Finite Group Databasebeta

← #11166410

Subgroups — #11166410

Order 768.

2984 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5674C211yesmaximal, characteristic, complemented
2C2×#5630C211yesmaximal, characteristic, complemented
3C3×#2426C211yesmaximal, characteristic, complemented
4#82974C211yesmaximal, characteristic, complemented
5#82755C211yesmaximal, characteristic, complemented
6#82653C211yesmaximal, characteristic, complemented
7#82640C211yesmaximal, characteristic, complemented
8#82476C211yesmaximal, characteristic, complemented
9#82457C211yesmaximal, characteristic, complemented
10#77448C212yesmaximal, complemented
11#77430C212yesmaximal, complemented
12#77138C212yesmaximal, complemented
13#77123C212yesmaximal, complemented
14#76464C212yesmaximal, complemented
15#76454C212yesmaximal, complemented
16#76318C211yesmaximal, characteristic, complemented
17#76314C211yesmaximal, characteristic, complemented
18#76249C211yesmaximal, characteristic, complemented
19#76004C211yesmaximal, characteristic, complemented
20#75916C212yesmaximal, complemented
21#75910C212yesmaximal, complemented
22#73587C211yesmaximal, characteristic, complemented
23#73582C211yesmaximal, characteristic, complemented
24#42966—31nomaximal, Sylow
25C22×#239C2211yescharacteristic
26C22×D3×D4C2211yescharacteristic, complemented
27C23×D12C2211yescharacteristic, complemented
28C2×C3×#124C2211yescharacteristic, complemented
29C2×C3×C22⋊Q8C2211yescharacteristic, complemented
30C2×C3×#121C2211yescharacteristic
31C2×C3×C4×Q8C2211yescharacteristic, complemented
32C2×#947C2211yescharacteristic, complemented
33C2×#947C2211yescharacteristic, complemented
34C2×Q8×Dic3C2211yescharacteristic, complemented
35C2×#940C2211yescharacteristic
36C2×#940C2211yescharacteristic
37C2×#937C2212yes—
38C2×#937C2212yescomplemented
39C2×#937C2212yescomplemented
40C2×#930C2211yescharacteristic
41C2×C4×#67C2211yescharacteristic
42#5674—28no—
43#5630—28no—
44C2×#895C2211yescharacteristic
45C2×#895C2212yes—
46C2×#894C2212yescomplemented
47C2×#894C2212yescomplemented
48C2×#893C2211yescharacteristic, complemented
49C2×#884C2212yescomplemented
50C2×#884C2212yescomplemented
51C2×#883C2212yescomplemented
52C2×#882C2212yes—
53C2×#882C2212yescomplemented
54C2×#882C2212yescomplemented
55C2×#882C2212yescomplemented
56C2×#882C2212yescomplemented
57C2×#882C2212yescomplemented
58C2×#882C2212yescomplemented
59C2×D3×C22⋊C4C2212yescomplemented
60C2×#874C2211yescharacteristic
61C2×#874C2211yescharacteristic
62C2×#872C2211yescharacteristic, complemented
63C3×#396C2212yescomplemented
64C3×#394C2212yescomplemented
65C3×#390C2211yescharacteristic, complemented
66C3×#390C2212yescomplemented
67C3×#389C2211yescharacteristic, complemented
68C3×#388C2212yescomplemented
69C3×C4×C22⋊C4C2211yescharacteristic, complemented
70#5223C2212yes—
71#5221C2211yescharacteristic, complemented
72C4×#217C2211yescharacteristic, complemented
73#4994C2212yescomplemented
74#4993C2212yescomplemented
75#4991C2212yescomplemented
76#4991C2212yescomplemented
77#4991C2212yescomplemented
78#4991C2212yescomplemented
79#4990C2212yescomplemented
80#4988C2212yescomplemented
81#4988C2211yescharacteristic, complemented
82#4988C2211yescharacteristic, complemented
83#4988C2211yescharacteristic, complemented
84#4988C2211yescharacteristic, complemented
85#4987C2212yescomplemented
86#4987C2211yescharacteristic, complemented
87#4972C2211yescharacteristic, complemented
88#4961C2211yescharacteristic
89#4961C2212yescomplemented
90#4961C2212yescomplemented
91#4961C2212yescomplemented
92#4961C2212yescomplemented
93#4960C2212yescomplemented
94#4960C2212yescomplemented
95#4960C2212yescomplemented
96#4960C2212yescomplemented
