Finite Group Databasebeta

← #16957352

Subgroups — #16957352

Order 4352.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762703C211yesmaximal, characteristic, complemented
2C2×#11762689C211yesmaximal, characteristic
3C2×#11762682C211yesmaximal, characteristic, complemented
4C2×#11762667C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic17C211yesmaximal, characteristic, complemented
7#14527039C211yesmaximal, characteristic, complemented
8#14527031C211yesmaximal, characteristic, complemented
9#14527027C211yesmaximal, characteristic, complemented
10#14527025C211yesmaximal, characteristic
11#14527021C211yesmaximal, characteristic, complemented
12#14527019C211yesmaximal, characteristic, complemented
13#14527015C211yesmaximal, characteristic, complemented
14#14527010C211yesmaximal, characteristic, complemented
15C2×C17×#386C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30#11762703—24no—
31#11762689C418yescomplemented
32#11762682—24no—
33#11762667—24no—
34C22⋊C4×Dic17—24no—
35C4×C22⋊Dic17—24no—
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
50C23×D4×C17C2211yescharacteristic
51C24×C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C17×#386—24no—
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×C17—22no—
68C23×C4×C17—22no—
69C23×C4×C17—22no—
70C23×C4×C17—22no—
71C23×C4×C17—22no—
72C23×C4×C17—41no—
73C23×C4×C17—41no—
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C23×Dic17—22no—
80C23×Dic17—22no—
81C23×Dic17—22no—
82C23×Dic17—22no—
83C23×Dic17—41no—
84C23×Dic17—41no—
85C23×Dic17C2×C414yescomplemented
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×C17—22no—
97C2×C22⋊C4×C17—22no—
98C2×C22⋊C4×C17—22no—
99C2×C22⋊C4×C17—22no—
100C2×C22⋊C4×C17—41no—
101C2×C22⋊C4×C17—41no—
102C2×C22⋊C4×C17D414yes—
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—22no—
113C2×C22⋊Dic17—22no—
114C2×C22⋊Dic17—22no—
115C2×C22⋊Dic17—22no—
116C2×C22⋊Dic17—22no—
117C2×C22⋊Dic17—22no—
118C2×C22⋊Dic17—22no—
119C2×C22⋊Dic17—41no—
120C2×C22⋊Dic17—41no—
121C2×C22⋊Dic17C2×C414yes—
122C2×C22⋊Dic17C2×C414yes—
123C2×C22⋊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—41no—
132C2×#63225—41no—
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—41no—
140C2×C4×Dic17—41no—
141C2×C4×Dic17—41no—
142C17×#95—22no—
143C17×#95—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—22no—
148#10587502—22no—
149#10587502—22no—
150#10587502—22no—
151#10587502—41no—
152#10587502—41no—
153#10587502—41no—
154#10587502C2×C414yescomplemented
155#10587502C2×C414yescomplemented
156#10587502D414yescomplemented
157#10587502D414yescomplemented
158C24×C17—21no—
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×C17C22×C412yes—
183C24×C17C22×C412yes—
184C24×C17C2×D412yes—
185C24×C17#4112yes—
186C24×C17#4112yes—
187C24×C17#4112yes—
188C24×C17C2411yescharacteristic
189C2×D4×C17—28no—
190C2×D4×C17—28no—
191C2×D4×C17—44no—
192C2×D4×C17—44no—
193C2×D4×C17—44no—
194C2×D4×C17—44no—
195C2×D4×C17—44no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—28no—
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—44no—
227C22×C4×C17—44no—
228C22×C4×C17—44no—
229C22×C4×C17—44no—
230C22×C4×C17—44no—
231C22×C4×C17—44no—
232C22×C4×C17C22×C412yes—
233C22×C4×C17C2×D412yes—
234C22×C4×C17C2×D412yes—
