Finite Group Databasebeta

← #16957525

Subgroups — #16957525

Order 4352.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762707C211yesmaximal, characteristic, complemented
2C2×#11762684C211yesmaximal, characteristic
3C2×#11762684C211yesmaximal, characteristic
4C2×#11762681C211yesmaximal, characteristic
5C2×#11762667C211yesmaximal, characteristic
6C22×#10587502C211yesmaximal, characteristic
7#14527048C211yesmaximal, characteristic, complemented
8#14527040C211yesmaximal, characteristic, complemented
9#14527036C211yesmaximal, characteristic, complemented
10#14527036C211yesmaximal, characteristic, complemented
11#14527017C211yesmaximal, characteristic, complemented
12#14527017C211yesmaximal, characteristic, complemented
13#14527014C211yesmaximal, characteristic, complemented
14#14527007C211yesmaximal, characteristic
15C2×C4×C22⋊C4×C17C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C4⋊Dic17C2211yescharacteristic
21C22×C4⋊Dic17C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28#11762707—24no—
29#11762684—24no—
30#11762684C418yescomplemented
31#11762681—24no—
32#11762667—24no—
33C2×#10587502—24no—
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C24×C4×C17C2211yescharacteristic
51C22×C22⋊C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C22×C42×C17C2211yescharacteristic
54C22×C42×C17C2211yescharacteristic
55C4×C22⋊C4×C17—24no—
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C25×C17C2311yescharacteristic
59C23×C4×C17—22no—
60C23×C4×C17—22no—
61C23×C4×C17—22no—
62C23×C4×C17—22no—
63C23×C4×C17—41no—
64C23×C4×C17—41no—
65C23×C4×C17Q814yes—
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×Dic17—22no—
73C23×Dic17—22no—
74C23×Dic17—22no—
75C23×Dic17—22no—
76C23×Dic17—22no—
77C23×Dic17—22no—
78C23×Dic17—22no—
79C23×Dic17—22no—
80C23×Dic17—22no—
81C23×Dic17—41no—
82C23×Dic17—41no—
83C23×Dic17—41no—
84C23×Dic17—41no—
85C23×Dic17C2×C414yes—
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
88C23×Dic17C2311yescharacteristic
89C23×Dic17C2311yescharacteristic
90C23×Dic17C2311yescharacteristic
91C23×Dic17C2311yescharacteristic
92C23×Dic17C2311yescharacteristic
93C23×Dic17C2311yescharacteristic
94C2×C22⋊C4×C17—22no—
95C2×C22⋊C4×C17—22no—
96C2×C22⋊C4×C17C2×C414yes—
97C2×C22⋊C4×C17D414yes—
98C2×C22⋊C4×C17D414yes—
99C2×C22⋊C4×C17Q814yes—
100C2×C42×C17—22no—
101C2×C42×C17—22no—
102C2×C42×C17—22no—
103C2×C42×C17—22no—
104C2×C42×C17—41no—
105C2×C42×C17—41no—
106C2×C22⋊Dic17—22no—
107C2×C22⋊Dic17—22no—
108C2×C22⋊Dic17—22no—
109C2×C22⋊Dic17—22no—
110C2×C22⋊Dic17—22no—
111C2×C22⋊Dic17C2×C414yes—
112C2×C4⋊Dic17—22no—
113C2×C4⋊Dic17—22no—
114C2×C4⋊Dic17—22no—
115C2×C4⋊Dic17—22no—
116C2×C4⋊Dic17—22no—
117C2×C4⋊Dic17—22no—
118C2×C4⋊Dic17—41no—
119C2×C4⋊Dic17—41no—
120C2×C4⋊Dic17—41no—
121C2×C4⋊Dic17—41no—
122C2×C4⋊Dic17C2×C414yescomplemented
123C2×C4⋊Dic17C2×C414yescomplemented
