Finite Group Databasebeta

← #16962776

Subgroups — #16962776

Order 4352.

1658 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762709C211yesmaximal, characteristic
2C2×#11762701C211yesmaximal, characteristic, complemented
3#14527032C211yesmaximal, characteristic, complemented
4#14527031C211yesmaximal, characteristic, complemented
5#14527029C211yesmaximal, characteristic, complemented
6#14527026C211yesmaximal, characteristic, complemented
7#14527023C211yesmaximal, characteristic
8#14527023C211yesmaximal, characteristic
9#14527022C211yesmaximal, characteristic, complemented
10#14527021C211yesmaximal, characteristic, complemented
11#14527017C211yesmaximal, characteristic, complemented
12#14527015C211yesmaximal, characteristic, complemented
13#14527013C211yesmaximal, characteristic, complemented
14#14527009C211yesmaximal, characteristic, complemented
15C2×C17×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×C22⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30#11762709C418yescomplemented
31#11762701—24no—
32C2×#10587502C2211yescharacteristic
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
46C22×C4⋊C4×C17C2211yescharacteristic
47C22×C22⋊C4×C17C2211yescharacteristic
48C22×C22⋊C4×C17C2211yescharacteristic
49C22×C22⋊C4×C17C2211yescharacteristic
50C22×C42×C17C2211yescharacteristic
51C17×#388—24no—
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C25×C17C2311yescharacteristic
55C24×D17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C22×C22⋊D17—22no—
63C22×C22⋊D17—22no—
64C22×C22⋊D17—41no—
65C22×C22⋊D17—41no—
66C22×C22⋊D17—41no—
67C22×C22⋊D17—41no—
68C22×C22⋊D17C2×C414yes—
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C2×C4⋊C4×C17—22no—
77C2×C4⋊C4×C17—22no—
78C2×C4⋊C4×C17—41no—
79C2×C22⋊C4×C17—22no—
80C2×C22⋊C4×C17—22no—
81C2×C22⋊C4×C17—22no—
82C2×C22⋊C4×C17—22no—
83C2×C22⋊C4×C17—22no—
84C2×C22⋊C4×C17—41no—
85C2×C22⋊C4×C17—41no—
86C2×C22⋊C4×C17—41no—
87C2×C22⋊C4×C17C2×C414yes—
88C2×C42×C17—22no—
89C2×C42×C17—41no—
90C2×C42×C17—41no—
91C2×C22⋊Dic17—22no—
92C2×C22⋊Dic17—41no—
93C2×C22⋊Dic17—41no—
94C2×C22⋊Dic17—41no—
95C2×C22⋊Dic17—41no—
96C2×C22⋊Dic17—41no—
97C2×C22⋊Dic17—41no—
98C2×C22⋊Dic17—41no—
99C2×C22⋊Dic17C2×C414yes—
100C2×#63227—22no—
101C2×#63227—22no—
102C2×#63227—22no—
103C2×#63227—22no—
104C2×#63227—22no—
105C2×#63227—22no—
106C2×#63227—41no—
107C2×#63227—41no—
108C2×#63227—41no—
109C2×#63227—41no—
110C2×#63227—41no—
111C2×#63227—41no—
112C2×#63227—41no—
113C2×#63227—41no—
114C2×#63227—41no—
115C2×#63227—41no—
116C2×#63227C2×C414yes—
117C2×#63227C2×C414yes—
118C2×C4⋊Dic17—22no—
119C2×C4⋊Dic17—22no—
120C2×C4⋊Dic17—41no—
121C2×#63225—41no—
122C2×#63225—41no—
123C2×#63225C2×C414yes—
124C2×C4×Dic17—22no—
125C2×C4×Dic17—41no—
126C2×C4×Dic17—41no—
127C2×C4×Dic17—41no—
128C2×C4×Dic17—41no—
129C2×C4×Dic17C2×C414yes—
130C17×#95—22no—
131C17×#95D414yescomplemented
132#10587502—22no—
133#10587502—22no—
134#10587502—22no—
135#10587502—22no—
136#10587502—22no—
137#10587502—22no—
138#10587502—41no—
139#10587502—41no—
140#10587502—41no—
141#10587502—41no—
