Finite Group Databasebeta

← #16957477

Subgroups — #16957477

Order 4352.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762685C211yesmaximal, characteristic
2C2×#11762685C211yesmaximal, characteristic
3C2×#11762685C211yesmaximal, characteristic
4C2×#11762666C211yesmaximal, characteristic, complemented
5C2×C4×#63227C211yesmaximal, characteristic, complemented
6C2×#95×D17C211yesmaximal, characteristic, complemented
7#14527045C211yesmaximal, characteristic, complemented
8#14527043C211yesmaximal, characteristic, complemented
9#14527031C211yesmaximal, characteristic, complemented
10#14527029C211yesmaximal, characteristic, complemented
11#14527021C211yesmaximal, characteristic, complemented
12#14527018C211yesmaximal, characteristic, complemented
13#14527011C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C2×C17×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C22×C4⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28#11762685—24no—
29#11762685—24no—
30#11762685C418yescomplemented
31#11762666—24no—
32C4×#63227—24no—
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49#95×D17—24no—
50C22×C4⋊C4×C17C2211yescharacteristic
51C22×C22⋊C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C42×C17C2211yescharacteristic
55C17×#388—24no—
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C25×C17C2311yescharacteristic
59C24×D17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C22×C22⋊D17—22no—
67C22×C22⋊D17—22no—
68C22×C22⋊D17—22no—
69C22×C22⋊D17—22no—
70C22×C22⋊D17—22no—
71C22×C22⋊D17—22no—
72C22×C22⋊D17C2×C414yes—
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C22×C4×D17—22no—
81C22×C4×D17—22no—
82C22×C4×D17—22no—
83C22×C4×D17—22no—
84C22×C4×D17—22no—
85C22×C4×D17—22no—
86C22×C4×D17—22no—
87C22×C4×D17—22no—
88C22×C4×D17—22no—
89C22×C4×D17—22no—
90C22×C4×D17—22no—
91C22×C4×D17—22no—
92C22×C4×D17—22no—
93C22×C4×D17—41no—
94C22×C4×D17—41no—
95C22×C4×D17—41no—
96C22×C4×D17—41no—
97C22×C4×D17—41no—
98C22×C4×D17—41no—
99C22×C4×D17C2×C414yes—
100C22×C4×D17D414yes—
101C2×C4⋊C4×C17—22no—
102C2×C4⋊C4×C17—22no—
103C2×C4⋊C4×C17—41no—
104C2×C22⋊C4×C17—22no—
105C2×C22⋊C4×C17—22no—
106C2×C22⋊C4×C17—22no—
107C2×C22⋊C4×C17—22no—
108C2×C22⋊C4×C17—22no—
109C2×C22⋊C4×C17—22no—
110C2×C22⋊C4×C17—22no—
111C2×C22⋊C4×C17—41no—
112C2×C22⋊C4×C17C2×C414yescomplemented
113C2×C42×C17—22no—
114C2×C42×C17—22no—
115C2×C42×C17—22no—
116C2×C22⋊Dic17—22no—
117C2×C22⋊Dic17—22no—
118C2×C22⋊Dic17—22no—
119C2×C22⋊Dic17—41no—
120C2×C22⋊Dic17—41no—
121C2×C22⋊Dic17—41no—
122C2×C22⋊Dic17—41no—
123C2×C22⋊Dic17—41no—
124C2×C22⋊Dic17C2×C414yescomplemented
125C2×#63227—22no—
126C2×#63227—22no—
127C2×#63227—22no—
128C2×#63227—22no—
129C2×#63227—22no—
130C2×#63227—22no—
131C2×#63227—22no—
132C2×#63227C2×C414yes—
133C2×#63227D414yes—
134C2×C4⋊Dic17—22no—
135C2×C4⋊Dic17—22no—
136C2×C4⋊Dic17—41no—
137C2×C4×Dic17—22no—
138C2×C4×Dic17—41no—
139C2×C4×Dic17—41no—
140C17×#95—22no—
141C17×#95D414yescomplemented
142#10587502—22no—
143#10587502—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—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#10587502C2×C414yescomplemented
