Finite Group Databasebeta

← #11097543

Subgroups — #11097543

Order 768.

3000 conjugacy classes of subgroups.

The subgroup lattice has 1248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5704C211yesmaximal, characteristic, complemented
2C2×#5676C211yesmaximal, characteristic, complemented
3C3×#2662C211yesmaximal, characteristic, complemented
4#83112C211yesmaximal, characteristic, complemented
5#83007C211yesmaximal, characteristic, complemented
6#77428C212yesmaximal, complemented
7#77418C212yesmaximal, complemented
8#77254C211yesmaximal, characteristic, complemented
9#77250C211yesmaximal, characteristic, complemented
10#77161C211yesmaximal, characteristic, complemented
11#77108C212yesmaximal, complemented
12#77003C212yesmaximal, complemented
13#76895C211yesmaximal, characteristic, complemented
14#76871C211yesmaximal, characteristic, complemented
15#76809C211yesmaximal, characteristic, complemented
16#76762C211yesmaximal, characteristic, complemented
17D3×#392C211yesmaximal, characteristic, complemented
18#76466C212yesmaximal, complemented
19#76436C212yesmaximal, complemented
20#75846C212yesmaximal, complemented
21#75686C212yesmaximal, complemented
22#73798C211yesmaximal, characteristic, complemented
23#73770C211yesmaximal, characteristic, complemented
24#40488—31nomaximal, Sylow
25C22×#239C2211yescharacteristic, complemented
26C22×D3×D4C2211yescharacteristic
27C22×D3×D4C2212yes—
28C2×C3×#126C2211yescharacteristic, complemented
29C2×C3×#124C2211yescharacteristic, complemented
30C2×#946C2211yescharacteristic
31C2×#938C2211yescharacteristic, complemented
32C2×#938C2212yescomplemented
33#5704—28no—
34#5676—28no—
35C2×#898C2211yescharacteristic, complemented
36C2×#897C2212yescomplemented
37C2×#896C2211yescharacteristic
38C2×#895C2211yescharacteristic
39C2×#895C2211yescharacteristic, complemented
40C2×#895C2212yescomplemented
41C2×#895C2212yescomplemented
42C2×#894C2211yescharacteristic, complemented
43C2×#893C2211yescharacteristic
44C2×#885C2211yescharacteristic, complemented
45C2×#884C2211yescharacteristic, complemented
46C2×#884C2212yescomplemented
47C2×#884C2212yescomplemented
48C2×#884C2212yescomplemented
49C2×#884C2212yescomplemented
50C2×#883C2212yescomplemented
51C2×#883C2211yescharacteristic, complemented
52C2×#882C2211yescharacteristic
53C2×#882C2212yes—
54C2×#882C2211yescharacteristic
55C2×#882C2212yes—
56C2×D3×C22⋊C4C2212yes—
57C2×D3×C22⋊C4C2211yescharacteristic
58C2×D3×C22⋊C4C2212yes—
59C2×#875C2211yescharacteristic, complemented
60C2×C4×D12C2212yes—
61C2×C4×D12C2211yescharacteristic
62C2×C4×D12C2211yescharacteristic, complemented
63C3×#396C2212yescomplemented
64C3×#395C2211yescharacteristic, complemented
65C3×#394C2212yescomplemented
66C3×#394C2211yescharacteristic, complemented
67C3×#393C2211yescharacteristic, complemented
68C3×#392C2211yescharacteristic
69C3×#390C2212yescomplemented
70C3×#388C2212yescomplemented
71C3×C4×C4⋊C4C2211yescharacteristic, complemented
72#5231C2211yescharacteristic, complemented
73#5231C2211yescharacteristic, complemented
74#5223C2211yescharacteristic
75#5223C2212yes—
76#5223C2212yescomplemented
77#5223C2211yescharacteristic, complemented
78#4994C2212yescomplemented
79#4991C2211yescharacteristic, complemented
80#4989C2212yes—
81#4989C2212yescomplemented
82#4989C2212yescomplemented
83#4989C2212yescomplemented
84#4989C2212yescomplemented
85#4987C2212yes—
86#4986C2211yescharacteristic, complemented
87#4961C2212yescomplemented