142#10587502—41no—
143#10587502—41no—
144#10587502—41no—
145#10587502—41no—
146C24×C17—21no—
147C24×C17—21no—
148C24×C17—21no—
149C24×C17—21no—
150C24×C17—21no—
151C24×C17—21no—
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×C17C22×C412yes—
161C24×C17C2411yescharacteristic
162C23×D17—21no—
163C23×D17—21no—
164C23×D17—21no—
165C23×D17—21no—
166C23×D17—21no—
167C23×D17—21no—
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×D17C22×C412yes—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
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×C17C22×C412yes—
213C22×C4×C17C22×C412yes—
214C22×C4×C17C2×D412yes—
215C22×C4×C17C2×D412yes—
216C22×C4×C17C2×D412yes—
217C22×C4×C17#4112yes—
218C22×C4×C17#4112yes—
219C2×C22⋊D17—28no—
220C2×C22⋊D17—44no—
221C2×C22⋊D17—44no—
222C2×C22⋊D17—44no—
223C2×C22⋊D17—44no—
224C2×C22⋊D17—44no—
225C2×C22⋊D17—44no—
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—21no—
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×Dic17C22×C412yes—
270C22×Dic17C22×C412yes—
271C22×Dic17C22×C412yes—
272C22×Dic17#4112yes—
273C22×Dic17#4112yes—
274C22×Dic17#4112yes—
275C4⋊C4×C17—44no—
276C22⋊C4×C17—28no—
277C22⋊C4×C17—44no—
278C22⋊C4×C17—44no—
279C42×C17—44no—
280C22⋊Dic17—44no—
281C22⋊Dic17—44no—
282C22⋊Dic17—44no—
283#63227—28no—
284#63227—44no—
285#63227—44no—
286#63227—44no—
287#63227—44no—
288#63227—44no—
289C4⋊Dic17—44no—
290#63225—44no—
291C4×Dic17—44no—
292C4×Dic17—44no—
293#14444—171nomaximal, Sylow
294C23×C17—22no—
295C23×C17—22no—
296C23×C17—22no—
297C23×C17—22no—
298C23×C17—22no—
299C23×C17—22no—
300C23×C17—22no—
301C23×C17—41no—
302C23×C17—41no—
303C23×C17—41no—
304C23×C17—41no—
305C23×C17—41no—
306C23×C17—41no—
307C23×C17—41no—
308C23×C17—41no—
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×C17C23×C411yescharacteristic
330C23×C17C22×D411yescharacteristic
331C23×C17C2×#4111yescharacteristic
332C23×C17C2×#4111yescharacteristic
333C23×C17C2×#4111yescharacteristic
334C23×C17C2×#4111yescharacteristic
335C23×C17C2×#4111yescharacteristic
336C23×C17H(5,𝔽2)11yescharacteristic
337C23×C17H(5,𝔽2)11yescharacteristic
338C23×C17H(5,𝔽2)11yescharacteristic
339C23×C17H(5,𝔽2)11yescharacteristic
340C23×C17H(5,𝔽2)11yescharacteristic
341C23×C17H(5,𝔽2)11yescharacteristic
342C23×C17H(5,𝔽2)11yescharacteristic
343C23×C172−1+411yescharacteristic
344C22×D17—22no—
345C22×D17—22no—
346C22×D17—22no—
347C22×D17—22no—
348C22×D17—22no—
349C22×D17—22no—
350C22×D17—22no—
351C22×D17—41no—
352C22×D17—41no—
353C22×D17—41no—
354C22×D17—41no—
355C22×D17—41no—
356C22×D17—41no—
357C22×D17—41no—
358C22×D17—41no—
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—
379C2×C4×C17—22no—
380C2×C4×C17—22no—
381C2×C4×C17—22no—
382C2×C4×C17—22no—
383C2×C4×C17—22no—
384C2×C4×C17—22no—
385C2×C4×C17—22no—
386C2×C4×C17—22no—
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—41no—
398C2×C4×C17—41no—
399C2×C4×C17—41no—
400C2×C4×C17—41no—
401C2×C4×C17—41no—
402C2×C4×C17—41no—
403C2×C4×C17—41no—
404C2×C4×C17—41no—
405C2×C4×C17—41no—
406C2×C4×C17—41no—
407C2×C4×C17—41no—
