205#930—28no—
206#930—42no—
207C4×#67—28no—
208C4×#67—24no—
209C4×#67D418yescomplemented
210C2×(C2×D3)⋊C4—44no—
211C2×(C2×D3)⋊C4C2311yescharacteristic
212C2×(C2×D3)⋊C4C2312yes—
213C2×(C2×D3)⋊C4C2312yes—
214C2×(C2×D3)⋊C4C2312yes—
215C2×(C2×D3)⋊C4C2311yescharacteristic
216C2×(C2×D3)⋊C4C2311yescharacteristic
217C2×(C2×D3)⋊C4C2312yes—
218C2×(C2×D3)⋊C4C2312yes—
219C2×(C2×D3)⋊C4C2311yescharacteristic
220C2×(C2×D3)⋊C4C2312yes—
221C2×(C2×D3)⋊C4C2312yes—
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)⋊C4C2312yes—
231C2×(C2×D3)⋊C4C2312yes—
232C2×(C2×D3)⋊C4C2311yescharacteristic
233C2×C4⋊Dic3—42no—
234C2×C4⋊Dic3C2312yes—
235C2×C4⋊Dic3C2311yescharacteristic
236C2×C4⋊Dic3C2311yescharacteristic
237C2×C4⋊Dic3C2311yescharacteristic
238C2×C4⋊Dic3C2311yescharacteristic
239C2×C4⋊Dic3C2312yes—
240C2×Dic3⋊C4C2311yescharacteristic
241C2×Dic3⋊C4C2311yescharacteristic
242C2×Dic3⋊C4C2312yes—
243C2×Dic3⋊C4C2311yescharacteristic
244C2×Dic3⋊C4C2312yes—
245C2×Dic3⋊C4C2312yes—
246C2×Dic3⋊C4C2312yes—
247C2×Dic3⋊C4C2312yes—
248C2×Dic3⋊C4C2311yescharacteristic
249C2×C4×Dic3C2312yes—
250C2×C4×Dic3C2312yes—
251C2×C4×Dic3C2311yescharacteristic
252#898—28no—
253#896—24no—
254#895—24no—
255#895—24no—
256#895—44no—
257#895—42no—
258#894—24no—
259#894—28no—
260#893—24no—
261#892—24no—
262D3×C4⋊C4—42no—
263#890—24no—
264#884—24no—
265#884—44no—
266#883—24no—
267#882—24no—
268#882—44no—
269#67⋊C4—44no—
270#878—24no—
271C4×D12—24no—
272#872—24no—
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—31no—
289C24×C4—31no—
290#553—68no—
291C2×#126—32no—
292C2×#125—31no—
293#525—68no—
294C2×#123—31no—
295C2×#123—32no—
296C2×#123—31no—
297C2×C22⋊Q8—31no—
298C2×C22⋊Q8—31no—
299C2×#121—31no—
300C2×#121—31no—
301C2×#121—32no—
302C2×#121—32no—
303C2×#121—31no—
304C2×#121—31no—
305C2×#121—31no—
306C2×#121—31no—
307C2×#121—32no—
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—32no—
316C2×C4×D4—31no—
317C2×C4×D4—32no—
318C2×C4×D4—31no—
319C2×C4×D4C2×D311yescharacteristic
320C2×#117—31no—
321C2×#117—31no—
322C22×C4⋊C4—31no—
323C22×C4⋊C4—31no—
324C22×C4⋊C4C2×D311yescharacteristic
325C22×C22⋊C4—32no—
326#400—32no—
327#400C2×D312yescomplemented
328#399C2×D312yescomplemented
329#398—32no—
330#398—32no—
331#397—32no—
332#396—32no—
333#396—32no—
334#396—32no—
335#396—32no—
336#394—32no—
337#394—32no—
338#394—32no—
339#394—32no—
340#394—32no—
341#394—32no—
342#393—32no—
343#392—32no—
344#392—32no—
345#392—32no—
346#391—32no—
347#390—32no—
348#390—32no—
349#390—31no—
350#389—31no—
