Finite Group Databasebeta

← #16963287

Subgroups — #16963287

Order 4352.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762702C211yesmaximal, characteristic
2C2×#11762684C211yesmaximal, characteristic
3#14527047C211yesmaximal, characteristic, complemented
4#14527040C211yesmaximal, characteristic, complemented
5#14527040C211yesmaximal, characteristic, complemented
6#14527036C211yesmaximal, characteristic, complemented
7#14527027C211yesmaximal, characteristic
8#14527027C211yesmaximal, characteristic
9#14527017C211yesmaximal, characteristic, complemented
10#14527014C211yesmaximal, characteristic, complemented
11#14527013C211yesmaximal, characteristic, complemented
12#14527010C211yesmaximal, characteristic, complemented
13#14527006C211yesmaximal, characteristic
14#14527006C211yesmaximal, characteristic
15C2×C17×#388C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C4×Dic17C2211yescharacteristic
26#11762702C418yescomplemented
27#11762684—24no—
28C2×#10587502C2211yescharacteristic
29C2×#10587502C2211yescharacteristic
30C2×#10587502C2211yescharacteristic
31C2×#10587502C2211yescharacteristic
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C22×C4⋊C4×C17C2211yescharacteristic
47C22×C22⋊C4×C17C2211yescharacteristic
48C22×C22⋊C4×C17C2211yescharacteristic
49C22×C22⋊C4×C17C2211yescharacteristic
50C22×C42×C17C2211yescharacteristic
51C17×#388—24no—
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C25×C17C2311yescharacteristic
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×Dic17—22no—
62C23×Dic17—22no—
63C23×Dic17—22no—
64C23×Dic17—41no—
65C23×Dic17—41no—
66C23×Dic17—41no—
67C23×Dic17—41no—
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C2×C4⋊C4×C17—22no—
77C2×C4⋊C4×C17—22no—
78C2×C4⋊C4×C17—41no—
79C2×C22⋊C4×C17—22no—
80C2×C22⋊C4×C17—22no—
81C2×C22⋊C4×C17—22no—
82C2×C22⋊C4×C17—22no—
83C2×C22⋊C4×C17—41no—
84C2×C22⋊C4×C17—41no—
85C2×C22⋊C4×C17C2×C414yes—
86C2×C22⋊C4×C17D414yes—
87C2×C22⋊C4×C17Q814yes—
88C2×C42×C17—22no—
89C2×C42×C17—22no—
90C2×C42×C17—41no—
91C2×C22⋊Dic17—22no—
92C2×C22⋊Dic17—41no—
93C2×C22⋊Dic17—41no—
94C2×C22⋊Dic17—41no—
95C2×C22⋊Dic17—41no—
96C2×C22⋊Dic17—41no—
97C2×C22⋊Dic17—41no—
98C2×C22⋊Dic17C2×C414yes—
99C2×C22⋊Dic17C2×C414yes—
100C2×C4⋊Dic17—22no—
101C2×C4⋊Dic17—22no—
102C2×C4⋊Dic17—22no—
103C2×C4⋊Dic17—22no—
104C2×C4⋊Dic17—41no—
105C2×C4⋊Dic17—41no—
106C2×C4⋊Dic17—41no—
107C2×C4⋊Dic17—41no—
108C2×C4⋊Dic17C2×C414yescomplemented
109C2×#63225—22no—
110C2×#63225—41no—
111C2×#63225—41no—
112C2×#63225—41no—
113C2×#63225—41no—
114C2×#63225—41no—
115C2×C4×Dic17—41no—
116C2×C4×Dic17—41no—
117C2×C4×Dic17C2×C414yescomplemented
118C17×#95—22no—
119C17×#95—22no—
120#10587502—22no—
121#10587502—22no—
122#10587502—22no—
123#10587502—22no—
124#10587502—22no—
125#10587502—41no—
126#10587502—41no—
127#10587502—41no—
128#10587502—41no—
129#10587502—41no—
130#10587502—41no—
131#10587502—41no—
132#10587502—41no—
133#10587502—41no—
134#10587502—41no—
135#10587502—41no—
136#10587502C2×C414yescomplemented
137#10587502C2×C414yescomplemented
138C24×C17—21no—
139C24×C17—21no—
