Finite Group Databasebeta

← #11028595

Subgroups — #11028595

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×#5828C211yesmaximal, characteristic, complemented
2C2×#5530C211yesmaximal, characteristic, complemented
3C3×#2311C211yesmaximal, characteristic, complemented
4#84098C211yesmaximal, characteristic, complemented
5#82283C211yesmaximal, characteristic, complemented
6#82193C211yesmaximal, characteristic, complemented
7C4⋊C4×#67C211yesmaximal, characteristic, complemented
8#76628C212yesmaximal, complemented
9#76565C212yesmaximal, complemented
10#76442C212yesmaximal, complemented
11#76389C212yesmaximal, complemented
12#74913C212yesmaximal, complemented
13#74902C212yesmaximal, complemented
14#74894C212yesmaximal, complemented
15#74805C212yesmaximal, complemented
16#74048C211yesmaximal, characteristic, complemented
17D3×#380C211yesmaximal, characteristic, complemented
18#73955C211yesmaximal, characteristic, complemented
19#73941C211yesmaximal, characteristic, complemented
20#73935C211yesmaximal, characteristic, complemented
21#73912C211yesmaximal, characteristic, complemented
22#73887C211yesmaximal, characteristic, complemented
23#73872C211yesmaximal, characteristic, complemented
24#37836—31nomaximal, Sylow
25C22×C3×#41C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C2×C3×#117C2211yescharacteristic, complemented
28C22×C3×C4⋊C4C2211yescharacteristic, complemented
29#5828—28no—
30C2×#946C2211yescharacteristic
31C2×#946C2211yescharacteristic
32C2×#938C2211yescharacteristic
33C2×#938C2211yescharacteristic
34C2×#937C2211yescharacteristic
35C2×#937C2211yescharacteristic
36C2×#935C2211yescharacteristic
37C2×#935C2211yescharacteristic
38C2×#930C2211yescharacteristic
39C2×#930C2212yes—
40C2×#930C2211yescharacteristic, complemented
41C2×#930C2211yescharacteristic, complemented
42C2×C4×#67C2211yescharacteristic
43C2×C4×#67C2211yescharacteristic
44C2×C4×#67C2211yescharacteristic
45C2×C4×#67C2212yes—
46C2×C4×#67C2211yescharacteristic
47C2×#926C2211yescharacteristic
48#5530—28no—
49C2×#895C2211yescharacteristic
50C2×#895C2211yescharacteristic
51C2×#893C2211yescharacteristic, complemented
52C2×D3×C4⋊C4C2211yescharacteristic
53C2×D3×C4⋊C4C2211yescharacteristic
54C2×#890C2211yescharacteristic, complemented
55C2×#884C2212yes—
56C2×#884C2212yes—
57C2×#884C2212yes—
58C2×#883C2212yescomplemented
59C2×#882C2212yes—
60C2×D3×C22⋊C4C2212yes—
61C2×#876C2212yescomplemented
62C2×C4×D12C2212yes—
63C3×#391C2212yescomplemented
64C3×#390C2212yes—
65C3×#386C2212yes—
66C3×#386C2212yescomplemented
67C3×#380C2211yescharacteristic
68C3×#380C2211yescharacteristic
69C3×#380C2211yescharacteristic, complemented
70C3×#380C2211yescharacteristic, complemented
71#5231C2212yescomplemented
72#5223C2212yes—
73#5223C2212yes—
74#5223C2212yescomplemented
75#5213C2212yescomplemented
76#5212C2211yescharacteristic
77#5212C2211yescharacteristic, complemented
78#5212C2211yescharacteristic, complemented
79#5210C2212yescomplemented
