Finite Group Databasebeta

← #17050416

Subgroups — #17050416

Order 4352.

1162 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763339C211yesmaximal, characteristic
2C2×#11762881C211yesmaximal, characteristic, complemented
3#14529723C211yesmaximal, characteristic, complemented
4#14529720C211yesmaximal, characteristic, complemented
5#14529081C211yesmaximal, characteristic, complemented
6#14529081C211yesmaximal, characteristic, complemented
7#14529079C211yesmaximal, characteristic, complemented
8#14529074C211yesmaximal, characteristic, complemented
9#14528853C211yesmaximal, characteristic, complemented
10#14528850C211yesmaximal, characteristic, complemented
11#14528765C211yesmaximal, characteristic, complemented
12#14528551C211yesmaximal, characteristic, complemented
13#14528482C211yesmaximal, characteristic, complemented
14#14528477C211yesmaximal, characteristic, complemented
15C2×C17×#436C211yesmaximal, characteristic, complemented
16C22×#63223C2211yescharacteristic
17C23×#3622C2211yescharacteristic
18#11763339—24no—
19#11763339—24no—
20C2×#10587584C411yescharacteristic
21C2×#10587565C411yescharacteristic
22C2×#10587575C411yescharacteristic
23C2×#10587571C411yescharacteristic
24C2×#10587572C411yescharacteristic
25C2×#10587621C411yescharacteristic
26C2×#10587564C411yescharacteristic
27C2×#10587625C411yescharacteristic
28C2×C4×Dic34C2211yescharacteristic
29C2×C4×C22⋊D17C2211yescharacteristic
30C2×C4×C22⋊D17C2211yescharacteristic
31C2×#10587612C2211yescharacteristic
32C2×#10587558C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34#11762881—24no—
35C2×C4⋊#3622C2211yescharacteristic
36C2×C22⋊#3622C2211yescharacteristic
37C2×C22⋊#3622C2211yescharacteristic
38C2×#10587491C2211yescharacteristic
39C2×#10587491C2211yescharacteristic
40C2×#10587491C2211yescharacteristic
41C2×#10587491C2211yescharacteristic
42C2×#10587474C2211yescharacteristic
43#11762563C2211yescharacteristic
44#11762563C2211yescharacteristic
45#11762563C2211yescharacteristic
46#11762563C2211yescharacteristic
47#11762563C2211yescharacteristic
48#11762563C2211yescharacteristic
49#11762563C2211yescharacteristic
50#11762563C2211yescharacteristic
51#11762563C2211yescharacteristic
52#11762563C2211yescharacteristic
53#11762563C2211yescharacteristic
54#11762563C2211yescharacteristic
55C22×M16×C17C2211yescharacteristic
56C22×M16×C17C2211yescharacteristic
57C2×C4×D4×C17C2211yescharacteristic
58C17×#436—24no—
59C2×C17×C4⋊C8C2211yescharacteristic
60C2×C17×C22⋊C8C2211yescharacteristic
61C2×C17×C22⋊C8C2211yescharacteristic
62C2×C4×C8×C17C2211yescharacteristic
63C22×D4×C17C2×C411yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C22×C22⋊D17C2×C411yescharacteristic
67C22×C22⋊D17C2×C411yescharacteristic
68C23×Dic17C2×C411yescharacteristic
69C23×Dic17C2×C411yescharacteristic
70C22×C4×D17C2311yescharacteristic
71C22×Dic34C2×C411yescharacteristic
72C2×M16×C17—22no—
73C2×M16×C17—22no—
74C2×M16×C17—22no—
75C2×M16×C17—22no—
76C2×M16×C17—41no—
77C2×M16×C17—41no—
