Finite Group Databasebeta

← #11028613

Subgroups — #11028613

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×#5695C211yesmaximal, characteristic, complemented
2C2×#5524C211yesmaximal, characteristic, complemented
3C3×#2629C211yesmaximal, characteristic, complemented
4#83063C211yesmaximal, characteristic, complemented
5#82236C211yesmaximal, characteristic, complemented
6#77967C212yesmaximal, complemented
7#77957C212yesmaximal, complemented
8#77953C212yesmaximal, complemented
9#77851C212yesmaximal, complemented
10#77416C212yesmaximal, complemented
11#77416C212yesmaximal, complemented
12#77354C212yesmaximal, complemented
13#77348C212yesmaximal, complemented
14#76232C211yesmaximal, characteristic, complemented
15#76230C211yesmaximal, characteristic, complemented
16#76211C211yesmaximal, characteristic, complemented
17#76211C211yesmaximal, characteristic, complemented
18#74368C211yesmaximal, characteristic, complemented
19#74360C211yesmaximal, characteristic, complemented
20#74048C211yesmaximal, characteristic, complemented
21#74030C211yesmaximal, characteristic, complemented
22#74003C211yesmaximal, characteristic, complemented
23D3×#380C211yesmaximal, characteristic, complemented
24#37836—31nomaximal, Sylow
25C22×#235C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C2×C3×#125C2211yescharacteristic, complemented
28C2×C3×#117C2211yescharacteristic
29C2×#930C2211yescharacteristic
30#5695—28no—
31#5524—28no—
32C2×#898C2212yescomplemented
33C2×#897C2211yescharacteristic
34C2×#897C2211yescharacteristic
35C2×#895C2211yescharacteristic
36C2×#895C2212yes—
37C2×#895C2211yescharacteristic
38C2×#895C2211yescharacteristic
39C2×#895C2211yescharacteristic
40C2×#895C2212yes—
41C2×#895C2212yes—
42C2×#895C2212yes—
43C2×#895C2211yescharacteristic, complemented
44C2×#895C2211yescharacteristic, complemented
45C2×#894C2212yescomplemented
46C2×#893C2212yes—
47C2×#893C2212yes—
48C2×#892C2211yescharacteristic, complemented
49C2×D3×C4⋊C4C2211yescharacteristic
50C2×D3×C4⋊C4C2211yescharacteristic
51C2×D3×C4⋊C4C2211yescharacteristic, complemented
52C2×#886C2211yescharacteristic
53C2×#886C2211yescharacteristic
54C2×#882C2211yescharacteristic
55C2×#882C2211yescharacteristic
56C2×#882C2212yes—
57C2×D3×C22⋊C4C2212yes—
58C2×C4×D12C2211yescharacteristic
59C2×C4×D12C2211yescharacteristic
60C2×C4×D12C2211yescharacteristic
61C2×C4×D12C2211yescharacteristic
62C2×C4×D12C2211yescharacteristic, complemented
63C3×#398C2212yescomplemented
64C3×#398C2212yescomplemented
65C3×#396C2212yes—
66C3×#396C2212yes—
67C3×#389C2211yescharacteristic, complemented
68C3×#389C2211yescharacteristic, complemented
69C3×#384C2211yescharacteristic, complemented
70C3×#380C2211yescharacteristic
71C3×#380C2211yescharacteristic
72#5212C2211yescharacteristic
73#4994C2212yescomplemented
74#4994C2212yescomplemented
75#4993C2212yescomplemented
76#4992C2212yescomplemented
77#4991C2212yes—
78#4991C2212yes—
79#4991C2212yescomplemented
80#4990C2212yes—
81#4990C2212yes—
82#4990C2212yescomplemented
83#4990C2212yescomplemented
84#4989C2212yes—
85#4989C2212yes—
86#4989C2212yescomplemented
