Finite Group Databasebeta

← #16961844

Subgroups — #16961844

Order 4352.

1866 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×#11762711C211yesmaximal, characteristic
2C2×#11762701C211yesmaximal, characteristic, complemented
3C2×#11762687C211yesmaximal, characteristic
4C2×#11762671C211yesmaximal, characteristic, complemented
5C2×#11762666C211yesmaximal, characteristic, complemented
6#14527049C211yesmaximal, characteristic, complemented
7#14527032C211yesmaximal, characteristic, complemented
8#14527030C211yesmaximal, characteristic, complemented
9#14527030C211yesmaximal, characteristic, complemented
10#14527026C211yesmaximal, characteristic, complemented
11#14527024C211yesmaximal, characteristic
12#14527020C211yesmaximal, characteristic, complemented
13#14527018C211yesmaximal, characteristic, complemented
14#14527011C211yesmaximal, characteristic, complemented
15C17×#1436C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C4⋊Dic17C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33#11762711—24no—
34#11762701—24no—
35#11762687C418yescomplemented
36#11762671—24no—
37#11762666—24no—
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C22×C4⋊C4×C17C2211yescharacteristic
50C22×C42×C17C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C24×D17C2311yescharacteristic
57C24×D17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C22×D68—22no—
72C22×D68—22no—
73C22×D68—22no—
74C22×D68—22no—
75C22×D68—41no—
76C22×D68—41no—
77C22×D68C2×C414yes—
78C22×C4×D17—22no—
79C22×C4×D17—22no—
80C22×C4×D17—22no—
81C22×C4×D17—22no—
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—41no—
88C2×C42×C17—22no—
89C2×C42×C17—22no—
90C2×C42×C17—41no—
91C2×#63227—22no—
92C2×#63227—22no—
93C2×#63227—22no—
94C2×#63227—22no—
95C2×#63227—22no—
96C2×#63227—22no—
97C2×#63227—22no—
98C2×#63227—22no—
99C2×#63227—22no—
100C2×#63227—22no—
101C2×#63227—22no—
102C2×#63227—41no—
103C2×#63227—41no—
104C2×#63227—41no—
105C2×#63227—41no—
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×#63227—41no—
117C2×#63227—41no—
118C2×#63227—41no—
119C2×#63227—41no—
120C2×#63227C2×C414yes—
121C2×#63227C2×C414yes—
122C2×#63227C2×C414yes—
123C2×#63227D414yes—
124C2×C4⋊Dic17—22no—
125C2×C4⋊Dic17—22no—
126C2×C4⋊Dic17—22no—
127C2×C4⋊Dic17—22no—
128C2×C4⋊Dic17—41no—
129C2×C4⋊Dic17—41no—
130C2×C4⋊Dic17—41no—
131C2×C4⋊Dic17—41no—
132C2×C4⋊Dic17—41no—
133C2×C4×Dic17—22no—
134C2×C4×Dic17—41no—
135C2×C4×Dic17—41no—
136C17×#95—22no—
137C17×#95—41no—
138C17×#95—41no—
139C17×#95C2×C414yes—
140C17×#95D414yescomplemented
141#10587502—22no—
142#10587502—22no—
143#10587502—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—22no—
148#10587502—41no—
149#10587502—41no—
150#10587502—41no—
151#10587502C2×C414yes—
152C24×C17C2411yescharacteristic
153C23×D17—21no—
154C23×D17—21no—
155C23×D17—21no—
156C23×D17—21no—
157C23×D17—21no—
158C23×D17—21no—
159C23×D17—21no—
160C23×D17—21no—
161C23×D17—21no—
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×D17—21no—
177C23×D17—21no—
178C23×D17—21no—
179C23×D17C22×C412yes—
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×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×C17C22×C412yes—
225C22×C4×C17C2×D412yes—
226C22×C4×C17C2×D412yes—
227C22×C4×C17C2×D412yes—
