Finite Group Databasebeta

← #17979285

Subgroups — #17979285

Order 4352.

2390 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545325C214yesmaximal, complemented
2#14545318C212yesmaximal, complemented
3#14545314C212yesmaximal, complemented
4#14545309C214yesmaximal, complemented
5#14545305C212yesmaximal, complemented
6D4×C4⋊#595C212yesmaximal, complemented
7#14545283C214yesmaximal, complemented
8#14545272C212yesmaximal, complemented
9#14545270C214yesmaximal, complemented
10#14545262C211yesmaximal, characteristic, complemented
11#121×#595C212yesmaximal, complemented
12#14545244C211yesmaximal, characteristic, complemented
13D17×#540C211yesmaximal, characteristic
14C2×D4×#595C2212yes—
15C2×D4×#595C2214yes—
16C2×D4×#595C2214yes—
17C2×D4×#595C2212yes—
18C2×#10587677C2211yescharacteristic
19C22×C4⋊#595C2214yes—
20C22×C4×#595C2211yescharacteristic
21#11763761C2212yes—
22#11763761C2212yes—
23#11763761C2214yes—
24#11763761C2214yes—
25#11763760C2212yes—
26#11763760C2212yes—
27#11763760C2212yes—
28#11763760C2214yes—
29#11763760C2212yes—
30#11763759C2214yes—
31#11763759C2214yes—
32#11763759C2214yes—
33#11763759C2214yes—
34#11763759C2214yes—
35#11763758C2214yes—
36#11763758C2214yes—
37#11763758C2214yes—
38#11763757C2214yes—
39#11763757C2214yes—
40#11763757C2214yes—
41#11763757C2214yes—
42#11763756C2212yes—
43#11763756C2212yes—
44#11763756C2214yes—
45#11763756C2214yes—
46#11763756C2214yes—
47#11763755C2211yescharacteristic
48#11763753C2211yescharacteristic
49#11763752C2214yes—
50#11763751C2212yes—
51#11763751C2214yes—
52C4⋊C4×#595C2212yes—
53C4⋊C4×#595C2212yes—
54C4⋊C4×#595C2214yes—
55C4×C4⋊#595C2212yes—
56C4×C4⋊#595C2212yes—
57C4×C4⋊#595C2212yes—
58C22⋊C4×#595C2214yes—
59C4×C22⋊#595C2214yes—
60#11763415C411yescharacteristic, complemented
61#11763414C411yescharacteristic, complemented
62#11763413C411yescharacteristic, complemented
63#11763412C412yescomplemented
64#11763411C414yescomplemented
65#11763410C412yescomplemented
66#11763409C414yescomplemented
67#127×D17C2211yescharacteristic
68#125×D17C2211yescharacteristic
69#123×D17C2214yes—
70#121×D17C2212yes—
71#121×D17C2214yes—
72C4×D4×D17C2212yes—
73#117×D17C2211yescharacteristic
74C17×#540C411yescharacteristic, complemented
75C23×#595C2311yescharacteristic
76C23×#595C2314yes—
77C23×#595C2311yescharacteristic
78C23×#595C2314yes—
79C2×D4×D17C2312yes—
80C2×D4×D17C2314yes—
81C2×D4×D17C2314yes—
82C22×C4×D17C2311yescharacteristic
83C22×C4×D17C2314yes—
84C2×C22⋊#595C2314yes—
85C2×C22⋊#595C2314yes—
86C2×C22⋊#595C2314yes—
87C2×C22⋊#595C2314yes—
88C2×C22⋊#595C2314yes—
89C2×C22⋊#595C2314yes—
90C2×C22⋊#595C2314yes—
91C2×C22⋊#595C2312yes—
92D4×#595—44no—
93D4×#595—44no—
94D4×#595—48no—
95D4×#595—48no—
96#10587677—42no—
97C2×C4⋊#595—48no—
98C2×C4⋊#595C2312yes—
99C2×C4⋊#595C2312yes—