87#4989C2212yescomplemented
88#4987C2211yescharacteristic
89#4987C2211yescharacteristic
90#4987C2211yescharacteristic
91#4987C2211yescharacteristic
92#4987C2211yescharacteristic, complemented
93#4987C2211yescharacteristic, complemented
94#4987C2212yescomplemented
95#4987C2211yescharacteristic, complemented
96#4987C2211yescharacteristic, complemented
97#4986C2212yescomplemented
98#4972C2212yescomplemented
99#4960C2212yes—
100#4960C2212yes—
101#4958C2212yes—
102#4957C2212yes—
103#4957C2212yes—
104#4956C2212yes—
105#4956C2212yes—
106#4942C2212yes—
107#4939C2211yescharacteristic, complemented
108C4×C4⋊Dic3C2211yescharacteristic, complemented
109#4928C2211yescharacteristic, complemented
110#4673C2212yescomplemented
111#4672C2212yes—
112#4672C2212yes—
113#4672C2212yescomplemented
114#4671C2212yescomplemented
115#4667C2212yes—
116#4665C2212yes—
117#4665C2212yes—
118#4665C2212yes—
119#4665C2212yes—
120#4665C2212yescomplemented
121#4665C2212yescomplemented
122D3×#95C2212yes—
123#4660C2212yescomplemented
124#4655C2212yescomplemented
125#4646C2212yescomplemented
126C2×#553—31no—
127C2×#525—31no—
128#2847—31no—
129#2705—32no—
130#2702—32no—
131#2693—32no—
132#2671—32no—
133#2629D311yescharacteristic, complemented
134#2615—31no—
135#2562—31no—
136#2543—32no—
137#2537—31no—
138#2487—31no—
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
150C23×C3×C4C2311yescharacteristic
151C22×#67C2311yescharacteristic
152C22×#67C2311yescharacteristic
153C22×#67C2312yes—
154C23×Dic3C2311yescharacteristic
155C2×#235—24no—
156C2×#235—24no—
157C2×#235—42no—
158C22×D12C2311yescharacteristic
159C22×D12C2312yes—
160C22×D12C2311yescharacteristic
161C22×D12C2311yescharacteristic
162C22×D12C2311yescharacteristic
163C22×D12C2311yescharacteristic
164C22×D12C2311yescharacteristic
165C22×D12C2312yes—
166C22×D12C2312yes—
167C22×D12C2312yes—
168C22×C4×D3—24no—
169C22×C4×D3—24no—
170C22×C4×D3—42no—
171C22×C4×D3C2311yescharacteristic
172C22×C4×D3C2311yescharacteristic
173C22×C4×D3C2311yescharacteristic
174C22×C4×D3C2311yescharacteristic
175C22×C4×D3C2311yescharacteristic
176C22×C4×D3C2311yescharacteristic
177C22×C4×D3C2312yes—
178C22×C4×D3C2312yes—
179C22×C4×D3C2312yes—
180C22×C4×D3C2312yes—
181C22×Dic6C2311yescharacteristic
182C3×#125—24no—
183C3×#117—24no—
184C2×C3×C4⋊C4C2312yes—
185C2×C3×C4⋊C4C2311yescharacteristic
186C2×C3×C4⋊C4C2311yescharacteristic
187C2×C3×C4⋊C4C2311yescharacteristic
188C2×C3×C4⋊C4C2311yescharacteristic
189C2×C3×C4⋊C4C2311yescharacteristic
190C2×C3×C4⋊C4C2312yes—
191C2×C3×C4⋊C4C2311yescharacteristic
192C2×C3×C4⋊C4C2312yes—
193C2×C3×C4⋊C4C2312yes—
194C2×C3×C4⋊C4C2312yes—
195C2×C3×C4⋊C4C2312yes—
196C2×C3×C22⋊C4C2311yescharacteristic
197C2×C3×C22⋊C4C2311yescharacteristic
198C2×C3×C22⋊C4C2312yes—
199C2×C3×C22⋊C4C2312yes—
200C2×C3×C42C2311yescharacteristic
201C2×C3×C42C2311yescharacteristic
202C2×#217C2312yes—
203#930—24no—
204C2×(C2×D3)⋊C4C2312yes—
205C2×(C2×D3)⋊C4C2311yescharacteristic
206C2×(C2×D3)⋊C4C2312yes—
207C2×(C2×D3)⋊C4C2312yes—
208C2×(C2×D3)⋊C4C2311yescharacteristic
209C2×(C2×D3)⋊C4C2312yes—
210C2×(C2×D3)⋊C4C2312yes—
211C2×(C2×D3)⋊C4C2312yes—