80#4994C2212yescomplemented
81#4991C2212yes—
82#4989C2212yes—
83#4988C2211yescharacteristic, complemented
84#4987C2211yescharacteristic
85#4987C2211yescharacteristic
86#4987C2211yescharacteristic
87#4987C2211yescharacteristic
88#4984C2211yescharacteristic, complemented
89#4976C2212yescomplemented
90#4975C2211yescharacteristic, complemented
91Dic3×C4⋊C4C2211yescharacteristic, complemented
92#4972C2211yescharacteristic, complemented
93#4972C2211yescharacteristic, complemented
94#4961C2212yes—
95#4959C2212yes—
96#4959C2212yescomplemented
97#4959C2212yescomplemented
98#4958C2212yes—
99#4957C2212yes—
100#4956C2212yes—
101#4956C2212yes—
102#4952C2212yescomplemented
103#4949C2212yescomplemented
104#4948C2212yes—
105#4948C2212yes—
106#4944C2212yescomplemented
107#4942C2212yes—
108#4940C2212yes—
109#4933C2212yescomplemented
110#4676C2212yescomplemented
111#4672C2212yes—
112#4670C2212yescomplemented
113#4669C2212yes—
114#4668C2212yes—
115#4668C2212yescomplemented
116#4667C2212yes—
117#4667C2212yescomplemented
118#4665C2212yes—
119#4665C2212yes—
120#4665C2212yes—
121D3×#95C2212yes—
122#4661C2212yescomplemented
123#4660C2212yescomplemented
124#4658C2212yescomplemented
125#4657C2212yescomplemented
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#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#2311D311yescharacteristic, complemented
148C2×#380—31no—
149C24×D3C2311yescharacteristic
150C2×C3×#41—24no—
151C2×C3×#41—24no—
152C2×C3×#41—42no—
153C22×C3×Q8C2311yescharacteristic
154C22×C3×D4C2311yescharacteristic
155C22×C3×D4C2311yescharacteristic
156C22×C3×D4C2311yescharacteristic
157C23×C3×C4C2311yescharacteristic
158C23×C3×C4C2311yescharacteristic
159C23×C3×C4C2311yescharacteristic
160C23×C3×C4C2312yes—
161C22×#67C2311yescharacteristic
162C22×#67C2311yescharacteristic
163C22×#67C2311yescharacteristic
164C22×#67C2311yescharacteristic
165C22×#67C2312yes—
166C22×#67C2312yes—
167C22×#67C2312yes—
168C23×Dic3C2311yescharacteristic
169C22×D12C2312yes—
170C22×D12C2311yescharacteristic
171C22×D12C2312yes—
172C22×C4×D3—24no—
173C22×C4×D3—24no—
174C22×C4×D3—42no—
175C22×C4×D3C2311yescharacteristic
176C22×C4×D3C2311yescharacteristic
177C22×C4×D3C2311yescharacteristic
178C22×C4×D3C2311yescharacteristic
179C22×C4×D3C2312yes—
180C22×C4×D3C2312yes—
181C22×C4×D3C2312yes—
182C3×#117—24no—
183C2×C3×C4⋊C4—42no—
184C2×C3×C4⋊C4C2311yescharacteristic
185C2×C3×C4⋊C4C2311yescharacteristic
186C2×C3×C4⋊C4C2311yescharacteristic
187C2×C3×C4⋊C4C2311yescharacteristic
188C2×C3×C4⋊C4C2312yes—
189C2×C3×C22⋊C4C2312yes—
190C2×C3×C22⋊C4C2312yes—
191C2×C3×C22⋊C4C2312yes—
192C2×C3×C22⋊C4C2312yes—
193C2×C3×C22⋊C4C2312yes—
194C2×C3×C42C2312yes—
195C2×#217C2311yescharacteristic
196C2×#217C2311yescharacteristic
197C2×#217C2311yescharacteristic
198C2×#217C2311yescharacteristic
199C2×#217C2311yescharacteristic
200C2×#217C2312yes—
201C2×#217C2312yes—
202C2×#217C2312yes—
203C2×#217C2311yescharacteristic
204#946—24no—
205#946—24no—
206#938—24no—
207#938—24no—
208#937—24no—