157#10587502C2×C414yescomplemented
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×C17C22×C412yes—
173C24×C17C2411yescharacteristic
174C23×D17—21no—
175C23×D17—21no—
176C23×D17—21no—
177C23×D17—21no—
178C23×D17—21no—
179C23×D17—21no—
180C23×D17—21no—
181C23×D17—21no—
182C23×D17C22×C412yes—
183C23×D17C2×D412yes—
184C23×D17C2×D412yes—
185C23×D17#4112yes—
186C23×D17#4112yes—
187C23×D17#4112yes—
188C23×D17#4112yes—
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—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×C17C22×C412yes—
223C22×C4×C17C22×C412yes—
224C22×C4×C17C2×D412yes—
225C22×C4×C17C2×D412yes—
226C22×C4×C17C2×D412yes—
227C22×C4×C17C2×D412yes—
228C22×C4×C17C2×D412yes—
229C22×C4×C17#4112yes—
230C22×C4×C17#4112yes—
231C2×C22⋊D17—28no—
232C2×C22⋊D17—28no—
233C2×C22⋊D17—28no—
234C2×C22⋊D17—44no—
235C2×C22⋊D17—44no—
236C2×C22⋊D17—44no—
237C2×C22⋊D17—44no—
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—21no—
277C22×Dic17—21no—
278C22×Dic17—21no—
279C22×Dic17—21no—
280C22×Dic17—21no—
281C22×Dic17C22×C412yes—
282C22×Dic17C22×C412yes—
283C22×Dic17C22×C412yes—
284C22×Dic17C2×D412yes—
285C22×Dic17C2×D412yes—
286C22×Dic17#4112yes—
287C2×C4×D17—28no—
288C2×C4×D17—28no—
289C2×C4×D17—28no—
290C2×C4×D17—28no—
291C2×C4×D17—28no—
292C2×C4×D17—44no—
293C2×C4×D17—44no—
294C2×C4×D17—44no—
295C2×C4×D17—44no—
296C2×C4×D17—44no—
297C2×C4×D17—44no—
298C2×C4×D17—44no—
299C2×C4×D17—44no—
300C2×C4×D17—44no—
301C2×C4×D17—44no—
302C2×C4×D17—44no—
303C2×C4×D17—44no—
304C2×C4×D17—44no—
305C2×C4×D17—44no—
306C2×C4×D17—44no—
307C2×C4×D17—44no—
308C4⋊C4×C17—44no—
309C22⋊C4×C17—28no—
310C22⋊C4×C17—44no—
311C22⋊C4×C17—44no—
312C42×C17—44no—
313C22⋊Dic17—44no—
314C22⋊Dic17—44no—
315C22⋊Dic17—44no—
316#63227—28no—
317#63227—28no—
318#63227—44no—
319C4⋊Dic17—44no—
320C4×Dic17—44no—
321#13999—171nomaximal, Sylow
322C23×C17—22no—
323C23×C17—22no—
324C23×C17—22no—
325C23×C17—22no—
326C23×C17—22no—
327C23×C17—22no—
328C23×C17—22no—
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×C17—41no—
354C23×C17—41no—
355C23×C17—41no—
356C23×C17—41no—
357C23×C17C23×C411yescharacteristic
358C23×C17C22×D411yescharacteristic
359C23×C17C22×D411yescharacteristic
360C23×C17C22×D411yescharacteristic
361C23×C17C2×#4111yescharacteristic
362C23×C17C2×#4111yescharacteristic
363C23×C17C2×#4111yescharacteristic
364C23×C17C2×#4111yescharacteristic
365C23×C17C2×#4111yescharacteristic
366C23×C17C2×#4111yescharacteristic
367C23×C17C2×#4111yescharacteristic
368C23×C17H(5,𝔽2)11yescharacteristic
369C23×C17H(5,𝔽2)11yescharacteristic
370C23×C17H(5,𝔽2)11yescharacteristic
371C23×C172−1+411yescharacteristic
372C22×D17—22no—
373C22×D17—22no—
374C22×D17—22no—
375C22×D17—22no—
376C22×D17—22no—
377C22×D17—22no—
378C22×D17—22no—
379C22×D17—22no—
380C22×D17—22no—
381C22×D17—22no—
382C22×D17—22no—
383C22×D17—22no—
384C22×D17—22no—
385C22×D17—22no—
386C22×D17—22no—
387C22×D17—22no—
388C22×D17—22no—
389C22×D17—22no—
390C22×D17—22no—
391C22×D17—22no—
392C22×D17—22no—
393C22×D17—22no—
394C22×D17—22no—
395C22×D17—22no—
396C22×D17—22no—
397C22×D17—22no—
398C22×D17—22no—
399C22×D17—22no—
400C22×D17#11714yes—
401C22×D17C4×D414yes—