235C22×C4×C17C2×D412yes—
236C22×C4×C17C2×D412yes—
237C22×C4×C17#4112yes—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17—21no—
246C22×Dic17—21no—
247C22×Dic17—21no—
248C22×Dic17—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×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—28no—
277C22×Dic17—28no—
278C22×Dic17—21no—
279C22×Dic17—21no—
280C22×Dic17—21no—
281C22×Dic17—21no—
282C22×Dic17—21no—
283C22×Dic17—21no—
284C22×Dic17—21no—
285C22×Dic17—44no—
286C22×Dic17—44no—
287C22×Dic17—44no—
288C22×Dic17—44no—
289C22×Dic17—44no—
290C22×Dic17C22×C412yes—
291C22×Dic17C22×C412yes—
292C22×Dic17C22×C412yes—
293C22×Dic17C22×C412yes—
294C22×Dic17C2×D412yes—
295C22×Dic17C2×D412yes—
296C22×Dic17C2×D412yes—
297C22×Dic17C2×D412yes—
298C22×Dic17#4112yes—
299C22×Dic17#4112yes—
300C22×Dic17#4112yes—
301C22⋊C4×C17—28no—
302C22⋊C4×C17—44no—
303C22⋊C4×C17—44no—
304C22⋊Dic17—28no—
305C22⋊Dic17—28no—
306C22⋊Dic17—28no—
307C22⋊Dic17—28no—
308C22⋊Dic17—28no—
309C22⋊Dic17—44no—
310C22⋊Dic17—44no—
311#63225—44no—
312#63225—44no—
313#63225—44no—
314C4×Dic17—44no—
315C4×Dic17—44no—
316C4×Dic17—44no—
317#13988—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—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—22no—
341C23×C17—22no—
342C23×C17—22no—
343C23×C17—22no—
344C23×C17—22no—
345C23×C17—22no—
346C23×C17—22no—
347C23×C17—22no—
348C23×C17—22no—
349C23×C17—22no—
350C23×C17—22no—
351C23×C17—22no—
352C23×C17—22no—
353C23×C17—22no—
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×C17—41no—
385C23×C17—41no—
386C23×C17#11714yes—
387C23×C17C4×D414yes—
388C23×C17C23×C411yescharacteristic
389C23×C17C22×D411yescharacteristic
390C23×C17C22×D411yescharacteristic
391C23×C17C22×D411yescharacteristic
392C23×C17C2×#4111yescharacteristic
393C23×C17C2×#4111yescharacteristic
394C23×C17C2×#4111yescharacteristic
395C23×C17C2×#4111yescharacteristic
396C23×C17C2×#4111yescharacteristic
397C23×C17C2×#4111yescharacteristic
398C23×C17C2×#4111yescharacteristic
399C23×C17H(5,𝔽2)11yescharacteristic
400C23×C17H(5,𝔽2)11yescharacteristic
401C23×C17H(5,𝔽2)11yescharacteristic
402C23×C172−1+411yescharacteristic
403D4×C17—416no—
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—416no—
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—41no—
436C2×C4×C17—41no—
437C2×C4×C17—41no—
438C2×C4×C17—41no—
439C2×C4×C17#12114yes—
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—416no—
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×Dic17—41no—
491C2×Dic17—41no—
492C2×Dic17—41no—
493C2×Dic17—41no—
494C2×Dic17—41no—
495C2×Dic17C4×D414yes—
496C2×Dic17C4×D414yes—
497C2×#388—171no—
498C2×#386—171no—
499C2×#386D1711yescharacteristic
500C2×#385—171no—
501C2×#380—171no—
502C2×C4×C22⋊C4—171no—
503C2×C4×C22⋊C4—171no—
504#1442—171no—
505#1440—171no—
506#1439—171no—
507#1438—171no—
508#1437—171no—
509#1436—171no—
510#1436—171no—
511#1434—171no—
512C22×C17—24no—
513C22×C17—24no—
514C22×C17—24no—
515C22×C17—24no—
516C22×C17—24no—
517C22×C17—24no—
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—42no—
531C22×C17—42no—
532C22×C17—42no—
533C22×C17—42no—
534C22×C17—42no—
535C22×C17—42no—
536C22×C17—42no—
537C22×C17—42no—
538C22×C17—42no—
539C22×C17—42no—
540C22×C17—42no—
541C22×C17—42no—
542C22×C17C2×#11711yescharacteristic
