Finite Group Databasebeta

← #11028591

Subgroups — #11028591

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×#5530C211yesmaximal, characteristic, complemented
3C3×#2485C211yesmaximal, characteristic, complemented
4#82352C211yesmaximal, characteristic, complemented
5#82270C211yesmaximal, characteristic, complemented
6#77682C212yesmaximal, complemented
7#77574C212yesmaximal, complemented
8#77130C212yesmaximal, complemented
9#77114C212yesmaximal, complemented
10#76251C211yesmaximal, characteristic, complemented
11#76232C211yesmaximal, characteristic, complemented
12#76211C211yesmaximal, characteristic, complemented
13#76198C211yesmaximal, characteristic, complemented
14#75846C212yesmaximal, complemented
15#75680C212yesmaximal, complemented
16#75322C212yesmaximal, complemented
17#75153C212yesmaximal, complemented
18#74048C211yesmaximal, characteristic, complemented
19#74030C211yesmaximal, characteristic, complemented
20#74010C211yesmaximal, characteristic, complemented
21D3×#380C211yesmaximal, characteristic, complemented
22#73941C211yesmaximal, characteristic, complemented
23#73935C211yesmaximal, characteristic, complemented
24#37836—31nomaximal, Sylow
25C22×#235C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×#117C2211yescharacteristic, complemented
29C2×#939C2211yescharacteristic
30C2×#939C2212yes—
31C2×#937C2211yescharacteristic
32C2×#930C2211yescharacteristic
33C2×#930C2211yescharacteristic, complemented
34C2×C4×#67C2211yescharacteristic
35C2×C4×#67C2211yescharacteristic
36C22×C4⋊Dic3C2211yescharacteristic, complemented
37#5547—28no—
38#5530—28no—
39C2×#896C2211yescharacteristic
40C2×#895C2211yescharacteristic
41C2×#895C2211yescharacteristic
42C2×#895C2212yes—
43C2×#895C2211yescharacteristic, complemented
44C2×#894C2211yescharacteristic
45C2×#893C2211yescharacteristic, complemented
46C2×D3×C4⋊C4C2211yescharacteristic
47C2×D3×C4⋊C4C2211yescharacteristic
48C2×#890C2211yescharacteristic, complemented
49C2×#884C2211yescharacteristic
50C2×#884C2212yes—
51C2×#884C2212yes—
52C2×#883C2211yescharacteristic
53C2×#883C2212yescomplemented
54C2×#882C2211yescharacteristic
55C2×#882C2212yes—
56C2×#67⋊C4C2212yes—
57C2×D3×C22⋊C4C2212yes—
58C2×#878C2211yescharacteristic
59C2×#876C2212yescomplemented
60C2×C4×D12C2211yescharacteristic
61C2×C4×D12C2212yes—
62C2×#872C2211yescharacteristic
63C3×#397C2212yescomplemented
64C3×#394C2212yes—
65C3×#389C2211yescharacteristic, complemented
66C3×#389C2211yescharacteristic, complemented
67C3×#388C2212yes—
68C3×#387C2212yescomplemented
69C3×#380C2211yescharacteristic
70C3×#380C2211yescharacteristic
71C3×#380C2211yescharacteristic, complemented
72#5212C2211yescharacteristic
73#4994C2212yes—
74#4994C2212yescomplemented
75#4994C2212yescomplemented
76#4993C2212yescomplemented
77#4989C2212yes—
78#4989C2212yescomplemented
79#4988C2212yes—
80#4987C2211yescharacteristic
81#4987C2211yescharacteristic
82#4987C2211yescharacteristic
83#4987C2211yescharacteristic
84#4987C2211yescharacteristic, complemented
85#4987C2211yescharacteristic, complemented
86#4987C2211yescharacteristic, complemented