124C2×#63225—22no—
125C2×#63225—22no—
126C2×#63225—22no—
127C2×#63225—22no—
128C2×#63225—22no—
129C2×#63225—22no—
130C2×#63225—22no—
131C2×#63225—22no—
132C2×#63225—41no—
133C2×#63225—41no—
134C2×#63225—41no—
135C2×#63225—41no—
136C17×#95—22no—
137C17×#95—22no—
138#10587502—22no—
139#10587502—22no—
140#10587502—22no—
141#10587502—22no—
142#10587502—22no—
143#10587502—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—22no—
148#10587502—22no—
149#10587502—41no—
150#10587502—41no—
151#10587502C2×C414yescomplemented
152#10587502C2×C414yescomplemented
153#10587502D414yes—
154C24×C17—21no—
155C24×C17—21no—
156C24×C17—21no—
157C24×C17—21no—
158C24×C17—21no—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17C22×C412yes—
163C24×C17C2×D412yes—
164C24×C17C2×D412yes—
165C24×C17C2×Q812yes—
166C24×C17C2×Q812yes—
167C24×C17#4112yes—
168C24×C17#4112yes—
169C24×C17C2411yescharacteristic
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—28no—
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—28no—
202C22×C4×C17—44no—
203C22×C4×C17—44no—
204C22×C4×C17—44no—
205C22×C4×C17—44no—
206C22×C4×C17—44no—
207C22×C4×C17C22×C412yes—
208C22×C4×C17C22×C412yes—
209C22×C4×C17C2×D412yes—
210C22×C4×C17C2×D412yes—
211C22×C4×C17C2×D412yes—
212C22×C4×C17C2×D412yes—
213C22×C4×C17C2×D412yes—
214C22×C4×C17C2×Q812yes—
215C22×C4×C17C2×Q812yes—
216C22×C4×C17C2×Q812yes—
217C22×C4×C17C2×Q812yes—
218C22×C4×C17#4112yes—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—28no—
224C22×Dic17—28no—
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—28no—
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—21no—
260C22×Dic17—21no—
261C22×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17—21no—
268C22×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—44no—
271C22×Dic17—44no—
272C22×Dic17—44no—
273C22×Dic17—44no—
274C22×Dic17—44no—
275C22×Dic17—44no—
276C22×Dic17—44no—
277C22×Dic17—44no—
278C22×Dic17—44no—
279C22×Dic17—44no—
280C22×Dic17—44no—
281C22×Dic17C22×C412yes—
282C22×Dic17C22×C412yes—
283C22×Dic17C22×C412yes—
284C22×Dic17C22×C412yes—
285C22×Dic17C2×D412yes—
286C22×Dic17C2×D412yes—
287C22×Dic17#4112yes—
288C22×Dic17#4112yes—
289C22⋊C4×C17—28no—
290C22⋊C4×C17C4⋊C4116yescomplemented
291C42×C17—44no—
292C42×C17—44no—
293C22⋊Dic17—28no—
294C22⋊Dic17—44no—
295C4⋊Dic17—28no—
296C4⋊Dic17—44no—
297C4⋊Dic17—44no—
298C4⋊Dic17—44no—
299#63225—44no—
300#63225—44no—
301#63225—44no—
302#63225—44no—
303#14004—171nomaximal, Sylow
304C23×C17—22no—
305C23×C17—22no—
306C23×C17—22no—
307C23×C17—22no—
308C23×C17—22no—
309C23×C17—22no—
310C23×C17—22no—
311C23×C17—22no—
312C23×C17—22no—
313C23×C17—22no—
314C23×C17—22no—
315C23×C17—22no—
316C23×C17—22no—
317C23×C17—22no—
318C23×C17—22no—
319C23×C17—22no—
320C23×C17—22no—
321C23×C17—22no—
322C23×C17—22no—
323C23×C17—22no—
324C23×C17—22no—
