Finite Group Databasebeta

← #16958477

Subgroups — #16958477

Order 4352.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762709C211yesmaximal, characteristic
2C2×#11762699C211yesmaximal, characteristic, complemented
3C2×#11762685C211yesmaximal, characteristic
4C2×C4×#63227C211yesmaximal, characteristic, complemented
5#14527039C211yesmaximal, characteristic, complemented
6#14527032C211yesmaximal, characteristic, complemented
7#14527031C211yesmaximal, characteristic, complemented
8#14527023C211yesmaximal, characteristic
9#14527021C211yesmaximal, characteristic, complemented
10#14527021C211yesmaximal, characteristic, complemented
11#14527016C211yesmaximal, characteristic, complemented
12#14527015C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14C4×#10587502C211yesmaximal, characteristic, complemented
15C2×C17×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×C22⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30#11762709—24no—
31#11762699—24no—
32#11762685C418yescomplemented
33C4×#63227—24no—
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C22×C4⋊C4×C17C2211yescharacteristic
49C22×C22⋊C4×C17C2211yescharacteristic
50C22×C22⋊C4×C17C2211yescharacteristic
51C22×C22⋊C4×C17C2211yescharacteristic
52C22×C42×C17C2211yescharacteristic
53C17×#388—24no—
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C25×C17C2311yescharacteristic
57C24×D17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C22×C22⋊D17—22no—
65C22×C22⋊D17—22no—
66C22×C22⋊D17—22no—
67C22×C22⋊D17—22no—
68C22×C22⋊D17—41no—
69C22×C22⋊D17—41no—
70C22×C22⋊D17C2×C414yes—
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C22×C4×D17—22no—
79C22×C4×D17—22no—
80C22×C4×D17—41no—
81C22×C4×D17—41no—
82C22×C4×D17—41no—
83C22×C4×D17—41no—
84C22×C4×D17C2×C414yes—
85C2×C4⋊C4×C17—22no—
86C2×C4⋊C4×C17—22no—
87C2×C4⋊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—41no—
95C2×C22⋊C4×C17—41no—
96C2×C22⋊C4×C17C2×C414yes—
97C2×C42×C17—41no—
98C2×C42×C17—41no—
99C2×C42×C17D414yescomplemented
100C2×C22⋊Dic17—22no—
101C2×C22⋊Dic17—22no—
102C2×C22⋊Dic17—22no—
103C2×C22⋊Dic17—22no—
104C2×C22⋊Dic17—41no—
105C2×C22⋊Dic17—41no—
106C2×C22⋊Dic17—41no—
107C2×C22⋊Dic17—41no—
108C2×C22⋊Dic17C2×C414yes—
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—22no—
119C2×#63227—22no—
120C2×#63227—41no—
121C2×#63227—41no—
122C2×#63227C2×C414yes—
123C2×#63227D414yes—
124C2×#63225—22no—
125C2×#63225—22no—
126C2×#63225—41no—
127C2×C4×Dic17—22no—
128C2×C4×Dic17—22no—
129C2×C4×Dic17—22no—
130C2×C4×Dic17—22no—
131C2×C4×Dic17—22no—
132C2×C4×Dic17—41no—
133C2×C4×Dic17—41no—
134C2×C4×Dic17—41no—
135C2×C4×Dic17—41no—
136C17×#95—22no—
137C17×#95—22no—
138#10587502—22no—
139#10587502—22no—
140#10587502—22no—
141#10587502—22no—
142#10587502—22no—
143#10587502—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—41no—
148#10587502—41no—
149#10587502—41no—
150#10587502C2×C414yes—
151#10587502C2×C414yes—
152C24×C17—21no—
153C24×C17—21no—
154C24×C17—21no—
155C24×C17—21no—
156C24×C17—21no—
157C24×C17—21no—
158C24×C17—21no—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17—21no—
163C24×C17—21no—
164C24×C17—21no—
165C24×C17—21no—
166C24×C17C22×C412yes—
167C24×C17C2411yescharacteristic