351#389—32no—
352#389C2×D311yescharacteristic, complemented
353#389C2×D311yescharacteristic, complemented
354#388—32no—
355#388—32no—
356#388—32no—
357#388—32no—
358#387—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#385—32no—
371#385C2×D312yes—
372#384—31no—
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#380—31no—
383#380—32no—
384#380C2×D311yescharacteristic
385#380C2×D311yescharacteristic, complemented
386#380C2×D311yescharacteristic, complemented
387C4×C4⋊C4—31no—
388C2×#95—32no—
389C24×C3C2411yescharacteristic
390C24×C3C2411yescharacteristic
391C23×D3—22no—
392C23×D3—22no—
393C23×D3—22no—
394C23×D3—22no—
395C23×D3—22no—
396C23×D3—41no—
397C23×D3—41no—
398C23×D3C2412yes—
399C23×D3C2411yescharacteristic
400C23×D3C2411yescharacteristic
401C23×D3C2411yescharacteristic
402C2×C3×D4—22no—
403C2×C3×D4—22no—
404C2×C3×D4—22no—
405C22×C3×C4—22no—
406C22×C3×C4—22no—
407C22×C3×C4—24no—
408C22×C3×C4—22no—
409C22×C3×C4—22no—
410C22×C3×C4—22no—
411C22×C3×C4—42no—
412C22×C3×C4—42no—
413C22×C3×C4C2×D414yes—
414C22×C3×C4C2412yes—
415C22×C3×C4C2411yescharacteristic
416C22×C3×C4C2412yes—
417C22×C3×C4C2412yes—
418C22×C3×C4C2411yescharacteristic
419C22×C3×C4C2412yes—
420C22×C3×C4C2411yescharacteristic
421C22×C3×C4C2411yescharacteristic
422C22×C3×C4C2411yescharacteristic
423C2×#67—22no—
424C2×#67—22no—
425C2×#67—24no—
426C2×#67—24no—
427C2×#67—24no—
428C2×#67—22no—
429C2×#67—22no—
430C2×#67—22no—
431C2×#67—22no—
432C2×#67—22no—
433C2×#67—22no—
434C2×#67—41no—
435C2×#67—41no—
436C2×#67—41no—
437C2×#67—42no—
438C2×#67—42no—
439C2×#67—42no—
440C2×#67C2×D414yes—
441C22×Dic3—22no—
442C22×Dic3—24no—
443C22×Dic3—22no—
444C22×Dic3—41no—
445C22×Dic3—42no—
446C22×Dic3—42no—
447C22×Dic3C2411yescharacteristic
448C22×Dic3C2412yes—
449C22×Dic3C2412yes—
450C22×Dic3C2412yes—
451C22×Dic3C2411yescharacteristic
452C22×Dic3C2411yescharacteristic
453C22×Dic3C2411yescharacteristic
454C22×Dic3C2411yescharacteristic
455#235—416no—
456C2×D12—22no—
457C2×D12—22no—
458C2×D12—22no—
459C2×D12—22no—
460C2×D12—22no—
461C2×D12—22no—
462C2×D12—22no—
463C2×D12—24no—
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×D12—42no—
473C2×D12—42no—
474C2×C4×D3—22no—
475C2×C4×D3—22no—
476C2×C4×D3—22no—
477C2×C4×D3—22no—
478C2×C4×D3—22no—
479C2×C4×D3—22no—
480C2×C4×D3—22no—
481C2×C4×D3—22no—
482C2×C4×D3—22no—
483C2×C4×D3—22no—
484C2×C4×D3—22no—
485C2×C4×D3—24no—
486C2×C4×D3—416no—
487C2×C4×D3—41no—
488C2×C4×D3—41no—
489C2×C4×D3—42no—
490C2×C4×D3—42no—
491C2×C4×D3—42no—
492C2×C4×D3—42no—
