Finite Group Databasebeta

← #17038303

Subgroups — #17038303

Order 4352.

1460 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
1C2×#11763607C211yesmaximal, characteristic
2#14537373C211yesmaximal, characteristic, complemented
3C2×#11762825C211yesmaximal, characteristic, complemented
4C2×#11762783C211yesmaximal, characteristic, complemented
5C2×#11762782C211yesmaximal, characteristic, complemented
6#14537202C211yesmaximal, characteristic, complemented
7#14529681C218yesmaximal, complemented
8C2×C17×#421C211yesmaximal, characteristic, complemented
9C22×#63252C2211yescharacteristic
10#11763607—22no—
11#11763607—22no—
12#11763607—22no—
13#11763607—22no—
14C2×#10587628C412yescomplemented
15C2×#10587637C412yescomplemented
16C2×#10587618C412yescomplemented
17C2×#10587635C412yescomplemented
18C2×#10587636C2214yes—
19C22×#63223C2211yescharacteristic
20C2×#10587612C2211yescharacteristic
21C2×#10587612C2211yescharacteristic
22#11762852—22no—
23#11762849—22no—
24#11762845C2214yescomplemented
25#11762825—22no—
26#11762825C2214yescomplemented
27C2×#10587496—22no—
28#11762783—22no—
29#11762783C2214yescomplemented
30#11762782—22no—
31#11762782C2214yescomplemented
32C2×#10587505—22no—
33C2×#10587477—22no—
34#11762767C2214yescomplemented
35#11762764—22no—
36M16×Dic17—22no—
37C22×#41×C17C2211yescharacteristic
38C22×M16×C17C2211yescharacteristic
39C2×C17×#117C2211yescharacteristic
40C17×#421—22no—
41C17×#421C2214yescomplemented
42C2×C17×#104—22no—
43C2×#41×C17—21no—
44C2×#41×C17—21no—
45C2×#41×C17—21no—
46C2×#41×C17—21no—
47C2×#41×C17—21no—
48C2×#41×C17—21no—
49C2×#41×C17—21no—
50C2×#41×C17—21no—
51C2×#41×C17—21no—
52C2×#41×C17—21no—
53C2×#41×C17C2×C412yes—
54C2×#41×C17C2312yes—
55C22×Q8×C17C2×C411yescharacteristic
56C22×D4×C17—21no—
57C22×D4×C17C2×C411yescharacteristic
58C23×C4×C17—21no—
59C23×C4×C17C2311yescharacteristic
60C22×C22⋊D17—21no—
61C2×#63252—21no—
62C2×#63252—21no—
63C2×#63252—21no—
64C2×#63252—21no—
65C2×#63252—21no—
66C2×#63252—21no—
67C2×#63252—21no—
68C2×#63252—21no—
69C2×#63252—21no—
70C2×#63252—21no—
71C2×#63252C2×C412yes—
72C2×#63252C2312yes—
73C22×D68C2×C411yescharacteristic
74C22×C4×D17—21no—
75C22×Dic34C2×C411yescharacteristic
76C2×M16×C17—21no—
77C2×M16×C17—21no—
78C2×M16×C17—21no—
79C2×M16×C17D412yes—
80C2×M16×C17D412yes—
81C2×M16×C17C2312yes—
82C22×C8×C17—21no—
83C17×#117—21no—
84C17×#117—21no—
85C17×#117—21no—
86C17×#117C2312yes—
87C2×C4⋊C4×C17—21no—
88C2×C22⋊C4×C17—21no—
89C2×C42×C17—21no—
90C2×C22⋊Dic17—21no—
91C2×C22⋊Dic17D412yes—
92#10587637—24no—
93#10587637—24no—
94#10587636—28no—
95#10587636—28no—
96#10587635—24no—
97#10587635—24no—
98C2×#63231C2×C414yescomplemented
99#10587628—24no—
100#10587628—24no—
101C2×#63230C2×C414yescomplemented
102C2×#63229C2×C414yescomplemented
103#10587618—24no—
104#10587618—24no—
105C2×#63228C2×C414yescomplemented
106#10587612—21no—
107#10587612—21no—
108#10587612—21no—
109#10587612—21no—
110#10587612—21no—
111#10587612D412yes—
112#10587612C2312yes—
113#10587612C2312yes—