168C23×D17—21no—
169C23×D17—21no—
170C23×D17—21no—
171C23×D17—21no—
172C23×D17—21no—
173C23×D17—21no—
174C23×D17—21no—
175C23×D17—21no—
176C23×D17—21no—
177C23×D17—21no—
178C23×D17—21no—
179C23×D17—21no—
180C23×D17C22×C412yes—
181C23×D17C2×D412yes—
182C23×D17#4112yes—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—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×C17C22×C412yes—
218C22×C4×C17C22×C412yes—
219C22×C4×C17C2×D412yes—
220C22×C4×C17C2×D412yes—
221C22×C4×C17C2×D412yes—
222C22×C4×C17C2×D412yes—
223C22×C4×C17#4112yes—
224C22×C4×C17#4112yes—
225C2×C22⋊D17—28no—
226C2×C22⋊D17—28no—
227C2×C22⋊D17—44no—
228C2×C22⋊D17—44no—
229C2×C22⋊D17—44no—
230C2×C22⋊D17—44no—
231C2×C22⋊D17—44no—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17—21no—
246C22×Dic17—21no—
247C22×Dic17—21no—
248C22×Dic17—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—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×Dic17C22×C412yes—
273C22×Dic17C22×C412yes—
274C22×Dic17C22×C412yes—
275C22×Dic17C2×D412yes—
276C22×Dic17#4112yes—
277C22×Dic17#4112yes—
278C22×Dic17#4112yes—
279C22×Dic17#4112yes—
280C22×Dic17#4112yes—
281C2×C4×D17—28no—
282C2×C4×D17—44no—
283C2×C4×D17—44no—
284C2×C4×D17—44no—
285C2×C4×D17—44no—
286C2×C4×D17—44no—
287C2×C4×D17—44no—
288C4⋊C4×C17—44no—
289C22⋊C4×C17—28no—
290C22⋊C4×C17—44no—
291C22⋊C4×C17—44no—
292C42×C17—44no—
293C22⋊Dic17—44no—
294C22⋊Dic17—44no—
295C22⋊Dic17—44no—
296#63227—28no—
297#63227—28no—
298#63227—28no—
299#63227—44no—
300#63227—44no—
301#63225—44no—
302C4×Dic17—44no—
303C4×Dic17—44no—
304C4×Dic17—44no—
305#14076—171nomaximal, Sylow
306C23×C17—22no—
307C23×C17—22no—
308C23×C17—22no—
309C23×C17—22no—
310C23×C17—22no—
311C23×C17—22no—
312C23×C17—22no—
313C23×C17—41no—
314C23×C17—41no—
315C23×C17—41no—
316C23×C17—41no—
317C23×C17—41no—
318C23×C17—41no—
319C23×C17—41no—
320C23×C17—41no—
321C23×C17—41no—
322C23×C17—41no—
323C23×C17—41no—
324C23×C17—41no—
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×C17C23×C411yescharacteristic
342C23×C17C22×D411yescharacteristic
343C23×C17C22×D411yescharacteristic
344C23×C17C2×#4111yescharacteristic
345C23×C17C2×#4111yescharacteristic
346C23×C17C2×#4111yescharacteristic
347C23×C17C2×#4111yescharacteristic
348C23×C17C2×#4111yescharacteristic
349C23×C17C2×#4111yescharacteristic
350C23×C17C2×#4111yescharacteristic
351C23×C17C2×#4111yescharacteristic
352C23×C17H(5,𝔽2)11yescharacteristic
353C23×C17H(5,𝔽2)11yescharacteristic
354C23×C17H(5,𝔽2)11yescharacteristic
355C23×C17H(5,𝔽2)11yescharacteristic
356C22×D17—22no—
357C22×D17—22no—
358C22×D17—22no—
359C22×D17—22no—
360C22×D17—22no—
361C22×D17—22no—
362C22×D17—22no—
363C22×D17—22no—
364C22×D17—22no—
365C22×D17—22no—
366C22×D17—22no—
367C22×D17—22no—
368C22×D17—22no—
369C22×D17—22no—
370C22×D17—22no—
371C22×D17—22no—
372C22×D17—22no—
373C22×D17—22no—
374C22×D17—41no—
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×D17C4×D414yes—
391C2×C4×C17—22no—
392C2×C4×C17—22no—
393C2×C4×C17—22no—
394C2×C4×C17—22no—
395C2×C4×C17—22no—
396C2×C4×C17—22no—
397C2×C4×C17—22no—
398C2×C4×C17—22no—
399C2×C4×C17—22no—
400C2×C4×C17—22no—
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—41no—
