Finite Group Databasebeta

← #16964271

Subgroups — #16964271

Order 4352.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762725C211yesmaximal, characteristic
2C2×#11762709C211yesmaximal, characteristic
3C2×#11762707C211yesmaximal, characteristic, complemented
4C2×#11762701C211yesmaximal, characteristic, complemented
5#14527029C211yesmaximal, characteristic, complemented
6#14527028C211yesmaximal, characteristic, complemented
7#14527027C211yesmaximal, characteristic, complemented
8#14527026C211yesmaximal, characteristic, complemented
9#14527023C211yesmaximal, characteristic
10#14527022C211yesmaximal, characteristic, complemented
11#14527021C211yesmaximal, characteristic, complemented
12#14527018C211yesmaximal, characteristic, complemented
13#14527016C211yesmaximal, characteristic, complemented
14#14527015C211yesmaximal, characteristic, complemented
15C2×C17×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32#11762725C418yescomplemented
33#11762709—24no—
34#11762707—24no—
35#11762701—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
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—41no—
67C22×C22⋊D17—41no—
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
78C2×C4⋊C4×C17—22no—
79C2×C4⋊C4×C17—22no—
80C2×C4⋊C4×C17—41no—
81C2×C22⋊C4×C17—22no—
82C2×C22⋊C4×C17—22no—
83C2×C22⋊C4×C17—22no—
84C2×C22⋊C4×C17—22no—
85C2×C22⋊C4×C17—22no—
86C2×C22⋊C4×C17—22no—
87C2×C22⋊C4×C17—41no—
88C2×C22⋊C4×C17—41no—
89C2×C22⋊C4×C17C2×C414yes—
90C2×C42×C17—22no—
91C2×C42×C17—22no—
92C2×C42×C17—41no—
93C2×C22⋊Dic17—22no—
94C2×C22⋊Dic17—22no—
95C2×C22⋊Dic17—41no—
96C2×C22⋊Dic17—41no—
97C2×C22⋊Dic17—41no—
98C2×C22⋊Dic17—41no—
99C2×C22⋊Dic17—41no—
100C2×C22⋊Dic17—41no—
101C2×C22⋊Dic17C2×C414yes—
102C2×#63227—22no—
103C2×#63227—22no—
104C2×#63227—22no—
105C2×#63227—22no—
106C2×#63227—22no—
107C2×#63227—22no—
108C2×#63227—22no—
109C2×#63227—22no—
110C2×#63227—41no—
111C2×#63227—41no—
112C2×#63227—41no—
113C2×#63227—41no—
114C2×#63227—41no—
115C2×#63227—41no—
116C2×#63227—41no—
117C2×#63227—41no—
118C2×#63227C2×C414yes—
119C2×#63227C2×C414yes—
120C2×C4⋊Dic17—22no—
121C2×C4⋊Dic17—22no—
122C2×C4⋊Dic17—22no—
123C2×C4⋊Dic17—22no—
124C2×C4⋊Dic17—41no—
125C2×C4⋊Dic17C2×C414yes—
126C2×#63225—22no—
127C2×#63225—41no—
128C2×#63225—41no—
129C2×#63225—41no—
130C2×#63225—41no—
131C2×#63225D414yes—
132C2×C4×Dic17—22no—
133C2×C4×Dic17—22no—
134C2×C4×Dic17—41no—
135C2×C4×Dic17—41no—
136C2×C4×Dic17—41no—
137C2×C4×Dic17—41no—
138C17×#95—22no—
139C17×#95D414yescomplemented
140#10587502—22no—
141#10587502—22no—
142#10587502—22no—
143#10587502—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—41no—
147#10587502—41no—
148#10587502—41no—
149#10587502—41no—
150#10587502—41no—
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×D17—21no—
181C23×D17—21no—
182C23×D17C22×C412yes—
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—44no—
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×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17C22×C412yes—
275C22×Dic17C22×C412yes—
276C22×Dic17C22×C412yes—
277C22×Dic17C2×D412yes—
278C22×Dic17C2×D412yes—
279C22×Dic17#4112yes—
280C22×Dic17#4112yes—
281C4⋊C4×C17—44no—
282C22⋊C4×C17—28no—
283C22⋊C4×C17—44no—
284C22⋊C4×C17—44no—
285C42×C17—44no—
286C22⋊Dic17—44no—
287C22⋊Dic17—44no—
288C22⋊Dic17—44no—
289#63227—28no—
290#63227—44no—
291#63227—44no—