97#4959C2211yescharacteristic
98#4959C2212yescomplemented
99#4959C2212yescomplemented
100#4957C2212yescomplemented
101#4957C2212yescomplemented
102#4957C2212yescomplemented
103#4956C2212yescomplemented
104#4955C2212yescomplemented
105#4952C2211yescharacteristic, complemented
106#4949C2211yescharacteristic, complemented
107#4939C2211yescharacteristic, complemented
108#4939C2212yescomplemented
109#4939C2211yescharacteristic, complemented
110#4939C2212yescomplemented
111#4939C2212yescomplemented
112C4×(C2×D3)⋊C4C2211yescharacteristic, complemented
113C4×(C2×D3)⋊C4C2212yescomplemented
114C4×C4⋊Dic3C2211yescharacteristic, complemented
115C4×Dic3⋊C4C2211yescharacteristic, complemented
116#4675C2212yescomplemented
117#4675C2211yescharacteristic, complemented
118#4674C2211yescharacteristic, complemented
119#4672C2212yescomplemented
120#4672C2212yescomplemented
121#4671C2212yescomplemented
122#4671C2212yescomplemented
123#4665C2212yescomplemented
124#4658C2211yescharacteristic, complemented
125#4657C2211yescharacteristic, complemented
126C2×#546—31no—
127C2×#535—31no—
128#2813—32no—
129#2679—32no—
130#2679—32no—
131#2678—32no—
132#2678—32no—
133#2661—32no—
134#2624—31no—
135#2617—32no—
136#2548—31no—
137#2548—31no—
138#2539—32no—
139#2445—31no—
140#2445—31no—
141#2433—31no—
142#2433—31no—
143#2433—31no—
144#2426—31no—
145#2426D311yescharacteristic, complemented
146#2408—31no—
147#2395—31no—
148#2341—31no—
149C24×D3C2312yes—
150C24×D3C2312yes—
151C22×C3×Q8C2311yescharacteristic
152C22×C3×D4C2311yescharacteristic
153C22×C3×D4C2312yes—
154C23×C3×C4C2311yescharacteristic
155C22×#67C2311yescharacteristic
156C22×#67C2312yes—
157C22×#67C2312yes—
158C22×#67C2312yes—
159C22×#67C2312yes—
160C22×#67C2312yes—
161C22×#67C2312yes—
162C2×#239—42no—
163C2×#239—42no—
164C2×#239D418yescomplemented
165C2×D3×D4—24no—
166C2×D3×D4—42no—
167C2×D3×D4—42no—
168C22×D12—24no—
169C22×D12—42no—
170C22×D12—42no—
171C22×D12C2311yescharacteristic
172C22×D12C2311yescharacteristic
173C22×D12C2311yescharacteristic
174C22×D12C2312yes—
175C22×D12C2312yes—
176C22×D12C2312yes—
177C22×D12C2312yes—
178C22×D12C2312yes—
179C22×D12C2312yes—
180C22×D12C2312yes—
181C22×C4×D3C2311yescharacteristic
182C22×C4×D3C2312yes—
183C22×C4×D3C2312yes—
184C3×#124—24no—
185C3×C22⋊Q8—24no—
186C3×#121—42no—
187C3×C4×Q8—42no—
188C2×C3×C4⋊C4C2311yescharacteristic
189C2×C3×C4⋊C4C2311yescharacteristic
190C2×C3×C4⋊C4C2312yes—
191C2×C3×C4⋊C4C2312yes—
192C2×C3×C4⋊C4C2312yes—
193C2×C3×C22⋊C4C2311yescharacteristic
194C2×C3×C22⋊C4C2311yescharacteristic
195C2×C3×C22⋊C4C2312yes—
196C2×C3×C22⋊C4C2312yes—
197C2×C3×C22⋊C4C2312yes—
198C2×C3×C22⋊C4C2312yes—
199C2×C3×C22⋊C4C2312yes—
200C2×C3×C22⋊C4C2312yes—
201C2×C3×C42C2311yescharacteristic
202C2×C3×C42C2311yescharacteristic
203C2×C3×C42C2312yes—
204C2×#217C2311yescharacteristic
205C2×#217C2311yescharacteristic
206C2×#217C2311yescharacteristic
207C2×#217C2312yes—
208C2×#217C2312yes—
209#947—24no—
210#947—24no—
211Q8×Dic3—42no—
212#940—24no—
213#940—42no—
214#937—44no—
215#937—44no—
216#937—44no—
217#930—42no—
218C4×#67—24no—
219C2×(C2×D3)⋊C4C2312yes—
220C2×(C2×D3)⋊C4C2311yescharacteristic
221C2×(C2×D3)⋊C4C2312yes—
222C2×(C2×D3)⋊C4C2312yes—
223C2×(C2×D3)⋊C4C2312yes—
224C2×(C2×D3)⋊C4C2311yescharacteristic
225C2×(C2×D3)⋊C4C2311yescharacteristic
226C2×(C2×D3)⋊C4C2311yescharacteristic
227C2×(C2×D3)⋊C4C2312yes—
228C2×(C2×D3)⋊C4C2311yescharacteristic
229C2×(C2×D3)⋊C4C2312yes—
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)⋊C4C2312yes—
237C2×(C2×D3)⋊C4C2312yes—
238C2×(C2×D3)⋊C4C2312yes—
239C2×(C2×D3)⋊C4C2312yes—
240C2×(C2×D3)⋊C4C2312yes—
241C2×(C2×D3)⋊C4C2312yes—
242C2×(C2×D3)⋊C4C2312yes—
243C2×(C2×D3)⋊C4C2312yes—