88#4961C2212yescomplemented
89#4961C2212yescomplemented
90#4961C2212yescomplemented
91#4960C2211yescharacteristic
92#4960C2212yes—
93#4960C2212yescomplemented
94#4960C2212yescomplemented
95#4960C2212yescomplemented
96#4959C2212yescomplemented
97#4957C2212yescomplemented
98#4956C2212yescomplemented
99#4955C2212yes—
100#4955C2212yes—
101#4949C2211yescharacteristic, complemented
102#4949C2212yescomplemented
103#4948C2212yescomplemented
104#4948C2212yescomplemented
105#4947C2212yescomplemented
106#4939C2212yescomplemented
107#4939C2212yescomplemented
108#4936C2211yescharacteristic, complemented
109#4928C2212yescomplemented
110#4677C2211yescharacteristic, complemented
111#4677C2211yescharacteristic, complemented
112#4676C2212yescomplemented
113#4671C2211yescharacteristic
114#4671C2211yescharacteristic, complemented
115#4671C2212yescomplemented
116#4668C2212yes—
117#4667C2211yescharacteristic
118#4667C2211yescharacteristic, complemented
119#4667C2212yescomplemented
120#4665C2212yes—
121#4665C2212yescomplemented
122#4665C2212yescomplemented
123D3×#95C2211yescharacteristic
124D3×#95C2211yescharacteristic, complemented
125#4654C2212yescomplemented
126C2×#546—31no—
127C2×#538—31no—
128#2819—31no—
129#2813—31no—
130#2705—32no—
131#2682—32no—
132#2676—32no—
133#2675—32no—
134#2662D311yescharacteristic, complemented
135#2656—31no—
136#2636—31no—
137#2626—31no—
138#2615—31no—
139#2564—31no—
140#2540—31no—
141#2437—32no—
142#2430—31no—
143#2424—32no—
144#2410—32no—
145#2408—31no—
146#2408—32no—
147C2×#392—31no—
148#2349—31no—
149C24×D3C2312yes—
150C24×D3C2311yescharacteristic
151C22×C3×Q8C2311yescharacteristic
152C22×C3×D4C2312yes—
153C22×C3×D4C2311yescharacteristic
154C22×#67C2312yes—
155C22×#67C2312yes—
156C22×#67C2311yescharacteristic
157C22×#67C2312yes—
158C22×#67C2311yescharacteristic
159C22×#67C2312yes—
160C22×#67C2312yes—
161C2×#239—24no—
162C2×#239—44no—
163C2×D3×D4—24no—
164C2×D3×D4—44no—
165C2×D3×D4—44no—
166C2×D3×D4—44no—
167C2×D3×D4—44no—
168C22×D12C2311yescharacteristic
169C22×D12C2311yescharacteristic
170C22×D12C2312yes—
171C22×D12C2312yes—
172C22×D12C2311yescharacteristic
173C22×D12C2312yes—
174C22×D12C2311yescharacteristic
175C22×D12C2311yescharacteristic
176C22×D12C2311yescharacteristic
177C22×C4×D3C2312yes—
178C22×C4×D3C2312yes—
179C22×C4×D3C2312yes—
180C22×C4×D3C2311yescharacteristic
181C22×C4×D3C2312yes—
182C22×C4×D3C2311yescharacteristic
183C22×C4×D3C2311yescharacteristic
184C22×C4×D3C2311yescharacteristic
185C22×Dic6C2311yescharacteristic
186C3×#126—24no—
187C3×#124—24no—
188C2×C3×C4⋊C4C2311yescharacteristic
189C2×C3×C4⋊C4C2312yes—
190C2×C3×C4⋊C4C2311yescharacteristic
191C2×C3×C4⋊C4C2311yescharacteristic
192C2×C3×C4⋊C4C2312yes—
193C2×C3×C22⋊C4C2312yes—
194C2×C3×C22⋊C4C2312yes—
195C2×C3×C22⋊C4C2311yescharacteristic
196C2×C3×C22⋊C4C2311yescharacteristic
197C2×C3×C22⋊C4C2312yes—
198C2×C3×C22⋊C4C2311yescharacteristic
199C2×C3×C22⋊C4C2312yes—
200C2×C3×C22⋊C4C2312yes—
201C2×C3×C22⋊C4C2312yes—
202C2×C3×C42C2312yes—
203C2×C3×C42C2311yescharacteristic
204C2×#217C2311yescharacteristic
205C2×#217C2312yes—
206C2×#217C2312yes—
207C2×#217C2312yes—
208C2×#217C2312yes—
209#946—24no—
210#938—24no—
211#938—44no—
212C2×(C2×D3)⋊C4C2312yes—
213C2×(C2×D3)⋊C4C2312yes—
214C2×(C2×D3)⋊C4C2311yescharacteristic
215C2×(C2×D3)⋊C4C2311yescharacteristic
216C2×(C2×D3)⋊C4C2312yes—
217C2×(C2×D3)⋊C4C2312yes—
218C2×(C2×D3)⋊C4C2311yescharacteristic
219C2×(C2×D3)⋊C4C2311yescharacteristic