292#63227—44no—
293#63227—44no—
294#63227—44no—
295C4⋊Dic17—28no—
296C4⋊Dic17—44no—
297#63225—44no—
298#63225—44no—
299C4×Dic17—44no—
300C4×Dic17—44no—
301#14563—171nomaximal, Sylow
302C23×C17—22no—
303C23×C17—22no—
304C23×C17—22no—
305C23×C17—22no—
306C23×C17—22no—
307C23×C17—22no—
308C23×C17—22no—
309C23×C17—41no—
310C23×C17—41no—
311C23×C17—41no—
312C23×C17—41no—
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×C17C23×C411yescharacteristic
338C23×C17C22×D411yescharacteristic
339C23×C17C22×D411yescharacteristic
340C23×C17C2×#4111yescharacteristic
341C23×C17C2×#4111yescharacteristic
342C23×C17C2×#4111yescharacteristic
343C23×C17C2×#4111yescharacteristic
344C23×C17H(5,𝔽2)11yescharacteristic
345C23×C17H(5,𝔽2)11yescharacteristic
346C23×C17H(5,𝔽2)11yescharacteristic
347C23×C17H(5,𝔽2)11yescharacteristic
348C23×C17H(5,𝔽2)11yescharacteristic
349C23×C17H(5,𝔽2)11yescharacteristic
350C23×C172−1+411yescharacteristic
351C23×C172−1+411yescharacteristic
352C22×D17—22no—
353C22×D17—22no—
354C22×D17—22no—
355C22×D17—22no—
356C22×D17—22no—
357C22×D17—22no—
358C22×D17—22no—
359C22×D17—41no—
360C22×D17—41no—
361C22×D17—41no—
362C22×D17—41no—
363C22×D17—41no—
364C22×D17—41no—
365C22×D17—41no—
366C22×D17—41no—
367C22×D17—41no—
368C22×D17—41no—
369C22×D17—41no—
370C22×D17—41no—
371C22×D17—41no—
372C22×D17—41no—
373C22×D17—41no—
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—
387C2×C4×C17—22no—
388C2×C4×C17—22no—
389C2×C4×C17—22no—
390C2×C4×C17—22no—
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—41no—
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×C17C4×D414yes—
429C22⋊D17—416no—
430C2×Dic17—22no—
431C2×Dic17—22no—
432C2×Dic17—22no—
433C2×Dic17—22no—
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—41no—
449C2×Dic17—41no—
450C2×Dic17—41no—
451C2×Dic17—41no—
452C2×Dic17—41no—
453C2×Dic17—41no—
454C2×Dic17—41no—
455C2×Dic17—41no—
456C2×Dic17—41no—
457C2×Dic17—41no—
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×Dic17C4×D414yes—
479C2×#394—171no—
480C2×#390—171no—
481C2×#389—171no—
482C2×#388—171no—
483C2×#388D1711yescharacteristic, complemented
484#1439—171no—
485#1439—171no—
486#1439—171no—
487#1439—171no—
488#1438—171no—
489#1437—171no—
490#1437—171no—
491#1436—171no—
492#1436—171no—
493#1436—171no—
494C22×C17—42no—
495C22×C17—42no—
496C22×C17—42no—
497C22×C17—42no—
498C22×C17—42no—
499C22×C17—42no—
500C22×C17—42no—
501C22×C17—81no—
502C22×C17—81no—
503C22×C17—81no—
504C22×C17—81no—
505C22×C17—81no—
506C22×C17—81no—
507C22×C17—81no—
508C22×C17—81no—
509C22×C17C2×C4×D411yescharacteristic
510C22×C17C2×C4×D411yescharacteristic
511C22×C17C4×#4111yescharacteristic
512C22×C17#51811yescharacteristic
513C22×C17#51811yescharacteristic
514C22×C17#52011yescharacteristic
515C22×C17#52011yescharacteristic
516C22×C17#53411yescharacteristic
517C22×C17#53511yescharacteristic
518C22×C17#53511yescharacteristic
519C22×C17#53711yescharacteristic
520C22×C17#53811yescharacteristic
521C22×C17#53811yescharacteristic
522C22×C17#53811yescharacteristic
523C22×C17#53911yescharacteristic
524C22×C17#54011yescharacteristic
525C22×C17#54011yescharacteristic
526C22×C17#54211yescharacteristic
527C22×C17#54211yescharacteristic
528C22×C17D4211yescharacteristic
529C22×C17#54611yescharacteristic
530C22×C17#54611yescharacteristic
531C22×C17#54711yescharacteristic
