Finite Group Databasebeta

← #17044620

Subgroups — #17044620

Order 4352.

1010 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762776C211yesmaximal, characteristic
2#14531376C211yesmaximal, characteristic
3#14528983C211yesmaximal, characteristic, complemented
4#14528983C211yesmaximal, characteristic, complemented
5#14528981C211yesmaximal, characteristic, complemented
6#14528981C211yesmaximal, characteristic, complemented
7#14528977C211yesmaximal, characteristic, complemented
8#14528976C211yesmaximal, characteristic, complemented
9#14528972C211yesmaximal, characteristic, complemented
10#14528971C211yesmaximal, characteristic, complemented
11#14528815C211yesmaximal, characteristic, complemented
12#14528815C211yesmaximal, characteristic, complemented
13#14528811C211yesmaximal, characteristic, complemented
14#14528807C211yesmaximal, characteristic, complemented
15C17×#2311C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic
17C23×#3622C2211yescharacteristic
18C2×#10587612C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C2×#10587478C2211yescharacteristic
21C2×#10587478C2211yescharacteristic
22C2×#10587478C2211yescharacteristic
23C2×#10587478C2211yescharacteristic
24C2×#10587479C2211yescharacteristic
25C2×#10587479C2211yescharacteristic
26C2×#10587479C2211yescharacteristic
27C2×#10587479C2211yescharacteristic
28#11762776C418yescomplemented
29C2×C22⋊#3622C2211yescharacteristic
30C2×C22⋊#3622C2211yescharacteristic
31C2×C22⋊#3622C2211yescharacteristic
32C2×C22⋊#3622C2211yescharacteristic
33#11762716—21no—
34#11762712—21no—
35#11762689—21no—
36#11762689—21no—
37#11762669C2211yescharacteristic
38#11762669C2211yescharacteristic
39#11762669C2211yescharacteristic
40#11762669C2211yescharacteristic
41#11762571C2211yescharacteristic
42#11762571C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49C22×#41×C17C2211yescharacteristic
50C2×C17×#117C2211yescharacteristic
51C22×C4⋊C4×C17C2211yescharacteristic
52C17×#391—21no—
53C17×#390—21no—
54C17×#386—21no—
55C17×#386—21no—
56C17×#380C2211yescharacteristic
57C17×#380C2211yescharacteristic
58C17×#380C2211yescharacteristic
59C17×#380C2211yescharacteristic
60C2×#41×C17—41no—
61C2×#41×C17—41no—
62C2×#41×C17—41no—
63C2×#41×C17—41no—
64C2×#41×C17C2×C414yes—
65C2×#41×C17Q814yes—
66C22×Q8×C17D411yescharacteristic
67C22×D4×C17D411yescharacteristic
68C22×D4×C17D411yescharacteristic
69C22×D4×C17D411yescharacteristic
70C23×C4×C17—21no—
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×Dic17—21no—
75C17×#117—41no—
76C17×#117—41no—
77C2×C4⋊C4×C17—21no—
78C2×C4⋊C4×C17—41no—
79C2×C4⋊C4×C17—41no—
80C2×C4⋊C4×C17C2311yescharacteristic
81C2×C4⋊C4×C17C2311yescharacteristic
82C2×C4⋊C4×C17C2311yescharacteristic
83C2×C4⋊C4×C17C2311yescharacteristic
84C2×C22⋊C4×C17—21no—
85C2×C22⋊C4×C17—21no—
86C2×C22⋊C4×C17—21no—
87C2×C22⋊C4×C17—21no—
88C2×C22⋊C4×C17—21no—
89C2×C42×C17—21no—
90C2×C22⋊Dic17—21no—
91C2×C22⋊Dic17—21no—
92C2×C22⋊Dic17—21no—
93C2×C22⋊Dic17—21no—
94C2×C22⋊Dic17—21no—
95#10587612—41no—
96#10587612—41no—
97C2×C4⋊Dic17—21no—
98C2×C4⋊Dic17—41no—
99C2×C4⋊Dic17—41no—
