Finite Group Databasebeta

← #16964597

Subgroups — #16964597

Order 4352.

1390 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762731C211yesmaximal, characteristic
2C2×#11762701C211yesmaximal, characteristic
3C2×#11762696C211yesmaximal, characteristic, complemented
4#14527053C211yesmaximal, characteristic, complemented
5#14527032C211yesmaximal, characteristic
6#14527032C211yesmaximal, characteristic
7#14527026C211yesmaximal, characteristic
8#14527020C211yesmaximal, characteristic
9#14527020C211yesmaximal, characteristic
10#14527019C211yesmaximal, characteristic, complemented
11#14527018C211yesmaximal, characteristic, complemented
12#14527016C211yesmaximal, characteristic, complemented
13#14527013C211yesmaximal, characteristic, complemented
14#14527010C211yesmaximal, characteristic, complemented
15C17×#1441C211yesmaximal, characteristic, complemented
16C22×C4⋊Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63227C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×C4×Dic17C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29#11762731C418yescomplemented
30#11762701—24no—
31#11762696—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
46C2×#10587502C2211yescharacteristic
47C22×C4⋊C4×C17C2211yescharacteristic
48C22×C4⋊C4×C17C2211yescharacteristic
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C24×D17C2311yescharacteristic
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×Dic17C2311yescharacteristic
63C23×Dic17C2311yescharacteristic
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C2×C4⋊C4×C17—22no—
70C2×C4⋊C4×C17—41no—
71C2×C4⋊C4×C17—41no—
72C2×C4⋊C4×C17—41no—
73C2×C4⋊C4×C17—41no—
74C2×C4⋊C4×C17C2×C414yes—
75C2×#63227—22no—
76C2×#63227—22no—
77C2×#63227—22no—
78C2×#63227—22no—
79C2×#63227—22no—
80C2×#63227—22no—
81C2×#63227—22no—
82C2×#63227—22no—
83C2×#63227—41no—
84C2×#63227—41no—
85C2×#63227—41no—
86C2×#63227—41no—
87C2×#63227—41no—
88C2×#63227—41no—
89C2×#63227—41no—
90C2×#63227—41no—
91C2×#63227—41no—
92C2×#63227—41no—
93C2×#63227C2×C414yes—
94C2×#63227C2×C414yes—
95C2×#63227C2×C414yes—
96C2×C4⋊Dic17—41no—
97C2×C4⋊Dic17—41no—
98C2×C4⋊Dic17—41no—
99C2×C4⋊Dic17—41no—
100C2×C4⋊Dic17C2×C414yes—
101C2×C4⋊Dic17D414yes—
102C2×#63225—22no—
103C2×#63225—22no—
104C2×#63225C2×C414yes—
105C2×C4×Dic17—22no—
106C2×C4×Dic17—22no—
107C2×C4×Dic17—22no—
108C2×C4×Dic17—22no—
109C2×C4×Dic17—41no—
110C2×C4×Dic17—41no—
111C2×C4×Dic17—41no—
112C2×C4×Dic17—41no—
113C2×C4×Dic17—41no—
114C17×#95—22no—
115C17×#95—22no—
116C17×#95—22no—
117C17×#95—41no—
118C17×#95—41no—
119#10587502—22no—
120#10587502—22no—
121#10587502—22no—
122#10587502—22no—
123#10587502—22no—
124#10587502—22no—
125#10587502—22no—
126#10587502—22no—
127#10587502—22no—
128#10587502—41no—
129#10587502—41no—
130#10587502—41no—
131#10587502—41no—
132#10587502—41no—
133#10587502C2×C414yes—
134C24×C17C2411yescharacteristic
135C23×D17—21no—
136C23×D17—21no—
137C23×D17—21no—
138C23×D17—21no—
139C23×D17—21no—
140C23×D17—21no—
141C23×D17—21no—
142C23×D17—21no—
143C23×D17—21no—
144C23×D17—21no—
