Finite Group Databasebeta

← #17054586

Subgroups — #17054586

Order 4352.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762962C211yesmaximal, characteristic
2C2×#11762911C211yesmaximal, characteristic, complemented
3C22×#10587492C211yesmaximal, characteristic
4#14531787C211yesmaximal, characteristic, complemented
5C22⋊C4×D68C211yesmaximal, characteristic
6#14529665C211yesmaximal, characteristic, complemented
7#14529481C211yesmaximal, characteristic, complemented
8#14529405C211yesmaximal, characteristic, complemented
9#14529207C211yesmaximal, characteristic, complemented
10#14529138C211yesmaximal, characteristic, complemented
11#14529117C211yesmaximal, characteristic, complemented
12#14529034C211yesmaximal, characteristic, complemented
13#14528974C211yesmaximal, characteristic, complemented
14#14528610C211yesmaximal, characteristic, complemented
15C17×#1752C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C22×#63219C2211yescharacteristic
18C22×#63219C2211yescharacteristic
19C2×#10587610C2211yescharacteristic
20C2×C4×Dic34C2211yescharacteristic, complemented
21C2×C4×D68C2211yescharacteristic
22C2×C4×D68C2211yescharacteristic
23C22×C4⋊Dic17C2211yescharacteristic
24C2×C22⋊C4×D17—21no—
25#11762962C418yescomplemented
26#11762911—24no—
27C2×#10587489C2211yescharacteristic, complemented
28C2×#10587489C2211yescharacteristic, complemented
29C2×#10587487C2211yescharacteristic, complemented
30C2×#10587487C2211yescharacteristic, complemented
31C2×#10587492—24no—
32C2×#10587492C2211yescharacteristic
33C2×#10587492C2211yescharacteristic
34C2×#10587492C2211yescharacteristic
35C2×#10587492C2211yescharacteristic
36C2×#10587492C2211yescharacteristic
37C2×#10587492C2211yescharacteristic
38#11762715C2211yescharacteristic, complemented
39#11762711C2211yescharacteristic
40#11762711C2211yescharacteristic
41#11762707C2211yescharacteristic, complemented
42#11762706—21no—
43#11762696—21no—
44#11762687—21no—
45#11762687—21no—
46#11762681—21no—
47#11762669C2211yescharacteristic
48#11762664—21no—
49C4×C4⋊Dic17C2211yescharacteristic, complemented
50C22⋊C4×Dic17—21no—
51#11762572C2211yescharacteristic, complemented
52#11762572C2211yescharacteristic, complemented
53#11762572C2211yescharacteristic, complemented
54#11762572C2211yescharacteristic, complemented
55C23×C8×C17C2211yescharacteristic
56C2×C17×C22⋊C8C2211yescharacteristic
57C2×C17×#97C2211yescharacteristic, complemented
58C2×C17×#97C2211yescharacteristic, complemented
59C4×C22⋊C4×C17C2211yescharacteristic
60C17×#336C2211yescharacteristic, complemented
61C17×#336C2211yescharacteristic, complemented
62C24×D17—21no—
63C23×C4×C17C2311yescharacteristic
64C23×Dic17—21no—
65C22×D68—22no—
66C22×D68—22no—
67C22×D68—21no—
68C22×D68—22no—
69C22×D68—41no—
70C22×D68—41no—
71C22×D68C2×C414yes—
72C22×D68C2311yescharacteristic
73C22×D68C2311yescharacteristic
74C22×C4×D17—21no—
75C22×C4×D17—21no—
76C22×Dic34C2311yescharacteristic
77C22×C8×C17—22no—
78C22×C8×C17—22no—
79C22×C8×C17—41no—
80C22×C8×C17C2311yescharacteristic
81C22×C8×C17C2311yescharacteristic
