Finite Group Databasebeta

← #11028603

Subgroups — #11028603

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×#5558C211yesmaximal, characteristic, complemented
2C2×#5524C211yesmaximal, characteristic, complemented
3C3×#2324C211yesmaximal, characteristic, complemented
4#82723C211yesmaximal, characteristic, complemented
5#82709C211yesmaximal, characteristic, complemented
6#82417C211yesmaximal, characteristic, complemented
7#82265C211yesmaximal, characteristic, complemented
8#76442C212yesmaximal, complemented
9#76439C211yesmaximal, characteristic, complemented
10#76439C211yesmaximal, characteristic, complemented
11#76388C212yesmaximal, complemented
12#76232C211yesmaximal, characteristic, complemented
13#76229C211yesmaximal, characteristic, complemented
14#75882C212yesmaximal, complemented
15#75682C212yesmaximal, complemented
16#74894C212yesmaximal, complemented
17#74804C212yesmaximal, complemented
18#74627C212yesmaximal, complemented
19#74610C212yesmaximal, complemented
20#74003C211yesmaximal, characteristic, complemented
21D3×#380C211yesmaximal, characteristic, complemented
22#73806C211yesmaximal, characteristic, complemented
23C4⋊C4×D12C211yesmaximal, characteristic, complemented
24#37836—31nomaximal, Sylow
25C22×#235C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C2×C3×#121C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic, complemented
29C2×C3×#117C2211yescharacteristic
30C2×#938C2211yescharacteristic
31C2×#938C2211yescharacteristic
32C2×#938C2211yescharacteristic, complemented
33C2×#938C2211yescharacteristic, complemented
34C2×#937C2212yes—
35C2×#930C2212yes—
36C2×#929C2212yescomplemented
37C2×C4×#67C2212yes—
38#5558—28no—
39#5524—28no—
40C2×#897C2211yescharacteristic
41C2×#897C2211yescharacteristic
42C2×#895C2211yescharacteristic
43C2×#895C2211yescharacteristic
44C2×#892C2211yescharacteristic, complemented
45C2×D3×C4⋊C4C2211yescharacteristic
46C2×D3×C4⋊C4C2211yescharacteristic
47C2×D3×C4⋊C4C2211yescharacteristic, complemented
48C2×#886C2211yescharacteristic
49C2×#886C2211yescharacteristic
50C2×#884C2212yes—
51C2×#884C2212yes—
52C2×#884C2212yes—
53C2×#882C2211yescharacteristic
54C2×#882C2211yescharacteristic
55C2×D3×C22⋊C4C2212yes—
56C2×#879C2212yescomplemented
57C2×C4×D12C2211yescharacteristic
58C2×C4×D12C2211yescharacteristic
59C2×C4×D12C2211yescharacteristic
60C2×C4×D12C2212yes—
61C2×C4×D12C2211yescharacteristic
62C2×#870C2211yescharacteristic, complemented
63C3×#390C2212yes—
64C3×#390C2211yescharacteristic, complemented
65C3×#389C2211yescharacteristic, complemented
66C3×#388C2212yescomplemented
67C3×#386C2212yes—
68C3×#385C2212yescomplemented
69C3×#380C2211yescharacteristic
70C3×C4×C4⋊C4C2211yescharacteristic, complemented
71#5223C2212yes—
72#5223C2212yes—
73#5220C2212yes—
74#5212C2211yescharacteristic
75#5212C2211yescharacteristic