402C22×D17C4×D414yes—
403C22×D17#12114yes—
404C22×D17#12314yes—
405C22×D17#12414yes—
406C22×D17#12614yes—
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—22no—
425C2×C4×C17—22no—
426C2×C4×C17—22no—
427C2×C4×C17—22no—
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×C17—41no—
444C2×C4×C17—41no—
445C2×C4×C17—41no—
446C2×C4×C17—41no—
447C2×C4×C17C4×D414yes—
448C2×C4×C17#12114yes—
449C22⋊D17—416no—
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—22no—
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×Dic17—41no—
496C2×Dic17—41no—
497C2×Dic17—41no—
498C2×Dic17—41no—
499C4×D17—416no—
500C4×D17—416no—
501C4×D17—416no—
502C2×#388D1711yescharacteristic, complemented
503C2×#386—171no—
504C2×#386—171no—
505C2×#386—171no—
506C2×#380—171no—
507C2×C4×C22⋊C4—171no—
508C22×#95—171no—
509#1443—171no—
510#1442—171no—
511#1440—171no—
512#1439—171no—
513#1437—171no—
514#1436—171no—
515#1434—171no—
516C22⋊#95—171no—
517C22×C17—42no—
518C22×C17—42no—
519C22×C17—42no—
520C22×C17—42no—
521C22×C17—42no—
522C22×C17—42no—
523C22×C17—42no—
524C22×C17—81no—
525C22×C17—81no—
526C22×C17—81no—
527C22×C17—81no—
528C22×C17—81no—
529C22×C17—81no—
530C22×C17—81no—
531C22×C17—81no—
532C22×C17C2×#11711yescharacteristic
533C22×C17C2×C4×D411yescharacteristic
534C22×C17C2×C4×D411yescharacteristic
535C22×C17C2×C4×D411yescharacteristic
536C22×C17C4×#4111yescharacteristic
537C22×C17#51811yescharacteristic
538C22×C17#52011yescharacteristic
539C22×C17C2×#12111yescharacteristic
540C22×C17C2×#12111yescharacteristic
541C22×C17C2×#12311yescharacteristic
542C22×C17#52511yescharacteristic
543C22×C17C2×#12411yescharacteristic
544C22×C17C2×#12611yescharacteristic
545C22×C17#52911yescharacteristic
546C22×C17#53211yescharacteristic
547C22×C17#53411yescharacteristic
548C22×C17#53711yescharacteristic
549C22×C17#53811yescharacteristic
550C22×C17#53911yescharacteristic
551C22×C17D4211yescharacteristic
552C22×C17#54611yescharacteristic
553C22×C17#54611yescharacteristic
554C22×C17#54611yescharacteristic
555C22×C17#54611yescharacteristic
556C22×C17#54711yescharacteristic
557C22×C17#54811yescharacteristic
558C22×C17#55111yescharacteristic
559C22×C17#55111yescharacteristic
560C22×C17#55111yescharacteristic
561C22×C17#55111yescharacteristic
562C22×C17#55211yescharacteristic
563C22×C17#55211yescharacteristic
564C22×C17#55311yescharacteristic
565C22×C17#55311yescharacteristic
566C22×C17#55311yescharacteristic
567C2×D17—24no—
568C2×D17—24no—
569C2×D17—24no—
570C2×D17—24no—
571C2×D17—24no—
572C2×D17—24no—
573C2×D17—24no—
574C2×D17—24no—
575C2×D17—24no—
576C2×D17—24no—
577C2×D17—24no—
578C2×D17—24no—
579C2×D17—24no—
580C2×D17—24no—
581C2×D17#38818yescomplemented
582C4×C17—24no—
583C4×C17—24no—
584C4×C17—42no—
585C4×C17—42no—
586C4×C17—42no—
587C4×C17—81no—
588Dic17—42no—
589Dic17—42no—
590Dic17—42no—
591Dic17—42no—
592Dic17—42no—
593Dic17—42no—
594Dic17—81no—
595C23×D4—171no—
596C24×C4—171no—
597C24×C4—171no—
598C24×C4—171no—
599C22×C4⋊C4—171no—
600C22×C4⋊C4C2×D1711yescharacteristic
601C22×C22⋊C4—171no—
602C22×C22⋊C4—171no—
603C22×C22⋊C4—171no—
604C22×C22⋊C4—171no—
605C22×C22⋊C4—171no—
606C22×C22⋊C4—171no—
