Finite Group Databasebeta

← #16958401

Subgroups — #16958401

Order 4352.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587563C211yesmaximal, characteristic, complemented
2C2×#11762712C211yesmaximal, characteristic
3C2×#11762703C211yesmaximal, characteristic, complemented
4C2×#11762697C211yesmaximal, characteristic, complemented
5C2×#11762689C211yesmaximal, characteristic
6#14527048C211yesmaximal, characteristic, complemented
7#14527027C211yesmaximal, characteristic, complemented
8#14527027C211yesmaximal, characteristic, complemented
9#14527021C211yesmaximal, characteristic, complemented
10#14527021C211yesmaximal, characteristic, complemented
11#14527018C211yesmaximal, characteristic, complemented
12#14527015C211yesmaximal, characteristic, complemented
13#14527006C211yesmaximal, characteristic, complemented
14#95×Dic17C211yesmaximal, characteristic, complemented
15C17×#1438C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C2×#10587563—24no—
18C2×#10587563—24no—
19C2×#10587563—24no—
20C22×C4⋊Dic17C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×C22⋊Dic17C2211yescharacteristic
29C22×C22⋊Dic17C2211yescharacteristic
30C22×C22⋊Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35#11762712—24no—
36#11762703—24no—
37#11762697—24no—
38#11762689C418yescomplemented
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C23×D4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C22×C22⋊C4×C17C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C25×C17C2311yescharacteristic
59C25×C17C2311yescharacteristic
60C22×D4×C17—22no—
61C22×D4×C17—22no—
62C22×D4×C17—22no—
63C22×D4×C17—22no—
64C22×D4×C17—41no—
65C22×D4×C17—41no—
66C22×D4×C17C2×C414yes—
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×Dic17C2×C414yes—
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C2×C22⋊C4×C17—22no—
88C2×C22⋊C4×C17—22no—
89C2×C22⋊C4×C17—22no—
90C2×C22⋊C4×C17—22no—
91C2×C22⋊C4×C17—22no—
92C2×C22⋊C4×C17—22no—
93C2×C22⋊C4×C17—22no—
94C2×C22⋊C4×C17—22no—
95C2×C22⋊C4×C17—41no—
96C2×C22⋊C4×C17—41no—
97C2×C22⋊C4×C17—41no—
98C2×C22⋊C4×C17—41no—
99C2×C22⋊Dic17—22no—
100C2×C22⋊Dic17—22no—
101C2×C22⋊Dic17—22no—
102C2×C22⋊Dic17—22no—
103C2×C22⋊Dic17—22no—
104C2×C22⋊Dic17—22no—
105C2×C22⋊Dic17—22no—
106C2×C22⋊Dic17—22no—
107C2×C22⋊Dic17—22no—
108C2×C22⋊Dic17—22no—
109C2×C22⋊Dic17—22no—
110C2×C22⋊Dic17—22no—
111C2×C22⋊Dic17—22no—
112C2×C22⋊Dic17—41no—
113C2×C22⋊Dic17—41no—
114C2×C22⋊Dic17—41no—
115C2×C22⋊Dic17—41no—
116C2×C22⋊Dic17C2×C414yes—
117C2×C22⋊Dic17C2×C414yes—
118C2×C22⋊Dic17C2×C414yes—
119C2×C22⋊Dic17D414yes—
120C2×C4⋊Dic17—22no—
121C2×C4⋊Dic17—22no—
122C2×C4⋊Dic17—41no—
123C2×#63225—22no—
124C2×#63225—22no—
125C2×#63225—22no—
126C2×#63225—22no—
127C2×#63225—22no—
128C2×#63225—22no—
129C2×#63225—41no—
130C2×#63225—41no—
131C2×#63225D414yescomplemented
132C2×C4×Dic17—22no—
133C2×C4×Dic17—22no—
134C2×C4×Dic17—22no—
135C2×C4×Dic17—22no—
136C2×C4×Dic17—22no—
137C2×C4×Dic17—22no—