220C2×(C2×D3)⋊C4C2311yescharacteristic
221C2×(C2×D3)⋊C4C2311yescharacteristic
222C2×(C2×D3)⋊C4C2311yescharacteristic
223C2×(C2×D3)⋊C4C2312yes—
224C2×(C2×D3)⋊C4C2311yescharacteristic
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)⋊C4C2312yes—
233C2×(C2×D3)⋊C4C2311yescharacteristic
234C2×(C2×D3)⋊C4C2311yescharacteristic
235C2×C4⋊Dic3C2312yes—
236C2×C4⋊Dic3C2311yescharacteristic
237C2×C4⋊Dic3C2312yes—
238C2×C4⋊Dic3C2312yes—
239C2×C4⋊Dic3C2311yescharacteristic
240C2×Dic3⋊C4C2312yes—
241C2×Dic3⋊C4C2311yescharacteristic
242C2×Dic3⋊C4C2311yescharacteristic
243C2×Dic3⋊C4C2312yes—
244C2×Dic3⋊C4C2312yes—
245C2×Dic3⋊C4C2312yes—
246C2×C4×Dic3C2311yescharacteristic
247#898—24no—
248#897—44no—
249#896—24no—
250#895—24no—
251#895—24no—
252#895—44no—
253#895—44no—
254#894—24no—
255#893—24no—
256#885—24no—
257#884—24no—
258#884—28no—
259#884—44no—
260#884—44no—
261#884—44no—
262#883—28no—
263#883—24no—
264#882—28no—
265#882—24no—
266#882—24no—
267#882—44no—
268D3×C22⋊C4—24no—
269D3×C22⋊C4—28no—
270D3×C22⋊C4—44no—
271#875—24no—
272C4×D12—24no—
273C4×D12—44no—
274C4×D12D418yescomplemented
275C3×#95C2312yes—
276C3×#95C2311yescharacteristic
277C3×#95C2311yescharacteristic
278C3×#95C2312yes—
279C3⋊#95C2312yes—
280C3⋊#95C2312yes—
281C3⋊#95C2312yes—
282C3⋊#95C2311yescharacteristic
283C3⋊#95C2312yes—
284C3⋊#95C2311yescharacteristic
285C3⋊#95C2312yes—
286C3⋊#95C2312yes—
287C3⋊#95C2312yes—
288C22×#41—31no—
289C23×D4—31no—
290C23×D4—32no—
291#546—68no—
292#538—68no—
293C2×#126—31no—
294C2×#126C2×D311yescharacteristic, complemented
295C2×#124—31no—
296C2×#124—31no—
297C2×#124C2×D311yescharacteristic, complemented
298C2×#123—31no—
299C2×#123—31no—
300C2×#123—32no—
301C2×C22⋊Q8—31no—
302C2×C22⋊Q8—31no—
303C2×C22⋊Q8—32no—
304C2×#121—31no—
305C2×#121—32no—
306C2×#121—31no—
307C2×#121—31no—
308C2×#121—32no—
309C2×#121—32no—
310C2×#121—31no—
311C2×#121—32no—
312C2×#121—32no—
313C2×#121—32no—
314C2×#121—32no—
315C2×#120—31no—
316C2×#120—32no—
317C2×#120—31no—
318C2×#120—32no—
319C2×C4×D4—31no—
320C2×C4×D4—31no—
321C2×C4×D4—31no—
322C2×C4×D4—32no—
323C22×C22⋊C4—31no—
324C22×C22⋊C4—32no—
325C22×C22⋊C4—32no—
326#400—31no—
327#399—31no—
328#399—32no—
329#399—31no—
330#399—31no—
331#396—32no—
332#396—32no—
333#396—32no—
334#396—32no—
335#396C2×D312yescomplemented
336#395C2×D311yescharacteristic, complemented
337#394—31no—
338#394—32no—
339#394—32no—
340#394—32no—
341#394—32no—
342#394—32no—
343#394C2×D311yescharacteristic, complemented
344#394C2×D312yescomplemented
345#393—31no—
346#393—31no—
347#393—32no—
348#393C2×D311yescharacteristic, complemented
349#392—31no—
350#392—31no—
351#392—32no—
352#392—32no—
353#392—32no—
354#392—31no—
355#392—32no—
356#392—32no—
357#392—32no—
358#392—31no—
359#392—32no—
360#392—31no—
361#392C2×D311yescharacteristic
362#390—32no—
363#390—32no—
364#390—32no—
365#390C2×D312yescomplemented
366#389—32no—
367#388C2×D312yescomplemented
368#387—32no—
369#386—32no—
370#386—32no—
371#386—32no—
372#386—32no—
373#385—32no—
374#385—32no—
375#385—32no—
376#385—32no—
377#385—32no—
378#385—32no—
379#382—31no—
380#380—32no—
381#380—31no—
382#380—31no—
383#380—32no—
384#379—32no—
385#379—32no—
386C4×C4⋊C4C2×D311yescharacteristic, complemented
387C2×#95—31no—
388C2×#95—31no—
389C24×C3C2411yescharacteristic
390C24×C3C2412yes—
391C23×D3—24no—
392C23×D3—22no—
393C23×D3—24no—
394C23×D3—24no—
395C23×D3—24no—
396C23×D3—22no—
397C23×D3—22no—
398C23×D3—42no—
399C23×D3—42no—