114C2×C4⋊Dic17—21no—
115C2×C4⋊Dic17—21no—
116C2×C4×Dic17—21no—
117C2×C4×Dic17—21no—
118C2×#63223C2×C412yes—
119C2×#63223C2×C412yes—
120C2×#63223D412yes—
121C2×#63223D412yes—
122C2×#63223D412yes—
123C2×#63223D412yes—
124C22×#3622C2312yes—
125C17×#104—28no—
126#10587505—28no—
127#10587496—28no—
128#10587486—24no—
129C8×Dic17—24no—
130#10587479—24no—
131#10587478—24no—
132#10587477—28no—
133C24×C17—21no—
134C24×C17C2×D411yescharacteristic
135C23×D17—21no—
136#41×C17—22no—
137#41×C17—22no—
138#41×C17—22no—
139#41×C17—22no—
140#41×C17—22no—
141#41×C17—22no—
142#41×C17—22no—
143#41×C17—22no—
144#41×C17—41no—
145#41×C17—41no—
146#41×C17—41no—
147#41×C17—41no—
148#41×C17—41no—
149#41×C17—41no—
150#41×C17—41no—
151#41×C17—41no—
152C2×Q8×C17—21no—
153C2×Q8×C17—21no—
154C2×Q8×C17—21no—
155C2×Q8×C17—21no—
156C2×Q8×C17—21no—
157C2×Q8×C17C22×C412yes—
158C2×D4×C17—22no—
159C2×D4×C17—22no—
160C2×D4×C17—21no—
161C2×D4×C17—21no—
162C2×D4×C17—21no—
163C2×D4×C17—21no—
164C2×D4×C17—21no—
165C2×D4×C17—41no—
166C2×D4×C17—41no—
167C2×D4×C17—41no—
168C2×D4×C17—41no—
169C2×D4×C17C22×C412yes—
170C22×C4×C17—21no—
171C22×C4×C17—22no—
172C22×C4×C17—22no—
173C22×C4×C17—41no—
174C22×C4×C17—41no—
175C22×C4×C17—41no—
176C22×C4×C17—41no—
177C22×C4×C17—41no—
178C22×C4×C17C22×C411yescharacteristic
179C22×C4×C17C22×C411yescharacteristic
180C22×C4×C17C2×D411yescharacteristic
181C22×C4×C17C2×D411yescharacteristic
182C22×C4×C17C2×D411yescharacteristic
183C22×C4×C17C2×D411yescharacteristic
184C22×C4×C17C2×D411yescharacteristic
185C22×C4×C17C2×D411yescharacteristic
186C22×C4×C17C2×D411yescharacteristic
187C22×C4×C17#4111yescharacteristic
188C22×C4×C17#4111yescharacteristic
189C22×C4×C17#4111yescharacteristic
190C22×C4×C17#4111yescharacteristic
191C22×C4×C17C2411yescharacteristic
192C2×C22⋊D17—22no—
193C2×C22⋊D17—22no—
194C2×C22⋊D17—41no—
195C2×C22⋊D17—41no—
196C2×C22⋊D17—41no—
197C2×C22⋊D17—41no—
198C22×Dic17—21no—
199C22×Dic17—22no—
200C22×Dic17—41no—
201#63252—22no—
202#63252—22no—
203#63252—22no—
204#63252—22no—
205#63252—22no—
206#63252—22no—
207#63252—22no—
208#63252—22no—
209#63252—41no—
210#63252—41no—
211#63252—41no—
212#63252—41no—
213#63252—41no—
214#63252—41no—
215#63252—41no—
216#63252—41no—
217C2×D68—21no—
218C2×D68—21no—
219C2×D68—21no—
220C2×D68—21no—
221C2×D68—21no—
222C2×D68C22×C412yes—
223C2×C4×D17—22no—
224C2×C4×D17—22no—
225C2×C4×D17—41no—
226C2×C4×D17—41no—
227C2×C4×D17—41no—
228C2×C4×D17—41no—
229C2×Dic34—21no—
230C2×Dic34—21no—
231C2×Dic34—21no—
232C2×Dic34—21no—
233C2×Dic34—21no—
234C2×Dic34C22×C412yes—
235M16×C17—22no—
236M16×C17—22no—
237M16×C17—22no—
238M16×C17C2×D414yes—
239C2×C8×C17—22no—
240C2×C8×C17—22no—
241C2×C8×C17—22no—
242C4⋊C4×C17—22no—
243C4⋊C4×C17—41no—
244C22⋊C4×C17—22no—
245C22⋊C4×C17—41no—
246C42×C17—22no—
247C42×C17—41no—
248C22⋊Dic17—22no—
249C22⋊Dic17—22no—
250C22⋊Dic17—41no—
251C22⋊Dic17C2×D414yes—
252#63231—28no—
253#63230—28no—
254#63229—28no—
255#63228—28no—
256C4⋊Dic17—22no—
257C4⋊Dic17—22no—