607C22×C22⋊C4C2×D1711yescharacteristic
608C22×C22⋊C4C2×D1711yescharacteristic
609C22×C22⋊C4C2×D1711yescharacteristic
610C22×C42—171no—
611C22×C42C2×D1711yescharacteristic
612#388—24no—
613#386—178no—
614#386—344no—
615#386—344no—
616#380—344no—
617C4×C22⋊C4—344no—
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×#95—171no—
631C2×#95—171no—
632C2×#95—171no—
633C2×#95—171no—
634C2×#95—344no—
635C2×#95C2×D1711yescharacteristic
636C2×#95C2×D1711yescharacteristic
637C2×C17—82no—
638C2×C17C2×#38811yescharacteristic
639C2×C17C4×#12111yescharacteristic
640C2×C17#232511yescharacteristic
641C2×C17#235211yescharacteristic
642C2×C17#235311yescharacteristic
643C2×C17#235811yescharacteristic
644C2×C17#235911yescharacteristic
645C2×C17#241211yescharacteristic
646C2×C17#241611yescharacteristic
647C2×C17#247211yescharacteristic
648C2×C17#248111yescharacteristic
649C2×C17#248811yescharacteristic
650C2×C17#249811yescharacteristic
651C2×C17#251011yescharacteristic
652C2×C17#254311yescharacteristic
653D17—28no—
654C25—171no—
655C25C22×D1711yescharacteristic
656C22×D4—174no—
657C22×D4—342no—
658C22×D4—342no—
659C22×D4—342no—
660C22×D4—342no—
661C22×D4—342no—
662C22×D4—342no—
663C23×C4—171no—
664C23×C4—171no—
665C23×C4—171no—
666C23×C4—171no—
667C23×C4—171no—
668C23×C4—171no—
669C23×C4—174no—
670C23×C4—174no—
671C23×C4—171no—
672C23×C4—342no—
673C23×C4—342no—
674C23×C4—342no—
675C23×C4—342no—
676C23×C4—342no—
677C23×C4—342no—
678C23×C4—342no—
679C23×C4—342no—
680C23×C4—342no—
681C23×C4—342no—
682C23×C4—342no—
683C23×C4—342no—
684C23×C4—342no—
685C23×C4—681no—
686C23×C4—681no—
687C23×C4—681no—
688C23×C4—681no—
689C23×C4—681no—
690C23×C4—681no—
691C23×C4C22×D1711yescharacteristic
692C23×C4C22×D1711yescharacteristic
693C23×C4C22×D1711yescharacteristic
694C23×C4C22×D1711yescharacteristic
695C23×C4C22×D1711yescharacteristic
696C23×C4C22×D1711yescharacteristic
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—41no—
700C2×C4⋊C4—342no—
701C2×C4⋊C4—342no—
702C2×C4⋊C4—681no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—174no—
712C2×C22⋊C4—174no—
713C2×C22⋊C4—174no—
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—342no—
722C2×C22⋊C4—342no—
723C2×C22⋊C4—342no—
724C2×C22⋊C4—681no—
725C2×C22⋊C4—681no—
726C2×C22⋊C4—681no—
727C2×C22⋊C4—681no—
728C2×C22⋊C4—681no—
729C2×C22⋊C4C4×D1714yescomplemented
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—342no—
734C2×C42—681no—
735C2×C42—681no—
736#95—22no—
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—342no—
747#95—342no—
748#95—342no—
749#95—342no—
750#95—342no—
751#95—681no—
752#95—681no—
753#95C22⋊D1714yescomplemented
754C17#1399911yescharacteristic, complemented, Sylow
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—172no—
770C24—172no—
771C24—172no—
772C24—172no—
773C24—172no—
774C24—172no—
775C24—172no—
776C24—341no—
777C24—341no—
778C24—341no—
779C24—341no—
780C24—341no—
781C24—341no—
782C24—341no—
783C24—341no—
784C24C2×C4×D1712yes—
785C24C23×D1711yescharacteristic
786C2×D4—348no—
787C2×D4—348no—
788C2×D4—348no—
789C2×D4—684no—
790C2×D4—684no—
791C2×D4—684no—
792C2×D4—684no—