87#4983C2212yescomplemented
88#4975C2211yescharacteristic, complemented
89Dic3×C4⋊C4C2211yescharacteristic, complemented
90#4961C2212yes—
91#4961C2212yes—
92#4960C2212yes—
93#4960C2212yescomplemented
94#4959C2212yes—
95#4958C2212yes—
96#4958C2212yes—
97#4958C2212yescomplemented
98#4958C2212yescomplemented
99#4946C2212yescomplemented
100#4944C2212yes—
101#4942C2212yes—
102#4939C2212yes—
103#4939C2211yescharacteristic, complemented
104#4929C2212yescomplemented
105#4928C2211yescharacteristic, complemented
106#4676C2212yes—
107#4673C2212yescomplemented
108#4672C2212yescomplemented
109#4672C2212yescomplemented
110#4671C2212yes—
111#4669C2212yescomplemented
112#4669C2212yescomplemented
113#4668C2212yes—
114#4667C2212yes—
115#4667C2212yescomplemented
116#4665C2212yes—
117#4665C2212yes—
118#4665C2212yes—
119#4665C2212yes—
120#4665C2212yes—
121D3×#95C2212yes—
122#4660C2212yescomplemented
123#4660C2212yescomplemented
124#4657C2212yescomplemented
125#4647C2212yescomplemented
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#2487—31no—
139#2485D311yescharacteristic, complemented
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
153C22×#67C2311yescharacteristic
154C22×#67C2311yescharacteristic
155C22×#67C2311yescharacteristic
156C22×#67C2311yescharacteristic
157C22×#67C2312yes—
158C22×#67C2312yes—
159C23×Dic3C2311yescharacteristic
160C23×Dic3C2312yes—
161C2×#235—24no—
162C2×#235—24no—
163C2×#235—42no—
164C22×D12C2311yescharacteristic
165C22×D12C2312yes—
166C22×D12C2311yescharacteristic
167C22×D12C2311yescharacteristic
168C22×D12C2312yes—
169C22×D12C2312yes—
170C22×C4×D3—24no—
171C22×C4×D3—24no—
172C22×C4×D3—42no—
173C22×C4×D3C2311yescharacteristic
174C22×C4×D3C2311yescharacteristic
175C22×C4×D3C2311yescharacteristic
176C22×C4×D3C2311yescharacteristic
177C22×C4×D3C2311yescharacteristic
178C22×C4×D3C2312yes—
179C22×C4×D3C2312yes—
180C22×C4×D3C2312yes—
181C22×Dic6C2311yescharacteristic
182C3×C4×D4—24no—
183C3×#117—24no—
184C2×C3×C4⋊C4C2311yescharacteristic
185C2×C3×C4⋊C4C2311yescharacteristic
186C2×C3×C4⋊C4C2311yescharacteristic
187C2×C3×C4⋊C4C2311yescharacteristic
188C2×C3×C4⋊C4C2311yescharacteristic
189C2×C3×C4⋊C4C2312yes—
190C2×C3×C4⋊C4C2312yes—
191C2×C3×C22⋊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×C3×C42C2312yes—
199C2×#217C2312yes—
200C2×#217C2311yescharacteristic
201C2×#217C2311yescharacteristic
202#939—24no—
203#939—44no—
204#937—24no—
205#930—24no—
206#930—42no—
207C4×#67—24no—
208C4×#67D418yescomplemented
209C2×(C2×D3)⋊C4C2312yes—
210C2×(C2×D3)⋊C4C2311yescharacteristic
211C2×(C2×D3)⋊C4C2311yescharacteristic
212C2×(C2×D3)⋊C4C2312yes—
213C2×(C2×D3)⋊C4C2312yes—
214C2×(C2×D3)⋊C4C2311yescharacteristic
215C2×(C2×D3)⋊C4C2312yes—
216C2×(C2×D3)⋊C4C2312yes—
217C2×(C2×D3)⋊C4C2311yescharacteristic
218C2×(C2×D3)⋊C4C2311yescharacteristic
219C2×(C2×D3)⋊C4C2312yes—
220C2×(C2×D3)⋊C4C2312yes—
221C2×(C2×D3)⋊C4C2312yes—
222C2×(C2×D3)⋊C4C2312yes—
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)⋊C4C2311yescharacteristic
230C2×C4⋊Dic3—42no—
231C2×C4⋊Dic3C2312yes—
232C2×C4⋊Dic3C2311yescharacteristic
233C2×C4⋊Dic3C2311yescharacteristic