400C23×D3—42no—
401C23×D3—42no—
402C23×D3—42no—
403C23×D3C2411yescharacteristic
404C23×D3C2411yescharacteristic
405C23×D3C2411yescharacteristic
406C23×D3C2412yes—
407C23×D3C2411yescharacteristic
408C2×C3×Q8—22no—
409C2×C3×Q8—42no—
410C2×C3×D4—22no—
411C2×C3×D4—24no—
412C2×C3×D4—42no—
413C2×C3×D4—42no—
414C2×C3×D4—42no—
415C22×C3×C4C2411yescharacteristic
416C22×C3×C4C2412yes—
417C22×C3×C4C2411yescharacteristic
418C22×C3×C4C2411yescharacteristic
419C22×C3×C4C2412yes—
420C22×C3×C4C2411yescharacteristic
421C22×C3×C4C2411yescharacteristic
422C22×C3×C4C2411yescharacteristic
423C22×C3×C4C2412yes—
424C2×#67—24no—
425C2×#67—24no—
426C2×#67—22no—
427C2×#67—24no—
428C2×#67—24no—
429C2×#67—22no—
430C2×#67—42no—
431C2×#67—42no—
432C2×#67—42no—
433C2×#67—42no—
434C2×#67—42no—
435C2×#67—42no—
436C2×#67—42no—
437C2×#67—42no—
438C2×#67—42no—
439C2×#67—42no—
440C2×#67—42no—
441C2×#67—42no—
442C2×#67—42no—
443C22×Dic3C2412yes—
444C22×Dic3C2412yes—
445C22×Dic3C2411yescharacteristic
446C22×Dic3C2412yes—
447C22×Dic3C2411yescharacteristic
448C22×Dic3C2411yescharacteristic
449C22×Dic3C2411yescharacteristic
450#239—416no—
451D3×D4—416no—
452D3×D4—432no—
453C2×D12—22no—
454C2×D12—24no—
455C2×D12—22no—
456C2×D12—22no—
457C2×D12—24no—
458C2×D12—22no—
459C2×D12—22no—
460C2×D12—24no—
461C2×D12—24no—
462C2×D12—22no—
463C2×D12—24no—
464C2×D12—22no—
465C2×D12—22no—
466C2×D12—24no—
467C2×D12—22no—
468C2×D12—42no—
469C2×D12—42no—
470C2×D12—42no—
471C2×D12—42no—
472C2×D12—42no—
473C2×D12—42no—
474C2×D12—42no—
475C2×D12C2×D414yes—
476C2×C4×D3—24no—
477C2×C4×D3—24no—
478C2×C4×D3—24no—
479C2×C4×D3—24no—
480C2×C4×D3—22no—
481C2×C4×D3—24no—
482C2×C4×D3—24no—
483C2×C4×D3—22no—
484C2×C4×D3—42no—
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×D414yescomplemented
496C2×Dic6—22no—
497C2×Dic6—42no—
498C3×C4⋊C4—22no—
499C3×C4⋊C4—22no—
500C3×C4⋊C4—22no—
501C3×C4⋊C4—24no—
502C3×C4⋊C4—42no—
503C3×C22⋊C4—24no—
504C3×C22⋊C4—22no—
505C3×C22⋊C4—24no—
506C3×C22⋊C4—22no—
507C3×C22⋊C4—22no—
508C3×C22⋊C4—24no—
509C3×C22⋊C4—42no—
510C3×C22⋊C4—42no—
511C3×C22⋊C4—42no—
512C3×C42—42no—
513C3×C42C2×D414yescomplemented
514#217—22no—
515#217—24no—
516#217—42no—
517#217—42no—
518#217—42no—
519(C2×D3)⋊C4—24no—
520(C2×D3)⋊C4—22no—
521(C2×D3)⋊C4—22no—
522(C2×D3)⋊C4—24no—
523(C2×D3)⋊C4—24no—
524(C2×D3)⋊C4—24no—
525(C2×D3)⋊C4—22no—
526(C2×D3)⋊C4—22no—
527(C2×D3)⋊C4—22no—
528(C2×D3)⋊C4—22no—
529(C2×D3)⋊C4—24no—
530(C2×D3)⋊C4—24no—
531(C2×D3)⋊C4—22no—
532(C2×D3)⋊C4—22no—
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)⋊C4C2×D414yes—
541(C2×D3)⋊C4C2×D414yescomplemented
542C4⋊Dic3—22no—
543C4⋊Dic3—24no—
544C4⋊Dic3—42no—
545C4⋊Dic3—42no—
546C4⋊Dic3C2×D414yescomplemented
547Dic3⋊C4—24no—
548Dic3⋊C4—22no—
549Dic3⋊C4—22no—
550Dic3⋊C4—42no—
551Dic3⋊C4—42no—
552Dic3⋊C4—42no—
553C4×Dic3—22no—
554C25—32no—
555C25—31no—
556C2×#41—64no—
557C2×#41—124no—
558C22×Q8—31no—
559C22×Q8C22×D311yescharacteristic
560C22×D4—32no—
561C22×D4—32no—
562C22×D4—31no—
563C22×D4—31no—
564C22×D4—32no—
565C22×D4—32no—
566C22×D4—32no—
567C22×D4—31no—
568C22×D4—31no—
569C22×D4—31no—
570C22×D4—32no—
571C22×D4—32no—
572C22×D4—31no—
573C22×D4—31no—
574C22×D4—32no—
575C22×D4—31no—
576C22×D4—64no—
577C22×D4—124no—
578C22×D4—124no—
579C22×D4—124no—
580C22×D4—124no—
581C22×D4C22×D311yescharacteristic
582C22×D4C22×D312yes—
583C23×C4—31no—
584C23×C4—31no—
585C23×C4—32no—
586C23×C4—32no—
587C23×C4—31no—
588C23×C4—32no—
589C23×C4—31no—
590C23×C4—32no—