138C2×C4×Dic17—22no—
139C2×C4×Dic17—22no—
140C2×C4×Dic17—22no—
141C2×C4×Dic17—41no—
142C2×C4×Dic17—41no—
143C2×C4×Dic17D414yescomplemented
144#10587563—232no—
145C17×#95—22no—
146C17×#95—22no—
147#10587502—22no—
148#10587502—22no—
149#10587502—22no—
150#10587502—22no—
151#10587502—22no—
152#10587502—22no—
153#10587502—22no—
154#10587502—41no—
155#10587502—41no—
156#10587502—41no—
157#10587502C2×C414yes—
158#10587502C2×C414yes—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17—21no—
163C24×C17—21no—
164C24×C17—21no—
165C24×C17—21no—
166C24×C17—21no—
167C24×C17—21no—
168C24×C17—21no—
169C24×C17—21no—
170C24×C17—21no—
171C24×C17—21no—
172C24×C17—21no—
173C24×C17—21no—
174C24×C17—21no—
175C24×C17—21no—
176C24×C17—21no—
177C24×C17—21no—
178C24×C17—21no—
179C24×C17—21no—
180C24×C17—21no—
181C24×C17—21no—
182C24×C17—21no—
183C24×C17—21no—
184C24×C17—21no—
185C24×C17C22×C412yes—
186C24×C17C22×C412yes—
187C24×C17C2×D412yes—
188C24×C17#4112yes—
189C24×C17C2411yescharacteristic
190C2×D4×C17—28no—
191C2×D4×C17—28no—
192C2×D4×C17—44no—
193C2×D4×C17—44no—
194C2×D4×C17—44no—
195C2×D4×C17—44no—
196C2×D4×C17—44no—
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×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17—21no—
226C22×C4×C17C22×C412yes—
227C22×C4×C17C2×D412yes—
228C22×C4×C17C2×D412yes—
229C22×C4×C17#4112yes—
230C22×C4×C17#4112yes—
231C22×C4×C17#4112yes—
232C22×Dic17—28no—
233C22×Dic17—28no—
234C22×Dic17—28no—
235C22×Dic17—28no—
236C22×Dic17—28no—
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—28no—
250C22×Dic17—28no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
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—21no—
271C22×Dic17—21no—
272C22×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17—21no—
275C22×Dic17—21no—
276C22×Dic17—21no—
277C22×Dic17—21no—
278C22×Dic17—21no—
279C22×Dic17—21no—
280C22×Dic17—21no—
281C22×Dic17—21no—
282C22×Dic17C22×C412yes—
283C22×Dic17C22×C412yes—
284C22×Dic17C22×C412yes—
285C22×Dic17C22×C412yes—
286C22×Dic17C2×D412yes—
287C22×Dic17C2×D412yes—
288C22×Dic17C2×D412yes—
289C22×Dic17C2×D412yes—
290C22×Dic17C2×D412yes—
291C22×Dic17C2×D412yes—
292C22×Dic17#4112yes—
293C22×Dic17#4112yes—
294C22×Dic17#4112yes—
295C22⋊C4×C17—28no—
296C22⋊C4×C17—44no—
297C22⋊C4×C17—44no—
298C22⋊C4×C17—44no—
299C22⋊Dic17—28no—
300C22⋊Dic17—28no—
301C22⋊Dic17—28no—
302C22⋊Dic17—44no—
303C22⋊Dic17—44no—
304C22⋊Dic17—44no—
305C22⋊Dic17—44no—
306C4⋊Dic17—44no—
307#63225—28no—
308#63225—28no—
309#63225—44no—
310C4×Dic17—28no—
311C4×Dic17—28no—
312C4×Dic17—44no—
313C4×Dic17—44no—
314#14071—171nomaximal, Sylow
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×C17—22no—
333C23×C17—22no—
334C23×C17—22no—
335C23×C17—22no—
336C23×C17—22no—
337C23×C17—22no—
338C23×C17—22no—
339C23×C17—22no—
340C23×C17—41no—
341C23×C17—41no—
342C23×C17—41no—
343C23×C17—41no—
344C23×C17—41no—
345C23×C17—41no—
346C23×C17—41no—
347C23×C17—41no—
348C23×C17—41no—
349C23×C17—41no—