410C2×C4×C17—41no—
411C2×C4×C17—41no—
412C2×C4×C17—41no—
413C2×C4×C17—41no—
414C2×C4×C17—41no—
415C2×C4×C17—41no—
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×C17C4×D414yes—
432C2×C4×C17#12114yes—
433C22⋊D17—416no—
434C2×Dic17—22no—
435C2×Dic17—22no—
436C2×Dic17—22no—
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—41no—
459C2×Dic17—41no—
460C2×Dic17—41no—
461C2×Dic17—41no—
462C2×Dic17—41no—
463C2×Dic17—41no—
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#11714yes—
483C4×D17—416no—
484C2×#390—171no—
485C2×#388—171no—
486C2×#388D1711yescharacteristic, complemented
487C2×#386—171no—
488C2×C4×C22⋊C4—171no—
489#1442—171no—
490#1440—171no—
491#1440—171no—
492#1438—171no—
493#1437—171no—
494#1437—171no—
495#1436—171no—
496#1436—171no—
497C22⋊#95—171no—
498C4×#95—171no—
499C22×C17—42no—
500C22×C17—42no—
501C22×C17—42no—
502C22×C17—42no—
503C22×C17—42no—
504C22×C17—42no—
505C22×C17—42no—
506C22×C17—81no—
507C22×C17—81no—
508C22×C17—81no—
509C22×C17—81no—
510C22×C17—81no—
511C22×C17—81no—
512C22×C17—81no—
513C22×C17—81no—
514C22×C17C2×#11711yescharacteristic
515C22×C17C2×C4×D411yescharacteristic
516C22×C17C2×C4×D411yescharacteristic
517C22×C17C4×#4111yescharacteristic
518C22×C17C4×#4111yescharacteristic
519C22×C17#51811yescharacteristic
520C22×C17#51811yescharacteristic
521C22×C17C2×#12111yescharacteristic
522C22×C17#52511yescharacteristic
523C22×C17#52911yescharacteristic
524C22×C17#52911yescharacteristic
525C22×C17#52911yescharacteristic
526C22×C17#53211yescharacteristic
527C22×C17#53211yescharacteristic
528C22×C17#53211yescharacteristic
529C22×C17#53411yescharacteristic
530C22×C17#53511yescharacteristic
531C22×C17#53811yescharacteristic
532C22×C17#53811yescharacteristic
533C22×C17#54611yescharacteristic
534C22×C17#54611yescharacteristic
535C22×C17#54611yescharacteristic
536C22×C17#54611yescharacteristic
537C22×C17#55111yescharacteristic
538C22×C17#55111yescharacteristic
539C22×C17#55111yescharacteristic
540C22×C17#55311yescharacteristic
541C22×C17#55311yescharacteristic
542C22×C17#55311yescharacteristic
543C22×C17#55311yescharacteristic
544C22×C17#55311yescharacteristic
545C22×C17#55311yescharacteristic
546C22×C17#55911yescharacteristic
547C22×C17#55911yescharacteristic
548C22×C17#55911yescharacteristic
549C2×D17—24no—
550C2×D17—24no—
551C2×D17—24no—
552C2×D17—42no—
553C2×D17—42no—
554C2×D17—42no—
555C2×D17—42no—
556C2×D17—42no—
557C2×D17—42no—
558C2×D17—42no—
559C2×D17—42no—
560C2×D17—42no—
561C2×D17—42no—
562C2×D17—42no—
563C2×D17—42no—
564C4×C17—24no—
565C4×C17—24no—
566C4×C17—42no—
567C4×C17—42no—
568C4×C17—81no—
569C4×C17—81no—
570Dic17—24no—
571Dic17—42no—
572Dic17—42no—
573Dic17—42no—
574Dic17—42no—
575Dic17—42no—
576Dic17—42no—
577C23×D4—171no—
578C24×C4—171no—
579C22×C4⋊C4—171no—
580C22×C4⋊C4C2×D1711yescharacteristic
581C22×C22⋊C4—171no—
582C22×C22⋊C4—171no—
583C22×C22⋊C4—171no—
584C22×C22⋊C4—171no—
585C22×C22⋊C4—171no—
586C22×C22⋊C4—171no—
587C22×C22⋊C4—171no—
588C22×C22⋊C4—171no—
589C22×C22⋊C4C2×D1711yescharacteristic
590C22×C22⋊C4C2×D1711yescharacteristic
591C22×C22⋊C4C2×D1711yescharacteristic
592C22×C42—171no—
593C22×C42—171no—
594C22×C42—171no—
595C22×C42C2×D1711yescharacteristic