258C4⋊Dic17—22no—
259C4⋊Dic17—41no—
260C4×Dic17—22no—
261C4×Dic17—22no—
262C4×Dic17—22no—
263C4×Dic17—41no—
264#63223C22⋊C414yes—
265#63223C22⋊C414yes—
266#63223C22⋊C414yes—
267#63223C22⋊C414yes—
268C2×#3622C22×C414yes—
269C2×#3622C2×D414yes—
270C2×#3622C2×D414yes—
271#21244—171nomaximal, Sylow
272C23×C17—22no—
273C23×C17—41no—
274C23×C17—41no—
275C23×C17—81no—
276C23×C17—82no—
277C23×C17C4×D411yescharacteristic
278C23×C17C4×D411yescharacteristic
279C23×C17#12111yescharacteristic
280C23×C17#12111yescharacteristic
281C23×C17#12711yescharacteristic
282C23×C17#12711yescharacteristic
283C23×C17C22×D411yescharacteristic
284C22×D17—22no—
285C22×D17—41no—
286C22×D17—41no—
287C22×D17—82no—
288Q8×C17—22no—
289Q8×C17—22no—
290Q8×C17—41no—
291Q8×C17—41no—
292D4×C17—22no—
293D4×C17—22no—
294D4×C17—42no—
295D4×C17—42no—
296D4×C17—42no—
297D4×C17—42no—
298D4×C17—41no—
299D4×C17—41no—
300C2×C4×C17—22no—
301C2×C4×C17—41no—
302C2×C4×C17—41no—
303C2×C4×C17—42no—
304C2×C4×C17—42no—
305C2×C4×C17—42no—
306C2×C4×C17—42no—
307C2×C4×C17—42no—
308C2×C4×C17—82no—
309C2×C4×C17C2×C22⋊C411yescharacteristic
310C2×C4×C17C2×C22⋊C411yescharacteristic
311C2×C4×C17C2×C22⋊C411yescharacteristic
312C2×C4×C17C2×C22⋊C411yescharacteristic
313C2×C4×C17C4×D411yescharacteristic
314C2×C4×C17C4×D411yescharacteristic
315C2×C4×C17C4×D411yescharacteristic
316C2×C4×C17C4×D411yescharacteristic
317C2×C4×C17C4×D411yescharacteristic
318C2×C4×C17C4×D411yescharacteristic
319C2×C4×C17#12111yescharacteristic
320C2×C4×C17#12111yescharacteristic
321C2×C4×C17#12111yescharacteristic
322C2×C4×C17#12111yescharacteristic
323C2×C4×C17#12111yescharacteristic
324C2×C4×C17#12111yescharacteristic
325C2×C4×C17#12411yescharacteristic
326C2×C4×C17#12411yescharacteristic
327C2×C4×C17#12411yescharacteristic
328C2×C4×C17#12411yescharacteristic
329C2×C4×C17#12711yescharacteristic
330C2×C4×C17#12711yescharacteristic
331C2×C4×C17C23×C411yescharacteristic
332C2×C4×C17C22×D411yescharacteristic
333C2×C4×C17C22×D411yescharacteristic
334C2×C4×C17C22×D411yescharacteristic
335C2×C4×C17C2×#4111yescharacteristic
336C2×C4×C17C2×#4111yescharacteristic
337C22⋊D17—42no—
338C22⋊D17—42no—
339C22⋊D17—42no—
340C22⋊D17—42no—
341C2×Dic17—22no—
342C2×Dic17—24no—
343C2×Dic17—41no—
344C2×Dic17—41no—
345C2×Dic17—42no—
346C2×Dic17—82no—
347C2×Dic17—82no—
348D68—22no—
349D68—22no—
350D68—41no—
351D68—41no—
352C4×D17—42no—
353C4×D17—42no—
354C4×D17—42no—
355C4×D17—42no—
356Dic34—22no—
357Dic34—22no—
358Dic34—41no—
359Dic34—41no—
360C8×C17—24no—
361#3622C2×C22⋊C418yes—
362C2×#575—171no—
363#2911—171no—
364C2×#421—171no—
365C2×#421D1711yescharacteristic, complemented
366C2×#410—171no—
367C2×#410—171no—
368#2873—171no—
369#1976—178no—
370C22×C17—41no—
371C22×C17—41no—
372C22×C17—41no—
373C22×C17—41no—
374C22×C17—41no—
375C22×C17—41no—
376C22×C17—41no—
377C22×C17—42no—
378C22×C17—82no—
379C22×C17—82no—
380C22×C17—82no—
381C22×C17#39011yescharacteristic
382C22×C17#39011yescharacteristic
383C22×C17#39011yescharacteristic