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×C17C4×D414yes—
421C22⋊D17—416no—
422C2×Dic17—22no—
423C2×Dic17—22no—
424C2×Dic17—22no—
425C2×Dic17—22no—
426C2×Dic17—22no—
427C2×Dic17—22no—
428C2×Dic17—22no—
429C2×Dic17—22no—
430C2×Dic17—22no—
431C2×Dic17—22no—
432C2×Dic17—22no—
433C2×Dic17—22no—
434C2×Dic17—22no—
435C2×Dic17—22no—
436C2×Dic17—22no—
437C2×Dic17—41no—
438C2×Dic17—41no—
439C2×Dic17—41no—
440C2×Dic17—41no—
441C2×Dic17—41no—
442C2×Dic17—41no—
443C2×Dic17—41no—
444C2×Dic17—41no—
445C2×Dic17—41no—
446C2×Dic17—41no—
447C2×Dic17—41no—
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#11714yes—
471C2×#390—171no—
472C2×#388—171no—
473C2×#388D1711yescharacteristic, complemented
474#1440—171no—
475#1440—171no—
476#1439—171no—
477#1439—171no—
478#1438—171no—
479#1438—171no—
480#1437—171no—
481#1437—171no—
482#1436—171no—
483#1436—171no—
484C4⋊#95—171no—
485#1434—171no—
486C22×C17—42no—
487C22×C17—42no—
488C22×C17—42no—
489C22×C17—42no—
490C22×C17—42no—
491C22×C17—42no—
492C22×C17—42no—
493C22×C17—81no—
494C22×C17—81no—
495C22×C17—81no—
496C22×C17—81no—
497C22×C17—81no—
498C22×C17—81no—
499C22×C17—81no—
500C22×C17—81no—
501C22×C17C2×#11711yescharacteristic
502C22×C17C2×C4×D411yescharacteristic
503C22×C17C4×#4111yescharacteristic
504C22×C17#51811yescharacteristic
505C22×C17#51811yescharacteristic
506C22×C17#51811yescharacteristic
507C22×C17#52011yescharacteristic
508C22×C17#53511yescharacteristic
509C22×C17#53511yescharacteristic
510C22×C17#53811yescharacteristic
511C22×C17#53811yescharacteristic
512C22×C17#53811yescharacteristic
513C22×C17#53811yescharacteristic
514C22×C17#53811yescharacteristic
515C22×C17#53811yescharacteristic
516C22×C17#54011yescharacteristic
517C22×C17#54011yescharacteristic
518C22×C17#54211yescharacteristic
519C22×C17#54211yescharacteristic
520C22×C17#54611yescharacteristic
521C22×C17#54611yescharacteristic
522C22×C17#54711yescharacteristic
523C22×C17#55011yescharacteristic
524C22×C17#55311yescharacteristic
525C22×C17#55311yescharacteristic
526C22×C17#55311yescharacteristic
527C22×C17#55311yescharacteristic
528C22×C17#55511yescharacteristic
529C22×C17#55611yescharacteristic
530C22×C17#55911yescharacteristic
531C22×C17#55911yescharacteristic
532C22×C17#56011yescharacteristic
533C22×C17#56011yescharacteristic
534C22×C17#56211yescharacteristic
535C22×C17#56211yescharacteristic
536C2×D17—42no—
537C2×D17—42no—
538C2×D17—42no—
539C2×D17—42no—
540C2×D17—42no—
541C2×D17—42no—
542C2×D17—42no—
543C2×D17—81no—
544C2×D17—81no—
545C2×D17—81no—
546C2×D17—81no—
547C2×D17—81no—
548C2×D17—81no—
549C2×D17—81no—
550C2×D17—81no—
551C4×C17—24no—
552C4×C17—42no—
553C4×C17—42no—
554C4×C17—42no—
555C4×C17—42no—
556C4×C17—81no—
557Dic17—24no—
558Dic17—42no—
559Dic17—42no—
560Dic17—42no—
561Dic17—81no—
562Dic17—81no—
563Dic17—81no—
564C23×D4—171no—
565C22×C4⋊C4—171no—
566C22×C4⋊C4—171no—
567C22×C4⋊C4C2×D1711yescharacteristic
568C22×C22⋊C4—171no—
569C22×C22⋊C4—171no—
570C22×C22⋊C4—171no—
571C22×C22⋊C4—171no—
572C22×C22⋊C4—171no—
573C22×C22⋊C4—171no—
574C22×C22⋊C4—171no—
575C22×C22⋊C4—171no—
576C22×C22⋊C4—171no—