244C2×C4⋊Dic3C2311yescharacteristic
245C2×C4⋊Dic3C2311yescharacteristic
246C2×C4⋊Dic3C2311yescharacteristic
247C2×C4⋊Dic3C2312yes—
248C2×Dic3⋊C4C2311yescharacteristic
249C2×Dic3⋊C4C2311yescharacteristic
250C2×Dic3⋊C4C2311yescharacteristic
251C2×Dic3⋊C4C2311yescharacteristic
252C2×Dic3⋊C4C2311yescharacteristic
253C2×Dic3⋊C4C2312yes—
254C2×C4×Dic3C2311yescharacteristic
255C2×C4×Dic3C2311yescharacteristic
256C2×C4×Dic3C2311yescharacteristic
257C2×C4×Dic3C2312yes—
258#895—28no—
259#895—24no—
260#894—28no—
261#894—44no—
262#893—24no—
263#884—28no—
264#884—28no—
265#883—44no—
266#882—28no—
267#882—28no—
268#882—28no—
269#882—44no—
270#882—44no—
271#882—44no—
272#882—44no—
273D3×C22⋊C4—28no—
274#874—24no—
275#874—42no—
276#872—24no—
277C3×#95C2311yescharacteristic
278C3×#95C2311yescharacteristic
279C3×#95C2312yes—
280C3⋊#95C2311yescharacteristic
281C3⋊#95C2311yescharacteristic
282C3⋊#95C2311yescharacteristic
283C3⋊#95C2311yescharacteristic
284C3⋊#95C2311yescharacteristic
285C3⋊#95C2311yescharacteristic
286C3⋊#95C2311yescharacteristic
287C3⋊#95C2311yescharacteristic
288C3⋊#95C2312yes—
289C3⋊#95C2312yes—
290C22×#41—31no—
291C23×D4—31no—
292C23×D4—31no—
293#546—68no—
294#535—68no—
295C2×#127—31no—
296C2×#127—31no—
297C2×#127—31no—
298C2×#127—31no—
299C2×#124—31no—
300C2×#124—31no—
301C2×#124C2×D311yescharacteristic, complemented
302C2×#123—32no—
303C2×#123—32no—
304C2×#123—32no—
305C2×C22⋊Q8C2×D311yescharacteristic, complemented
306C2×#121—31no—
307C2×#121—31no—
308C2×#121—32no—
309C2×#121—32no—
310C2×#121—32no—
311C2×#121C2×D311yescharacteristic
312C2×#120—32no—
313C2×#120—32no—
314C2×#120—32no—
315C2×#120—32no—
316C2×#120—32no—
317C2×#120—32no—
318C2×#120—32no—
319C2×#120—32no—
320C2×#120—32no—
321C2×#120—32no—
322C2×C4×Q8—31no—
323C2×C4×Q8C2×D311yescharacteristic, complemented
324C2×C4×D4—31no—
325C2×C4×D4—31no—
326C2×#117—31no—
327C22×C22⋊C4—32no—
328#400—31no—
329#399—32no—
330#399—31no—
331#398—31no—
332#397—31no—
333#397—32no—
334#397—31no—
335#397—31no—
336#396—32no—
337#396C2×D312yescomplemented
338#394—32no—
339#394—32no—
340#394—32no—
341#394—32no—
342#394—32no—
343#394—32no—
344#394—31no—
345#394—31no—
346#394—32no—
347#394—32no—
348#394—32no—
349#394—32no—
350#394—32no—
351#394—32no—
352#394C2×D312yescomplemented
353#392—32no—
354#392—32no—
355#392—32no—
356#392—32no—
357#392—32no—
358#392—32no—
359#392—32no—
360#390—31no—
361#390—32no—
362#390—31no—
363#390—31no—
364#390—31no—
365#390—31no—
366#390—32no—
367#390—32no—
368#390—32no—
369#390—32no—
370#390—31no—
371#390—31no—
372#390—32no—
373#390—32no—
374#390C2×D312yescomplemented
375#390C2×D311yescharacteristic, complemented
376#389—31no—
377#389C2×D311yescharacteristic, complemented
378#388—32no—
379#388C2×D312yescomplemented
380#386—32no—
381#386—32no—
382#380—32no—
383#380—31no—
384#379—32no—
385C4×C4⋊C4—31no—
386C4×C4⋊C4—31no—
387C4×C22⋊C4—31no—
388C4×C22⋊C4—31no—
389C4×C22⋊C4—32no—
390C4×C22⋊C4C2×D311yescharacteristic, complemented
391C24×C3C2412yes—
392C24×C3C2411yescharacteristic
393C23×D3—24no—
394C23×D3—24no—
395C23×D3—24no—
396C23×D3—42no—
397C23×D3—42no—
398C23×D3—42no—
399C23×D3—42no—
400C23×D3—42no—
401C23×D3—42no—
402C23×D3—42no—
403C23×D3—42no—
404C23×D3—42no—
405C23×D3—42no—
406C23×D3—42no—
407C23×D3C2412yes—
408C23×D3C2412yes—
409C23×D3C2411yescharacteristic
410C23×D3C2412yes—
411C2×C3×Q8—22no—
412C2×C3×Q8—22no—
413C2×C3×Q8C2×D414yes—
414C2×C3×D4—24no—
415C2×C3×D4—22no—
416C2×C3×D4—22no—
417C2×C3×D4—22no—
418C2×C3×D4—42no—
419C2×C3×D4—42no—
420C22×C3×C4—22no—
421C22×C3×C4—22no—
422C22×C3×C4—22no—
423C22×C3×C4C2411yescharacteristic
424C22×C3×C4C2411yescharacteristic
425C22×C3×C4C2411yescharacteristic
426C22×C3×C4C2411yescharacteristic