234C2×C4⋊Dic3C2311yescharacteristic
235C2×C4⋊Dic3C2311yescharacteristic
236C2×C4⋊Dic3C2312yes—
237C2×Dic3⋊C4C2311yescharacteristic
238C2×Dic3⋊C4C2311yescharacteristic
239C2×Dic3⋊C4C2312yes—
240C2×Dic3⋊C4C2311yescharacteristic
241C2×Dic3⋊C4C2312yes—
242C2×Dic3⋊C4C2312yes—
243C2×Dic3⋊C4C2312yes—
244C2×Dic3⋊C4C2312yes—
245C2×Dic3⋊C4C2312yes—
246C2×Dic3⋊C4C2311yescharacteristic
247C2×C4×Dic3C2312yes—
248C2×C4×Dic3C2311yescharacteristic
249#896—24no—
250#895—24no—
251#895—24no—
252#895—42no—
253#895—44no—
254#894—24no—
255#893—24no—
256D3×C4⋊C4—24no—
257D3×C4⋊C4—42no—
258#890—24no—
259#884—28no—
260#884—24no—
261#884—44no—
262#883—24no—
263#883—28no—
264#882—24no—
265#882—44no—
266#67⋊C4—44no—
267D3×C22⋊C4—44no—
268#878—24no—
269#876—28no—
270C4×D12—24no—
271C4×D12—28no—
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—31no—
296C2×#123—32no—
297C2×C22⋊Q8—31no—
298C2×C22⋊Q8—31no—
299C2×#121—31no—
300C2×#121—31no—
301C2×#121—32no—
302C2×#121—31no—
303C2×#121—31no—
304C2×#121—31no—
305C2×#121—31no—
306C2×#121—32no—
307C2×#121—31no—
308C2×#121—32no—
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—32no—
317C2×C4×D4—31no—
318C2×C4×D4—32no—
319C2×C4×D4C2×D311yescharacteristic
320C2×#117—31no—
321C2×#117C2×D311yescharacteristic, complemented
322C22×C4⋊C4—31no—
323C22×C4⋊C4—31no—
324C22×C4⋊C4—31no—
325C22×C22⋊C4—32no—
326#400—32no—
327#400—32no—
328#399—32no—
329#398—32no—
330#398—32no—
331#397C2×D312yescomplemented
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#394C2×D312yes—
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#388C2×D312yes—
358#387C2×D312yescomplemented
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#385—32no—
369#385—32no—
370#385—32no—
371#385—32no—
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—31no—
381#380—32no—
382#380—32no—
383#380—32no—
384#380C2×D311yescharacteristic
385#380C2×D311yescharacteristic
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—41no—
405C22×C3×C4—22no—
406C22×C3×C4—22no—
407C22×C3×C4—22no—
408C22×C3×C4—22no—
409C22×C3×C4—22no—
410C22×C3×C4C2×D414yes—
411C22×C3×C4C2412yes—
412C22×C3×C4C2411yescharacteristic
413C22×C3×C4C2411yescharacteristic
414C22×C3×C4C2412yes—
415C22×C3×C4C2412yes—
416C22×C3×C4C2412yes—
417C22×C3×C4C2411yescharacteristic
418C22×C3×C4C2411yescharacteristic
419C22×C3×C4C2411yescharacteristic
420C2×#67—22no—
421C2×#67—22no—
422C2×#67—22no—
423C2×#67—22no—
424C2×#67—22no—
425C2×#67—22no—
426C2×#67—24no—
427C2×#67—24no—
428C2×#67—22no—
429C2×#67—22no—
430C2×#67—41no—
431C2×#67—41no—
432C2×#67—41no—
433C2×#67—42no—
434C2×#67—42no—
435C2×#67—42no—
436C2×#67—42no—
437C2×#67C2×D414yes—
438C22×Dic3—22no—
439C22×Dic3—22no—
440C22×Dic3—41no—
441C22×Dic3—42no—
442C22×Dic3—42no—
443C22×Dic3—42no—
444C22×Dic3C2411yescharacteristic
445C22×Dic3C2412yes—
446C22×Dic3C2412yes—
447C22×Dic3C2412yes—
448C22×Dic3C2411yescharacteristic
449C22×Dic3C2411yescharacteristic
450C22×Dic3C2411yescharacteristic
451C22×Dic3C2411yescharacteristic
452#235—416no—
453C2×D12—22no—
454C2×D12—24no—
455C2×D12—22no—
456C2×D12—24no—
457C2×D12—22no—
458C2×D12—22no—
