Finite Group Databasebeta

← #16957500

Subgroups — #16957500

Order 4352.

2038 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762709C211yesmaximal, characteristic
2C2×#11762709C211yesmaximal, characteristic
3C2×#11762709C211yesmaximal, characteristic
4C2×#11762701C211yesmaximal, characteristic, complemented
5C2×#11762700C211yesmaximal, characteristic, complemented
6C2×#11762697C211yesmaximal, characteristic, complemented
7C2×#11762678C211yesmaximal, characteristic, complemented
8C2×C4×#63225C211yesmaximal, characteristic, complemented
9#14527029C211yesmaximal, characteristic, complemented
10#14527028C211yesmaximal, characteristic, complemented
11#14527027C211yesmaximal, characteristic, complemented
12#14527026C211yesmaximal, characteristic, complemented
13#14527012C211yesmaximal, characteristic, complemented
14#95×Dic17C211yesmaximal, characteristic, complemented
15C2×C17×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35C22×C4×Dic17C2211yescharacteristic
36#11762709—24no—
37#11762709—24no—
38#11762709C418yescomplemented
39#11762701—24no—
40#11762700—24no—
41#11762697—24no—
42#11762678—24no—
43C4×#63225—24no—
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C22×C4⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C22×C22⋊C4×C17C2211yescharacteristic
56C22×C42×C17C2211yescharacteristic
57C17×#388—24no—
58C2×C17×#95C2211yescharacteristic
59C2×C17×#95C2211yescharacteristic
60C25×C17C2311yescharacteristic
61C24×D17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C22×C22⋊D17—22no—
69C22×C22⋊D17—22no—
70C22×C22⋊D17—22no—
71C22×C22⋊D17—22no—
72C22×C22⋊D17—22no—
73C22×C22⋊D17—22no—
74C22×C22⋊D17C2×C414yes—
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C2×C4⋊C4×C17—22no—
83C2×C4⋊C4×C17—22no—
84C2×C4⋊C4×C17—41no—
85C2×C22⋊C4×C17—22no—
86C2×C22⋊C4×C17—22no—
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—41no—
93C2×C22⋊C4×C17C2×C414yes—
94C2×C42×C17—22no—
95C2×C42×C17—22no—
96C2×C42×C17—22no—
97C2×C22⋊Dic17—22no—
98C2×C22⋊Dic17—22no—
99C2×C22⋊Dic17—22no—
100C2×C22⋊Dic17—22no—
101C2×C22⋊Dic17—22no—
102C2×C22⋊Dic17—41no—
103C2×C22⋊Dic17—41no—
104C2×C22⋊Dic17—41no—
105C2×C22⋊Dic17C2×C414yes—
106C2×#63227—22no—
107C2×#63227—22no—
108C2×#63227—22no—
109C2×#63227—22no—
110C2×#63227—22no—
111C2×#63227—22no—
112C2×#63227—22no—
113C2×#63227—22no—
114C2×#63227—22no—
115C2×#63227—22no—
116C2×#63227—22no—
117C2×#63227—22no—
118C2×#63227—41no—
119C2×#63227—41no—
120C2×#63227—41no—
121C2×#63227—41no—
122C2×#63227C2×C414yes—
123C2×#63227C2×C414yes—
124C2×C4⋊Dic17—22no—
125C2×C4⋊Dic17—22no—
126C2×C4⋊Dic17—41no—
127C2×#63225—22no—
128C2×#63225—22no—
129C2×#63225—22no—
130C2×#63225—22no—
131C2×#63225—22no—
132C2×#63225—22no—
133C2×#63225—22no—
134C2×#63225—22no—
135C2×#63225—22no—
136C2×#63225—22no—
137C2×#63225—22no—
138C2×#63225—41no—
139C2×#63225—41no—
140C2×#63225C2×C414yes—
141C2×#63225D414yes—
142C2×C4×Dic17—22no—
143C2×C4×Dic17—22no—
144C2×C4×Dic17—22no—
145C2×C4×Dic17—22no—
146C2×C4×Dic17—22no—
147C2×C4×Dic17—22no—
148C2×C4×Dic17—22no—
149C2×C4×Dic17—22no—
150C2×C4×Dic17—22no—
151C2×C4×Dic17—22no—
152C2×C4×Dic17C2×C414yes—
153C2×C4×Dic17D414yes—
154C17×#95—22no—
155C17×#95D414yescomplemented
156#10587502—22no—