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—21no—
826C22×C4—172no—
827C22×C4—172no—
828C22×C4—172no—
829C22×C4—172no—
830C22×C4—172no—
831C22×C4—172no—
832C22×C4—348no—
833C22×C4—348no—
834C22×C4—348no—
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—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—348no—
872C22×C4—348no—
873C22×C4—341no—
874C22×C4—341no—
875C22×C4—341no—
876C22×C4—341no—
877C22×C4—341no—
878C22×C4—341no—
879C22×C4—341no—
880C22×C4—684no—
881C22×C4—684no—
882C22×C4—684no—
883C22×C4—684no—
884C22×C4—684no—
885C22×C4—684no—
886C22×C4—684no—
887C22×C4—684no—
888C22×C4—684no—
889C22×C4—684no—
890C22×C4—684no—
891C22×C4—684no—
892C22×C4—684no—
893C22×C4—684no—
894C22×C4—684no—
895C22×C4—684no—
896C22×C4C2×C4×D1712yes—
897C22×C4C2×C4×D1712yes—
898C22×C4#6325212yes—
899C22×C4D4×D1712yes—
900C22×C4D4×D1712yes—
901C22×C4#6325412yes—
902C22×C4C2×C22⋊D1712yes—
903C22×C4C2×C22⋊D1712yes—
904C22×C4C2×C22⋊D1712yes—
905C4⋊C4—44no—
906C4⋊C4—684no—
907C22⋊C4—28no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—348no—
911C22⋊C4—348no—
912C22⋊C4—684no—
913C22⋊C4—684no—
914C22⋊C4—684no—
915C22⋊C4—684no—
916C42—44no—
917C42—684no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
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—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—174no—
954C23—174no—
955C23—174no—
956C23—174no—
957C23—174no—
958C23—174no—
959C23—174no—
960C23—342no—
961C23—342no—
962C23—342no—
963C23—342no—
964C23—342no—
965C23—342no—
966C23—342no—
967C23—342no—
968C23—342no—
969C23—342no—
970C23—342no—
971C23—342no—
972C23—342no—
973C23—342no—
974C23—342no—
975C23—342no—
976C23—342no—
977C23—342no—
978C23—342no—
979C23—342no—
980C23—342no—
981C23—342no—
982C23—342no—
983C23—342no—
984C23—342no—
985C23—342no—
986C23—342no—
987C23—342no—
988C23C22×C4×D1711yescharacteristic
989C23C2×#6325211yescharacteristic
990C23C2×D4×D1711yescharacteristic
991C23C2×D4×D1711yescharacteristic
992C23C2×#6325411yescharacteristic
993C23#1058769111yescharacteristic
994C23#41×D1711yescharacteristic
995C23#41×D1711yescharacteristic
996C23#41×D1711yescharacteristic
997C23#41×D1711yescharacteristic
998C23#41×D1711yescharacteristic
999C23#1058769611yescharacteristic
1000C23#1058769611yescharacteristic
1001C23#1058769711yescharacteristic
1002C23C22×C22⋊D1711yescharacteristic
1003D4—6816no—
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—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
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—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
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—342no—
1060C2×C4—342no—
1061C2×C4—342no—
1062C2×C4—6816no—
1063C2×C4—6816no—
1064C2×C4—6816no—
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—681no—
1088C2×C4—681no—
1089C2×C4—681no—
1090C2×C4—681no—
1091C2×C4—681no—
1092C2×C4—681no—
1093C2×C4—681no—
1094C2×C4—681no—
1095C2×C4—681no—
1096C2×C4C4×C22⋊D1714yes—
1097C2×C4#1058762414yes—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—178no—
1114C22—344no—
1115C22—344no—
1116C22—344no—
1117C22—344no—
1118C22—344no—
1119C22—344no—
1120C22—344no—
