Finite Group Databasebeta

← #16964923

Subgroups — #16964923

Order 4352.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762727C211yesmaximal, characteristic
2#14527050C211yesmaximal, characteristic, complemented
3#14527032C211yesmaximal, characteristic, complemented
4#14527032C211yesmaximal, characteristic, complemented
5#14527024C211yesmaximal, characteristic
6#14527024C211yesmaximal, characteristic
7#14527022C211yesmaximal, characteristic, complemented
8#14527022C211yesmaximal, characteristic, complemented
9#14527020C211yesmaximal, characteristic, complemented
10#14527020C211yesmaximal, characteristic, complemented
11#14527020C211yesmaximal, characteristic, complemented
12#14527020C211yesmaximal, characteristic, complemented
13#14527015C211yesmaximal, characteristic, complemented
14#14527009C211yesmaximal, characteristic, complemented
15C17×#1434C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×#63227C2211yescharacteristic
19C22×#63227C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32#11762727C418yescomplemented
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C22×C42×C17C2211yescharacteristic
46C2×C17×#95C2211yescharacteristic
47C2×C17×#95C2211yescharacteristic
48C2×C17×#95C2211yescharacteristic
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C24×D17C2311yescharacteristic
53C24×D17C2311yescharacteristic
54C23×C4×C17C2311yescharacteristic
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×Dic17C2311yescharacteristic
62C23×Dic17C2311yescharacteristic
63C23×Dic17C2311yescharacteristic
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C22×D68—41no—
68C22×D68—41no—
69C22×D68—41no—
70C22×D68—41no—
71C22×D68—41no—
72C22×D68—41no—
73C22×D68C2×C414yes—
74C2×C42×C17—22no—
75C2×C42×C17—41no—
76C2×C42×C17—41no—
77C2×#63227—22no—
78C2×#63227—22no—
79C2×#63227—22no—
80C2×#63227—22no—
81C2×#63227—22no—
82C2×#63227—22no—
83C2×#63227—22no—
84C2×#63227—22no—
85C2×#63227—22no—
86C2×#63227—22no—
87C2×#63227—22no—
88C2×#63227—22no—
89C2×#63227—41no—
90C2×#63227—41no—
91C2×#63227—41no—
92C2×#63227—41no—
93C2×#63227—41no—
94C2×#63227—41no—
95C2×#63227—41no—
96C2×#63227—41no—
97C2×#63227—41no—
98C2×#63227—41no—
99C2×#63227—41no—
100C2×#63227—41no—
101C2×#63227—41no—
102C2×#63227—41no—
103C2×#63227—41no—
104C2×#63227—41no—
105C2×#63227—41no—
106C2×#63227—41no—
107C2×#63227—41no—
108C2×#63227—41no—
109C2×#63227C2×C414yes—
110C2×#63227C2×C414yes—
111C2×#63227C2×C414yes—
112C2×#63227C2×C414yes—
113C2×#63225—41no—
114C2×#63225—41no—
115C2×#63225C2×C414yes—
116C2×C4×Dic17—22no—
117C2×C4×Dic17—41no—
118C2×C4×Dic17—41no—
119C2×C4×Dic17—41no—
120C2×C4×Dic17—41no—
121C2×C4×Dic17—41no—
122C17×#95—22no—
123C17×#95—41no—
124C17×#95—41no—
125C17×#95—41no—
126C17×#95—41no—
127C17×#95C2×C414yes—
128#10587502—22no—
129#10587502—22no—
130#10587502—22no—
131#10587502—41no—
132#10587502—41no—
133#10587502—41no—
134#10587502—41no—
135#10587502—41no—
136#10587502—41no—