493C2×C4×D3—42no—
494C2×C4×D3C2×D414yes—
495C2×C4×D3#4114yes—
496C2×Dic6—22no—
497C2×Dic6—22no—
498C2×Dic6—41no—
499C3×C4⋊C4—22no—
500C3×C4⋊C4—22no—
501C3×C4⋊C4—22no—
502C3×C4⋊C4—24no—
503C3×C4⋊C4—22no—
504C3×C4⋊C4—22no—
505C3×C4⋊C4—42no—
506C3×C4⋊C4—42no—
507C3×C22⋊C4—22no—
508C3×C22⋊C4—24no—
509C3×C22⋊C4—22no—
510C3×C22⋊C4—42no—
511C3×C22⋊C4—42no—
512C3×C42—22no—
513#217—22no—
514#217—42no—
515#217C2×D414yes—
516(C2×D3)⋊C4—22no—
517(C2×D3)⋊C4—24no—
518(C2×D3)⋊C4—24no—
519(C2×D3)⋊C4—24no—
520(C2×D3)⋊C4—24no—
521(C2×D3)⋊C4—22no—
522(C2×D3)⋊C4—22no—
523(C2×D3)⋊C4—22no—
524(C2×D3)⋊C4—22no—
525(C2×D3)⋊C4—24no—
526(C2×D3)⋊C4—24no—
527(C2×D3)⋊C4—24no—
528(C2×D3)⋊C4—42no—
529(C2×D3)⋊C4—42no—
530(C2×D3)⋊C4—42no—
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)⋊C4C2×D414yes—
538C4⋊Dic3—22no—
539C4⋊Dic3—22no—
540C4⋊Dic3—22no—
541C4⋊Dic3—22no—
542C4⋊Dic3—24no—
543C4⋊Dic3—42no—
544Dic3⋊C4—22no—
545Dic3⋊C4—22no—
546Dic3⋊C4—22no—
547Dic3⋊C4—24no—
548Dic3⋊C4—42no—
549Dic3⋊C4—42no—
550Dic3⋊C4—42no—
551Dic3⋊C4—42no—
552Dic3⋊C4C2×D414yes—
553C4×Dic3—24no—
554C4×Dic3—42no—
555C4×Dic3C2×D414yes—
556C25—31no—
557C2×#41—64no—
558C2×#41—64no—
559C2×#41—122no—
560C22×Q8—31no—
561C22×D4—31no—
562C22×D4—32no—
563C22×D4—31no—
564C22×D4—31no—
565C22×D4—31no—
566C22×D4—32no—
567C22×D4—31no—
568C22×D4—31no—
569C22×D4—31no—
570C22×D4—32no—
571C22×D4—32no—
572C22×D4—32no—
573C22×D4C22×D311yescharacteristic
574C23×C4—31no—
575C23×C4—31no—
576C23×C4—31no—
577C23×C4—32no—
578C23×C4—31no—
579C23×C4—31no—
580C23×C4—31no—
581C23×C4—32no—
582C23×C4—32no—
583C23×C4—64no—
584C23×C4—64no—
585C23×C4—122no—
586C23×C4C22×D311yescharacteristic
587C23×C4C22×D311yescharacteristic
588C23×C4C22×D312yes—
589#126—68no—
590#125—64no—
591#123—64no—
592#123—64no—
593#123—68no—
594C22⋊Q8—64no—
595C22⋊Q8—64no—
596#121—64no—
597#121—64no—
598#121—64no—
599#121—68no—
600#121—64no—
601#121—64no—
602#121—124no—
603#121—124no—
604#121—122no—
605#121—122no—
606#121—124no—
607#120—64no—
608#120—64no—
609#120—124no—
610C4×D4—24no—
611C4×D4—38no—
612C4×D4—64no—
613C4×D4—64no—
614C4×D4—64no—
615C4×D4—68no—
616C4×D4—124no—
617#117—64no—
618#117—64no—
619C2×C4⋊C4—24no—
620C2×C4⋊C4—31no—
621C2×C4⋊C4—31no—
622C2×C4⋊C4—31no—
623C2×C4⋊C4—31no—
624C2×C4⋊C4—31no—
625C2×C4⋊C4—31no—
626C2×C4⋊C4—31no—
627C2×C4⋊C4—31no—
628C2×C4⋊C4—32no—
629C2×C4⋊C4—32no—
630C2×C4⋊C4—32no—
631C2×C4⋊C4—32no—
632C2×C4⋊C4—32no—
633C2×C4⋊C4—32no—
634C2×C4⋊C4—32no—
635C2×C4⋊C4—122no—
636C2×C4⋊C4—122no—
637C2×C4⋊C4C22×D311yescharacteristic