228C22×C4×C17C2×D412yes—
229C22×C4×C17#4112yes—
230C22×C4×C17#4112yes—
231C22×C4×C17#4112yes—
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×Dic17C22×C412yes—
272C22×Dic17C22×C412yes—
273C22×Dic17C2×D412yes—
274C2×D68—28no—
275C2×D68—28no—
276C2×D68—44no—
277C2×D68—44no—
278C2×D68—44no—
279C2×D68—44no—
280C2×D68—44no—
281C2×C4×D17—28no—
282C2×C4×D17—28no—
283C2×C4×D17—44no—
284C2×C4×D17—44no—
285C2×C4×D17—44no—
286C2×C4×D17—44no—
287C2×C4×D17—44no—
288C4⋊C4×C17—44no—
289C42×C17—44no—
290#63227—28no—
291#63227—44no—
292#63227—44no—
293#63227—44no—
294#63227—44no—
295#63227—44no—
296#63227—44no—
297#63227—44no—
298#63227—44no—
299#63227—44no—
300#63227—44no—
301C4⋊Dic17—44no—
302C4⋊Dic17—44no—
303C4⋊Dic17—44no—
304C4×Dic17—44no—
305#14374—171nomaximal, Sylow
306C23×C17C23×C411yescharacteristic
307C23×C17C22×D411yescharacteristic
308C23×C17C22×D411yescharacteristic
309C23×C17C2×#4111yescharacteristic
310C23×C17C2×#4111yescharacteristic
311C23×C17C2×#4111yescharacteristic
312C23×C17C2×#4111yescharacteristic
313C23×C17H(5,𝔽2)11yescharacteristic
314C23×C17H(5,𝔽2)11yescharacteristic
315C23×C17H(5,𝔽2)11yescharacteristic
316C23×C17H(5,𝔽2)11yescharacteristic
317C23×C17H(5,𝔽2)11yescharacteristic
318C23×C17H(5,𝔽2)11yescharacteristic
319C23×C172−1+411yescharacteristic
320C23×C172−1+411yescharacteristic
321C22×D17—22no—
322C22×D17—22no—
323C22×D17—22no—
324C22×D17—22no—
325C22×D17—22no—
326C22×D17—22no—
327C22×D17—22no—
328C22×D17—22no—
329C22×D17—22no—
330C22×D17—22no—
331C22×D17—22no—
332C22×D17—22no—
333C22×D17—22no—
334C22×D17—22no—
335C22×D17—22no—
336C22×D17—22no—
337C22×D17—22no—
338C22×D17—22no—
339C22×D17—22no—
340C22×D17—22no—
341C22×D17—22no—
342C22×D17—22no—
343C22×D17—22no—
344C22×D17—22no—
345C22×D17—22no—
346C22×D17—41no—
347C22×D17—41no—
348C22×D17—41no—
349C22×D17—41no—
350C22×D17—41no—
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—
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—22no—
410C2×C4×C17—22no—
411C2×C4×C17—22no—
412C2×C4×C17—22no—
413C2×C4×C17—22no—
414C2×C4×C17—22no—
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×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#11714yes—
439C2×C4×C17C4×D414yes—
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—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×Dic17—41no—
479C2×Dic17—41no—
480C2×Dic17—41no—
481C2×Dic17—41no—
482D68—416no—
483C4×D17—416no—
484C2×#390—171no—
485C2×#388—171no—
486C2×#386—171no—
487C2×#381—171no—
488C2×#380—171no—
489#1444—171no—
490#1440—171no—
491#1439—171no—
492#1439—171no—
493#1439—171no—
494#1438—171no—
495#1437—171no—
496#1436—171no—
497#1436D1711yescharacteristic, complemented
498#1434—171no—
499C22×C17C2×#11711yescharacteristic
500C22×C17C2×C4×D411yescharacteristic
501C22×C17C2×C4×D411yescharacteristic
502C22×C17#51811yescharacteristic
503C22×C17#51811yescharacteristic
504C22×C17#52011yescharacteristic
505C22×C17#52011yescharacteristic
506C22×C17#53411yescharacteristic
507C22×C17#53511yescharacteristic
508C22×C17#53611yescharacteristic
509C22×C17#53711yescharacteristic
510C22×C17#53911yescharacteristic
511C22×C17#53911yescharacteristic
512C22×C17#54011yescharacteristic
513C22×C17#54011yescharacteristic
514C22×C17#54011yescharacteristic