137#10587502—41no—
138#10587502—41no—
139#10587502—41no—
140C24×C17C2411yescharacteristic
141C23×D17—21no—
142C23×D17—21no—
143C23×D17—21no—
144C23×D17—21no—
145C23×D17—21no—
146C23×D17—21no—
147C23×D17—21no—
148C23×D17—21no—
149C23×D17—21no—
150C23×D17—21no—
151C23×D17—21no—
152C23×D17—21no—
153C23×D17—21no—
154C23×D17—21no—
155C23×D17—21no—
156C23×D17—21no—
157C23×D17—21no—
158C23×D17—21no—
159C23×D17—21no—
160C23×D17—21no—
161C23×D17—21no—
162C23×D17—21no—
163C23×D17—21no—
164C23×D17—21no—
165C23×D17—21no—
166C23×D17—21no—
167C23×D17—21no—
168C23×D17—21no—
169C23×D17C22×C412yes—
170C23×D17C22×C412yes—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17C22×C412yes—
215C22×C4×C17C22×C412yes—
216C22×C4×C17C22×C412yes—
217C22×C4×C17#4112yes—
218C22×C4×C17#4112yes—
219C22×C4×C17#4112yes—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—21no—
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—21no—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17—21no—
246C22×Dic17—21no—
247C22×Dic17—21no—
248C22×Dic17—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17C22×C412yes—
258C22×Dic17C22×C412yes—
259C22×Dic17#4112yes—
260C22×Dic17#4112yes—
261C22×Dic17#4112yes—
262C2×D68—44no—
263C2×D68—44no—
264C2×D68—44no—
265C2×D68—44no—
266C2×D68—44no—
267C2×D68—44no—
268C2×D68—44no—
269C42×C17—44no—
270#63227—44no—
271#63227—44no—
272#63227—44no—
273#63227—44no—
274#63227—44no—
275#63227—44no—
276#63227—44no—
277#63227—44no—
278#63227—44no—
279#63227—44no—
280#63227—44no—
281#63227—44no—
282#63225—44no—
283C4×Dic17—44no—
284C4×Dic17—44no—
285#14617—171nomaximal, Sylow
286C23×C17C23×C411yescharacteristic
287C23×C17C2×#4111yescharacteristic
288C23×C17C2×#4111yescharacteristic
289C23×C17C2×#4111yescharacteristic
290C23×C17C2×#4111yescharacteristic
291C23×C17C2×#4111yescharacteristic
292C23×C17C2×#4111yescharacteristic
293C23×C17H(5,𝔽2)11yescharacteristic
294C23×C17H(5,𝔽2)11yescharacteristic
295C23×C17H(5,𝔽2)11yescharacteristic
296C23×C17H(5,𝔽2)11yescharacteristic
297C23×C17H(5,𝔽2)11yescharacteristic
298C23×C17H(5,𝔽2)11yescharacteristic
299C23×C17H(5,𝔽2)11yescharacteristic
300C23×C17H(5,𝔽2)11yescharacteristic
301C22×D17—22no—
302C22×D17—22no—
303C22×D17—22no—
304C22×D17—22no—
305C22×D17—22no—
306C22×D17—22no—
307C22×D17—22no—
308C22×D17—22no—
309C22×D17—22no—
310C22×D17—22no—
311C22×D17—22no—
312C22×D17—22no—
313C22×D17—22no—
314C22×D17—22no—
315C22×D17—41no—
316C22×D17—41no—
317C22×D17—41no—
318C22×D17—41no—
319C22×D17—41no—
320C22×D17—41no—
321C22×D17—41no—
322C22×D17—41no—
323C22×D17—41no—
324C22×D17—41no—
325C22×D17—41no—
326C22×D17—41no—
327C22×D17—41no—
328C22×D17—41no—
329C22×D17—41no—
330C22×D17—41no—
331C22×D17—41no—
332C22×D17—41no—
333C22×D17—41no—
334C22×D17—41no—
335C22×D17—41no—
336C22×D17—41no—
337C22×D17—41no—
338C22×D17—41no—
339C22×D17—41no—
340C22×D17—41no—
341C22×D17—41no—
342C22×D17—41no—
343C22×D17—41no—
344C22×D17—41no—