325C23×C17—22no—
326C23×C17—22no—
327C23×C17—22no—
328C23×C17—22no—
329C23×C17—22no—
330C23×C17—22no—
331C23×C17—22no—
332C23×C17C2×C4⋊C414yes—
333C23×C17C4×D414yes—
334C23×C17C4×Q814yes—
335C23×C17#12114yes—
336C23×C17C22⋊Q814yes—
337C23×C17#12514yes—
338C23×C17C4⋊Q814yes—
339C23×C17C23×C411yescharacteristic
340C23×C17C22×D411yescharacteristic
341C23×C17C22×D411yescharacteristic
342C23×C17C22×D411yescharacteristic
343C23×C17C22×Q811yescharacteristic
344C23×C17C22×Q811yescharacteristic
345C23×C17C2×#4111yescharacteristic
346C23×C17C2×#4111yescharacteristic
347C23×C17C2×#4111yescharacteristic
348C23×C17C2×#4111yescharacteristic
349C23×C17C2×#4111yescharacteristic
350C23×C17H(5,𝔽2)11yescharacteristic
351C23×C17H(5,𝔽2)11yescharacteristic
352C23×C17H(5,𝔽2)11yescharacteristic
353C23×C172−1+411yescharacteristic
354C2×C4×C17—22no—
355C2×C4×C17—22no—
356C2×C4×C17—22no—
357C2×C4×C17—22no—
358C2×C4×C17—22no—
359C2×C4×C17—22no—
360C2×C4×C17—22no—
361C2×C4×C17—22no—
362C2×C4×C17—22no—
363C2×C4×C17—22no—
364C2×C4×C17—22no—
365C2×C4×C17—22no—
366C2×C4×C17—22no—
367C2×C4×C17—22no—
368C2×C4×C17—22no—
369C2×C4×C17—22no—
370C2×C4×C17—22no—
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—416no—
382C2×C4×C17—41no—
383C2×C4×C17—41no—
384C2×C4×C17—41no—
385C2×C4×C17—41no—
386C2×C4×C17—41no—
387C2×C4×C17—41no—
388C2×C4×C17—41no—
389C2×C4×C17—41no—
390C2×C4×C17—41no—
391C2×C4×C17—41no—
392C2×C4×C17—41no—
393C2×C4×C17—41no—
394C2×C4×C17C2×C4⋊C414yes—
395C2×C4×C17C2×C4⋊C414yes—
396C2×C4×C17C22⋊Q814yes—
397C2×Dic17—22no—
398C2×Dic17—22no—
399C2×Dic17—22no—
400C2×Dic17—22no—
401C2×Dic17—22no—
402C2×Dic17—22no—
403C2×Dic17—22no—
404C2×Dic17—22no—
405C2×Dic17—22no—
406C2×Dic17—22no—
407C2×Dic17—22no—
408C2×Dic17—22no—
409C2×Dic17—22no—
410C2×Dic17—22no—
411C2×Dic17—22no—
412C2×Dic17—22no—
413C2×Dic17—22no—
414C2×Dic17—22no—
415C2×Dic17—22no—
416C2×Dic17—22no—
417C2×Dic17—22no—
418C2×Dic17—416no—
419C2×Dic17—416no—
420C2×Dic17—41no—
421C2×Dic17—41no—
422C2×Dic17—41no—
423C2×Dic17—41no—
424C2×Dic17—41no—
425C2×Dic17—41no—
426C2×Dic17—41no—
427C2×Dic17—41no—
428C2×Dic17—41no—
429C2×Dic17—41no—
430C2×Dic17—41no—
431C2×Dic17—41no—
432C2×Dic17—41no—
433C2×Dic17—41no—
434C2×Dic17—41no—
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×Dic17C4×D414yes—
455C2×#389—171no—
456C2×#385—171no—
457C2×#385—171no—
458C2×#385—171no—
459C2×#380—171no—
460C2×C4×C22⋊C4D1711yescharacteristic
461C22×#95—171no—
462#1444—171no—
463#1442—171no—
464#1441—171no—
465#1441—171no—
466#1436—171no—
467#1436—171no—
468C4⋊#95—171no—
469C22⋊#95—171no—
470C22×C17—24no—
471C22×C17—24no—
472C22×C17—24no—
473C22×C17—24no—
474C22×C17—24no—
475C22×C17—24no—
476C22×C17—24no—
477C22×C17—24no—
478C22×C17—24no—
479C22×C17—24no—
480C22×C17—24no—
481C22×C17—24no—
482C22×C17—24no—
483C22×C17—24no—
484C22×C17#38918yescomplemented