76#5212C2212yescomplemented
77#4993C2212yescomplemented
78#4991C2212yes—
79#4989C2212yes—
80#4987C2211yescharacteristic
81#4987C2211yescharacteristic
82#4987C2211yescharacteristic
83#4987C2211yescharacteristic
84#4987C2211yescharacteristic, complemented
85#4987C2211yescharacteristic, complemented
86#4987C2211yescharacteristic, complemented
87#4987C2211yescharacteristic, complemented
88#4982C2212yescomplemented
89#4982C2212yescomplemented
90#4980C2212yescomplemented
91#4961C2212yes—
92#4961C2212yescomplemented
93#4960C2212yescomplemented
94#4959C2212yes—
95#4959C2212yescomplemented
96#4957C2212yes—
97#4956C2212yes—
98#4956C2212yes—
99#4956C2212yes—
100#4956C2212yes—
101#4956C2212yescomplemented
102#4948C2212yes—
103#4948C2212yes—
104#4948C2212yescomplemented
105#4948C2212yescomplemented
106#4947C2212yescomplemented
107#4942C2212yes—
108#4940C2212yes—
109#4940C2212yescomplemented
110#4935C2211yescharacteristic, complemented
111#4928C2212yescomplemented
112#4928C2211yescharacteristic, complemented
113#4928C2211yescharacteristic, complemented
114#4675C2212yescomplemented
115#4672C2212yes—
116#4669C2212yes—
117#4668C2212yes—
118#4668C2212yescomplemented
119#4667C2212yes—
120#4665C2212yes—
121#4665C2212yescomplemented
122D3×#95C2212yes—
123#4660C2212yescomplemented
124#4659C2212yescomplemented
125#4646C2212yescomplemented
126C2×#553—31no—
127C2×#525—31no—
128#2847—31no—
129#2705—32no—
130#2702—32no—
131#2693—32no—
132#2671—32no—
133#2629—31no—
134#2615—31no—
135#2562—31no—
136#2543—32no—
137#2537—31no—
138#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#2324D311yescharacteristic, complemented
147#2311—31no—
148C2×#380—31no—
149C24×D3C2311yescharacteristic
150C22×C3×D4C2311yescharacteristic
151C22×C3×D4C2312yes—
152C23×C3×C4C2311yescharacteristic
153C23×C3×C4C2312yes—
154C22×#67C2312yes—
155C22×#67C2311yescharacteristic
156C22×#67C2311yescharacteristic
157C22×#67C2312yes—
158C22×#67C2312yes—
159C22×#67C2312yes—
160C23×Dic3C2311yescharacteristic
161C2×#235—24no—
162C2×#235—24no—
163C2×#235—42no—
164C22×D12C2311yescharacteristic
165C22×D12C2311yescharacteristic
166C22×D12C2311yescharacteristic
167C22×D12C2311yescharacteristic
168C22×D12C2311yescharacteristic
169C22×C4×D3—24no—
170C22×C4×D3—24no—
171C22×C4×D3—42no—
172C22×C4×D3C2311yescharacteristic
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×#121—24no—
183C3×C4×D4—24no—
184C3×#117—24no—
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×C22⋊C4C2312yes—
192C2×C3×C22⋊C4C2311yescharacteristic
193C2×C3×C22⋊C4C2311yescharacteristic
194C2×C3×C22⋊C4C2312yes—
195C2×C3×C22⋊C4C2312yes—
196C2×C3×C22⋊C4C2312yes—
197C2×C3×C22⋊C4C2312yes—
198C2×C3×C42C2311yescharacteristic
199C2×C3×C42C2312yes—
200C2×C3×C42C2311yescharacteristic
201C2×#217C2312yes—
202C2×#217C2312yes—
203C2×#217C2312yes—