345C22×D17—41no—
346C22×D17—41no—
347C22×D17—41no—
348C22×D17—41no—
349C22×D17—41no—
350C22×D17—41no—
351C22×D17—41no—
352C22×D17—41no—
353C22×D17—41no—
354C22×D17—41no—
355C22×D17—41no—
356C22×D17—41no—
357C22×D17—41no—
358C22×D17—41no—
359C22×D17—41no—
360C22×D17—41no—
361C22×D17—41no—
362C22×D17—41no—
363C22×D17—41no—
364C22×D17—41no—
365C22×D17—41no—
366C22×D17—41no—
367C22×D17—41no—
368C22×D17—41no—
369C22×D17—41no—
370C22×D17—41no—
371C2×C4×C17—22no—
372C2×C4×C17—22no—
373C2×C4×C17—22no—
374C2×C4×C17—22no—
375C2×C4×C17—22no—
376C2×C4×C17—22no—
377C2×C4×C17—22no—
378C2×C4×C17—22no—
379C2×C4×C17—22no—
380C2×C4×C17—22no—
381C2×C4×C17—22no—
382C2×C4×C17—22no—
383C2×C4×C17—22no—
384C2×C4×C17—22no—
385C2×C4×C17—22no—
386C2×C4×C17—22no—
387C2×C4×C17—22no—
388C2×C4×C17—22no—
389C2×C4×C17—41no—
390C2×C4×C17—41no—
391C2×C4×C17—41no—
392C2×C4×C17—41no—
393C2×C4×C17—41no—
394C2×C4×C17—41no—
395C2×C4×C17—41no—
396C2×C4×C17—41no—
397C2×C4×C17—41no—
398C2×C4×C17—41no—
399C2×C4×C17—41no—
400C2×C4×C17—41no—
401C2×C4×C17—41no—
402C2×C4×C17—41no—
403C2×C4×C17—41no—
404C2×C4×C17—41no—
405C2×C4×C17—41no—
406C2×C4×C17—41no—
407C2×C4×C17—41no—
408C2×C4×C17—41no—
409C2×C4×C17—41no—
410C2×C4×C17—41no—
411C2×C4×C17—41no—
412C2×C4×C17—41no—
413C2×C4×C17—41no—
414C2×C4×C17—41no—
415C2×C4×C17—41no—
416C2×C4×C17—41no—
417C2×C4×C17—41no—
418C2×C4×C17—41no—
419C2×C4×C17—41no—
420C2×Dic17—22no—
421C2×Dic17—22no—
422C2×Dic17—22no—
423C2×Dic17—22no—
424C2×Dic17—22no—
425C2×Dic17—22no—
426C2×Dic17—22no—
427C2×Dic17—22no—
428C2×Dic17—22no—
429C2×Dic17—22no—
430C2×Dic17—22no—
431C2×Dic17—22no—
432C2×Dic17—22no—
433C2×Dic17—22no—
434C2×Dic17—22no—
435C2×Dic17—41no—
436C2×Dic17—41no—
437C2×Dic17—41no—
438C2×Dic17—41no—
439C2×Dic17—41no—
440C2×Dic17—41no—
441C2×Dic17—41no—
442C2×Dic17—41no—
443C2×Dic17—41no—
444C2×Dic17—41no—
445C2×Dic17—41no—
446C2×Dic17—41no—
447C2×Dic17—41no—
448C2×Dic17—41no—
449C2×Dic17—41no—
450C2×Dic17—41no—
451C2×Dic17—41no—
452C2×Dic17—41no—
453C2×Dic17—41no—
454C2×Dic17—41no—
455C2×Dic17—41no—
456C2×Dic17—41no—
457C2×Dic17—41no—
458C2×Dic17—41no—
459C2×Dic17—41no—
460C2×Dic17—41no—
461C2×Dic17—41no—
462D68—416no—
463C2×#394—171no—
464#1445—171no—
465#1440—171no—
466#1440—171no—
467#1438—171no—
468#1438—171no—
469#1437—171no—
470#1437—171no—
471#1437—171no—
472#1437—171no—
473#1437—171no—
474#1437—171no—
475#1436—171no—
476#1434—171no—
477#1434D1711yescharacteristic, complemented
478C22×C17C4×#4111yescharacteristic
479C22×C17C4×#4111yescharacteristic
480C22×C17C4×#4111yescharacteristic
481C22×C17#51811yescharacteristic
482C22×C17#51811yescharacteristic
483C22×C17#51811yescharacteristic
484C22×C17#51811yescharacteristic
485C22×C17#53811yescharacteristic
486C22×C17#53811yescharacteristic
487C22×C17#53811yescharacteristic
488C22×C17#53811yescharacteristic
489C22×C17#53811yescharacteristic
490C22×C17#53811yescharacteristic
491C22×C17#54011yescharacteristic