212C2×(C2×D3)⋊C4C2311yescharacteristic
213C2×(C2×D3)⋊C4C2312yes—
214C2×(C2×D3)⋊C4C2311yescharacteristic
215C2×(C2×D3)⋊C4C2312yes—
216C2×(C2×D3)⋊C4C2311yescharacteristic
217C2×(C2×D3)⋊C4C2311yescharacteristic
218C2×(C2×D3)⋊C4C2312yes—
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)⋊C4C2311yescharacteristic
228C2×(C2×D3)⋊C4C2311yescharacteristic
229C2×C4⋊Dic3C2311yescharacteristic
230C2×C4⋊Dic3C2311yescharacteristic
231C2×C4⋊Dic3C2311yescharacteristic
232C2×C4⋊Dic3C2311yescharacteristic
233C2×C4⋊Dic3C2311yescharacteristic
234C2×C4⋊Dic3C2311yescharacteristic
235C2×C4⋊Dic3C2311yescharacteristic
236C2×Dic3⋊C4C2312yes—
237C2×Dic3⋊C4C2312yes—
238C2×Dic3⋊C4C2312yes—
239C2×Dic3⋊C4C2312yes—
240C2×C4×Dic3C2312yes—
241C2×C4×Dic3C2312yes—
242#898—28no—
243#897—24no—
244#897—24no—
245#895—28no—
246#895—24no—
247#895—24no—
248#895—24no—
249#895—24no—
250#895—44no—
251#895—44no—
252#895—42no—
253#895—42no—
254#895—44no—
255#894—28no—
256#893—28no—
257#893—44no—
258#892—24no—
259D3×C4⋊C4—24no—
260D3×C4⋊C4—42no—
261D3×C4⋊C4—42no—
262#886—24no—
263#886—24no—
264#882—24no—
265#882—24no—
266#882—44no—
267D3×C22⋊C4—44no—
268C4×D12—24no—
269C4×D12—24no—
270C4×D12—24no—
271C4×D12—24no—
272C4×D12D418yescomplemented
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×#125C2×D311yescharacteristic, complemented
293#525—68no—
294C2×#123—32no—
295C2×#123—31no—
296C2×#123—31no—
297C2×C22⋊Q8—31no—
298C2×C22⋊Q8—31no—
299C2×#121—31no—
300C2×#121—31no—
301C2×#121—31no—
302C2×#121—31no—
303C2×#121—31no—
304C2×#121—32no—
305C2×#121—31no—
306C2×#121—31no—
307C2×#121—32no—
308C2×#121—32no—
309C2×#121—32no—
310C2×#120—31no—
311C2×#120—31no—
312C2×#120—32no—
313C2×C4×D4—32no—
314C2×C4×D4—32no—
315C2×C4×D4—31no—
316C2×C4×D4—31no—
317C2×C4×D4—31no—
318C2×C4×D4—31no—
319C2×C4×D4—31no—
320C2×#117—31no—
321C2×#117C2×D311yescharacteristic
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#398C2×D312yescomplemented
330#398C2×D312yescomplemented
331#397—32no—
332#396—32no—
333#396—32no—
334#396C2×D312yes—
335#396C2×D312yes—
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—32no—
351#389—31no—
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#386—32no—
368#385—32no—
369#385—32no—
370#385—32no—
371#385—32no—
372#384C2×D311yescharacteristic, complemented
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—32no—
385#380C2×D311yescharacteristic
386#380C2×D311yescharacteristic
387C4×C4⋊C4—31no—
388C2×#95—32no—
389C24×C3C2411yescharacteristic
390C23×D3—22no—
391C23×D3—22no—
392C23×D3—22no—
393C23×D3—22no—
394C23×D3—22no—
395C23×D3—41no—
396C23×D3—41no—
397C23×D3C2412yes—
398C23×D3C2411yescharacteristic
399C23×D3C2411yescharacteristic
400C23×D3C2411yescharacteristic
401C23×D3C2411yescharacteristic
402C22×C3×C4—22no—
403C22×C3×C4—22no—
404C22×C3×C4#4114yes—
405C22×C3×C4C2412yes—
406C22×C3×C4C2412yes—
407C22×C3×C4C2412yes—
408C22×C3×C4C2412yes—
409C22×C3×C4C2411yescharacteristic
410C22×C3×C4C2411yescharacteristic
411C22×C3×C4C2411yescharacteristic
412C22×C3×C4C2411yescharacteristic
413C22×C3×C4C2411yescharacteristic
414C22×C3×C4C2411yescharacteristic