596#390—344no—
597#388—24no—
598#388—344no—
599#386—178no—
600C4×C22⋊C4—344no—
601C2×#95—171no—
602C2×#95—171no—
603C2×#95—171no—
604C2×#95—171no—
605C2×#95—171no—
606C2×#95—171no—
607C2×#95—171no—
608C2×#95—171no—
609C2×#95—171no—
610C2×#95—171no—
611C2×#95—171no—
612C2×#95—171no—
613C2×#95—171no—
614C2×#95—171no—
615C2×#95C2×D1711yescharacteristic
616C2×#95C2×D1711yescharacteristic
617C2×C17—82no—
618C2×C17#229311yescharacteristic
619C2×C17C4×#12111yescharacteristic
620C2×C17#232111yescharacteristic
621C2×C17#234211yescharacteristic
622C2×C17#235711yescharacteristic
623C2×C17#236411yescharacteristic
624C2×C17#237411yescharacteristic
625C2×C17#254311yescharacteristic
626C2×C17#254411yescharacteristic
627C2×C17#255711yescharacteristic
628C2×C17#255911yescharacteristic
629C2×C17#259511yescharacteristic
630C2×C17#259711yescharacteristic
631C2×C17#260211yescharacteristic
632C2×C17#260311yescharacteristic
633D17—44no—
634C25—171no—
635C25C22×D1711yescharacteristic
636C22×D4—174no—
637C22×D4—342no—
638C22×D4—342no—
639C22×D4—342no—
640C22×D4—342no—
641C22×D4—681no—
642C22×D4—681no—
643C23×C4—171no—
644C23×C4—171no—
645C23×C4—171no—
646C23×C4—171no—
647C23×C4—171no—
648C23×C4—171no—
649C23×C4—171no—
650C23×C4—174no—
651C23×C4—342no—
652C23×C4—342no—
653C23×C4—681no—
654C23×C4—681no—
655C23×C4—681no—
656C23×C4—681no—
657C23×C4C22×D1711yescharacteristic
658C23×C4C22×D1711yescharacteristic
659C23×C4C22×D1711yescharacteristic
660C23×C4C22×D1711yescharacteristic
661C23×C4C22×D1711yescharacteristic
662C23×C4C22×D1711yescharacteristic
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—342no—
667C2×C4⋊C4—342no—
668C2×C4⋊C4—681no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—41no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—174no—
678C2×C22⋊C4—174no—
679C2×C22⋊C4—174no—
680C2×C22⋊C4—342no—
681C2×C22⋊C4—342no—
682C2×C22⋊C4—342no—
683C2×C22⋊C4—342no—
684C2×C22⋊C4—342no—
685C2×C22⋊C4—342no—
686C2×C22⋊C4—342no—
687C2×C22⋊C4—342no—
688C2×C22⋊C4—342no—
689C2×C22⋊C4—342no—
690C2×C22⋊C4—342no—
691C2×C22⋊C4—342no—
692C2×C22⋊C4—342no—
693C2×C22⋊C4—342no—
694C2×C22⋊C4—342no—
695C2×C22⋊C4—681no—
696C2×C22⋊C4—681no—
697C2×C22⋊C4—681no—
698C2×C22⋊C4—681no—
699C2×C22⋊C4—681no—
700C2×C22⋊C4—681no—
701C2×C22⋊C4C4×D1714yes—
702C2×C42—41no—
703C2×C42—41no—
704C2×C42—342no—
705C2×C42—342no—
706C2×C42—342no—
707C2×C42—342no—
708C2×C42—342no—
709C2×C42—681no—
710C2×C42—681no—
711C2×C42—681no—
712C2×C42—681no—
713C2×C42C22⋊D1714yescomplemented
714#95—22no—
715#95—22no—
716#95—174no—
717#95—174no—
718#95—342no—
719#95—342no—
720#95—342no—
721#95—342no—
722#95—342no—
723#95—342no—
724#95—342no—
725#95—342no—
726#95—342no—
727#95—681no—
728#95—681no—
729#95—681no—
730C17#1407611yescharacteristic, complemented, Sylow
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—172no—
746C24—172no—
747C24—172no—
748C24—341no—
749C24—341no—
750C24—341no—
751C24—341no—
752C24—341no—
753C24—341no—
754C24—341no—
755C24—341no—
756C24—341no—
757C24—341no—
758C24—341no—
759C24—341no—
760C24C2×C4×D1712yes—
761C24C23×D1711yescharacteristic
762C2×D4—348no—
763C2×D4—348no—
764C2×D4—684no—
765C2×D4—684no—
766C2×D4—684no—
767C2×D4—684no—