140C24×C17—21no—
141C24×C17—21no—
142C24×C17—21no—
143C24×C17—21no—
144C24×C17—21no—
145C24×C17—21no—
146C24×C17—21no—
147C24×C17—21no—
148C24×C17—21no—
149C24×C17—21no—
150C24×C17C22×C412yes—
151C24×C17C2×D412yes—
152C24×C17C2×Q812yes—
153C24×C17C2411yescharacteristic
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—21no—
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×C17C22×C412yes—
189C22×C4×C17C22×C412yes—
190C22×C4×C17C2×D412yes—
191C22×C4×C17C2×D412yes—
192C22×C4×C17C2×Q812yes—
193C22×C4×C17C2×Q812yes—
194C22×C4×C17#4112yes—
195C22×C4×C17#4112yes—
196C22×Dic17—21no—
197C22×Dic17—21no—
198C22×Dic17—21no—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C22×Dic17—21no—
218C22×Dic17—21no—
219C22×Dic17—21no—
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—44no—
247C22×Dic17—44no—
248C22×Dic17—44no—
249C22×Dic17—44no—
250C22×Dic17—44no—
251C22×Dic17—44no—
252C22×Dic17—44no—
253C22×Dic17C22×C412yes—
254C22×Dic17C22×C412yes—
255C22×Dic17C22×C412yes—
256C22×Dic17C22×C412yes—
257C22×Dic17#4112yes—
258C22×Dic17#4112yes—
259C4⋊C4×C17—44no—
260C22⋊C4×C17—44no—
261C22⋊C4×C17—44no—
262C22⋊C4×C17C4⋊C4116yescomplemented
263C42×C17—44no—
264C22⋊Dic17—44no—
265C22⋊Dic17—44no—
266C22⋊Dic17—44no—
267C4⋊Dic17—44no—
268C4⋊Dic17—44no—
269C4⋊Dic17—44no—
270#63225—44no—
271#63225—44no—
272C4×Dic17—44no—
273#14488—171nomaximal, Sylow
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—22no—
277C23×C17—22no—
278C23×C17—22no—
279C23×C17—22no—
280C23×C17—22no—
281C23×C17—22no—
282C23×C17—22no—
283C23×C17—22no—
284C23×C17—22no—
285C23×C17—22no—
286C23×C17—22no—
287C23×C17—22no—
288C23×C17—22no—
289C23×C17—22no—
290C23×C17—22no—
291C23×C17—22no—
292C23×C17—41no—
293C23×C17—41no—
294C23×C17—41no—
295C23×C17—41no—
296C23×C17—41no—
297C23×C17—41no—
298C23×C17—41no—
299C23×C17—41no—
300C23×C17—41no—
301C23×C17—41no—
302C23×C17—41no—
303C23×C17—41no—
304C23×C17—41no—
305C23×C17—41no—
306C23×C17—41no—
307C23×C17—41no—
308C23×C17C2×C4⋊C414yes—
309C23×C17C23×C411yescharacteristic
310C23×C17C22×D411yescharacteristic
311C23×C17C22×Q811yescharacteristic
312C23×C17C2×#4111yescharacteristic
313C23×C17C2×#4111yescharacteristic
314C23×C17C2×#4111yescharacteristic
315C23×C17C2×#4111yescharacteristic
316C23×C17H(5,𝔽2)11yescharacteristic
317C23×C17H(5,𝔽2)11yescharacteristic
318C23×C17H(5,𝔽2)11yescharacteristic
319C23×C17H(5,𝔽2)11yescharacteristic
320C23×C17H(5,𝔽2)11yescharacteristic
321C23×C17H(5,𝔽2)11yescharacteristic
322C23×C172−1+411yescharacteristic
323C23×C172−1+411yescharacteristic
324C2×C4×C17—22no—
325C2×C4×C17—22no—
326C2×C4×C17—22no—
327C2×C4×C17—22no—
328C2×C4×C17—22no—
329C2×C4×C17—22no—
330C2×C4×C17—22no—
331C2×C4×C17—22no—
332C2×C4×C17—22no—
333C2×C4×C17—22no—
334C2×C4×C17—22no—
335C2×C4×C17—22no—
336C2×C4×C17—22no—
337C2×C4×C17—22no—
338C2×C4×C17—22no—
339C2×C4×C17—22no—
340C2×C4×C17—22no—
341C2×C4×C17—22no—
342C2×C4×C17—41no—
343C2×C4×C17—41no—
344C2×C4×C17—41no—
345C2×C4×C17—41no—
346C2×C4×C17—41no—
347C2×C4×C17—41no—
348C2×C4×C17—41no—
349C2×C4×C17—41no—
350C2×C4×C17—41no—
351C2×C4×C17—41no—