492C22×C17#54011yescharacteristic
493C22×C17#54011yescharacteristic
494C22×C17#54011yescharacteristic
495C22×C17#54011yescharacteristic
496C22×C17#54011yescharacteristic
497C22×C17#55111yescharacteristic
498C22×C17#55111yescharacteristic
499C22×C17#55111yescharacteristic
500C22×C17#55111yescharacteristic
501C22×C17#55311yescharacteristic
502C22×C17#55311yescharacteristic
503C22×C17#55311yescharacteristic
504C22×C17#55311yescharacteristic
505C22×C17#55511yescharacteristic
506C22×C17#55511yescharacteristic
507C22×C17#55911yescharacteristic
508C22×C17#55911yescharacteristic
509C22×C17#56011yescharacteristic
510C22×C17#56011yescharacteristic
511C22×C17#56011yescharacteristic
512C22×C17H(3,𝔽4)11yescharacteristic
513C2×D17—42no—
514C2×D17—42no—
515C2×D17—42no—
516C2×D17—42no—
517C2×D17—42no—
518C2×D17—42no—
519C2×D17—42no—
520C2×D17—42no—
521C2×D17—42no—
522C2×D17—42no—
523C2×D17—42no—
524C2×D17—42no—
525C2×D17—42no—
526C2×D17—42no—
527C2×D17—81no—
528C2×D17—81no—
529C2×D17—81no—
530C2×D17—81no—
531C2×D17—81no—
532C2×D17—81no—
533C2×D17—81no—
534C2×D17—81no—
535C2×D17—81no—
536C2×D17—81no—
537C2×D17—81no—
538C2×D17—81no—
539C2×D17—81no—
540C2×D17—81no—
541C2×D17—81no—
542C2×D17—81no—
543C4×C17—42no—
544C4×C17—42no—
545C4×C17—42no—
546C4×C17—42no—
547C4×C17—42no—
548C4×C17—42no—
549C4×C17—81no—
550Dic17—42no—
551Dic17—42no—
552Dic17—42no—
553Dic17—42no—
554Dic17—42no—
555Dic17—81no—
556C23×D4—171no—
557C22×C4⋊C4—171no—
558C22×C22⋊C4—171no—
559C22×C22⋊C4—171no—
560C22×C22⋊C4—171no—
561C22×C22⋊C4—171no—
562C22×C22⋊C4—171no—
563C22×C22⋊C4—171no—
564C22×C22⋊C4—171no—
565C22×C22⋊C4—171no—
566C22×C22⋊C4—171no—
567C22×C22⋊C4—171no—
568C22×C22⋊C4—171no—
569C22×C22⋊C4—171no—
570C22×C42—171no—
571C22×C42—171no—
572C22×C42C2×D1711yescharacteristic
573#394—178no—
574C2×#95—171no—
575C2×#95—171no—
576C2×#95—171no—
577C2×#95—171no—
578C2×#95—171no—
579C2×#95—171no—
580C2×#95—171no—
581C2×#95—171no—
582C2×#95—171no—
583C2×#95—171no—
584C2×#95—171no—
585C2×#95—171no—
586C2×#95C2×D1711yescharacteristic
587C2×#95C2×D1711yescharacteristic
588C2×#95C2×D1711yescharacteristic
589C2×#95C2×D1711yescharacteristic
590C2×#95C2×D1711yescharacteristic
591C2×#95C2×D1711yescharacteristic
592C2×C17#233311yescharacteristic
593C2×C17#233311yescharacteristic
594C2×C17#233311yescharacteristic
595C2×C17#237211yescharacteristic
596C2×C17#237411yescharacteristic
597C2×C17#237411yescharacteristic
598C2×C17#237511yescharacteristic
599C2×C17#275211yescharacteristic
600C2×C17#275211yescharacteristic
601C2×C17#275311yescharacteristic
602C2×C17#275311yescharacteristic
603C2×C17#275611yescharacteristic
604C2×C17#275611yescharacteristic
605C2×C17#280311yescharacteristic
606C2×C17#280311yescharacteristic
607D17—82no—
608D17—82no—
609C25—171no—
610C25—171no—
611C22×D4—174no—
612C22×D4—681no—
613C22×D4—681no—
614C22×D4—681no—
615C22×D4—681no—
616C22×D4—681no—
617C22×D4—681no—
618C23×C4—171no—
619C23×C4—171no—