82C22×C8×C17C2311yescharacteristic
83C22×C8×C17C2311yescharacteristic
84C2×C22⋊C4×C17D411yescharacteristic
85C2×C22⋊C4×C17D411yescharacteristic
86C2×C42×C17C2311yescharacteristic
87C2×C42×C17C2311yescharacteristic
88C2×C22⋊Dic17—21no—
89C2×C22⋊Dic17—21no—
90C2×#63227—21no—
91C2×#63227—21no—
92C2×#63227—21no—
93C2×#63227—21no—
94C2×#63227—21no—
95C2×#63227—21no—
96C2×C4⋊Dic17—21no—
97C2×C4⋊Dic17—22no—
98C2×C4⋊Dic17—41no—
99C2×C4⋊Dic17C2311yescharacteristic
100C2×C4⋊Dic17C2311yescharacteristic
101C2×C4⋊Dic17C2311yescharacteristic
102C2×C4⋊Dic17C2311yescharacteristic
103C2×C4⋊Dic17C2311yescharacteristic
104#10587610—22no—
105#10587610C2×C414yescomplemented
106C2×#63225—21no—
107C2×#63225—21no—
108C2×#63225—21no—
109C2×C4×Dic17—21no—
110C2×C4×Dic17—21no—
111C2×#63219—22no—
112C2×#63219—22no—
113C2×#63219—41no—
114C2×#63219—41no—
115C2×#63219C2×C414yescomplemented
116C2×#63219C2×C414yescomplemented
117C22⋊C4×D17—44no—
118C4×D68—22no—
119C4×D68—22no—
120C4×D68—41no—
121C4×D68—41no—
122C4×Dic34—22no—
123C4×Dic34—41no—
124C17×C22⋊C8C2×C414yescomplemented
125C17×#97—22no—
126C17×#97—41no—
127C17×#95D411yescharacteristic
128C17×#95D411yescharacteristic
129#10587502—21no—
130#10587502—21no—
131#10587502—21no—
132#10587502—21no—
133#10587502—21no—
134#10587492—22no—
135#10587492—22no—
136#10587492—22no—
137#10587492C2×C414yescomplemented
138#10587492C2×C414yescomplemented
139#10587492D414yes—
140#10587489—22no—
141#10587489—41no—
142#10587487—22no—
143#10587487—41no—
144C24×C17C2×D411yescharacteristic
145C23×D17—21no—
146C23×D17—21no—
147C23×D17—24no—
148C23×D17—42no—
149C23×D17—42no—
150C23×D17—42no—
151C23×D17—42no—
152C23×D17—81no—
153C23×D17—81no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17C22×C412yes—
159C22×C4×C17C2×D411yescharacteristic
160C22×C4×C17C2×D411yescharacteristic
161C22×C4×C17C2×D411yescharacteristic
162C22×C4×C17C2×D411yescharacteristic
163C22×C4×C17C2×D411yescharacteristic
164C22×C4×C17#4112yes—
165C22×C4×C17C2411yescharacteristic
166C22×Dic17—21no—
167C22×Dic17—21no—
168C22×Dic17—21no—
169C22×Dic17—21no—
170C22×Dic17—21no—
171C22×Dic17—21no—
172C22×Dic17—42no—
173C22×Dic17—42no—
174C22×Dic17—81no—
175C2×D68—21no—
176C2×D68—21no—
177C2×D68—21no—
178C2×D68—21no—
179C2×D68—21no—
180C2×D68—21no—
181C2×D68—21no—
182C2×D68—28no—
183C2×D68—24no—
184C2×D68—21no—
185C2×D68—44no—
186C2×D68—44no—
187C2×D68—44no—
188C2×D68—42no—
189C2×D68—42no—
190C2×D68C22×C412yes—
191C2×D68C22×C412yes—
192C2×D68C2×D412yes—
193C2×D68#4112yes—
194C2×C4×D17—42no—
195C2×C4×D17—42no—
196C2×C4×D17—42no—
197C2×C4×D17—42no—
198C2×C4×D17—81no—
199C2×C4×D17—81no—
200C2×Dic34—21no—
201C2×Dic34—21no—
202C2×Dic34—21no—
203C2×Dic34—21no—
204C2×Dic34—21no—
205C2×Dic34C22×C412yes—
206C2×C8×C17—21no—
207C2×C8×C17—21no—
208C2×C8×C17—21no—
209C2×C8×C17—21no—
210C2×C8×C17—21no—
211C2×C8×C17—21no—
212C2×C8×C17—21no—
213C2×C8×C17—21no—
214C2×C8×C17—21no—
215C2×C8×C17—44no—
216C2×C8×C17C22×C412yes—
217C2×C8×C17C22×C412yes—
218C2×C8×C17C2×D412yes—
219C22⋊C4×C17—22no—
220C22⋊C4×C17—22no—
221C42×C17—21no—
222C42×C17—21no—