459C2×D12—24no—
460C2×D12—22no—
461C2×D12—22no—
462C2×D12—22no—
463C2×D12—22no—
464C2×D12—24no—
465C2×D12—41no—
466C2×D12—42no—
467C2×D12—42no—
468C2×D12—42no—
469C2×D12—42no—
470C2×D12—42no—
471C2×C4×D3—22no—
472C2×C4×D3—22no—
473C2×C4×D3—22no—
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—24no—
483C2×C4×D3—24no—
484C2×C4×D3—24no—
485C2×C4×D3—416no—
486C2×C4×D3—41no—
487C2×C4×D3—41no—
488C2×C4×D3—42no—
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—22no—
503C3×C4⋊C4—22no—
504C3×C4⋊C4—42no—
505C3×C4⋊C4—42no—
506C3×C22⋊C4—24no—
507C3×C22⋊C4—22no—
508C3×C22⋊C4—24no—
509C3×C22⋊C4—22no—
510C3×C22⋊C4—42no—
511C3×C22⋊C4—42no—
512C3×C42—22no—
513C3×C42—24no—
514#217—24no—
515#217—22no—
516#217C2×D414yes—
517(C2×D3)⋊C4—22no—
518(C2×D3)⋊C4—24no—
519(C2×D3)⋊C4—24no—
520(C2×D3)⋊C4—22no—
521(C2×D3)⋊C4—22no—
522(C2×D3)⋊C4—22no—
523(C2×D3)⋊C4—24no—
524(C2×D3)⋊C4—24no—
525(C2×D3)⋊C4—22no—
526(C2×D3)⋊C4—24no—
527(C2×D3)⋊C4—42no—
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—24no—
547Dic3⋊C4—24no—
548Dic3⋊C4—22no—
549Dic3⋊C4—42no—
550Dic3⋊C4—42no—
551Dic3⋊C4—42no—
552Dic3⋊C4—42no—
553Dic3⋊C4C2×D414yes—
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—31no—
563C22×D4—31no—
564C22×D4—31no—
565C22×D4—32no—
566C22×D4—32no—
567C22×D4—31no—
568C22×D4—32no—
569C22×D4—31no—
570C22×D4—31no—
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—32no—
584C23×C4—64no—
585C23×C4—64no—
586C23×C4—122no—
587C23×C4C22×D311yescharacteristic
588C23×C4C22×D311yescharacteristic
589#126—68no—
590#125—64no—
591#123—64no—
592#123—68no—
593#123—64no—
594C22⋊Q8—64no—
595C22⋊Q8—64no—
596#121—64no—
597#121—68no—
598#121—64no—
599#121—64no—
600#121—64no—
601#121—64no—
602#121—124no—
603#121—124no—
604#121—122no—
605#121—124no—
606#121—122no—
607#120—64no—
608#120—64no—
609#120—124no—
610C4×D4—24no—
611C4×D4—38no—
612C4×D4—68no—
613C4×D4—64no—
614C4×D4—64no—
615C4×D4—64no—
616C4×D4—124no—
617#117—24no—
618#117—64no—
619C2×C4⋊C4—31no—
620C2×C4⋊C4—31no—
621C2×C4⋊C4—31no—
622C2×C4⋊C4—31no—
623C2×C4⋊C4—32no—
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—64no—
636C2×C4⋊C4—122no—
637C2×C4⋊C4—122no—
638C2×C4⋊C4C22×D311yescharacteristic
639C2×C4⋊C4C22×D311yescharacteristic
640C2×C4⋊C4C22×D311yescharacteristic
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—32no—
648C2×C22⋊C4—31no—
649C2×C22⋊C4—31no—
650C2×C22⋊C4—31no—
651C2×C22⋊C4—31no—
652C2×C22⋊C4—32no—
653C2×C22⋊C4—31no—
654C2×C22⋊C4—31no—
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×D311yescharacteristic
673C2×C22⋊C4C22×D311yescharacteristic
674C2×C22⋊C4C22×D312yes—
675C2×C22⋊C4C22×D312yes—
676C2×C42—31no—
677C2×C42—32no—
678C2×C42C22×D311yescharacteristic
679C2×C42C22×D312yes—
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×C3—21no—
707C23×C3C22×D412yes—
708C23×C3H(5,𝔽2)12yes—
709C23×C3C2511yescharacteristic
710C22×D3—21no—
711C22×D3—21no—
712C22×D3—21no—
713C22×D3—21no—
714C22×D3—28no—
715C22×D3—21no—
716C22×D3—21no—
717C22×D3—21no—
718C22×D3—21no—
719C22×D3—21no—
720C22×D3—21no—
721C22×D3—22no—
722C22×D3—21no—
723C22×D3—22no—
724C22×D3—21no—
725C22×D3—21no—
