Finite Group Databasebeta

← #17979269

Subgroups — #17979269

Order 4352.

2410 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545325C214yesmaximal, complemented
2#14545315C214yesmaximal, complemented
3#14545301C214yesmaximal, complemented
4#14545289C212yesmaximal, complemented
5#14545287C212yesmaximal, complemented
6#14545281C214yesmaximal, complemented
7#14545276C212yesmaximal, complemented
8#14545275C212yesmaximal, complemented
9#14545266C214yesmaximal, complemented
10#14545231C211yesmaximal, characteristic, complemented
11#14545231C211yesmaximal, characteristic, complemented
12D17×#532C211yesmaximal, characteristic
13C2×Q8×#595C2214yes—
14C2×D4×#595C2214yes—
15(C2×#595)⋊Q8C2214yes—
16#11763761C2214yes—
17#11763761C2218yes—
18#11763759C2218yes—
19#11763759C2218yes—
20#11763758C2218yes—
21#11763758C2218yes—
22#11763757C2218yes—
23#11763757C2218yes—
24#11763757C2218yes—
25#11763756C2218yes—
26#11763754C2212yes—
27#11763754C2212yes—
28#11763753C2212yes—
29#11763753C2212yes—
30#11763752C2212yes—
31#11763752C2212yes—
32#11763752C2214yes—
33#11763751C2212yes—
34#11763751C2212yes—
35#11763751C2214yes—
36C4×C4⋊#595C2212yes—
37C4×C4⋊#595C2212yes—
38C22⋊C4×#595C2218yes—
39C4×C22⋊#595C2212yes—
40C4×C22⋊#595C2211yescharacteristic
41C4×C22⋊#595C2211yescharacteristic
42C4×C22⋊#595C2214yes—
43#11763745C2212yes—
44#11763745C2212yes—
45C2×(C2×#595)⋊C4C2214yes—
46C2×#41×D17C2212yes—
47#11763360C411yescharacteristic, complemented
48#11763359C411yescharacteristic, complemented
49#11763358C412yescomplemented
50#11763357C411yescharacteristic, complemented
51#11763356C412yescomplemented
52#11763356C412yescomplemented
53#11763355C412yescomplemented
54#11763354C412yescomplemented
55#11763354C412yescomplemented
56C4⋊Q8×D17C2211yescharacteristic
57#127×D17C2211yescharacteristic
58#124×D17C2212yes—
59#121×D17C2212yes—
60#121×D17C2212yes—
61C4×D4×D17C2212yes—
62C4×D4×D17C2212yes—
63C2×C42×D17C2211yescharacteristic
64C17×#532C411yescharacteristic, complemented
65C23×#595C2318yes—
66C2×#41×C17C2×C412yescomplemented
67#41×D17—48no—
68C2×#63256C2×C412yescomplemented
69C2×Q8×D17C2312yes—
70C2×#63254C2×C414yescomplemented
71C2×#63254C2×C412yescomplemented
72C2×D4×D17C2312yes—
73C2×D4×D17C2312yes—
74C2×D4×D17C2312yes—
75C2×D4×D17C2314yes—
76C2×#63252C2×C412yescomplemented
77C2×#63252C2×C414yescomplemented
78C22×C4×D17C2311yescharacteristic
79C22×C4×D17C2314yes—
80C22×C4×D17C2311yescharacteristic
81C22×C4×D17C2311yescharacteristic
82C2×C22⋊#595C2312yes—
83C2×C22⋊#595C2314yes—
84C2×C22⋊#595C2312yes—
85C2×C22⋊#595C2318yes—
86C2×C22⋊#595C2318yes—
87C2×C22⋊#595C2318yes—
88Q8×#595—48no—
89D4×#595—48no—
90C2×C4⋊#595C2314yes—
91C2×C4⋊#595C2314yes—
92C2×C4⋊#595C2318yes—
93C2×C4×#595C2312yes—
94C2×C4×#595C2312yes—
95C2×C4×#595C2314yes—
96C2×C4×#595C2318yes—
97C17×C4⋊Q8C2×C411yescharacteristic, complemented