1121C22—344no—
1122C22—344no—
1123C22—344no—
1124C22—344no—
1125C22—344no—
1126C22—344no—
1127C22—344no—
1128C22#117×D1711yescharacteristic
1129C22C4×D4×D1711yescharacteristic
1130C22C4×D4×D1711yescharacteristic
1131C22C2×C4×C22⋊D1711yescharacteristic
1132C22C4×#6325411yescharacteristic
1133C22#1176328111yescharacteristic
1134C22#1176328911yescharacteristic
1135C22#121×D1711yescharacteristic
1136C22C2×#1058762411yescharacteristic
1137C22#123×D1711yescharacteristic
1138C22#1176331611yescharacteristic
1139C22#124×D1711yescharacteristic
1140C22#126×D1711yescharacteristic
1141C22#1176334111yescharacteristic
1142C22#1176335611yescharacteristic
1143C22#1176337011yescharacteristic
1144C22#1176338811yescharacteristic
1145C22#1176339311yescharacteristic
1146C22#1176340011yescharacteristic
1147C22D4×C22⋊D1711yescharacteristic
1148C22#1176344711yescharacteristic
1149C22#1176344711yescharacteristic
1150C22#1176345211yescharacteristic
1151C22#1176345511yescharacteristic
1152C22#1176345911yescharacteristic
1153C22#1176346611yescharacteristic
1154C22#1176348211yescharacteristic
1155C22#1176348211yescharacteristic
1156C22#1176348811yescharacteristic
1157C22#1176348911yescharacteristic
1158C22#1176349511yescharacteristic
1159C22#1176349811yescharacteristic
1160C22#1176350311yescharacteristic
1161C22#1176350611yescharacteristic
1162C22#1176351011yescharacteristic
1163C4—24no—
1164C4—24no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—81no—
1169C4—682no—
1170C4—682no—
1171C4—682no—
1172C4—682no—
1173C4—682no—
1174C4—682no—
1175C4—1361no—
1176C2—82no—
1177C2—348no—
1178C2D17×#38811yescharacteristic
1179C2C4×#1058762411yescharacteristic
1180C2#1453148811yescharacteristic
1181C2#1453171411yescharacteristic
1182C2#1453171911yescharacteristic
1183C2#1453176111yescharacteristic
1184C2#1453177511yescharacteristic
1185C2#1453217611yescharacteristic
1186C2#1453222011yescharacteristic
1187C2#1453290611yescharacteristic
1188C2#1453304111yescharacteristic
1189C2#1453310911yescharacteristic
1190C2#1453322711yescharacteristic
1191C2#1453334911yescharacteristic
1192C2#1453374911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×#388D17
hypocenterC17#13999
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
4. C2×#11762666C2semidirect
5. C2×C4×#63227C2semidirect
6. C2×#95×D17C2semidirect
7. #14527045C2semidirect
8. #14527043C2semidirect
9. #14527031C2semidirect
10. #14527029C2semidirect
11. #14527021C2semidirect
12. #14527018C2semidirect
13. #14527011C2semidirect
14. #14527005C2semidirect
15. C2×C17×#388C2semidirect
30. #11762685C4semidirect
112. C2×C22⋊C4×C17C2×C4semidirect
124. C2×C22⋊Dic17C2×C4semidirect
141. C17×#95D4semidirect
156. #10587502C2×C4semidirect
157. #10587502C2×C4semidirect
502. C2×#388D17semidirect
581. C2×D17#388semidirect
729. C2×C22⋊C4C4×D17semidirect
753. #95C22⋊D17semidirect
754. C17#13999semidirect

Maximal subgroups

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

subgroupindex
C2×#117626852
C2×#117626662
C2×C4×#632272
C2×#95×D172
#145270452
#145270432
#145270312
#145270292
#145270212
#145270182
#145270112
#145270052
C2×C17×#3882
#1399917