157#10587502—22no—
158#10587502—22no—
159#10587502—22no—
160#10587502—22no—
161#10587502—22no—
162#10587502—22no—
163#10587502D414yescomplemented
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×C17C22×C412yes—
179C24×C17C2411yescharacteristic
180C23×D17—21no—
181C23×D17—21no—
182C23×D17—21no—
183C23×D17—21no—
184C23×D17—21no—
185C23×D17—21no—
186C23×D17—21no—
187C23×D17—21no—
188C23×D17—21no—
189C23×D17—21no—
190C23×D17—21no—
191C23×D17—21no—
192C23×D17—21no—
193C23×D17—21no—
194C23×D17C22×C412yes—
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×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×C17—21no—
227C22×C4×C17—21no—
228C22×C4×C17C22×C412yes—
229C22×C4×C17C22×C412yes—
230C22×C4×C17C2×D412yes—
231C22×C4×C17C2×D412yes—
232C22×C4×C17C2×D412yes—
233C22×C4×C17C2×D412yes—
234C22×C4×C17C2×D412yes—
235C22×C4×C17C2×D412yes—
236C22×C4×C17#4112yes—
237C2×C22⋊D17—28no—
238C2×C22⋊D17—28no—
239C2×C22⋊D17—28no—
240C2×C22⋊D17—44no—
241C2×C22⋊D17—44no—
242C2×C22⋊D17—44no—
243C2×C22⋊D17—44no—
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×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×Dic17C22×C412yes—
280C22×Dic17C22×C412yes—
281C22×Dic17C22×C412yes—
282C22×Dic17C2×D412yes—
283C22×Dic17C2×D412yes—
284C22×Dic17C2×D412yes—
285C22×Dic17C2×D412yes—
286C22×Dic17C2×D412yes—
287C22×Dic17C2×D412yes—
288C22×Dic17#4112yes—
289C22×Dic17#4112yes—
290C22×Dic17#4112yes—
291C22×Dic17#4112yes—
292C22×Dic17#4112yes—
293C4⋊C4×C17—44no—
294C22⋊C4×C17—28no—
295C22⋊C4×C17—44no—
296C22⋊C4×C17—44no—
297C42×C17—44no—
298C22⋊Dic17—28no—
299C22⋊Dic17—44no—
300C22⋊Dic17—44no—
301#63227—28no—
302#63227—28no—
303#63227—44no—
304#63227—44no—
305#63227—44no—
306#63227—44no—
307C4⋊Dic17—44no—
308#63225—28no—
309#63225—28no—
310#63225—44no—
311#63225—44no—
312#63225—44no—
313C4×Dic17—28no—
314C4×Dic17—28no—
315C4×Dic17—44no—
316C4×Dic17—44no—
317#14001—171nomaximal, Sylow
318C23×C17—22no—
319C23×C17—22no—
320C23×C17—22no—
321C23×C17—22no—
322C23×C17—22no—
323C23×C17—22no—
324C23×C17—22no—
325C23×C17—41no—
326C23×C17—41no—
327C23×C17—41no—
328C23×C17—41no—
329C23×C17—41no—
330C23×C17—41no—
331C23×C17—41no—
332C23×C17—41no—
333C23×C17—41no—
334C23×C17—41no—
335C23×C17—41no—
336C23×C17—41no—
337C23×C17—41no—
338C23×C17—41no—
339C23×C17—41no—
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×C17C23×C411yescharacteristic
354C23×C17C22×D411yescharacteristic
355C23×C17C22×D411yescharacteristic
356C23×C17C22×D411yescharacteristic
357C23×C17C22×D411yescharacteristic
358C23×C17C2×#4111yescharacteristic
359C23×C17C2×#4111yescharacteristic
360C23×C17C2×#4111yescharacteristic
361C23×C17C2×#4111yescharacteristic
362C23×C17C2×#4111yescharacteristic
363C23×C17C2×#4111yescharacteristic
364C23×C17H(5,𝔽2)11yescharacteristic
365C23×C17H(5,𝔽2)11yescharacteristic
366C23×C172−1+411yescharacteristic
367C23×C172−1+411yescharacteristic
368C22×D17—22no—
369C22×D17—22no—
370C22×D17—22no—
371C22×D17—22no—
372C22×D17—22no—
373C22×D17—22no—
374C22×D17—22no—
375C22×D17—41no—
376C22×D17—41no—
377C22×D17—41no—
378C22×D17—41no—
379C22×D17—41no—
380C22×D17—41no—
381C22×D17—41no—
382C22×D17—41no—
383C22×D17—41no—
384C22×D17—41no—
385C22×D17—41no—
386C22×D17—41no—
