Finite Group Databasebeta

← #17050674

Subgroups — #17050674

Order 4352.

1390 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763463C211yesmaximal, characteristic
2#14531713C211yesmaximal, characteristic, complemented
3#14529757C211yesmaximal, characteristic, complemented
4#14529731C211yesmaximal, characteristic, complemented
5#14529222C211yesmaximal, characteristic, complemented
6#14529212C211yesmaximal, characteristic, complemented
7#14529104C211yesmaximal, characteristic, complemented
8#14529099C211yesmaximal, characteristic, complemented
9#14528875C211yesmaximal, characteristic, complemented
10#14528871C211yesmaximal, characteristic, complemented
11#14528795C211yesmaximal, characteristic, complemented
12#14528610C211yesmaximal, characteristic, complemented
13#14528504C211yesmaximal, characteristic, complemented
14C2×#11762572C211yesmaximal, characteristic, complemented
15C2×C17×#435C211yesmaximal, characteristic, complemented
16C22×#63254—21no—
17#11763463—24no—
18#11763463C418yescomplemented
19C2×#10587555C2211yescharacteristic
20C2×#10587572—21no—
21C2×#10587572—21no—
22C2×#10587583—21no—
23C2×#10587616C2211yescharacteristic
24C2×#10587616C2211yescharacteristic
25C2×C4×D68C2211yescharacteristic
26C2×#10587612C2211yescharacteristic
27C22×C4⋊Dic17C2211yescharacteristic
28C22×C4⋊Dic17C2211yescharacteristic
29C22×C4⋊Dic17C2211yescharacteristic
30C2×#10587492C2211yescharacteristic
31C2×#10587492C2211yescharacteristic
32C2×#10587492C2211yescharacteristic
33C2×#10587492C2211yescharacteristic
34#11762702—21no—
35#11762695—21no—
36#11762689—21no—
37#11762675C2211yescharacteristic
38#11762669C2211yescharacteristic
39#11762669C2211yescharacteristic
40C4×C4⋊Dic17C2211yescharacteristic
41C22⋊C4×Dic17—21no—
42#11762572C2211yescharacteristic
43#11762572C2211yescharacteristic
44#11762572C2211yescharacteristic
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762572C2211yescharacteristic
50#11762572C2211yescharacteristic
51#11762572C2211yescharacteristic
52#11762572C2211yescharacteristic
53#11762572C2211yescharacteristic
54C22×M16×C17C2211yescharacteristic
55C23×C8×C17C2211yescharacteristic
56C2×C4×D4×C17C2211yescharacteristic
57C17×#435—24no—
58C2×C17×C4⋊C8C2211yescharacteristic
59C2×C17×C22⋊C8C2211yescharacteristic
60C2×C17×C22⋊C8C2211yescharacteristic
61C2×C17×#97C2211yescharacteristic
62C22×D4×C17D411yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C22×C22⋊D17—21no—
66C22×C22⋊D17—21no—
67C23×Dic17—21no—
68C23×Dic17—21no—
69C23×Dic17—21no—
70C2×#63254—28no—
71C2×#63254—44no—
72C2×#63254—44no—
73C22×D68C2311yescharacteristic