384C22×C17#39011yescharacteristic
385C22×C17C2×C4×D411yescharacteristic
386C22×C17C2×#12111yescharacteristic
387C22×C17C2×#12711yescharacteristic
388C2×D17—42no—
389C2×D17—82no—
390C2×D17—82no—
391C2×D17—82no—
392C4×C17—42no—
393C4×C17—82no—
394C4×C17#39011yescharacteristic
395C4×C17#39011yescharacteristic
396C4×C17#39011yescharacteristic
397C4×C17#39011yescharacteristic
398C4×C17C22×C22⋊C411yescharacteristic
399C4×C17C2×C4×D411yescharacteristic
400C4×C17C2×#12111yescharacteristic
401C4×C17C2×#12411yescharacteristic
402Dic17—44no—
403Dic17—42no—
404Dic17—82no—
405C22×#41—171no—
406C22×#41C2×D1711yescharacteristic
407#575—342no—
408#575—342no—
409#575—342no—
410#575—342no—
411C2×#137—172no—
412C2×#137—172no—
413C2×AGL(1,ℤ/8)—172no—
414C2×AGL(1,ℤ/8)—172no—
415C2×#135—174no—
416C22×M16—171no—
417C22×M16C2×D1711yescharacteristic
418C2×#117—171no—
419C2×#117—171no—
420C2×#117C2×D1711yescharacteristic
421#428—342no—
422#428—342no—
423#427—174no—
424#421—22no—
425#421—174no—
426#421—342no—
427#421C2×D1714yescomplemented
428C2×#104—22no—
429C2×#104—342no—
430#410—174no—
431#410—174no—
432#410—342no—
433#410—342no—
434C2×#99—342no—
435C2×#99—342no—
436#405—174no—
437#405—342no—
438C4×M16—342no—
439C2×C17—21no—
440C2×C17—21no—
441C2×C17—21no—
442C2×C17—21no—
443C2×C17—21no—
444C2×C17—21no—
445C2×C17—21no—
446C2×C17—82no—
447C2×C17C2×#39011yescharacteristic
448D17—82no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—172no—
460C2×#41—172no—
461C2×#41—341no—
462C2×#41—341no—
463C2×#41—341no—
464C2×#41—341no—
465C2×#41—341no—
466C2×#41—341no—
467C2×#41—341no—
468C2×#41—341no—
469C2×#41—341no—
470C2×#41—341no—
471C2×#41C4×D1712yes—
472C2×#41C22×D1712yes—
473C22×Q8—171no—
474C22×Q8C4×D1711yescharacteristic
475C22×D4—21no—
476C22×D4—171no—
477C22×D4—341no—
478C22×D4C4×D1711yescharacteristic
479C23×C4—21no—
480C23×C4—341no—
481C23×C4C22×D1711yescharacteristic
482#137—344no—
483#137—344no—
484#137—344no—
485#137—344no—
486AGL(1,ℤ/8)—344no—
487AGL(1,ℤ/8)—344no—
488AGL(1,ℤ/8)—344no—
489AGL(1,ℤ/8)—344no—
490#135—348no—
491#135—348no—
492C2×Q16—174no—
493C2×SD16—174no—
494C2×SD16—174no—
495C2×D8—174no—
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—172no—
500C2×M16—172no—
501C2×M16—172no—
502C2×M16—172no—
503C2×M16—172no—
504C2×M16—172no—
505C2×M16C22⋊D1712yes—
506C2×M16C22⋊D1712yes—
507C2×M16C22×D1712yes—
508C22×C8—21no—
509C22×C8—172no—
510#117—21no—
511#117—21no—
512#117—21no—
513#117—172no—
514#117—172no—
515#117—172no—
516#117—341no—
517#117—341no—
518#117—341no—
519#117—341no—
520#117—341no—
521#117C22×D1712yes—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—341no—
524C2×C4⋊C4—341no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—172no—
527C2×C22⋊C4—341no—
528C2×C42—21no—
529C2×C42—341no—
530C2×C42—341no—
531#107—344no—
532#106—344no—
533#104—28no—
534#104—348no—
535#99—348no—
536#99—348no—
537#97—344no—
538C4×C8—344no—
539C17#2124411yescharacteristic, complemented, Sylow
540C24—21no—
541C24—341no—