387C22×D17—41no—
388C22×D17—41no—
389C22×D17—41no—
390C22×D17—41no—
391C22×D17—41no—
392C22×D17—41no—
393C22×D17—41no—
394C22×D17—41no—
395C22×D17—41no—
396C22×D17—41no—
397C22×D17—41no—
398C22×D17—41no—
399C22×D17—41no—
400C22×D17—41no—
401C22×D17—41no—
402C22×D17—41no—
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—22no—
417C2×C4×C17—22no—
418C2×C4×C17—22no—
419C2×C4×C17—22no—
420C2×C4×C17—22no—
421C2×C4×C17—22no—
422C2×C4×C17—22no—
423C2×C4×C17—22no—
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—41no—
436C2×C4×C17—41no—
437C2×C4×C17—41no—
438C2×C4×C17—41no—
439C2×C4×C17—41no—
440C2×C4×C17—41no—
441C2×C4×C17—41no—
442C2×C4×C17—41no—
443C2×C4×C17C4×D414yes—
444C2×C4×C17#12714yes—
445C22⋊D17—416no—
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—41no—
465C2×Dic17—41no—
466C2×Dic17—41no—
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#11714yes—
488C2×Dic17C4×D414yes—
489C2×Dic17C4×D414yes—
490C2×Dic17C4×D414yes—
491C2×Dic17#12114yes—
492C2×Dic17#12314yes—
493C2×Dic17#12414yes—
494C2×Dic17#12614yes—
495C2×#390—171no—
496C2×#390—171no—
497C2×#390—171no—
498C2×#388—171no—
499C2×#388—171no—
500C2×#388—171no—
501C2×#388D1711yescharacteristic, complemented
502C2×#384—171no—
503C2×C4×C4⋊C4—171no—
504#1439—171no—
505#1439—171no—
506#1439—171no—
507#1439—171no—
508C4⋊#95—171no—
509C4×#95—171no—
510C22×C17—42no—
511C22×C17—42no—
512C22×C17—42no—
513C22×C17—42no—
514C22×C17—42no—
515C22×C17—42no—
516C22×C17—42no—
517C22×C17—81no—
518C22×C17—81no—
519C22×C17—81no—
520C22×C17—81no—
521C22×C17—81no—
522C22×C17—81no—
523C22×C17—81no—
524C22×C17—81no—
525C22×C17C2×#11711yescharacteristic
526C22×C17C2×C4×D411yescharacteristic
527C22×C17C2×C4×D411yescharacteristic
528C22×C17C2×C4×D411yescharacteristic
529C22×C17C2×C4×D411yescharacteristic
530C22×C17#52011yescharacteristic
531C22×C17#52011yescharacteristic
532C22×C17C2×#12111yescharacteristic
533C22×C17C2×#12311yescharacteristic
534C22×C17C2×#12411yescharacteristic
535C22×C17C2×#12611yescharacteristic
536C22×C17C2×#12711yescharacteristic
537C22×C17#53211yescharacteristic
538C22×C17#53211yescharacteristic
539C22×C17#53211yescharacteristic
540C22×C17#53511yescharacteristic
541C22×C17#53611yescharacteristic
542C22×C17#54211yescharacteristic
543C22×C17#54211yescharacteristic
544C22×C17D4211yescharacteristic
545C22×C17D4211yescharacteristic
546C22×C17#54711yescharacteristic
547C22×C17#54711yescharacteristic
548C22×C17#54711yescharacteristic
549C22×C17#54711yescharacteristic
550C22×C17#54811yescharacteristic
551C22×C17#54811yescharacteristic
552C22×C17#55011yescharacteristic
553C22×C17#55011yescharacteristic
554C22×C17#55311yescharacteristic
555C22×C17#55311yescharacteristic
556C22×C17#55511yescharacteristic
557C22×C17#55511yescharacteristic
558C22×C17#55611yescharacteristic
559C22×C17#55611yescharacteristic
560C2×D17—42no—
561C2×D17—42no—
562C2×D17—42no—
563C2×D17—42no—
564C2×D17—42no—
565C2×D17—42no—
566C2×D17—42no—
567C2×D17—81no—
568C2×D17—81no—
569C2×D17—81no—
570C2×D17—81no—
571C2×D17—81no—
572C2×D17—81no—
573C2×D17—81no—
574C2×D17—81no—
575C4×C17—24no—
576C4×C17—24no—
577C4×C17—42no—
578C4×C17—42no—
579C4×C17—42no—
580C4×C17—81no—
581Dic17—24no—
582Dic17—42no—