543C22×C17C2×C4×D411yescharacteristic
544C22×C17C2×C4×D411yescharacteristic
545C22×C17C2×C4×D411yescharacteristic
546C22×C17C4×#4111yescharacteristic
547C22×C17#51811yescharacteristic
548C22×C17#52011yescharacteristic
549C22×C17C2×#12111yescharacteristic
550C22×C17#52511yescharacteristic
551C22×C17#52511yescharacteristic
552C22×C17#52511yescharacteristic
553C22×C17#52911yescharacteristic
554C22×C17#52911yescharacteristic
555C22×C17#52911yescharacteristic
556C22×C17#53211yescharacteristic
557C22×C17#53811yescharacteristic
558C22×C17#53911yescharacteristic
559C22×C17#54011yescharacteristic
560C22×C17#54211yescharacteristic
561C22×C17D4211yescharacteristic
562C22×C17D4211yescharacteristic
563C22×C17#54611yescharacteristic
564C22×C17#54611yescharacteristic
565C22×C17#54611yescharacteristic
566C22×C17#54611yescharacteristic
567C22×C17#54611yescharacteristic
568C22×C17#54711yescharacteristic
569C22×C17#54811yescharacteristic
570C22×C17#54811yescharacteristic
571C22×C17#55111yescharacteristic
572C22×C17#55111yescharacteristic
573C22×C17#55111yescharacteristic
574C22×C17#55211yescharacteristic
575C22×C17#55311yescharacteristic
576C22×C17#55311yescharacteristic
577C4×C17—24no—
578C4×C17—42no—
579C4×C17—42no—
580C4×C17—42no—
581C4×C17—81no—
582Dic17—24no—
583Dic17—24no—
584Dic17—42no—
585Dic17—42no—
586Dic17—42no—
587Dic17—42no—
588Dic17—42no—
589Dic17—81no—
590C23×D4C2×D1711yescharacteristic
591C24×C4—171no—
592C24×C4C2×D1711yescharacteristic
593C22×C4⋊C4—171no—
594C22×C4⋊C4—171no—
595C22×C4⋊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⋊C4—171no—
603C22×C22⋊C4C2×D1711yescharacteristic
604C22×C22⋊C4C2×D1711yescharacteristic
605C22×C22⋊C4C2×D1711yescharacteristic
606C22×C42—171no—
607C22×C42—171no—
608C22×C42—171no—
609#388—344no—
610#386—24no—
611#386—178no—
612#385—344no—
613#380—344no—
614C4×C22⋊C4—344no—
615C4×C22⋊C4—344no—
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×#95—171no—
627C2×#95—171no—
628C2×#95—171no—
629C2×#95—171no—
630C2×#95C2×D1711yescharacteristic
631C2×#95C2×D1711yescharacteristic
632C2×C17—44no—
633C2×C17—44no—
634C2×C17#229011yescharacteristic
635C2×C17C4×#12111yescharacteristic
636C2×C17#233511yescharacteristic
637C2×C17#234211yescharacteristic
638C2×C17#235211yescharacteristic
639C2×C17#235811yescharacteristic
640C2×C17#236111yescharacteristic
641C2×C17#242411yescharacteristic
642C2×C17#242711yescharacteristic
643C2×C17#245711yescharacteristic
644C2×C17#246311yescharacteristic
645C2×C17#246411yescharacteristic
646C2×C17#247711yescharacteristic
647C2×C17#255311yescharacteristic
648C2×C17#257811yescharacteristic
649C25C22×D1711yescharacteristic
650C25C22×D1711yescharacteristic
651C22×D4—22no—
652C22×D4—22no—
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—41no—
656C22×D4—41no—
657C22×D4C4×D1714yes—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—41no—
664C23×C4—41no—
665C23×C4—171no—
666C23×C4—171no—
667C23×C4—171no—
668C23×C4—171no—
669C23×C4—171no—
670C23×C4—171no—
671C23×C4—171no—
672C23×C4—174no—
673C23×C4—171no—
674C23×C4—342no—
675C23×C4—342no—
676C23×C4—342no—
677C23×C4—342no—
678C23×C4—681no—
679C23×C4—681no—
680C23×C4C22×D1711yescharacteristic
681C23×C4C22×D1711yescharacteristic
682C23×C4C22×D1711yescharacteristic
683C23×C4C22×D1711yescharacteristic