209#937—24no—
210#935—24no—
211#935—24no—
212#930—24no—
213#930—24no—
214#930—42no—
215#930—44no—
216C4×#67—24no—
217C4×#67—24no—
218C4×#67—24no—
219C4×#67—44no—
220C4×#67D418yescomplemented
221C2×(C2×D3)⋊C4C2311yescharacteristic
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)⋊C4C2312yes—
229C2×(C2×D3)⋊C4C2311yescharacteristic
230C2×(C2×D3)⋊C4C2312yes—
231C2×(C2×D3)⋊C4C2312yes—
232C2×(C2×D3)⋊C4C2312yes—
233C2×(C2×D3)⋊C4C2312yes—
234C2×(C2×D3)⋊C4C2312yes—
235C2×(C2×D3)⋊C4C2312yes—
236C2×(C2×D3)⋊C4C2311yescharacteristic
237#926—24no—
238C2×C4⋊Dic3C2311yescharacteristic
239C2×C4⋊Dic3C2312yes—
240C2×C4⋊Dic3C2311yescharacteristic
241C2×C4⋊Dic3C2311yescharacteristic
242C2×C4⋊Dic3C2311yescharacteristic
243C2×C4⋊Dic3C2311yescharacteristic
244C2×C4⋊Dic3C2312yes—
245C2×Dic3⋊C4C2312yes—
246C2×Dic3⋊C4C2311yescharacteristic
247C2×Dic3⋊C4C2312yes—
248C2×Dic3⋊C4C2311yescharacteristic
249C2×Dic3⋊C4C2311yescharacteristic
250C2×Dic3⋊C4C2312yes—
251C2×Dic3⋊C4C2312yes—
252C2×Dic3⋊C4C2312yes—
253C2×Dic3⋊C4C2312yes—
254C2×Dic3⋊C4C2312yes—
255C2×Dic3⋊C4C2311yescharacteristic
256C2×C4×Dic3C2311yescharacteristic
257C2×C4×Dic3C2312yes—
258C2×C4×Dic3C2311yescharacteristic
259#895—24no—
260#895—42no—
261#893—24no—
262D3×C4⋊C4—24no—
263D3×C4⋊C4—42no—
264#890—24no—
265#884—28no—
266#884—44no—
267#884—44no—
268#883—28no—
269#882—44no—
270D3×C22⋊C4—44no—
271#876—28no—
272C4×D12—28no—
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×#41C2×D311yescharacteristic
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—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—31no—
314C2×C4×D4—31no—
315C2×C4×D4—31no—
316C2×C4×D4—31no—
317C2×C4×D4—32no—
318C2×C4×D4—31no—
319C2×C4×D4—32no—
320C2×#117—31no—
321C2×#117C2×D311yescharacteristic, complemented
322C22×C4⋊C4—31no—
323C22×C4⋊C4—31no—
324C22×C4⋊C4C2×D311yescharacteristic, complemented
325C22×C22⋊C4—32no—
326#400—32no—
327#400—32no—
328#399—32no—
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#391C2×D312yescomplemented
347#390—31no—
348#390—32no—
349#390C2×D312yes—
350#389—31no—
351#389—32no—
352#389—31no—
353#389—31no—
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#386C2×D312yes—
367#386C2×D312yescomplemented
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—32no—
381#380—32no—
382#380—32no—
383#380C2×D311yescharacteristic
384#380C2×D311yescharacteristic
385#380C2×D311yescharacteristic, complemented
386#380C2×D311yescharacteristic, complemented
387C4×C4⋊C4—31no—
388C2×#95—32no—
389C24×C3C2411yescharacteristic
390C24×C3C2411yescharacteristic
391C24×C3C2411yescharacteristic
392C23×D3—22no—
393C23×D3—22no—
394C23×D3—22no—
395C23×D3—22no—
396C23×D3—22no—
397C23×D3—41no—
398C23×D3—41no—
399C23×D3C2412yes—
400C23×D3C2411yescharacteristic
401C23×D3C2411yescharacteristic
402C3×#41—416no—
403C2×C3×Q8—22no—
404C2×C3×Q8—22no—
405C2×C3×Q8—41no—
406C2×C3×D4—22no—
407C2×C3×D4—22no—
408C2×C3×D4—22no—
409C2×C3×D4—22no—
410C2×C3×D4—22no—
411C2×C3×D4—22no—
412C2×C3×D4—41no—