620C23×C4—171no—
621C23×C4—171no—
622C23×C4—171no—
623C23×C4—171no—
624C23×C4C22×D1711yescharacteristic
625C23×C4C22×D1711yescharacteristic
626C23×C4C22×D1711yescharacteristic
627C23×C4C22×D1711yescharacteristic
628C23×C4C22×D1711yescharacteristic
629C23×C4C22×D1711yescharacteristic
630C23×C4C22×D1711yescharacteristic
631C2×C4⋊C4—174no—
632C2×C4⋊C4—681no—
633C2×C4⋊C4—681no—
634C2×C22⋊C4—174no—
635C2×C22⋊C4—174no—
636C2×C22⋊C4—174no—
637C2×C22⋊C4—174no—
638C2×C22⋊C4—342no—
639C2×C22⋊C4—342no—
640C2×C22⋊C4—342no—
641C2×C22⋊C4—342no—
642C2×C22⋊C4—342no—
643C2×C22⋊C4—342no—
644C2×C22⋊C4—342no—
645C2×C22⋊C4—342no—
646C2×C22⋊C4—342no—
647C2×C22⋊C4—342no—
648C2×C22⋊C4—342no—
649C2×C22⋊C4—342no—
650C2×C22⋊C4—681no—
651C2×C22⋊C4—681no—
652C2×C22⋊C4—681no—
653C2×C22⋊C4—681no—
654C2×C22⋊C4—681no—
655C2×C22⋊C4—681no—
656C2×C22⋊C4—681no—
657C2×C22⋊C4—681no—
658C2×C22⋊C4—681no—
659C2×C22⋊C4—681no—
660C2×C22⋊C4—681no—
661C2×C22⋊C4—681no—
662C2×C22⋊C4—681no—
663C2×C22⋊C4—681no—
664C2×C22⋊C4—681no—
665C2×C22⋊C4—681no—
666C2×C22⋊C4—681no—
667C2×C22⋊C4—681no—
668C2×C22⋊C4—681no—
669C2×C22⋊C4—681no—
670C2×C42—22no—
671C2×C42—41no—
672C2×C42—41no—
673C2×C42—342no—
674C2×C42—681no—
675C2×C42—681no—
676C2×C42—681no—
677C2×C42—681no—
678C2×C42—681no—
679#95—22no—
680#95—41no—
681#95—41no—
682#95—41no—
683#95—41no—
684#95—342no—
685#95—342no—
686#95—342no—
687#95—681no—
688#95—681no—
689#95—681no—
690#95—681no—
691#95—681no—
692#95—681no—
693#95—681no—
694#95—681no—
695#95—681no—
696#95C4×D1714yes—
697C17#1461711yescharacteristic, complemented, Sylow
698C24—172no—
699C24—172no—
700C24—341no—
701C24—341no—
702C24—341no—
703C24—341no—
704C24—341no—
705C24—341no—
706C24—341no—
707C24—341no—
708C24—341no—
709C24—341no—
710C24—341no—
711C24—341no—
712C24—341no—
713C24—341no—
714C24—341no—
715C24—341no—
716C24—341no—
717C24—341no—
718C24—341no—
719C24—341no—
720C24—341no—
721C24—341no—
722C24—341no—
723C24—341no—
724C24—341no—
725C24—341no—
726C24—341no—
727C24—341no—
728C24C23×D1711yescharacteristic
729C2×D4—684no—
730C2×D4—684no—
731C2×D4—684no—
732C2×D4—684no—
733C2×D4—684no—
734C2×D4—684no—
735C2×D4—684no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—172no—
780C22×C4—172no—
781C22×C4—172no—
782C22×C4—172no—
783C22×C4—172no—
784C22×C4—341no—
785C22×C4—341no—
786C22×C4—341no—
787C22×C4—341no—
788C22×C4—341no—
789C22×C4—341no—
790C22×C4—341no—
791C22×C4—341no—
792C22×C4—341no—
793C22×C4—341no—
794C22×C4—341no—
795C22×C4—341no—
796C22×C4—341no—
797C22×C4—341no—
798C22×C4—341no—
799C22×C4—341no—
800C22×C4—341no—
801C22×C4—341no—
802C22×C4—341no—
803C22×C4—341no—
804C22×C4—341no—
805C22×C4—341no—
806C22×C4—341no—
807C22×C4—341no—
808C22×C4—341no—
809C22×C4—341no—
810C22×C4—341no—
811C22×C4—341no—
812C22×C4—341no—
813C22×C4—341no—
814C22×C4—341no—
815C22×C4—341no—
816C22×C4—341no—
817C22×C4—341no—
818C22×C4—341no—
819C22×C4—341no—
820C22×C4—341no—
821C22×C4C2×C4×D1712yes—
822C22×C4C2×C4×D1712yes—