100C2×C4⋊#595C2312yes—
101C2×C4⋊#595C2312yes—
102C2×C4⋊#595C2314yes—
103C2×C4⋊#595C2312yes—
104C2×C4⋊#595C2312yes—
105C2×C4⋊#595C2314yes—
106C2×C4⋊#595C2311yescharacteristic
107C2×C4⋊#595C2314yes—
108C2×C4⋊#595C2311yescharacteristic
109C2×C4×#595—42no—
110C2×C4×#595C2312yes—
111C2×C4×#595C2312yes—
112C2×C4×#595C2314yes—
113C2×C4×#595C2314yes—
114C2×C4×#595C2312yes—
115C2×C4×#595C2314yes—
116C17×#127C2×C411yescharacteristic, complemented
117C17×#125C2×C411yescharacteristic, complemented
118C17×#123C2×C414yescomplemented
119C17×#121C2×C414yescomplemented
120C17×#121C2×C412yescomplemented
121C4×D4×C17C2×C412yescomplemented
122C17×#117C2×C411yescharacteristic, complemented
123#10587626C2×C414yescomplemented
124#10587626C2×C412yescomplemented
125#10587625C2×C414yescomplemented
126#10587625C2×C414yescomplemented
127#10587625C2×C414yescomplemented
128#10587624C2×C414yescomplemented
129#10587624C2×C412yescomplemented
130#10587621C2×C414yescomplemented
131D4×Dic17C2×C412yescomplemented
132#10587616C2×C414yescomplemented
133#10587616C2×C412yescomplemented
134#10587615C2×C414yescomplemented
135C4×C22⋊D17C2×C414yescomplemented
136#10587612C2×C411yescharacteristic, complemented
137#10587581C2×C412yescomplemented
138#10587581C2×C414yescomplemented
139#10587580C2×C414yescomplemented
140#10587580C2×C414yescomplemented
141#10587579C2×C412yescomplemented
142#10587578C2×C412yescomplemented
143C4⋊C4×D17C2312yes—
144C4⋊C4×D17C2314yes—
145C4⋊C4×D17C2312yes—
146#10587576C2×C412yescomplemented
147#10587575C2×C414yescomplemented
148#10587572C2×C414yescomplemented
149#10587570C2×C414yescomplemented
150#10587570C2×C414yescomplemented
151#10587570C2×C414yescomplemented
152#10587569C2×C414yescomplemented
153#10587569C2×C414yescomplemented
154#10587567C2×C414yescomplemented
155C22⋊C4×D17C2314yes—
156C22⋊C4×D17C2312yes—
157C22⋊C4×D17C2314yes—
158#10587563C2×C412yescomplemented
159#10587560C2×C411yescharacteristic, complemented
160C4×D68C2×C412yescomplemented
161#10587558C2×C411yescharacteristic, complemented
162#10587558C2×C411yescharacteristic, complemented
163C42×D17C2311yescharacteristic
164C42×D17C2311yescharacteristic
165#10587556C2×C411yescharacteristic, complemented
166(C2×#595)⋊C4C2312yes—
167(C2×#595)⋊C4C2314yes—
168(C2×#595)⋊C4C2314yes—
169(C2×#595)⋊C4C2314yes—
170(C2×#595)⋊C4C2312yes—
171(C2×#595)⋊C4C2312yes—
172(C2×#595)⋊C4C2312yes—
173(C2×#595)⋊C4C2314yes—
174(C2×#595)⋊C4C2314yes—
175(C2×#595)⋊C4C2314yes—
176(C2×#595)⋊C4C2314yes—
177C23×D17C2414yes—
178C23×D17C2411yescharacteristic
179C22×#595—24no—
180C22×#595—28no—
181C22×#595—41no—
182C22×#595—41no—
183C22×#595—42no—
184C22×#595—44no—
185C22×#595—44no—
186C22×#595—44no—
187C22×#595—44no—
188C22×#595—44no—
189C22×#595C2412yes—
190C22×#595C2414yes—
191C22×#595C2412yes—
192C22×#595C2412yes—