638C2×C4⋊C4C22×D311yescharacteristic
639C2×C4⋊C4C22×D311yescharacteristic
640C2×C4⋊C4C22×D312yes—
641C2×C4⋊C4C22×D311yescharacteristic
642C2×C4⋊C4C22×D311yescharacteristic
643C2×C4⋊C4C22×D312yes—
644C2×C4⋊C4C22×D312yes—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—31no—
647C2×C22⋊C4—31no—
648C2×C22⋊C4—32no—
649C2×C22⋊C4—32no—
650C2×C22⋊C4—31no—
651C2×C22⋊C4—31no—
652C2×C22⋊C4—32no—
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—32no—
668C2×C22⋊C4—32no—
669C2×C22⋊C4—32no—
670C2×C22⋊C4—124no—
671C2×C22⋊C4C22×D312yes—
672C2×C22⋊C4C22×D311yescharacteristic
673C2×C22⋊C4C22×D311yescharacteristic
674C2×C22⋊C4C22×D312yes—
675C2×C22⋊C4C22×D312yes—
676C2×C42—31no—
677C2×C42—32no—
678C2×C42—32no—
679C2×C42C22×D311yescharacteristic
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#95C22×D312yes—
691#95C22×D312yes—
692#95C22×D312yes—
693#95C22×D312yes—
694#95C22×D312yes—
695C23×C3—21no—
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×C3C22×D412yes—
707C23×C3H(5,𝔽2)12yes—
708C23×C32−1+412yes—
709C23×C3C2511yescharacteristic
710C22×D3—28no—
711C22×D3—21no—
712C22×D3—21no—
713C22×D3—21no—
714C22×D3—21no—
715C22×D3—21no—
716C22×D3—21no—
717C22×D3—21no—
718C22×D3—21no—
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—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×D3C2×#4112yes—
744C22×D3H(5,𝔽2)12yes—
745C3×D4—44no—
746C2×C3×C4—21no—
747C2×C3×C4—21no—
748C2×C3×C4—28no—
749C2×C3×C4—22no—
750C2×C3×C4—21no—
751C2×C3×C4—22no—
752C2×C3×C4—21no—
753C2×C3×C4—21no—
754C2×C3×C4—22no—
755C2×C3×C4—21no—
756C2×C3×C4—22no—
757C2×C3×C4—21no—
758C2×C3×C4—22no—
759C2×C3×C4—22no—
760C2×C3×C4—22no—
761C2×C3×C4—22no—
762C2×C3×C4—22no—
763C2×C3×C4—21no—
764C2×C3×C4—21no—
765C2×C3×C4—21no—
766C2×C3×C4—22no—
767C2×C3×C4—22no—
768C2×C3×C4—21no—
769C2×C3×C4—22no—
770C2×C3×C4—44no—
771C2×C3×C4—84no—
772C2×C3×C4C22×D412yes—
773C2×C3×C4C22×D412yes—
774C2×C3×C4C2×#4112yes—
775C2×C3×C4H(5,𝔽2)12yes—
776#67—28no—
777#67—44no—
778#67—44no—
779#67—44no—
780#67—48no—
781#67—84no—
782C2×Dic3—21no—
783C2×Dic3—21no—
784C2×Dic3—21no—
785C2×Dic3—21no—
786C2×Dic3—21no—
787C2×Dic3—21no—
788C2×Dic3—21no—
789C2×Dic3—21no—
790C2×Dic3—22no—
791C2×Dic3—21no—
792C2×Dic3—21no—
793C2×Dic3—22no—
794C2×Dic3—22no—
795C2×Dic3—22no—
796C2×Dic3—22no—
797C2×Dic3—22no—
798C2×Dic3—22no—
799C2×Dic3—22no—
800C2×Dic3—21no—
801C2×Dic3—22no—
802C2×Dic3—44no—
803C2×Dic3—84no—
804C2×Dic3C22×D412yes—
805C2×Dic3C22×D412yes—
806C2×Dic3C22×D412yes—
807C2×Dic3C2×#4112yes—