352C2×C4×C17—41no—
353C2×C4×C17—41no—
354C2×C4×C17—41no—
355C2×C4×C17—41no—
356C2×C4×C17—41no—
357C2×C4×C17—41no—
358C2×C4×C17—41no—
359C2×C4×C17—41no—
360C2×C4×C17—41no—
361C2×C4×C17—41no—
362C2×C4×C17—41no—
363C2×C4×C17—41no—
364C2×C4×C17C2×C4⋊C414yes—
365C2×C4×C17C2×C4⋊C414yes—
366C2×Dic17—22no—
367C2×Dic17—22no—
368C2×Dic17—22no—
369C2×Dic17—22no—
370C2×Dic17—22no—
371C2×Dic17—22no—
372C2×Dic17—22no—
373C2×Dic17—22no—
374C2×Dic17—22no—
375C2×Dic17—22no—
376C2×Dic17—22no—
377C2×Dic17—22no—
378C2×Dic17—22no—
379C2×Dic17—22no—
380C2×Dic17—22no—
381C2×Dic17—22no—
382C2×Dic17—22no—
383C2×Dic17—22no—
384C2×Dic17—416no—
385C2×Dic17—41no—
386C2×Dic17—41no—
387C2×Dic17—41no—
388C2×Dic17—41no—
389C2×Dic17—41no—
390C2×Dic17—41no—
391C2×Dic17—41no—
392C2×Dic17—41no—
393C2×Dic17—41no—
394C2×Dic17—41no—
395C2×Dic17—41no—
396C2×Dic17—41no—
397C2×Dic17—41no—
398C2×Dic17—41no—
399C2×Dic17—41no—
400C2×Dic17—41no—
401C2×Dic17—41no—
402C2×Dic17—41no—
403C2×Dic17—41no—
404C2×Dic17—41no—
405C2×Dic17—41no—
406C2×Dic17—41no—
407C2×Dic17—41no—
408C2×Dic17—41no—
409C2×Dic17—41no—
410C2×Dic17—41no—
411C2×Dic17—41no—
412C2×Dic17—41no—
413C2×Dic17—41no—
414C2×Dic17—41no—
415C2×Dic17—41no—
416C2×Dic17—41no—
417C2×Dic17—41no—
418C2×Dic17—41no—
419C2×Dic17—41no—
420C2×Dic17—41no—
421C2×Dic17—41no—
422C2×Dic17—41no—
423C2×#388—171no—
424C2×#388D1711yescharacteristic
425C2×#385—171no—
426#1444—171no—
427#1442—171no—
428#1442—171no—
429#1441—171no—
430#1439—171no—
431#1439—171no—
432#1436—171no—
433C4⋊#95—171no—
434C4⋊#95—171no—
435#1434—171no—
436C22⋊#95—171no—
437C22⋊#95—171no—
438C22×C17—24no—
439C22×C17—24no—
440C22×C17—24no—
441C22×C17—42no—
442C22×C17—42no—
443C22×C17—42no—
444C22×C17—42no—
445C22×C17—42no—
446C22×C17—42no—
447C22×C17—42no—
448C22×C17—42no—
449C22×C17—42no—
450C22×C17—42no—
451C22×C17—42no—
452C22×C17—42no—
453C22×C17C22×C4⋊C411yescharacteristic
454C22×C17C4×#4111yescharacteristic
455C22×C17C4×#4111yescharacteristic
456C22×C17#51811yescharacteristic
457C22×C17#51811yescharacteristic
458C22×C17#52011yescharacteristic
459C22×C17#52011yescharacteristic
460C22×C17#53511yescharacteristic
461C22×C17#53611yescharacteristic
462C22×C17#53811yescharacteristic
463C22×C17#53811yescharacteristic
464C22×C17#53811yescharacteristic
465C22×C17#53911yescharacteristic
466C22×C17#54011yescharacteristic
467C22×C17#54211yescharacteristic
468C22×C17#54211yescharacteristic
469C22×C17#54211yescharacteristic
470C22×C17#54411yescharacteristic
471C22×C17#54411yescharacteristic
472C22×C17#54611yescharacteristic
473C22×C17#54611yescharacteristic
474C22×C17#54611yescharacteristic
475C22×C17#54611yescharacteristic
476C22×C17#55111yescharacteristic
477C22×C17#55211yescharacteristic
478C22×C17#55311yescharacteristic
479C22×C17#55411yescharacteristic
480C22×C17#55411yescharacteristic
481C22×C17#55411yescharacteristic
482C22×C17#55411yescharacteristic
483C22×C17#55611yescharacteristic
484C22×C17#56011yescharacteristic
485C22×C17#56011yescharacteristic
486C22×C17#56211yescharacteristic
487C22×C17#56211yescharacteristic