515C22×C17#54211yescharacteristic
516C22×C17#54211yescharacteristic
517C22×C17#54211yescharacteristic
518C22×C17D4211yescharacteristic
519C22×C17#54611yescharacteristic
520C22×C17#54611yescharacteristic
521C22×C17#54611yescharacteristic
522C22×C17#54611yescharacteristic
523C22×C17#54711yescharacteristic
524C22×C17#55011yescharacteristic
525C22×C17#55111yescharacteristic
526C22×C17#55111yescharacteristic
527C22×C17#55111yescharacteristic
528C22×C17#55511yescharacteristic
529C22×C17#55611yescharacteristic
530C22×C17#56011yescharacteristic
531C22×C17#56011yescharacteristic
532C22×C17#56211yescharacteristic
533C22×C17#56211yescharacteristic
534C2×D17—24no—
535C2×D17—24no—
536C2×D17—24no—
537C2×D17—42no—
538C2×D17—42no—
539C2×D17—42no—
540C2×D17—42no—
541C2×D17—42no—
542C2×D17—42no—
543C2×D17—42no—
544C2×D17—42no—
545C2×D17—42no—
546C2×D17—42no—
547C2×D17—42no—
548C2×D17—42no—
549C2×D17—42no—
550C2×D17—42no—
551C2×D17—42no—
552C2×D17—42no—
553C2×D17—42no—
554C2×D17—42no—
555C2×D17—42no—
556C2×D17—81no—
557C2×D17—81no—
558C2×D17—81no—
559C2×D17—81no—
560C2×D17—81no—
561C2×D17—81no—
562C2×D17—81no—
563C2×D17—81no—
564C4×C17—24no—
565C4×C17—24no—
566C4×C17—42no—
567C4×C17—42no—
568C4×C17—42no—
569C4×C17—42no—
570C4×C17—81no—
571Dic17—42no—
572Dic17—42no—
573Dic17—42no—
574Dic17—81no—
575Dic17—81no—
576Dic17—81no—
577C23×D4—171no—
578C24×C4—171no—
579C22×C4⋊C4—171no—
580C22×C4⋊C4—171no—
581C22×C4⋊C4—171no—
582C22×C4⋊C4C2×D1711yescharacteristic
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⋊C4—171no—
590C22×C22⋊C4—171no—
591C22×C22⋊C4—171no—
592C22×C22⋊C4—171no—
593C22×C22⋊C4—171no—
594C22×C42—171no—
595C22×C42C2×D1711yescharacteristic
596#390—344no—
597#388—344no—
598#386—178no—
599#381—344no—
600#380—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×#95C2×D1711yescharacteristic
613C2×#95C2×D1711yescharacteristic
614C2×#95C2×D1711yescharacteristic
615C2×#95C2×D1711yescharacteristic
616C2×#95C2×D1711yescharacteristic
617C2×C17#231911yescharacteristic
618C2×C17#232211yescharacteristic
619C2×C17#232411yescharacteristic
620C2×C17#234211yescharacteristic
621C2×C17#235411yescharacteristic
622C2×C17#235811yescharacteristic
623C2×C17#237711yescharacteristic
624C2×C17#267211yescharacteristic
625C2×C17#267311yescharacteristic
626C2×C17#269911yescharacteristic
627C2×C17#270011yescharacteristic
628C2×C17#270511yescharacteristic
629C2×C17#270611yescharacteristic
630C2×C17#273711yescharacteristic
631C2×C17#274011yescharacteristic
632D17—44no—
633D17—82no—
634C25—171no—
635C25—171no—
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—174no—
647C23×C4—171no—
648C23×C4—171no—
649C23×C4—171no—
650C23×C4—342no—
651C23×C4—342no—
652C23×C4—342no—
653C23×C4—342no—
654C23×C4—681no—
655C23×C4—681no—
656C23×C4C22×D1711yescharacteristic
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—41no—
666C2×C4⋊C4—342no—
667C2×C4⋊C4—342no—
668C2×C4⋊C4—342no—
669C2×C4⋊C4—342no—
670C2×C4⋊C4—681no—
671C2×C4⋊C4—681no—
672C2×C4⋊C4—681no—
673C2×C4⋊C4—681no—
674C2×C4⋊C4—681no—
675C2×C22⋊C4—174no—
676C2×C22⋊C4—174no—
677C2×C22⋊C4—174no—
678C2×C22⋊C4—174no—
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—342no—
688C2×C22⋊C4—342no—
689C2×C22⋊C4—342no—
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⋊C4—681no—