823C22×C4C2×C4×D1712yes—
824C22×C4#6325212yes—
825C22×C4#6325212yes—
826C22×C4#6325612yes—
827C4⋊C4—684no—
828C22⋊C4—684no—
829C22⋊C4—684no—
830C22⋊C4—684no—
831C22⋊C4—684no—
832C22⋊C4—684no—
833C22⋊C4—684no—
834C22⋊C4—684no—
835C22⋊C4—684no—
836C22⋊C4—684no—
837C22⋊C4—684no—
838C22⋊C4—684no—
839C22⋊C4—684no—
840C42—44no—
841C42—684no—
842C42—684no—
843C23—342no—
844C23—342no—
845C23—342no—
846C23—342no—
847C23—342no—
848C23—342no—
849C23—342no—
850C23—342no—
851C23—342no—
852C23—342no—
853C23—342no—
854C23—342no—
855C23—342no—
856C23—342no—
857C23—681no—
858C23—681no—
859C23—681no—
860C23—681no—
861C23—681no—
862C23—681no—
863C23—681no—
864C23—681no—
865C23—681no—
866C23—681no—
867C23—681no—
868C23—681no—
869C23—681no—
870C23—681no—
871C23—681no—
872C23—681no—
873C23—681no—
874C23—681no—
875C23—681no—
876C23—681no—
877C23—681no—
878C23—681no—
879C23—681no—
880C23—681no—
881C23—681no—
882C23—681no—
883C23—681no—
884C23—681no—
885C23—681no—
886C23—681no—
887C23—681no—
888C23—681no—
889C23—681no—
890C23—681no—
891C23—681no—
892C23—681no—
893C23—681no—
894C23—681no—
895C23—681no—
896C23—681no—
897C23—681no—
898C23—681no—
899C23—681no—
900C23—681no—
901C23—681no—
902C23—681no—
903C23—681no—
904C23—681no—
905C23—681no—
906C23—681no—
907C23—681no—
908C23—681no—
909C23—681no—
910C23—681no—
911C23—681no—
912C23—681no—
913C23C22×C4×D1711yescharacteristic
914C23C2×#6325211yescharacteristic
915C23C2×#6325211yescharacteristic
916C23#1058769111yescharacteristic
917C23#1058769111yescharacteristic
918C23#1058769111yescharacteristic
919C23C2×#6325611yescharacteristic
920C23#41×D1711yescharacteristic
921C23#41×D1711yescharacteristic
922C23#41×D1711yescharacteristic
923C23#1058769611yescharacteristic
924C23#1058769611yescharacteristic
925C23#1058769611yescharacteristic
926C23#1058769611yescharacteristic
927C23#1058769611yescharacteristic
928D4—6816no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—342no—
979C2×C4—342no—
980C2×C4—342no—
981C2×C4—342no—
982C2×C4—342no—
983C2×C4—342no—
984C2×C4—342no—
985C2×C4—342no—
986C2×C4—342no—
987C2×C4—342no—
988C2×C4—342no—
989C2×C4—342no—
990C2×C4—342no—
991C2×C4—342no—
992C2×C4—342no—
993C2×C4—681no—
994C2×C4—681no—
995C2×C4—681no—
996C2×C4—681no—
997C2×C4—681no—
998C2×C4—681no—
999C2×C4—681no—
1000C2×C4—681no—
1001C2×C4—681no—
1002C2×C4—681no—
1003C2×C4—681no—
1004C2×C4—681no—
1005C2×C4—681no—
1006C2×C4—681no—
1007C2×C4—681no—
1008C2×C4—681no—
1009C2×C4—681no—
1010C2×C4—681no—
1011C2×C4—681no—
1012C2×C4—681no—
1013C2×C4—681no—
1014C2×C4—681no—
1015C2×C4—681no—
1016C2×C4—681no—
1017C2×C4—681no—
1018C2×C4—681no—
1019C2×C4—681no—
1020C22—682no—
1021C22—682no—
1022C22—682no—
1023C22—682no—
1024C22—682no—
1025C22—682no—
1026C22—682no—
1027C22—682no—
1028C22—682no—
1029C22—682no—
1030C22—682no—
1031C22—682no—
1032C22—682no—
1033C22—682no—
1034C22—1361no—
1035C22—1361no—
1036C22—1361no—
1037C22—1361no—
1038C22—1361no—