350C23×C17—41no—
351C23×C17—41no—
352C23×C17—41no—
353C23×C17—41no—
354C23×C17—41no—
355C23×C17—41no—
356C23×C17—41no—
357C23×C17—41no—
358C23×C17—41no—
359C23×C17—41no—
360C23×C17—41no—
361C23×C17—41no—
362C23×C17—41no—
363C23×C17—41no—
364C23×C17—41no—
365C23×C17—41no—
366C23×C17—41no—
367C23×C17—41no—
368C23×C17—41no—
369C23×C17—41no—
370C23×C17—41no—
371C23×C17—41no—
372C23×C17—41no—
373C23×C17—41no—
374C23×C17—41no—
375C23×C17—41no—
376C23×C17—41no—
377C23×C17—41no—
378C23×C17—41no—
379C23×C17—41no—
380C23×C17—41no—
381C23×C17—41no—
382C23×C17—41no—
383C23×C17—41no—
384C23×C17C4×D414yes—
385C23×C17C23×C411yescharacteristic
386C23×C17C22×D411yescharacteristic
387C23×C17C22×D411yescharacteristic
388C23×C17C22×D411yescharacteristic
389C23×C17C2×#4111yescharacteristic
390C23×C17C2×#4111yescharacteristic
391C23×C17C2×#4111yescharacteristic
392C23×C17C2×#4111yescharacteristic
393C23×C17C2×#4111yescharacteristic
394C23×C17C2×#4111yescharacteristic
395C23×C17C2×#4111yescharacteristic
396C23×C17H(5,𝔽2)11yescharacteristic
397C23×C17H(5,𝔽2)11yescharacteristic
398C23×C17H(5,𝔽2)11yescharacteristic
399C23×C172−1+411yescharacteristic
400D4×C17—416no—
401C2×C4×C17—22no—
402C2×C4×C17—22no—
403C2×C4×C17—22no—
404C2×C4×C17—22no—
405C2×C4×C17—22no—
406C2×C4×C17—22no—
407C2×C4×C17—22no—
408C2×C4×C17—22no—
409C2×C4×C17—22no—
410C2×C4×C17—22no—
411C2×C4×C17—22no—
412C2×C4×C17—22no—
413C2×C4×C17—22no—
414C2×C4×C17—22no—
415C2×C4×C17—22no—
416C2×C4×C17—41no—
417C2×C4×C17—41no—
418C2×C4×C17—41no—
419C2×C4×C17—41no—
420C2×C4×C17—41no—
421C2×C4×C17—41no—
422C2×C4×C17—41no—
423C2×C4×C17—41no—
424C2×C4×C17—41no—
425C2×C4×C17—41no—
426C2×C4×C17—41no—
427C2×C4×C17—41no—
428C2×C4×C17—41no—
429C2×C4×C17—41no—
430C2×C4×C17—41no—
431C2×C4×C17—41no—
432C2×C4×C17—41no—
433C2×C4×C17—41no—
434C2×C4×C17—41no—
435C2×C4×C17#11714yescomplemented
436C2×Dic17—232no—
437C2×Dic17—22no—
438C2×Dic17—22no—
439C2×Dic17—22no—
440C2×Dic17—22no—
441C2×Dic17—22no—
442C2×Dic17—22no—
443C2×Dic17—22no—
444C2×Dic17—22no—
445C2×Dic17—22no—
446C2×Dic17—22no—
447C2×Dic17—22no—
448C2×Dic17—22no—
449C2×Dic17—22no—
450C2×Dic17—22no—
451C2×Dic17—22no—
452C2×Dic17—22no—
453C2×Dic17—22no—
454C2×Dic17—22no—
455C2×Dic17—22no—
456C2×Dic17—22no—
457C2×Dic17—22no—
458C2×Dic17—22no—
459C2×Dic17—22no—
460C2×Dic17—22no—
461C2×Dic17—22no—
462C2×Dic17—22no—
463C2×Dic17—22no—
464C2×Dic17—22no—
465C2×Dic17—22no—
466C2×Dic17—22no—
467C2×Dic17—41no—
468C2×Dic17—41no—
469C2×Dic17—41no—
470C2×Dic17—41no—
471C2×Dic17—41no—
472C2×Dic17—41no—
473C2×Dic17—41no—
474C2×Dic17—41no—
475C2×Dic17—41no—
476C2×Dic17—41no—
477C2×Dic17—41no—
478C2×Dic17—41no—
479C2×Dic17—41no—
480C2×Dic17—41no—
481C2×Dic17—41no—
482C2×Dic17—41no—
483C2×Dic17—41no—
484C2×Dic17—41no—
485C2×Dic17—41no—
486C2×Dic17—41no—
487C2×Dic17—41no—
488C2×Dic17—41no—
489C2×Dic17—41no—
490C2×Dic17C4×D414yes—
491C2×Dic17C4×D414yes—
492C2×Dic17#12014yes—
493C22×#117—171no—
494C2×#390—171no—