193C22×#595C2414yes—
194C22×#595C2412yes—
195C2×D4×C17C22×C412yes—
196C2×D4×C17C22×C414yes—
197C2×D4×C17C22×C414yes—
198C22×C4×C17C22×C411yescharacteristic
199C22×C4×C17C22×C414yes—
200C2×C22⋊D17C22×C414yes—
201C2×C22⋊D17C22×C414yes—
202C2×C22⋊D17C22×C414yes—
203C2×C22⋊D17C22×C414yes—
204C2×C22⋊D17C22×C414yes—
205C22×Dic17C22×C411yescharacteristic
206C22×Dic17C22×C414yes—
207D4×D17—24no—
208D4×D17—24no—
209D4×D17—44no—
210D4×D17—44no—
211D4×D17—44no—
212D4×D17—44no—
213C2×D68C22×C412yes—
214C2×D68C22×C414yes—
215C2×D68C22×C414yes—
216C2×C4×D17—22no—
217C2×C4×D17—22no—
218C2×C4×D17—44no—
219C2×C4×D17—44no—
220C2×C4×D17C22×C411yescharacteristic
221C2×C4×D17C22×C411yescharacteristic
222C2×C4×D17C22×C414yes—
223C2×C4×D17C22×C414yes—
224C2×C4×D17C2414yes—
225C2×C4×D17C2411yescharacteristic
226C2×C4×D17C2412yes—
227C2×C4×D17C2412yes—
228C2×C4×D17C2411yescharacteristic
229C22⋊#595—28no—
230C22⋊#595—42no—
231C22⋊#595—44no—
232C22⋊#595—44no—
233C22⋊#595—44no—
234C22⋊#595—44no—
235C22⋊#595—44no—
236C22⋊#595—44no—
237C4⋊#595—24no—
238C4⋊#595—28no—
239C4⋊#595—24no—
240C4⋊#595—24no—
241C4⋊#595—24no—
242C4⋊#595—44no—
243C4⋊#595—44no—
244C4⋊#595—42no—
245C4⋊#595—42no—
246C4⋊#595—41no—
247C4⋊#595—41no—
248C4×#595—24no—
249C4×#595—24no—
250C4×#595—42no—
251C4×#595—44no—
252C4×#595—44no—
253C4×#595—44no—
254C4⋊C4×C17C22×C412yes—
255C4⋊C4×C17C22×C414yes—
256C4⋊C4×C17C22×C412yes—
257C22⋊C4×C17C22×C414yes—
258C22⋊C4×C17C22×C414yes—
259C22⋊C4×C17C22×C412yes—
260C42×C17C22×C411yescharacteristic
261C42×C17C22×C411yescharacteristic
262C22⋊Dic17C22×C412yes—
263C22⋊Dic17C22×C414yes—
264C22⋊Dic17C22×C414yes—
265#63227C22×C412yes—
266#63227C22×C412yes—
267#63227C22×C414yes—
268#63227C22×C414yes—
269#63227C22×C414yes—
270#63227C22×C414yes—
271C4⋊Dic17C22×C412yes—
272C4⋊Dic17C22×C412yes—
273C4⋊Dic17C22×C414yes—
274#63225C22×C414yes—
275#63225C22×C412yes—
276#63225C22×C412yes—
277#63225C22×C414yes—
278#63225C22×C414yes—
279C4×Dic17C22×C411yescharacteristic
280C4×Dic17C22×C411yescharacteristic
281C4×Dic17C22×C412yes—
282C4×Dic17C22×C412yes—
283#34418—171nomaximal, Sylow
284C23×C17C23×C411yescharacteristic
285C23×C17C23×C414yes—
286C22×D17—24no—
287C22×D17—21no—
288C22×D17—24no—
289C22×D17—22no—
290C22×D17—24no—
291C22×D17—21no—
292C22×D17—24no—
293C22×D17—24no—
294C22×D17—24no—
295C22×D17—22no—
296C22×D17C23×C411yescharacteristic
297C22×D17C23×C414yes—
298C22×D17C2511yescharacteristic
299C2×#595—22no—
300C2×#595—22no—
301C2×#595—22no—
302C2×#595—22no—
303C2×#595—22no—
304C2×#595—24no—
305C2×#595—24no—
306C2×#595—22no—
307C2×#595—24no—
308C2×#595—24no—
309C2×#595—22no—
310C2×#595—24no—
311C2×#595—22no—
312C2×#595—24no—
313C2×#595—22no—
314C2×#595—22no—
315C2×#595—22no—
316C2×#595—44no—
317C2×#595—44no—
318C2×#595—88no—
319C2×#595—88no—