591#126—24no—
592#126—64no—
593#124—24no—
594#124—64no—
595#124—64no—
596#123—64no—
597#123—68no—
598#123—64no—
599C22⋊Q8—64no—
600C22⋊Q8—64no—
601C22⋊Q8—124no—
602#121—68no—
603#121—64no—
604#121—64no—
605#121—64no—
606#121—64no—
607#121—124no—
608#121—124no—
609#121—124no—
610#121—124no—
611#121—124no—
612#121—124no—
613#120—64no—
614#120—64no—
615#120—68no—
616#120—124no—
617C4×D4—38no—
618C4×D4—64no—
619C4×D4—64no—
620C4×D4—124no—
621C2×C4⋊C4—31no—
622C2×C4⋊C4—31no—
623C2×C4⋊C4—32no—
624C2×C4⋊C4—31no—
625C2×C4⋊C4—32no—
626C2×C4⋊C4—31no—
627C2×C4⋊C4—32no—
628C2×C4⋊C4—32no—
629C2×C4⋊C4—32no—
630C2×C4⋊C4—32no—
631C2×C4⋊C4—32no—
632C2×C4⋊C4C22×D311yescharacteristic
633C2×C4⋊C4C22×D311yescharacteristic
634C2×C4⋊C4C22×D312yes—
635C2×C4⋊C4C22×D311yescharacteristic
636C2×C4⋊C4C22×D312yes—
637C2×C22⋊C4—31no—
638C2×C22⋊C4—31no—
639C2×C22⋊C4—32no—
640C2×C22⋊C4—31no—
641C2×C22⋊C4—32no—
642C2×C22⋊C4—31no—
643C2×C22⋊C4—32no—
644C2×C22⋊C4—31no—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—32no—
647C2×C22⋊C4—32no—
648C2×C22⋊C4—31no—
649C2×C22⋊C4—31no—
650C2×C22⋊C4—31no—
651C2×C22⋊C4—32no—
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—68no—
666C2×C22⋊C4—64no—
667C2×C22⋊C4—124no—
668C2×C22⋊C4C22×D312yes—
669C2×C22⋊C4C22×D311yescharacteristic
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×C22⋊C4C22×D312yes—
677C2×C42—31no—
678C2×C42C22×D312yes—
679C2×C42C22×D311yescharacteristic
680#95—31no—
681#95—31no—
682#95—32no—
683#95—32no—
684#95—32no—
685#95—32no—
686#95—32no—
687#95—32no—
688#95—32no—
689#95C22×D311yescharacteristic
690#95C22×D311yescharacteristic
691#95C22×D312yes—
692#95C22×D312yes—
693C23×C3—21no—
694C23×C3—22no—
695C23×C3—22no—
696C23×C3—22no—
697C23×C3—22no—
698C23×C3—22no—
699C23×C3—22no—
700C23×C3—22no—
701C23×C3—21no—
702C23×C3—22no—
703C23×C3—22no—
704C23×C3—21no—
705C23×C3C2511yescharacteristic
706C22×D3—22no—
707C22×D3—22no—
708C22×D3—22no—
709C22×D3—22no—
710C22×D3—21no—
711C22×D3—22no—
712C22×D3—22no—
713C22×D3—22no—
714C22×D3—22no—
715C22×D3—22no—
716C22×D3—21no—
717C22×D3—22no—
718C22×D3—21no—
719C22×D3—21no—
720C22×D3—22no—
721C22×D3—22no—
722C22×D3—22no—
723C22×D3—22no—
724C22×D3—21no—
725C22×D3—21no—
726C22×D3—21no—
727C22×D3—21no—
728C22×D3—48no—
729C22×D3—48no—
730C22×D3—48no—
731C22×D3—48no—
732C22×D3—48no—
733C22×D3—44no—
734C22×D3—82no—
735C22×D3—84no—
736C22×D3—82no—
737C22×D3—84no—
738C22×D3—84no—
739C22×D3—84no—
740C22×D3C22×D412yes—
741C22×D3C22×D412yes—
742C22×D3H(5,𝔽2)14yes—
743C22×D3H(5,𝔽2)12yes—
744C22×D32−1+412yes—
745C3×Q8—44no—
746C3×D4—44no—
747C3×D4—48no—
748C2×C3×C4—21no—
749C2×C3×C4—22no—
750C2×C3×C4—22no—
751C2×C3×C4—22no—
752C2×C3×C4—22no—
753C2×C3×C4—21no—
754C2×C3×C4—21no—
755C2×C3×C4—22no—
756C2×C3×C4—21no—
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—22no—
765C2×C3×C4—22no—
766C2×C3×C4—21no—
767C2×C3×C4C22×D412yes—
768C2×C3×C4C22×D412yes—
769C2×C3×C4C22×D412yes—
770C2×C3×C4H(5,𝔽2)14yes—
771#67—48no—
772#67—48no—
773#67—48no—
774#67—82no—
775#67—82no—
776#67—84no—
777#67—84no—
778C2×Dic3—22no—
779C2×Dic3—22no—
780C2×Dic3—21no—
781C2×Dic3—22no—
782C2×Dic3—21no—
783C2×Dic3—22no—
784C2×Dic3—22no—
785C2×Dic3—22no—
786C2×Dic3—22no—
787C2×Dic3—22no—
788C2×Dic3—22no—
789C2×Dic3—22no—
790C2×Dic3—22no—
791C2×Dic3—22no—
792C2×Dic3—22no—
793C2×Dic3C22×D412yes—
794C2×Dic3C22×D412yes—
795D12—28no—
796D12—28no—
797D12—48no—
798D12—48no—
799D12—44no—
800D12—82no—
801D12—82no—
802D12—82no—
803D12—84no—