98C17×#127C2×C411yescharacteristic
99C17×#124C2×C412yescomplemented
100C17×#121C2×C412yescomplemented
101C17×#121C2×C412yescomplemented
102C4×D4×C17C2×C412yescomplemented
103C4×D4×C17C2×C412yescomplemented
104C2×C42×C17C2×C411yescharacteristic, complemented
105#10587633C2×C412yescomplemented
106#10587630C2×C412yescomplemented
107#10587626C2×C412yes—
108#10587626C2×C412yes—
109#10587626C2×C412yes—
110#10587625C2×C414yescomplemented
111#10587625C2×C414yescomplemented
112#10587624C2×C412yescomplemented
113#10587624C2×C412yescomplemented
114#10587622C2×C412yescomplemented
115D4×Dic17C2×C412yescomplemented
116D4×Dic17C2×C412yescomplemented
117#10587616C2×C412yescomplemented
118#10587616C2×C412yescomplemented
119C4×C22⋊D17C2×C414yescomplemented
120C4×C22⋊D17C2×C414yescomplemented
121C2×C4×Dic17C2×C411yescharacteristic, complemented
122C2×C4×Dic17C2×C411yescharacteristic, complemented
123C2×C4×Dic17C2×C411yescharacteristic, complemented
124#10587581C2×C412yescomplemented
125#10587581C2×C412yescomplemented
126#10587579C2×C412yescomplemented
127#10587579C2×C412yescomplemented
128C4⋊C4×D17C2312yes—
129C4⋊C4×D17C2312yes—
130#10587574C2×C412yescomplemented
131#10587574C2×C412yescomplemented
132#10587571C2×C414yescomplemented
133#10587571C2×C414yescomplemented
134#10587570C2×C414yescomplemented
135#10587570C2×C414yescomplemented
136#10587567C2×C414yescomplemented
137#10587567C2×C414yescomplemented
138C22⋊C4×D17C2314yes—
139C22⋊C4×D17C2314yes—
140#10587561C2×C412yescomplemented
141#10587560C2×C411yescharacteristic
142C4×D68C2×C412yescomplemented
143C4×D68C2×C412yescomplemented
144C42×D17C2×C411yescharacteristic, complemented
145C42×D17C2×C411yescharacteristic, complemented
146C42×D17C2×C411yescharacteristic, complemented
147C42×D17C2×C411yescharacteristic, complemented
148C42×D17C2311yescharacteristic
149C42×D17C2311yescharacteristic
150C42×D17C2311yescharacteristic
151C42×D17C2311yescharacteristic
152#10587555C2×C411yescharacteristic, complemented
153(C2×#595)⋊C4C2312yes—
154(C2×#595)⋊C4C2314yes—
155(C2×#595)⋊C4C2318yes—
156(C2×#595)⋊C4C2314yes—
157(C2×#595)⋊C4C2314yes—
158(C2×#595)⋊C4C2314yes—
159(C2×#595)⋊C4C2312yes—
160(C2×#595)⋊C4C2314yes—
161(C2×#595)⋊C4C2314yes—
162(C2×#595)⋊C4C2318yes—
163(C2×#595)⋊C4C2314yes—
164C23×D17C2411yescharacteristic
165C23×D17C2414yes—
166C22×#595—48no—
167C22×#595—48no—
168C22×#595—48no—
169C22×#595C2414yes—
170C22×#595C2418yes—
171C22×#595C2414yes—
172#41×C17—44no—
173C2×Q8×C17C22×C412yes—
174C2×D4×C17C22×C412yes—
175C2×D4×C17C22×C412yes—
176C2×D4×C17C22×C412yes—
177C2×D4×C17C22×C414yes—
178C22×C4×C17C22×C411yescharacteristic
179C22×C4×C17C22×C414yes—
180C22×C4×C17C22×C411yescharacteristic
181C22×C4×C17C22×C411yescharacteristic
182C2×C22⋊D17C22×C414yes—
183C2×C22⋊D17C22×C414yes—
184C2×C22⋊D17C22×C414yes—
185C2×C22⋊D17C22×C414yes—