320C2×#595H(5,𝔽2)14yes—
321D4×C17—24no—
322D4×C17—44no—
323D4×C17—44no—
324C2×C4×C17—22no—
325C2×C4×C17—44no—
326C2×C4×C17C23×C412yes—
327C2×C4×C17C23×C412yes—
328C2×C4×C17C23×C411yescharacteristic
329C2×C4×C17C23×C414yes—
330C2×C4×C17C23×C411yescharacteristic
331C22⋊D17—28no—
332C22⋊D17—44no—
333C22⋊D17—44no—
334C22⋊D17—44no—
335C22⋊D17—44no—
336C2×Dic17—22no—
337C2×Dic17—44no—
338C2×Dic17C23×C411yescharacteristic
339C2×Dic17C23×C412yes—
340C2×Dic17C23×C414yes—
341C2×Dic17C23×C412yes—
342C2×Dic17C23×C411yescharacteristic
343D68—24no—
344D68—44no—
345D68—44no—
346C4×D17—22no—
347C4×D17—21no—
348C4×D17—24no—
349C4×D17—22no—
350C4×D17—21no—
351C4×D17—24no—
352C4×D17—22no—
353C4×D17—22no—
354C4×D17—22no—
355C4×D17—22no—
356C4×D17—44no—
357C4×D17—44no—
358C4×D17H(5,𝔽2)12yes—
359C4×D172−1+412yes—
360C2×#540—171no—
361#2377—174no—
362#2370—172no—
363#2366—172no—
364#2361—174no—
365#2357—172no—
366D4×C4⋊C4—172no—
367#2335—174no—
368#2324—172no—
369#2322—174no—
370#2314—171no—
371C4×#121—172no—
372#2296—171no—
373C22×C17—21no—
374C22×C17—24no—
375C22×C17—24no—
376C22×C17—24no—
377C22×C17—22no—
378C22×C17C24×C411yescharacteristic
379C2×D17—21no—
380C2×D17—24no—
381C2×D17—24no—
382C2×D17—24no—
383C2×D17—22no—
384C2×D17—41no—
385C2×D17—44no—
386C2×D17—41no—
387C2×D17—44no—
388C2×D17—44no—
389C2×D17—42no—
390C2×D17—44no—
391C2×D17C2×H(5,𝔽2)11yescharacteristic
392C2×D17C2×H(5,𝔽2)12yes—
393C2×D17C2×2−1+411yescharacteristic
394C2×D17#58512yes—
395#595—24no—
396#595—42no—
397#595—44no—
398#595—42no—
399#595—42no—
400#595—44no—
401C4×C17—21no—
402C4×C17—22no—
403C4×C17—24no—
404C4×C17—22no—
405C4×C17#52012yes—
406Dic17—21no—
407Dic17—22no—
408Dic17—24no—
409Dic17—22no—
410Dic17#52012yes—
411#540—171no—
412#540—171no—
413#540—174no—
414#540—174no—
415#540—172no—
416#540—172no—
417#540—171no—
418#540#59511yescharacteristic, complemented
419C2×#127—171no—
420C2×#125—171no—
421C2×#123—174no—
422C2×#121—172no—
423C2×#121—174no—
424C2×C4×D4—172no—
425C2×C4×D4—174no—
426C2×C4×D4—172no—
427C2×C4×D4—172no—
428C2×C4×D4—174no—
429C2×#117—171no—
430C2×#117—171no—
431C22×C4⋊C4—174no—
432C22×C42—171no—
433#390—172no—
434#390—174no—
435#390—174no—
436#390—172no—
437#389—172no—
438#389—174no—
439#389—172no—
440#389—172no—
441#389—172no—
442#388—174no—
443#388—174no—
444#388—174no—
445#388—174no—
446#388—174no—
447#387—174no—
448#387—174no—
449#387—174no—
450#386—174no—
451#386—174no—
452#386—174no—
453#386—174no—
454#385—174no—
455#385—174no—
456#385—174no—
457#385—172no—
458#385—172no—
459#384—171no—
460#382—171no—
461#381—174no—
462#380—172no—
463#380—174no—
464C4×C4⋊C4—172no—
465C4×C4⋊C4—172no—
466C4×C4⋊C4—174no—
467C4×C4⋊C4—172no—
468C4×C4⋊C4—172no—
469C4×C4⋊C4—172no—
470C4×C22⋊C4—174no—
471C4×C22⋊C4—174no—
472C2×C17—41no—
473C2×C17—44no—