726C22×D3—22no—
727C22×D3—21no—
728C22×D3—22no—
729C22×D3—22no—
730C22×D3—21no—
731C22×D3—22no—
732C22×D3—21no—
733C22×D3—21no—
734C22×D3—22no—
735C22×D3—44no—
736C22×D3—44no—
737C22×D3—44no—
738C22×D3—44no—
739C22×D3—44no—
740C22×D3—44no—
741C22×D3C22×D412yes—
742C22×D3C2×#4112yes—
743C22×D3H(5,𝔽2)12yes—
744C22×D32−1+412yes—
745C3×D4—44no—
746C2×C3×C4—21no—
747C2×C3×C4—21no—
748C2×C3×C4—28no—
749C2×C3×C4—21no—
750C2×C3×C4—22no—
751C2×C3×C4—21no—
752C2×C3×C4—22no—
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×C4C22×D412yes—
772C2×C3×C4C22×D412yes—
773C2×C3×C4C2×#4112yes—
774C2×C3×C4H(5,𝔽2)12yes—
775#67—28no—
776#67—44no—
777#67—44no—
778#67—44no—
779#67—84no—
780#67—84no—
781C2×Dic3—21no—
782C2×Dic3—21no—
783C2×Dic3—21no—
784C2×Dic3—21no—
785C2×Dic3—21no—
786C2×Dic3—21no—
787C2×Dic3—21no—
788C2×Dic3—21no—
789C2×Dic3—22no—
790C2×Dic3—21no—
791C2×Dic3—21no—
792C2×Dic3—22no—
793C2×Dic3—22no—
794C2×Dic3—22no—
795C2×Dic3—22no—
796C2×Dic3—22no—
797C2×Dic3—22no—
798C2×Dic3—22no—
799C2×Dic3—21no—
800C2×Dic3—22no—
801C2×Dic3—44no—
802C2×Dic3—84no—
803C2×Dic3C22×D412yes—
804C2×Dic3C22×D412yes—
805C2×Dic3C22×D412yes—
806C2×Dic3C2×#4112yes—
807D12—44no—
808D12—44no—
809D12—48no—
810D12—44no—
811D12—84no—
812D12—84no—
813C4×D3—28no—
814C4×D3—28no—
815C4×D3—44no—
816C4×D3—44no—
817C4×D3—44no—
818C4×D3—84no—
819C4×D3—84no—
820C4×D3—84no—
821Dic6—44no—
822C24—31no—
823C24—31no—
824C24—32no—
825C24—31no—
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—34no—
842C2×D4—41no—
843C2×D4—62no—
844C2×D4—64no—
845C2×D4—64no—
846C2×D4—62no—
847C2×D4—62no—
848C2×D4—62no—
849C2×D4—64no—
850C2×D4—64no—
851C2×D4—62no—
852C2×D4—62no—
853C2×D4—62no—
854C2×D4—62no—
855C2×D4—62no—
856C2×D4—62no—
857C2×D4—62no—
858C2×D4—62no—
859C2×D4—64no—
860C2×D4—64no—
861C2×D4—62no—
862C2×D4—62no—
863C2×D4—62no—
864C2×D4—62no—
865C2×D4—121no—
866C2×D4—122no—
867C2×D4—122no—
868C2×D4—122no—
869C2×D4—122no—
870C2×D4—122no—
871C2×D4—121no—
872C2×D4—121no—
873C2×D4—121no—
874C2×D4—122no—
875C2×D4—122no—
876C2×D4—122no—
877C2×D4—122no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—31no—
884C22×C4—31no—
885C22×C4—31no—
886C22×C4—31no—
887C22×C4—34no—
888C22×C4—34no—
889C22×C4—31no—
890C22×C4—32no—
891C22×C4—32no—
892C22×C4—32no—
893C22×C4—62no—
894C22×C4—62no—
895C22×C4—64no—
896C22×C4—62no—
897C22×C4—62no—
898C22×C4—64no—
899C22×C4—64no—
900C22×C4—62no—
901C22×C4—62no—
902C22×C4—62no—
903C22×C4—62no—
904C22×C4—62no—
905C22×C4—62no—
906C22×C4—62no—
907C22×C4—62no—
908C22×C4—62no—
909C22×C4—121no—
910C22×C4—121no—
911C22×C4—122no—
912C22×C4—122no—
913C22×C4—122no—
914C22×C4—122no—
915C22×C4—122no—
916C22×C4—122no—
917C22×C4—1216no—
918C22×C4—121no—
919C22×C4—122no—
920C22×C4—122no—
921C22×C4—122no—
922C22×C4D3×D414yes—
923C22×C4C23×D312yes—
924C22×C4C23×D311yescharacteristic
925C22×C4C23×D311yescharacteristic
926C22×C4C23×D312yes—
927C22×C4C23×D312yes—
928C22×C4C23×D312yes—
929C22×C4C23×D311yescharacteristic
930C22×C4C23×D311yescharacteristic
931C22×C4C23×D311yescharacteristic
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—34no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—64no—