485C22×C17C22×C4⋊C411yescharacteristic
486C22×C17C2×C4×D411yescharacteristic
487C22×C17C2×C4×D411yescharacteristic
488C22×C17C2×C4×Q811yescharacteristic
489C22×C17C4×#4111yescharacteristic
490C22×C17#51811yescharacteristic
491C22×C17#52011yescharacteristic
492C22×C17C2×#12111yescharacteristic
493C22×C17C2×C22⋊Q811yescharacteristic
494C22×C17C2×C22⋊Q811yescharacteristic
495C22×C17#52511yescharacteristic
496C22×C17C2×#12511yescharacteristic
497C22×C17#52911yescharacteristic
498C22×C17C2×C4⋊Q811yescharacteristic
499C22×C17#53311yescharacteristic
500C22×C17#53811yescharacteristic
501C22×C17#53911yescharacteristic
502C22×C17#54311yescharacteristic
503C22×C17#54411yescharacteristic
504C22×C17D4211yescharacteristic
505C22×C17D4211yescharacteristic
506C22×C17#54611yescharacteristic
507C22×C17#54611yescharacteristic
508C22×C17#54611yescharacteristic
509C22×C17#54611yescharacteristic
510C22×C17#54611yescharacteristic
511C22×C17#54711yescharacteristic
512C22×C17#54711yescharacteristic
513C22×C17D4×Q811yescharacteristic
514C22×C17#55111yescharacteristic
515C22×C17#55111yescharacteristic
516C22×C17#55211yescharacteristic
517C22×C17#55411yescharacteristic
518C22×C17#55411yescharacteristic
519C22×C17#55411yescharacteristic
520C4×C17—24no—
521C4×C17—24no—
522C4×C17—24no—
523C4×C17—42no—
524C4×C17—42no—
525C4×C17—42no—
526Dic17—24no—
527Dic17—42no—
528Dic17—42no—
529Dic17—42no—
530Dic17—42no—
531Dic17—42no—
532Dic17—81no—
533Dic17—81no—
534C24×C4—171no—
535C24×C4—171no—
536C24×C4C2×D1711yescharacteristic
537C22×C4⋊C4—171no—
538C22×C4⋊C4—171no—
539C22×C4⋊C4—171no—
540C22×C4⋊C4—171no—
541C22×C4⋊C4—171no—
542C22×C4⋊C4—171no—
543C22×C4⋊C4—171no—
544C22×C4⋊C4—171no—
545C22×C22⋊C4—171no—
546C22×C22⋊C4—171no—
547C22×C22⋊C4C2×D1711yescharacteristic
548C22×C22⋊C4C2×D1711yescharacteristic
549C22×C42C2×D1711yescharacteristic
550C22×C42C2×D1711yescharacteristic
551#389—344no—
552#385—178no—
553#385—344no—
554#385—344no—
555#380—344no—
556C4×C22⋊C4—24no—
557C2×#95—171no—
558C2×#95—171no—
559C2×#95—171no—
560C2×#95—171no—
561C2×#95—171no—
562C2×#95—171no—
563C2×#95—171no—
564C2×#95—171no—
565C2×#95—171no—
566C2×#95—171no—
567C2×#95—171no—
568C2×#95—171no—
569C2×#95—171no—
570C2×#95—171no—
571C2×#95—171no—
572C2×#95—171no—
573C2×#95—344no—
574C2×#95C2×D1711yescharacteristic
575C2×#95C2×D1711yescharacteristic
576C2×C17—28no—
577C2×C17C2×#38911yescharacteristic
578C2×C17C4×C22⋊Q811yescharacteristic
579C2×C17#232911yescharacteristic
580C2×C17D4×C4⋊C411yescharacteristic
581C2×C17#234911yescharacteristic
582C2×C17#235811yescharacteristic
583C2×C17#235911yescharacteristic
584C2×C17#242411yescharacteristic
585C2×C17#242511yescharacteristic
586C2×C17#243711yescharacteristic
587C2×C17#243811yescharacteristic
588C2×C17#244011yescharacteristic
589C2×C17#247311yescharacteristic
590C2×C17#250511yescharacteristic