223C42×C17—21no—
224C42×C17—21no—
225C22⋊Dic17—24no—
226C22⋊Dic17—42no—
227#63227—42no—
228#63227—42no—
229#63227—42no—
230#63227—42no—
231#63227—81no—
232#63227—81no—
233C4⋊Dic17—21no—
234C4⋊Dic17—21no—
235C4⋊Dic17—21no—
236C4⋊Dic17—21no—
237C4⋊Dic17—21no—
238C4⋊Dic17—21no—
239C4⋊Dic17—21no—
240C4⋊Dic17—21no—
241C4⋊Dic17—42no—
242C4⋊Dic17C22×C412yes—
243C4⋊Dic17C2×D412yes—
244#63225—24no—
245#63225—42no—
246#63225—81no—
247C4×Dic17—42no—
248C4×Dic17—81no—
249#63219—28no—
250#63219—44no—
251#22854—171nomaximal, Sylow
252C23×C17—21no—
253C23×C17—21no—
254C23×C17—21no—
255C23×C17—21no—
256C23×C17C4×D412yes—
257C23×C17AGL(1,ℤ/8)12yes—
258C23×C17#13712yes—
259C23×C17C22×D411yescharacteristic
260C22×D17—22no—
261C22×D17—22no—
262C22×D17—22no—
263C22×D17—22no—
264C22×D17—48no—
265C22×D17—41no—
266C22×D17—41no—
267C22×D17—41no—
268C22×D17—41no—
269C22×D17—41no—
270C22×D17—41no—
271C22×D17—41no—
272C22×D17—41no—
273C22×D17—41no—
274C22×D17—41no—
275C22×D17—48no—
276C22×D17—84no—
277C22×D17—84no—
278C22×D17—84no—
279C22×D17—84no—
280C22×D17—84no—
281C2×C4×C17—21no—
282C2×C4×C17—21no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—21no—
288C2×C4×C17—21no—
289C2×C4×C17—21no—
290C2×C4×C17—21no—
291C2×C4×C17—21no—
292C2×C4×C17—21no—
293C2×C4×C17—21no—
294C2×C4×C17—21no—
295C2×C4×C17—21no—
296C2×C4×C17—21no—
297C2×C4×C17—21no—
298C2×C4×C17—21no—
299C2×C4×C17C4×D412yes—
300C2×C4×C17C23×C411yescharacteristic
301C2×C4×C17C22×D411yescharacteristic
302C2×C4×C17C2×#4111yescharacteristic
303C2×C4×C17C2×#4111yescharacteristic
304C2×C4×C17H(5,𝔽2)11yescharacteristic
305C2×C4×C17H(5,𝔽2)11yescharacteristic
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17—41no—
312C2×Dic17—41no—
313C2×Dic17—41no—
314C2×Dic17—41no—
315C2×Dic17—41no—
316C2×Dic17—41no—
317C2×Dic17—41no—
318C2×Dic17—41no—
319C2×Dic17—41no—
320C2×Dic17—41no—
321C2×Dic17—41no—
322C2×Dic17—41no—
323C2×Dic17—41no—
324C2×Dic17—84no—
325D68—22no—
326D68—22no—
327D68—22no—
328D68—22no—
329D68—22no—
330D68—48no—
331D68—41no—
332D68—41no—
333D68C4×D414yes—
334C4×D17—84no—
335C4×D17—84no—
336Dic34—22no—
337Dic34—22no—
338Dic34—41no—
339Dic34—41no—
340C8×C17—22no—
341C8×C17—22no—
342C8×C17—22no—
343C8×C17—41no—
344C2×#450—171no—
345C2×#440—171no—
346C22×#102—171no—
347#2360—171no—
348D4×C22⋊C4—171no—
349#1973—171no—
350#1936—171no—
351#1925—171no—
352#1892—171no—
353#1880—171no—
354#1877—171no—
355#1862—171no—
356#1852—171no—
357#1762—171no—
358#1752D1711yescharacteristic, complemented
359C22×C17—22no—
360C22×C17—22no—
361C22×C17—22no—
362C22×C17—22no—
363C22×C17—22no—
364C22×C17—22no—
365C22×C17#44014yescomplemented
366C22×C17C2×C4×D411yescharacteristic
367C22×C17D4211yescharacteristic
368C22×C17#54611yescharacteristic
369C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C17C2×#13711yescharacteristic
371C22×C17#57611yescharacteristic
372C22×C17#57711yescharacteristic
373C2×D17—24no—
374C2×D17—42no—
375C2×D17—42no—
376C2×D17—42no—
377C2×D17—42no—
378C2×D17—42no—
379C2×D17—42no—
380C2×D17—42no—
381C2×D17—42no—
382C2×D17—42no—
383C2×D17—816no—
384C2×D17—81no—