1039C22—1361no—
1040C22—1361no—
1041C22—1361no—
1042C22—1361no—
1043C22—1361no—
1044C22—1361no—
1045C22—1361no—
1046C22—1361no—
1047C22—1361no—
1048C22—1361no—
1049C22—1361no—
1050C22#1176327711yescharacteristic
1051C22C4×#6325211yescharacteristic
1052C22C4×#6325611yescharacteristic
1053C22#1176328111yescharacteristic
1054C22#1176328111yescharacteristic
1055C22#1176328111yescharacteristic
1056C22#1176328311yescharacteristic
1057C22#1176339211yescharacteristic
1058C22#1176339311yescharacteristic
1059C22#1176339711yescharacteristic
1060C22#1176339811yescharacteristic
1061C22#1176339811yescharacteristic
1062C22#1176339911yescharacteristic
1063C22#1176340911yescharacteristic
1064C22#1176341011yescharacteristic
1065C22#1176341111yescharacteristic
1066C22#1176341111yescharacteristic
1067C22#1176341411yescharacteristic
1068C22#1176341511yescharacteristic
1069C22#1176348311yescharacteristic
1070C22#1176348311yescharacteristic
1071C22#1176348311yescharacteristic
1072C22#1176348611yescharacteristic
1073C22#1176350711yescharacteristic
1074C22#1176350811yescharacteristic
1075C22#1176351011yescharacteristic
1076C22#1176351211yescharacteristic
1077C22#1176352211yescharacteristic
1078C22#1176352211yescharacteristic
1079C22#1176354311yescharacteristic
1080C22#1176354411yescharacteristic
1081C22#1176354711yescharacteristic
1082C22#1176354911yescharacteristic
1083C22#1176355011yescharacteristic
1084C22#1176355111yescharacteristic
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—42no—
1091C4—81no—
1092C4—682no—
1093C4—682no—
1094C4—682no—
1095C4—682no—
1096C4—682no—
1097C4—1361no—
1098C2—1362no—
1099C2—1362no—
1100C2#1453154411yescharacteristic
1101C2#1453154711yescharacteristic
1102C2#1453154811yescharacteristic
1103C2#1453189411yescharacteristic
1104C2#1453191311yescharacteristic
1105C2#1453191611yescharacteristic
1106C2#1453192411yescharacteristic
1107C2#1453604711yescharacteristic
1108C2#1453604811yescharacteristic
1109C2#1453605611yescharacteristic
1110C2#1453605711yescharacteristic
1111C2#1453610211yescharacteristic
1112C2#1453610711yescharacteristic
1113C2#1453671211yescharacteristic
1114C2#1453672111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1434C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1434D17
hypocenterC17#14617
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. #14527050C2semidirect
3. #14527032C2semidirect
4. #14527032C2semidirect
7. #14527022C2semidirect
8. #14527022C2semidirect
9. #14527020C2semidirect
10. #14527020C2semidirect
11. #14527020C2semidirect
12. #14527020C2semidirect
13. #14527015C2semidirect
14. #14527009C2semidirect
15. C17×#1434C2semidirect
32. #11762727C4semidirect
477. #1434D17semidirect
697. C17#14617semidirect

Maximal subgroups

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

subgroupindex
C2×#117627272
#145270502
#145270322
#145270242
#145270222
#145270202
#145270152
#145270092
C17×#14342
#1461717