542C24D4×D1711yescharacteristic
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—342no—
560#41—342no—
561#41—342no—
562#41—342no—
563#41—342no—
564#41—342no—
565#41—342no—
566#41—342no—
567#41—681no—
568#41—681no—
569#41—681no—
570#41—681no—
571#41—681no—
572#41—681no—
573#41—681no—
574#41—681no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—172no—
581C2×Q8—341no—
582C2×Q8—341no—
583C2×Q8—341no—
584C2×Q8—341no—
585C2×Q8—341no—
586C2×Q8C2×C4×D1712yes—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—172no—
599C2×D4—342no—
600C2×D4—342no—
601C2×D4—341no—
602C2×D4—341no—
603C2×D4—341no—
604C2×D4—341no—
605C2×D4—341no—
606C2×D4—681no—
607C2×D4—681no—
608C2×D4—681no—
609C2×D4—681no—
610C2×D4C2×C4×D1712yes—
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—341no—
620C22×C4—342no—
621C22×C4—342no—
622C22×C4—342no—
623C22×C4—681no—
624C22×C4—681no—
625C22×C4—681no—
626C22×C4—681no—
627C22×C4—681no—
628C22×C4C2×C4×D1711yescharacteristic
629C22×C4C2×C4×D1711yescharacteristic
630C22×C4#6325211yescharacteristic
631C22×C4#6325211yescharacteristic
632C22×C4D4×D1711yescharacteristic
633C22×C4D4×D1711yescharacteristic
634C22×C4D4×D1711yescharacteristic
635C22×C4D4×D1711yescharacteristic
636C22×C4D4×D1711yescharacteristic
637C22×C4#6325411yescharacteristic
638C22×C4#6325411yescharacteristic
639C22×C4C2×C22⋊D1711yescharacteristic
640C22×C4C2×C22⋊D1711yescharacteristic
641C22×C4C23×D1711yescharacteristic
642Q16—348no—
643SD16—348no—
644SD16—348no—
645D8—348no—
646M16—22no—
647M16—22no—
648M16—22no—
649M16—174no—
650M16—174no—
651M16—174no—
652M16—174no—
653M16C2×C22⋊D1714yes—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—174no—
658C2×C8—174no—
659C2×C8—174no—
660C4⋊C4—22no—
661C4⋊C4—41no—
662C4⋊C4—342no—
663C4⋊C4—342no—
664C4⋊C4—342no—
665C4⋊C4—681no—
666C22⋊C4—22no—
667C22⋊C4—41no—
668C22⋊C4—174no—
669C22⋊C4—342no—
670C22⋊C4—342no—
671C22⋊C4—681no—
672C42—22no—
673C42—41no—
674C42—342no—
675C42—342no—
676C42—342no—
677C42—681no—
678C23—22no—
679C23—41no—
680C23—41no—
681C23—81no—
682C23—82no—
683C23—342no—
684C23—681no—
685C23—681no—
686C23—1362no—
687C23#1058756711yescharacteristic
688C23#1058756711yescharacteristic
689C23#1058757011yescharacteristic
690C23#1058757011yescharacteristic
691C23#1058762611yescharacteristic
692C23#1058762611yescharacteristic
693C23C2×D4×D1711yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—41no—
697Q8—41no—
698Q8—342no—
699Q8—342no—
700Q8—681no—
701Q8—681no—
702D4—22no—
703D4—22no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—41no—
709D4—41no—
710D4—342no—
711D4—342no—
712D4—682no—
713D4—682no—
714D4—682no—
715D4—682no—
716D4—681no—
717D4—681no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—82no—
727C2×C4—342no—
728C2×C4—344no—
729C2×C4—681no—
730C2×C4—681no—
731C2×C4—682no—
732C2×C4—682no—
733C2×C4—682no—
734C2×C4—682no—
735C2×C4—682no—
736C2×C4—1362no—
737C2×C4—1362no—
738C2×C4C22⋊C4×D1711yescharacteristic
739C2×C4C22⋊C4×D1711yescharacteristic