427C22×C3×C4C2412yes—
428C22×C3×C4C2412yes—
429C22×C3×C4C2412yes—
430C22×C3×C4C2411yescharacteristic
431C22×C3×C4C2411yescharacteristic
432C2×#67—22no—
433C2×#67—22no—
434C2×#67—24no—
435C2×#67—24no—
436C2×#67—24no—
437C2×#67—24no—
438C2×#67—24no—
439C2×#67—42no—
440C2×#67—42no—
441C2×#67—41no—
442C2×#67—42no—
443C2×#67—42no—
444C2×#67—42no—
445C2×#67—42no—
446C2×#67—42no—
447C2×#67—42no—
448C2×#67—42no—
449C2×#67—42no—
450C2×#67—42no—
451C2×#67—42no—
452C2×#67—42no—
453C22×Dic3C2411yescharacteristic
454C22×Dic3C2411yescharacteristic
455C22×Dic3C2411yescharacteristic
456C22×Dic3C2411yescharacteristic
457C22×Dic3C2412yes—
458C22×Dic3C2411yescharacteristic
459C22×Dic3C2411yescharacteristic
460C22×Dic3C2411yescharacteristic
461#239—416no—
462D3×D4—416no—
463C2×D12—22no—
464C2×D12—22no—
465C2×D12—24no—
466C2×D12—22no—
467C2×D12—22no—
468C2×D12—22no—
469C2×D12—22no—
470C2×D12—22no—
471C2×D12—22no—
472C2×D12—24no—
473C2×D12—24no—
474C2×D12—24no—
475C2×D12—24no—
476C2×D12—416no—
477C2×D12—42no—
478C2×D12—42no—
479C2×D12—42no—
480C2×D12—42no—
481C2×D12—42no—
482C2×D12—42no—
483C2×D12—42no—
484C2×D12—42no—
485C2×D12—42no—
486C2×D12—42no—
487C2×D12—42no—
488C2×D12—42no—
489C2×D12—42no—
490C2×D12—42no—
491C2×D12—42no—
492C2×D12C2×D414yes—
493C2×D12C2×D418yes—
494C2×C4×D3—22no—
495C2×C4×D3—22no—
496C2×C4×D3—24no—
497C2×C4×D3—42no—
498C2×C4×D3—42no—
499C2×C4×D3—42no—
500C2×C4×D3—42no—
501C2×C4×D3C2×D414yes—
502C2×C4×D3C2×D418yes—
503C3×C4⋊C4—22no—
504C3×C4⋊C4—24no—
505C3×C4⋊C4—22no—
506C3×C4⋊C4—42no—
507C3×C4⋊C4—42no—
508C3×C22⋊C4—22no—
509C3×C22⋊C4—24no—
510C3×C22⋊C4—24no—
511C3×C22⋊C4—24no—
512C3×C22⋊C4—22no—
513C3×C22⋊C4—24no—
514C3×C22⋊C4—42no—
515C3×C22⋊C4—42no—
516C3×C42—22no—
517C3×C42—22no—
518C3×C42—42no—
519#217—22no—
520#217—22no—
521#217—22no—
522#217—42no—
523#217—42no—
524(C2×D3)⋊C4—22no—
525(C2×D3)⋊C4—22no—
526(C2×D3)⋊C4—24no—
527(C2×D3)⋊C4—22no—
528(C2×D3)⋊C4—24no—
529(C2×D3)⋊C4—24no—
530(C2×D3)⋊C4—24no—
531(C2×D3)⋊C4—24no—
532(C2×D3)⋊C4—22no—
533(C2×D3)⋊C4—24no—
534(C2×D3)⋊C4—24no—
535(C2×D3)⋊C4—22no—
536(C2×D3)⋊C4—24no—
537(C2×D3)⋊C4—24no—
538(C2×D3)⋊C4—42no—
539(C2×D3)⋊C4—42no—
540(C2×D3)⋊C4—42no—
541(C2×D3)⋊C4—42no—
542(C2×D3)⋊C4—42no—
543(C2×D3)⋊C4—42no—
544(C2×D3)⋊C4—42no—
545(C2×D3)⋊C4—42no—
546(C2×D3)⋊C4—42no—
547(C2×D3)⋊C4—42no—
548(C2×D3)⋊C4—42no—
549C4⋊Dic3—22no—
550C4⋊Dic3—22no—
551C4⋊Dic3—41no—
552C4⋊Dic3—42no—
553Dic3⋊C4—22no—
554Dic3⋊C4—22no—
555Dic3⋊C4—22no—
556Dic3⋊C4—22no—
557Dic3⋊C4—42no—
558Dic3⋊C4—41no—
559C4×Dic3—22no—
560C4×Dic3—22no—
561C4×Dic3—22no—
562C4×Dic3—42no—
563C25—32no—
564C25—32no—
565C2×#41—38no—
566C2×#41—122no—
567C2×#41—122no—
568C22×Q8C22×D311yescharacteristic
569C22×D4—31no—
570C22×D4—32no—
571C22×D4—32no—
572C22×D4—32no—
573C22×D4—32no—
574C22×D4—32no—
575C22×D4—32no—
576C22×D4—31no—
577C22×D4—32no—
578C22×D4—31no—
579C22×D4—31no—
580C22×D4—32no—
581C22×D4—32no—
582C22×D4—32no—
583C22×D4—32no—
584C22×D4—32no—
585C22×D4—32no—
586C22×D4—64no—
587C22×D4—64no—
588C22×D4—122no—
589C22×D4—122no—
590C22×D4—122no—
591C22×D4—122no—
592C22×D4C22×D311yescharacteristic
593C22×D4C22×D312yes—
594C23×C4—31no—
595C23×C4—32no—
596C23×C4—32no—
597C23×C4C22×D311yescharacteristic
598#127—64no—
599#127—64no—
600#127—122no—
601#127—122no—
602#124—24no—
603#124—64no—
604#124—64no—
605#123—68no—
606#123—124no—
607#123—124no—
608C22⋊Q8—24no—
609#121—42no—
610#121—68no—
611#121—68no—
612#121—64no—
613#121—68no—
614#121—122no—
615#120—68no—
616#120—68no—
617#120—68no—
618#120—124no—
619#120—124no—
620#120—124no—
621#120—124no—
622#120—124no—
623#120—124no—
624#120—124no—
625C4×Q8—42no—
626C4×Q8—122no—
627C4×D4—64no—
628C4×D4—64no—
629#117—64no—
630C2×C4⋊C4—31no—
631C2×C4⋊C4—31no—