474C2×C17C2×#52011yescharacteristic
475C2×C17C4×H(5,𝔽2)12yes—
476D17—41no—
477D17—44no—
478D17#353711yescharacteristic
479D17#353911yescharacteristic
480D17#355412yes—
481C22×D4—172no—
482C22×D4—174no—
483C22×D4—174no—
484C23×C4—171no—
485C23×C4—174no—
486C23×C4—171no—
487C23×C4—174no—
488C23×C4—174no—
489C23×C4—171no—
490#127—174no—
491#127—172no—
492#127—171no—
493#127C2×#59511yescharacteristic, complemented
494#125—174no—
495#125—172no—
496#125—171no—
497#125C2×#59511yescharacteristic, complemented
498#123—174no—
499#123—174no—
500#123—174no—
501#123—174no—
502#123—174no—
503#123—174no—
504#123—174no—
505#123C2×#59514yescomplemented
506#121—174no—
507#121—172no—
508#121—174no—
509#121—174no—
510#121—174no—
511#121—174no—
512#121—172no—
513#121—174no—
514#121—172no—
515#121—174no—
516#121—174no—
517#121—174no—
518#121C2×#59514yescomplemented
519#121C2×#59512yescomplemented
520C4×D4—172no—
521C4×D4—174no—
522C4×D4—172no—
523C4×D4—174no—
524C4×D4—172no—
525C4×D4—684no—
526C4×D4—684no—
527C4×D4—688no—
528C4×D4—688no—
529C4×D4C2×#59512yescomplemented
530#117—171no—
531#117—172no—
532#117—172no—
533#117—171no—
534#117—171no—
535#117—682no—
536#117C2×#59511yescharacteristic, complemented
537C2×C4⋊C4—172no—
538C2×C4⋊C4—172no—
539C2×C4⋊C4—174no—
540C2×C4⋊C4—172no—
541C2×C4⋊C4—174no—
542C2×C4⋊C4—172no—
543C2×C4⋊C4—172no—
544C2×C4⋊C4—172no—
545C2×C4⋊C4—174no—
546C2×C4⋊C4—174no—
547C2×C4⋊C4—171no—
548C2×C4⋊C4—171no—
549C2×C4⋊C4—172no—
550C2×C4⋊C4—172no—
551C2×C4⋊C4—688no—
552C2×C22⋊C4—172no—
553C2×C22⋊C4—174no—
554C2×C22⋊C4—174no—
555C2×C22⋊C4—174no—
556C2×C22⋊C4—172no—
557C2×C22⋊C4—174no—
558C2×C22⋊C4—174no—
559C2×C22⋊C4—174no—
560C2×C22⋊C4—174no—
561C2×C22⋊C4—174no—
562C2×C22⋊C4—174no—
563C2×C42—171no—
564C2×C42—171no—
565C2×C42—172no—
566C2×C42—172no—
567C2×C42—174no—
568C2×C42—174no—
569C2×C42—172no—
570C2×C42—174no—
571C2×C42—682no—
572#95—172no—
573#95—174no—
574#95—174no—
575#95—174no—
576#95—172no—
577#95—174no—
578#95—172no—
579#95—174no—
580#95—174no—
581#95—172no—
582#95—174no—
583C17#3441811yescharacteristic, complemented, Sylow
584C24—174no—
585C24—171no—
586C2×D4—174no—
587C2×D4—174no—
588C2×D4—174no—
589C2×D4—174no—
590C2×D4—174no—
591C2×D4—172no—
592C2×D4—174no—
593C2×D4—174no—
594C2×D4—344no—
595C2×D4—344no—
596C2×D4—684no—
597C2×D4—684no—
598C2×D4—684no—
599C2×D4—684no—
600C2×D4C22×#59512yes—
601C2×D4C22×#59514yes—
602C2×D4C22×#59514yes—
603C22×C4—171no—
604C22×C4—172no—
605C22×C4—171no—
606C22×C4—174no—
607C22×C4—171no—
608C22×C4—171no—
609C22×C4—172no—
610C22×C4—171no—
611C22×C4—174no—
612C22×C4—172no—
613C22×C4—174no—
614C22×C4—174no—
615C22×C4—174no—
616C22×C4—172no—
617C22×C4—172no—
618C22×C4—172no—
619C22×C4—174no—
620C22×C4—342no—
621C22×C4—342no—
622C22×C4—344no—
623C22×C4—348no—
624C22×C4—684no—