740C2×C4C22⋊C4×D1711yescharacteristic
741C2×C4C22⋊C4×D1711yescharacteristic
742C2×C4#1058756711yescharacteristic
743C2×C4#1058756711yescharacteristic
744C2×C4#1058757011yescharacteristic
745C2×C4#1058757011yescharacteristic
746C2×C4#1058757111yescharacteristic
747C2×C4#1058757111yescharacteristic
748C2×C4#1058757111yescharacteristic
749C2×C4#1058757111yescharacteristic
750C2×C4C4×C22⋊D1711yescharacteristic
751C2×C4C4×C22⋊D1711yescharacteristic
752C2×C4C4×C22⋊D1711yescharacteristic
753C2×C4C4×C22⋊D1711yescharacteristic
754C2×C4#1058762511yescharacteristic
755C2×C4#1058762511yescharacteristic
756C2×C4#1058762511yescharacteristic
757C2×C4#1058762511yescharacteristic
758C2×C4#1058762611yescharacteristic
759C2×C4#1058762611yescharacteristic
760C2×C4C22×C4×D1711yescharacteristic
761C2×C4C2×#6325211yescharacteristic
762C2×C4C2×D4×D1711yescharacteristic
763C2×C4C2×D4×D1711yescharacteristic
764C2×C4C2×#6325411yescharacteristic
765C2×C4C22×C22⋊D1711yescharacteristic
766C8—24no—
767C8—178no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—682no—
780C22—1362no—
781C22—1362no—
782C22—1362no—
783C22#1176270911yescharacteristic
784C22#1176270911yescharacteristic
785C22#1176270911yescharacteristic
786C22#1176270911yescharacteristic
787C22C2×#1058756711yescharacteristic
788C22C2×#1058757011yescharacteristic
789C22C2×#1058762611yescharacteristic
790C4—42no—
791C4—82no—
792C4—684no—
793C4—682no—
794C4—1362no—
795C4#1176270911yescharacteristic
796C4#1176270911yescharacteristic
797C4#1176270911yescharacteristic
798C4#1176270911yescharacteristic
799C4C2×C22⋊C4×D1711yescharacteristic
800C4C2×C4×C22⋊D1711yescharacteristic
801C4C2×#1058762511yescharacteristic
802C4C2×#1058757111yescharacteristic
803C2—21no—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—21no—
808C2—21no—
809C2—21no—
810C2—82no—
811C2—1362no—
812C2C2×#1176270911yescharacteristic
subgroupG/H
centerC4C2×#10587625
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#421C2
socleC2×C17C2×#390
prime radicalC2×#11763607C2
cosocleC22×C4×C17C24
hypercenterC2×#421D17
hypocenterC17#21244
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. #14537373C2semidirect
3. C2×#11762825C2semidirect
4. C2×#11762783C2semidirect
5. C2×#11762782C2semidirect
6. #14537202C2semidirect
7. #14529681C2semidirect
8. C2×C17×#421C2semidirect
14. C2×#10587628C4semidirect
15. C2×#10587637C4semidirect
16. C2×#10587618C4semidirect
17. C2×#10587635C4semidirect
24. #11762845C22semidirect
26. #11762825C22semidirect
29. #11762783C22semidirect
31. #11762782C22semidirect
34. #11762767C22semidirect
41. C17×#421C22semidirect
98. C2×#63231C2×C4semidirect
101. C2×#63230C2×C4semidirect
102. C2×#63229C2×C4semidirect
105. C2×#63228C2×C4semidirect
365. C2×#421D17semidirect
427. #421C2×D17semidirect
539. C17#21244semidirect

Maximal subgroups

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

subgroupindex
C2×#117636072
#145373732
C2×#117628252
C2×#117627832
C2×#117627822
#145372022
#145296812
C2×C17×#4212
#2124417