591C2×C17#254911yescharacteristic
592C25C22×D1711yescharacteristic
593C23×C4—22no—
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—41no—
598C23×C4—41no—
599C23×C4—171no—
600C23×C4—171no—
601C23×C4—171no—
602C23×C4—171no—
603C23×C4—171no—
604C23×C4—171no—
605C23×C4—174no—
606C23×C4—171no—
607C23×C4—171no—
608C23×C4—342no—
609C23×C4—342no—
610C23×C4—342no—
611C23×C4—342no—
612C23×C4—342no—
613C23×C4—342no—
614C23×C4—342no—
615C23×C4—342no—
616C23×C4—342no—
617C23×C4—681no—
618C23×C4—681no—
619C23×C4—681no—
620C23×C4—681no—
621C23×C4Dic3414yes—
622C23×C4C22×D1711yescharacteristic
623C23×C4C22×D1711yescharacteristic
624C23×C4C22×D1711yescharacteristic
625C23×C4C22×D1711yescharacteristic
626C23×C4C22×D1711yescharacteristic
627C23×C4C22×D1711yescharacteristic
628C2×C4⋊C4—174no—
629C2×C4⋊C4—174no—
630C2×C4⋊C4—342no—
631C2×C4⋊C4—342no—
632C2×C4⋊C4—342no—
633C2×C4⋊C4—342no—
634C2×C4⋊C4—342no—
635C2×C4⋊C4—342no—
636C2×C4⋊C4—342no—
637C2×C4⋊C4—342no—
638C2×C4⋊C4—342no—
639C2×C4⋊C4—342no—
640C2×C4⋊C4—342no—
641C2×C4⋊C4—342no—
642C2×C4⋊C4—342no—
643C2×C4⋊C4—342no—
644C2×C4⋊C4—681no—
645C2×C4⋊C4—681no—
646C2×C4⋊C4—681no—
647C2×C4⋊C4—681no—
648C2×C4⋊C4—681no—
649C2×C4⋊C4—681no—
650C2×C4⋊C4—681no—
651C2×C4⋊C4—681no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—174no—
655C2×C22⋊C4—342no—
656C2×C22⋊C4—342no—
657C2×C22⋊C4—342no—
658C2×C22⋊C4—342no—
659C2×C22⋊C4—342no—
660C2×C22⋊C4Dic3414yes—
661C2×C22⋊C4C4×D1714yes—
662C2×C22⋊C4D6814yes—
663C2×C22⋊C4C22⋊D1714yes—
664C2×C42—22no—
665C2×C42—22no—
666C2×C42—22no—
667C2×C42—22no—
668C2×C42—41no—
669C2×C42—41no—
670#95—22no—
671#95—22no—
672#95—174no—
673#95—174no—
674#95—174no—
675#95—342no—
676#95—342no—
677#95—342no—
678#95—342no—
679#95—342no—
680#95—342no—
681#95—342no—
682#95—342no—
683#95—342no—
684#95—342no—
685#95—342no—
686#95—681no—
687#95—681no—
688C17#1400411yescharacteristic, complemented, Sylow
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C2×Dic3412yes—
698C24C2×Dic3412yes—
699C24C2×C4×D1712yes—
700C24C2×D6812yes—
701C24#6325212yes—
702C24#6325212yes—
703C24C2×C22⋊D1712yes—
704C24C23×D1711yescharacteristic
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—172no—
743C22×C4—172no—
744C22×C4—172no—
745C22×C4—172no—
746C22×C4—172no—
747C22×C4—172no—
748C22×C4—172no—
749C22×C4—172no—
750C22×C4—348no—
751C22×C4—341no—
752C22×C4—341no—
753C22×C4—341no—
754C22×C4—341no—
755C22×C4—348no—
756C22×C4—341no—
757C22×C4—341no—
758C22×C4—341no—
759C22×C4—341no—
760C22×C4—341no—
761C22×C4—341no—
762C22×C4—341no—
763C22×C4—341no—
764C22×C4—341no—
765C22×C4—341no—
766C22×C4—341no—
767C22×C4—341no—
768C22×C4—341no—
769C22×C4—341no—
770C22×C4—341no—
771C22×C4—341no—
772C22×C4—341no—
773C22×C4—341no—
774C22×C4—341no—
775C22×C4—341no—
776C22×C4—341no—
777C22×C4—341no—
778C22×C4—341no—
779C22×C4—341no—
780C22×C4—341no—