145C23×D17—21no—
146C23×D17—21no—
147C23×D17—21no—
148C23×D17—21no—
149C23×D17C22×C412yes—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
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×C17C22×C412yes—
193C22×C4×C17C22×C412yes—
194C22×C4×C17C22×C412yes—
195C22×C4×C17C2×D412yes—
196C22×C4×C17#4112yes—
197C22×C4×C17#4112yes—
198C22×C4×C17#4112yes—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C22×Dic17—21no—
218C22×Dic17—21no—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—21no—
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×Dic17C22×C412yes—
242C22×Dic17C22×C412yes—
243C22×Dic17C22×C412yes—
244C22×Dic17C2×D412yes—
245C22×Dic17C2×D412yes—
246C22×Dic17#4112yes—
247C22×Dic17#4112yes—
248C4⋊C4×C17—44no—
249C4⋊C4×C17—44no—
250#63227—28no—
251#63227—44no—
252#63227—44no—
253#63227—44no—
254#63227—44no—
255#63227—44no—
256#63227—44no—
257C4⋊Dic17—44no—
258C4⋊Dic17—44no—
259#63225—28no—
260C4×Dic17—44no—
261C4×Dic17—44no—
262C4×Dic17—44no—
263#14588—171nomaximal, Sylow
264C23×C17C23×C411yescharacteristic
265C23×C17C22×D411yescharacteristic
266C23×C17C2×#4111yescharacteristic
267C23×C17C2×#4111yescharacteristic
268C23×C17C2×#4111yescharacteristic
269C23×C17C2×#4111yescharacteristic
270C23×C17C2×#4111yescharacteristic
271C23×C17H(5,𝔽2)11yescharacteristic
272C23×C17H(5,𝔽2)11yescharacteristic
273C23×C17H(5,𝔽2)11yescharacteristic
274C23×C17H(5,𝔽2)11yescharacteristic
275C23×C17H(5,𝔽2)11yescharacteristic
276C23×C172−1+411yescharacteristic
277C23×C172−1+411yescharacteristic
278C23×C172−1+411yescharacteristic
279C22×D17—22no—
280C22×D17—22no—
281C22×D17—22no—
282C22×D17—22no—
283C22×D17—22no—
284C22×D17—22no—
285C22×D17—22no—
286C22×D17—41no—
287C22×D17—41no—
288C22×D17—41no—
289C22×D17—41no—
290C22×D17—41no—
291C22×D17—41no—
292C22×D17—41no—
293C22×D17—41no—
294C22×D17—41no—
295C22×D17—41no—
296C22×D17—41no—
297C22×D17—41no—
298C22×D17—41no—
299C22×D17—41no—
300C22×D17—41no—
301C22×D17—41no—
302C22×D17—41no—
303C22×D17—41no—
304C22×D17—41no—
305C22×D17—41no—
306C22×D17—41no—
307C22×D17—41no—
308C22×D17—41no—
309C22×D17—41no—
310C22×D17—41no—
311C22×D17—41no—
312C22×D17—41no—
313C22×D17—41no—
314C2×C4×C17—22no—
315C2×C4×C17—22no—
316C2×C4×C17—22no—
317C2×C4×C17—22no—
318C2×C4×C17—22no—
319C2×C4×C17—22no—
320C2×C4×C17—22no—
321C2×C4×C17—22no—
322C2×C4×C17—22no—
323C2×C4×C17—22no—
324C2×C4×C17—22no—
325C2×C4×C17—22no—
326C2×C4×C17—22no—
327C2×C4×C17—22no—
328C2×C4×C17—22no—
329C2×C4×C17—22no—
330C2×C4×C17—22no—
331C2×C4×C17—22no—
332C2×C4×C17—41no—
333C2×C4×C17—41no—
334C2×C4×C17—41no—
335C2×C4×C17—41no—
336C2×C4×C17—41no—
337C2×C4×C17—41no—
338C2×C4×C17—41no—
339C2×C4×C17—41no—
340C2×C4×C17—41no—
341C2×C4×C17—41no—
342C2×C4×C17—41no—
343C2×C4×C17—41no—
344C2×C4×C17—41no—
345C2×C4×C17—41no—
346C2×C4×C17—41no—
347C2×C4×C17—41no—
348C2×C4×C17—41no—
349C2×C4×C17—41no—
350C2×C4×C17—41no—
351C2×C4×C17—41no—
352C2×C4×C17—41no—
353C2×C4×C17—41no—
354C2×C4×C17—41no—
355C2×C4×C17—41no—
356C2×C4×C17—41no—
357C2×C4×C17—41no—
358C2×C4×C17—41no—