415C2×#67—22no—
416C2×#67—22no—
417C2×#67—22no—
418C2×#67—24no—
419C2×#67—22no—
420C2×#67—41no—
421C2×#67—41no—
422C2×#67—42no—
423C2×#67—42no—
424C22×Dic3—22no—
425C22×Dic3—22no—
426C22×Dic3—41no—
427C22×Dic3C2412yes—
428C22×Dic3C2411yescharacteristic
429C22×Dic3C2411yescharacteristic
430C22×Dic3C2412yes—
431C22×Dic3C2412yes—
432C22×Dic3C2411yescharacteristic
433C22×Dic3C2411yescharacteristic
434#235—416no—
435C2×D12—22no—
436C2×D12—22no—
437C2×D12—22no—
438C2×D12—22no—
439C2×D12—24no—
440C2×D12—22no—
441C2×D12—24no—
442C2×D12—22no—
443C2×D12—22no—
444C2×D12—22no—
445C2×D12—22no—
446C2×D12—24no—
447C2×D12—22no—
448C2×D12—22no—
449C2×D12—22no—
450C2×D12—22no—
451C2×D12—22no—
452C2×D12—24no—
453C2×D12—24no—
454C2×D12—41no—
455C2×D12—41no—
456C2×D12—41no—
457C2×D12—42no—
458C2×D12—42no—
459C2×D12—42no—
460C2×D12—42no—
461C2×D12—42no—
462C2×D12—42no—
463C2×D12—42no—
464C2×D12C2×D414yes—
465C2×C4×D3—22no—
466C2×C4×D3—22no—
467C2×C4×D3—22no—
468C2×C4×D3—22no—
469C2×C4×D3—22no—
470C2×C4×D3—22no—
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—24no—
480C2×C4×D3—24no—
481C2×C4×D3—24no—
482C2×C4×D3—416no—
483C2×C4×D3—41no—
484C2×C4×D3—41no—
485C2×C4×D3—42no—
486C2×C4×D3—42no—
487C2×C4×D3—42no—
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×D3C2×D414yes—
496C2×Dic6—22no—
497C2×Dic6—22no—
498C2×Dic6—41no—
499C3×C4⋊C4—22no—
500C3×C4⋊C4—22no—
501C3×C4⋊C4—24no—
502C3×C4⋊C4—22no—
503C3×C4⋊C4—22no—
504C3×C4⋊C4—24no—
505C3×C4⋊C4—22no—
506C3×C4⋊C4—22no—
507C3×C4⋊C4—42no—
508C3×C4⋊C4—42no—
509C3×C4⋊C4—42no—
510C3×C4⋊C4—42no—
511C3×C22⋊C4—22no—
512C3×C22⋊C4—22no—
513C3×C22⋊C4—42no—
514C3×C22⋊C4—42no—
515C3×C42—22no—
516C3×C42C2×D414yes—
517#217—42no—
518(C2×D3)⋊C4—22no—
519(C2×D3)⋊C4—22no—
520(C2×D3)⋊C4—24no—
521(C2×D3)⋊C4—24no—
522(C2×D3)⋊C4—24no—
523(C2×D3)⋊C4—24no—
524(C2×D3)⋊C4—22no—
525(C2×D3)⋊C4—22no—
526(C2×D3)⋊C4—24no—
527(C2×D3)⋊C4—24no—
528(C2×D3)⋊C4—22no—
529(C2×D3)⋊C4—22no—
530(C2×D3)⋊C4—24no—
531(C2×D3)⋊C4—24no—
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)⋊C4—42no—
540(C2×D3)⋊C4—42no—
541(C2×D3)⋊C4C2×D414yes—
542(C2×D3)⋊C4C2×D414yes—
543C4⋊Dic3—22no—
544C4⋊Dic3—22no—
545C4⋊Dic3—22no—
546C4⋊Dic3—22no—
547C4⋊Dic3—22no—
548C4⋊Dic3—22no—
549C4⋊Dic3C2×D414yes—
550Dic3⋊C4—24no—
551Dic3⋊C4—42no—
552Dic3⋊C4—42no—
553Dic3⋊C4—42no—
554C4×Dic3—24no—
555C4×Dic3—42no—
556C25—31no—
557C2×#41—64no—
558C2×#41—64no—
559C2×#41—122no—
560C22×Q8—31no—
561C22×D4—31no—
562C22×D4—31no—
563C22×D4—32no—
564C22×D4—31no—
565C22×D4—32no—
566C22×D4—31no—
567C22×D4—31no—
568C22×D4—31no—
569C22×D4—31no—
570C22×D4—31no—
571C22×D4—32no—
572C22×D4—32no—
573C22×D4—32no—
574C23×C4—31no—
575C23×C4—31no—
576C23×C4—31no—
577C23×C4—31no—
578C23×C4—31no—
579C23×C4—31no—
580C23×C4—31no—
581C23×C4—32no—
582C23×C4—32no—
583C23×C4—32no—
584C23×C4—32no—
585C23×C4—64no—
586C23×C4—64no—
587C23×C4—122no—
588C23×C4C22×D311yescharacteristic
589#126—68no—
590#125—24no—
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—64no—
600#121—68no—
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—38no—
611C4×D4—64no—
612C4×D4—64no—
613C4×D4—68no—