632C2×C4⋊C4—31no—
633C2×C4⋊C4—31no—
634C2×C4⋊C4—31no—
635C2×C4⋊C4—31no—
636C2×C4⋊C4—32no—
637C2×C4⋊C4—32no—
638C2×C4⋊C4—31no—
639C2×C4⋊C4—31no—
640C2×C4⋊C4C22×D311yescharacteristic
641C2×C4⋊C4C22×D311yescharacteristic
642C2×C4⋊C4C22×D312yes—
643C2×C4⋊C4C22×D312yes—
644C2×C4⋊C4C22×D312yes—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—31no—
647C2×C22⋊C4—31no—
648C2×C22⋊C4—32no—
649C2×C22⋊C4—32no—
650C2×C22⋊C4—31no—
651C2×C22⋊C4—31no—
652C2×C22⋊C4—32no—
653C2×C22⋊C4—31no—
654C2×C22⋊C4—31no—
655C2×C22⋊C4—31no—
656C2×C22⋊C4—32no—
657C2×C22⋊C4—32no—
658C2×C22⋊C4—32no—
659C2×C22⋊C4—32no—
660C2×C22⋊C4—32no—
661C2×C22⋊C4—32no—
662C2×C22⋊C4—32no—
663C2×C22⋊C4—32no—
664C2×C22⋊C4—32no—
665C2×C22⋊C4—32no—
666C2×C22⋊C4—32no—
667C2×C22⋊C4—32no—
668C2×C22⋊C4—32no—
669C2×C22⋊C4—32no—
670C2×C22⋊C4—32no—
671C2×C22⋊C4—32no—
672C2×C22⋊C4—32no—
673C2×C22⋊C4—32no—
674C2×C22⋊C4—32no—
675C2×C22⋊C4—68no—
676C2×C22⋊C4C22×D312yes—
677C2×C22⋊C4C22×D311yescharacteristic
678C2×C22⋊C4C22×D311yescharacteristic
679C2×C22⋊C4C22×D312yes—
680C2×C22⋊C4C22×D312yes—
681C2×C22⋊C4C22×D312yes—
682C2×C22⋊C4C22×D312yes—
683C2×C22⋊C4C22×D312yes—
684C2×C42—31no—
685C2×C42—31no—
686C2×C42—31no—
687C2×C42—32no—
688C2×C42C22×D311yescharacteristic
689C2×C42C22×D311yescharacteristic
690C2×C42C22×D312yes—
691#95—31no—
692#95—31no—
693#95—32no—
694#95—31no—
695#95—31no—
696#95—31no—
697#95—31no—
698#95—31no—
699#95—31no—
700#95—32no—
701#95C22×D311yescharacteristic
702#95C22×D311yescharacteristic
703#95C22×D312yes—
704C23×C3—21no—
705C23×C3—21no—
706C23×C3—21no—
707C23×C3—21no—
708C23×C3—21no—
709C23×C3—21no—
710C23×C3—22no—
711C23×C3—22no—
712C23×C3—22no—
713C23×C3—22no—
714C23×C3—22no—
715C23×C3—22no—
716C23×C3—22no—
717C23×C3H(5,𝔽2)12yes—
718C23×C3C2511yescharacteristic
719C22×D3—22no—
720C22×D3—22no—
721C22×D3—21no—
722C22×D3—21no—
723C22×D3—22no—
724C22×D3—21no—
725C22×D3—21no—
726C22×D3—21no—
727C22×D3—22no—
728C22×D3—22no—
729C22×D3—22no—
730C22×D3—21no—
731C22×D3—22no—
732C22×D3—22no—
733C22×D3—22no—
734C22×D3—22no—
735C22×D3—22no—
736C22×D3—22no—
737C22×D3—22no—
738C22×D3—22no—
739C22×D3—22no—
740C22×D3—22no—
741C22×D3—22no—
742C22×D3—22no—
743C22×D3—22no—
744C22×D3—22no—
745C22×D3—48no—
746C22×D3—48no—
747C22×D3—48no—
748C22×D3—84no—
749C22×D3—84no—
750C22×D3—84no—
751C22×D3—84no—
752C22×D3—84no—
753C22×D3—84no—
754C22×D3—84no—
755C22×D3—84no—
756C22×D3—84no—
757C22×D3—84no—
758C22×D3—84no—
759C22×D3C22×D412yes—
760C22×D3C22×D414yes—
761C3×Q8—28no—
762C3×D4—44no—
763C3×D4—84no—
764C2×C3×C4—22no—
765C2×C3×C4—21no—
766C2×C3×C4—22no—
767C2×C3×C4—21no—
768C2×C3×C4—21no—
769C2×C3×C4—21no—
770C2×C3×C4—21no—
771C2×C3×C4—22no—
772C2×C3×C4—21no—
773C2×C3×C4—22no—
774C2×C3×C4—22no—
775C2×C3×C4—21no—
776C2×C3×C4—22no—
777C2×C3×C4—22no—
778C2×C3×C4—21no—
779C2×C3×C4—21no—
780C2×C3×C4—21no—
781C2×C3×C4—21no—
782C2×C3×C4—21no—
783C2×C3×C4—22no—
784C2×C3×C4—21no—
785C2×C3×C4—21no—
786C2×C3×C4—44no—
787C2×C3×C4C22×D414yes—
788C2×C3×C4C22×D412yes—
789C2×C3×C4H(5,𝔽2)12yes—
790C2×C3×C4H(5,𝔽2)12yes—
791C2×C3×C4H(5,𝔽2)12yes—
792#67—48no—
793#67—44no—
794#67—84no—
795#67—84no—
796#67—84no—
797#67—84no—
798#67—84no—
799C2×Dic3—21no—
800C2×Dic3—21no—
801C2×Dic3—21no—
802C2×Dic3—21no—
803C2×Dic3—21no—
804C2×Dic3—21no—
805C2×Dic3—21no—
806C2×Dic3—21no—
807C2×Dic3—21no—
808C2×Dic3—22no—
809C2×Dic3—21no—
810C2×Dic3—21no—
811C2×Dic3—22no—
812C2×Dic3—21no—
813C2×Dic3—21no—
814C2×Dic3—22no—
815C2×Dic3—21no—
816C2×Dic3—21no—
817C2×Dic3—21no—
818C2×Dic3—21no—
819C2×Dic3—21no—
820C2×Dic3—21no—
821C2×Dic3C22×D412yes—
822C2×Dic3H(5,𝔽2)12yes—
823D12—28no—
824D12—48no—
825D12—48no—
826D12—44no—
827D12—44no—
828D12—84no—
829D12—84no—
830D12—84no—
831D12—84no—
832D12—84no—