625C22×C4—684no—
626C22×C4—681no—
627C22×C4—681no—
628C22×C4—682no—
629C22×C4—684no—
630C22×C4—684no—
631C22×C4—684no—
632C22×C4—684no—
633C22×C4—684no—
634C22×C4C22×#59511yescharacteristic
635C22×C4C22×#59514yes—
636C4⋊C4—172no—
637C4⋊C4—172no—
638C4⋊C4—172no—
639C4⋊C4—174no—
640C4⋊C4—172no—
641C4⋊C4—174no—
642C4⋊C4—174no—
643C4⋊C4—174no—
644C4⋊C4—344no—
645C4⋊C4—344no—
646C4⋊C4—348no—
647C4⋊C4—344no—
648C4⋊C4—344no—
649C4⋊C4—682no—
650C4⋊C4—682no—
651C4⋊C4—684no—
652C4⋊C4—684no—
653C4⋊C4—681no—
654C4⋊C4—681no—
655C4⋊C4C22×#59512yes—
656C4⋊C4C22×#59512yes—
657C4⋊C4C22×#59514yes—
658C22⋊C4—172no—
659C22⋊C4—174no—
660C22⋊C4—174no—
661C22⋊C4—172no—
662C22⋊C4—172no—
663C22⋊C4—174no—
664C22⋊C4—174no—
665C22⋊C4—174no—
666C22⋊C4—174no—
667C22⋊C4—348no—
668C22⋊C4—684no—
669C22⋊C4—684no—
670C22⋊C4—682no—
671C22⋊C4—684no—
672C22⋊C4—684no—
673C22⋊C4—684no—
674C22⋊C4—684no—
675C22⋊C4C22×#59512yes—
676C22⋊C4C22×#59514yes—
677C22⋊C4C22×#59514yes—
678C42—172no—
679C42—171no—
680C42—172no—
681C42—171no—
682C42—344no—
683C42—344no—
684C42—684no—
685C42—682no—
686C42—684no—
687C42—684no—
688C42C22×#59511yescharacteristic
689C42C22×#59511yescharacteristic
690C23—171no—
691C23—171no—
692C23—174no—
693C23—344no—
694C23—341no—
695C23—342no—
696C23—344no—
697C23—344no—
698C23—344no—
699C23—344no—
700C23—341no—
701C23—342no—
702C23—344no—
703C23C23×#59511yescharacteristic
704C23C23×#59514yes—
705D4—24no—
706D4—44no—
707D4—44no—
708D4—348no—
709D4—344no—
710D4—684no—
711D4—684no—
712D4—684no—
713D4—684no—
714D4—684no—
715D4—684no—
716C2×C4—22no—
717C2×C4—44no—
718C2×C4—171no—
719C2×C4—172no—
720C2×C4—172no—
721C2×C4—174no—
722C2×C4—172no—
723C2×C4—172no—
724C2×C4—171no—
725C2×C4—174no—
726C2×C4—342no—
727C2×C4—342no—
728C2×C4—341no—
729C2×C4—344no—
730C2×C4—344no—
731C2×C4—342no—
732C2×C4—342no—
733C2×C4—342no—
734C2×C4—341no—
735C2×C4—342no—
736C2×C4—342no—
737C2×C4—342no—
738C2×C4—342no—
739C2×C4—342no—
740C2×C4—342no—
741C2×C4—342no—
742C2×C4—344no—
743C2×C4—342no—
744C2×C4—344no—
745C2×C4—344no—
746C2×C4—344no—
747C2×C4—342no—
748C2×C4—342no—
749C2×C4—342no—
750C2×C4—344no—
751C2×C4—342no—
752C2×C4—344no—
753C2×C4—342no—
754C2×C4—684no—
755C2×C4—684no—
756C2×C4—684no—
757C2×C4—684no—
758C2×C4—684no—
759C2×C4—1368no—
760C2×C4—1368no—
761C2×C4C23×#59512yes—
762C2×C4C23×#59512yes—
763C2×C4C23×#59511yescharacteristic
764C2×C4C23×#59514yes—
765C2×C4C23×#59511yescharacteristic
766C22—21no—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—22no—
771C22—171no—
772C22—171no—
773C22—172no—
774C22—172no—
775C22—341no—
776C22—344no—
777C22—344no—
778C22—344no—
779C22—342no—
780C22—681no—
781C22—681no—
782C22—684no—
783C22—684no—
784C22—684no—
785C22—682no—
786C22—684no—
787C22C24×#59511yescharacteristic
788C4—21no—
789C4—22no—
790C4—24no—