495C2×#388—171no—
496C2×#388—171no—
497C2×#386—171no—
498#1444—171no—
499#1439—171no—
500#1439—171no—
501#1438D1711yescharacteristic
502#1437—171no—
503#1437—171no—
504#1436—171no—
505#1436—171no—
506C22⋊#95—171no—
507C4×#95—171no—
508C22×C17—24no—
509C22×C17—24no—
510C22×C17—24no—
511C22×C17—42no—
512C22×C17—42no—
513C22×C17—42no—
514C22×C17—42no—
515C22×C17—42no—
516C22×C17—42no—
517C22×C17—42no—
518C22×C17—42no—
519C22×C17—42no—
520C22×C17—42no—
521C22×C17—42no—
522C22×C17—42no—
523C22×C17—42no—
524C22×C17—42no—
525C22×C17—42no—
526C22×C17—42no—
527C22×C17—42no—
528C22×C17—42no—
529C22×C17—42no—
530C22×C17—81no—
531C22×C17—81no—
532C22×C17—81no—
533C22×C17—81no—
534C22×C17—81no—
535C22×C17—81no—
536C22×C17—81no—
537C22×C17—81no—
538C22×C17C2×#11711yescharacteristic
539C22×C17C2×C4×D411yescharacteristic
540C22×C17C2×C4×D411yescharacteristic
541C22×C17C2×C4×D411yescharacteristic
542C22×C17C4×#4111yescharacteristic
543C22×C17#51811yescharacteristic
544C22×C17#52011yescharacteristic
545C22×C17C2×#12011yescharacteristic
546C22×C17#52511yescharacteristic
547C22×C17#52511yescharacteristic
548C22×C17#52511yescharacteristic
549C22×C17#52911yescharacteristic
550C22×C17#52911yescharacteristic
551C22×C17#53211yescharacteristic
552C22×C17#53211yescharacteristic
553C22×C17#53511yescharacteristic
554C22×C17#53711yescharacteristic
555C22×C17#54011yescharacteristic
556C22×C17#54211yescharacteristic
557C22×C17#54611yescharacteristic
558C22×C17#54611yescharacteristic
559C22×C17#54611yescharacteristic
560C22×C17#54611yescharacteristic
561C22×C17#54711yescharacteristic
562C22×C17#54711yescharacteristic
563C22×C17#55011yescharacteristic
564C22×C17#55011yescharacteristic
565C22×C17#55111yescharacteristic
566C22×C17#55111yescharacteristic
567C22×C17#55111yescharacteristic
568C22×C17#55211yescharacteristic
569C22×C17#55311yescharacteristic
570C22×C17#55511yescharacteristic
571C22×C17#55511yescharacteristic
572C22×C17#55611yescharacteristic
573C4×C17—24no—
574C4×C17—42no—
575C4×C17—42no—
576C4×C17—42no—
577C4×C17—81no—
578Dic17—24no—
579Dic17—24no—
580Dic17—24no—
581Dic17—42no—
582Dic17—42no—
583Dic17—42no—
584Dic17—42no—
585Dic17—81no—
586C23×D4C2×D1711yescharacteristic
587C24×C4—171no—
588C2×#117—344no—
589C2×#117—344no—
590C2×#117—344no—
591C22×C4⋊C4—171no—
592C22×C4⋊C4—171no—
593C22×C4⋊C4—171no—
594C22×C4⋊C4—171no—
595C22×C22⋊C4—171no—
596C22×C22⋊C4—171no—
597C22×C22⋊C4—171no—
598C22×C22⋊C4—171no—
599C22×C22⋊C4—171no—
600C22×C22⋊C4—171no—
601C22×C22⋊C4—171no—
602C22×C22⋊C4C2×D1711yescharacteristic
603C22×C22⋊C4C2×D1711yescharacteristic
604C22×C22⋊C4C2×D1711yescharacteristic
605C22×C22⋊C4C2×D1711yescharacteristic
606C22×C42—171no—
607C22×C42—171no—
608C22×C42—171no—
609C22×C42—171no—
610#390—344no—
611#388—344no—
612#388—344no—
613#386—178no—
614C2×#95—171no—
615C2×#95—171no—
616C2×#95—171no—
617C2×#95—171no—
618C2×#95—171no—
619C2×#95—171no—
620C2×#95—171no—
621C2×#95—171no—
622C2×#95—171no—