413C2×C3×D4—41no—
414C2×C3×D4—41no—
415C22×C3×C4—22no—
416C22×C3×C4—22no—
417C22×C3×C4—22no—
418C22×C3×C4—22no—
419C22×C3×C4—22no—
420C22×C3×C4—22no—
421C22×C3×C4—22no—
422C22×C3×C4—42no—
423C22×C3×C4—42no—
424C22×C3×C4—42no—
425C22×C3×C4C2×D414yes—
426C22×C3×C4#4114yes—
427C22×C3×C4C2411yescharacteristic
428C22×C3×C4C2412yes—
429C22×C3×C4C2412yes—
430C22×C3×C4C2412yes—
431C22×C3×C4C2412yes—
432C22×C3×C4C2411yescharacteristic
433C22×C3×C4C2411yescharacteristic
434C22×C3×C4C2411yescharacteristic
435C2×#67—22no—
436C2×#67—22no—
437C2×#67—22no—
438C2×#67—22no—
439C2×#67—22no—
440C2×#67—22no—
441C2×#67—22no—
442C2×#67—22no—
443C2×#67—24no—
444C2×#67—24no—
445C2×#67—22no—
446C2×#67—41no—
447C2×#67—41no—
448C2×#67—42no—
449C2×#67—42no—
450C2×#67—42no—
451C2×#67—42no—
452C2×#67—42no—
453C2×#67—42no—
454C2×#67—42no—
455C2×#67C2×D414yes—
456C22×Dic3—22no—
457C22×Dic3—22no—
458C22×Dic3—41no—
459C22×Dic3C2412yes—
460C22×Dic3C2411yescharacteristic
461C22×Dic3C2411yescharacteristic
462C22×Dic3C2412yes—
463C22×Dic3C2412yes—
464C22×Dic3C2411yescharacteristic
465C22×Dic3C2411yescharacteristic
466C22×Dic3C2411yescharacteristic
467C22×Dic3C2411yescharacteristic
468C2×D12—24no—
469C2×D12—24no—
470C2×D12—24no—
471C2×D12—22no—
472C2×D12—22no—
473C2×D12—22no—
474C2×D12—24no—
475C2×D12—42no—
476C2×D12—42no—
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—22no—
486C2×C4×D3—24no—
487C2×C4×D3—24no—
488C2×C4×D3—24no—
489C2×C4×D3—416no—
490C2×C4×D3—41no—
491C2×C4×D3—41no—
492C2×C4×D3—42no—
493C2×C4×D3—42no—
494C2×C4×D3—42no—
495C2×C4×D3—42no—
496C2×C4×D3—42no—
497C2×C4×D3—42no—
498C2×C4×D3C2×D414yes—
499C3×C4⋊C4—22no—
500C3×C4⋊C4—22no—
501C3×C4⋊C4—22no—
502C3×C4⋊C4—22no—
503C3×C4⋊C4—42no—
504C3×C22⋊C4—24no—
505C3×C22⋊C4—42no—
506C3×C22⋊C4—42no—
507C3×C22⋊C4—42no—
508C3×C22⋊C4—42no—
509C3×C42—24no—
510#217—22no—
511#217—22no—
512#217—22no—
513#217—22no—
514#217—22no—
515#217—42no—
516#217—42no—
517#217—42no—
518#217C2×D414yes—
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—24no—
526(C2×D3)⋊C4—24no—
527(C2×D3)⋊C4—24no—
528(C2×D3)⋊C4—22no—
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)⋊C4C2×D414yes—
535C4⋊Dic3—22no—
536C4⋊Dic3—22no—
537C4⋊Dic3—22no—
538C4⋊Dic3—24no—
539C4⋊Dic3—22no—
540C4⋊Dic3—22no—
541C4⋊Dic3—42no—
542Dic3⋊C4—22no—
543Dic3⋊C4—24no—
544Dic3⋊C4—24no—
545Dic3⋊C4—22no—
546Dic3⋊C4—22no—
547Dic3⋊C4—42no—
548Dic3⋊C4—42no—
549Dic3⋊C4—42no—
550Dic3⋊C4—42no—
551Dic3⋊C4—42no—
552Dic3⋊C4C2×D414yes—
553C4×Dic3—22no—
554C4×Dic3—42no—
555C4×Dic3C2×D414yes—
556C25—31no—
557C2×#41—24no—
558C2×#41—24no—
559C2×#41—42no—
560C22×Q8C22×D311yescharacteristic
561C22×D4—31no—
562C22×D4—31no—
563C22×D4—31no—
564C22×D4—31no—
565C22×D4—32no—
566C22×D4—32no—
567C22×D4—32no—
568C22×D4—32no—
569C22×D4—31no—
570C22×D4—32no—
571C22×D4C22×D311yescharacteristic
572C22×D4C22×D311yescharacteristic
573C22×D4C22×D311yescharacteristic
574C23×C4—31no—
575C23×C4—31no—
576C23×C4—31no—
577C23×C4—31no—
578C23×C4—31no—
579C23×C4—32no—