532C22×C17#54811yescharacteristic
533C22×C17#54811yescharacteristic
534C22×C17#55011yescharacteristic
535C22×C17#55311yescharacteristic
536C22×C17#55311yescharacteristic
537C22×C17#55511yescharacteristic
538C22×C17#55611yescharacteristic
539C22×C17#55911yescharacteristic
540C22×C17#56011yescharacteristic
541C22×C17#56211yescharacteristic
542C22×C17#56211yescharacteristic
543C22×C17#56311yescharacteristic
544C2×D17—42no—
545C2×D17—42no—
546C2×D17—42no—
547C2×D17—42no—
548C2×D17—42no—
549C2×D17—42no—
550C2×D17—42no—
551C2×D17—81no—
552C2×D17—81no—
553C2×D17—81no—
554C2×D17—81no—
555C2×D17—81no—
556C2×D17—81no—
557C2×D17—81no—
558C2×D17—81no—
559C4×C17—24no—
560C4×C17—42no—
561C4×C17—42no—
562C4×C17—42no—
563C4×C17—42no—
564C4×C17—42no—
565Dic17—24no—
566Dic17—42no—
567Dic17—42no—
568Dic17—42no—
569Dic17—42no—
570Dic17—81no—
571Dic17—81no—
572C23×D4—171no—
573C22×C4⋊C4—171no—
574C22×C4⋊C4—171no—
575C22×C4⋊C4—171no—
576C22×C4⋊C4—171no—
577C22×C4⋊C4C2×D1711yescharacteristic
578C22×C22⋊C4—171no—
579C22×C22⋊C4—171no—
580C22×C22⋊C4—171no—
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⋊C4C2×D1711yescharacteristic
588C22×C22⋊C4C2×D1711yescharacteristic
589C22×C22⋊C4C2×D1711yescharacteristic
590C22×C42—171no—
591C22×C42—171no—
592C22×C42C2×D1711yescharacteristic
593#394—178no—
594#390—344no—
595#389—344no—
596#388—24no—
597#388—344no—
598C2×#95—171no—
599C2×#95—171no—
600C2×#95—171no—
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×#95C2×D1711yescharacteristic
611C2×#95C2×D1711yescharacteristic
612C2×C17—82no—
613C2×C17#232111yescharacteristic
614C2×C17#232411yescharacteristic
615C2×C17#233511yescharacteristic
616C2×C17#236111yescharacteristic
617C2×C17#236311yescharacteristic
618C2×C17#236711yescharacteristic
619C2×C17#237611yescharacteristic
620C2×C17#267311yescharacteristic
621C2×C17#267611yescharacteristic
622C2×C17#271011yescharacteristic
623C2×C17#271111yescharacteristic
624C2×C17#272711yescharacteristic
625C2×C17#273111yescharacteristic
626C2×C17#280011yescharacteristic
627C2×C17#280311yescharacteristic
628D17—82no—
629C25—171no—
630C25C22×D1711yescharacteristic
631C22×D4—174no—
632C22×D4—342no—
633C22×D4—342no—
634C22×D4—681no—
635C22×D4—681no—
636C22×D4—681no—
637C22×D4—681no—
638C23×C4—171no—
639C23×C4—171no—
640C23×C4—171no—
641C23×C4—171no—
642C23×C4—171no—
643C23×C4—171no—
644C23×C4—171no—
645C23×C4C22×D1711yescharacteristic
646C23×C4C22×D1711yescharacteristic
647C23×C4C22×D1711yescharacteristic
648C23×C4C22×D1711yescharacteristic
649C23×C4C22×D1711yescharacteristic
650C23×C4C22×D1711yescharacteristic
651C2×C4⋊C4—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—174no—
655C2×C4⋊C4—174no—
656C2×C4⋊C4—342no—
657C2×C4⋊C4—342no—
658C2×C4⋊C4—342no—
659C2×C4⋊C4—342no—
660C2×C4⋊C4—342no—
661C2×C4⋊C4—681no—
662C2×C4⋊C4—681no—
663C2×C4⋊C4—681no—
664C2×C4⋊C4—681no—
665C2×C4⋊C4—681no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—174no—
675C2×C22⋊C4—174no—
676C2×C22⋊C4—174no—
677C2×C22⋊C4—342no—
678C2×C22⋊C4—342no—
679C2×C22⋊C4—342no—
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—681no—
688C2×C22⋊C4—681no—
689C2×C22⋊C4—681no—
690C2×C22⋊C4—681no—
691C2×C22⋊C4—681no—
692C2×C22⋊C4—681no—
693C2×C22⋊C4—681no—
694C2×C22⋊C4—681no—
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—22no—
703C2×C42—22no—
704C2×C42—41no—
705C2×C42—342no—
706C2×C42—342no—