74C22×C4×D17—21no—
75C22×Dic34—21no—
76C2×M16×C17—22no—
77C2×M16×C17—22no—
78C2×M16×C17—41no—
79C22×C8×C17—22no—
80C22×C8×C17—22no—
81C22×C8×C17—41no—
82C22×C8×C17C2311yescharacteristic
83C22×C8×C17C2311yescharacteristic
84C22×C8×C17C2311yescharacteristic
85C22×C8×C17C2311yescharacteristic
86C4×D4×C17C2×C414yes—
87C4×D4×C17D414yes—
88C2×C4⋊C4×C17D411yescharacteristic
89C2×C22⋊C4×C17D411yescharacteristic
90C2×C22⋊C4×C17D411yescharacteristic
91C2×C42×C17C2311yescharacteristic
92C2×C22⋊Dic17—21no—
93C2×C22⋊Dic17—21no—
94C2×C22⋊Dic17—21no—
95#10587616—22no—
96#10587616—22no—
97#10587616C2×C414yes—
98#10587616C2×C414yescomplemented
99C2×#63227—21no—
100C2×#63227—21no—
101C2×#63227—21no—
102#10587612—22no—
103#10587612—41no—
104C2×C4⋊Dic17—22no—
105C2×C4⋊Dic17—22no—
106C2×C4⋊Dic17—21no—
107C2×C4⋊Dic17—21no—
108C2×C4⋊Dic17—21no—
109C2×C4⋊Dic17—21no—
110C2×C4⋊Dic17—22no—
111C2×C4⋊Dic17—41no—
112C2×C4⋊Dic17C2×C414yes—
113C2×C4⋊Dic17C2×C414yescomplemented
114C2×C4⋊Dic17C2311yescharacteristic
115C2×C4⋊Dic17C2311yescharacteristic
116C2×C4⋊Dic17C2311yescharacteristic
117C2×C4⋊Dic17C2311yescharacteristic
118C2×C4⋊Dic17C2311yescharacteristic
119C2×C4⋊Dic17C2311yescharacteristic
120C2×C4⋊Dic17C2311yescharacteristic
121C2×C4×Dic17—21no—
122C2×C4×Dic17—21no—
123#10587583—28no—
124#10587572—28no—
125#10587572—28no—
126C4×D68—22no—
127C4×D68C2×C414yescomplemented
128#10587555—22no—
129#10587555C2×C414yescomplemented
130C17×C4⋊C8—22no—
131C17×C22⋊C8—22no—
132C17×C22⋊C8—22no—
133C17×#97—22no—
134#10587502—21no—
135#10587502—21no—
136#10587502—21no—
137#10587502—21no—
138#10587502—21no—
139#10587492—22no—
140#10587492—22no—
141#10587492—41no—
142#10587492—41no—
143C24×C17C2×D411yescharacteristic
144C24×C17C2×D411yescharacteristic
145C23×D17—21no—
146C2×D4×C17—22no—
147C2×D4×C17—22no—
148C2×D4×C17C22⋊C414yes—
149C22×C4×C17—21no—
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×C17C22×C412yes—
158C22×C4×C17C22×C412yes—
159C22×C4×C17C2×D411yescharacteristic
160C22×C4×C17C2×D411yescharacteristic
161C22×C4×C17C2×D411yescharacteristic
162C22×C4×C17C2×D411yescharacteristic
163C22×C4×C17C2×D412yes—
164C22×C4×C17C2×D412yes—
165C22×C4×C17C2411yescharacteristic
166C2×C22⋊D17—24no—
167C2×C22⋊D17—24no—
168C2×C22⋊D17—42no—
169C2×C22⋊D17—42no—
170C2×C22⋊D17—42no—
171C2×C22⋊D17—42no—
172C22×Dic17—24no—
173C22×Dic17—24no—
174C22×Dic17—21no—
175C22×Dic17—21no—
176C22×Dic17—21no—
177C22×Dic17—21no—
178C22×Dic17—21no—
179C22×Dic17—21no—
180C22×Dic17—21no—
181C22×Dic17—42no—
182C22×Dic17—42no—
183C22×Dic17—42no—
184C22×Dic17—42no—
185C22×Dic17—42no—
186C22×Dic17—42no—
187C22×Dic17—81no—