577C22×C22⋊C4C2×D1711yescharacteristic
578C22×C22⋊C4C2×D1711yescharacteristic
579C22×C22⋊C4C2×D1711yescharacteristic
580C22×C42—171no—
581C22×C42—171no—
582C22×C42C2×D1711yescharacteristic
583#390—178no—
584#388—24no—
585#388—344no—
586C2×#95—171no—
587C2×#95—171no—
588C2×#95—171no—
589C2×#95—171no—
590C2×#95—171no—
591C2×#95—171no—
592C2×#95—171no—
593C2×#95—171no—
594C2×#95—171no—
595C2×#95—171no—
596C2×#95—171no—
597C2×#95—171no—
598C2×#95—171no—
599C2×#95—171no—
600C2×#95C2×D1711yescharacteristic
601C2×#95C2×D1711yescharacteristic
602C2×C17—82no—
603C2×C17#231211yescharacteristic
604C2×C17#232811yescharacteristic
605C2×C17#233711yescharacteristic
606C2×C17#235411yescharacteristic
607C2×C17#235711yescharacteristic
608C2×C17#236411yescharacteristic
609C2×C17#237711yescharacteristic
610C2×C17#271011yescharacteristic
611C2×C17#271011yescharacteristic
612C2×C17#271411yescharacteristic
613C2×C17#271411yescharacteristic
614C2×C17#280011yescharacteristic
615C2×C17#280011yescharacteristic
616C2×C17#280311yescharacteristic
617C2×C17#280311yescharacteristic
618D17—82no—
619C25—171no—
620C25C22×D1711yescharacteristic
621C22×D4—174no—
622C22×D4—342no—
623C22×D4—342no—
624C22×D4—681no—
625C22×D4—681no—
626C22×D4—681no—
627C22×D4—681no—
628C23×C4—171no—
629C23×C4—171no—
630C23×C4—171no—
631C23×C4—171no—
632C23×C4—171no—
633C23×C4—171no—
634C23×C4—171no—
635C23×C4C22×D1711yescharacteristic
636C23×C4C22×D1711yescharacteristic
637C23×C4C22×D1711yescharacteristic
638C23×C4C22×D1711yescharacteristic
639C23×C4C22×D1711yescharacteristic
640C23×C4C22×D1711yescharacteristic
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—174no—
645C2×C4⋊C4—342no—
646C2×C4⋊C4—342no—
647C2×C4⋊C4—681no—
648C2×C4⋊C4—681no—
649C2×C4⋊C4—681no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—41no—
656C2×C22⋊C4—41no—
657C2×C22⋊C4—41no—
658C2×C22⋊C4—174no—
659C2×C22⋊C4—174no—
660C2×C22⋊C4—174no—
661C2×C22⋊C4—342no—
662C2×C22⋊C4—342no—
663C2×C22⋊C4—342no—
664C2×C22⋊C4—342no—
665C2×C22⋊C4—342no—
666C2×C22⋊C4—342no—
667C2×C22⋊C4—342no—
668C2×C22⋊C4—681no—
669C2×C22⋊C4—681no—
670C2×C22⋊C4—681no—
671C2×C22⋊C4—681no—
672C2×C22⋊C4—681no—
673C2×C22⋊C4—681no—
674C2×C22⋊C4—681no—
675C2×C22⋊C4—681no—
676C2×C22⋊C4—681no—
677C2×C22⋊C4—681no—
678C2×C22⋊C4—681no—
679C2×C22⋊C4—681no—
680C2×C22⋊C4—681no—
681C2×C22⋊C4—681no—
682C2×C22⋊C4—681no—
683C2×C22⋊C4—681no—
684C2×C22⋊C4—681no—
685C2×C22⋊C4C4×D1714yes—
686C2×C42—22no—
687C2×C42—41no—
688C2×C42—41no—
689C2×C42—174no—
690C2×C42—342no—
691C2×C42—681no—
692C2×C42—681no—
693C2×C42—681no—
694C2×C42—681no—
695#95—22no—
696#95—342no—
697#95—342no—
698#95—342no—
699#95—342no—
700#95—342no—
701#95—342no—
702#95—681no—
703#95—681no—
704#95—681no—
705#95—681no—
706#95—681no—
707#95—681no—
708#95—681no—
709#95—681no—
710#95C22⋊D1714yescomplemented
711C17#1444411yescharacteristic, complemented, Sylow
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—172no—
727C24—341no—
728C24—341no—
729C24—341no—
730C24—341no—
731C24—341no—
732C24—341no—
733C24—341no—
734C24—341no—
735C24—341no—