808D12—44no—
809D12—44no—
810D12—44no—
811D12—84no—
812D12—84no—
813D12—84no—
814C4×D3—28no—
815C4×D3—28no—
816C4×D3—44no—
817C4×D3—44no—
818C4×D3—44no—
819C4×D3—84no—
820C4×D3—84no—
821Dic6—44no—
822C24—31no—
823C24—31no—
824C24—31no—
825C24—32no—
826C24—62no—
827C24—62no—
828C24—62no—
829C24—62no—
830C24—62no—
831C24—121no—
832C24—121no—
833C24C23×D311yescharacteristic
834C24C23×D311yescharacteristic
835#41—1216no—
836C2×Q8—62no—
837C2×Q8—62no—
838C2×Q8—121no—
839C2×D4—22no—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—34no—
843C2×D4—62no—
844C2×D4—62no—
845C2×D4—62no—
846C2×D4—62no—
847C2×D4—64no—
848C2×D4—64no—
849C2×D4—64no—
850C2×D4—62no—
851C2×D4—62no—
852C2×D4—62no—
853C2×D4—62no—
854C2×D4—62no—
855C2×D4—62no—
856C2×D4—62no—
857C2×D4—62no—
858C2×D4—64no—
859C2×D4—64no—
860C2×D4—64no—
861C2×D4—62no—
862C2×D4—62no—
863C2×D4—62no—
864C2×D4—121no—
865C2×D4—121no—
866C2×D4—122no—
867C2×D4—122no—
868C2×D4—122no—
869C2×D4—122no—
870C2×D4—122no—
871C2×D4—122no—
872C2×D4—121no—
873C2×D4—121no—
874C2×D4—121no—
875C2×D4—122no—
876C2×D4—122no—
877C2×D4—122no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—24no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—31no—
885C22×C4—31no—
886C22×C4—31no—
887C22×C4—31no—
888C22×C4—34no—
889C22×C4—34no—
890C22×C4—31no—
891C22×C4—32no—
892C22×C4—32no—
893C22×C4—32no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—62no—
897C22×C4—64no—
898C22×C4—62no—
899C22×C4—62no—
900C22×C4—62no—
901C22×C4—62no—
902C22×C4—62no—
903C22×C4—62no—
904C22×C4—62no—
905C22×C4—64no—
906C22×C4—62no—
907C22×C4—62no—
908C22×C4—62no—
909C22×C4—62no—
910C22×C4—62no—
911C22×C4—121no—
912C22×C4—121no—
913C22×C4—1216no—
914C22×C4—122no—
915C22×C4—122no—
916C22×C4—122no—
917C22×C4—122no—
918C22×C4—122no—
919C22×C4—121no—
920C22×C4—122no—
921C22×C4—122no—
922C22×C4D3×D414yes—
923C22×C4C23×D312yes—
924C22×C4C23×D311yescharacteristic
925C22×C4C23×D312yes—
926C22×C4C23×D312yes—
927C22×C4C23×D311yescharacteristic
928C22×C4C23×D312yes—
929C22×C4C23×D311yescharacteristic
930C22×C4C23×D311yescharacteristic
931C22×C4C23×D311yescharacteristic
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—24no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—34no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—62no—
942C4⋊C4—62no—
943C4⋊C4—62no—
944C4⋊C4—62no—
945C4⋊C4—64no—
946C4⋊C4—64no—
947C4⋊C4—62no—
948C4⋊C4—62no—
949C4⋊C4—62no—
950C4⋊C4—122no—
951C4⋊C4—122no—
952C4⋊C4—122no—
953C4⋊C4—122no—
954C4⋊C4—122no—