623C2×#95—171no—
624C2×#95—171no—
625C2×#95—171no—
626C2×#95C2×D1711yescharacteristic
627C2×#95C2×D1711yescharacteristic
628C2×C17—44no—
629C2×C17—82no—
630C2×C17#229311yescharacteristic
631C2×C17C4×#12011yescharacteristic
632C2×C17#232411yescharacteristic
633C2×C17#234211yescharacteristic
634C2×C17#235411yescharacteristic
635C2×C17#235911yescharacteristic
636C2×C17#236311yescharacteristic
637C2×C17#243011yescharacteristic
638C2×C17#243111yescharacteristic
639C2×C17#247111yescharacteristic
640C2×C17#247411yescharacteristic
641C2×C17#247611yescharacteristic
642C2×C17#247911yescharacteristic
643C2×C17#260111yescharacteristic
644C2×C17#261011yescharacteristic
645C25C22×D1711yescharacteristic
646C25C22×D1711yescharacteristic
647C22×D4—22no—
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—41no—
652C22×D4—41no—
653C22×D4C4×D1714yes—
654C23×C4—171no—
655C23×C4—171no—
656C23×C4—171no—
657C23×C4—174no—
658C23×C4—171no—
659C23×C4—171no—
660C23×C4—171no—
661C23×C4—171no—
662C23×C4—171no—
663C23×C4—342no—
664C23×C4—342no—
665C23×C4—342no—
666C23×C4—342no—
667C23×C4—342no—
668C23×C4—342no—
669C23×C4C22×D1711yescharacteristic
670C23×C4C22×D1711yescharacteristic
671C23×C4C22×D1711yescharacteristic
672C23×C4C22×D1711yescharacteristic
673C23×C4C22×D1711yescharacteristic
674#117—3432no—
675C2×C4⋊C4—174no—
676C2×C4⋊C4—342no—
677C2×C4⋊C4—342no—
678C2×C4⋊C4—342no—
679C2×C4⋊C4—342no—
680C2×C4⋊C4—342no—
681C2×C4⋊C4—342no—
682C2×C4⋊C4—342no—
683C2×C4⋊C4—342no—
684C2×C4⋊C4—681no—
685C2×C4⋊C4—681no—
686C2×C4⋊C4—681no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—174no—
700C2×C22⋊C4—174no—
701C2×C22⋊C4—174no—
702C2×C22⋊C4—174no—
703C2×C22⋊C4—342no—
704C2×C22⋊C4—342no—
705C2×C22⋊C4—342no—
706C2×C22⋊C4—342no—
707C2×C22⋊C4—342no—
708C2×C22⋊C4—342no—
709C2×C22⋊C4—342no—
710C2×C22⋊C4—342no—
711C2×C22⋊C4—342no—
712C2×C22⋊C4—342no—
713C2×C22⋊C4—342no—
714C2×C22⋊C4—342no—
715C2×C22⋊C4—342no—
716C2×C22⋊C4—681no—
717C2×C22⋊C4—681no—
718C2×C22⋊C4—681no—
719C2×C22⋊C4—681no—
720C2×C42—174no—
721C2×C42—342no—
722C2×C42—342no—
723C2×C42—342no—
724C2×C42—342no—
725C2×C42—342no—
726C2×C42—342no—
727C2×C42—342no—
728C2×C42—342no—
729C2×C42—342no—
730C2×C42—681no—
731C2×C42—681no—
732#95—22no—
733#95—22no—
734#95—174no—
735#95—174no—
736#95—342no—
737#95—342no—
738#95—342no—
739#95—342no—
740#95—342no—
741#95—342no—
742#95—342no—
743#95—681no—
744#95—681no—
745#95—681no—
746C17#1407111yescharacteristic, complemented, Sylow
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24C2×C4×D1712yes—
774C24C2×C4×D1712yes—
775C24D4×D1712yes—
776C24#6325412yes—
777C24C23×D1711yescharacteristic
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—172no—
815C22×C4—172no—
816C22×C4—172no—
817C22×C4—172no—
818C22×C4—172no—
819C22×C4—172no—
820C22×C4—172no—
821C22×C4—172no—
822C22×C4—172no—
823C22×C4—172no—
824C22×C4—172no—
825C22×C4—172no—
826C22×C4—172no—
827C22×C4—348no—
828C22×C4—348no—
829C22×C4—348no—