385C2×D17—81no—
386C2×D17—81no—
387C2×D17—81no—
388C4×C17—22no—
389C4×C17—41no—
390C4×C17—41no—
391C4×C17—41no—
392C4×C17—41no—
393C4×C17C2×C4×D411yescharacteristic
394C4×C17#51811yescharacteristic
395C4×C17#54611yescharacteristic
396C4×C17#55111yescharacteristic
397Dic17—42no—
398Dic17—42no—
399Dic17—42no—
400Dic17—81no—
401Dic17—81no—
402Dic17—81no—
403C23×D4—171no—
404C22×SD16—171no—
405C22×SD16—171no—
406C23×C8C2×D1711yescharacteristic
407C2×C22⋊Q8—171no—
408C2×C4×Q8—171no—
409C2×C4×D4—171no—
410C2×C4×D4—171no—
411C22×C4⋊C4—171no—
412C22×C22⋊C4—341no—
413#450—178no—
414#440—344no—
415C2×#107—171no—
416C2×#107—171no—
417C2×#103—171no—
418C2×#103—171no—
419C2×#102—171no—
420C2×#102—171no—
421C2×#102—171no—
422C2×#102—171no—
423C2×#102—171no—
424C2×#102—171no—
425C2×#102—344no—
426C2×C22⋊C8C2×D1711yescharacteristic
427C2×#97C2×D1711yescharacteristic, complemented
428C2×#97C2×D1711yescharacteristic, complemented
429#391—171no—
430#390—171no—
431#390—171no—
432#389—171no—
433#389—341no—
434#387—341no—
435#386—341no—
436#386—341no—
437#385—341no—
438#380—171no—
439#379—341no—
440C4×C4⋊C4—171no—
441C4×C22⋊C4—341no—
442C4×C22⋊C4C2×D1711yescharacteristic
443#340—171no—
444#340—171no—
445#340—171no—
446#340—171no—
447#336C2×D1711yescharacteristic, complemented
448#336C2×D1711yescharacteristic, complemented
449C2×C17—24no—
450C2×C17#235811yescharacteristic
451C2×C17C2×#44011yescharacteristic
452C2×C17#294611yescharacteristic
453C2×C17#326411yescharacteristic
454C2×C17#326611yescharacteristic
455C2×C17#331011yescharacteristic
456C2×C17#331411yescharacteristic
457D17—44no—
458D17—82no—
459C25—341no—
460C22×Q8—171no—
461C22×D4—174no—
462C22×D4—171no—
463C22×D4—171no—
464C22×D4—342no—
465C22×D4—342no—
466C22×D4—341no—
467C22×D4—342no—
468C22×D4—681no—
469C22×D4—681no—
470C23×C4—341no—
471C23×C4—341no—
472C23×C4—341no—
473C23×C4C22×D1711yescharacteristic
474C2×SD16—174no—
475C2×SD16—174no—
476C2×SD16—342no—
477C2×SD16—342no—
478C2×SD16—681no—
479C2×SD16—681no—
480C22×C8—22no—
481C22×C8—22no—
482C22×C8—41no—
483C22×C8C22×D1711yescharacteristic
484C22×C8C22×D1711yescharacteristic
485C22×C8C22×D1711yescharacteristic
486C22×C8C22×D1711yescharacteristic
487C22⋊Q8—174no—
488C22⋊Q8—342no—
489C4×Q8—342no—
490C4×Q8—681no—
491C4×D4—342no—
492C4×D4—342no—
493C4×D4—681no—
494C4×D4—681no—
495C2×C4⋊C4—171no—
496C2×C4⋊C4—171no—
497C2×C4⋊C4—171no—
498C2×C4⋊C4—171no—
499C2×C4⋊C4—171no—
500C2×C4⋊C4—342no—
501C2×C4⋊C4—341no—
502C2×C4⋊C4—341no—
503C2×C4⋊C4—341no—
504C2×C4⋊C4—341no—
505C2×C4⋊C4—681no—
506C2×C22⋊C4—341no—
507C2×C22⋊C4—341no—
508C2×C22⋊C4—341no—
509C2×C22⋊C4—341no—
510C2×C22⋊C4—341no—
511C2×C22⋊C4—341no—
512C2×C22⋊C4—341no—
513C2×C22⋊C4—341no—
514C2×C22⋊C4—684no—
515C2×C22⋊C4D6811yescharacteristic
516C2×C22⋊C4D6811yescharacteristic
517C2×C42—341no—
518C2×C42—341no—
519C2×C42C22×D1711yescharacteristic
520C2×C42C22×D1711yescharacteristic
521#107—342no—
522#107—681no—
523#103—342no—
524#103—681no—
525#102—174no—
526#102—174no—
527#102—174no—
528#102—342no—
529#102—342no—
530#102—342no—