204C2×#217C2312yes—
205C2×#217C2312yes—
206C2×#217C2312yes—
207#938—24no—
208#938—24no—
209#938—42no—
210#938—42no—
211#937—44no—
212#930—44no—
213#929—28no—
214C4×#67—28no—
215C2×(C2×D3)⋊C4C2312yes—
216C2×(C2×D3)⋊C4C2312yes—
217C2×(C2×D3)⋊C4C2312yes—
218C2×(C2×D3)⋊C4C2312yes—
219C2×(C2×D3)⋊C4C2311yescharacteristic
220C2×(C2×D3)⋊C4C2311yescharacteristic
221C2×(C2×D3)⋊C4C2311yescharacteristic
222C2×(C2×D3)⋊C4C2311yescharacteristic
223C2×(C2×D3)⋊C4C2311yescharacteristic
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)⋊C4C2311yescharacteristic
231C2×(C2×D3)⋊C4C2311yescharacteristic
232C2×C4⋊Dic3C2311yescharacteristic
233C2×C4⋊Dic3C2311yescharacteristic
234C2×C4⋊Dic3C2311yescharacteristic
235C2×C4⋊Dic3C2311yescharacteristic
236C2×C4⋊Dic3C2311yescharacteristic
237C2×C4⋊Dic3C2311yescharacteristic
238C2×C4⋊Dic3C2311yescharacteristic
239C2×C4⋊Dic3C2312yes—
240C2×C4⋊Dic3C2312yes—
241C2×C4⋊Dic3C2311yescharacteristic
242C2×Dic3⋊C4C2312yes—
243C2×Dic3⋊C4C2312yes—
244C2×Dic3⋊C4C2312yes—
245C2×Dic3⋊C4C2312yes—
246C2×Dic3⋊C4C2312yes—
247C2×Dic3⋊C4C2312yes—
248C2×Dic3⋊C4C2312yes—
249C2×C4×Dic3C2312yes—
250#897—24no—
251#897—24no—
252#895—24no—
253#895—24no—
254#892—24no—
255D3×C4⋊C4—24no—
256D3×C4⋊C4—42no—
257D3×C4⋊C4—42no—
258#886—24no—
259#886—24no—
260#884—28no—
261#884—44no—
262#884—44no—
263#882—24no—
264#882—24no—
265D3×C22⋊C4—44no—
266#879—28no—
267C4×D12—24no—
268C4×D12—24no—
269C4×D12—24no—
270C4×D12—44no—
271C4×D12D418yescomplemented
272#870—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—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—32no—
304C2×#121—31no—
305C2×#121—31no—
306C2×#121—32no—
307C2×#121—32no—
308C2×#121—32no—
309C2×#121C2×D311yescharacteristic
310C2×#120—32no—
311C2×#120—31no—
312C2×#120—31no—
313C2×C4×D4—32no—
314C2×C4×D4—31no—
315C2×C4×D4—31no—
316C2×C4×D4—31no—
317C2×C4×D4—31no—
318C2×C4×D4—32no—
319C2×C4×D4C2×D311yescharacteristic, complemented
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#398—32no—
330#398—32no—
331#397—32no—
332#396—32no—
333#396—32no—
334#396—32no—
335#396—32no—
336#394—32no—
337#394—32no—
338#394—32no—
339#394—32no—
340#394—32no—
341#394—32no—
342#393—32no—
343#392—32no—
344#392—32no—
345#392—32no—
346#391—32no—
347#390—32no—
348#390C2×D312yes—
349#390C2×D311yescharacteristic, complemented
350#389—32no—
351#389—31no—
352#389—31no—
353#389C2×D311yescharacteristic, complemented
354#388—32no—
355#388—32no—
356#388—32no—
357#388C2×D312yescomplemented
358#387—32no—
359#386—32no—
360#386—32no—
361#386—32no—
362#386—32no—
363#386—32no—
364#386—32no—
365#386—32no—
366#386—32no—
367#386C2×D312yes—
368#385—32no—
369#385—32no—
370#385—32no—
371#385C2×D312yescomplemented
372#384—31no—
373#380—31no—
374#380—31no—
375#380—32no—
376#380—31no—
377#380—31no—
378#380—31no—
379#380—31no—
380#380—31no—