100C2×C4⋊Dic17C2311yescharacteristic
101C2×C4⋊Dic17C2311yescharacteristic
102C2×C4⋊Dic17C2311yescharacteristic
103C2×C4⋊Dic17C2311yescharacteristic
104C2×C4×Dic17—21no—
105C2×#63223—41no—
106C2×#63223—41no—
107C2×#63223C2×C414yescomplemented
108C22×#3622—41no—
109C22×#3622—41no—
110C22×#3622C2×C414yescomplemented
111C22×#3622C2311yescharacteristic
112C22×#3622C2311yescharacteristic
113C22×#3622C2311yescharacteristic
114C22×#3622C2311yescharacteristic
115C17×#95—21no—
116C17×#95—21no—
117C17×#95—21no—
118C17×#95—21no—
119#10587502—21no—
120#10587502—21no—
121#10587502—21no—
122#10587502—21no—
123C22⋊#3622C2×C414yescomplemented
124C22⋊#3622C2×C414yescomplemented
125C22⋊#3622C2×C414yescomplemented
126C22⋊#3622C2×C414yescomplemented
127#10587479—41no—
128#10587479—41no—
129#10587479—41no—
130#10587479—41no—
131#10587478—41no—
132#10587478—41no—
133#10587478—41no—
134#10587478—41no—
135C24×C17C2×D411yescharacteristic
136C24×C17C2×D411yescharacteristic
137C24×C17C2×D411yescharacteristic
138#41×C17—44no—
139#41×C17—44no—
140#41×C17—44no—
141#41×C17—44no—
142C2×Q8×C17—41no—
143C2×Q8×C17—41no—
144C2×Q8×C17C4⋊C414yes—
145C2×D4×C17—41no—
146C2×D4×C17—41no—
147C2×D4×C17—41no—
148C2×D4×C17—41no—
149C2×D4×C17—41no—
150C2×D4×C17—41no—
151C2×D4×C17C4⋊C414yes—
152C2×D4×C17C4⋊C414yes—
153C2×D4×C17C4⋊C414yes—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—42no—
171C22×C4×C17—81no—
172C22×C4×C17—81no—
173C22×C4×C17C22×C412yes—
174C22×C4×C17C22×C412yes—
175C22×C4×C17C22×C412yes—
176C22×C4×C17C2×D411yescharacteristic
177C22×C4×C17C2×D411yescharacteristic
178C22×C4×C17C2×D411yescharacteristic
179C22×C4×C17C2×Q812yes—
180C22×C4×C17C2×Q812yes—
181C22×C4×C17C2×Q812yes—
182C22×C4×C17C2411yescharacteristic
183C22×Dic17—21no—
184C22×Dic17—21no—
185C22×Dic17—21no—
186C22×Dic17—21no—
187C22×Dic17—42no—
188C22×Dic17—81no—
189C22×Dic17—81no—
190C4⋊C4×C17—21no—
191C4⋊C4×C17—21no—
192C4⋊C4×C17—21no—
193C4⋊C4×C17—21no—
194C4⋊C4×C17—21no—
195C4⋊C4×C17—21no—
196C4⋊C4×C17—21no—
197C4⋊C4×C17—21no—
198C4⋊C4×C17—42no—
199C22⋊C4×C17—42no—
200C22⋊C4×C17—81no—
201C22⋊C4×C17—81no—
202C22⋊C4×C17—81no—
203C22⋊C4×C17—81no—
204C42×C17—42no—
205C22⋊Dic17—42no—
206C22⋊Dic17—81no—
207C22⋊Dic17—81no—
208C22⋊Dic17—81no—
209C22⋊Dic17—81no—
210C4⋊Dic17—21no—
211C4⋊Dic17—21no—
212C4⋊Dic17—21no—
213C4⋊Dic17—21no—
214C4⋊Dic17—21no—
215C4⋊Dic17—21no—
216C4⋊Dic17—21no—
217C4⋊Dic17—21no—
218C4⋊Dic17—42no—
219C4×Dic17—42no—
220#63223—44no—
221C2×#3622—21no—
222C2×#3622—21no—
223C2×#3622—21no—
224C2×#3622—21no—
225C2×#3622—21no—
226C2×#3622—21no—
227C2×#3622—21no—
228C2×#3622—21no—
229C2×#3622—44no—
230C2×#3622C22×C412yes—
231C2×#3622C22×C412yes—
232C2×#3622C22×C412yes—
233C2×#3622C22×C412yes—
234#21945—171nomaximal, Sylow
235C23×C17—21no—
236C23×C17—21no—
237C23×C17—21no—
238C23×C17—21no—
239C23×C17—21no—
240C23×C17—21no—
241C23×C17—21no—
242C23×C17—21no—
243C23×C17—21no—
244C23×C17—21no—
245C23×C17—21no—
246C23×C17—21no—
247C23×C17—21no—
248C23×C17—21no—
249C23×C17—21no—
250C23×C17—21no—
251C23×C17—21no—
252C23×C17—21no—
253C23×C17C2×C4⋊C412yes—