531C22⋊C8C4×D1714yescomplemented
532#97—22no—
533#97—41no—
534#95—341no—
535#95—341no—
536#95—341no—
537#95—341no—
538#95—341no—
539#95D6811yescharacteristic
540#95D6811yescharacteristic
541C17#2285411yescharacteristic, complemented, Sylow
542C24—341no—
543C24—341no—
544C24—344no—
545C24—682no—
546C24—682no—
547C24—682no—
548C24—682no—
549C24—1361no—
550C24—1361no—
551C24C2×D6811yescharacteristic
552C2×Q8—172no—
553C2×Q8—341no—
554C2×Q8—341no—
555C2×Q8—341no—
556C2×Q8—341no—
557C2×Q8—341no—
558C2×D4—172no—
559C2×D4—172no—
560C2×D4—172no—
561C2×D4—172no—
562C2×D4—348no—
563C2×D4—341no—
564C2×D4—341no—
565C2×D4—341no—
566C2×D4—341no—
567C2×D4—341no—
568C2×D4—341no—
569C2×D4—341no—
570C2×D4—341no—
571C2×D4—344no—
572C2×D4—684no—
573C2×D4—684no—
574C2×D4—684no—
575C2×D4—682no—
576C2×D4—682no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—341no—
582C22×C4—341no—
583C22×C4—341no—
584C22×C4—341no—
585C22×C4—341no—
586C22×C4—341no—
587C22×C4—682no—
588C22×C4—682no—
589C22×C4—682no—
590C22×C4—682no—
591C22×C4—682no—
592C22×C4—682no—
593C22×C4—1361no—
594C22×C4—1361no—
595C22×C4—1361no—
596C22×C4C2×C4×D1712yes—
597C22×C4C2×D6811yescharacteristic
598C22×C4C2×D6811yescharacteristic
599C22×C4C2×D6811yescharacteristic
600C22×C4C2×D6811yescharacteristic
601C22×C4C2×D6811yescharacteristic
602C22×C4#6325212yes—
603C22×C4C23×D1711yescharacteristic
604SD16—348no—
605SD16—684no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—44no—
616C2×C8C2×C4×D1712yes—
617C2×C8C2×C4×D1712yes—
618C2×C8D4×D1712yes—
619C4⋊C4—172no—
620C4⋊C4—172no—
621C4⋊C4—341no—
622C4⋊C4—341no—
623C4⋊C4—344no—
624C4⋊C4—341no—
625C4⋊C4—341no—
626C4⋊C4—341no—
627C4⋊C4—341no—
628C4⋊C4—341no—
629C4⋊C4—341no—
630C4⋊C4—682no—
631C4⋊C4—682no—
632C4⋊C4—1361no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—344no—
636C22⋊C4—682no—
637C22⋊C4—682no—
638C22⋊C4—682no—
639C22⋊C4—682no—
640C22⋊C4—682no—
641C22⋊C4—1361no—
642C22⋊C4—1361no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—682no—
648C42—1361no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—342no—
654C23—342no—
655C23—342no—
656C23—342no—
657C23—688no—
658C23—681no—
659C23—681no—
660C23—681no—
661C23—681no—
662C23—681no—
663C23—681no—
664C23—681no—
665C23—681no—
666C23—688no—
667C23—681no—
668C23—681no—
669C23—1364no—
670C23—1364no—
671C23—1364no—
672C23—1364no—
673C23—1364no—
674C23C4×D6812yes—
675C23#1058759412yes—
676C23#1058759512yes—
677C23C22×D6811yescharacteristic
678Q8—342no—
679Q8—342no—
680Q8—681no—
681Q8—681no—
682D4—174no—
683D4—342no—
684D4—342no—
685D4—342no—
686D4—342no—
687D4—342no—
688D4—688no—
689D4—681no—
690D4—681no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—342no—
710C2×C4—342no—
711C2×C4—342no—
712C2×C4—681no—
713C2×C4—681no—
714C2×C4—681no—
715C2×C4—681no—
716C2×C4—681no—
717C2×C4—681no—
718C2×C4—681no—
719C2×C4—681no—
720C2×C4—681no—
721C2×C4—681no—
722C2×C4—681no—
723C2×C4—681no—
724C2×C4—681no—
725C2×C4—681no—
726C2×C4—681no—
727C2×C4—1364no—
728C2×C4—1364no—
729C2×C4—1364no—
730C2×C4C4×D6812yes—
731C2×C4C22×C4×D1711yescharacteristic