381#380—31no—
382#380—31no—
383#380—31no—
384#380—32no—
385#380—32no—
386#380C2×D311yescharacteristic
387C4×C4⋊C4C2×D311yescharacteristic, complemented
388C2×#95—32no—
389C24×C3C2412yes—
390C24×C3C2411yescharacteristic
391C23×D3—22no—
392C23×D3—22no—
393C23×D3—22no—
394C23×D3—22no—
395C23×D3—22no—
396C23×D3—41no—
397C23×D3—41no—
398C23×D3C2411yescharacteristic
399C23×D3C2411yescharacteristic
400C23×D3C2411yescharacteristic
401C23×D3C2411yescharacteristic
402C2×C3×D4—24no—
403C2×C3×D4—22no—
404C2×C3×D4—22no—
405C2×C3×D4—22no—
406C2×C3×D4—42no—
407C2×C3×D4—42no—
408C22×C3×C4—22no—
409C22×C3×C4—22no—
410C22×C3×C4—24no—
411C22×C3×C4—42no—
412C22×C3×C4—42no—
413C22×C3×C4#4114yes—
414C22×C3×C4C2412yes—
415C22×C3×C4C2412yes—
416C22×C3×C4C2411yescharacteristic
417C22×C3×C4C2412yes—
418C22×C3×C4C2411yescharacteristic
419C22×C3×C4C2411yescharacteristic
420C22×C3×C4C2411yescharacteristic
421C22×C3×C4C2411yescharacteristic
422C22×C3×C4C2411yescharacteristic
423C2×#67—22no—
424C2×#67—22no—
425C2×#67—22no—
426C2×#67—24no—
427C2×#67—24no—
428C2×#67—24no—
429C2×#67—24no—
430C2×#67—24no—
431C2×#67—22no—
432C2×#67—41no—
433C2×#67—41no—
434C2×#67—42no—
435C2×#67—42no—
436C2×#67—42no—
437C2×#67—42no—
438C2×#67—42no—
439C2×#67—42no—
440C2×#67—42no—
441C22×Dic3—22no—
442C22×Dic3—22no—
443C22×Dic3—41no—
444C22×Dic3C2411yescharacteristic
445C22×Dic3C2411yescharacteristic
446C22×Dic3C2412yes—
447C22×Dic3C2412yes—
448C22×Dic3C2412yes—
449C22×Dic3C2412yes—
450C22×Dic3C2411yescharacteristic
451C22×Dic3C2411yescharacteristic
452#235—416no—
453C2×D12—22no—
454C2×D12—22no—
455C2×D12—22no—
456C2×D12—22no—
457C2×D12—22no—
458C2×D12—22no—
459C2×D12—22no—
460C2×D12—22no—
461C2×D12—22no—
462C2×D12—22no—
463C2×D12—22no—
464C2×D12—41no—
465C2×D12—41no—
466C2×D12—41no—
467C2×D12C2×D414yes—
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—22no—
480C2×C4×D3—22no—
481C2×C4×D3—22no—
482C2×C4×D3—24no—
483C2×C4×D3—24no—
484C2×C4×D3—416no—
485C2×C4×D3—41no—
486C2×C4×D3—41no—
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—22no—
502C3×C4⋊C4—22no—
503C3×C4⋊C4—22no—
504C3×C4⋊C4—42no—
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—22no—
513C3×C42—42no—
514C3×C42C2×D414yes—
515#217—24no—
516#217—24no—
517#217—42no—
518#217—42no—
519#217—42no—
520#217—42no—
521(C2×D3)⋊C4—22no—
522(C2×D3)⋊C4—22no—
523(C2×D3)⋊C4—24no—
524(C2×D3)⋊C4—24no—
525(C2×D3)⋊C4—24no—
526(C2×D3)⋊C4—24no—
527(C2×D3)⋊C4—22no—
528(C2×D3)⋊C4—22no—
529(C2×D3)⋊C4—22no—
530(C2×D3)⋊C4—22no—
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)⋊C4C2×D414yes—
537(C2×D3)⋊C4C2×D414yes—
538C4⋊Dic3—22no—
539C4⋊Dic3—22no—
540C4⋊Dic3—22no—
541C4⋊Dic3—22no—
542C4⋊Dic3—22no—
543C4⋊Dic3—22no—
544C4⋊Dic3—22no—
545C4⋊Dic3—42no—
546C4⋊Dic3—42no—
547C4⋊Dic3C2×D414yes—
548Dic3⋊C4—24no—
549Dic3⋊C4—24no—
550Dic3⋊C4—24no—