833C4×D3—28no—
834C4×D3—48no—
835C4×D3—84no—
836C24—31no—
837C24—32no—
838C24—32no—
839C24—32no—
840C24—64no—
841C24—64no—
842C24—64no—
843C24—122no—
844C24—122no—
845C24—122no—
846C24—122no—
847C24—122no—
848C24—122no—
849C24—122no—
850C24—122no—
851C24—122no—
852C24—122no—
853C24—122no—
854C24C23×D312yes—
855C24C23×D311yescharacteristic
856#41—1216no—
857C2×Q8—22no—
858C2×Q8—22no—
859C2×Q8D3×D414yes—
860C2×D4—24no—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—34no—
865C2×D4—38no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—64no—
869C2×D4—64no—
870C2×D4—64no—
871C2×D4—64no—
872C2×D4—64no—
873C2×D4—64no—
874C2×D4—62no—
875C2×D4—62no—
876C2×D4—64no—
877C2×D4—64no—
878C2×D4—64no—
879C2×D4—62no—
880C2×D4—62no—
881C2×D4—62no—
882C2×D4—62no—
883C2×D4—62no—
884C2×D4—62no—
885C2×D4—62no—
886C2×D4—62no—
887C2×D4—64no—
888C2×D4—122no—
889C2×D4—122no—
890C2×D4—122no—
891C2×D4—122no—
892C2×D4—122no—
893C2×D4—122no—
894C2×D4—122no—
895C2×D4—122no—
896C2×D4—122no—
897C2×D4—122no—
898C2×D4—122no—
899C2×D4—122no—
900C2×D4—122no—
901C2×D4—122no—
902C2×D4—122no—
903C2×D4—1216no—
904C2×D4—1216no—
905C2×D4—122no—
906C2×D4—122no—
907C2×D4—121no—
908C2×D4—122no—
909C2×D4—122no—
910C2×D4—122no—
911C2×D4—122no—
912C2×D4—122no—
913C2×D4—122no—
914C2×D4—122no—
915C2×D4—122no—
916C2×D4—122no—
917C2×D4—122no—
918C2×D4—122no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4—22no—
922C22×C4—31no—
923C22×C4—31no—
924C22×C4—34no—
925C22×C4—38no—
926C22×C4—31no—
927C22×C4—31no—
928C22×C4—31no—
929C22×C4—32no—
930C22×C4—31no—
931C22×C4—31no—
932C22×C4—64no—
933C22×C4—62no—
934C22×C4—62no—
935C22×C4—122no—
936C22×C4—122no—
937C22×C4—122no—
938C22×C4—122no—
939C22×C4C23×D311yescharacteristic
940C22×C4C23×D311yescharacteristic
941C22×C4C23×D311yescharacteristic
942C22×C4C23×D312yes—
943C22×C4C23×D311yescharacteristic
944C22×C4C23×D312yes—
945C22×C4C23×D312yes—
946C22×C4C23×D311yescharacteristic
947C22×C4C23×D311yescharacteristic
948C4⋊C4—22no—
949C4⋊C4—24no—
950C4⋊C4—22no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—62no—
954C4⋊C4—62no—
955C4⋊C4—62no—
956C4⋊C4—62no—
957C4⋊C4—62no—
958C4⋊C4—62no—
959C4⋊C4—122no—
960C4⋊C4—122no—
961C4⋊C4—121no—
962C4⋊C4—121no—
963C22⋊C4—22no—
964C22⋊C4—24no—
965C22⋊C4—24no—
966C22⋊C4—24no—
967C22⋊C4—22no—
968C22⋊C4—24no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—64no—
972C22⋊C4—62no—
973C22⋊C4—64no—
974C22⋊C4—64no—
975C22⋊C4—62no—
976C22⋊C4—62no—
977C22⋊C4—64no—
978C22⋊C4—62no—
979C22⋊C4—62no—
980C22⋊C4—62no—
981C22⋊C4—62no—
982C22⋊C4—64no—
983C22⋊C4—64no—
984C22⋊C4—64no—
985C22⋊C4—64no—
986C22⋊C4—62no—
987C22⋊C4—64no—
988C22⋊C4—122no—
989C22⋊C4—122no—
990C22⋊C4—122no—
991C22⋊C4—122no—
992C22⋊C4—122no—
993C22⋊C4—122no—
994C22⋊C4—122no—
995C22⋊C4—122no—
996C22⋊C4—122no—
997C22⋊C4—122no—
998C22⋊C4—122no—
999C22⋊C4—122no—
1000C22⋊C4—122no—
1001C42—22no—
1002C42—22no—
1003C42—42no—
1004C42—62no—
1005C42—62no—
1006C42—62no—
1007C42—122no—
1008C22×C3—22no—
1009C22×C3—22no—
1010C22×C3—22no—
1011C22×C3—41no—
1012C22×C3—41no—
1013C22×C3—41no—
1014C22×C3—41no—
1015C22×C3—42no—
1016C22×C3—42no—
1017C22×C3—42no—
1018C22×C3—42no—
1019C22×C3—42no—
1020C22×C3—42no—
1021C22×C3—42no—
1022C22×C3C23×D411yescharacteristic
1023C22×C3C2×H(5,𝔽2)11yescharacteristic
1024C22×C3C2×H(5,𝔽2)11yescharacteristic
1025C22×C3C2×H(5,𝔽2)11yescharacteristic
1026C22×C3C2×H(5,𝔽2)11yescharacteristic
1027C22×C3C2×H(5,𝔽2)11yescharacteristic
1028C22×C3#58511yescharacteristic
1029C2×D3—22no—
1030C2×D3—24no—
1031C2×D3—24no—
1032C2×D3—22no—
1033C2×D3—24no—
1034C2×D3—22no—
1035C2×D3—42no—
1036C2×D3—42no—
1037C2×D3—41no—
1038C2×D3—41no—
1039C2×D3—42no—
1040C2×D3—42no—
1041C2×D3—41no—
1042C2×D3—41no—
1043C2×D3—42no—