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—32no—
623C2×C4⋊C4—31no—
624C2×C4⋊C4—31no—
625C2×C4⋊C4—31no—
626C2×C4⋊C4—31no—
627C2×C4⋊C4—32no—
628C2×C4⋊C4—32no—
629C2×C4⋊C4—32no—
630C2×C4⋊C4—64no—
631C2×C4⋊C4—122no—
632C2×C4⋊C4—122no—
633C2×C4⋊C4C22×D311yescharacteristic
634C2×C4⋊C4C22×D311yescharacteristic
635C2×C4⋊C4C22×D311yescharacteristic
636C2×C4⋊C4C22×D311yescharacteristic
637C2×C4⋊C4C22×D311yescharacteristic
638C2×C4⋊C4C22×D311yescharacteristic
639C2×C4⋊C4C22×D312yes—
640C2×C4⋊C4C22×D312yes—
641C2×C4⋊C4C22×D312yes—
642C2×C4⋊C4C22×D312yes—
643C2×C4⋊C4C22×D312yes—
644C2×C4⋊C4C22×D312yes—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—31no—
647C2×C22⋊C4—32no—
648C2×C22⋊C4—32no—
649C2×C22⋊C4—32no—
650C2×C22⋊C4—31no—
651C2×C22⋊C4—31no—
652C2×C22⋊C4—31no—
653C2×C22⋊C4—32no—
654C2×C22⋊C4—31no—
655C2×C22⋊C4—31no—
656C2×C22⋊C4—31no—
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—32no—
671C2×C22⋊C4—124no—
672C2×C22⋊C4C22×D311yescharacteristic
673C2×C22⋊C4C22×D311yescharacteristic
674C2×C22⋊C4C22×D312yes—
675C2×C22⋊C4C22×D312yes—
676C2×C42—32no—
677C2×C42—32no—
678C2×C42C22×D311yescharacteristic
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#95—32no—
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×C3C2×#4112yes—
702C23×C3C2511yescharacteristic
703C22×D3—21no—
704C22×D3—21no—
705C22×D3—21no—
706C22×D3—21no—
707C22×D3—28no—
708C22×D3—21no—
709C22×D3—21no—
710C22×D3—21no—
711C22×D3—21no—
712C22×D3—21no—
713C22×D3—21no—
714C22×D3—21no—
715C22×D3—21no—
716C22×D3—21no—
717C22×D3—21no—
718C22×D3—21no—
719C22×D3—21no—
720C22×D3—22no—
721C22×D3—21no—
722C22×D3—22no—
723C22×D3—21no—
724C22×D3—22no—
725C22×D3—21no—
726C22×D3—21no—
727C22×D3—22no—
728C22×D3—22no—
729C22×D3—21no—
730C22×D3—22no—
731C22×D3—21no—
732C22×D3—21no—
733C22×D3—22no—
734C22×D3—44no—
735C22×D3—44no—
736C22×D3—44no—
737C22×D3—44no—
738C22×D3—44no—
739C22×D3—44no—
740C22×D3C22×D412yes—
741C22×D3C22×D412yes—
742C22×D3H(5,𝔽2)12yes—
743C22×D3H(5,𝔽2)12yes—
744C22×D32−1+412yes—
745C2×C3×C4—21no—
746C2×C3×C4—21no—
747C2×C3×C4—21no—
748C2×C3×C4—21no—
749C2×C3×C4—21no—
750C2×C3×C4—21no—
751C2×C3×C4—28no—
752C2×C3×C4—22no—
753C2×C3×C4—22no—
754C2×C3×C4—21no—
755C2×C3×C4—21no—
756C2×C3×C4—22no—
757C2×C3×C4—22no—
758C2×C3×C4—22no—
759C2×C3×C4—22no—
760C2×C3×C4—22no—
761C2×C3×C4—22no—
762C2×C3×C4—21no—
763C2×C3×C4—21no—
764C2×C3×C4—22no—
765C2×C3×C4—22no—
766C2×C3×C4—22no—
767C2×C3×C4—21no—
768C2×C3×C4—21no—
769C2×C3×C4—22no—
770C2×C3×C4C22×D412yes—
771C2×C3×C4C22×D412yes—
772C2×C3×C4C22×D412yes—
773C2×C3×C4C2×#4112yes—
774C2×C3×C4C2×#4112yes—
775C2×C3×C4H(5,𝔽2)12yes—
776#67—44no—
777#67—44no—
778#67—84no—
779C2×Dic3—21no—
780C2×Dic3—21no—
781C2×Dic3—21no—
782C2×Dic3—21no—
783C2×Dic3—22no—
784C2×Dic3—21no—
785C2×Dic3—21no—
786C2×Dic3—22no—
787C2×Dic3—21no—
788C2×Dic3—21no—
789C2×Dic3—22no—
790C2×Dic3—22no—
791C2×Dic3—22no—
792C2×Dic3—22no—
793C2×Dic3—22no—
794C2×Dic3—21no—
795C2×Dic3—21no—
796C2×Dic3—22no—
797C2×Dic3—22no—
798C2×Dic3—44no—
799C2×Dic3C22×D412yes—
800C2×Dic3C22×D412yes—
801D12—28no—
802D12—44no—
803D12—44no—
804D12—44no—
805D12—44no—
806D12—48no—