702C2×C22⋊C4—681no—
703C2×C22⋊C4—681no—
704C2×C22⋊C4—681no—
705C2×C22⋊C4—681no—
706C2×C22⋊C4—681no—
707C2×C22⋊C4—681no—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—41no—
711C2×C42—342no—
712C2×C42—681no—
713C2×C42—681no—
714#95—22no—
715#95—41no—
716#95—41no—
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—681no—
726#95—681no—
727#95—681no—
728#95C4×D1714yes—
729#95D6814yescomplemented
730C17#1437411yescharacteristic, complemented, Sylow
731C24—172no—
732C24—172no—
733C24—172no—
734C24—172no—
735C24—341no—
736C24—341no—
737C24—341no—
738C24—341no—
739C24—341no—
740C24—341no—
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—
755C24—341no—
756C24—341no—
757C24—341no—
758C24—341no—
759C24—341no—
760C24—341no—
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—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—172no—
809C22×C4—172no—
810C22×C4—172no—
811C22×C4—348no—
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—348no—
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—684no—
853C22×C4—684no—
854C22×C4—684no—
855C22×C4—684no—
856C22×C4—684no—
857C22×C4C2×C4×D1712yes—
858C22×C4C2×C4×D1712yes—
859C22×C4C2×C4×D1712yes—
860C22×C4C2×D6812yes—
861C22×C4C2×D6812yes—
862C22×C4C2×D6812yes—
863C22×C4#6325212yes—
864C22×C4D4×D1712yes—
865C22×C4#6325412yes—
866C22×C4#6325612yes—
867C4⋊C4—44no—
868C4⋊C4—684no—
869C4⋊C4—684no—
870C4⋊C4—684no—
871C22⋊C4—348no—
872C22⋊C4—684no—
873C22⋊C4—684no—
874C22⋊C4—684no—
875C22⋊C4—684no—
876C22⋊C4—684no—
877C22⋊C4—684no—
878C22⋊C4—684no—
879C22⋊C4—684no—
880C22⋊C4—684no—
881C22⋊C4—684no—
882C42—44no—
883C42—684no—
884C23—174no—
885C23—342no—
886C23—342no—
887C23—342no—
888C23—342no—
889C23—342no—
890C23—342no—
891C23—342no—
892C23—342no—
893C23—342no—
894C23—342no—
895C23—342no—
896C23—342no—
897C23—342no—
898C23—342no—
899C23—342no—
900C23—342no—
901C23—342no—
902C23—342no—
903C23—342no—
904C23—342no—
905C23—342no—
906C23—342no—
907C23—342no—
908C23—342no—
909C23—342no—
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—
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—
945C23—681no—
946C23—681no—
947C23—681no—
948C23—681no—
949C23—681no—
950C23—681no—
951C23—681no—
952C23—681no—
953C23—681no—
954C23C22×C4×D1711yescharacteristic
955C23C22×D6811yescharacteristic
956C23C2×#6325211yescharacteristic
957C23C2×D4×D1711yescharacteristic
958C23C2×#6325411yescharacteristic
959C23#1058769111yescharacteristic
960C23#1058769111yescharacteristic
961C23C2×#6325611yescharacteristic
962C23#1058769411yescharacteristic
963C23#41×D1711yescharacteristic
964C23#1058769611yescharacteristic
965C23#1058769611yescharacteristic
966C23#1058769611yescharacteristic
967C23#1058769611yescharacteristic
968C23#1058769711yescharacteristic
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—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
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—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
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—6816no—
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×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×D6814yes—
1061C2×C4#1058757814yes—
1062C22—344no—
1063C22—344no—
1064C22—344no—
1065C22—682no—