188#63254—432no—
189C2×D68—21no—
190C2×D68—21no—
191C2×D68—21no—
192C2×D68—21no—
193C2×D68—21no—
194C2×D68C22×C412yes—
195C2×C4×D17—24no—
196C2×C4×D17—42no—
197C2×C4×D17—42no—
198C2×Dic34—24no—
199C2×Dic34—42no—
200C2×Dic34—42no—
201M16×C17—44no—
202C2×C8×C17—21no—
203C2×C8×C17—21no—
204C2×C8×C17—21no—
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—44no—
214C2×C8×C17#4112yescomplemented
215C4⋊C4×C17C22⋊C414yes—
216C22⋊C4×C17C22⋊C414yes—
217C22⋊C4×C17C22⋊C414yes—
218C42×C17C22×C412yes—
219C42×C17C2×D412yes—
220C22⋊Dic17—42no—
221C22⋊Dic17—42no—
222C22⋊Dic17—81no—
223#63227—24no—
224#63227—24no—
225#63227—24no—
226C4⋊Dic17—24no—
227C4⋊Dic17—24no—
228C4⋊Dic17—24no—
229C4⋊Dic17—21no—
230C4⋊Dic17—21no—
231C4⋊Dic17—21no—
232C4⋊Dic17—21no—
233C4⋊Dic17—21no—
234C4⋊Dic17—21no—
235C4⋊Dic17—21no—
236C4⋊Dic17—21no—
237C4⋊Dic17—21no—
238C4⋊Dic17—21no—
239C4⋊Dic17—42no—
240C4⋊Dic17C22×C412yes—
241C4⋊Dic17C22×C412yes—
242C4⋊Dic17C22×C412yes—
243C4⋊Dic17#4112yescomplemented
244C4×Dic17—42no—
245C4×Dic17—81no—
246#22495—171nomaximal, Sylow
247C23×C17—21no—
248C23×C17—21no—
249C23×C17—21no—
250C23×C17—21no—
251C23×C17—21no—
252C23×C17—21no—
253C23×C17—21no—
254C23×C17—21no—
255C23×C17—21no—
256C23×C17—21no—
257C23×C17C2×C22⋊C412yes—
258C23×C17C2×C22⋊C412yes—
259C23×C17AGL(1,ℤ/8)12yes—
260C23×C17AGL(1,ℤ/8)12yes—
261C23×C17C22×D411yescharacteristic
262C22×D17—22no—
263C22×D17—41no—
264C22×D17—41no—
265C22×D17—41no—
266C22×D17—41no—
267C22×D17—41no—
268C22×D17—41no—
269D4×C17—28no—
270C2×C4×C17—21no—
271C2×C4×C17—21no—
272C2×C4×C17—21no—
273C2×C4×C17—21no—
274C2×C4×C17—21no—
275C2×C4×C17—21no—
276C2×C4×C17—21no—
277C2×C4×C17—21no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17C2×C22⋊C412yes—
287C2×C4×C17C2×C22⋊C412yes—
288C2×C4×C17C2×C22⋊C412yes—
289C2×C4×C17C2×C22⋊C412yes—
290C2×C4×C17C23×C411yescharacteristic
291C2×C4×C17C22×D411yescharacteristic
292C2×C4×C17C2×#4111yescharacteristic
293C2×C4×C17C2×#4111yescharacteristic
294C2×C4×C17H(5,𝔽2)11yescharacteristic
295C2×C4×C172−1+411yescharacteristic
296C22⋊D17—48no—
297C22⋊D17—48no—
298C2×Dic17—22no—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17—22no—
302C2×Dic17—48no—
303C2×Dic17—41no—
304C2×Dic17—41no—
305C2×Dic17—41no—
306C2×Dic17—41no—
307C2×Dic17—41no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17—48no—
312C2×Dic17—41no—
313C2×Dic17—41no—
314C2×Dic17—41no—
315C2×Dic17—41no—
316C2×Dic17—41no—
317C2×Dic17—41no—
318C2×Dic17—41no—
319C2×Dic17—41no—
320C2×Dic17—41no—
321C2×Dic17—84no—
322D68—22no—
323D68—22no—
324D68—41no—
325D68—41no—
326C4×D17—48no—
327Dic34—48no—