807D12—44no—
808D12—84no—
809D12—84no—
810D12—84no—
811C4×D3—28no—
812C4×D3—28no—
813C4×D3—44no—
814C4×D3—44no—
815C4×D3—44no—
816C4×D3—44no—
817C4×D3—84no—
818C4×D3—84no—
819C4×D3—84no—
820C4×D3—84no—
821Dic6—44no—
822C24—31no—
823C24—31no—
824C24—31no—
825C24—32no—
826C24—31no—
827C24—62no—
828C24—62no—
829C24—62no—
830C24—62no—
831C24—62no—
832C24—121no—
833C24—121no—
834C24C23×D311yescharacteristic
835#41—1216no—
836C2×Q8—62no—
837C2×Q8—62no—
838C2×Q8—121no—
839C2×D4—34no—
840C2×D4—62no—
841C2×D4—62no—
842C2×D4—62no—
843C2×D4—62no—
844C2×D4—64no—
845C2×D4—64no—
846C2×D4—62no—
847C2×D4—62no—
848C2×D4—62no—
849C2×D4—62no—
850C2×D4—64no—
851C2×D4—62no—
852C2×D4—64no—
853C2×D4—64no—
854C2×D4—62no—
855C2×D4—62no—
856C2×D4—62no—
857C2×D4—62no—
858C2×D4—64no—
859C2×D4—62no—
860C2×D4—62no—
861C2×D4—62no—
862C2×D4—62no—
863C2×D4—62no—
864C2×D4—121no—
865C2×D4—121no—
866C2×D4—121no—
867C2×D4—122no—
868C2×D4—122no—
869C2×D4—122no—
870C2×D4—122no—
871C2×D4—122no—
872C2×D4—122no—
873C2×D4—122no—
874C2×D4—121no—
875C2×D4—121no—
876C2×D4—122no—
877C2×D4—122no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—31no—
881C22×C4—31no—
882C22×C4—34no—
883C22×C4—34no—
884C22×C4—32no—
885C22×C4—31no—
886C22×C4—31no—
887C22×C4—32no—
888C22×C4—32no—
889C22×C4—62no—
890C22×C4—62no—
891C22×C4—64no—
892C22×C4—64no—
893C22×C4—62no—
894C22×C4—62no—
895C22×C4—62no—
896C22×C4—62no—
897C22×C4—62no—
898C22×C4—62no—
899C22×C4—62no—
900C22×C4—62no—
901C22×C4—62no—
902C22×C4—62no—
903C22×C4—62no—
904C22×C4—62no—
905C22×C4—62no—
906C22×C4—62no—
907C22×C4—64no—
908C22×C4—121no—
909C22×C4—121no—
910C22×C4—1216no—
911C22×C4—122no—
912C22×C4—122no—
913C22×C4—122no—
914C22×C4—122no—
915C22×C4—122no—
916C22×C4—122no—
917C22×C4—122no—
918C22×C4—122no—
919C22×C4—122no—
920C22×C4—121no—
921C22×C4#23914yes—
922C22×C4C23×D312yes—
923C22×C4C23×D311yescharacteristic
924C22×C4C23×D312yes—
925C22×C4C23×D312yes—
926C22×C4C23×D312yes—
927C22×C4C23×D311yescharacteristic
928C22×C4C23×D311yescharacteristic
929C22×C4C23×D311yescharacteristic
930C22×C4C23×D311yescharacteristic
931C22×C4C23×D311yescharacteristic
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—24no—
937C4⋊C4—24no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—34no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—64no—
946C4⋊C4—62no—
947C4⋊C4—62no—
948C4⋊C4—62no—
949C4⋊C4—62no—
950C4⋊C4—62no—
951C4⋊C4—62no—
952C4⋊C4—122no—
953C4⋊C4—122no—
954C4⋊C4—122no—
955C22⋊C4—22no—
956C22⋊C4—22no—
957C22⋊C4—34no—
958C22⋊C4—34no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—62no—
962C22⋊C4—62no—
963C22⋊C4—64no—
964C22⋊C4—64no—
965C22⋊C4—64no—
966C22⋊C4—64no—
967C22⋊C4—64no—
968C22⋊C4—62no—
969C22⋊C4—62no—
970C22⋊C4—64no—
971C22⋊C4—62no—
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—22no—
986C42—64no—
987C42—122no—
988C42D3×D414yes—
989C22×C3—22no—
990C22×C3—22no—
991C22×C3—22no—
992C22×C3—41no—
993C22×C3—41no—
994C22×C3—41no—
995C22×C3—41no—
996C22×C3C23×D411yescharacteristic
997C22×C3C22×#4111yescharacteristic
998C22×C3C2×H(5,𝔽2)11yescharacteristic
999C22×C3C2×H(5,𝔽2)11yescharacteristic