580C23×C4—32no—
581C23×C4—32no—
582C23×C4—64no—
583C23×C4—64no—
584C23×C4—122no—
585C23×C4C22×D311yescharacteristic
586C23×C4C22×D311yescharacteristic
587C23×C4C22×D311yescharacteristic
588C23×C4C22×D312yes—
589#126—68no—
590#125—64no—
591#123—68no—
592#123—64no—
593#123—64no—
594C22⋊Q8—64no—
595C22⋊Q8—64no—
596#121—68no—
597#121—64no—
598#121—64no—
599#121—64no—
600#121—64no—
601#121—64no—
602#121—124no—
603#121—124no—
604#121—124no—
605#121—122no—
606#121—122no—
607#120—64no—
608#120—64no—
609#120—124no—
610C4×D4—38no—
611C4×D4—68no—
612C4×D4—64no—
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—32no—
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—31no—
631C2×C4⋊C4—32no—
632C2×C4⋊C4—32no—
633C2×C4⋊C4—32no—
634C2×C4⋊C4—32no—
635C2×C4⋊C4—32no—
636C2×C4⋊C4—32no—
637C2×C4⋊C4—42no—
638C2×C4⋊C4—64no—
639C2×C4⋊C4—122no—
640C2×C4⋊C4C22×D311yescharacteristic
641C2×C4⋊C4C22×D311yescharacteristic
642C2×C4⋊C4C22×D311yescharacteristic
643C2×C4⋊C4C22×D311yescharacteristic
644C2×C4⋊C4C22×D312yes—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—31no—
647C2×C22⋊C4—31no—
648C2×C22⋊C4—31no—
649C2×C22⋊C4—31no—
650C2×C22⋊C4—31no—
651C2×C22⋊C4—31no—
652C2×C22⋊C4—32no—
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—124no—
671C2×C22⋊C4C22×D312yes—
672C2×C22⋊C4C22×D312yes—
673C2×C22⋊C4C22×D312yes—
674C2×C22⋊C4C22×D312yes—
675C2×C22⋊C4C22×D312yes—
676C2×C42—31no—
677C2×C42—31no—
678C2×C42—32no—
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#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×C3—21no—
702C23×C3—21no—
703C23×C3—21no—
704C23×C3—21no—
705C23×C3—21no—
706C23×C3—21no—
707C23×C3—21no—
708C23×C3—21no—
709C23×C3—21no—
710C23×C3—21no—
711C23×C3—21no—
712C23×C3—21no—
713C23×C3—21no—
714C23×C3C22×D412yes—
715C23×C3C2×#4112yes—
716C23×C3C2511yescharacteristic
717C22×D3—21no—
718C22×D3—21no—
719C22×D3—21no—
720C22×D3—21no—
721C22×D3—28no—
722C22×D3—21no—
723C22×D3—21no—
724C22×D3—21no—
725C22×D3—21no—
726C22×D3—21no—
727C22×D3—21no—
728C22×D3—22no—
729C22×D3—22no—
730C22×D3—22no—
731C22×D3—22no—
732C22×D3—22no—
733C22×D3—22no—
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×D3H(5,𝔽2)12yes—
743C22×D3H(5,𝔽2)12yes—
744C22×D32−1+412yes—
745C3×Q8—44no—
746C3×D4—44no—
747C3×D4—44no—
748C3×D4—44no—
749C2×C3×C4—21no—
750C2×C3×C4—21no—
751C2×C3×C4—21no—
752C2×C3×C4—21no—
753C2×C3×C4—28no—
754C2×C3×C4—28no—
755C2×C3×C4—21no—
756C2×C3×C4—22no—
757C2×C3×C4—22no—
758C2×C3×C4—21no—
759C2×C3×C4—22no—
760C2×C3×C4—22no—
761C2×C3×C4—22no—
762C2×C3×C4—22no—
763C2×C3×C4—22no—
764C2×C3×C4—22no—
765C2×C3×C4—22no—
766C2×C3×C4—21no—
767C2×C3×C4—22no—
768C2×C3×C4—22no—
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×C4C2×#4112yes—
776C2×C3×C4H(5,𝔽2)12yes—
777#67—28no—
778#67—44no—
779#67—44no—
780#67—44no—
781#67—84no—
782#67—84no—
783#67—84no—
784C2×Dic3—21no—
785C2×Dic3—21no—
786C2×Dic3—21no—
787C2×Dic3—21no—
788C2×Dic3—21no—
789C2×Dic3—21no—
790C2×Dic3—21no—
791C2×Dic3—21no—
792C2×Dic3—22no—