328C8×C17—22no—
329C8×C17—41no—
330C8×C17—41no—
331C8×C17—41no—
332C2×#547—171no—
333C2×#435D1711yescharacteristic, complemented
334#2352—171no—
335#1993—171no—
336#1987—171no—
337#1895—171no—
338#1893—171no—
339#1875—171no—
340#1874—171no—
341#1824—171no—
342#1823—171no—
343#1804—171no—
344#1762—171no—
345#1736—171no—
346C2×#340—171no—
347C22×C17—22no—
348C22×C17—22no—
349C22×C17—22no—
350C22×C17—22no—
351C22×C17—22no—
352C22×C17—22no—
353C22×C17—22no—
354C22×C17—22no—
355C22×C17—22no—
356C22×C17—41no—
357C22×C17—41no—
358C22×C17—41no—
359C22×C17—41no—
360C22×C17#41814yes—
361C22×C17C22×C22⋊C411yescharacteristic
362C22×C17#54611yescharacteristic
363C22×C17#54711yescharacteristic
364C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C17#57711yescharacteristic
367C22×C17#57811yescharacteristic
368C2×D17—42no—
369C2×D17—42no—
370C2×D17—42no—
371C2×D17—81no—
372C2×D17—81no—
373C2×D17—81no—
374C2×D17—81no—
375C4×C17—22no—
376C4×C17—22no—
377C4×C17—22no—
378C4×C17—22no—
379C4×C17C4×#4111yescharacteristic
380C4×C17#52011yescharacteristic
381C4×C17#54611yescharacteristic
382C4×C17#54711yescharacteristic
383Dic17—42no—
384Dic17—42no—
385Dic17—42no—
386Dic17—42no—
387Dic17—81no—
388Dic17—81no—
389Dic17—81no—
390C22×#41—341no—
391C22×M16C2×D1711yescharacteristic
392C23×C8C2×D1711yescharacteristic
393#547—178no—
394#547—344no—
395C2×C4⋊Q8—171no—
396C2×#123—341no—
397C2×#123—341no—
398C2×C22⋊Q8—341no—
399C2×#121—171no—
400C2×#121—171no—
401C2×C4×D4—171no—
402C2×C4×D4C2×D1711yescharacteristic
403C2×#117—171no—
404C22×C4⋊C4—171no—
405C22×C4⋊C4—171no—
406C22×C4⋊C4—171no—
407#435—24no—
408C2×C4⋊C8C2×D1711yescharacteristic
409C2×#102—171no—
410C2×#102—171no—
411C2×#102—171no—
412C2×#102—171no—
413C2×C22⋊C8C2×D1711yescharacteristic
414C2×C22⋊C8C2×D1711yescharacteristic
415C2×#97C2×D1711yescharacteristic
416#388—341no—
417#387—341no—
418#386—341no—
419#382—171no—
420#380—171no—
421#380—171no—
422C4×C4⋊C4—171no—
423C4×C22⋊C4—341no—
424#340—171no—
425#340—171no—
426#340—171no—
427#340—171no—
428#340—171no—
429#340—171no—
430#340—171no—
431#340—171no—
432#340—171no—
433#340—171no—
434#340—171no—
435#340—171no—
436C2×C17—24no—
437C2×C17—42no—
438C2×C17#233911yescharacteristic
439C2×C17C2×#41811yescharacteristic
440C2×C17#289811yescharacteristic
441C2×C17#330611yescharacteristic
442C2×C17#330811yescharacteristic
443C2×C17#334311yescharacteristic
444C2×C17#334511yescharacteristic
445D17—82no—
446C2×#41—348no—
447C2×#41—684no—
448C2×#41—684no—
449C22×Q8—341no—
450C22×D4—171no—
451C22×D4—341no—
452C22×D4—341no—
453C22×D4D6811yescharacteristic
454C23×C4—341no—