186C2×C22⋊D17C22×C414yes—
187C22×Dic17C22×C411yescharacteristic
188C22×Dic17C22×C414yes—
189C22×Dic17C22×C411yescharacteristic
190C22×Dic17C22×C411yescharacteristic
191#63256—44no—
192Q8×D17—28no—
193#63254—44no—
194#63254—48no—
195D4×D17—28no—
196D4×D17—44no—
197D4×D17—44no—
198D4×D17—48no—
199#63252—48no—
200#63252—44no—
201C2×D68C22×C412yes—
202C2×D68C22×C414yes—
203C2×D68C22×C412yes—
204C2×D68C22×C412yes—
205C2×C4×D17—24no—
206C2×C4×D17—42no—
207C2×C4×D17—42no—
208C2×C4×D17—48no—
209C2×C4×D17C22×C411yescharacteristic
210C2×C4×D17C22×C411yescharacteristic
211C2×C4×D17C22×C414yes—
212C2×C4×D17C22×C414yes—
213C2×C4×D17C22×C411yescharacteristic
214C2×C4×D17C22×C411yescharacteristic
215C2×C4×D17C22×C411yescharacteristic
216C2×C4×D17C22×C411yescharacteristic
217C2×C4×D17C2411yescharacteristic
218C2×C4×D17C2414yes—
219C2×C4×D17C2411yescharacteristic
220C2×C4×D17C2411yescharacteristic
221C2×C4×D17C2411yescharacteristic
222C2×C4×D17C2411yescharacteristic
223C2×C4×D17C2411yescharacteristic
224C2×Dic34C22×C412yes—
225C2×Dic34C22×C414yes—
226C22⋊#595—48no—
227C22⋊#595—48no—
228C22⋊#595—48no—
229C22⋊#595—42no—
230C22⋊#595—44no—
231C22⋊#595—42no—
232C4⋊#595—28no—
233C4⋊#595—44no—
234C4⋊#595—48no—
235C4×#595—24no—
236C4×#595—24no—
237C4×#595—44no—
238C4×#595—48no—
239C4⋊C4×C17C22×C412yes—
240C4⋊C4×C17C22×C412yes—
241C22⋊C4×C17C22×C414yes—
242C22⋊C4×C17C22×C414yes—
243C42×C17C22×C411yescharacteristic
244C42×C17C22×C411yescharacteristic
245C42×C17C22×C411yescharacteristic
246C42×C17C22×C411yescharacteristic
247C22⋊Dic17C22×C414yes—
248C22⋊Dic17C22×C414yes—
249#63227C22×C414yes—
250#63227C22×C414yes—
251#63227C22×C414yes—
252#63227C22×C414yes—
253C4⋊Dic17C22×C412yes—
254C4⋊Dic17C22×C412yes—
255#63225C22×C414yes—
256#63225C22×C414yes—
257C4×Dic17C22×C411yescharacteristic
258C4×Dic17C22×C411yescharacteristic
259C4×Dic17C22×C411yescharacteristic
260C4×Dic17C22×C411yescharacteristic
261C4×Dic17C22×C411yescharacteristic
262C4×Dic17C22×C411yescharacteristic
263C4×Dic17C22×C411yescharacteristic
264C4×Dic17C22×C411yescharacteristic
265C4×Dic17C22×C411yescharacteristic
266C4×Dic17C22×C411yescharacteristic
267C4×Dic17C22×C411yescharacteristic
268C4×Dic17C22×C411yescharacteristic
269#34402—171nomaximal, Sylow
270C23×C17C23×C414yes—
271C23×C17C23×C411yescharacteristic
272C22×D17—28no—
273C22×D17—22no—
274C22×D17—22no—
275C22×D17—22no—
276C22×D17—24no—
277C22×D17—28no—
278C22×D17—24no—
279C22×D17C23×C411yescharacteristic
280C22×D17C23×C414yes—
281C22×D17C2511yescharacteristic
282C2×#595—24no—
283C2×#595—24no—
284C2×#595—28no—
285C2×#595—28no—
286C2×#595—24no—
287C2×#595—24no—
288C2×#595—24no—
289C2×#595—28no—
290C2×#595—24no—
291C2×#595—816no—
292Q8×C17—24no—
293D4×C17—24no—
294D4×C17—44no—
295D4×C17—42no—
296D4×C17—42no—
297C2×C4×C17—22no—
298C2×C4×C17—44no—
299C2×C4×C17—41no—