254C23×C17C2×C4⋊C412yes—
255C23×C17C2×C4⋊C412yes—
256C23×C17C22×D411yescharacteristic
257Q8×C17—44no—
258D4×C17—44no—
259D4×C17—44no—
260D4×C17—44no—
261C2×C4×C17—21no—
262C2×C4×C17—21no—
263C2×C4×C17—21no—
264C2×C4×C17—21no—
265C2×C4×C17—21no—
266C2×C4×C17—21no—
267C2×C4×C17—22no—
268C2×C4×C17—22no—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—22no—
279C2×C4×C17—41no—
280C2×C4×C17—41no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—41no—
284C2×C4×C17—41no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—41no—
288C2×C4×C17—41no—
289C2×C4×C17—41no—
290C2×C4×C17—41no—
291C2×C4×C17—84no—
292C2×C4×C17C2×C4⋊C412yes—
293C2×C4×C17C2×C4⋊C412yes—
294C2×C4×C17C2×C4⋊C412yes—
295C2×C4×C17C23×C411yescharacteristic
296C2×C4×C17C22×Q811yescharacteristic
297C2×C4×C17H(5,𝔽2)11yescharacteristic
298C2×C4×C17H(5,𝔽2)11yescharacteristic
299C2×C4×C17H(5,𝔽2)11yescharacteristic
300C2×C4×C17H(5,𝔽2)11yescharacteristic
301C2×Dic17—41no—
302C2×Dic17—41no—
303C2×Dic17—41no—
304C2×Dic17—41no—
305C2×Dic17—41no—
306C2×Dic17—41no—
307C2×Dic17—41no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17—41no—
312C2×Dic17—41no—
313C2×Dic17—84no—
314#3622—22no—
315#3622—22no—
316#3622—22no—
317#3622—22no—
318C2×#408—171no—
319#2311—171no—
320#2311D1711yescharacteristic
321#1854—171no—
322#1854—171no—
323#1854—171no—
324#1854—171no—
325#1853—171no—
326#1853—171no—
327#1852—171no—
328#1852—171no—
329#1809—171no—
330#1809—171no—
331#1808—171no—
332#1807—171no—
333C22×C17—22no—
334C22×C17—22no—
335C22×C17—22no—
336C22×C17—22no—
337C22×C17—22no—
338C22×C17—22no—
339C22×C17—22no—
340C22×C17—22no—
341C22×C17—22no—
342C22×C17—41no—
343C22×C17—41no—
344C22×C17—41no—
345C22×C17—41no—
346C22×C17—41no—
347C22×C17—41no—
348C22×C17—41no—
349C22×C17—41no—
350C22×C17—41no—
351C22×C17—41no—
352C22×C17—41no—
353C22×C17—41no—
354C22×C17C22×C4⋊C411yescharacteristic
355C22×C17#53411yescharacteristic
356C22×C17#53411yescharacteristic
357C22×C17#57611yescharacteristic
358C22×C17#57711yescharacteristic
359C22×C17#57711yescharacteristic
360C22×C17#57811yescharacteristic
361C4×C17—22no—
362C4×C17—22no—
363C4×C17—22no—
364C4×C17—81no—
365C4×C17—81no—
366C4×C17—81no—
367C4×C17—81no—
368C4×C17#51811yescharacteristic
369C4×C17#51811yescharacteristic
370C4×C17#54311yescharacteristic
371C4×C17#54311yescharacteristic
372Dic17—81no—
373Dic17—81no—
374Dic17—81no—
375Dic17—81no—
376C22×#41C2×D1711yescharacteristic
377C22×M16—171no—
378C23×C8—171no—
379C2×#117—171no—
380C2×#117C2×D1711yescharacteristic
381C22×C4⋊C4—171no—
382C22×C4⋊C4C2×D1711yescharacteristic
383C2×#107—171no—
384C2×#107—171no—
385C2×#107—171no—
386C2×#107—171no—
387C2×#106—171no—
388C2×#106—171no—
389C2×#106—171no—
390C2×#106—171no—
391#408—178no—
392C2×C22⋊C8—171no—
393C2×C22⋊C8—171no—
394C2×C22⋊C8—171no—
395C2×C22⋊C8—171no—
396#391—21no—
397#391—341no—
398#390—21no—
399#390—341no—
400#386—21no—
401#386—21no—
402#386—341no—
403#386—341no—
404#380—171no—
405#380—171no—
406#380—171no—
407#380—171no—
408#380C2×D1711yescharacteristic
409#380C2×D1711yescharacteristic
410#380C2×D1711yescharacteristic