736C24—341no—
737C24—341no—
738C24—341no—
739C24—341no—
740C24—341no—
741C24C2×C4×D1712yes—
742C24C23×D1711yescharacteristic
743C2×D4—348no—
744C2×D4—684no—
745C2×D4—684no—
746C2×D4—684no—
747C2×D4—684no—
748C2×D4—684no—
749C2×D4—684no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
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—172no—
786C22×C4—172no—
787C22×C4—172no—
788C22×C4—172no—
789C22×C4—172no—
790C22×C4—172no—
791C22×C4—341no—
792C22×C4—341no—
793C22×C4—341no—
794C22×C4—341no—
795C22×C4—341no—
796C22×C4—341no—
797C22×C4—341no—
798C22×C4—341no—
799C22×C4—341no—
800C22×C4—341no—
801C22×C4—341no—
802C22×C4—341no—
803C22×C4—341no—
804C22×C4—341no—
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×C4C2×C4×D1712yes—
835C22×C4C2×C4×D1712yes—
836C22×C4#6325212yes—
837C22×C4#6325412yes—
838C22×C4C2×C22⋊D1712yes—
839C22×C4C2×C22⋊D1712yes—
840C22×C4C2×C22⋊D1712yes—
841C4⋊C4—44no—
842C4⋊C4—684no—
843C4⋊C4—684no—
844C22⋊C4—28no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—348no—
848C22⋊C4—684no—
849C22⋊C4—684no—
850C22⋊C4—684no—
851C22⋊C4—684no—
852C22⋊C4—684no—
853C22⋊C4—684no—
854C22⋊C4—684no—
855C22⋊C4—684no—
856C42—44no—
857C42—684no—
858C42—684no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
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—342no—
895C23—342no—
896C23—342no—
897C23—342no—
898C23—342no—
899C23—342no—
900C23—342no—
901C23—681no—
902C23—681no—
903C23—681no—
904C23—681no—
905C23—681no—
906C23—681no—
907C23—681no—
908C23—681no—
909C23—681no—
910C23—681no—
911C23—681no—
912C23—681no—
913C23—681no—
914C23—681no—
915C23—681no—
916C23—681no—
917C23—681no—
918C23—681no—
919C23—681no—
920C23—681no—
921C23—681no—
922C23—681no—
923C23—681no—
924C23—681no—
925C23—681no—
926C23—681no—
927C23—681no—
928C23—681no—
929C23C22×C4×D1711yescharacteristic
930C23C2×#6325211yescharacteristic
931C23C2×#6325411yescharacteristic
932C23#1058769111yescharacteristic
933C23#1058769111yescharacteristic
934C23#1058769111yescharacteristic
935C23#41×D1711yescharacteristic
936C23#41×D1711yescharacteristic
937C23#41×D1711yescharacteristic
938C23#1058769611yescharacteristic
939C23#1058769611yescharacteristic
940C23#1058769611yescharacteristic
941C23#1058769611yescharacteristic
942C23#1058769711yescharacteristic
943C23C22×C22⋊D1711yescharacteristic
944D4—6816no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—174no—
987C2×C4—342no—
988C2×C4—342no—
989C2×C4—342no—
990C2×C4—342no—
991C2×C4—342no—
992C2×C4—342no—
993C2×C4—342no—
994C2×C4—342no—
995C2×C4—342no—
996C2×C4—342no—
997C2×C4—342no—
998C2×C4—342no—
999C2×C4—342no—
1000C2×C4—342no—
1001C2×C4—342no—
1002C2×C4—681no—
1003C2×C4—681no—
1004C2×C4—681no—
1005C2×C4—681no—
1006C2×C4—681no—
1007C2×C4—681no—
1008C2×C4—681no—
1009C2×C4—681no—
1010C2×C4—681no—
1011C2×C4—681no—
1012C2×C4—681no—
1013C2×C4—681no—
1014C2×C4—681no—
1015C2×C4—681no—
1016C2×C4—681no—
1017C2×C4—681no—
1018C2×C4—681no—
1019C2×C4—681no—
1020C2×C4—681no—
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×C4C4×C22⋊D1714yes—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—682no—