707C2×C42—681no—
708C2×C42—681no—
709C2×C42—681no—
710C2×C42—681no—
711#95—22no—
712#95—174no—
713#95—342no—
714#95—342no—
715#95—342no—
716#95—342no—
717#95—342no—
718#95—342no—
719#95—681no—
720#95—681no—
721#95—681no—
722#95—681no—
723#95—681no—
724#95C22⋊D1714yescomplemented
725C17#1456311yescharacteristic, complemented, Sylow
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—172no—
741C24—341no—
742C24—341no—
743C24—341no—
744C24—341no—
745C24—341no—
746C24—341no—
747C24—341no—
748C24—341no—
749C24—341no—
750C24—341no—
751C24—341no—
752C24—341no—
753C24—341no—
754C24—341no—
755C24C2×C4×D1712yes—
756C24C23×D1711yescharacteristic
757C2×D4—348no—
758C2×D4—684no—
759C2×D4—684no—
760C2×D4—684no—
761C2×D4—684no—
762C2×D4—684no—
763C2×D4—684no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
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—172no—
799C22×C4—172no—
800C22×C4—172no—
801C22×C4—172no—
802C22×C4—172no—
803C22×C4—172no—
804C22×C4—172no—
805C22×C4—341no—
806C22×C4—341no—
807C22×C4—341no—
808C22×C4—341no—
809C22×C4—341no—
810C22×C4—341no—
811C22×C4—341no—
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×C4C2×C4×D1712yes—
848C22×C4C2×C4×D1712yes—
849C22×C4#6325212yes—
850C22×C4D4×D1712yes—
851C22×C4#6325412yes—
852C22×C4C2×C22⋊D1712yes—
853C22×C4C2×C22⋊D1712yes—
854C22×C4C2×C22⋊D1712yes—
855C4⋊C4—44no—
856C4⋊C4—348no—
857C4⋊C4—684no—
858C4⋊C4—684no—
859C4⋊C4—684no—
860C22⋊C4—28no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—348no—
864C22⋊C4—684no—
865C22⋊C4—684no—
866C22⋊C4—684no—
867C22⋊C4—684no—
868C22⋊C4—684no—
869C22⋊C4—684no—
870C22⋊C4—684no—
871C22⋊C4—684no—
872C42—44no—
873C42—684no—
874C42—684no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
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—342no—
911C23—342no—
912C23—342no—
913C23—342no—
914C23—342no—
915C23—342no—
916C23—342no—
917C23—681no—
918C23—681no—
919C23—681no—
920C23—681no—
921C23—681no—
922C23—681no—
923C23—681no—
924C23—681no—
925C23—681no—
926C23—681no—
927C23—681no—
928C23—681no—
929C23—681no—
930C23—681no—
931C23—681no—
932C23—681no—
933C23—681no—
934C23—681no—
935C23—681no—
936C23—681no—
937C23—681no—
938C23—681no—
939C23—681no—
940C23—681no—
941C23—681no—
942C23—681no—
943C23—681no—
944C23—681no—
945C23C22×C4×D1711yescharacteristic
946C23C2×#6325211yescharacteristic
947C23C2×D4×D1711yescharacteristic
948C23C2×#6325411yescharacteristic
949C23#1058769111yescharacteristic
950C23#1058769111yescharacteristic
951C23#41×D1711yescharacteristic
952C23#41×D1711yescharacteristic
953C23#1058769611yescharacteristic
954C23#1058769611yescharacteristic
955C23#1058769611yescharacteristic
956C23#1058769611yescharacteristic
957C23#1058769711yescharacteristic
958C23#1058769711yescharacteristic
959C23C22×C22⋊D1711yescharacteristic
960D4—6816no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
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—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
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—174no—
1003C2×C4—342no—
1004C2×C4—342no—
1005C2×C4—342no—
1006C2×C4—342no—
1007C2×C4—342no—
1008C2×C4—342no—
1009C2×C4—342no—
1010C2×C4—342no—
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—681no—
1022C2×C4—681no—
1023C2×C4—681no—
1024C2×C4—681no—
1025C2×C4—681no—
1026C2×C4—681no—
1027C2×C4—681no—