684C23×C4C22×D1711yescharacteristic
685C2×C4⋊C4—342no—
686C2×C4⋊C4—342no—
687C2×C4⋊C4—342no—
688C2×C4⋊C4—342no—
689C2×C4⋊C4—342no—
690C2×C4⋊C4—342no—
691C2×C4⋊C4—342no—
692C2×C4⋊C4—681no—
693C2×C4⋊C4—681no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—174no—
703C2×C22⋊C4—174no—
704C2×C22⋊C4—174no—
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—342no—
721C2×C22⋊C4—681no—
722C2×C22⋊C4—681no—
723C2×C22⋊C4C22⋊D1714yes—
724C2×C42—342no—
725C2×C42—342no—
726C2×C42—342no—
727C2×C42—342no—
728C2×C42—342no—
729C2×C42—342no—
730C2×C42—681no—
731C2×C42—681no—
732C2×C42—681no—
733#95—22no—
734#95—22no—
735#95—174no—
736#95—174no—
737#95—174no—
738#95—174no—
739#95—342no—
740#95—342no—
741#95—342no—
742#95—342no—
743#95—342no—
744#95—342no—
745#95—342no—
746#95—681no—
747#95—681no—
748#95—681no—
749C17#1398811yescharacteristic, complemented, Sylow
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—
773C24—21no—
774C24C2×C4×D1712yes—
775C24C2×C4×D1712yes—
776C24#6325212yes—
777C24#6325412yes—
778C24#6325412yes—
779C24C2×C22⋊D1712yes—
780C24C23×D1711yescharacteristic
781C2×D4—28no—
782C2×D4—28no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—28no—
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—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—172no—
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—348no—
836C22×C4—348no—
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—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×C4—341no—
875C22×C4—341no—
876C22×C4—341no—
877C22×C4—341no—
878C22×C4—341no—
879C22×C4—341no—
880C22×C4—341no—
881C22×C4—341no—
882C22×C4—684no—
883C22×C4—684no—
884C22×C4—684no—
885C22×C4—684no—
886C22×C4—684no—
887C22×C4C2×C4×D1712yes—
888C22×C4D4×D1712yes—
889C22×C4D4×D1712yes—
890C22×C4#6325412yes—
891C22×C4C2×C22⋊D1712yes—
892C22×C4C2×C22⋊D1712yes—
893C4⋊C4—684no—
894C4⋊C4—684no—
895C4⋊C4—684no—
896C22⋊C4—28no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—348no—
900C22⋊C4—348no—
901C22⋊C4—348no—
902C22⋊C4—348no—
903C22⋊C4—348no—
904C22⋊C4—684no—
905C22⋊C4—684no—
906C42—684no—
907C42—684no—
908C42—684no—
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—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
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—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23#1058756314yes—
978C23C4×C22⋊D1714yes—
979C23C22×C4×D1711yescharacteristic
980C23C2×#6325211yescharacteristic
981C23C2×D4×D1711yescharacteristic
982C23C2×D4×D1711yescharacteristic
983C23C2×#6325411yescharacteristic
984C23C2×#6325411yescharacteristic
985C23C2×#6325411yescharacteristic
986C23#1058769111yescharacteristic
987C23#1058769111yescharacteristic
988C23#1058769111yescharacteristic
989C23#41×D1711yescharacteristic
990C23#41×D1711yescharacteristic
991C23#41×D1711yescharacteristic
992C23#1058769711yescharacteristic
993C23C22×C22⋊D1711yescharacteristic
994D4—416no—
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—416no—
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—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—174no—
1031C2×C4—174no—
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—342no—
1057C2×C4—342no—
1058C2×C4—342no—
1059C2×C4—6816no—