781C22×C4—341no—
782C22×C4—341no—
783C22×C4—341no—
784C22×C4—341no—
785C22×C4—341no—
786C22×C4—348no—
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—684no—
802C22×C4—684no—
803C22×C4—684no—
804C22×C4—684no—
805C22×C4—684no—
806C22×C4—684no—
807C22×C4—684no—
808C22×C4—684no—
809C22×C4—684no—
810C22×C4—684no—
811C22×C4—684no—
812C22×C4C2×Dic3412yes—
813C22×C4C2×Dic3412yes—
814C22×C4C2×Dic3412yes—
815C22×C4C2×Dic3412yes—
816C22×C4C2×C4×D1712yes—
817C22×C4C2×C4×D1712yes—
818C22×C4C2×D6812yes—
819C22×C4C2×D6812yes—
820C22×C4D4×D1712yes—
821C22×C4#6325412yes—
822C22×C4C2×C22⋊D1712yes—
823C22×C4C2×C22⋊D1712yes—
824C4⋊C4—348no—
825C4⋊C4—684no—
826C4⋊C4—684no—
827C4⋊C4—684no—
828C4⋊C4—684no—
829C4⋊C4—684no—
830C4⋊C4—684no—
831C4⋊C4—684no—
832C22⋊C4—28no—
833C22⋊C4—348no—
834C22⋊C4—684no—
835C22⋊C4#63225116yescomplemented
836C42—44no—
837C42—44no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23C4×Dic3414yes—
867C23#1058755514yes—
868C23#1058755614yes—
869C23C4×D6814yes—
870C23C2×#6322514yes—
871C23#1058761014yes—
872C23#1058761614yes—
873C23C22×Dic3411yescharacteristic
874C23C22×Dic3411yescharacteristic
875C23C22×C4×D1711yescharacteristic
876C23C22×D6811yescharacteristic
877C23C2×#6325211yescharacteristic
878C23C2×#6325211yescharacteristic
879C23C2×D4×D1711yescharacteristic
880C23C2×#6325411yescharacteristic
881C23#1058769111yescharacteristic
882C23#1058769111yescharacteristic
883C23#41×D1711yescharacteristic
884C23#41×D1711yescharacteristic
885C23#1058769611yescharacteristic
886C23#1058769711yescharacteristic
887C23C22×C22⋊D1711yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—416no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—174no—
929C2×C4—342no—
930C2×C4—342no—
931C2×C4—342no—
932C2×C4—342no—
933C2×C4—342no—
934C2×C4—342no—
935C2×C4—342no—
936C2×C4—342no—
937C2×C4—342no—
938C2×C4—342no—
939C2×C4—342no—
940C2×C4—342no—
941C2×C4—342no—
942C2×C4—342no—
943C2×C4—342no—
944C2×C4—342no—
945C2×C4—342no—
946C2×C4—342no—
947C2×C4—342no—
948C2×C4—342no—
949C2×C4—342no—
950C2×C4—6816no—
951C2×C4—6816no—
952C2×C4—681no—
953C2×C4—681no—
954C2×C4—681no—
955C2×C4—681no—
956C2×C4—681no—
957C2×C4—681no—
958C2×C4—681no—
959C2×C4—681no—
960C2×C4—681no—
961C2×C4—681no—
962C2×C4—681no—
963C2×C4—681no—
964C2×C4—681no—
965C2×C4—681no—
966C2×C4—681no—
967C2×C4—681no—
968C2×C4—681no—
969C2×C4—681no—
970C2×C4—681no—
971C2×C4—681no—
972C2×C4—681no—
973C2×C4—681no—
974C2×C4—681no—
975C2×C4—681no—
976C2×C4—681no—
977C2×C4—681no—
978C2×C4—681no—
979C2×C4—681no—
980C2×C4—681no—
981C2×C4—681no—
982C2×C4—681no—
983C2×C4—681no—
984C2×C4—681no—
985C2×C4—681no—
986C2×C4#1058756414yes—
987C2×C4C2×#6322514yes—
988C2×C4C2×#6322514yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22#1176270718yescomplemented
1004C22C22×#6322511yescharacteristic
1005C22C4×D4×D1711yescharacteristic