830C22×C4—348no—
831C22×C4—348no—
832C22×C4—348no—
833C22×C4—341no—
834C22×C4—341no—
835C22×C4—341no—
836C22×C4—341no—
837C22×C4—341no—
838C22×C4—341no—
839C22×C4—341no—
840C22×C4—341no—
841C22×C4—341no—
842C22×C4—341no—
843C22×C4—341no—
844C22×C4—341no—
845C22×C4—348no—
846C22×C4—341no—
847C22×C4—341no—
848C22×C4—341no—
849C22×C4—341no—
850C22×C4—341no—
851C22×C4—341no—
852C22×C4—341no—
853C22×C4—341no—
854C22×C4—341no—
855C22×C4—341no—
856C22×C4—341no—
857C22×C4—341no—
858C22×C4—341no—
859C22×C4—341no—
860C22×C4—341no—
861C22×C4—341no—
862C22×C4—341no—
863C22×C4—341no—
864C22×C4—341no—
865C22×C4—341no—
866C22×C4—341no—
867C22×C4—341no—
868C22×C4—341no—
869C22×C4—341no—
870C22×C4—341no—
871C22×C4—341no—
872C22×C4—341no—
873C22×C4—341no—
874C22×C4—341no—
875C22×C4—341no—
876C22×C4—341no—
877C22×C4C2×C4×D1712yes—
878C22×C4D4×D1712yes—
879C22×C4D4×D1712yes—
880C22×C4#6325412yes—
881C22×C4#6325412yes—
882C22×C4#6325412yes—
883C4⋊C4—348no—
884C4⋊C4—348no—
885C4⋊C4—684no—
886C4⋊C4—684no—
887C22⋊C4—28no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—348no—
892C22⋊C4—348no—
893C22⋊C4—348no—
894C22⋊C4—684no—
895C22⋊C4—684no—
896C22⋊C4—684no—
897C22⋊C4—684no—
898C42—348no—
899C42—348no—
900C42—684no—
901C42—684no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23#1058756714yes—
972C23C22×C4×D1711yescharacteristic
973C23C2×D4×D1711yescharacteristic
974C23C2×D4×D1711yescharacteristic
975C23C2×D4×D1711yescharacteristic
976C23C2×#6325411yescharacteristic
977C23C2×#6325411yescharacteristic
978C23C2×#6325411yescharacteristic
979C23C2×#6325411yescharacteristic
980C23#1058769111yescharacteristic
981C23#1058769111yescharacteristic
982C23#1058769111yescharacteristic
983C23#41×D1711yescharacteristic
984C23#41×D1711yescharacteristic
985C23#41×D1711yescharacteristic
986C23#1058769711yescharacteristic
987D4—416no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—174no—
1023C2×C4—174no—
1024C2×C4—174no—
1025C2×C4—3432no—
1026C2×C4—342no—
1027C2×C4—342no—
1028C2×C4—342no—
1029C2×C4—342no—
1030C2×C4—342no—
1031C2×C4—342no—
1032C2×C4—342no—
1033C2×C4—342no—
1034C2×C4—342no—
1035C2×C4—342no—
1036C2×C4—342no—
1037C2×C4—342no—
1038C2×C4—342no—
1039C2×C4—342no—
1040C2×C4—342no—
1041C2×C4—342no—
1042C2×C4—342no—
1043C2×C4—342no—
1044C2×C4—342no—
1045C2×C4—342no—
1046C2×C4—342no—
1047C2×C4—342no—
1048C2×C4—342no—
1049C2×C4—342no—
1050C2×C4—342no—
1051C2×C4—342no—
1052C2×C4—342no—
1053C2×C4—342no—
1054C2×C4—342no—
1055C2×C4—342no—
1056C2×C4—681no—
1057C2×C4—681no—
1058C2×C4—681no—
1059C2×C4—681no—
1060C2×C4—681no—
1061C2×C4—681no—
1062C2×C4—681no—
1063C2×C4—681no—
1064C2×C4—681no—
1065C2×C4—681no—
1066C2×C4—681no—
1067C2×C4—681no—
1068C2×C4—681no—
1069C2×C4—681no—
1070C2×C4—681no—
1071C2×C4—681no—
1072C2×C4—681no—
1073C2×C4—681no—
1074C2×C4—681no—
1075C2×C4—681no—
1076C2×C4—681no—
1077C2×C4—681no—
1078C2×C4—681no—
1079C2×C4#1058756314yescomplemented