583Dic17—42no—
584Dic17—42no—
585Dic17—42no—
586Dic17—81no—
587Dic17#38818yescomplemented
588C23×D4—171no—
589C22×C4⋊C4—171no—
590C22×C4⋊C4—171no—
591C22×C4⋊C4—171no—
592C22×C4⋊C4—171no—
593C22×C4⋊C4—171no—
594C22×C4⋊C4—171no—
595C22×C4⋊C4C2×D1711yescharacteristic
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⋊C4—171no—
603C22×C22⋊C4—171no—
604C22×C22⋊C4—171no—
605C22×C22⋊C4C2×D1711yescharacteristic
606C22×C22⋊C4C2×D1711yescharacteristic
607C22×C22⋊C4C2×D1711yescharacteristic
608C22×C42—171no—
609C22×C42—171no—
610C22×C42—171no—
611C22×C42—171no—
612C22×C42C2×D1711yescharacteristic
613#390—178no—
614#390—344no—
615#390—344no—
616#388—24no—
617#388—344no—
618#388—344no—
619#388—344no—
620#384—344no—
621C4×C4⋊C4—344no—
622C2×#95—171no—
623C2×#95—171no—
624C2×#95—171no—
625C2×#95—171no—
626C2×#95—171no—
627C2×#95—171no—
628C2×#95—171no—
629C2×#95—171no—
630C2×#95C2×D1711yescharacteristic
631C2×#95C2×D1711yescharacteristic
632C2×C17—82no—
633C2×C17C2×#38811yescharacteristic
634C2×C17C4×#12711yescharacteristic
635C2×C17#232611yescharacteristic
636C2×C17#235411yescharacteristic
637C2×C17#235411yescharacteristic
638C2×C17#236111yescharacteristic
639C2×C17#236111yescharacteristic
640C2×C17#249111yescharacteristic
641C2×C17#249111yescharacteristic
642C2×C17#250011yescharacteristic
643C2×C17#250111yescharacteristic
644C2×C17#251211yescharacteristic
645C2×C17#251211yescharacteristic
646C2×C17#254111yescharacteristic
647C2×C17#254511yescharacteristic
648D17—82no—
649C25—171no—
650C25C22×D1711yescharacteristic
651C22×D4—174no—
652C22×D4—342no—
653C22×D4—342no—
654C22×D4—342no—
655C22×D4—342no—
656C22×D4—342no—
657C22×D4—342no—
658C23×C4—171no—
659C23×C4—171no—
660C23×C4—171no—
661C23×C4—171no—
662C23×C4—171no—
663C23×C4—171no—
664C23×C4—171no—
665C23×C4C22×D1711yescharacteristic
666C23×C4C22×D1711yescharacteristic
667C23×C4C22×D1711yescharacteristic
668C23×C4C22×D1711yescharacteristic
669C23×C4C22×D1711yescharacteristic
670C23×C4C22×D1711yescharacteristic
671C2×C4⋊C4—22no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4—174no—
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—342no—
685C2×C4⋊C4—342no—
686C2×C4⋊C4—342no—
687C2×C4⋊C4—342no—
688C2×C4⋊C4—342no—
689C2×C4⋊C4—681no—
690C2×C4⋊C4—681no—
691C2×C4⋊C4—681no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—41no—
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—342no—
717C2×C22⋊C4—342no—
718C2×C22⋊C4—342no—
719C2×C22⋊C4—342no—
720C2×C22⋊C4—681no—
721C2×C22⋊C4—681no—
722C2×C22⋊C4—681no—
723C2×C22⋊C4—681no—
724C2×C22⋊C4—681no—
725C2×C22⋊C4—681no—
726C2×C22⋊C4—681no—
727C2×C22⋊C4C4×D1714yes—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—174no—
732C2×C42—174no—
733C2×C42—342no—
734C2×C42—342no—
735C2×C42—342no—
736C2×C42—342no—
737C2×C42—342no—
738C2×C42—342no—
739C2×C42—342no—
740C2×C42—342no—
741C2×C42—342no—
742C2×C42—342no—
743#95—22no—
744#95—174no—
745#95—342no—
746#95—342no—
747#95—342no—
748#95—342no—
749#95—342no—
750#95—342no—
751#95—342no—
752#95C22⋊D1714yescomplemented
753C17#1400111yescharacteristic, complemented, Sylow
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—172no—
769C24—341no—
770C24—341no—
771C24—341no—
772C24—341no—