359C2×C4×C17—41no—
360C2×C4×C17—41no—
361C2×C4×C17—41no—
362C2×C4×C17C4×D414yes—
363C2×Dic17—22no—
364C2×Dic17—22no—
365C2×Dic17—22no—
366C2×Dic17—22no—
367C2×Dic17—22no—
368C2×Dic17—22no—
369C2×Dic17—22no—
370C2×Dic17—22no—
371C2×Dic17—22no—
372C2×Dic17—22no—
373C2×Dic17—22no—
374C2×Dic17—22no—
375C2×Dic17—22no—
376C2×Dic17—22no—
377C2×Dic17—22no—
378C2×Dic17—22no—
379C2×Dic17—22no—
380C2×Dic17—22no—
381C2×Dic17—22no—
382C2×Dic17—22no—
383C2×Dic17—22no—
384C2×Dic17—41no—
385C2×Dic17—41no—
386C2×Dic17—41no—
387C2×Dic17—41no—
388C2×Dic17—41no—
389C2×Dic17—41no—
390C2×Dic17—41no—
391C2×Dic17—41no—
392C2×Dic17—41no—
393C2×Dic17—41no—
394C2×Dic17—41no—
395C2×Dic17—41no—
396C2×Dic17—41no—
397C2×Dic17—41no—
398C2×Dic17—41no—
399C2×Dic17—41no—
400C2×Dic17—41no—
401C2×Dic17—41no—
402C2×Dic17—41no—
403C2×Dic17—41no—
404C2×Dic17—41no—
405C2×Dic17—41no—
406C2×Dic17—41no—
407C2×Dic17—41no—
408C2×Dic17—41no—
409C2×Dic17—41no—
410C2×Dic17—41no—
411C2×Dic17—41no—
412C2×#396—171no—
413C2×#388—171no—
414C2×#387—171no—
415#1445—171no—
416#1441D1711yescharacteristic, complemented
417#1440—171no—
418#1440—171no—
419#1439—171no—
420#1437—171no—
421#1437—171no—
422#1436—171no—
423#1436—171no—
424#1436—171no—
425C4⋊#95—171no—
426#1434—171no—
427C22×C17C2×C4×D411yescharacteristic
428C22×C17C4×#4111yescharacteristic
429C22×C17C4×#4111yescharacteristic
430C22×C17#51811yescharacteristic
431C22×C17#51811yescharacteristic
432C22×C17#51911yescharacteristic
433C22×C17#52011yescharacteristic
434C22×C17#53411yescharacteristic
435C22×C17#53711yescharacteristic
436C22×C17#53811yescharacteristic
437C22×C17#53811yescharacteristic
438C22×C17#53811yescharacteristic
439C22×C17#53911yescharacteristic
440C22×C17#53911yescharacteristic
441C22×C17#53911yescharacteristic
442C22×C17#54011yescharacteristic
443C22×C17#54011yescharacteristic
444C22×C17#54211yescharacteristic
445C22×C17#54211yescharacteristic
446C22×C17#54611yescharacteristic
447C22×C17#54711yescharacteristic
448C22×C17#54811yescharacteristic
449C22×C17#55011yescharacteristic
450C22×C17#55111yescharacteristic
451C22×C17#55211yescharacteristic
452C22×C17#55211yescharacteristic
453C22×C17#55311yescharacteristic
454C22×C17#55311yescharacteristic
455C22×C17#55511yescharacteristic
456C22×C17#55611yescharacteristic
457C22×C17#55611yescharacteristic
458C22×C17#56211yescharacteristic
459C22×C17#56211yescharacteristic
460C22×C17#56311yescharacteristic
461C22×C17#56311yescharacteristic
462C2×D17—42no—
463C2×D17—42no—
464C2×D17—42no—
465C2×D17—42no—
466C2×D17—42no—
467C2×D17—42no—
468C2×D17—42no—
469C2×D17—81no—
470C2×D17—81no—
471C2×D17—81no—
472C2×D17—81no—
473C2×D17—81no—
474C2×D17—81no—
475C2×D17—81no—
476C2×D17—81no—
477C4×C17—24no—
478C4×C17—42no—
479C4×C17—42no—
480C4×C17—42no—
481C4×C17—42no—
482C4×C17—81no—
483C4×C17—81no—
484Dic17—42no—
485Dic17—42no—
486Dic17—42no—
487Dic17—42no—
488Dic17—42no—
489Dic17—42no—
490Dic17—42no—
491C22×C4⋊C4—171no—
492C22×C4⋊C4—171no—
493C22×C4⋊C4—171no—
494C22×C4⋊C4C2×D1711yescharacteristic
495C22×C4⋊C4C2×D1711yescharacteristic
