Finite Group Databasebeta

← #16964389

Subgroups — #16964389

Order 4352.

1858 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×#11762727C211yesmaximal, characteristic
2C2×#11762710C211yesmaximal, characteristic
3C2×#11762699C211yesmaximal, characteristic, complemented
4C2×#11762690C211yesmaximal, characteristic, complemented
5C2×#11762687C211yesmaximal, characteristic
6#14527032C211yesmaximal, characteristic, complemented
7#14527026C211yesmaximal, characteristic, complemented
8#14527026C211yesmaximal, characteristic, complemented
9#14527026C211yesmaximal, characteristic, complemented
10#14527020C211yesmaximal, characteristic, complemented
11#14527019C211yesmaximal, characteristic, complemented
12#14527009C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1444C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63227C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32#11762727C418yescomplemented
33#11762710—24no—
34#11762699—24no—
35#11762690—24no—
36#11762687—24no—
37C2×#10587502C2211yescharacteristic
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×C4⋊C4×C17C2211yescharacteristic
51C22×C4⋊C4×C17C2211yescharacteristic
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—41no—
82C22×C4×D17—41no—
83C22×C4×D17—41no—
84C22×C4×D17—41no—
85C2×C4⋊C4×C17—22no—
86C2×C4⋊C4×C17—22no—
87C2×C4⋊C4×C17—22no—
88C2×C4⋊C4×C17—41no—
89C2×C4⋊C4×C17—41no—
90C2×C4⋊C4×C17—41no—
91C2×C4⋊C4×C17—41no—
92C2×C4⋊C4×C17—41no—
93C2×C4⋊C4×C17—41no—
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—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×#63227—41no—
117C2×#63227—41no—
118C2×#63227—41no—
119C2×#63227—41no—
120C2×#63227—41no—
121C2×#63227—41no—
122C2×#63227C2×C414yes—
123C2×#63227C2×C414yes—
124C2×#63227C2×C414yescomplemented
125C2×#63227C2×C414yescomplemented
126C2×#63227D414yes—
127C2×#63225—22no—
128C2×#63225—22no—
129C2×#63225C2×C414yescomplemented
130C2×C4×Dic17—22no—
131C2×C4×Dic17—22no—
132C2×C4×Dic17—22no—
133C2×C4×Dic17—22no—
134C2×C4×Dic17—41no—
135C2×C4×Dic17—41no—
136C17×#95—22no—
137C17×#95—41no—
138C17×#95—41no—
139C17×#95C2×C414yescomplemented
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#10587502—41no—
151#10587502D414yes—
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×C17—21no—
223C22×C4×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17C22×C412yes—
226C22×C4×C17C22×C412yes—
227C22×C4×C17C22×C412yes—
228C22×C4×C17C2×D412yes—
229C22×C4×C17C2×D412yes—
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×Dic17C22×C412yes—
269C22×Dic17C22×C412yes—
270C22×Dic17C2×D412yes—
271C22×Dic17C2×D412yes—
272C22×Dic17C2×D412yes—
273C22×Dic17#4112yes—
274C2×D68—28no—
275C2×D68—28no—
276C2×D68—44no—
277C2×D68—44no—
278C2×D68—44no—
279C2×D68—44no—
280C2×D68—44no—
281C2×C4×D17—44no—
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—
289C4⋊C4×C17—44no—
290C4⋊C4×C17—44no—
291#63227—28no—
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—
301#63227—44no—
302#63225—28no—
303C4×Dic17—44no—
304C4×Dic17—44no—
305#14573—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—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×C17—41no—
432C2×C4×C17—41no—
433C2×C4×C17—41no—
434C2×C4×C17—41no—
435C2×C4×C17—41no—
436C2×C4×C17—41no—
437C2×C4×C17—41no—
438C2×C4×C17—41no—
439C2×C4×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—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—
482D68—416no—
483C4×D17—416no—
484C2×#394—171no—
485C2×#390—171no—
486C2×#388—171no—
487C2×#387—171no—
488C2×#386—171no—
489#1444D1711yescharacteristic, complemented
490#1440—171no—
491#1439—171no—
492#1439—171no—
493#1439—171no—
494#1437—171no—
495#1436—171no—
496#1434—171no—
497C22⋊#95—171no—
498C22⋊#95—171no—
499C22×C17C2×C4×D411yescharacteristic
500C22×C17C2×C4×D411yescharacteristic
501C22×C17C4×#4111yescharacteristic
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#53811yescharacteristic
511C22×C17#53811yescharacteristic
512C22×C17#53911yescharacteristic
513C22×C17#53911yescharacteristic
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#55211yescharacteristic
528C22×C17#55311yescharacteristic
529C22×C17#55511yescharacteristic
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—42no—
566C4×C17—42no—
567C4×C17—42no—
568C4×C17—42no—
569C4×C17—81no—
570C4×C17—81no—
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×C4⋊C4C2×D1711yescharacteristic
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×C42—171no—
596#394—178no—
597#390—344no—
598#388—344no—
599#387—344no—
600#386—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×#95C2×D1711yescharacteristic
614C2×#95C2×D1711yescharacteristic
615C2×#95C2×D1711yescharacteristic
616C2×#95C2×D1711yescharacteristic
617C2×C17#232511yescharacteristic
618C2×C17#232611yescharacteristic
619C2×C17#233511yescharacteristic
620C2×C17#235811yescharacteristic
621C2×C17#235911yescharacteristic
622C2×C17#236311yescharacteristic
623C2×C17#237711yescharacteristic
624C2×C17#267211yescharacteristic
625C2×C17#267311yescharacteristic
626C2×C17#268511yescharacteristic
627C2×C17#268611yescharacteristic
628C2×C17#269111yescharacteristic
629C2×C17#269411yescharacteristic
630C2×C17#273711yescharacteristic