1044C2×D3—42no—
1045C2×D3—42no—
1046C2×D3—42no—
1047C2×D3—42no—
1048C2×D3—42no—
1049C2×D3—42no—
1050C2×D3—42no—
1051C2×D3—42no—
1052C2×D3—42no—
1053C2×D3—42no—
1054C2×D3—42no—
1055C2×D3—42no—
1056C2×D3—42no—
1057C2×D3—816no—
1058C2×D3—816no—
1059C3×C4—24no—
1060C3×C4—22no—
1061C3×C4—41no—
1062C3×C4—41no—
1063C3×C4—42no—
1064C3×C4—41no—
1065C3×C4—41no—
1066C3×C4—42no—
1067C3×C4#53414yes—
1068Dic3—22no—
1069Dic3—22no—
1070Dic3—41no—
1071Dic3—41no—
1072Dic3—41no—
1073Dic3—41no—
1074Dic3—42no—
1075Dic3—41no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—32no—
1090C23—34no—
1091C23—61no—
1092C23—62no—
1093C23—62no—
1094C23—61no—
1095C23—61no—
1096C23—62no—
1097C23—61no—
1098C23—62no—
1099C23—62no—
1100C23—61no—
1101C23—62no—
1102C23—61no—
1103C23—62no—
1104C23—62no—
1105C23—62no—
1106C23—62no—
1107C23—62no—
1108C23—62no—
1109C23—62no—
1110C23—62no—
1111C23—62no—
1112C23—62no—
1113C23—62no—
1114C23—62no—
1115C23—62no—
1116C23—62no—
1117C23—128no—
1118C23—128no—
1119C23—128no—
1120C23—244no—
1121C23—244no—
1122C23—244no—
1123C23—244no—
1124C23—244no—
1125C23—244no—
1126C23—244no—
1127C23—244no—
1128C23—244no—
1129C23—244no—
1130C23—244no—
1131C23#100912yes—
1132C23C24×D311yescharacteristic
1133Q8—28no—
1134D4—44no—
1135D4—68no—
1136D4—84no—
1137D4—128no—
1138D4—128no—
1139D4—128no—
1140D4—124no—
1141D4—124no—
1142D4—124no—
1143D4—244no—
1144D4—244no—
1145D4—244no—
1146D4—244no—
1147D4—244no—
1148D4—244no—
1149D4—244no—
1150D4—244no—
1151D4—244no—
1152D4—244no—
1153C2×C4—21no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—22no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—22no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—32no—
1176C2×C4—32no—
1177C2×C4—44no—
1178C2×C4—61no—
1179C2×C4—61no—
1180C2×C4—61no—
1181C2×C4—61no—
1182C2×C4—68no—
1183C2×C4—61no—
1184C2×C4—61no—
1185C2×C4—61no—
1186C2×C4—61no—
1187C2×C4—61no—
1188C2×C4—62no—
1189C2×C4—62no—
1190C2×C4—61no—
1191C2×C4—61no—
1192C2×C4—61no—
1193C2×C4—62no—
1194C2×C4—61no—
1195C2×C4—61no—
1196C2×C4—61no—
1197C2×C4—61no—
1198C2×C4—61no—
1199C2×C4—61no—
1200C2×C4—61no—
1201C2×C4—128no—
1202C2×C4—244no—
1203C2×C4C2×D3×D414yes—
1204C2×C4C2×D3×D412yes—
1205C2×C4#100412yes—
1206C2×C4#100912yes—
1207C2×C4#100912yes—
1208C2×C3—42no—
1209C2×C3—82no—
1210C2×C3C2×#53411yescharacteristic
1211C2×C3#348811yescharacteristic
1212C2×C3#349811yescharacteristic
1213C2×C3#354311yescharacteristic
1214C2×C3#354311yescharacteristic
1215C2×C3#355811yescharacteristic
1216C2×C3#355811yescharacteristic
1217D3—44no—
1218D3—42no—
1219D3—82no—
1220D3—82no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—62no—
1236C22—64no—
1237C22—62no—
1238C22—64no—
1239C22—64no—
1240C22—62no—
1241C22—121no—
1242C22—122no—
1243C22—121no—
1244C22—122no—
1245C22—121no—
1246C22—122no—
1247C22—121no—
1248C22—122no—
1249C22—122no—
1250C22—122no—
1251C22—122no—
1252C22—122no—
1253C22—122no—
1254C22—122no—
1255C22—122no—
1256C22—122no—
1257C22—122no—
1258C22—122no—
1259C22—122no—
1260C22—122no—
1261C22—122no—
1262C22—122no—
1263C22—2416no—
1264C22—2416no—
1265C22C22×D3×D411yescharacteristic
1266C22C2×#100411yescharacteristic
1267C22C2×#100911yescharacteristic
1268C22C2×#100911yescharacteristic
1269C22C2×#100911yescharacteristic
1270C22D3×H(5,𝔽2)11yescharacteristic
1271C22#596811yescharacteristic
1272C4—24no—
1273C4—22no—
1274C4—42no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—42no—
1279C4—41no—
1280C4—62no—
1281C4—62no—
1282C4—121no—
1283C4—122no—
1284C4—121no—
1285C4—121no—
1286C4—121no—
1287C4—121no—
1288C4#560514yes—
1289C3#4296611yescharacteristic, complemented, Sylow
1290C2—42no—
1291C2—82no—
1292C2—122no—
1293C2—124no—
1294C2—242no—
1295C2—242no—