488C4×C17—24no—
489C4×C17—24no—
490C4×C17—42no—
491C4×C17—42no—
492C4×C17—81no—
493C4×C17—81no—
494Dic17—42no—
495Dic17—42no—
496Dic17—42no—
497Dic17—42no—
498Dic17—42no—
499Dic17—42no—
500Dic17—81no—
501Dic17—81no—
502C24×C4—171no—
503C22×C4⋊C4—171no—
504C22×C4⋊C4—171no—
505C22×C4⋊C4—171no—
506C22×C4⋊C4—171no—
507C22×C4⋊C4—171no—
508C22×C4⋊C4C2×D1711yescharacteristic
509C22×C22⋊C4—171no—
510C22×C22⋊C4—171no—
511C22×C22⋊C4—171no—
512C22×C22⋊C4C2×D1711yescharacteristic
513C22×C22⋊C4C2×D1711yescharacteristic
514C22×C22⋊C4C2×D1711yescharacteristic
515C22×C42—171no—
516C22×C42C2×D1711yescharacteristic
517#388—24no—
518#388—178no—
519#385—344no—
520C2×#95—171no—
521C2×#95—171no—
522C2×#95—171no—
523C2×#95—171no—
524C2×#95—171no—
525C2×#95—171no—
526C2×#95—171no—
527C2×#95—171no—
528C2×#95—171no—
529C2×#95—171no—
530C2×#95—171no—
531C2×#95—171no—
532C2×#95—171no—
533C2×#95—171no—
534C2×#95—171no—
535C2×#95—171no—
536C2×#95—171no—
537C2×#95—171no—
538C2×#95C2×D1711yescharacteristic
539C2×#95C2×D1711yescharacteristic
540C2×C17—44no—
541C2×C17#231711yescharacteristic
542C2×C17#233511yescharacteristic
543C2×C17#233711yescharacteristic
544C2×C17#234911yescharacteristic
545C2×C17#234911yescharacteristic
546C2×C17#237311yescharacteristic
547C2×C17#237711yescharacteristic
548C2×C17#268511yescharacteristic
549C2×C17#268711yescharacteristic
550C2×C17#270011yescharacteristic
551C2×C17#270311yescharacteristic
552C2×C17#274211yescharacteristic
553C2×C17#276811yescharacteristic
554C2×C17#278811yescharacteristic
555C2×C17#279011yescharacteristic
556C25C22×D1711yescharacteristic
557C23×C4—171no—
558C23×C4—171no—
559C23×C4—171no—
560C23×C4—171no—
561C23×C4—171no—
562C23×C4—171no—
563C23×C4—171no—
564C23×C4—171no—
565C23×C4—342no—
566C23×C4—342no—
567C23×C4—342no—
568C23×C4—681no—
569C23×C4—681no—
570C23×C4—681no—
571C23×C4—681no—
572C23×C4C22×D1711yescharacteristic
573C23×C4C22×D1711yescharacteristic
574C23×C4C22×D1711yescharacteristic
575C23×C4C22×D1711yescharacteristic
576C23×C4C22×D1711yescharacteristic
577C23×C4C22×D1711yescharacteristic
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—174no—
582C2×C4⋊C4—342no—
583C2×C4⋊C4—342no—
584C2×C4⋊C4—342no—
585C2×C4⋊C4—342no—
586C2×C4⋊C4—342no—
587C2×C4⋊C4—681no—
588C2×C4⋊C4—681no—
589C2×C4⋊C4—681no—
590C2×C4⋊C4—681no—
591C2×C4⋊C4—681no—
592C2×C4⋊C4—681no—
593C2×C4⋊C4—681no—
594C2×C4⋊C4—681no—
595C2×C4⋊C4—681no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—174no—
603C2×C22⋊C4—174no—
604C2×C22⋊C4—342no—
605C2×C22⋊C4—681no—
606C2×C22⋊C4—681no—
607C2×C22⋊C4—681no—
608C2×C22⋊C4—681no—
609C2×C22⋊C4—681no—
610C2×C22⋊C4—681no—
611C2×C22⋊C4Dic3414yes—
612C2×C22⋊C4C4×D1714yes—
613C2×C22⋊C4C22⋊D1714yes—
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—41no—
617C2×C42—174no—
618C2×C42—681no—
619C2×C42—681no—
620#95—22no—
621#95—22no—
622#95—174no—
623#95—174no—
624#95—342no—
625#95—342no—
626#95—342no—
627#95—342no—
628#95—342no—
629#95—681no—
630#95—681no—
631#95—681no—
632#95—681no—
633#95—681no—
634#95—681no—
635#95—681no—
636#95—681no—
637#95—681no—