496C22×C22⋊C4—171no—
497C22×C22⋊C4—171no—
498C22×C22⋊C4—171no—
499C22×C22⋊C4—171no—
500C22×C22⋊C4—171no—
501C22×C22⋊C4—171no—
502C22×C22⋊C4—171no—
503C22×C42—171no—
504C22×C42—171no—
505C22×C42—171no—
506#396—178no—
507#388—344no—
508#387—344no—
509C2×#95—171no—
510C2×#95—171no—
511C2×#95—171no—
512C2×#95—171no—
513C2×#95—171no—
514C2×#95—171no—
515C2×#95—171no—
516C2×#95—171no—
517C2×#95—171no—
518C2×#95—171no—
519C2×#95—171no—
520C2×#95—171no—
521C2×#95—171no—
522C2×#95—171no—
523C2×#95—171no—
524C2×#95C2×D1711yescharacteristic
525C2×#95C2×D1711yescharacteristic
526C2×#95C2×D1711yescharacteristic
527C2×#95C2×D1711yescharacteristic
528C2×#95C2×D1711yescharacteristic
529C2×C17#232511yescharacteristic
530C2×C17#233211yescharacteristic
531C2×C17#233311yescharacteristic
532C2×C17#236211yescharacteristic
533C2×C17#236311yescharacteristic
534C2×C17#237311yescharacteristic
535C2×C17#237811yescharacteristic
536C2×C17#270111yescharacteristic
537C2×C17#270711yescharacteristic
538C2×C17#272711yescharacteristic
539C2×C17#273011yescharacteristic
540C2×C17#277511yescharacteristic
541C2×C17#278111yescharacteristic
542C2×C17#278611yescharacteristic
543C2×C17#279311yescharacteristic
544D17—82no—
545C25—171no—
546C23×C4—171no—
547C23×C4—171no—
548C23×C4—171no—
549C23×C4—171no—
550C23×C4—171no—
551C23×C4—171no—
552C23×C4—171no—
553C23×C4C22×D1711yescharacteristic
554C23×C4C22×D1711yescharacteristic
555C23×C4C22×D1711yescharacteristic
556C23×C4C22×D1711yescharacteristic
557C23×C4C22×D1711yescharacteristic
558C23×C4C22×D1711yescharacteristic
559C23×C4C22×D1711yescharacteristic
560C2×C4⋊C4—22no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—174no—
566C2×C4⋊C4—174no—
567C2×C4⋊C4—174no—
568C2×C4⋊C4—342no—
569C2×C4⋊C4—342no—
570C2×C4⋊C4—681no—
571C2×C4⋊C4—681no—
572C2×C4⋊C4—681no—
573C2×C4⋊C4—681no—
574C2×C4⋊C4C4×D1714yes—
575C2×C22⋊C4—174no—
576C2×C22⋊C4—174no—
577C2×C22⋊C4—174no—
578C2×C22⋊C4—342no—
579C2×C22⋊C4—342no—
580C2×C22⋊C4—342no—
581C2×C22⋊C4—342no—
582C2×C22⋊C4—342no—
583C2×C22⋊C4—342no—
584C2×C22⋊C4—342no—
585C2×C22⋊C4—342no—
586C2×C22⋊C4—681no—
587C2×C22⋊C4—681no—
588C2×C22⋊C4—681no—
589C2×C22⋊C4—681no—
590C2×C22⋊C4—681no—
591C2×C22⋊C4—681no—
592C2×C22⋊C4—681no—
593C2×C22⋊C4—681no—
594C2×C22⋊C4—681no—
595C2×C22⋊C4—681no—
596C2×C42—342no—
597C2×C42—342no—
598C2×C42—342no—
599C2×C42—342no—
600C2×C42—681no—
601C2×C42—681no—
602C2×C42—681no—
603C2×C42—681no—
604C2×C42—681no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—41no—
609#95—41no—
610#95—174no—
611#95—342no—
612#95—342no—
613#95—342no—
614#95—342no—
615#95—342no—
616#95—342no—
617#95—342no—
618#95—342no—
619#95—342no—
620#95—681no—
621#95—681no—
622#95—681no—
623#95—681no—
624#95—681no—
625C17#1458811yescharacteristic, complemented, Sylow
626C24—172no—
627C24—341no—
628C24—341no—
629C24—341no—
630C24—341no—
631C24—341no—
632C24—341no—
633C24—341no—
634C24—341no—
635C24—341no—
636C24—341no—
637C24—341no—
638C24—341no—
639C24—341no—
640C24—341no—
641C24C23×D1711yescharacteristic