773C24—341no—
774C24—341no—
775C24—341no—
776C24—341no—
777C24—341no—
778C24—341no—
779C24—341no—
780C24—341no—
781C24—341no—
782C24—341no—
783C24C2×C4×D1712yes—
784C24C23×D1711yescharacteristic
785C2×D4—348no—
786C2×D4—348no—
787C2×D4—348no—
788C2×D4—684no—
789C2×D4—684no—
790C2×D4—684no—
791C2×D4—684no—
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—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—172no—
826C22×C4—172no—
827C22×C4—172no—
828C22×C4—172no—
829C22×C4—172no—
830C22×C4—172no—
831C22×C4—172no—
832C22×C4—172no—
833C22×C4—172no—
834C22×C4—172no—
835C22×C4—172no—
836C22×C4—172no—
837C22×C4—172no—
838C22×C4—172no—
839C22×C4—341no—
840C22×C4—341no—
841C22×C4—341no—
842C22×C4—341no—
843C22×C4—341no—
844C22×C4—341no—
845C22×C4—341no—
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×C4C2×C4×D1712yes—
875C22×C4C2×C4×D1712yes—
876C22×C4#6325212yes—
877C22×C4D4×D1712yes—
878C22×C4D4×D1712yes—
879C22×C4D4×D1712yes—
880C22×C4C2×C22⋊D1712yes—
881C22×C4C2×C22⋊D1712yes—
882C22×C4C2×C22⋊D1712yes—
883C4⋊C4—44no—
884C4⋊C4—348no—
885C4⋊C4—348no—
886C4⋊C4—684no—
887C4⋊C4—684no—
888C4⋊C4—684no—
889C4⋊C4—684no—
890C22⋊C4—28no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—348no—
894C22⋊C4—348no—
895C22⋊C4—348no—
896C22⋊C4—684no—
897C22⋊C4—684no—
898C22⋊C4—684no—
899C22⋊C4—684no—
900C22⋊C4—684no—
901C22⋊C4—684no—
902C42—44no—
903C42—348no—
904C42—348no—
905C42—684no—
906C42—684no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
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—342no—
943C23—342no—
944C23—342no—
945C23—342no—
946C23—342no—
947C23—342no—
948C23—342no—
949C23—681no—
950C23—681no—
951C23—681no—
952C23—681no—
953C23—681no—
954C23—681no—
955C23—681no—
956C23—681no—
957C23—681no—
958C23—681no—
959C23—681no—
960C23—681no—
961C23—681no—
962C23—681no—
963C23—681no—
964C23—681no—
965C23—681no—
966C23—681no—
967C23—681no—
968C23—681no—
969C23—681no—
970C23—681no—
971C23—681no—
972C23—681no—
973C23—681no—
974C23—681no—
975C23—681no—
976C23—681no—
977C23C22×C4×D1711yescharacteristic
978C23C2×#6325211yescharacteristic
979C23C2×D4×D1711yescharacteristic
980C23C2×D4×D1711yescharacteristic
981C23C2×D4×D1711yescharacteristic
982C23#1058769111yescharacteristic
983C23#41×D1711yescharacteristic
984C23#41×D1711yescharacteristic
985C23#41×D1711yescharacteristic
986C23#41×D1711yescharacteristic
987C23#41×D1711yescharacteristic
988C23#1058769611yescharacteristic
989C23#1058769711yescharacteristic
990C23#1058769711yescharacteristic
991C23C22×C22⋊D1711yescharacteristic
992D4—6816no—
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—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
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—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—174no—
1034C2×C4—174no—
1035C2×C4—174no—
1036C2×C4—174no—
1037C2×C4—174no—
1038C2×C4—174no—
1039C2×C4—174no—
1040C2×C4—174no—
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—342no—
1057C2×C4—342no—
1058C2×C4—342no—
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—681no—
1080C2×C4—681no—
1081C2×C4—681no—
1082C2×C4C4×C22⋊D1714yes—
1083C2×C4#1058762614yes—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22—81no—