638#95—681no—
639#95—681no—
640C17#1448811yescharacteristic, complemented, Sylow
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×Dic3412yes—
654C24C2×C4×D1712yes—
655C24C2×C22⋊D1712yes—
656C24C23×D1711yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—172no—
692C22×C4—172no—
693C22×C4—172no—
694C22×C4—172no—
695C22×C4—172no—
696C22×C4—172no—
697C22×C4—341no—
698C22×C4—341no—
699C22×C4—341no—
700C22×C4—341no—
701C22×C4—341no—
702C22×C4—341no—
703C22×C4—341no—
704C22×C4—341no—
705C22×C4—341no—
706C22×C4—341no—
707C22×C4—341no—
708C22×C4—341no—
709C22×C4—341no—
710C22×C4—341no—
711C22×C4—341no—
712C22×C4—341no—
713C22×C4—341no—
714C22×C4—341no—
715C22×C4—341no—
716C22×C4—341no—
717C22×C4—341no—
718C22×C4—341no—
719C22×C4—341no—
720C22×C4—341no—
721C22×C4—341no—
722C22×C4—341no—
723C22×C4—341no—
724C22×C4—341no—
725C22×C4—341no—
726C22×C4—341no—
727C22×C4—341no—
728C22×C4—341no—
729C22×C4—341no—
730C22×C4—341no—
731C22×C4—341no—
732C22×C4—341no—
733C22×C4—341no—
734C22×C4—341no—
735C22×C4—341no—
736C22×C4—341no—
737C22×C4—341no—
738C22×C4—341no—
739C22×C4—341no—
740C22×C4—341no—
741C22×C4—341no—
742C22×C4—341no—
743C22×C4—341no—
744C22×C4—341no—
745C22×C4—341no—
746C22×C4—341no—
747C22×C4—684no—
748C22×C4—684no—
749C22×C4—684no—
750C22×C4—684no—
751C22×C4—684no—
752C22×C4—684no—
753C22×C4—684no—
754C22×C4C2×Dic3412yes—
755C22×C4C2×Dic3412yes—
756C22×C4C2×C4×D1712yes—
757C22×C4C2×C4×D1712yes—
758C22×C4#6325412yes—
759C22×C4#6325412yes—
760C22×C4C2×C22⋊D1712yes—
761C22×C4C2×C22⋊D1712yes—
762C4⋊C4—44no—
763C4⋊C4—684no—
764C4⋊C4—684no—
765C4⋊C4—684no—
766C4⋊C4—684no—
767C4⋊C4—684no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—684no—
771C22⋊C4—684no—
772C22⋊C4—684no—
773C22⋊C4#63225116yescomplemented
774C42—44no—
775C42—684no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×#6322514yes—
811C23C22×Dic3411yescharacteristic
812C23C22×C4×D1711yescharacteristic
813C23C2×#6325411yescharacteristic
814C23C2×#6325411yescharacteristic
815C23#1058769111yescharacteristic
816C23#1058769111yescharacteristic
817C23#41×D1711yescharacteristic
818C23#41×D1711yescharacteristic
819C23#1058769611yescharacteristic
820C23#1058769611yescharacteristic
821C23#1058769611yescharacteristic
822C23#1058769611yescharacteristic
823C23#1058769711yescharacteristic
824C23#1058769711yescharacteristic
825C23C22×C22⋊D1711yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—342no—
867C2×C4—342no—
868C2×C4—342no—
869C2×C4—342no—
870C2×C4—342no—
871C2×C4—342no—
872C2×C4—342no—
873C2×C4—342no—
874C2×C4—342no—
875C2×C4—342no—
876C2×C4—342no—
877C2×C4—342no—
878C2×C4—342no—
879C2×C4—342no—
880C2×C4—342no—
881C2×C4—342no—
882C2×C4—342no—
883C2×C4—342no—
884C2×C4—6816no—
885C2×C4—681no—
886C2×C4—681no—
887C2×C4—681no—
888C2×C4—681no—
889C2×C4—681no—
890C2×C4—681no—
891C2×C4—681no—
892C2×C4—681no—
893C2×C4—681no—
894C2×C4—681no—
895C2×C4—681no—
896C2×C4—681no—
897C2×C4—681no—
898C2×C4—681no—
899C2×C4—681no—
900C2×C4—681no—
901C2×C4—681no—
902C2×C4—681no—
903C2×C4—681no—
904C2×C4—681no—
905C2×C4—681no—
906C2×C4—681no—