551Dic3⋊C4—42no—
552Dic3⋊C4—42no—
553Dic3⋊C4—42no—
554Dic3⋊C4—42no—
555C4×Dic3—24no—
556C25—31no—
557C2×#41—64no—
558C2×#41—64no—
559C2×#41—122no—
560C22×Q8—31no—
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—31no—
571C22×D4—31no—
572C22×D4C22×D311yescharacteristic
573C22×D4C22×D312yes—
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—64no—
585C23×C4—64no—
586C23×C4—122no—
587C23×C4C22×D311yescharacteristic
588C23×C4C22×D312yes—
589#126—68no—
590#125—64no—
591#123—64no—
592#123—64no—
593#123—68no—
594C22⋊Q8—64no—
595C22⋊Q8—64no—
596#121—24no—
597#121—68no—
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—24no—
611C4×D4—38no—
612C4×D4—64no—
613C4×D4—64no—
614C4×D4—68no—
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—32no—
636C2×C4⋊C4—64no—
637C2×C4⋊C4—122no—
638C2×C4⋊C4—122no—
639C2×C4⋊C4C22×D311yescharacteristic
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—32no—
648C2×C22⋊C4—32no—
649C2×C22⋊C4—32no—
650C2×C22⋊C4—32no—
651C2×C22⋊C4—32no—
652C2×C22⋊C4—31no—
653C2×C22⋊C4—31no—
654C2×C22⋊C4—31no—
655C2×C22⋊C4—32no—
656C2×C22⋊C4—31no—
657C2×C22⋊C4—31no—
658C2×C22⋊C4—31no—
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—124no—
669C2×C22⋊C4C22×D311yescharacteristic
670C2×C22⋊C4C22×D311yescharacteristic
671C2×C22⋊C4C22×D312yes—
672C2×C22⋊C4C22×D312yes—
673C2×C22⋊C4C22×D312yes—
674C2×C22⋊C4C22×D312yes—
675C2×C22⋊C4C22×D312yes—
676C2×C42—32no—
677C2×C42C22×D311yescharacteristic
678C2×C42C22×D312yes—
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#95—32no—
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—22no—
702C23×C3—22no—
703C23×C3—22no—
704C23×C3—22no—
705C23×C3—22no—
706C23×C3—22no—
707C23×C3—22no—
708C23×C3C2×#4112yes—
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—21no—
722C22×D3—21no—
723C22×D3—21no—
724C22×D3—21no—
725C22×D3—21no—
726C22×D3—21no—
727C22×D3—21no—
728C22×D3—21no—
729C22×D3—21no—
730C22×D3—21no—
731C22×D3—21no—
732C22×D3—21no—
733C22×D3—21no—
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—
745C3×D4—44no—
746C3×D4—84no—
747C2×C3×C4—21no—
748C2×C3×C4—21no—
749C2×C3×C4—21no—
750C2×C3×C4—21no—
751C2×C3×C4—21no—
752C2×C3×C4—21no—
753C2×C3×C4—28no—
754C2×C3×C4—22no—
755C2×C3×C4—21no—
756C2×C3×C4—21no—
757C2×C3×C4—22no—
758C2×C3×C4—21no—
759C2×C3×C4—21no—
760C2×C3×C4—22no—
761C2×C3×C4—22no—
762C2×C3×C4—22no—
763C2×C3×C4—22no—
764C2×C3×C4—22no—
765C2×C3×C4—21no—
766C2×C3×C4—22no—
767C2×C3×C4—21no—
768C2×C3×C4—22no—
769C2×C3×C4—84no—
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—48no—
779#67—84no—
780#67—84no—
781#67—84no—
782C2×Dic3—21no—
783C2×Dic3—21no—
784C2×Dic3—21no—
785C2×Dic3—21no—
786C2×Dic3—22no—
787C2×Dic3—22no—
788C2×Dic3—21no—
789C2×Dic3—21no—
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—22no—
800C2×Dic3—21no—
801C2×Dic3—21no—
802C2×Dic3—22no—