1000C22×C3C2×H(5,𝔽2)11yescharacteristic
1001C22×C3C2×2−1+411yescharacteristic
1002C22×C3#58511yescharacteristic
1003C2×D3—22no—
1004C2×D3—22no—
1005C2×D3—22no—
1006C2×D3—22no—
1007C2×D3—22no—
1008C2×D3—22no—
1009C2×D3—22no—
1010C2×D3—22no—
1011C2×D3—22no—
1012C2×D3—22no—
1013C2×D3—22no—
1014C2×D3—22no—
1015C2×D3—416no—
1016C2×D3—41no—
1017C2×D3—41no—
1018C2×D3—41no—
1019C2×D3—41no—
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—42no—
1035C2×D3—41no—
1036C2×D3—42no—
1037C2×D3—41no—
1038C2×D3#53714yes—
1039C3×C4—22no—
1040C3×C4—22no—
1041C3×C4—22no—
1042C3×C4—42no—
1043C3×C4—41no—
1044C3×C4—42no—
1045C3×C4—41no—
1046C3×C4—42no—
1047C3×C4—42no—
1048C3×C4#54614yes—
1049Dic3—22no—
1050Dic3—22no—
1051Dic3—41no—
1052Dic3—41no—
1053Dic3—42no—
1054Dic3—42no—
1055Dic3—42no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—32no—
1063C23—32no—
1064C23—32no—
1065C23—32no—
1066C23—32no—
1067C23—68no—
1068C23—61no—
1069C23—61no—
1070C23—61no—
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—62no—
1085C23—61no—
1086C23—62no—
1087C23—61no—
1088C23—62no—
1089C23—61no—
1090C23—61no—
1091C23—61no—
1092C23—62no—
1093C23—62no—
1094C23—62no—
1095C23—61no—
1096C23—61no—
1097C23—62no—
1098C23—124no—
1099C23—124no—
1100C23—124no—
1101C23—124no—
1102C23—124no—
1103C23—124no—
1104C23C2×#23912yes—
1105C23C24×D311yescharacteristic
1106Q8—124no—
1107D4—68no—
1108D4—124no—
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—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—28no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—21no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—32no—
1146C2×C4—32no—
1147C2×C4—61no—
1148C2×C4—61no—
1149C2×C4—61no—
1150C2×C4—61no—
1151C2×C4—68no—
1152C2×C4—68no—
1153C2×C4—62no—
1154C2×C4—61no—
1155C2×C4—61no—
1156C2×C4—62no—
1157C2×C4—61no—
1158C2×C4—61no—
1159C2×C4—61no—
1160C2×C4—61no—
1161C2×C4—62no—
1162C2×C4—62no—
1163C2×C4—62no—
1164C2×C4—62no—
1165C2×C4—62no—
1166C2×C4—62no—
1167C2×C4—62no—
1168C2×C4—124no—
1169C2×C4—124no—
1170C2×C4—124no—
1171C2×C4—124no—
1172C2×C4—124no—
1173C2×C4—244no—
1174C2×C4—244no—
1175C2×C4—244no—
1176C2×C4—244no—
1177C2×C4C2×D3×D412yes—
1178C2×C4C2×D3×D412yes—
1179C2×C4C2×D3×D412yes—
1180C2×C4C2×#23912yes—
1181C2×C4C2×#23912yes—
1182C2×C4#100912yes—
1183C2×C3—42no—
1184C2×C3C2×#53711yescharacteristic
1185C2×C3C2×#54611yescharacteristic
1186C2×C3#348811yescharacteristic
1187C2×C3#349211yescharacteristic
1188C2×C3#349411yescharacteristic
1189C2×C3#353711yescharacteristic
1190C2×C3#354111yescharacteristic
1191D3—24no—
1192D3—42no—
1193D3—42no—
1194D3—81no—
1195D3—82no—
1196C22—22no—
1197C22—22no—
1198C22—22no—
1199C22—34no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—62no—
1205C22—62no—
1206C22—62no—
1207C22—62no—
1208C22—62no—
1209C22—62no—
1210C22—62no—
1211C22—62no—
1212C22—62no—
1213C22—62no—
1214C22—62no—
1215C22—62no—
1216C22—1216no—
1217C22—121no—
1218C22—121no—
1219C22—121no—
1220C22—121no—
1221C22—121no—
1222C22—121no—
1223C22—121no—
1224C22—121no—
1225C22—122no—
1226C22—121no—
1227C22—122no—
1228C22—121no—
1229C22—122no—
1230C22—121no—
1231C22—122no—