300C2×C4×C17—41no—
301C2×C4×C17C23×C411yescharacteristic
302C2×C4×C17C23×C411yescharacteristic
303C2×C4×C17C23×C411yescharacteristic
304C2×C4×C17C23×C411yescharacteristic
305C2×C4×C17C23×C411yescharacteristic
306C2×C4×C17C23×C414yes—
307C2×C4×C17C23×C411yescharacteristic
308C22⋊D17—28no—
309C22⋊D17—44no—
310C22⋊D17—44no—
311C22⋊D17—44no—
312C22⋊D17—44no—
313C2×Dic17—22no—
314C2×Dic17—44no—
315C2×Dic17—41no—
316C2×Dic17—41no—
317C2×Dic17C23×C411yescharacteristic
318C2×Dic17C23×C411yescharacteristic
319C2×Dic17C23×C414yes—
320C2×Dic17C23×C411yescharacteristic
321C2×Dic17C23×C411yescharacteristic
322C2×Dic17C23×C411yescharacteristic
323C2×Dic17C23×C411yescharacteristic
324D68—24no—
325D68—44no—
326D68—42no—
327D68—42no—
328C4×D17—28no—
329C4×D17—22no—
330C4×D17—22no—
331C4×D17—22no—
332C4×D17—22no—
333C4×D17—22no—
334C4×D17—22no—
335C4×D17—22no—
336C4×D17—41no—
337C4×D17—41no—
338C4×D17—41no—
339C4×D17—41no—
340C4×D17—44no—
341C4×D17—44no—
342C4×D17H(5,𝔽2)14yes—
343Dic34—24no—
344Dic34—28no—
345C2×#532—171no—
346#2377—174no—
347#2367—174no—
348#2353—174no—
349#2341—172no—
350#2339—172no—
351#2333—174no—
352#2328—172no—
353#2327—172no—
354#2318—174no—
355#2283—171no—
356#2283—171no—
357C22×C17—21no—
358C22×C17—24no—
359C22×C17—21no—
360C22×C17—21no—
361C22×C17—24no—
362C22×C17—24no—
363C22×C17C24×C411yescharacteristic
364C2×D17—21no—
365C2×D17—24no—
366C2×D17—21no—
367C2×D17—21no—
368C2×D17—24no—
369C2×D17—24no—
370C2×D17—48no—
371C2×D17—48no—
372C2×D17—44no—
373C2×D17C2×H(5,𝔽2)12yes—
374C2×D17#58512yes—
375C2×D17#58512yes—
376#595—44no—
377#595—48no—
378#595—44no—
379C4×C17—24no—
380C4×C17—21no—
381C4×C17—21no—
382C4×C17—21no—
383C4×C17—21no—
384C4×C17—21no—
385C4×C17#51812yes—
386Dic17—24no—
387Dic17—21no—
388Dic17—21no—
389Dic17—21no—
390Dic17—21no—
391Dic17—21no—
392Dic17#51812yes—
393C22×#41—172no—
394#532—172no—
395#532—171no—
396#532—171no—
397#532—172no—
398#532—172no—
399#532—172no—
400#532—172no—
401#532—172no—
402#532—171no—
403#532#59511yescharacteristic, complemented
404C2×C4⋊Q8—171no—
405C2×#127—171no—
406C2×#124—172no—
407C2×#121—172no—
408C2×#121—172no—
409C2×C4×Q8—174no—
410C2×C4×D4—172no—
411C2×C4×D4—172no—
412C2×C4×D4—174no—
413C22×C42—171no—
414#391—174no—
415#390—174no—
416#390—178no—
417#388—178no—
418#388—178no—
419#387—178no—
420#387—178no—
421#386—178no—
422#386—178no—
423#386—178no—
424#385—178no—
425#383—172no—
426#383—172no—
427#382—172no—
428#382—172no—
429#381—174no—
430#381—172no—
431#381—172no—
432#380—174no—
433#380—172no—
434#380—172no—
435C4×C4⋊C4—172no—
436C4×C4⋊C4—172no—
437C4×C22⋊C4—174no—
438C4×C22⋊C4—172no—
439C4×C22⋊C4—178no—
440C4×C22⋊C4—171no—
441C4×C22⋊C4—171no—
442#376—172no—
443#376—172no—
444C2×#95—174no—
445C2×C17—44no—
446C2×C17—41no—
447C2×C17C2×#51811yescharacteristic
448C2×C17#342811yescharacteristic