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×C4—681no—
1083C2×C4—681no—
1084C2×C4—681no—
1085C2×C4—681no—
1086C2×C4—681no—
1087C2×C4#1058762514yes—
1088C22—24no—
1089C22—24no—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22C2×#1058756311yescharacteristic
1119C22C4×D4×D1711yescharacteristic
1120C22C4×D4×D1711yescharacteristic
1121C22C2×C4×C22⋊D1711yescharacteristic
1122C22C4×#6325411yescharacteristic
1123C22#1176328211yescharacteristic
1124C22#1176328811yescharacteristic
1125C22C2×#1058762511yescharacteristic
1126C22#1176331511yescharacteristic
1127C22#1176331811yescharacteristic
1128C22#1176331911yescharacteristic
1129C22#1176333611yescharacteristic
1130C22#1176333911yescharacteristic
1131C22#1176334011yescharacteristic
1132C22#1176335511yescharacteristic
1133C22#1176339411yescharacteristic
1134C22#1176340211yescharacteristic
1135C22#1176340911yescharacteristic
1136C22#1176342611yescharacteristic
1137C22#1176344111yescharacteristic
1138C22D4×C22⋊D1711yescharacteristic
1139C22#1176344611yescharacteristic
1140C22#1176345311yescharacteristic
1141C22#1176345311yescharacteristic
1142C22#1176345611yescharacteristic
1143C22#1176345611yescharacteristic
1144C22#1176345811yescharacteristic
1145C22#1176346511yescharacteristic
1146C22#1176346811yescharacteristic
1147C22#1176348511yescharacteristic
1148C22#1176348511yescharacteristic
1149C22#1176348711yescharacteristic
1150C22#1176349611yescharacteristic
1151C22#1176350211yescharacteristic
1152C22#1176350811yescharacteristic
1153C4—24no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—81no—
1158C4—344no—
1159C4—344no—
1160C4—682no—
1161C4—682no—
1162C4—682no—
1163C4—682no—
1164C4—682no—
1165C4—1361no—
1166C2—44no—
1167C2—44no—
1168C2#1453122411yescharacteristic
1169C2C4×#1058762511yescharacteristic
1170C2#1453157511yescharacteristic
1171C2#1453162911yescharacteristic
1172C2#1453171111yescharacteristic
1173C2#1453176711yescharacteristic
1174C2#1453180111yescharacteristic
1175C2#1453232411yescharacteristic
1176C2#1453236311yescharacteristic
1177C2#1453269511yescharacteristic
1178C2#1453278211yescharacteristic
1179C2#1453279511yescharacteristic
1180C2#1453298211yescharacteristic
1181C2#1453382511yescharacteristic
1182C2#1453411511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#386C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenterC2×#386D17
hypocenterC17#13988
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C2×#11762703C2semidirect
3. C2×#11762682C2semidirect
4. C2×#11762667C2semidirect
5. C2×C22⋊C4×Dic17C2semidirect
6. C2×C4×C22⋊Dic17C2semidirect
7. #14527039C2semidirect
8. #14527031C2semidirect
9. #14527027C2semidirect
11. #14527021C2semidirect
12. #14527019C2semidirect
13. #14527015C2semidirect
14. #14527010C2semidirect
31. #11762689C4semidirect
85. C23×Dic17C2×C4semidirect
123. C2×C22⋊Dic17C2×C4semidirect
154. #10587502C2×C4semidirect
155. #10587502C2×C4semidirect
156. #10587502D4semidirect
157. #10587502D4semidirect
749. C17#13988semidirect

Maximal subgroups

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

subgroupindex
C2×#117627032
C2×#117626892
C2×#117626822
C2×#117626672
C2×C22⋊C4×Dic172
C2×C4×C22⋊Dic172
#145270392
#145270312
#145270272
#145270252
#145270212
#145270192
#145270152
#145270102
C2×C17×#3862
#1398817