1232C22—121no—
1233C22—122no—
1234C22—121no—
1235C22—121no—
1236C22—122no—
1237C22—122no—
1238C22—121no—
1239C22C22×D3×D411yescharacteristic
1240C22C22×#23911yescharacteristic
1241C22C2×#100911yescharacteristic
1242C22D3×H(5,𝔽2)11yescharacteristic
1243C22D3×H(5,𝔽2)11yescharacteristic
1244C22D3×2−1+411yescharacteristic
1245C22#596811yescharacteristic
1246C4—22no—
1247C4—22no—
1248C4—22no—
1249C4—41no—
1250C4—42no—
1251C4—42no—
1252C4—41no—
1253C4—42no—
1254C4—42no—
1255C4—62no—
1256C4—62no—
1257C4—122no—
1258C4—122no—
1259C4—122no—
1260C4—121no—
1261C4—121no—
1262C4#563014yes—
1263C3#3783611yescharacteristic, complemented, Sylow
1264C2—42no—
1265C2—64no—
1266C2—122no—
1267C2—122no—
1268C2—242no—
1269C2—241no—
1270C2C2×#563011yescharacteristic
1271C2D3×#53711yescharacteristic
1272C2#8637911yescharacteristic
1273C2#8649111yescharacteristic
1274C2#8651611yescharacteristic
1275C2#8659611yescharacteristic
1276C2#8659711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2629C2
hypercenter#2629D3
hypocenterC3#37836
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2629

Complements

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

NH ≅ G/Ntype
1. C2×#5695C2semidirect
2. C2×#5524C2semidirect
3. C3×#2629C2semidirect
4. #83063C2semidirect
5. #82236C2semidirect
6. #77967C2semidirect
7. #77957C2semidirect
8. #77953C2semidirect
9. #77851C2semidirect
10. #77416C2semidirect
11. #77416C2semidirect
12. #77354C2semidirect
13. #77348C2semidirect
14. #76232C2semidirect
15. #76230C2semidirect
16. #76211C2semidirect
17. #76211C2semidirect
18. #74368C2semidirect
19. #74360C2semidirect
20. #74048C2semidirect
21. #74030C2semidirect
22. #74003C2semidirect
23. D3×#380C2semidirect
27. C2×C3×#125C22semidirect
32. C2×#898C22semidirect
43. C2×#895C22semidirect
44. C2×#895C22semidirect
45. C2×#894C22semidirect
48. C2×#892C22semidirect
51. C2×D3×C4⋊C4C22semidirect
62. C2×C4×D12C22semidirect
63. C3×#398C22semidirect
64. C3×#398C22semidirect
67. C3×#389C22semidirect
68. C3×#389C22semidirect
69. C3×#384C22semidirect
73. #4994C22semidirect
74. #4994C22semidirect
75. #4993C22semidirect
76. #4992C22semidirect
79. #4991C22semidirect
82. #4990C22semidirect
83. #4990C22semidirect
86. #4989C22semidirect
87. #4989C22semidirect
92. #4987C22semidirect
93. #4987C22semidirect
94. #4987C22semidirect
95. #4987C22semidirect
96. #4987C22semidirect
97. #4986C22semidirect
98. #4972C22semidirect
107. #4939C22semidirect
108. C4×C4⋊Dic3C22semidirect
109. #4928C22semidirect
110. #4673C22semidirect
113. #4672C22semidirect
114. #4671C22semidirect
120. #4665C22semidirect
121. #4665C22semidirect
123. #4660C22semidirect
124. #4655C22semidirect
125. #4646C22semidirect
133. #2629D3semidirect
272. C4×D12D4semidirect
292. C2×#125C2×D3semidirect
329. #398C2×D3semidirect
330. #398C2×D3semidirect
352. #389C2×D3semidirect
353. #389C2×D3semidirect
372. #384C2×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×#56952
C2×#55242
C3×#26292
#830632
#822362
#779672
#779572
#779532
#778512
#774162
#773542
#773482
#762322
#762302
#762112
#743682
#743602
#740482
#740302
#740032
D3×#3802
#378363