449C2×C17#342811yescharacteristic
450D17—41no—
451D17—44no—
452D17#356214yes—
453C2×#41—172no—
454C2×#41—174no—
455C2×#41—172no—
456C2×#41—174no—
457C2×#41—172no—
458C2×#41—688no—
459C2×#41C2×#59512yescomplemented
460C22×Q8—172no—
461C22×D4—172no—
462C22×D4—172no—
463C22×D4—172no—
464C22×D4—174no—
465C23×C4—171no—
466C23×C4—174no—
467C23×C4—171no—
468C23×C4—171no—
469C23×C4—178no—
470C4⋊Q8—172no—
471C4⋊Q8—172no—
472C4⋊Q8—172no—
473C4⋊Q8—171no—
474C4⋊Q8C2×#59511yescharacteristic, complemented
475#127—172no—
476#127—172no—
477#127—172no—
478#127—171no—
479#127C2×#59511yescharacteristic
480#124—172no—
481#124—172no—
482#124—174no—
483#124—174no—
484#124—172no—
485#124C2×#59512yescomplemented
486#121—172no—
487#121—172no—
488#121—174no—
489#121—174no—
490#121—172no—
491#121—172no—
492#121—172no—
493#121—172no—
494#121—174no—
495#121—174no—
496#121C2×#59512yescomplemented
497#121C2×#59512yescomplemented
498C4×Q8—688no—
499C4×D4—172no—
500C4×D4—172no—
501C4×D4—174no—
502C4×D4—174no—
503C4×D4—172no—
504C4×D4—172no—
505C4×D4—174no—
506C4×D4—174no—
507C4×D4—172no—
508C4×D4—172no—
509C4×D4—688no—
510C4×D4C2×#59512yescomplemented
511C4×D4C2×#59512yescomplemented
512C2×C4⋊C4—172no—
513C2×C4⋊C4—172no—
514C2×C4⋊C4—174no—
515C2×C4⋊C4—178no—
516C2×C4⋊C4—174no—
517C2×C22⋊C4—174no—
518C2×C22⋊C4—174no—
519C2×C22⋊C4—178no—
520C2×C22⋊C4—172no—
521C2×C22⋊C4—174no—
522C2×C22⋊C4—172no—
523C2×C22⋊C4—178no—
524C2×C22⋊C4—178no—
525C2×C42—171no—
526C2×C42—171no—
527C2×C42—171no—
528C2×C42—171no—
529C2×C42—171no—
530C2×C42—171no—
531C2×C42—171no—
532C2×C42—171no—
533C2×C42—171no—
534C2×C42—171no—
535C2×C42—171no—
536C2×C42—172no—
537C2×C42—172no—
538C2×C42—178no—
539C2×C42—174no—
540C2×C42C2×#59511yescharacteristic, complemented
541#95—172no—
542#95—174no—
543#95—178no—
544#95—174no—
545#95—174no—
546#95—174no—
547#95—172no—
548#95—174no—
549#95—178no—
550#95—174no—
551#95—174no—
552C17#3440211yescharacteristic, complemented, Sylow
553C24—174no—
554C24—171no—
555#41—44no—
556#41—684no—
557#41—688no—
558#41—684no—
559#41—688no—
560#41—684no—
561C2×Q8—174no—
562C2×Q8—172no—
563C2×Q8—348no—
564C2×Q8C22×#59512yes—
565C2×D4—174no—
566C2×D4—174no—
567C2×D4—174no—
568C2×D4—174no—
569C2×D4—174no—
570C2×D4—172no—
571C2×D4—172no—
572C2×D4—172no—
573C2×D4—174no—
574C2×D4—348no—
575C2×D4—684no—
576C2×D4—684no—
577C2×D4—688no—
578C2×D4C22×#59512yes—
579C2×D4C22×#59512yes—
580C2×D4C22×#59512yes—
581C2×D4C22×#59514yes—
582C22×C4—171no—
583C22×C4—171no—
584C22×C4—171no—
585C22×C4—171no—
586C22×C4—174no—
587C22×C4—171no—
588C22×C4—171no—
589C22×C4—171no—
590C22×C4—171no—
591C22×C4—171no—
592C22×C4—171no—
593C22×C4—171no—
594C22×C4—174no—
595C22×C4—171no—
596C22×C4—171no—
597C22×C4—171no—
598C22×C4—171no—
599C22×C4—174no—
600C22×C4—174no—
601C22×C4—174no—
602C22×C4—178no—
603C22×C4—174no—
604C22×C4—344no—
605C22×C4—682no—