793C2×Dic3—21no—
794C2×Dic3—22no—
795C2×Dic3—21no—
796C2×Dic3—22no—
797C2×Dic3—21no—
798C2×Dic3—22no—
799C2×Dic3—22no—
800C2×Dic3—22no—
801C2×Dic3—21no—
802C2×Dic3—22no—
803C2×Dic3—21no—
804C2×Dic3—21no—
805C2×Dic3—21no—
806C2×Dic3—22no—
807C2×Dic3—22no—
808C2×Dic3—44no—
809C2×Dic3C22×D412yes—
810C2×Dic3C22×D412yes—
811C2×Dic3C22×D412yes—
812D12—48no—
813D12—44no—
814D12—84no—
815C4×D3—28no—
816C4×D3—44no—
817C4×D3—44no—
818C4×D3—44no—
819C4×D3—84no—
820C4×D3—84no—
821C4×D3—84no—
822C24—31no—
823C24—31no—
824C24—32no—
825C24—62no—
826C24—62no—
827C24—62no—
828C24—62no—
829C24—62no—
830C24—121no—
831C24—121no—
832C24C23×D311yescharacteristic
833C24C23×D311yescharacteristic
834C24C23×D311yescharacteristic
835#41—416no—
836C2×Q8—22no—
837C2×Q8—22no—
838C2×Q8—41no—
839C2×D4—22no—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—22no—
844C2×D4—22no—
845C2×D4—34no—
846C2×D4—41no—
847C2×D4—41no—
848C2×D4—41no—
849C2×D4—64no—
850C2×D4—64no—
851C2×D4—64no—
852C2×D4—64no—
853C2×D4—62no—
854C2×D4—62no—
855C2×D4—62no—
856C2×D4—62no—
857C2×D4—62no—
858C2×D4—62no—
859C2×D4—62no—
860C2×D4—62no—
861C2×D4—62no—
862C2×D4—64no—
863C2×D4—64no—
864C2×D4—62no—
865C2×D4—62no—
866C2×D4—62no—
867C2×D4—122no—
868C2×D4—122no—
869C2×D4—121no—
870C2×D4—121no—
871C2×D4—122no—
872C2×D4—122no—
873C2×D4—122no—
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—22no—
884C22×C4—22no—
885C22×C4—31no—
886C22×C4—31no—
887C22×C4—31no—
888C22×C4—34no—
889C22×C4—32no—
890C22×C4—31no—
891C22×C4—31no—
892C22×C4—32no—
893C22×C4—32no—
894C22×C4—31no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—62no—
899C22×C4—64no—
900C22×C4—62no—
901C22×C4—64no—
902C22×C4—64no—
903C22×C4—62no—
904C22×C4—62no—
905C22×C4—62no—
906C22×C4—62no—
907C22×C4—62no—
908C22×C4—62no—
909C22×C4—62no—
910C22×C4—62no—
911C22×C4—62no—
912C22×C4—121no—
913C22×C4—121no—
914C22×C4—1216no—
915C22×C4—122no—
916C22×C4—122no—
917C22×C4—122no—
918C22×C4—122no—
919C22×C4—122no—
920C22×C4—122no—
921C22×C4—121no—
922C22×C4#23514yes—
923C22×C4D3×D414yes—
924C22×C4C23×D311yescharacteristic
925C22×C4C23×D312yes—
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—34no—
937C4⋊C4—42no—
938C4⋊C4—64no—
939C4⋊C4—62no—
940C4⋊C4—62no—
941C4⋊C4—62no—
942C4⋊C4—62no—
943C4⋊C4—64no—
944C4⋊C4—64no—
945C4⋊C4—62no—
946C4⋊C4—62no—
947C4⋊C4—62no—
948C4⋊C4—62no—
949C4⋊C4—122no—
950C4⋊C4—122no—
951C4⋊C4—122no—
952C4⋊C4—122no—
953C4⋊C4—122no—
954C4⋊C4—122no—
955C22⋊C4—24no—
956C22⋊C4—34no—
957C22⋊C4—34no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—62no—
963C22⋊C4—64no—
964C22⋊C4—64no—
965C22⋊C4—64no—
966C22⋊C4—64no—
967C22⋊C4—62no—
968C22⋊C4—64no—
969C22⋊C4—62no—
970C22⋊C4—62no—
971C22⋊C4—62no—
972C22⋊C4—62no—
973C22⋊C4—62no—
974C22⋊C4—64no—
975C22⋊C4—62no—
976C22⋊C4—64no—
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—34no—
987C42—62no—
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×C3—41no—
1004C22×C3—41no—
1005C22×C3—41no—
1006C22×C3—41no—
1007C22×C3—41no—
1008C22×C3—41no—