804C4×D3—44no—
805C4×D3—44no—
806C4×D3—48no—
807C4×D3—48no—
808C4×D3—82no—
809C4×D3—84no—
810C4×D3—84no—
811C4×D3—82no—
812Dic6—82no—
813C24—31no—
814C24—32no—
815C24—31no—
816C24—31no—
817C24—31no—
818C24—62no—
819C24—64no—
820C24—64no—
821C24—64no—
822C24—64no—
823C24—62no—
824C24—62no—
825C24—122no—
826C24—122no—
827C24—122no—
828C24—122no—
829C24—122no—
830C24C23×D311yescharacteristic
831C24C23×D312yes—
832#41—1216no—
833C2×Q8—22no—
834C2×Q8—42no—
835C2×Q8—62no—
836C2×Q8—122no—
837C2×D4—22no—
838C2×D4—24no—
839C2×D4—34no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—62no—
844C2×D4—64no—
845C2×D4—62no—
846C2×D4—62no—
847C2×D4—64no—
848C2×D4—62no—
849C2×D4—64no—
850C2×D4—64no—
851C2×D4—62no—
852C2×D4—62no—
853C2×D4—62no—
854C2×D4—64no—
855C2×D4—64no—
856C2×D4—62no—
857C2×D4—64no—
858C2×D4—64no—
859C2×D4—64no—
860C2×D4—62no—
861C2×D4—62no—
862C2×D4—62no—
863C2×D4—64no—
864C2×D4—122no—
865C2×D4—122no—
866C2×D4—122no—
867C2×D4—122no—
868C2×D4—122no—
869C2×D4—122no—
870C2×D4—122no—
871C2×D4—122no—
872C2×D4—122no—
873C2×D4—122no—
874C2×D4—122no—
875C2×D4—122no—
876C2×D4—122no—
877C2×D4—122no—
878C2×D4—122no—
879C2×D4—122no—
880C2×D4—122no—
881C2×D4—122no—
882C2×D4—122no—
883C2×D4—122no—
884C2×D4—1216no—
885C2×D4—1232no—
886C22×C4—31no—
887C22×C4—31no—
888C22×C4—34no—
889C22×C4—34no—
890C22×C4—32no—
891C22×C4—32no—
892C22×C4—31no—
893C22×C4—31no—
894C22×C4—32no—
895C22×C4—64no—
896C22×C4—62no—
897C22×C4—64no—
898C22×C4—64no—
899C22×C4—62no—
900C22×C4—64no—
901C22×C4—64no—
902C22×C4—64no—
903C22×C4—122no—
904C22×C4—122no—
905C22×C4—122no—
906C22×C4—122no—
907C22×C4—122no—
908C22×C4—122no—
909C22×C4—122no—
910C22×C4—122no—
911C22×C4—122no—
912C22×C4—122no—
913C22×C4C23×D311yescharacteristic
914C22×C4C23×D312yes—
915C22×C4C23×D311yescharacteristic
916C22×C4C23×D312yes—
917C22×C4C23×D311yescharacteristic
918C22×C4C23×D311yescharacteristic
919C22×C4C23×D311yescharacteristic
920C22×C4C23×D311yescharacteristic
921C22×C4C23×D312yes—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—24no—
926C4⋊C4—34no—
927C4⋊C4—42no—
928C4⋊C4—64no—
929C4⋊C4—62no—
930C4⋊C4—62no—
931C4⋊C4—62no—
932C4⋊C4—64no—
933C4⋊C4—122no—
934C4⋊C4—122no—
935C4⋊C4—122no—
936C4⋊C4—122no—
937C4⋊C4—122no—
938C22⋊C4—24no—
939C22⋊C4—22no—
940C22⋊C4—24no—
941C22⋊C4—22no—
942C22⋊C4—22no—
943C22⋊C4—24no—
944C22⋊C4—34no—
945C22⋊C4—34no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—62no—
950C22⋊C4—62no—
951C22⋊C4—64no—
952C22⋊C4—62no—
953C22⋊C4—64no—
954C22⋊C4—62no—
955C22⋊C4—64no—
956C22⋊C4—64no—
957C22⋊C4—62no—
958C22⋊C4—62no—
959C22⋊C4—64no—
960C22⋊C4—62no—
961C22⋊C4—62no—
962C22⋊C4—62no—
963C22⋊C4—64no—
964C22⋊C4—64no—
965C22⋊C4—122no—
966C22⋊C4—122no—
967C22⋊C4—122no—
968C22⋊C4—122no—
969C22⋊C4—122no—
970C22⋊C4—122no—
971C22⋊C4—122no—
972C22⋊C4—122no—
973C22⋊C4—122no—
974C22⋊C4—122no—
975C42—42no—
976C42—62no—
977C42D3×D414yescomplemented
978C22×C3—41no—
979C22×C3—42no—
980C22×C3—42no—
981C22×C3—41no—
982C22×C3—41no—
983C22×C3—42no—
984C22×C3—42no—
985C22×C3—42no—
986C22×C3—42no—
987C22×C3—42no—
988C22×C3—42no—
989C22×C3—42no—
990C22×C3C23×D411yescharacteristic
991C22×C3C2×H(5,𝔽2)12yes—
992C22×C3C2×H(5,𝔽2)11yescharacteristic
993C22×C3C2×H(5,𝔽2)12yes—
994C22×C3C2×2−1+411yescharacteristic
995C2×D3—22no—
996C2×D3—22no—
997C2×D3—24no—
998C2×D3—24no—
999C2×D3—22no—
1000C2×D3—24no—
1001C2×D3—22no—
1002C2×D3—22no—
1003C2×D3—24no—
1004C2×D3—24no—
1005C2×D3—42no—
1006C2×D3—42no—
1007C2×D3—42no—