78C22×C8×C17C2311yescharacteristic
79C22×C8×C17C2311yescharacteristic
80C22×C8×C17C2311yescharacteristic
81C22×C8×C17C2311yescharacteristic
82C4×D4×C17D414yes—
83C4×D4×C17D414yes—
84C2×C4⋊C4×C17C2×C411yescharacteristic
85C2×C22⋊C4×C17C2×C411yescharacteristic
86C2×C22⋊C4×C17C2×C411yescharacteristic
87C2×C42×C17C2311yescharacteristic
88C2×C22⋊Dic17C2×C411yescharacteristic
89C2×C22⋊Dic17C2×C411yescharacteristic
90C2×C22⋊Dic17C2×C411yescharacteristic
91C2×C22⋊Dic17C2×C411yescharacteristic
92#10587625—24no—
93#10587621—24no—
94C4×C22⋊D17—22no—
95C4×C22⋊D17—22no—
96C4×C22⋊D17—22no—
97C4×C22⋊D17—22no—
98C2×#63227C2×C411yescharacteristic
99C2×#63227C2×C411yescharacteristic
100C2×#63227C2×C411yescharacteristic
101C2×#63227C2×C411yescharacteristic
102#10587612—22no—
103#10587612—22no—
104C2×C4⋊Dic17C2×C411yescharacteristic
105C2×C4⋊Dic17C2×C411yescharacteristic
106C2×C4⋊Dic17C2×C411yescharacteristic
107C2×#63225C2×C411yescharacteristic
108C2×#63225C2×C411yescharacteristic
109C2×#63225C2×C411yescharacteristic
110C2×#63225C2×C411yescharacteristic
111C2×#63225C2×C411yescharacteristic
112C2×#63225C2×C411yescharacteristic
113C2×C4×Dic17—22no—
114C2×C4×Dic17—22no—
115C2×C4×Dic17C2×C411yescharacteristic
116C2×C4×Dic17C2×C411yescharacteristic
117C2×C4×Dic17C2311yescharacteristic
118C2×C4×Dic17C2311yescharacteristic
119C2×C4×Dic17C2311yescharacteristic
120C2×#63223—22no—
121C2×#63223—22no—
122C2×#63223—41no—
123C22×#3622—22no—
124C22×#3622—22no—
125C22×#3622—41no—
126C22×#3622C2311yescharacteristic
127C22×#3622C2311yescharacteristic
128C22×#3622C2311yescharacteristic
129C22×#3622C2311yescharacteristic
130#10587584—24no—
131#10587575—24no—
132#10587572—24no—
133#10587571—24no—
134#10587565—24no—
135#10587564—24no—
136#10587558—22no—
137#10587558—22no—
138C4×Dic34—22no—
139C4×Dic34—22no—
140C17×C4⋊C8—22no—
141C17×C22⋊C8—22no—
142C17×C22⋊C8—22no—
143C4×C8×C17—22no—
144C22⋊#3622—22no—
145C22⋊#3622—22no—
146#10587491—22no—
147#10587491—22no—
148#10587491—41no—
149#10587491—41no—
150C4⋊#3622—22no—
151#10587474—22no—
152C24×C17C22×C411yescharacteristic
153C24×C17C22×C411yescharacteristic
154C23×D17C22×C411yescharacteristic
155C2×D4×C17—41no—
156C2×D4×C17—41no—
157C2×D4×C17C22⋊C414yes—
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×C17C22×C411yescharacteristic
167C22×C4×C17C22×C411yescharacteristic
168C22×C4×C17C22×C411yescharacteristic
169C22×C4×C17C22×C411yescharacteristic
170C22×C4×C17C2×D412yes—
171C22×C4×C17C2×D412yes—
172C22×C4×C17C2×D412yes—
173C22×C4×C17C2×D412yes—
174C22×C4×C17C2411yescharacteristic
175C2×C22⋊D17—22no—
176C2×C22⋊D17—22no—
177C2×C22⋊D17—22no—
178C2×C22⋊D17—41no—
179C2×C22⋊D17—41no—
180C2×C22⋊D17—41no—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—41no—
185C22×Dic17—41no—
186C22×Dic17—41no—
187C22×Dic17C22×C411yescharacteristic
188C22×Dic17C22×C411yescharacteristic
189C22×Dic17C22×C411yescharacteristic
190C22×Dic17C22×C411yescharacteristic
191C22×Dic17C22×C411yescharacteristic
192C22×Dic17C22×C411yescharacteristic