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—172no—
685C22×C4—172no—
686C22×C4—172no—
687C22×C4—172no—
688C22×C4—172no—
689C22×C4—172no—
690C22×C4—172no—
691C22×C4—341no—
692C22×C4—341no—
693C22×C4—341no—
694C22×C4—341no—
695C22×C4—341no—
696C22×C4—341no—
697C22×C4—341no—
698C22×C4—341no—
699C22×C4—341no—
700C22×C4—341no—
701C22×C4—341no—
702C22×C4—341no—
703C22×C4—341no—
704C22×C4—341no—
705C22×C4—341no—
706C22×C4—341no—
707C22×C4—341no—
708C22×C4—341no—
709C22×C4—341no—
710C22×C4—341no—
711C22×C4—341no—
712C22×C4—341no—
713C22×C4—341no—
714C22×C4—341no—
715C22×C4—341no—
716C22×C4—341no—
717C22×C4—341no—
718C22×C4—341no—
719C22×C4—341no—
720C22×C4—341no—
721C22×C4—341no—
722C22×C4—341no—
723C22×C4—341no—
724C22×C4—341no—
725C22×C4—341no—
726C22×C4—341no—
727C22×C4—341no—
728C22×C4—341no—
729C22×C4—341no—
730C22×C4—341no—
731C22×C4—341no—
732C22×C4—341no—
733C22×C4C2×C4×D1712yes—
734C22×C4C2×C4×D1712yes—
735C22×C4C2×C4×D1712yes—
736C22×C4D4×D1712yes—
737C22×C4#6325412yes—
738C22×C4#6325612yes—
739C22×C4#6325612yes—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C4⋊C4—348no—
743C4⋊C4—684no—
744C4⋊C4—684no—
745C22⋊C4—348no—
746C22⋊C4—684no—
747C22⋊C4—684no—
748C22⋊C4—684no—
749C22⋊C4—684no—
750C22⋊C4—684no—
751C22⋊C4—684no—
752C42—684no—
753C42—684no—
754C42—684no—
755C23—342no—
756C23—342no—
757C23—342no—
758C23—342no—
759C23—342no—
760C23—342no—
761C23—342no—
762C23—681no—
763C23—681no—
764C23—681no—
765C23—681no—
766C23—681no—
767C23—681no—
768C23—681no—
769C23—681no—
770C23—681no—
771C23—681no—
772C23—681no—
773C23—681no—
774C23—681no—
775C23—681no—
776C23—681no—
777C23—681no—
778C23—681no—
779C23—681no—
780C23—681no—
781C23—681no—
782C23—681no—
783C23—681no—
784C23—681no—
785C23—681no—
786C23—681no—
787C23—681no—
788C23—681no—
789C23—681no—
790C23C22×C4×D1711yescharacteristic
791C23C2×D4×D1711yescharacteristic
792C23C2×#6325411yescharacteristic
793C23#1058769111yescharacteristic
794C23#1058769111yescharacteristic
795C23#1058769111yescharacteristic
796C23C2×#6325611yescharacteristic
797C23C2×#6325611yescharacteristic
798C23#1058769411yescharacteristic
799C23#41×D1711yescharacteristic
800C23#41×D1711yescharacteristic
801C23#1058769611yescharacteristic
802C23#1058769611yescharacteristic
803C23#1058769711yescharacteristic
804C23#1058769711yescharacteristic
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—342no—
854C2×C4—342no—
855C2×C4—342no—
856C2×C4—342no—
857C2×C4—342no—
858C2×C4—342no—
859C2×C4—342no—
860C2×C4—342no—
861C2×C4—342no—
862C2×C4—342no—
863C2×C4—342no—
864C2×C4—342no—
865C2×C4—342no—
866C2×C4—342no—
867C2×C4—342no—
868C2×C4—342no—
869C2×C4—342no—
870C2×C4—342no—
871C2×C4—342no—
872C2×C4—342no—
873C2×C4—342no—
874C2×C4—681no—
875C2×C4—681no—
876C2×C4—681no—
877C2×C4—681no—
878C2×C4—681no—
879C2×C4—681no—
880C2×C4—681no—
881C2×C4—681no—
882C2×C4—681no—
883C2×C4—681no—
884C2×C4—681no—
885C2×C4—681no—
886C2×C4—681no—
887C2×C4—681no—
888C2×C4—681no—
889C2×C4—681no—
890C2×C4—681no—
891C2×C4—681no—
892C2×C4—681no—
893C2×C4—681no—