955C22⋊C4—22no—
956C22⋊C4—24no—
957C22⋊C4—22no—
958C22⋊C4—34no—
959C22⋊C4—34no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—62no—
963C22⋊C4—62no—
964C22⋊C4—62no—
965C22⋊C4—62no—
966C22⋊C4—64no—
967C22⋊C4—64no—
968C22⋊C4—64no—
969C22⋊C4—64no—
970C22⋊C4—64no—
971C22⋊C4—64no—
972C22⋊C4—62no—
973C22⋊C4—62no—
974C22⋊C4—64no—
975C22⋊C4—122no—
976C22⋊C4—122no—
977C22⋊C4—122no—
978C22⋊C4—122no—
979C22⋊C4—122no—
980C22⋊C4—122no—
981C22⋊C4—122no—
982C22⋊C4—122no—
983C22⋊C4—122no—
984C22⋊C4—122no—
985C42—22no—
986C42—34no—
987C42—64no—
988C42—122no—
989C22×C3—22no—
990C22×C3—22no—
991C22×C3—22no—
992C22×C3—22no—
993C22×C3—22no—
994C22×C3—22no—
995C22×C3—41no—
996C22×C3—41no—
997C22×C3—41no—
998C22×C3—41no—
999C22×C3—41no—
1000C22×C3—41no—
1001C22×C3—41no—
1002C22×C3#53714yes—
1003C22×C3C23×D411yescharacteristic
1004C22×C3C22×#4111yescharacteristic
1005C22×C3C2×H(5,𝔽2)11yescharacteristic
1006C22×C3C2×H(5,𝔽2)11yescharacteristic
1007C22×C3C2×H(5,𝔽2)11yescharacteristic
1008C22×C3C2×2−1+411yescharacteristic
1009C22×C3#58511yescharacteristic
1010C2×D3—22no—
1011C2×D3—22no—
1012C2×D3—22no—
1013C2×D3—22no—
1014C2×D3—22no—
1015C2×D3—22no—
1016C2×D3—22no—
1017C2×D3—22no—
1018C2×D3—22no—
1019C2×D3—416no—
1020C2×D3—41no—
1021C2×D3—41no—
1022C2×D3—41no—
1023C2×D3—41no—
1024C2×D3—41no—
1025C2×D3—41no—
1026C2×D3—41no—
1027C2×D3—41no—
1028C2×D3—41no—
1029C2×D3—41no—
1030C2×D3—41no—
1031C2×D3—41no—
1032C2×D3—42no—
1033C2×D3—42no—
1034C2×D3—42no—
1035C2×D3—42no—
1036C2×D3—42no—
1037C2×D3—42no—
1038C2×D3—42no—
1039C3×C4—22no—
1040C3×C4—41no—
1041C3×C4—41no—
1042C3×C4—42no—
1043C3×C4—41no—
1044C3×C4—42no—
1045C3×C4—42no—
1046C3×C4—42no—
1047C3×C4#54614yes—
1048Dic3—22no—
1049Dic3—22no—
1050Dic3—22no—
1051Dic3—22no—
1052Dic3—42no—
1053Dic3—41no—
1054Dic3—42no—
1055Dic3—42no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—32no—
1068C23—32no—
1069C23—32no—
1070C23—68no—
1071C23—61no—
1072C23—61no—
1073C23—61no—
1074C23—61no—
1075C23—61no—
1076C23—61no—
1077C23—61no—
1078C23—61no—
1079C23—61no—
1080C23—61no—
1081C23—61no—
1082C23—61no—
1083C23—61no—
1084C23—61no—
1085C23—61no—
1086C23—61no—
1087C23—61no—
1088C23—61no—
1089C23—62no—
1090C23—62no—
1091C23—62no—
1092C23—62no—
1093C23—62no—
1094C23—62no—
1095C23—62no—
1096C23—124no—
1097C23—124no—
1098C23—124no—
1099C23—124no—
1100C23—124no—
1101C23—124no—
1102C23C2×D3×D412yes—
1103C23#100712yes—
1104C23#100912yes—
1105C23C24×D311yescharacteristic
1106Q8—124no—
1107D4—44no—
1108D4—68no—
1109D4—124no—
1110D4—124no—