193C22×Dic17C22×C411yescharacteristic
194C2×C4×D17—21no—
195C2×C4×D17—21no—
196C2×C4×D17—21no—
197C2×C4×D17—21no—
198C2×C4×D17—21no—
199C2×C4×D17—21no—
200C2×Dic34—22no—
201C2×Dic34—22no—
202C2×Dic34—41no—
203M16×C17—44no—
204M16×C17—44no—
205C2×C8×C17—21no—
206C2×C8×C17—21no—
207C2×C8×C17—21no—
208C2×C8×C17—21no—
209C2×C8×C17—21no—
210C2×C8×C17—21no—
211C2×C8×C17—21no—
212C2×C8×C17—21no—
213C2×C8×C17—21no—
214C2×C8×C17—21no—
215C2×C8×C17—21no—
216C2×C8×C17#4112yes—
217C4⋊C4×C17C22⋊C414yes—
218C22⋊C4×C17C22⋊C414yes—
219C22⋊C4×C17C22⋊C414yes—
220C42×C17C2×D412yes—
221C42×C17C2×D412yes—
222C22⋊Dic17—22no—
223C22⋊Dic17—22no—
224C22⋊Dic17—22no—
225C22⋊Dic17—22no—
226#63227—22no—
227#63227—22no—
228#63227—22no—
229#63227—22no—
230C4⋊Dic17—22no—
231C4⋊Dic17—22no—
232C4⋊Dic17—22no—
233#63225—22no—
234#63225—22no—
235#63225—22no—
236#63225—22no—
237#63225—22no—
238#63225—22no—
239C4×Dic17—22no—
240C4×Dic17—22no—
241C4×Dic17—21no—
242C4×Dic17—21no—
243C4×Dic17—21no—
244C4×Dic17—21no—
245C4×Dic17—21no—
246C4×Dic17—21no—
247#63223—44no—
248C2×#3622—21no—
249C2×#3622—21no—
250C2×#3622—21no—
251C2×#3622—21no—
252C2×#3622—21no—
253C2×#3622—21no—
254C2×#3622—21no—
255C2×#3622—21no—
256C2×#3622—21no—
257C2×#3622—21no—
258C2×#3622—21no—
259C2×#3622—44no—
260C2×#3622#4112yes—
261#22472—171nomaximal, Sylow
262C23×C17—21no—
263C23×C17—21no—
264C23×C17—21no—
265C23×C17—21no—
266C23×C17—21no—
267C23×C17—21no—
268C23×C17—21no—
269C23×C17—21no—
270C23×C17—21no—
271C23×C17—21no—
272C23×C17—21no—
273C23×C17—21no—
274C23×C17C2×C22⋊C412yes—
275C23×C17C2×C22⋊C412yes—
276C23×C17C23×C411yescharacteristic
277C22×D17—21no—
278C22×D17—21no—
279C22×D17—21no—
280C22×D17—21no—
281C22×D17—21no—
282C22×D17—21no—
283C22×D17—21no—
284D4×C17—44no—
285C2×C4×C17—21no—
286C2×C4×C17—21no—
287C2×C4×C17—21no—
288C2×C4×C17—21no—
289C2×C4×C17—21no—
290C2×C4×C17—21no—
291C2×C4×C17—21no—
292C2×C4×C17—21no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—22no—
300C2×C4×C17—22no—
301C2×C4×C17C2×C22⋊C412yes—
302C2×C4×C17C2×C22⋊C412yes—
303C2×C4×C17C2×C22⋊C412yes—
304C2×C4×C17C2×C22⋊C412yes—
305C2×C4×C17C22×D411yescharacteristic
306C2×C4×C17C22×D411yescharacteristic
307C2×C4×C17C2×#4111yescharacteristic
308C2×C4×C17C2×#4111yescharacteristic
309C2×C4×C17H(5,𝔽2)11yescharacteristic
310C2×C4×C172−1+411yescharacteristic
311C22⋊D17—44no—
312C22⋊D17—44no—
313C2×Dic17—21no—
314C2×Dic17—21no—
315C2×Dic17—21no—
316C2×Dic17—21no—
317C2×Dic17—21no—
318C2×Dic17—21no—
319C2×Dic17—21no—
320C2×Dic17—21no—
321C2×Dic17—21no—
322C2×Dic17—21no—
323C2×Dic17—21no—
324C2×Dic17—21no—
325C2×Dic17—21no—
326C2×Dic17—21no—
327C2×Dic17—21no—
328C2×Dic17—21no—
329C2×Dic17—21no—
330C2×Dic17—21no—
331C2×Dic17—21no—
332C2×Dic17—21no—
333C2×Dic17—44no—
334C2×Dic17—44no—
335C2×Dic17#13112yes—
336C4×D17—41no—
337C4×D17—41no—
338C4×D17—41no—
339C4×D17—41no—
340Dic34—44no—
341C8×C17—22no—
342C8×C17—41no—
343C8×C17—41no—
344C8×C17—41no—
345#3622—22no—
346#3622—41no—
347#3622—41no—
348#3622—41no—