894C2×C4—681no—
895C2×C4—681no—
896C2×C4—681no—
897C2×C4—681no—
898C2×C4—681no—
899C2×C4—681no—
900C2×C4—681no—
901C2×C4—681no—
902C2×C4#1058757914yes—
903C22—682no—
904C22—682no—
905C22—682no—
906C22—682no—
907C22—682no—
908C22—682no—
909C22—682no—
910C22—1361no—
911C22—1361no—
912C22—1361no—
913C22—1361no—
914C22—1361no—
915C22—1361no—
916C22—1361no—
917C22—1361no—
918C22C2×#1058757911yescharacteristic
919C22C4×#6325411yescharacteristic
920C22C4×#6325611yescharacteristic
921C22#1176328111yescharacteristic
922C22#1176328211yescharacteristic
923C22#1176328511yescharacteristic
924C22#1176328911yescharacteristic
925C22#1176336711yescharacteristic
926C22#1176338611yescharacteristic
927C22#1176339111yescharacteristic
928C22#1176339411yescharacteristic
929C22#1176339911yescharacteristic
930C22#1176340511yescharacteristic
931C22#1176340811yescharacteristic
932C22#1176340811yescharacteristic
933C22#1176341111yescharacteristic
934C22#1176341211yescharacteristic
935C22#1176342311yescharacteristic
936C22#1176343311yescharacteristic
937C22#1176345011yescharacteristic
938C22#1176346111yescharacteristic
939C22#1176346511yescharacteristic
940C22#1176347711yescharacteristic
941C22#1176348211yescharacteristic
942C22#1176349711yescharacteristic
943C22#1176350111yescharacteristic
944C22#1176351211yescharacteristic
945C22#1176351211yescharacteristic
946C22#1176352511yescharacteristic
947C22#1176352611yescharacteristic
948C22#1176353311yescharacteristic
949C22#1176355611yescharacteristic
950C22#1176355711yescharacteristic
951C22#1176356011yescharacteristic
952C22#1176356111yescharacteristic
953C4—24no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—81no—
959C4—81no—
960C4—682no—
961C4—682no—
962C4—682no—
963C4—682no—
964C4—682no—
965C4—682no—
966C4—682no—
967C2—1362no—
968C2#1453148411yescharacteristic
969C2#1453153911yescharacteristic
970C2#1453155011yescharacteristic
971C2#1453181011yescharacteristic
972C2#1453182111yescharacteristic
973C2#1453190311yescharacteristic
974C2#1453194911yescharacteristic
975C2#1453539611yescharacteristic
976C2#1453548611yescharacteristic
977C2#1453574111yescharacteristic
978C2#1453577411yescharacteristic
979C2#1453636311yescharacteristic
980C2#1453645311yescharacteristic
981C2#1453650611yescharacteristic
982C2#1453659911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1441C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenter#1441D17
hypocenterC17#14588
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. C2×#11762696C2semidirect
4. #14527053C2semidirect
10. #14527019C2semidirect
11. #14527018C2semidirect
12. #14527016C2semidirect
13. #14527013C2semidirect
14. #14527010C2semidirect
15. C17×#1441C2semidirect
29. #11762731C4semidirect
416. #1441D17semidirect
625. C17#14588semidirect

Maximal subgroups

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

subgroupindex
C2×#117627312
C2×#117627012
C2×#117626962
#145270532
#145270322
#145270262
#145270202
#145270192
#145270182
#145270162
#145270132
#145270102
C17×#14412
#1458817