803C2×Dic3—22no—
804C2×Dic3—44no—
805C2×Dic3C22×D412yes—
806C2×Dic3C22×D412yes—
807D12—28no—
808D12—44no—
809D12—44no—
810D12—44no—
811D12—44no—
812C4×D3—28no—
813C4×D3—28no—
814C4×D3—44no—
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—31no—
825C24—31no—
826C24—62no—
827C24—62no—
828C24—62no—
829C24—62no—
830C24—62no—
831C24—121no—
832C24—121no—
833C24C23×D312yes—
834C24C23×D311yescharacteristic
835#41—1216no—
836C2×Q8—62no—
837C2×Q8—62no—
838C2×Q8—121no—
839C2×D4—24no—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—34no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—62no—
847C2×D4—62no—
848C2×D4—62no—
849C2×D4—62no—
850C2×D4—62no—
851C2×D4—62no—
852C2×D4—62no—
853C2×D4—62no—
854C2×D4—62no—
855C2×D4—62no—
856C2×D4—64no—
857C2×D4—62no—
858C2×D4—64no—
859C2×D4—64no—
860C2×D4—62no—
861C2×D4—62no—
862C2×D4—64no—
863C2×D4—64no—
864C2×D4—62no—
865C2×D4—62no—
866C2×D4—121no—
867C2×D4—121no—
868C2×D4—121no—
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—24no—
881C22×C4—31no—
882C22×C4—31no—
883C22×C4—34no—
884C22×C4—34no—
885C22×C4—31no—
886C22×C4—31no—
887C22×C4—32no—
888C22×C4—32no—
889C22×C4—32no—
890C22×C4—32no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—62no—
894C22×C4—62no—
895C22×C4—64no—
896C22×C4—64no—
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—62no—
908C22×C4—62no—
909C22×C4—62no—
910C22×C4—62no—
911C22×C4—121no—
912C22×C4—121no—
913C22×C4—1216no—
914C22×C4—122no—
915C22×C4—122no—
916C22×C4—122no—
917C22×C4—122no—
918C22×C4—122no—
919C22×C4—122no—
920C22×C4—122no—
921C22×C4—121no—
922C22×C4#23514yes—
923C22×C4C23×D312yes—
924C22×C4C23×D312yes—
925C22×C4C23×D311yescharacteristic
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—22no—
937C4⋊C4—34no—
938C4⋊C4—42no—
939C4⋊C4—64no—
940C4⋊C4—62no—
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—122no—
950C4⋊C4—122no—
951C4⋊C4—122no—
952C4⋊C4—122no—
953C4⋊C4—122no—
954C4⋊C4—122no—
955C22⋊C4—24no—
956C22⋊C4—22no—
957C22⋊C4—22no—
958C22⋊C4—24no—
959C22⋊C4—34no—
960C22⋊C4—34no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—62no—
965C22⋊C4—62no—
966C22⋊C4—64no—
967C22⋊C4—64no—
968C22⋊C4—64no—
969C22⋊C4—62no—
970C22⋊C4—62no—
971C22⋊C4—64no—
972C22⋊C4—64no—
973C22⋊C4—64no—
974C22⋊C4—62no—
975C22⋊C4—62no—
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—42no—
987C42—64no—
988C42D3×D414yes—
989C22×C3—22no—
990C22×C3—22no—
991C22×C3—22no—
992C22×C3—41no—
993C22×C3—41no—
994C22×C3—41no—
995C22×C3—41no—
996C22×C3—42no—
997C22×C3—42no—
998C22×C3—42no—
999C22×C3—42no—
1000C22×C3—42no—
1001C22×C3—42no—
1002C22×C3—42no—
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—22no—
1020C2×D3—22no—
1021C2×D3—22no—
1022C2×D3—416no—
1023C2×D3—41no—
1024C2×D3—41no—
1025C2×D3—41no—
1026C2×D3—41no—
1027C2×D3—41no—
1028C2×D3—41no—
1029C2×D3—41no—
1030C2×D3—41no—