1296C2C2×#560511yescharacteristic
1297C2#8617211yescharacteristic
1298C2#8656711yescharacteristic
1299C2#8665111yescharacteristic
1300C2#8671311yescharacteristic
1301C2#8673011yescharacteristic
1302C2#8677011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2426C2
hypercenter#2426D3
hypocenterC3#42966
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2426

Complements

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

NH ≅ G/Ntype
1. C2×#5674C2semidirect
2. C2×#5630C2semidirect
3. C3×#2426C2semidirect
4. #82974C2semidirect
5. #82755C2semidirect
6. #82653C2semidirect
7. #82640C2semidirect
8. #82476C2semidirect
9. #82457C2semidirect
10. #77448C2semidirect
11. #77430C2semidirect
12. #77138C2semidirect
13. #77123C2semidirect
14. #76464C2semidirect
15. #76454C2semidirect
16. #76318C2semidirect
17. #76314C2semidirect
18. #76249C2semidirect
19. #76004C2semidirect
20. #75916C2semidirect
21. #75910C2semidirect
22. #73587C2semidirect
23. #73582C2semidirect
26. C22×D3×D4C22semidirect
27. C23×D12C22semidirect
28. C2×C3×#124C22semidirect
29. C2×C3×C22⋊Q8C22semidirect
31. C2×C3×C4×Q8C22semidirect
32. C2×#947C22semidirect
33. C2×#947C22semidirect
34. C2×Q8×Dic3C22semidirect
38. C2×#937C22semidirect
39. C2×#937C22semidirect
46. C2×#894C22semidirect
47. C2×#894C22semidirect
48. C2×#893C22semidirect
49. C2×#884C22semidirect
50. C2×#884C22semidirect
51. C2×#883C22semidirect
53. C2×#882C22semidirect
54. C2×#882C22semidirect
55. C2×#882C22semidirect
56. C2×#882C22semidirect
57. C2×#882C22semidirect
58. C2×#882C22semidirect
59. C2×D3×C22⋊C4C22semidirect
62. C2×#872C22semidirect
63. C3×#396C22semidirect
64. C3×#394C22semidirect
65. C3×#390C22semidirect
66. C3×#390C22semidirect
67. C3×#389C22semidirect
68. C3×#388C22semidirect
69. C3×C4×C22⋊C4C22semidirect
71. #5221C22semidirect
72. C4×#217C22semidirect
73. #4994C22semidirect
74. #4993C22semidirect
75. #4991C22semidirect
76. #4991C22semidirect
77. #4991C22semidirect
78. #4991C22semidirect
79. #4990C22semidirect
80. #4988C22semidirect
81. #4988C22semidirect
82. #4988C22semidirect
83. #4988C22semidirect
84. #4988C22semidirect
85. #4987C22semidirect
86. #4987C22semidirect
87. #4972C22semidirect
89. #4961C22semidirect
90. #4961C22semidirect
91. #4961C22semidirect
92. #4961C22semidirect
93. #4960C22semidirect
94. #4960C22semidirect
95. #4960C22semidirect
96. #4960C22semidirect
98. #4959C22semidirect
99. #4959C22semidirect
100. #4957C22semidirect
101. #4957C22semidirect
102. #4957C22semidirect
103. #4956C22semidirect
104. #4955C22semidirect
105. #4952C22semidirect
106. #4949C22semidirect
107. #4939C22semidirect
108. #4939C22semidirect
109. #4939C22semidirect
110. #4939C22semidirect
111. #4939C22semidirect
112. C4×(C2×D3)⋊C4C22semidirect
113. C4×(C2×D3)⋊C4C22semidirect
114. C4×C4⋊Dic3C22semidirect
115. C4×Dic3⋊C4C22semidirect
116. #4675C22semidirect
117. #4675C22semidirect
118. #4674C22semidirect
119. #4672C22semidirect
120. #4672C22semidirect
121. #4671C22semidirect
122. #4671C22semidirect
123. #4665C22semidirect
124. #4658C22semidirect
125. #4657C22semidirect
145. #2426D3semidirect
164. C2×#239D4semidirect
301. C2×#124C2×D3semidirect
305. C2×C22⋊Q8C2×D3semidirect
323. C2×C4×Q8C2×D3semidirect
337. #396C2×D3semidirect
352. #394C2×D3semidirect
374. #390C2×D3semidirect
375. #390C2×D3semidirect
377. #389C2×D3semidirect
379. #388C2×D3semidirect
390. C4×C22⋊C4C2×D3semidirect
1289. C3#42966semidirect

Maximal subgroups

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

subgroupindex
C2×#56742
C2×#56302
C3×#24262
#829742
#827552
#826532
#826402
#824762
#824572
#774482
#774302
#771382
#771232
#764642
#764542
#763182
#763142
#762492
#760042
#759162
#759102
#735872
#735822
#429663