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—24no—
956C22⋊C4—22no—
957C22⋊C4—24no—
958C22⋊C4—22no—
959C22⋊C4—34no—
960C22⋊C4—34no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—62no—
964C22⋊C4—62no—
965C22⋊C4—62no—
966C22⋊C4—62no—
967C22⋊C4—64no—
968C22⋊C4—64no—
969C22⋊C4—64no—
970C22⋊C4—62no—
971C22⋊C4—64no—
972C22⋊C4—62no—
973C22⋊C4—64no—
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—24no—
986C42—22no—
987C42—34no—
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—41no—
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—42no—
1025C2×D3—41no—
1026C2×D3—41no—
1027C2×D3—42no—
1028C2×D3—42no—
1029C2×D3—41no—
1030C2×D3—42no—
1031C2×D3—41no—
1032C2×D3—42no—
1033C2×D3—41no—
1034C2×D3—41no—
1035C2×D3—42no—
1036C2×D3—42no—
1037C2×D3—41no—
1038C2×D3#53714yes—
1039C3×C4—22no—
1040C3×C4—41no—
1041C3×C4—42no—
1042C3×C4—41no—
1043C3×C4—42no—
1044C3×C4—41no—
1045C3×C4—42no—
1046C3×C4—42no—
1047C3×C4#54614yes—
1048Dic3—22no—
1049Dic3—22no—
1050Dic3—22no—
1051Dic3—22no—
1052Dic3—41no—
1053Dic3—42no—
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—21no—
1068C23—32no—
1069C23—32no—
1070C23—32no—
1071C23—32no—
1072C23—68no—
1073C23—61no—
1074C23—61no—
1075C23—61no—
1076C23—61no—
1077C23—61no—
1078C23—61no—
1079C23—61no—
1080C23—61no—
1081C23—61no—
1082C23—61no—
1083C23—62no—
1084C23—61no—
1085C23—62no—
1086C23—61no—
1087C23—61no—
1088C23—62no—
1089C23—62no—
1090C23—61no—
1091C23—61no—
1092C23—62no—
1093C23—61no—
1094C23—62no—
1095C23—62no—
1096C23—61no—
1097C23—124no—
1098C23—124no—
1099C23—124no—
1100C23—124no—
1101C23—124no—
1102C23—124no—
1103C23C2×D3×D412yes—
1104C23#100912yes—
1105C23C24×D311yescharacteristic
1106Q8—124no—
1107D4—44no—
1108D4—68no—
1109D4—124no—
1110D4—124no—
1111D4—128no—
1112D4—124no—
1113D4—124no—
1114D4—124no—
1115D4—124no—
1116D4—244no—
1117D4—244no—
1118D4—244no—
1119D4—244no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—28no—
1123C2×C4—21no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—21no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—21no—
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—61no—
1160C2×C4—62no—
1161C2×C4—61no—
1162C2×C4—62no—
1163C2×C4—62no—
1164C2×C4—61no—
1165C2×C4—62no—
1166C2×C4—62no—
1167C2×C4—62no—
1168C2×C4—62no—
1169C2×C4—62no—
1170C2×C4—62no—
1171C2×C4—124no—
1172C2×C4—124no—
1173C2×C4—124no—
1174C2×C4—124no—
1175C2×C4—244no—
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—42no—
1184C2×C3—42no—
1185C2×C3C2×#53711yescharacteristic
1186C2×C3C2×#54611yescharacteristic
1187C2×C3#348811yescharacteristic
1188C2×C3#349211yescharacteristic
1189C2×C3#349411yescharacteristic
1190C2×C3#353711yescharacteristic
1191C2×C3#354111yescharacteristic
1192D3—24no—
1193D3—42no—
1194D3—81no—
1195D3—82no—
1196C22—22no—
1197C22—22no—
1198C22—22no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—34no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—62no—
1212C22—62no—
1213C22—62no—
1214C22—62no—
1215C22—62no—
1216C22—62no—
1217C22—62no—
1218C22—62no—
1219C22—62no—
1220C22—1216no—
1221C22—121no—