1111D4—124no—
1112D4—124no—
1113D4—124no—
1114D4—128no—
1115D4—124no—
1116D4—244no—
1117D4—244no—
1118D4—244no—
1119D4—244no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—28no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—22no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—21no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—21no—
1143C2×C4—22no—
1144C2×C4—32no—
1145C2×C4—32no—
1146C2×C4—32no—
1147C2×C4—32no—
1148C2×C4—44no—
1149C2×C4—61no—
1150C2×C4—61no—
1151C2×C4—61no—
1152C2×C4—61no—
1153C2×C4—61no—
1154C2×C4—61no—
1155C2×C4—61no—
1156C2×C4—61no—
1157C2×C4—68no—
1158C2×C4—68no—
1159C2×C4—62no—
1160C2×C4—61no—
1161C2×C4—62no—
1162C2×C4—61no—
1163C2×C4—62no—
1164C2×C4—62no—
1165C2×C4—61no—
1166C2×C4—62no—
1167C2×C4—62no—
1168C2×C4—62no—
1169C2×C4—62no—
1170C2×C4—62no—
1171C2×C4—84no—
1172C2×C4—124no—
1173C2×C4—124no—
1174C2×C4—124no—
1175C2×C4—124no—
1176C2×C4—244no—
1177C2×C4—244no—
1178C2×C4—244no—
1179C2×C4C2×D3×D412yes—
1180C2×C4C2×D3×D412yes—
1181C2×C4D3×#4112yes—
1182C2×C4#100912yes—
1183C2×C3—24no—
1184C2×C3—81no—
1185C2×C3C2×#53711yescharacteristic
1186C2×C3C2×#54611yescharacteristic
1187C2×C3#348811yescharacteristic
1188C2×C3#349211yescharacteristic
1189C2×C3#349411yescharacteristic
1190C2×C3#353711yescharacteristic
1191C2×C3#354111yescharacteristic
1192D3—42no—
1193D3—42no—
1194D3—42no—
1195D3—82no—
1196C22—22no—
1197C22—22no—
1198C22—22no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—62no—
1210C22—62no—
1211C22—62no—
1212C22—62no—
1213C22—62no—
1214C22—62no—
1215C22—62no—
1216C22—62no—
1217C22—62no—
1218C22—1216no—
1219C22—121no—
1220C22—121no—
1221C22—121no—
1222C22—121no—
1223C22—121no—
1224C22—121no—
1225C22—121no—
1226C22—121no—
1227C22—121no—
1228C22—121no—
1229C22—121no—
1230C22—121no—
1231C22—122no—
1232C22—122no—
1233C22—122no—
1234C22—122no—
1235C22—122no—
1236C22—122no—
1237C22—122no—
1238C22#562914yes—
1239C22C22×D3×D411yescharacteristic
1240C22C2×#100711yescharacteristic
1241C22C2×D3×#4111yescharacteristic
1242C22C2×#100911yescharacteristic
1243C22C2×#100911yescharacteristic
1244C22D3×H(5,𝔽2)11yescharacteristic
1245C22#596611yescharacteristic
1246C4—22no—
1247C4—42no—
1248C4—42no—
1249C4—41no—
1250C4—42no—
1251C4—42no—
1252C4—41no—
1253C4—41no—
1254C4—62no—
1255C4—62no—
1256C4—62no—
1257C4—62no—
1258C4—122no—
1259C4—122no—
1260C4—122no—
1261C4—121no—
1262C4#565414yes—
1263C3#3783611yescharacteristic, complemented, Sylow
1264C2—24no—
1265C2—81no—
1266C2—122no—
1267C2—122no—