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C2×#1058756311yescharacteristic
1111C22C4×D4×D1711yescharacteristic
1112C22C4×D4×D1711yescharacteristic
1113C22C2×#1058756711yescharacteristic
1114C22C4×#6325411yescharacteristic
1115C22#1176328211yescharacteristic
1116C22#1176328811yescharacteristic
1117C22#120×D1711yescharacteristic
1118C22#1176331711yescharacteristic
1119C22#1176331911yescharacteristic
1120C22#1176331911yescharacteristic
1121C22#1176333811yescharacteristic
1122C22#1176334011yescharacteristic
1123C22#1176335411yescharacteristic
1124C22#1176335711yescharacteristic
1125C22#1176337411yescharacteristic
1126C22#1176338811yescharacteristic
1127C22#1176340911yescharacteristic
1128C22#1176342711yescharacteristic
1129C22#1176344611yescharacteristic
1130C22#1176344611yescharacteristic
1131C22#1176344611yescharacteristic
1132C22#1176344811yescharacteristic
1133C22#1176345911yescharacteristic
1134C22#1176345911yescharacteristic
1135C22#1176347711yescharacteristic
1136C22#1176347911yescharacteristic
1137C22#1176349011yescharacteristic
1138C22#1176349011yescharacteristic
1139C22#1176349011yescharacteristic
1140C22#1176349611yescharacteristic
1141C22#1176350411yescharacteristic
1142C22#1176352311yescharacteristic
1143C22#1176352311yescharacteristic
1144C22#1176352811yescharacteristic
1145C4—24no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—81no—
1150C4—344no—
1151C4—344no—
1152C4—344no—
1153C4—682no—
1154C4—682no—
1155C4—682no—
1156C4—682no—
1157C4—1361no—
1158C2—44no—
1159C2—82no—
1160C2#1453124611yescharacteristic
1161C2#1453128911yescharacteristic
1162C2#1453147411yescharacteristic
1163C2#1453163511yescharacteristic
1164C2#1453173211yescharacteristic
1165C2#1453178211yescharacteristic
1166C2#1453182511yescharacteristic
1167C2#1453238711yescharacteristic
1168C2#1453239811yescharacteristic
1169C2#1453289611yescharacteristic
1170C2#1453293511yescharacteristic
1171C2#1453296511yescharacteristic
1172C2#1453301611yescharacteristic
1173C2#1453437411yescharacteristic
1174C2#1453446411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1438C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenter#1438D17
hypocenterC17#14071
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. C22×#10587563C2semidirect
3. C2×#11762703C2semidirect
4. C2×#11762697C2semidirect
6. #14527048C2semidirect
7. #14527027C2semidirect
8. #14527027C2semidirect
9. #14527021C2semidirect
10. #14527021C2semidirect
11. #14527018C2semidirect
12. #14527015C2semidirect
13. #14527006C2semidirect
14. #95×Dic17C2semidirect
38. #11762689C4semidirect
131. C2×#63225D4semidirect
143. C2×C4×Dic17D4semidirect
435. C2×C4×C17#117semidirect
746. C17#14071semidirect
1079. C2×C4#10587563semidirect

Maximal subgroups

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

subgroupindex
C22×#105875632
C2×#117627122
C2×#117627032
C2×#117626972
C2×#117626892
#145270482
#145270272
#145270212
#145270182
#145270152
#145270062
#95×Dic172
C17×#14382
#1407117