411#380C2×D1711yescharacteristic
412#340—171no—
413#340—171no—
414#340—171no—
415#340—171no—
416#340—171no—
417#340—171no—
418#340—171no—
419#340—171no—
420C2×C17—42no—
421C2×C17—42no—
422C2×C17—42no—
423C2×C17#231511yescharacteristic
424C2×C17#291211yescharacteristic
425C2×C17#291311yescharacteristic
426C2×C17#319811yescharacteristic
427C2×C17#319811yescharacteristic
428C2×C17#320111yescharacteristic
429C2×C17#320111yescharacteristic
430C2×#41—41no—
431C2×#41—41no—
432C2×#41—41no—
433C2×#41—41no—
434C2×#41Dic3414yes—
435C2×#41C4×D1714yes—
436C22×Q8C22⋊D1711yescharacteristic
437C22×D4C22⋊D1711yescharacteristic
438C22×D4C22⋊D1711yescharacteristic
439C22×D4C22⋊D1711yescharacteristic
440C23×C4—21no—
441C23×C4—341no—
442C23×C4C22×D1711yescharacteristic
443C23×C4C22×D1711yescharacteristic
444C23×C4C22×D1711yescharacteristic
445C2×M16—174no—
446C2×M16—681no—
447C2×M16—681no—
448C22×C8—171no—
449C22×C8—171no—
450C22×C8—171no—
451C22×C8—171no—
452C22×C8—174no—
453C22×C8—681no—
454C22×C8—681no—
455#117—41no—
456#117—41no—
457#117—681no—
458#117—681no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—41no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—171no—
463C2×C4⋊C4—171no—
464C2×C4⋊C4—171no—
465C2×C4⋊C4—171no—
466C2×C4⋊C4—341no—
467C2×C4⋊C4—681no—
468C2×C4⋊C4—681no—
469C2×C4⋊C4C22×D1711yescharacteristic
470C2×C4⋊C4C22×D1711yescharacteristic
471C2×C4⋊C4C22×D1711yescharacteristic
472C2×C4⋊C4C22×D1711yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—341no—
479C2×C22⋊C4—341no—
480C2×C22⋊C4—341no—
481C2×C22⋊C4—341no—
482C2×C22⋊C4—341no—
483C2×C42—21no—
484C2×C42—341no—
485#107—681no—
486#107—681no—
487#107—681no—
488#107—681no—
489#106—681no—
490#106—681no—
491#106—681no—
492#106—681no—
493C22⋊C8—174no—
494C22⋊C8—174no—
495C22⋊C8—174no—
496C22⋊C8—174no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—341no—
502#95—341no—
503#95—341no—
504#95—341no—
505C17#2194511yescharacteristic, complemented, Sylow
506C24C2×C22⋊D1711yescharacteristic
507C24C2×C22⋊D1711yescharacteristic
508C24C2×C22⋊D1711yescharacteristic
509#41—44no—
510#41—44no—
511#41—44no—
512#41—44no—
513C2×Q8—41no—
514C2×Q8—41no—
515C2×Q8#6322514yes—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4#6322514yes—
523C2×D4#6322514yes—
524C2×D4#6322514yes—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—81no—
543C22×C4—81no—
544C22×C4—341no—
545C22×C4—341no—
546C22×C4—341no—
547C22×C4—341no—
548C22×C4—682no—
549C22×C4—1361no—
550C22×C4—1361no—
551C22×C4C2×Dic3412yes—
552C22×C4C2×Dic3412yes—
553C22×C4C2×Dic3412yes—
554C22×C4C2×C4×D1712yes—
555C22×C4C2×C4×D1712yes—
556C22×C4C2×C4×D1712yes—
557C22×C4C2×C22⋊D1711yescharacteristic
558C22×C4C2×C22⋊D1711yescharacteristic
559C22×C4C2×C22⋊D1711yescharacteristic
560C22×C4C23×D1711yescharacteristic
561M16—684no—
562C2×C8—172no—
563C2×C8—172no—
564C2×C8—172no—
565C2×C8—172no—
566C2×C8—341no—
567C2×C8—341no—
568C2×C8—341no—
569C2×C8—341no—
570C2×C8—341no—
571C2×C8—341no—
572C2×C8—341no—
573C2×C8—341no—
574C2×C8—684no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—42no—
584C4⋊C4—341no—