1066C22—682no—
1067C22—682no—
1068C22—682no—
1069C22—682no—
1070C22—682no—
1071C22—682no—
1072C22—682no—
1073C22—682no—
1074C22—682no—
1075C22—682no—
1076C22—682no—
1077C22—682no—
1078C22—682no—
1079C22—682no—
1080C22—682no—
1081C22—682no—
1082C22—682no—
1083C22—682no—
1084C22—1361no—
1085C22—1361no—
1086C22—1361no—
1087C22—1361no—
1088C22—1361no—
1089C22—1361no—
1090C22—1361no—
1091C22—1361no—
1092C22C2×#1058757811yescharacteristic
1093C22C4×D4×D1711yescharacteristic
1094C22C2×C4×D6811yescharacteristic
1095C22#1176328111yescharacteristic
1096C22#1176328111yescharacteristic
1097C22#1176328911yescharacteristic
1098C22#1176329111yescharacteristic
1099C22#1176337011yescharacteristic
1100C22#1176337811yescharacteristic
1101C22#1176338211yescharacteristic
1102C22#1176339011yescharacteristic
1103C22#1176340011yescharacteristic
1104C22#1176340711yescharacteristic
1105C22#1176341011yescharacteristic
1106C22#1176341211yescharacteristic
1107C22#1176341511yescharacteristic
1108C22#1176343111yescharacteristic
1109C22#1176343211yescharacteristic
1110C22#1176343311yescharacteristic
1111C22D4×D6811yescharacteristic
1112C22#1176344611yescharacteristic
1113C22#1176344911yescharacteristic
1114C22#1176345011yescharacteristic
1115C22#1176345411yescharacteristic
1116C22#1176346311yescharacteristic
1117C22#1176348111yescharacteristic
1118C22#1176348211yescharacteristic
1119C22#1176348311yescharacteristic
1120C22#1176348611yescharacteristic
1121C22#1176352411yescharacteristic
1122C22#1176353211yescharacteristic
1123C22#1176354711yescharacteristic
1124C22#1176355011yescharacteristic
1125C22#1176355311yescharacteristic
1126C22#1176355611yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—81no—
1134C4—682no—
1135C4—682no—
1136C4—682no—
1137C4—1361no—
1138C4—1361no—
1139C4—1361no—
1140C2—684no—
1141C2—1362no—
1142C2#1453142311yescharacteristic
1143C2#1453145711yescharacteristic
1144C2#1453147811yescharacteristic
1145C2#1453163111yescharacteristic
1146C2#1453173111yescharacteristic
1147C2#1453176611yescharacteristic
1148C2#1453193711yescharacteristic
1149C2#1453503811yescharacteristic
1150C2#1453505311yescharacteristic
1151C2#1453537311yescharacteristic
1152C2#1453538511yescharacteristic
1153C2#1453545511yescharacteristic
1154C2#1453547011yescharacteristic
1155C2#1453583411yescharacteristic
1156C2#1453587911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1436C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1436D17
hypocenterC17#14374
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#11762701C2semidirect
4. C2×#11762671C2semidirect
5. C2×#11762666C2semidirect
6. #14527049C2semidirect
7. #14527032C2semidirect
8. #14527030C2semidirect
9. #14527030C2semidirect
10. #14527026C2semidirect
12. #14527020C2semidirect
13. #14527018C2semidirect
14. #14527011C2semidirect
15. C17×#1436C2semidirect
35. #11762687C4semidirect
140. C17×#95D4semidirect
497. #1436D17semidirect
729. #95D68semidirect
730. C17#14374semidirect

Maximal subgroups

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

subgroupindex
C2×#117627112
C2×#117627012
C2×#117626872
C2×#117626712
C2×#117626662
#145270492
#145270322
#145270302
#145270262
#145270242
#145270202
#145270182
#145270112
C17×#14362
#1437417