606C22×C4—682no—
607C22×C4—688no—
608C22×C4—688no—
609C22×C4—688no—
610C22×C4—688no—
611C22×C4C22×#59511yescharacteristic
612C22×C4C22×#59511yescharacteristic
613C22×C4C22×#59511yescharacteristic
614C22×C4C22×#59514yes—
615C4⋊C4—174no—
616C4⋊C4—174no—
617C4⋊C4—172no—
618C4⋊C4—172no—
619C4⋊C4—348no—
620C4⋊C4—684no—
621C4⋊C4—688no—
622C4⋊C4C22×#59512yes—
623C4⋊C4C22×#59512yes—
624C22⋊C4—174no—
625C22⋊C4—174no—
626C22⋊C4—174no—
627C22⋊C4—174no—
628C22⋊C4—174no—
629C22⋊C4—174no—
630C22⋊C4—688no—
631C22⋊C4—682no—
632C22⋊C4—688no—
633C22⋊C4—684no—
634C22⋊C4—682no—
635C22⋊C4—688no—
636C22⋊C4C22×#59514yes—
637C22⋊C4C22×#59514yes—
638C42—171no—
639C42—171no—
640C42—171no—
641C42—171no—
642C42—171no—
643C42—171no—
644C42—171no—
645C42—171no—
646C42—171no—
647C42—171no—
648C42—171no—
649C42—171no—
650C42—344no—
651C42—344no—
652C42—684no—
653C42—688no—
654C42C22×#59511yescharacteristic
655C42C22×#59511yescharacteristic
656C42C22×#59511yescharacteristic
657C42C22×#59511yescharacteristic
658C23—171no—
659C23—174no—
660C23—171no—
661C23—342no—
662C23—342no—
663C23—344no—
664C23—348no—
665C23—348no—
666C23—342no—
667C23—344no—
668C23C23×#59514yes—
669C23C23×#59511yescharacteristic
670Q8—24no—
671Q8—348no—
672Q8—344no—
673D4—24no—
674D4—44no—
675D4—42no—
676D4—42no—
677D4—348no—
678D4—344no—
679D4—684no—
680D4—682no—
681D4—682no—
682D4—684no—
683D4—684no—
684D4—684no—
685D4—684no—
686C2×C4—22no—
687C2×C4—44no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—171no—
691C2×C4—174no—
692C2×C4—171no—
693C2×C4—171no—
694C2×C4—171no—
695C2×C4—171no—
696C2×C4—171no—
697C2×C4—174no—
698C2×C4—342no—
699C2×C4—342no—
700C2×C4—348no—
701C2×C4—342no—
702C2×C4—342no—
703C2×C4—342no—
704C2×C4—342no—
705C2×C4—342no—
706C2×C4—342no—
707C2×C4—344no—
708C2×C4—344no—
709C2×C4—348no—
710C2×C4—348no—
711C2×C4—344no—
712C2×C4—344no—
713C2×C4—348no—
714C2×C4—344no—
715C2×C4—344no—
716C2×C4—684no—
717C2×C4—684no—
718C2×C4—681no—
719C2×C4—681no—
720C2×C4—681no—
721C2×C4—681no—
722C2×C4—684no—
723C2×C4—681no—
724C2×C4—681no—
725C2×C4—13616no—
726C2×C4C23×#59511yescharacteristic
727C2×C4C23×#59511yescharacteristic
728C2×C4C23×#59511yescharacteristic
729C2×C4C23×#59511yescharacteristic
730C2×C4C23×#59511yescharacteristic
731C2×C4C23×#59514yes—
732C2×C4C23×#59511yescharacteristic
733C22—21no—
734C22—24no—
735C22—21no—
736C22—21no—
737C22—24no—
738C22—24no—
739C22—172no—
740C22—172no—
741C22—172no—
742C22—341no—
743C22—344no—
744C22—341no—
745C22—341no—
746C22—344no—
747C22—344no—
748C22—688no—
749C22—684no—
750C22—688no—
751C22C24×#59511yescharacteristic
752C4—21no—
753C4—24no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—172no—
759C4—341no—
760C4—344no—
761C4—341no—
762C4—341no—
763C4—341no—
764C4—341no—
765C4—684no—
766C4—688no—
767C4—684no—
768C4#1176387612yes—
769C2—41no—
770C2—44no—
771C2—174no—