1009C22×C3—41no—
1010C22×C3C23×D411yescharacteristic
1011C22×C3C22×#4111yescharacteristic
1012C22×C3C2×H(5,𝔽2)11yescharacteristic
1013C22×C3C2×H(5,𝔽2)11yescharacteristic
1014C22×C3C2×H(5,𝔽2)11yescharacteristic
1015C22×C3C2×2−1+411yescharacteristic
1016C22×C3#58511yescharacteristic
1017C2×D3—22no—
1018C2×D3—22no—
1019C2×D3—22no—
1020C2×D3—22no—
1021C2×D3—22no—
1022C2×D3—22no—
1023C2×D3—22no—
1024C2×D3—22no—
1025C2×D3—22no—
1026C2×D3—416no—
1027C2×D3—41no—
1028C2×D3—41no—
1029C2×D3—41no—
1030C2×D3—41no—
1031C2×D3—42no—
1032C2×D3—42no—
1033C2×D3—42no—
1034C2×D3—42no—
1035C2×D3—42no—
1036C2×D3—42no—
1037C2×D3—42no—
1038C2×D3#53714yes—
1039C3×C4—22no—
1040C3×C4—22no—
1041C3×C4—42no—
1042C3×C4—41no—
1043C3×C4—42no—
1044C3×C4—42no—
1045C3×C4—42no—
1046C3×C4#54614yes—
1047Dic3—22no—
1048Dic3—22no—
1049Dic3—22no—
1050Dic3—41no—
1051Dic3—41no—
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—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—32no—
1076C23—32no—
1077C23—32no—
1078C23—32no—
1079C23—68no—
1080C23—61no—
1081C23—61no—
1082C23—61no—
1083C23—61no—
1084C23—61no—
1085C23—61no—
1086C23—61no—
1087C23—61no—
1088C23—61no—
1089C23—61no—
1090C23—62no—
1091C23—62no—
1092C23—62no—
1093C23—62no—
1094C23—62no—
1095C23—62no—
1096C23—62no—
1097C23—124no—
1098C23—124no—
1099C23—124no—
1100C23—124no—
1101C23—124no—
1102C23—124no—
1103C23C2×#23512yes—
1104C23C2×D3×D412yes—
1105C23C24×D311yescharacteristic
1106Q8—44no—
1107D4—44no—
1108D4—44no—
1109D4—44no—
1110D4—68no—
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—28no—
1125C2×C4—28no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—32no—
1142C2×C4—32no—
1143C2×C4—32no—
1144C2×C4—44no—
1145C2×C4—61no—
1146C2×C4—61no—
1147C2×C4—61no—
1148C2×C4—61no—
1149C2×C4—61no—
1150C2×C4—61no—
1151C2×C4—68no—
1152C2×C4—62no—
1153C2×C4—61no—
1154C2×C4—61no—
1155C2×C4—61no—
1156C2×C4—61no—
1157C2×C4—62no—
1158C2×C4—61no—
1159C2×C4—62no—
1160C2×C4—62no—
1161C2×C4—62no—
1162C2×C4—62no—
1163C2×C4—61no—
1164C2×C4—61no—
1165C2×C4—62no—
1166C2×C4—61no—
1167C2×C4—62no—
1168C2×C4—62no—
1169C2×C4—61no—
1170C2×C4—84no—
1171C2×C4—124no—
1172C2×C4—124no—
1173C2×C4—124no—
1174C2×C4—124no—
1175C2×C4—244no—
1176C2×C4—244no—
1177C2×C4—244no—
1178C2×C4C2×#23512yes—
1179C2×C4C2×#23512yes—
1180C2×C4C2×D3×D412yes—
1181C2×C4C2×D3×D412yes—
1182C2×C4#100412yes—
1183C2×C3—42no—
1184C2×C3—42no—
1185C2×C3—81no—
1186C2×C3C2×#53711yescharacteristic
1187C2×C3C2×#54611yescharacteristic
1188C2×C3#348811yescharacteristic
1189C2×C3#349211yescharacteristic
1190C2×C3#349411yescharacteristic
1191C2×C3#353711yescharacteristic
1192C2×C3#354111yescharacteristic
1193D3—24no—
1194D3—42no—
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—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—62no—
1219C22—62no—
1220C22—62no—
1221C22—62no—
1222C22—62no—
1223C22—62no—
1224C22—62no—
1225C22—62no—
1226C22—62no—
1227C22—1216no—
1228C22—121no—
1229C22—121no—
1230C22—121no—
1231C22—121no—
1232C22—122no—