1031C2×D3—41no—
1032C2×D3—41no—
1033C2×D3—41no—
1034C2×D3—41no—
1035C2×D3—41no—
1036C2×D3—41no—
1037C2×D3—41no—
1038C2×D3#53714yes—
1039C3×C4—22no—
1040C3×C4—22no—
1041C3×C4—22no—
1042C3×C4—41no—
1043C3×C4—42no—
1044C3×C4—41no—
1045C3×C4—42no—
1046C3×C4—42no—
1047C3×C4#54614yes—
1048Dic3—22no—
1049Dic3—22no—
1050Dic3—42no—
1051Dic3—41no—
1052Dic3—41no—
1053Dic3—42no—
1054Dic3—42no—
1055Dic3—42no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—32no—
1070C23—32no—
1071C23—32no—
1072C23—32no—
1073C23—32no—
1074C23—68no—
1075C23—61no—
1076C23—61no—
1077C23—61no—
1078C23—61no—
1079C23—61no—
1080C23—61no—
1081C23—61no—
1082C23—61no—
1083C23—61no—
1084C23—61no—
1085C23—61no—
1086C23—61no—
1087C23—61no—
1088C23—61no—
1089C23—61no—
1090C23—61no—
1091C23—61no—
1092C23—61no—
1093C23—61no—
1094C23—61no—
1095C23—61no—
1096C23—61no—
1097C23—61no—
1098C23—124no—
1099C23—124no—
1100C23—124no—
1101C23—124no—
1102C23—124no—
1103C23—124no—
1104C23C2×#23512yes—
1105C23C24×D311yescharacteristic
1106Q8—124no—
1107D4—44no—
1108D4—68no—
1109D4—84no—
1110D4—124no—
1111D4—124no—
1112D4—124no—
1113D4—124no—
1114D4—124no—
1115D4—124no—
1116D4—128no—
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—22no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—21no—
1142C2×C4—32no—
1143C2×C4—32no—
1144C2×C4—61no—
1145C2×C4—61no—
1146C2×C4—61no—
1147C2×C4—61no—
1148C2×C4—68no—
1149C2×C4—68no—
1150C2×C4—61no—
1151C2×C4—61no—
1152C2×C4—62no—
1153C2×C4—61no—
1154C2×C4—61no—
1155C2×C4—62no—
1156C2×C4—61no—
1157C2×C4—61no—
1158C2×C4—62no—
1159C2×C4—62no—
1160C2×C4—62no—
1161C2×C4—62no—
1162C2×C4—62no—
1163C2×C4—62no—
1164C2×C4—62no—
1165C2×C4—62no—
1166C2×C4—62no—
1167C2×C4—62no—
1168C2×C4—84no—
1169C2×C4—124no—
1170C2×C4—124no—
1171C2×C4—124no—
1172C2×C4—124no—
1173C2×C4—124no—
1174C2×C4—244no—
1175C2×C4—244no—
1176C2×C4—244no—
1177C2×C4C2×#23512yes—
1178C2×C4C2×#23512yes—
1179C2×C4C2×D3×D412yes—
1180C2×C4C2×D3×D412yes—
1181C2×C4C2×D3×D412yes—
1182C2×C4#100912yes—
1183C2×C3—42no—
1184C2×C3—82no—
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—42no—
1195D3—81no—
1196C22—22no—
1197C22—22no—
1198C22—22no—
1199C22—34no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—62no—
1212C22—62no—
1213C22—62no—
1214C22—62no—
1215C22—62no—
1216C22—62no—
1217C22—62no—
1218C22—62no—
1219C22—62no—
1220C22—62no—
1221C22—62no—
1222C22—62no—
1223C22—1216no—
1224C22—121no—
1225C22—121no—
1226C22—121no—
1227C22—121no—
1228C22—121no—
1229C22—121no—
1230C22—121no—
1231C22—121no—
1232C22—121no—
1233C22—121no—
1234C22—121no—
1235C22—121no—
1236C22—121no—
1237C22—121no—
1238C22—121no—
1239C22C22×#23511yescharacteristic
1240C22C22×D3×D411yescharacteristic
1241C22C2×#100911yescharacteristic
1242C22D3×H(5,𝔽2)11yescharacteristic
1243C22D3×H(5,𝔽2)11yescharacteristic
1244C22#596611yescharacteristic