455C23×C4—341no—
456C23×C4—341no—
457C23×C4—341no—
458C23×C4C22×D1711yescharacteristic
459C23×C4C22×D1711yescharacteristic
460C2×M16—22no—
461C2×M16—22no—
462C2×M16—41no—
463C22×C8—22no—
464C22×C8—22no—
465C22×C8—41no—
466C22×C8C22×D1711yescharacteristic
467C22×C8C22×D1711yescharacteristic
468C22×C8C22×D1711yescharacteristic
469C22×C8C22×D1711yescharacteristic
470C4⋊Q8—174no—
471C4⋊Q8—342no—
472#123—348no—
473#123—348no—
474C22⋊Q8—348no—
475#121—174no—
476#121—174no—
477#121—342no—
478#121—342no—
479C4×D4—174no—
480C4×D4—342no—
481C4×D4C4×D1714yes—
482C4×D4C22⋊D1714yes—
483#117—342no—
484#117—681no—
485C2×C4⋊C4—174no—
486C2×C4⋊C4—174no—
487C2×C4⋊C4—171no—
488C2×C4⋊C4—171no—
489C2×C4⋊C4—171no—
490C2×C4⋊C4—171no—
491C2×C4⋊C4—171no—
492C2×C4⋊C4—171no—
493C2×C4⋊C4—171no—
494C2×C4⋊C4—342no—
495C2×C4⋊C4—341no—
496C2×C4⋊C4—341no—
497C2×C4⋊C4—341no—
498C2×C4⋊C4—342no—
499C2×C4⋊C4—342no—
500C2×C4⋊C4—341no—
501C2×C4⋊C4—681no—
502C2×C4⋊C4D6811yescharacteristic
503C2×C22⋊C4—341no—
504C2×C22⋊C4—341no—
505C2×C22⋊C4—341no—
506C2×C22⋊C4—341no—
507C2×C22⋊C4—341no—
508C2×C22⋊C4—341no—
509C2×C22⋊C4D6811yescharacteristic
510C2×C22⋊C4D6811yescharacteristic
511C2×C42—341no—
512C2×C42—341no—
513C2×C42C22×D1711yescharacteristic
514C4⋊C8—22no—
515#102—342no—
516#102—342no—
517#102—681no—
518#102—681no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521#97—22no—
522#95—341no—
523#95—341no—
524#95—341no—
525#95—341no—
526#95—341no—
527C17#2249511yescharacteristic, complemented, Sylow
528C24—341no—
529C24C2×D6811yescharacteristic
530C24C2×D6811yescharacteristic
531#41—6832no—
532C2×Q8—344no—
533C2×Q8—682no—
534C2×Q8—682no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—172no—
538C2×D4—344no—
539C2×D4—344no—
540C2×D4—341no—
541C2×D4—341no—
542C2×D4—341no—
543C2×D4—341no—
544C2×D4—341no—
545C2×D4—682no—
546C2×D4—682no—
547C2×D4—682no—
548C2×D4—682no—
549C2×D4#6322714yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—341no—
559C22×C4—341no—
560C22×C4—341no—
561C22×C4—341no—
562C22×C4—344no—
563C22×C4—344no—
564C22×C4—344no—
565C22×C4—341no—
566C22×C4—341no—
567C22×C4—341no—
568C22×C4—682no—
569C22×C4—682no—
570C22×C4—682no—
571C22×C4—682no—
572C22×C4—682no—
573C22×C4—682no—
574C22×C4—682no—
575C22×C4—682no—
576C22×C4—1361no—
577C22×C4C2×C4×D1712yes—
578C22×C4C2×C4×D1712yes—
579C22×C4C2×D6811yescharacteristic
580C22×C4C2×D6811yescharacteristic
581C22×C4C2×D6811yescharacteristic
582C22×C4C2×D6811yescharacteristic
583C22×C4C2×C22⋊D1712yes—
584C22×C4C2×C22⋊D1712yes—
585C22×C4C23×D1711yescharacteristic
586M16—44no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—44no—