772C2—681no—
773C2—684no—
774C2C2×#1176387611yescharacteristic
775C2#1454576411yescharacteristic
776C2#1454576411yescharacteristic
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC17×#532C4
prime radicalD17×#532C2
cosocleC22×D17C25
hypercenter#532#595
hypocenterC17#34402
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #14545325C2semidirect
2. #14545315C2semidirect
3. #14545301C2semidirect
4. #14545289C2semidirect
5. #14545287C2semidirect
6. #14545281C2semidirect
7. #14545276C2semidirect
8. #14545275C2semidirect
9. #14545266C2semidirect
10. #14545231C2semidirect
11. #14545231C2semidirect
47. #11763360C4semidirect
48. #11763359C4semidirect
49. #11763358C4semidirect
50. #11763357C4semidirect
51. #11763356C4semidirect
52. #11763356C4semidirect
53. #11763355C4semidirect
54. #11763354C4semidirect
55. #11763354C4semidirect
64. C17×#532C4semidirect
66. C2×#41×C17C2×C4semidirect
68. C2×#63256C2×C4semidirect
70. C2×#63254C2×C4semidirect
71. C2×#63254C2×C4semidirect
76. C2×#63252C2×C4semidirect
77. C2×#63252C2×C4semidirect
97. C17×C4⋊Q8C2×C4semidirect
99. C17×#124C2×C4semidirect
100. C17×#121C2×C4semidirect
101. C17×#121C2×C4semidirect
102. C4×D4×C17C2×C4semidirect
103. C4×D4×C17C2×C4semidirect
104. C2×C42×C17C2×C4semidirect
105. #10587633C2×C4semidirect
106. #10587630C2×C4semidirect
110. #10587625C2×C4semidirect
111. #10587625C2×C4semidirect
112. #10587624C2×C4semidirect
113. #10587624C2×C4semidirect
114. #10587622C2×C4semidirect
115. D4×Dic17C2×C4semidirect
116. D4×Dic17C2×C4semidirect
117. #10587616C2×C4semidirect
118. #10587616C2×C4semidirect
119. C4×C22⋊D17C2×C4semidirect
120. C4×C22⋊D17C2×C4semidirect
121. C2×C4×Dic17C2×C4semidirect
122. C2×C4×Dic17C2×C4semidirect
123. C2×C4×Dic17C2×C4semidirect
124. #10587581C2×C4semidirect
125. #10587581C2×C4semidirect
126. #10587579C2×C4semidirect
127. #10587579C2×C4semidirect
130. #10587574C2×C4semidirect
131. #10587574C2×C4semidirect
132. #10587571C2×C4semidirect
133. #10587571C2×C4semidirect
134. #10587570C2×C4semidirect
135. #10587570C2×C4semidirect
136. #10587567C2×C4semidirect
137. #10587567C2×C4semidirect
140. #10587561C2×C4semidirect
142. C4×D68C2×C4semidirect
143. C4×D68C2×C4semidirect
144. C42×D17C2×C4semidirect
145. C42×D17C2×C4semidirect
146. C42×D17C2×C4semidirect
147. C42×D17C2×C4semidirect
152. #10587555C2×C4semidirect
403. #532#595semidirect
459. C2×#41C2×#595semidirect
474. C4⋊Q8C2×#595semidirect
485. #124C2×#595semidirect
496. #121C2×#595semidirect
497. #121C2×#595semidirect
510. C4×D4C2×#595semidirect
511. C4×D4C2×#595semidirect
540. C2×C42C2×#595semidirect
552. C17#34402semidirect

Maximal subgroups

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

subgroupindex
#145453252
#145453152
#145453012
#145452892
#145452872
#145452812
#145452762
#145452752
#145452662
#145452312
D17×#5322
#3440217