1008C2×D3—42no—
1009C2×D3—42no—
1010C2×D3—42no—
1011C2×D3—41no—
1012C2×D3—41no—
1013C2×D3—41no—
1014C2×D3—41no—
1015C2×D3—41no—
1016C2×D3—41no—
1017C2×D3—42no—
1018C2×D3—42no—
1019C2×D3—42no—
1020C2×D3—42no—
1021C2×D3—816no—
1022C2×D3—88no—
1023C2×D3#53714yes—
1024C3×C4—22no—
1025C3×C4—22no—
1026C3×C4—22no—
1027C3×C4—24no—
1028C3×C4—41no—
1029C3×C4—42no—
1030C3×C4—41no—
1031C3×C4—41no—
1032C3×C4—42no—
1033Dic3—22no—
1034Dic3—22no—
1035Dic3—41no—
1036Dic3—41no—
1037Dic3—42no—
1038Dic3—42no—
1039Dic3—42no—
1040C23—21no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—21no—
1050C23—22no—
1051C23—21no—
1052C23—32no—
1053C23—32no—
1054C23—32no—
1055C23—32no—
1056C23—34no—
1057C23—62no—
1058C23—62no—
1059C23—62no—
1060C23—62no—
1061C23—62no—
1062C23—62no—
1063C23—61no—
1064C23—62no—
1065C23—62no—
1066C23—62no—
1067C23—61no—
1068C23—62no—
1069C23—61no—
1070C23—61no—
1071C23—62no—
1072C23—62no—
1073C23—62no—
1074C23—62no—
1075C23—61no—
1076C23—61no—
1077C23—61no—
1078C23—61no—
1079C23—128no—
1080C23—124no—
1081C23—128no—
1082C23—128no—
1083C23—128no—
1084C23—128no—
1085C23—244no—
1086C23—244no—
1087C23—242no—
1088C23—244no—
1089C23—244no—
1090C23—242no—
1091C23C24×D311yescharacteristic
1092Q8—44no—
1093Q8—242no—
1094D4—44no—
1095D4—48no—
1096D4—68no—
1097D4—68no—
1098D4—128no—
1099D4—124no—
1100D4—128no—
1101D4—128no—
1102D4—128no—
1103D4—128no—
1104D4—242no—
1105D4—242no—
1106D4—244no—
1107D4—242no—
1108D4—242no—
1109D4—244no—
1110D4—242no—
1111D4—244no—
1112C2×C4—22no—
1113C2×C4—21no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—21no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—21no—
1131C2×C4—32no—
1132C2×C4—32no—
1133C2×C4—62no—
1134C2×C4—62no—
1135C2×C4—61no—
1136C2×C4—61no—
1137C2×C4—62no—
1138C2×C4—62no—
1139C2×C4—62no—
1140C2×C4—62no—
1141C2×C4—62no—
1142C2×C4—62no—
1143C2×C4—62no—
1144C2×C4—62no—
1145C2×C4—62no—
1146C2×C4—62no—
1147C2×C4—62no—
1148C2×C4—124no—
1149C2×C4—124no—
1150C2×C4—128no—
1151C2×C4—128no—
1152C2×C4—244no—
1153C2×C4—244no—
1154C2×C4—242no—
1155C2×C4—242no—
1156C2×C4C2×D3×D412yes—
1157C2×C4C2×D3×D412yes—
1158C2×C4C2×D3×D412yes—
1159C2×C4#100914yes—
1160C2×C3—82no—
1161C2×C3—81no—
1162C2×C3C2×#53711yescharacteristic
1163C2×C3#348411yescharacteristic
1164C2×C3#349811yescharacteristic
1165C2×C3#353212yes—
1166C2×C3#353612yes—
1167D3—24no—
1168D3—42no—
1169D3—44no—
1170D3—81no—
1171D3—81no—
1172C22—34no—
1173C22—42no—
1174C22—42no—
1175C22—42no—
1176C22—42no—
1177C22—41no—
1178C22—41no—
1179C22—42no—
1180C22—42no—
1181C22—42no—
1182C22—42no—
1183C22—41no—
1184C22—42no—
1185C22—64no—
1186C22—62no—
1187C22—64no—
1188C22—62no—
1189C22—64no—
1190C22—64no—
1191C22—62no—
1192C22—62no—
1193C22—64no—
1194C22—62no—
1195C22—122no—
1196C22—122no—
1197C22—122no—
1198C22—122no—
1199C22—122no—
1200C22—122no—
1201C22—122no—
1202C22—122no—
1203C22—121no—
1204C22—121no—
1205C22—121no—
1206C22—121no—
1207C22—122no—
1208C22—122no—
1209C22—121no—
1210C22—121no—
1211C22—2416no—
1212C22—248no—
1213C22C22×D3×D411yescharacteristic
1214C22C2×#100912yes—
1215C22D3×H(5,𝔽2)12yes—
1216C22D3×H(5,𝔽2)11yescharacteristic
1217C22D3×2−1+411yescharacteristic
1218C4—22no—
1219C4—22no—
1220C4—24no—
1221C4—22no—
1222C4—42no—
1223C4—41no—
1224C4—41no—
1225C4—42no—
1226C4—41no—
1227C4—62no—
1228C4—62no—
1229C4—122no—
1230C4—122no—
1231C4—122no—
1232C4—121no—
1233C4—121no—
1234C3#4048811yescharacteristic, complemented, Sylow
1235C2—64no—
1236C2—82no—
1237C2—81no—