1006C22C2×C4×D6811yescharacteristic
1007C22C2×C4×Dic3411yescharacteristic
1008C22C4×#6325411yescharacteristic
1009C22#1176328111yescharacteristic
1010C22#1176328811yescharacteristic
1011C22C2×#1058761611yescharacteristic
1012C22C2×#1058756411yescharacteristic
1013C22C2×#1058761011yescharacteristic
1014C22#1176331811yescharacteristic
1015C22C2×#1058755611yescharacteristic
1016C22#1176333911yescharacteristic
1017C22C2×#1058755511yescharacteristic
1018C22#1176336211yescharacteristic
1019C22#1176339211yescharacteristic
1020C22#1176340111yescharacteristic
1021C22#1176343511yescharacteristic
1022C22#1176343711yescharacteristic
1023C22D4×C22⋊D1711yescharacteristic
1024C22D4×D6811yescharacteristic
1025C22#1176344711yescharacteristic
1026C22#1176344911yescharacteristic
1027C22#1176345311yescharacteristic
1028C22#1176345411yescharacteristic
1029C22#1176345411yescharacteristic
1030C22#1176345811yescharacteristic
1031C22#1176346311yescharacteristic
1032C22D4×Dic3411yescharacteristic
1033C22#1176348311yescharacteristic
1034C22#1176348511yescharacteristic
1035C22#1176349211yescharacteristic
1036C22#1176351611yescharacteristic
1037C22#1176351811yescharacteristic
1038C22#1176351811yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—344no—
1046C4—682no—
1047C4—682no—
1048C4—682no—
1049C4—682no—
1050C4—682no—
1051C4—1361no—
1052C4—1361no—
1053C2—28no—
1054C2C2×#1176270711yescharacteristic
1055C2C4×#1058756411yescharacteristic
1056C2#1453151211yescharacteristic
1057C2D4×#6322511yescharacteristic
1058C2#1453168911yescharacteristic
1059C2#1453176611yescharacteristic
1060C2#1453177811yescharacteristic
1061C2#1453231411yescharacteristic
1062C2#1453232911yescharacteristic
1063C2#1453244511yescharacteristic
1064C2#1453245411yescharacteristic
1065C2#1453248611yescharacteristic
1066C2#1453292511yescharacteristic
1067C2#1453327911yescharacteristic
1068C2#1453379011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C4×C22⋊C4×C17C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×C4×C22⋊C4D17
hypocenterC17#14004
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11762707C2semidirect
7. #14527048C2semidirect
8. #14527040C2semidirect
9. #14527036C2semidirect
10. #14527036C2semidirect
11. #14527017C2semidirect
12. #14527017C2semidirect
13. #14527014C2semidirect
30. #11762684C4semidirect
122. C2×C4⋊Dic17C2×C4semidirect
123. C2×C4⋊Dic17C2×C4semidirect
151. #10587502C2×C4semidirect
152. #10587502C2×C4semidirect
290. C22⋊C4×C17C4⋊C4semidirect
484. C22×C17#389semidirect
688. C17#14004semidirect
835. C22⋊C4#63225semidirect
1003. C22#11762707semidirect

Maximal subgroups

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

subgroupindex
C2×#117627072
C2×#117626842
C2×#117626812
C2×#117626672
C22×#105875022
#145270482
#145270402
#145270362
#145270172
#145270142
#145270072
C2×C4×C22⋊C4×C172
#1400417