1245C22D3×2−1+411yescharacteristic
1246C4—22no—
1247C4—22no—
1248C4—22no—
1249C4—42no—
1250C4—41no—
1251C4—41no—
1252C4—42no—
1253C4—42no—
1254C4—62no—
1255C4—62no—
1256C4—121no—
1257C4—121no—
1258C4—122no—
1259C4—122no—
1260C4—122no—
1261C4—122no—
1262C4#555014yes—
1263C3#3783611yescharacteristic, complemented, Sylow
1264C2—42no—
1265C2—64no—
1266C2—82no—
1267C2—122no—
1268C2—122no—
1269C2—241no—
1270C2C2×#555011yescharacteristic
1271C2#8586911yescharacteristic
1272C2#8590211yescharacteristic
1273C2#8633111yescharacteristic
1274C2D3×#53711yescharacteristic
1275C2#8649111yescharacteristic
1276C2#8656211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2324C2
hypercenter#2324D3
hypocenterC3#37836
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2324

Complements

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

NH ≅ G/Ntype
1. C2×#5558C2semidirect
2. C2×#5524C2semidirect
3. C3×#2324C2semidirect
4. #82723C2semidirect
5. #82709C2semidirect
6. #82417C2semidirect
7. #82265C2semidirect
8. #76442C2semidirect
9. #76439C2semidirect
10. #76439C2semidirect
11. #76388C2semidirect
12. #76232C2semidirect
13. #76229C2semidirect
14. #75882C2semidirect
15. #75682C2semidirect
16. #74894C2semidirect
17. #74804C2semidirect
18. #74627C2semidirect
19. #74610C2semidirect
20. #74003C2semidirect
21. D3×#380C2semidirect
22. #73806C2semidirect
23. C4⋊C4×D12C2semidirect
28. C2×C3×C4×D4C22semidirect
32. C2×#938C22semidirect
33. C2×#938C22semidirect
36. C2×#929C22semidirect
44. C2×#892C22semidirect
47. C2×D3×C4⋊C4C22semidirect
56. C2×#879C22semidirect
62. C2×#870C22semidirect
64. C3×#390C22semidirect
65. C3×#389C22semidirect
66. C3×#388C22semidirect
68. C3×#385C22semidirect
70. C3×C4×C4⋊C4C22semidirect
76. #5212C22semidirect
77. #4993C22semidirect
84. #4987C22semidirect
85. #4987C22semidirect
86. #4987C22semidirect
87. #4987C22semidirect
88. #4982C22semidirect
89. #4982C22semidirect
90. #4980C22semidirect
92. #4961C22semidirect
93. #4960C22semidirect
95. #4959C22semidirect
101. #4956C22semidirect
104. #4948C22semidirect
105. #4948C22semidirect
106. #4947C22semidirect
109. #4940C22semidirect
110. #4935C22semidirect
111. #4928C22semidirect
112. #4928C22semidirect
113. #4928C22semidirect
114. #4675C22semidirect
118. #4668C22semidirect
121. #4665C22semidirect
123. #4660C22semidirect
124. #4659C22semidirect
125. #4646C22semidirect
146. #2324D3semidirect
271. C4×D12D4semidirect
319. C2×C4×D4C2×D3semidirect
349. #390C2×D3semidirect
353. #389C2×D3semidirect
357. #388C2×D3semidirect
371. #385C2×D3semidirect
387. C4×C4⋊C4C2×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×#55582
C2×#55242
C3×#23242
#827232
#827092
#824172
#822652
#764422
#764392
#763882
#762322
#762292
#758822
#756822
#748942
#748042
#746272
#746102
#740032
D3×#3802
#738062
C4⋊C4×D122
#378363