768C2×D4—684no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
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—172no—
804C22×C4—172no—
805C22×C4—172no—
806C22×C4—172no—
807C22×C4—172no—
808C22×C4—172no—
809C22×C4—172no—
810C22×C4—172no—
811C22×C4—172no—
812C22×C4—341no—
813C22×C4—341no—
814C22×C4—341no—
815C22×C4—341no—
816C22×C4—341no—
817C22×C4—341no—
818C22×C4—341no—
819C22×C4—341no—
820C22×C4—341no—
821C22×C4—341no—
822C22×C4—341no—
823C22×C4—341no—
824C22×C4—341no—
825C22×C4—341no—
826C22×C4—341no—
827C22×C4—341no—
828C22×C4—341no—
829C22×C4—341no—
830C22×C4—341no—
831C22×C4—341no—
832C22×C4—341no—
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—341no—
846C22×C4—341no—
847C22×C4—341no—
848C22×C4—341no—
849C22×C4—341no—
850C22×C4—341no—
851C22×C4—341no—
852C22×C4—348no—
853C22×C4—684no—
854C22×C4—684no—
855C22×C4—684no—
856C22×C4—684no—
857C22×C4—684no—
858C22×C4—684no—
859C22×C4C2×C4×D1712yes—
860C22×C4C2×C4×D1712yes—
861C22×C4#6325212yes—
862C22×C4D4×D1712yes—
863C22×C4#6325412yes—
864C22×C4C2×C22⋊D1712yes—
865C22×C4C2×C22⋊D1712yes—
866C22×C4C2×C22⋊D1712yes—
867C4⋊C4—44no—
868C4⋊C4—684no—
869C22⋊C4—28no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—348no—
873C22⋊C4—348no—
874C22⋊C4—348no—
875C22⋊C4—684no—
876C22⋊C4—684no—
877C22⋊C4—684no—
878C22⋊C4—684no—
879C22⋊C4—684no—
880C42—44no—
881C42—684no—
882C42—684no—
883C42—684no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—174no—
920C23—342no—
921C23—342no—
922C23—342no—
923C23—342no—
924C23—342no—
925C23—342no—
926C23—342no—
927C23—342no—
928C23—342no—
929C23—342no—
930C23—342no—
931C23—342no—
932C23—342no—
933C23—342no—
934C23—342no—
935C23—342no—
936C23—342no—
937C23—342no—
938C23—681no—
939C23—681no—
940C23—681no—
941C23—681no—
942C23—681no—
943C23—681no—
944C23—681no—
945C23—681no—
946C23—681no—
947C23—681no—
948C23—681no—
949C23—681no—
950C23—681no—
951C23—681no—
952C23—681no—
953C23—681no—
954C23C22×C4×D1711yescharacteristic
955C23C2×#6325211yescharacteristic
956C23C2×D4×D1711yescharacteristic
957C23C2×#6325411yescharacteristic
958C23#1058769111yescharacteristic
959C23#1058769111yescharacteristic
960C23#41×D1711yescharacteristic
961C23#41×D1711yescharacteristic
962C23#41×D1711yescharacteristic
963C23#41×D1711yescharacteristic
964C23#41×D1711yescharacteristic
965C23#41×D1711yescharacteristic
966C23#1058769611yescharacteristic
967C23#1058769611yescharacteristic
968C23C22×C22⋊D1711yescharacteristic
969D4—6816no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—174no—
1011C2×C4—342no—
1012C2×C4—342no—
1013C2×C4—342no—
1014C2×C4—342no—
1015C2×C4—342no—
1016C2×C4—342no—
1017C2×C4—342no—
1018C2×C4—342no—
1019C2×C4—342no—
1020C2×C4—342no—
1021C2×C4—342no—
1022C2×C4—342no—
1023C2×C4—342no—
1024C2×C4—342no—
1025C2×C4—342no—
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—6816no—
1036C2×C4—681no—
1037C2×C4—681no—
1038C2×C4—681no—
1039C2×C4—681no—
1040C2×C4—681no—
1041C2×C4—681no—
1042C2×C4—681no—
1043C2×C4—681no—
1044C2×C4—681no—
1045C2×C4—681no—
1046C2×C4—681no—
1047C2×C4—681no—
1048C2×C4—681no—
1049C2×C4—681no—
1050C2×C4—681no—
1051C2×C4—681no—
1052C2×C4—681no—
1053C2×C4—681no—
1054C2×C4—681no—
1055C2×C4—681no—
1056C2×C4—681no—
1057C2×C4—681no—