631C2×C17#276111yescharacteristic
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—171no—
647C23×C4—171no—
648C23×C4—171no—
649C23×C4—342no—
650C23×C4—342no—
651C23×C4—342no—
652C23×C4—681no—
653C23×C4—681no—
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—22no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—174no—
673C2×C4⋊C4—342no—
674C2×C4⋊C4—342no—
675C2×C22⋊C4—174no—
676C2×C22⋊C4—174no—
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—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—342no—
709C2×C42—342no—
710C2×C42—342no—
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#95—681no—
729#95C4×D1714yescomplemented
730C17#1457311yescharacteristic, 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—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—172no—
812C22×C4—172no—
813C22×C4—172no—
814C22×C4—172no—
815C22×C4—172no—
816C22×C4—172no—
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—341no—
853C22×C4—684no—
854C22×C4—684no—
855C22×C4—684no—
856C22×C4—684no—
857C22×C4—684no—
858C22×C4—684no—
859C22×C4—684no—
860C22×C4C2×C4×D1712yes—
861C22×C4C2×C4×D1712yes—
862C22×C4C2×C4×D1712yes—
863C22×C4D4×D1712yes—
864C22×C4D4×D1712yes—
865C22×C4#6325612yes—
866C22×C4#6325612yes—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—348no—
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—684no—
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
955C23C2×D4×D1711yescharacteristic
956C23C2×D4×D1711yescharacteristic
957C23#1058769111yescharacteristic
958C23#1058769111yescharacteristic
959C23#1058769111yescharacteristic
960C23#1058769111yescharacteristic
961C23C2×#6325611yescharacteristic
962C23C2×#6325611yescharacteristic
963C23#1058769411yescharacteristic
964C23#1058769411yescharacteristic
965C23#41×D1711yescharacteristic
966C23#41×D1711yescharacteristic
967C23#1058769611yescharacteristic
968C23#1058769611yescharacteristic
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—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
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—342no—
1036C2×C4—6816no—
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×C4—681no—
1061C2×C4#1058757914yes—
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—
1092C22C4×D4×D1711yescharacteristic
1093C22C2×#1058757911yescharacteristic
1094C22C4×#6325611yescharacteristic
1095C22#1176328111yescharacteristic
1096C22#1176328111yescharacteristic
1097C22#1176329011yescharacteristic
1098C22#1176329011yescharacteristic
1099C22#1176336911yescharacteristic
1100C22#1176337211yescharacteristic
1101C22#1176338411yescharacteristic
1102C22#1176338911yescharacteristic
1103C22#1176339511yescharacteristic
1104C22#1176339911yescharacteristic
1105C22#1176340511yescharacteristic
1106C22#1176340711yescharacteristic
1107C22#1176340911yescharacteristic
1108C22#1176343311yescharacteristic
1109C22#1176343311yescharacteristic
1110C22#1176343311yescharacteristic
1111C22#1176344111yescharacteristic
1112C22#1176344811yescharacteristic
1113C22#1176345011yescharacteristic
1114C22#1176345011yescharacteristic
1115C22#1176345111yescharacteristic
1116C22#1176346211yescharacteristic
1117C22#1176347711yescharacteristic
1118C22#1176348611yescharacteristic
1119C22#1176348611yescharacteristic
1120C22#1176349111yescharacteristic
1121C22#1176351211yescharacteristic
1122C22#1176352511yescharacteristic
1123C22#1176354811yescharacteristic
1124C22#1176354911yescharacteristic
1125C22#1176355511yescharacteristic
1126C22#1176355511yescharacteristic
1127C4—24no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—81no—
1133C4—81no—
1134C4—682no—
1135C4—682no—
1136C4—682no—
1137C4—682no—
1138C4—682no—
1139C4—682no—
1140C2—684no—
1141C2—1362no—
1142C2#1453148111yescharacteristic
1143C2#1453149211yescharacteristic
1144C2#1453157711yescharacteristic
1145C2#1453176011yescharacteristic
1146C2#1453177111yescharacteristic
1147C2#1453182111yescharacteristic
1148C2#1453194011yescharacteristic
1149C2#1453503411yescharacteristic
1150C2#1453505211yescharacteristic
1151C2#1453516811yescharacteristic
1152C2#1453519711yescharacteristic
1153C2#1453527211yescharacteristic
1154C2#1453529711yescharacteristic
1155C2#1453584611yescharacteristic
1156C2#1453616411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1444C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1444D17
hypocenterC17#14573
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
3. C2×#11762699C2semidirect
4. C2×#11762690C2semidirect
6. #14527032C2semidirect
7. #14527026C2semidirect
8. #14527026C2semidirect
9. #14527026C2semidirect
10. #14527020C2semidirect
11. #14527019C2semidirect
12. #14527009C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×#1444C2semidirect
32. #11762727C4semidirect
124. C2×#63227C2×C4semidirect
125. C2×#63227C2×C4semidirect
129. C2×#63225C2×C4semidirect
139. C17×#95C2×C4semidirect
489. #1444D17semidirect
729. #95C4×D17semidirect
730. C17#14573semidirect

Maximal subgroups

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

subgroupindex
C2×#117627272
C2×#117627102
C2×#117626992
C2×#117626902
C2×#117626872
#145270322
#145270262
#145270202
#145270192
#145270092
#145270052
C17×#14442
#1457317