585C4⋊C4—341no—
586C4⋊C4—341no—
587C4⋊C4—341no—
588C4⋊C4—341no—
589C4⋊C4—341no—
590C4⋊C4—341no—
591C4⋊C4—341no—
592C4⋊C4—682no—
593C22⋊C4—42no—
594C22⋊C4—81no—
595C22⋊C4—81no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C22⋊C4—682no—
599C22⋊C4—1361no—
600C22⋊C4—1361no—
601C22⋊C4—1361no—
602C22⋊C4—1361no—
603C42—42no—
604C42—682no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23C2×#6322512yes—
624C23C2×#6322512yes—
625C23C2×#6322512yes—
626C23C22×C22⋊D1711yescharacteristic
627Q8—44no—
628D4—44no—
629D4—44no—
630D4—44no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—84no—
662C2×C4—681no—
663C2×C4—681no—
664C2×C4—681no—
665C2×C4—681no—
666C2×C4—681no—
667C2×C4—681no—
668C2×C4—681no—
669C2×C4—681no—
670C2×C4—681no—
671C2×C4—681no—
672C2×C4—681no—
673C2×C4—681no—
674C2×C4—1364no—
675C2×C4C2×#6322512yes—
676C2×C4C2×#6322512yes—
677C2×C4C2×#6322512yes—
678C2×C4C22×Dic3411yescharacteristic
679C2×C4C22×C4×D1711yescharacteristic
680C2×C4#1058769111yescharacteristic
681C2×C4#1058769111yescharacteristic
682C2×C4#1058769111yescharacteristic
683C2×C4#1058769111yescharacteristic
684C8—342no—
685C8—342no—
686C8—342no—
687C8—342no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22C22×#6322511yescharacteristic
710C22#1176336811yescharacteristic
711C22#1176336811yescharacteristic
712C22#1176361211yescharacteristic
713C22#1176361711yescharacteristic
714C22#1176362011yescharacteristic
715C22#1176362411yescharacteristic
716C4—22no—
717C4—22no—
718C4—22no—
719C4—81no—
720C4—81no—
721C4—81no—
722C4—81no—
723C4—1361no—
724C4—1361no—
725C4—1361no—
726C4—1361no—
727C4#1176328211yescharacteristic
728C4#1176328211yescharacteristic
729C4#1176343511yescharacteristic
730C4#1176343511yescharacteristic
731C2—42no—
732C2—42no—
733C2—42no—
734C2#1453139611yescharacteristic
735C2#1453737711yescharacteristic
736C2#1453738211yescharacteristic
737C2#1453963011yescharacteristic
738C2#1453963611yescharacteristic
739C2#1453966011yescharacteristic
740C2#1453966611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2311C2
socleC23×C17C22×D4
prime radicalC22×#41×C17C22
cosocleC22×C4×C17C24
hypercenter#2311D17
hypocenterC17#21945
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×#41 ◁ #2311

Complements

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

NH ≅ G/Ntype
3. #14528983C2semidirect
4. #14528983C2semidirect
5. #14528981C2semidirect
6. #14528981C2semidirect
7. #14528977C2semidirect
8. #14528976C2semidirect
9. #14528972C2semidirect
10. #14528971C2semidirect
11. #14528815C2semidirect
12. #14528815C2semidirect
13. #14528811C2semidirect
14. #14528807C2semidirect
28. #11762776C4semidirect
107. C2×#63223C2×C4semidirect
110. C22×#3622C2×C4semidirect
123. C22⋊#3622C2×C4semidirect
124. C22⋊#3622C2×C4semidirect
125. C22⋊#3622C2×C4semidirect
126. C22⋊#3622C2×C4semidirect
505. C17#21945semidirect

Maximal subgroups

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

subgroupindex
C2×#117627762
#145313762
#145289832
#145289812
#145289772
#145289762
#145289722
#145289712
#145288152
#145288112
#145288072
C17×#23112
#2194517