907C2×C4—681no—
908C2×C4—681no—
909C2×C4—681no—
910C2×C4—681no—
911C2×C4—681no—
912C2×C4—681no—
913C2×C4—681no—
914C2×C4—681no—
915C2×C4—681no—
916C2×C4—681no—
917C2×C4—681no—
918C2×C4—681no—
919C2×C4—681no—
920C2×C4—681no—
921C2×C4—681no—
922C2×C4—681no—
923C2×C4C2×#6322514yes—
924C2×C4C2×#6322514yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×#6322511yescharacteristic
941C22C4×#6325411yescharacteristic
942C22C4×#6325411yescharacteristic
943C22#1176328111yescharacteristic
944C22#1176328111yescharacteristic
945C22#1176328911yescharacteristic
946C22#1176328911yescharacteristic
947C22#1176337311yescharacteristic
948C22#1176338011yescharacteristic
949C22#1176339611yescharacteristic
950C22#1176339811yescharacteristic
951C22#1176339811yescharacteristic
952C22#1176340311yescharacteristic
953C22#1176341211yescharacteristic
954C22#1176342311yescharacteristic
955C22#1176342711yescharacteristic
956C22#1176342811yescharacteristic
957C22#1176343711yescharacteristic
958C22#1176343711yescharacteristic
959C22#1176344711yescharacteristic
960C22#1176344711yescharacteristic
961C22#1176345311yescharacteristic
962C22#1176345311yescharacteristic
963C22#1176348411yescharacteristic
964C22#1176349611yescharacteristic
965C22#1176351111yescharacteristic
966C22#1176351611yescharacteristic
967C22#1176351611yescharacteristic
968C22#1176351811yescharacteristic
969C22#1176351811yescharacteristic
970C22#1176352811yescharacteristic
971C22#1176354711yescharacteristic
972C22#1176355011yescharacteristic
973C22#1176355311yescharacteristic
974C22#1176355611yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—81no—
980C4—81no—
981C4—682no—
982C4—682no—
983C4—682no—
984C4—682no—
985C4—682no—
986C4—682no—
987C4—1361no—
988C4—1361no—
989C2—44no—
990C2#1453140411yescharacteristic
991C2#1453158111yescharacteristic
992C2#1453159111yescharacteristic
993C2#1453168911yescharacteristic
994C2#1453168911yescharacteristic
995C2#1453191111yescharacteristic
996C2#1453193711yescharacteristic
997C2#1453516911yescharacteristic
998C2#1453519911yescharacteristic
999C2#1453537611yescharacteristic
1000C2#1453542311yescharacteristic
1001C2#1453591011yescharacteristic
1002C2#1453626811yescharacteristic
1003C2#1453652711yescharacteristic
1004C2#1453655411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#388D17
hypocenterC17#14488
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. #14527047C2semidirect
4. #14527040C2semidirect
5. #14527040C2semidirect
6. #14527036C2semidirect
9. #14527017C2semidirect
10. #14527014C2semidirect
11. #14527013C2semidirect
12. #14527010C2semidirect
26. #11762702C4semidirect
108. C2×C4⋊Dic17C2×C4semidirect
117. C2×C4×Dic17C2×C4semidirect
136. #10587502C2×C4semidirect
137. #10587502C2×C4semidirect
262. C22⋊C4×C17C4⋊C4semidirect
640. C17#14488semidirect
773. C22⋊C4#63225semidirect

Maximal subgroups

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

subgroupindex
C2×#117627022
C2×#117626842
#145270472
#145270402
#145270362
#145270272
#145270172
#145270142
#145270132
#145270102
#145270062
C2×C17×#3882
#1448817