1268C2—122no—
1269C2—242no—
1270C2C2×#562911yescharacteristic
1271C2C2×#565411yescharacteristic
1272C2#8633111yescharacteristic
1273C2#8687711yescharacteristic
1274C2#8691611yescharacteristic
1275C2#8693711yescharacteristic
1276C2#8694711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2487C2
hypercenter#2487D3
hypocenterC3#37836
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2487

Complements

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

NH ≅ G/Ntype
1. C2×#5547C2semidirect
2. C2×#5514C2semidirect
3. C3×#2487C2semidirect
4. #82352C2semidirect
5. C2×#4987C2semidirect
6. #78370C2semidirect
7. #78238C2semidirect
8. #78113C2semidirect
9. #78065C2semidirect
10. #76251C2semidirect
11. #76229C2semidirect
12. #76211C2semidirect
13. #76198C2semidirect
14. #74893C2semidirect
15. #74752C2semidirect
16. #74605C2semidirect
17. #74423C2semidirect
18. #74048C2semidirect
19. #74030C2semidirect
20. #74010C2semidirect
21. #74003C2semidirect
22. #73940C2semidirect
23. #73935C2semidirect
34. C2×#930C22semidirect
42. C2×#898C22semidirect
47. C2×#895C22semidirect
49. C2×#894C22semidirect
50. C2×#893C22semidirect
51. C2×#892C22semidirect
52. C2×D3×C4⋊C4C22semidirect
53. C2×#890C22semidirect
63. C3×#400C22semidirect
64. C3×#399C22semidirect
65. C3×#389C22semidirect
66. C3×#389C22semidirect
70. C3×#380C22semidirect
71. C3×#380C22semidirect
72. #5212C22semidirect
75. #4994C22semidirect
76. #4994C22semidirect
78. #4989C22semidirect
88. #4987C22semidirect
89. #4983C22semidirect
90. #4980C22semidirect
91. #4975C22semidirect
92. Dic3×C4⋊C4C22semidirect
93. #4961C22semidirect
95. #4960C22semidirect
97. #4959C22semidirect
101. #4956C22semidirect
102. #4951C22semidirect
104. #4939C22semidirect
105. #4928C22semidirect
107. #4675C22semidirect
108. #4673C22semidirect
114. #4669C22semidirect
115. #4668C22semidirect
116. #4667C22semidirect
121. #4665C22semidirect
122. #4658C22semidirect
123. #4657C22semidirect
124. #4647C22semidirect
125. #4646C22semidirect
138. #2487D3semidirect
209. C4×#67D4semidirect
327. #400C2×D3semidirect
328. #399C2×D3semidirect
352. #389C2×D3semidirect
353. #389C2×D3semidirect
385. #380C2×D3semidirect
386. #380C2×D3semidirect
1263. C3#37836semidirect

Maximal subgroups

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

subgroupindex
C2×#55472
C2×#55142
C3×#24872
#823522
C2×#49872
#783702
#782382
#781132
#780652
#762512
#762292
#762112
#761982
#748932
#747522
#746052
#744232
#740482
#740302
#740102
#740032
#739402
#739352
#378363