349C2×#529—171no—
350C2×#436D1711yescharacteristic, complemented
351C2×#435—171no—
352#1985—171no—
353#1984—171no—
354#1870—171no—
355#1870—171no—
356#1870—171no—
357#1869—171no—
358#1818—171no—
359#1817—171no—
360#1798—171no—
361#1750—171no—
362#1729—171no—
363#1728—171no—
364C22×C17—22no—
365C22×C17—22no—
366C22×C17—22no—
367C22×C17—22no—
368C22×C17—22no—
369C22×C17—22no—
370C22×C17—41no—
371C22×C17—41no—
372C22×C17—41no—
373C22×C17—41no—
374C22×C17—41no—
375C22×C17—41no—
376C22×C17—41no—
377C22×C17—41no—
378C22×C17C22×C22⋊C411yescharacteristic
379C22×C17C4×#4111yescharacteristic
380C22×C17#52011yescharacteristic
381C22×C17C2×#13111yescharacteristic
382C22×C17#56811yescharacteristic
383C22×C17#56811yescharacteristic
384C22×C17#56811yescharacteristic
385C2×D17—41no—
386C2×D17—41no—
387C2×D17—41no—
388C2×D17—41no—
389C2×D17—41no—
390C2×D17—41no—
391C2×D17—41no—
392C4×C17—22no—
393C4×C17—22no—
394C4×C17—22no—
395C4×C17—22no—
396C4×C17#54611yescharacteristic
397C4×C17#54611yescharacteristic
398C4×C17#54711yescharacteristic
399C4×C17#54711yescharacteristic
400Dic17—22no—
401Dic17—41no—
402Dic17—41no—
403Dic17—41no—
404Dic17—41no—
405Dic17—41no—
406Dic17—41no—
407C22×M16—171no—
408C22×M16C2×D1711yescharacteristic
409C22×M16C2×D1711yescharacteristic
410C23×C8—171no—
411#529—344no—
412#529—344no—
413C2×#126—171no—
414C2×#126—171no—
415C2×#125—171no—
416C2×#124—171no—
417C2×#123—171no—
418C2×#123—171no—
419C2×C22⋊Q8—171no—
420C2×#121—171no—
421C2×C4×Q8—171no—
422C2×C4×D4—171no—
423C2×C4×D4—171no—
424C2×C4×D4C2×D1711yescharacteristic
425C2×#117—171no—
426C2×#117—171no—
427C22×C42—171no—
428#436—24no—
429#435—344no—
430C2×C4⋊C8—171no—
431C2×C4⋊C8C2×D1711yescharacteristic
432C2×C22⋊C8—171no—
433C2×C22⋊C8—171no—
434C2×C22⋊C8—171no—
435C2×C22⋊C8—171no—
436C2×C22⋊C8—171no—
437C2×C22⋊C8—171no—
438C2×C22⋊C8C2×D1711yescharacteristic
439C2×C22⋊C8C2×D1711yescharacteristic
440C2×#97—171no—
441C2×C4×C8C2×D1711yescharacteristic
442#336—171no—
443#336—171no—
444#336—171no—
445#336—171no—
446#336—171no—
447#336—171no—
448#336—171no—
449#336—171no—
450#336—171no—
451#336—171no—
452#336—171no—
453#336—171no—
454C2×C17—42no—
455C2×C17—42no—
456C2×C17#233911yescharacteristic
457C2×C17#287911yescharacteristic
458C2×C17#288011yescharacteristic
459C2×C17#296711yescharacteristic
460C2×C17#296911yescharacteristic
461C2×C17#299311yescharacteristic
462C2×C17#299511yescharacteristic
463D17—81no—
464C22×Q8—171no—
465C22×D4—171no—
466C22×D4—171no—
467C22×D4C4×D1711yescharacteristic
468C23×C4—171no—
469C23×C4—171no—
470C23×C4—171no—
471C23×C4C22×D1711yescharacteristic
472C23×C4C22×D1711yescharacteristic
473C2×M16—22no—
474C2×M16—22no—
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—41no—
478C2×M16—41no—
479C2×M16—342no—
480C2×M16—342no—
481C2×M16—681no—
482C22×C8—171no—
483C22×C8—171no—
484C22×C8—171no—
485C22×C8—171no—
486C22×C8—342no—
487C22×C8—342no—
488C22×C8—681no—
489C22×C8C22×D1711yescharacteristic
490C22×C8C22×D1711yescharacteristic