1058C2×C4—681no—
1059C2×C4—681no—
1060C2×C4C4×C22⋊D1714yes—
1061C2×C4#1058762414yes—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—344no—
1078C22—344no—
1079C22—344no—
1080C22—682no—
1081C22—682no—
1082C22—682no—
1083C22—682no—
1084C22—682no—
1085C22—682no—
1086C22—682no—
1087C22—682no—
1088C22—682no—
1089C22—682no—
1090C22—682no—
1091C22—682no—
1092C22#117×D1711yescharacteristic
1093C22C4×D4×D1711yescharacteristic
1094C22C2×C4×C22⋊D1711yescharacteristic
1095C22C4×#6325411yescharacteristic
1096C22#1176327711yescharacteristic
1097C22#1176328111yescharacteristic
1098C22#1176328111yescharacteristic
1099C22C2×#1058762411yescharacteristic
1100C22#1176331611yescharacteristic
1101C22#1176333711yescharacteristic
1102C22#1176333711yescharacteristic
1103C22#1176334111yescharacteristic
1104C22#1176335511yescharacteristic
1105C22#1176335511yescharacteristic
1106C22#1176335611yescharacteristic
1107C22#1176336811yescharacteristic
1108C22#1176337311yescharacteristic
1109C22#1176339211yescharacteristic
1110C22#1176339211yescharacteristic
1111C22#1176344811yescharacteristic
1112C22#1176344811yescharacteristic
1113C22#1176345211yescharacteristic
1114C22#1176345211yescharacteristic
1115C22#1176348411yescharacteristic
1116C22#1176348411yescharacteristic
1117C22#1176348711yescharacteristic
1118C22#1176350211yescharacteristic
1119C22#1176350211yescharacteristic
1120C22#1176350411yescharacteristic
1121C22#1176350411yescharacteristic
1122C22#1176351011yescharacteristic
1123C22#1176351011yescharacteristic
1124C22#1176354111yescharacteristic
1125C22#1176354111yescharacteristic
1126C22#1176354311yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—81no—
1132C4—81no—
1133C4—344no—
1134C4—682no—
1135C4—682no—
1136C4—682no—
1137C4—682no—
1138C4—682no—
1139C4—682no—
1140C2—82no—
1141C2—684no—
1142C2#1453124311yescharacteristic
1143C2C4×#1058762411yescharacteristic
1144C2#1453143811yescharacteristic
1145C2#1453163211yescharacteristic
1146C2#1453175411yescharacteristic
1147C2#1453182811yescharacteristic
1148C2#1453191211yescharacteristic
1149C2#1453374611yescharacteristic
1150C2#1453375611yescharacteristic
1151C2#1453388511yescharacteristic
1152C2#1453391511yescharacteristic
1153C2#1453430711yescharacteristic
1154C2#1453433711yescharacteristic
1155C2#1453439811yescharacteristic
1156C2#1453441311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×#388D17
hypocenterC17#14076
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#11762699C2semidirect
4. C2×C4×#63227C2semidirect
5. #14527039C2semidirect
6. #14527032C2semidirect
7. #14527031C2semidirect
9. #14527021C2semidirect
10. #14527021C2semidirect
11. #14527016C2semidirect
12. #14527015C2semidirect
13. #14527005C2semidirect
14. C4×#10587502C2semidirect
15. C2×C17×#388C2semidirect
32. #11762685C4semidirect
99. C2×C42×C17D4semidirect
486. C2×#388D17semidirect
713. C2×C42C22⋊D17semidirect
730. C17#14076semidirect

Maximal subgroups

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

subgroupindex
C2×#117627092
C2×#117626992
C2×#117626852
C2×C4×#632272
#145270392
#145270322
#145270312
#145270232
#145270212
#145270162
#145270152
#145270052
C4×#105875022
C2×C17×#3882
#1407617