791C4—22no—
792C4—172no—
793C4—344no—
794C4—341no—
795C4—342no—
796C4—344no—
797C4—342no—
798C4—682no—
799C4—682no—
800C4—684no—
801C4—682no—
802C4—684no—
803C4#1176387812yes—
804C2—41no—
805C2—44no—
806C2—171no—
807C2—171no—
808C2—172no—
809C2—681no—
810C2—684no—
811C2C2×#1176387811yescharacteristic
812C2H(5,𝔽2)×#59512yes—
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC17×#540C4
prime radicalD17×#540C2
cosocleC22×D17C25
hypercenter#540#595
hypocenterC17#34418
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #14545325C2semidirect
2. #14545318C2semidirect
3. #14545314C2semidirect
4. #14545309C2semidirect
5. #14545305C2semidirect
6. D4×C4⋊#595C2semidirect
7. #14545283C2semidirect
8. #14545272C2semidirect
9. #14545270C2semidirect
10. #14545262C2semidirect
11. #121×#595C2semidirect
12. #14545244C2semidirect
60. #11763415C4semidirect
61. #11763414C4semidirect
62. #11763413C4semidirect
63. #11763412C4semidirect
64. #11763411C4semidirect
65. #11763410C4semidirect
66. #11763409C4semidirect
74. C17×#540C4semidirect
116. C17×#127C2×C4semidirect
117. C17×#125C2×C4semidirect
118. C17×#123C2×C4semidirect
119. C17×#121C2×C4semidirect
120. C17×#121C2×C4semidirect
121. C4×D4×C17C2×C4semidirect
122. C17×#117C2×C4semidirect
123. #10587626C2×C4semidirect
124. #10587626C2×C4semidirect
125. #10587625C2×C4semidirect
126. #10587625C2×C4semidirect
127. #10587625C2×C4semidirect
128. #10587624C2×C4semidirect
129. #10587624C2×C4semidirect
130. #10587621C2×C4semidirect
131. D4×Dic17C2×C4semidirect
132. #10587616C2×C4semidirect
133. #10587616C2×C4semidirect
134. #10587615C2×C4semidirect
135. C4×C22⋊D17C2×C4semidirect
136. #10587612C2×C4semidirect
137. #10587581C2×C4semidirect
138. #10587581C2×C4semidirect
139. #10587580C2×C4semidirect
140. #10587580C2×C4semidirect
141. #10587579C2×C4semidirect
142. #10587578C2×C4semidirect
146. #10587576C2×C4semidirect
147. #10587575C2×C4semidirect
148. #10587572C2×C4semidirect
149. #10587570C2×C4semidirect
150. #10587570C2×C4semidirect
151. #10587570C2×C4semidirect
152. #10587569C2×C4semidirect
153. #10587569C2×C4semidirect
154. #10587567C2×C4semidirect
158. #10587563C2×C4semidirect
159. #10587560C2×C4semidirect
160. C4×D68C2×C4semidirect
161. #10587558C2×C4semidirect
162. #10587558C2×C4semidirect
165. #10587556C2×C4semidirect
418. #540#595semidirect
493. #127C2×#595semidirect
497. #125C2×#595semidirect
505. #123C2×#595semidirect
518. #121C2×#595semidirect
519. #121C2×#595semidirect
529. C4×D4C2×#595semidirect
536. #117C2×#595semidirect
583. C17#34418semidirect

Maximal subgroups

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

subgroupindex
#145453252
#145453182
#145453142
#145453092
#145453052
D4×C4⋊#5952
#145452832
#145452722
#145452702
#145452622
#121×#5952
#145452442
D17×#5402
#3441817