491C22×C8C22×D1711yescharacteristic
492C22×C8C22×D1711yescharacteristic
493#126—344no—
494#126—344no—
495#125—344no—
496#124—344no—
497#123—344no—
498#123—344no—
499C22⋊Q8—344no—
500#121—344no—
501C4×Q8—342no—
502C4×Q8—342no—
503C4×D4—342no—
504C4×D4—342no—
505C4×D4—342no—
506C4×D4—342no—
507C4×D4D6814yes—
508C4×D4C22⋊D1714yes—
509#117—342no—
510#117—342no—
511#117—342no—
512#117—342no—
513C2×C4⋊C4—171no—
514C2×C4⋊C4—171no—
515C2×C4⋊C4—171no—
516C2×C4⋊C4—171no—
517C2×C4⋊C4—171no—
518C2×C4⋊C4—171no—
519C2×C4⋊C4—171no—
520C2×C4⋊C4—171no—
521C2×C4⋊C4—171no—
522C2×C4⋊C4C4×D1711yescharacteristic
523C2×C22⋊C4—171no—
524C2×C22⋊C4—171no—
525C2×C22⋊C4—171no—
526C2×C22⋊C4—171no—
527C2×C22⋊C4—171no—
528C2×C22⋊C4—171no—
529C2×C22⋊C4—171no—
530C2×C22⋊C4—171no—
531C2×C22⋊C4C4×D1711yescharacteristic
532C2×C22⋊C4C4×D1711yescharacteristic
533C2×C42—171no—
534C2×C42—171no—
535C2×C42—171no—
536C2×C42—171no—
537C2×C42—171no—
538C2×C42—342no—
539C2×C42—342no—
540C2×C42C22×D1711yescharacteristic
541C4⋊C8—22no—
542C4⋊C8—342no—
543C22⋊C8—22no—
544C22⋊C8—22no—
545C22⋊C8—342no—
546C22⋊C8—342no—
547C22⋊C8—342no—
548C22⋊C8—342no—
549C22⋊C8—681no—
550C22⋊C8—681no—
551#97—342no—
552C4×C8—22no—
553C17#2247211yescharacteristic, complemented, Sylow
554C24—171no—
555C24C2×C4×D1711yescharacteristic
556C24C2×C4×D1711yescharacteristic
557C2×Q8—342no—
558C2×Q8—342no—
559C2×Q8—681no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—342no—
563C2×D4—342no—
564C2×D4—342no—
565C2×D4—681no—
566C2×D4—681no—
567C2×D4—681no—
568C2×D4#6322714yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—171no—
578C22×C4—171no—
579C22×C4—171no—
580C22×C4—171no—
581C22×C4—171no—
582C22×C4—171no—
583C22×C4—171no—
584C22×C4—342no—
585C22×C4—342no—
586C22×C4—342no—
587C22×C4—341no—
588C22×C4—341no—
589C22×C4—341no—
590C22×C4—341no—
591C22×C4—341no—
592C22×C4—341no—
593C22×C4—681no—
594C22×C4—681no—
595C22×C4—681no—
596C22×C4C2×C4×D1711yescharacteristic
597C22×C4C2×C4×D1711yescharacteristic
598C22×C4C2×C4×D1711yescharacteristic
599C22×C4C2×C4×D1711yescharacteristic
600C22×C4C2×D6812yes—
601C22×C4C2×D6812yes—
602C22×C4C2×C22⋊D1712yes—
603C22×C4C2×C22⋊D1712yes—
604C22×C4C23×D1711yescharacteristic
605M16—44no—
606M16—44no—
607M16—684no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—172no—
620C2×C8—341no—
621C2×C8—341no—
622C2×C8—341no—
623C2×C8—341no—
624C2×C8—341no—
625C2×C8—341no—
626C2×C8—341no—
627C2×C8—341no—
628C2×C8—341no—
629C2×C8—341no—
630C2×C8—341no—
631C2×C8—684no—
632C2×C8#6325412yes—
633C4⋊C4—342no—
634C4⋊C4—342no—
635C4⋊C4—342no—
636C4⋊C4—342no—
637C4⋊C4—342no—
638C4⋊C4—342no—
639C4⋊C4—342no—
640C4⋊C4—342no—
641C4⋊C4—342no—
642C4⋊C4#6322714yes—
643C22⋊C4—342no—
644C22⋊C4—342no—
645C22⋊C4—342no—
646C22⋊C4—342no—
647C22⋊C4—342no—
648C22⋊C4—342no—
649C22⋊C4—342no—
650C22⋊C4—342no—
651C22⋊C4#6322714yes—
652C22⋊C4#6322714yes—
653C42—341no—
654C42—341no—
655C42—341no—
656C42—341no—
657C42—341no—
658C42—341no—
659C42—342no—
660C42—342no—
661C42C2×D6812yes—