1233C22—122no—
1234C22—122no—
1235C22—122no—
1236C22—122no—
1237C22—122no—
1238C22—122no—
1239C22C22×#23511yescharacteristic
1240C22C22×D3×D411yescharacteristic
1241C22C2×#100411yescharacteristic
1242C22D3×H(5,𝔽2)11yescharacteristic
1243C22D3×H(5,𝔽2)11yescharacteristic
1244C22D3×2−1+411yescharacteristic
1245C22#596811yescharacteristic
1246C4—22no—
1247C4—22no—
1248C4—42no—
1249C4—42no—
1250C4—42no—
1251C4—42no—
1252C4—41no—
1253C4—62no—
1254C4—62no—
1255C4—62no—
1256C4—122no—
1257C4—121no—
1258C4—122no—
1259C4—121no—
1260C4—122no—
1261C4—121no—
1262C4#549014yes—
1263C3#3783611yescharacteristic, complemented, Sylow
1264C2—42no—
1265C2—42no—
1266C2—64no—
1267C2—81no—
1268C2—122no—
1269C2—242no—
1270C2C2×#549011yescharacteristic
1271C2#8590211yescharacteristic
1272C2#8590311yescharacteristic
1273C2#8633411yescharacteristic
1274C2#8636011yescharacteristic
1275C2D3×#53711yescharacteristic
1276C2#8637911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2311C2
hypercenter#2311D3
hypocenterC3#37836
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
1. C2×#5828C2semidirect
2. C2×#5530C2semidirect
3. C3×#2311C2semidirect
4. #84098C2semidirect
5. #82283C2semidirect
6. #82193C2semidirect
7. C4⋊C4×#67C2semidirect
8. #76628C2semidirect
9. #76565C2semidirect
10. #76442C2semidirect
11. #76389C2semidirect
12. #74913C2semidirect
13. #74902C2semidirect
14. #74894C2semidirect
15. #74805C2semidirect
16. #74048C2semidirect
17. D3×#380C2semidirect
18. #73955C2semidirect
19. #73941C2semidirect
20. #73935C2semidirect
21. #73912C2semidirect
22. #73887C2semidirect
23. #73872C2semidirect
27. C2×C3×#117C22semidirect
28. C22×C3×C4⋊C4C22semidirect
40. C2×#930C22semidirect
41. C2×#930C22semidirect
51. C2×#893C22semidirect
54. C2×#890C22semidirect
58. C2×#883C22semidirect
61. C2×#876C22semidirect
63. C3×#391C22semidirect
66. C3×#386C22semidirect
69. C3×#380C22semidirect
70. C3×#380C22semidirect
71. #5231C22semidirect
74. #5223C22semidirect
75. #5213C22semidirect
77. #5212C22semidirect
78. #5212C22semidirect
79. #5210C22semidirect
80. #4994C22semidirect
83. #4988C22semidirect
88. #4984C22semidirect
89. #4976C22semidirect
90. #4975C22semidirect
91. Dic3×C4⋊C4C22semidirect
92. #4972C22semidirect
93. #4972C22semidirect
96. #4959C22semidirect
97. #4959C22semidirect
102. #4952C22semidirect
103. #4949C22semidirect
106. #4944C22semidirect
109. #4933C22semidirect
110. #4676C22semidirect
112. #4670C22semidirect
115. #4668C22semidirect
117. #4667C22semidirect
122. #4661C22semidirect
123. #4660C22semidirect
124. #4658C22semidirect
125. #4657C22semidirect
147. #2311D3semidirect
220. C4×#67D4semidirect
321. C2×#117C2×D3semidirect
324. C22×C4⋊C4C2×D3semidirect
346. #391C2×D3semidirect
367. #386C2×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×#58282
C2×#55302
C3×#23112
#840982
#822832
#821932
C4⋊C4×#672
#766282
#765652
#764422
#763892
#749132
#749022
#748942
#748052
#740482
D3×#3802
#739552
#739412
#739352
#739122
#738872
#738722
#378363