1222C22—121no—
1223C22—121no—
1224C22—121no—
1225C22—122no—
1226C22—121no—
1227C22—122no—
1228C22—121no—
1229C22—122no—
1230C22—121no—
1231C22—121no—
1232C22—122no—
1233C22—122no—
1234C22—121no—
1235C22—122no—
1236C22—121no—
1237C22—121no—
1238C22—122no—
1239C22C22×D3×D411yescharacteristic
1240C22C2×D3×#4111yescharacteristic
1241C22C2×#100911yescharacteristic
1242C22C2×#100911yescharacteristic
1243C22#596411yescharacteristic
1244C22D3×H(5,𝔽2)11yescharacteristic
1245C22D3×2−1+411yescharacteristic
1246C4—22no—
1247C4—42no—
1248C4—41no—
1249C4—41no—
1250C4—42no—
1251C4—42no—
1252C4—42no—
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—42no—
1265C2—42no—
1266C2—64no—
1267C2—122no—
1268C2—242no—
1269C2—241no—
1270C2C2×#565411yescharacteristic
1271C2#8604111yescharacteristic
1272C2D3×#53711yescharacteristic
1273C2#8686011yescharacteristic
1274C2#8691611yescharacteristic
1275C2#8696011yescharacteristic
1276C2#8699411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2485C2
hypercenter#2485D3
hypocenterC3#37836
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2485

Complements

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

NH ≅ G/Ntype
1. C2×#5547C2semidirect
2. C2×#5530C2semidirect
3. C3×#2485C2semidirect
4. #82352C2semidirect
5. #82270C2semidirect
6. #77682C2semidirect
7. #77574C2semidirect
8. #77130C2semidirect
9. #77114C2semidirect
10. #76251C2semidirect
11. #76232C2semidirect
12. #76211C2semidirect
13. #76198C2semidirect
14. #75846C2semidirect
15. #75680C2semidirect
16. #75322C2semidirect
17. #75153C2semidirect
18. #74048C2semidirect
19. #74030C2semidirect
20. #74010C2semidirect
21. D3×#380C2semidirect
22. #73941C2semidirect
23. #73935C2semidirect
28. C2×C3×#117C22semidirect
33. C2×#930C22semidirect
36. C22×C4⋊Dic3C22semidirect
43. C2×#895C22semidirect
45. C2×#893C22semidirect
48. C2×#890C22semidirect
53. C2×#883C22semidirect
59. C2×#876C22semidirect
63. C3×#397C22semidirect
65. C3×#389C22semidirect
66. C3×#389C22semidirect
68. C3×#387C22semidirect
71. C3×#380C22semidirect
74. #4994C22semidirect
75. #4994C22semidirect
76. #4993C22semidirect
78. #4989C22semidirect
84. #4987C22semidirect
85. #4987C22semidirect
86. #4987C22semidirect
87. #4983C22semidirect
88. #4975C22semidirect
89. Dic3×C4⋊C4C22semidirect
93. #4960C22semidirect
97. #4958C22semidirect
98. #4958C22semidirect
99. #4946C22semidirect
103. #4939C22semidirect
104. #4929C22semidirect
105. #4928C22semidirect
107. #4673C22semidirect
108. #4672C22semidirect
109. #4672C22semidirect
111. #4669C22semidirect
112. #4669C22semidirect
115. #4667C22semidirect
122. #4660C22semidirect
123. #4660C22semidirect
124. #4657C22semidirect
125. #4647C22semidirect
139. #2485D3semidirect
208. C4×#67D4semidirect
321. C2×#117C2×D3semidirect
331. #397C2×D3semidirect
352. #389C2×D3semidirect
353. #389C2×D3semidirect
358. #387C2×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×#55302
C3×#24852
#823522
#822702
#776822
#775742
#771302
#771142
#762512
#762322
#762112
#761982
#758462
#756802
#753222
#751532
#740482
#740302
#740102
D3×#3802
#739412
#739352
#378363