662C42C2×C22⋊D1712yes—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—341no—
676C23—341no—
677C23—341no—
678C23—341no—
679C23—341no—
680C23—341no—
681C23—341no—
682C23C2×#6322712yes—
683C23C2×#6322712yes—
684C23C22×C4×D1711yescharacteristic
685Q8—684no—
686D4—44no—
687D4—684no—
688D4—684no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—172no—
706C2×C4—341no—
707C2×C4—341no—
708C2×C4—341no—
709C2×C4—341no—
710C2×C4—341no—
711C2×C4—341no—
712C2×C4—341no—
713C2×C4—341no—
714C2×C4—341no—
715C2×C4—341no—
716C2×C4—341no—
717C2×C4—341no—
718C2×C4—341no—
719C2×C4—341no—
720C2×C4—341no—
721C2×C4—341no—
722C2×C4—341no—
723C2×C4—341no—
724C2×C4—341no—
725C2×C4—341no—
726C2×C4—684no—
727C2×C4—684no—
728C2×C4—681no—
729C2×C4—681no—
730C2×C4—681no—
731C2×C4—681no—
732C2×C4C2×#6322712yes—
733C2×C4C2×#6322712yes—
734C2×C4C2×#6322712yes—
735C2×C4C2×#6322712yes—
736C2×C4C22×D6811yescharacteristic
737C2×C4C2×#6325411yescharacteristic
738C2×C4#1058769111yescharacteristic
739C2×C4#41×D1711yescharacteristic
740C2×C4#1058769711yescharacteristic
741C2×C4C22×C22⋊D1711yescharacteristic
742C8—22no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—342no—
747C8—681no—
748C8—681no—
749C8—681no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—681no—
765C22—681no—
766C22—681no—
767C22—681no—
768C22—681no—
769C22—681no—
770C22—681no—
771C22C22×#6322711yescharacteristic
772C22C4×#6325411yescharacteristic
773C22#1176328811yescharacteristic
774C22#131×D1711yescharacteristic
775C22#1176357411yescharacteristic
776C22#1176357511yescharacteristic
777C22#1176357511yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—342no—
783C4—681no—
784C4—681no—
785C4—681no—
786C4—681no—
787C4—681no—
788C4—681no—
789C4#1176345311yescharacteristic
790C4#1176345411yescharacteristic
791C4#1176345811yescharacteristic
792C4#1176346311yescharacteristic
793C2—42no—
794C2—42no—
795C2—1361no—
796C2#1453160911yescharacteristic
797C2#1453722811yescharacteristic
798C2#1453723111yescharacteristic
799C2#1453777011yescharacteristic
800C2#1453778311yescharacteristic
801C2#1453793011yescharacteristic
802C2#1453794811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC2×C17×#436C2
prime radicalC2×#10587625C4
cosocleC22×C4×C17C24
hypercenterC2×#436D17
hypocenterC17#22472
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. C2×#11762881C2semidirect
3. #14529723C2semidirect
4. #14529720C2semidirect
5. #14529081C2semidirect
6. #14529081C2semidirect
7. #14529079C2semidirect
8. #14529074C2semidirect
9. #14528853C2semidirect
10. #14528850C2semidirect
11. #14528765C2semidirect
12. #14528551C2semidirect
13. #14528482C2semidirect
14. #14528477C2semidirect
15. C2×C17×#436C2semidirect
350. C2×#436D17semidirect
553. C17#22472semidirect

Maximal subgroups

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

subgroupindex
C2×#117633392
C2×#117628812
#145297232
#145297202
#145290812
#145290792
#145290742
#145288532
#145288502
#145287652
#145285512
#145284822
#145284772
C2×C17×#4362
#2247217