1052C22—682no—
1053C22—682no—
1054C22—682no—
1055C22—682no—
1056C22—682no—
1057C22—682no—
1058C22—1361no—
1059C22—1361no—
1060C22—1361no—
1061C22—1361no—
1062C22—1361no—
1063C22—1361no—
1064C22—1361no—
1065C22—1361no—
1066C22#117×D1711yescharacteristic
1067C22C2×C4×C22⋊D1711yescharacteristic
1068C22C4×#6325411yescharacteristic
1069C22#1176328111yescharacteristic
1070C22#1176328111yescharacteristic
1071C22#1176328111yescharacteristic
1072C22#1176328911yescharacteristic
1073C22#1176337311yescharacteristic
1074C22#1176337611yescharacteristic
1075C22#1176339111yescharacteristic
1076C22#1176339311yescharacteristic
1077C22#1176339511yescharacteristic
1078C22#1176339611yescharacteristic
1079C22#1176339811yescharacteristic
1080C22#1176339811yescharacteristic
1081C22#1176341011yescharacteristic
1082C22#1176341011yescharacteristic
1083C22#1176342711yescharacteristic
1084C22#1176342811yescharacteristic
1085C22#1176344711yescharacteristic
1086C22#1176345311yescharacteristic
1087C22#1176345811yescharacteristic
1088C22#1176347811yescharacteristic
1089C22#1176350211yescharacteristic
1090C22#1176350511yescharacteristic
1091C22#1176350811yescharacteristic
1092C22#1176351011yescharacteristic
1093C22#1176352211yescharacteristic
1094C22#1176352711yescharacteristic
1095C22#1176354111yescharacteristic
1096C22#1176354311yescharacteristic
1097C22#1176354711yescharacteristic
1098C22#1176355011yescharacteristic
1099C22#1176355311yescharacteristic
1100C22#1176355611yescharacteristic
1101C4—24no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—81no—
1107C4—344no—
1108C4—682no—
1109C4—682no—
1110C4—682no—
1111C4—1361no—
1112C4—1361no—
1113C4—1361no—
1114C2—82no—
1115C2—1362no—
1116C2#1453137811yescharacteristic
1117C2#1453150611yescharacteristic
1118C2#1453159111yescharacteristic
1119C2#1453173411yescharacteristic
1120C2#1453175411yescharacteristic
1121C2#1453182911yescharacteristic
1122C2#1453193711yescharacteristic
1123C2#1453552011yescharacteristic
1124C2#1453552211yescharacteristic
1125C2#1453557411yescharacteristic
1126C2#1453557611yescharacteristic
1127C2#1453667511yescharacteristic
1128C2#1453668011yescharacteristic
1129C2#1453671211yescharacteristic
1130C2#1453671711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×#388D17
hypocenterC17#14444
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#11762701C2semidirect
3. #14527032C2semidirect
4. #14527031C2semidirect
5. #14527029C2semidirect
6. #14527026C2semidirect
9. #14527022C2semidirect
10. #14527021C2semidirect
11. #14527017C2semidirect
12. #14527015C2semidirect
13. #14527013C2semidirect
14. #14527009C2semidirect
15. C2×C17×#388C2semidirect
30. #11762709C4semidirect
131. C17×#95D4semidirect
473. C2×#388D17semidirect
710. #95C22⋊D17semidirect
711. C17#14444semidirect

Maximal subgroups

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

subgroupindex
C2×#117627092
C2×#117627012
#145270322
#145270312
#145270292
#145270262
#145270232
#145270222
#145270212
#145270172
#145270152
#145270132
#145270092
C2×C17×#3882
#1444417