1028C2×C4—681no—
1029C2×C4—681no—
1030C2×C4—681no—
1031C2×C4—681no—
1032C2×C4—681no—
1033C2×C4—681no—
1034C2×C4—681no—
1035C2×C4—681no—
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×C4C4×C22⋊D1714yes—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—682no—
1068C22—682no—
1069C22—682no—
1070C22—682no—
1071C22—682no—
1072C22—682no—
1073C22—682no—
1074C22—1361no—
1075C22—1361no—
1076C22—1361no—
1077C22—1361no—
1078C22—1361no—
1079C22—1361no—
1080C22—1361no—
1081C22—1361no—
1082C22C4×D4×D1711yescharacteristic
1083C22C2×C4×C22⋊D1711yescharacteristic
1084C22C4×#6325411yescharacteristic
1085C22#1176328111yescharacteristic
1086C22#1176328311yescharacteristic
1087C22#1176328811yescharacteristic
1088C22#1176328911yescharacteristic
1089C22#1176337011yescharacteristic
1090C22#1176337311yescharacteristic
1091C22#1176337511yescharacteristic
1092C22#1176338711yescharacteristic
1093C22#1176339311yescharacteristic
1094C22#1176339611yescharacteristic
1095C22#1176339811yescharacteristic
1096C22#1176340011yescharacteristic
1097C22#1176341111yescharacteristic
1098C22#1176341411yescharacteristic
1099C22#1176342811yescharacteristic
1100C22#1176343011yescharacteristic
1101C22D4×C22⋊D1711yescharacteristic
1102C22#1176345111yescharacteristic
1103C22#1176345311yescharacteristic
1104C22#1176345811yescharacteristic
1105C22#1176346511yescharacteristic
1106C22#1176346811yescharacteristic
1107C22#1176347811yescharacteristic
1108C22#1176350811yescharacteristic
1109C22#1176350911yescharacteristic
1110C22#1176352411yescharacteristic
1111C22#1176352611yescharacteristic
1112C22#1176354111yescharacteristic
1113C22#1176354911yescharacteristic
1114C22#1176355311yescharacteristic
1115C22#1176355411yescharacteristic
1116C22#1176356111yescharacteristic
1117C4—24no—
1118C4—42no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—42no—
1123C4—344no—
1124C4—682no—
1125C4—682no—
1126C4—682no—
1127C4—682no—
1128C4—1361no—
1129C4—1361no—
1130C2—82no—
1131C2—1362no—
1132C2#1453144611yescharacteristic
1133C2#1453147711yescharacteristic
1134C2#1453156711yescharacteristic
1135C2#1453180111yescharacteristic
1136C2#1453181811yescharacteristic
1137C2#1453185811yescharacteristic
1138C2#1453192611yescharacteristic
1139C2#1453505011yescharacteristic
1140C2#1453508511yescharacteristic
1141C2#1453552011yescharacteristic
1142C2#1453554511yescharacteristic
1143C2#1453574211yescharacteristic
1144C2#1453579511yescharacteristic
1145C2#1453667611yescharacteristic
1146C2#1453672011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×#388D17
hypocenterC17#14563
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×#11762707C2semidirect
4. C2×#11762701C2semidirect
5. #14527029C2semidirect
6. #14527028C2semidirect
7. #14527027C2semidirect
8. #14527026C2semidirect
10. #14527022C2semidirect
11. #14527021C2semidirect
12. #14527018C2semidirect
13. #14527016C2semidirect
14. #14527015C2semidirect
15. C2×C17×#388C2semidirect
32. #11762725C4semidirect
139. C17×#95D4semidirect
483. C2×#388D17semidirect
724. #95C22⋊D17semidirect
725. C17#14563semidirect

Maximal subgroups

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

subgroupindex
C2×#117627252
C2×#117627092
C2×#117627072
C2×#117627012
#145270292
#145270282
#145270272
#145270262
#145270232
#145270222
#145270212
#145270182
#145270162
#145270152
C2×C17×#3882
#1456317