1238C2—124no—
1239C2—122no—
1240C2—241no—
1241C2—241no—
1242C2#8624211yescharacteristic
1243C2#8633011yescharacteristic
1244C2D3×#53711yescharacteristic
1245C2#8641812yes—
1246C2#8656112yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2662C2
hypercenter#2662D3
hypocenterC3#40488
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2662

Complements

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

NH ≅ G/Ntype
1. C2×#5704C2semidirect
2. C2×#5676C2semidirect
3. C3×#2662C2semidirect
4. #83112C2semidirect
5. #83007C2semidirect
6. #77428C2semidirect
7. #77418C2semidirect
8. #77254C2semidirect
9. #77250C2semidirect
10. #77161C2semidirect
11. #77108C2semidirect
12. #77003C2semidirect
13. #76895C2semidirect
14. #76871C2semidirect
15. #76809C2semidirect
16. #76762C2semidirect
17. D3×#392C2semidirect
18. #76466C2semidirect
19. #76436C2semidirect
20. #75846C2semidirect
21. #75686C2semidirect
22. #73798C2semidirect
23. #73770C2semidirect
25. C22×#239C22semidirect
28. C2×C3×#126C22semidirect
29. C2×C3×#124C22semidirect
31. C2×#938C22semidirect
32. C2×#938C22semidirect
35. C2×#898C22semidirect
36. C2×#897C22semidirect
39. C2×#895C22semidirect
40. C2×#895C22semidirect
41. C2×#895C22semidirect
42. C2×#894C22semidirect
44. C2×#885C22semidirect
45. C2×#884C22semidirect
46. C2×#884C22semidirect
47. C2×#884C22semidirect
48. C2×#884C22semidirect
49. C2×#884C22semidirect
50. C2×#883C22semidirect
51. C2×#883C22semidirect
59. C2×#875C22semidirect
62. C2×C4×D12C22semidirect
63. C3×#396C22semidirect
64. C3×#395C22semidirect
65. C3×#394C22semidirect
66. C3×#394C22semidirect
67. C3×#393C22semidirect
69. C3×#390C22semidirect
70. C3×#388C22semidirect
71. C3×C4×C4⋊C4C22semidirect
72. #5231C22semidirect
73. #5231C22semidirect
76. #5223C22semidirect
77. #5223C22semidirect
78. #4994C22semidirect
79. #4991C22semidirect
81. #4989C22semidirect
82. #4989C22semidirect
83. #4989C22semidirect
84. #4989C22semidirect
86. #4986C22semidirect
87. #4961C22semidirect
88. #4961C22semidirect
89. #4961C22semidirect
90. #4961C22semidirect
93. #4960C22semidirect
94. #4960C22semidirect
95. #4960C22semidirect
96. #4959C22semidirect
97. #4957C22semidirect
98. #4956C22semidirect
101. #4949C22semidirect
102. #4949C22semidirect
103. #4948C22semidirect
104. #4948C22semidirect
105. #4947C22semidirect
106. #4939C22semidirect
107. #4939C22semidirect
108. #4936C22semidirect
109. #4928C22semidirect
110. #4677C22semidirect
111. #4677C22semidirect
112. #4676C22semidirect
114. #4671C22semidirect
115. #4671C22semidirect
118. #4667C22semidirect
119. #4667C22semidirect
121. #4665C22semidirect
122. #4665C22semidirect
124. D3×#95C22semidirect
125. #4654C22semidirect
134. #2662D3semidirect
274. C4×D12D4semidirect
294. C2×#126C2×D3semidirect
297. C2×#124C2×D3semidirect
335. #396C2×D3semidirect
336. #395C2×D3semidirect
343. #394C2×D3semidirect
344. #394C2×D3semidirect
348. #393C2×D3semidirect
365. #390C2×D3semidirect
367. #388C2×D3semidirect
386. C4×C4⋊C4C2×D3semidirect
495. C2×C4×D3C2×D4semidirect
513. C3×C42C2×D4semidirect
541. (C2×D3)⋊C4C2×D4semidirect
546. C4⋊Dic3C2×D4semidirect
977. C42D3×D4semidirect
1234. C3#40488semidirect

Maximal subgroups

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

subgroupindex
C2×#57042
C2×#56762
C3×#26622
#831122
#830072
#774282
#774182
#772542
#772502
#771612
#771082
#770032
#768952
#768712
#768092
#767622
D3×#3922
#764662
#764362
#758462
#756862
#737982
#737702
#404883