732C2×C4C2×#6325211yescharacteristic
733C2×C4C2×D4×D1711yescharacteristic
734C2×C4#1058769111yescharacteristic
735C2×C4#41×D1711yescharacteristic
736C2×C4#1058769611yescharacteristic
737C8—22no—
738C8—22no—
739C8—22no—
740C8—41no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—344no—
748C22—682no—
749C22—682no—
750C22—682no—
751C22—682no—
752C22—682no—
753C22—682no—
754C22—682no—
755C22—682no—
756C22—682no—
757C22—13616no—
758C22—1361no—
759C22—1361no—
760C22—1361no—
761C22—1361no—
762C22#1176291114yescomplemented
763C22C2×C4×D6811yescharacteristic
764C22D4×D6811yescharacteristic
765C22#1176345411yescharacteristic
766C22C2×#1058759411yescharacteristic
767C22C2×#1058759511yescharacteristic
768C22#1176361411yescharacteristic
769C22#1176362111yescharacteristic
770C4—22no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—682no—
776C4—682no—
777C4—682no—
778C4—1361no—
779C4—1361no—
780C4—1361no—
781C4C4×D4×D1711yescharacteristic
782C4#1176328111yescharacteristic
783C4#1176344911yescharacteristic
784C4#1176348311yescharacteristic
785C2—24no—
786C2—684no—
787C2—1362no—
788C2#1453176611yescharacteristic
789C2C2×#1176291111yescharacteristic
790C2#1453761811yescharacteristic
791C2#1454026911yescharacteristic
792C2#1454029911yescharacteristic
793C2#1454080711yescharacteristic
794C2#1454086711yescharacteristic
subgroupG/H
centerC23C22×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1752C2
socleC23×C17C22×D4
prime radicalC23×D68C22
cosocleC22×C4×C17C24
hypercenter#1752D17
hypocenterC17#22854
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
2. C2×#11762911C2semidirect
4. #14531787C2semidirect
6. #14529665C2semidirect
7. #14529481C2semidirect
8. #14529405C2semidirect
9. #14529207C2semidirect
10. #14529138C2semidirect
11. #14529117C2semidirect
12. #14529034C2semidirect
13. #14528974C2semidirect
14. #14528610C2semidirect
15. C17×#1752C2semidirect
20. C2×C4×Dic34C22semidirect
25. #11762962C4semidirect
27. C2×#10587489C22semidirect
28. C2×#10587489C22semidirect
29. C2×#10587487C22semidirect
30. C2×#10587487C22semidirect
38. #11762715C22semidirect
41. #11762707C22semidirect
49. C4×C4⋊Dic17C22semidirect
51. #11762572C22semidirect
52. #11762572C22semidirect
53. #11762572C22semidirect
54. #11762572C22semidirect
57. C2×C17×#97C22semidirect
58. C2×C17×#97C22semidirect
60. C17×#336C22semidirect
61. C17×#336C22semidirect
105. #10587610C2×C4semidirect
115. C2×#63219C2×C4semidirect
116. C2×#63219C2×C4semidirect
124. C17×C22⋊C8C2×C4semidirect
137. #10587492C2×C4semidirect
138. #10587492C2×C4semidirect
358. #1752D17semidirect
365. C22×C17#440semidirect
427. C2×#97C2×D17semidirect
428. C2×#97C2×D17semidirect
447. #336C2×D17semidirect
448. #336C2×D17semidirect
531. C22⋊C8C4×D17semidirect
541. C17#22854semidirect
762. C22#11762911semidirect

Maximal subgroups

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

subgroupindex
C2×#117629622
C2×#117629112
C22×#105874922
#145317872
C22⋊C4×D682
#145296652
#145294812
#145294052
#145292072
#145291382
#145291172
#145290342
#145289742
#145286102
C17×#17522
#2285417