1095C22—81no—
1096C22—81no—
1097C22—81no—
1098C22—81no—
1099C22—682no—
1100C22—682no—
1101C22—682no—
1102C22—682no—
1103C22—682no—
1104C22—682no—
1105C22—682no—
1106C22—1361no—
1107C22—1361no—
1108C22—1361no—
1109C22—1361no—
1110C22—1361no—
1111C22—1361no—
1112C22—1361no—
1113C22—1361no—
1114C22#117×D1711yescharacteristic
1115C22C4×D4×D1711yescharacteristic
1116C22C4×D4×D1711yescharacteristic
1117C22C4×D4×D1711yescharacteristic
1118C22C2×C4×C22⋊D1711yescharacteristic
1119C22#1176328811yescharacteristic
1120C22#1176328911yescharacteristic
1121C22#121×D1711yescharacteristic
1122C22#123×D1711yescharacteristic
1123C22#124×D1711yescharacteristic
1124C22#126×D1711yescharacteristic
1125C22C2×#1058762611yescharacteristic
1126C22#1176335511yescharacteristic
1127C22#1176335611yescharacteristic
1128C22#1176335611yescharacteristic
1129C22#1176337511yescharacteristic
1130C22#1176338111yescharacteristic
1131C22#1176342311yescharacteristic
1132C22#1176342511yescharacteristic
1133C22D4×C22⋊D1711yescharacteristic
1134C22#1176344311yescharacteristic
1135C22#1176345711yescharacteristic
1136C22#1176345711yescharacteristic
1137C22#1176345811yescharacteristic
1138C22#1176345811yescharacteristic
1139C22#1176346711yescharacteristic
1140C22#1176346811yescharacteristic
1141C22#1176347711yescharacteristic
1142C22#1176347811yescharacteristic
1143C22#1176350811yescharacteristic
1144C22#1176351011yescharacteristic
1145C22#1176352111yescharacteristic
1146C22#1176352211yescharacteristic
1147C22#1176352611yescharacteristic
1148C22#1176352711yescharacteristic
1149C4—24no—
1150C4—24no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—81no—
1155C4—178no—
1156C4—344no—
1157C4—682no—
1158C4—682no—
1159C4—682no—
1160C4—682no—
1161C4—1361no—
1162C2—82no—
1163C2—1362no—
1164C2D17×#38811yescharacteristic
1165C2C4×#1058762611yescharacteristic
1166C2#1453149311yescharacteristic
1167C2#1453173011yescharacteristic
1168C2#1453173411yescharacteristic
1169C2#1453179711yescharacteristic
1170C2#1453180111yescharacteristic
1171C2#1453314411yescharacteristic
1172C2#1453314611yescharacteristic
1173C2#1453324411yescharacteristic
1174C2#1453325311yescharacteristic
1175C2#1453336711yescharacteristic
1176C2#1453336911yescharacteristic
1177C2#1453372711yescharacteristic
1178C2#1453376211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×#388D17
hypocenterC17#14001
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
4. C2×#11762701C2semidirect
5. C2×#11762700C2semidirect
6. C2×#11762697C2semidirect
7. C2×#11762678C2semidirect
8. C2×C4×#63225C2semidirect
9. #14527029C2semidirect
10. #14527028C2semidirect
11. #14527027C2semidirect
12. #14527026C2semidirect
13. #14527012C2semidirect
14. #95×Dic17C2semidirect
15. C2×C17×#388C2semidirect
38. #11762709C4semidirect
155. C17×#95D4semidirect
163. #10587502D4semidirect
501. C2×#388D17semidirect
587. Dic17#388semidirect
752. #95C22⋊D17semidirect
753. C17#14001semidirect

Maximal subgroups

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

subgroupindex
C2×#117627092
C2×#117627012
C2×#117627002
C2×#117626972
C2×#117626782
C2×C4×#632252
#145270292
#145270282
#145270272
#145270262
#145270122
#95×Dic172
C2×C17×#3882
#1400117