599C2×C8#6325412yescomplemented
600C4⋊C4—172no—
601C4⋊C4—172no—
602C4⋊C4—172no—
603C4⋊C4—172no—
604C4⋊C4—341no—
605C4⋊C4—341no—
606C4⋊C4—341no—
607C4⋊C4—341no—
608C4⋊C4—344no—
609C4⋊C4—344no—
610C4⋊C4—344no—
611C4⋊C4—341no—
612C4⋊C4—341no—
613C4⋊C4—341no—
614C4⋊C4—341no—
615C4⋊C4—341no—
616C4⋊C4—341no—
617C4⋊C4—682no—
618C4⋊C4#6322714yes—
619C22⋊C4—344no—
620C22⋊C4—344no—
621C22⋊C4—344no—
622C22⋊C4—682no—
623C22⋊C4—682no—
624C22⋊C4—1361no—
625C22⋊C4#6322714yes—
626C22⋊C4#6322714yes—
627C42—682no—
628C42—1361no—
629C42C2×C4×D1712yes—
630C42C2×C22⋊D1712yes—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—342no—
642C23—681no—
643C23—681no—
644C23—681no—
645C23—681no—
646C23—681no—
647C23—681no—
648C23#1058759412yes—
649C23#1058759412yes—
650C23C2×#6322712yes—
651C23C2×#6322712yes—
652C23C22×D6811yescharacteristic
653Q8—688no—
654D4—28no—
655D4—342no—
656D4—342no—
657D4—688no—
658D4—688no—
659D4—681no—
660D4—681no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—342no—
678C2×C4—342no—
679C2×C4—342no—
680C2×C4—342no—
681C2×C4—688no—
682C2×C4—688no—
683C2×C4—688no—
684C2×C4—681no—
685C2×C4—681no—
686C2×C4—681no—
687C2×C4—681no—
688C2×C4—681no—
689C2×C4—681no—
690C2×C4—681no—
691C2×C4—681no—
692C2×C4—681no—
693C2×C4—681no—
694C2×C4—681no—
695C2×C4—681no—
696C2×C4—681no—
697C2×C4—681no—
698C2×C4—681no—
699C2×C4—681no—
700C2×C4—681no—
701C2×C4—1364no—
702C2×C4C2×#6322712yes—
703C2×C4C2×#6322712yes—
704C2×C4C2×#6322712yes—
705C2×C4C2×#6322712yes—
706C2×C4C22×C4×D1711yescharacteristic
707C2×C4C2×#6325411yescharacteristic
708C2×C4#1058769111yescharacteristic
709C2×C4#41×D1711yescharacteristic
710C2×C4#1058769711yescharacteristic
711C2×C4C22×C22⋊D1711yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—682no—
730C22—682no—
731C22—682no—
732C22—1361no—
733C22—1361no—
734C22—1361no—
735C22—1361no—
736C22#1176281514yes—
737C22C22×#6322711yescharacteristic
738C22#1176345411yescharacteristic
739C22#1176346311yescharacteristic
740C22C2×#1058759411yescharacteristic
741C22C2×#1058759411yescharacteristic
742C22#1176362111yescharacteristic
743C22#1176362611yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—682no—
749C4—682no—
750C4—682no—
751C4—682no—
752C4—1361no—
753C4—1361no—
754C4—1361no—
755C4C4×#6325411yescharacteristic
756C4#1176328811yescharacteristic
757C4#1176345311yescharacteristic
758C4#1176345811yescharacteristic
759C2—24no—
760C2—42no—
761C2—1362no—
762C2#1453160911yescharacteristic
763C2C2×#1176281511yescharacteristic
764C2#1453731811yescharacteristic
765C2#1454074711yescharacteristic
766C2#1454077711yescharacteristic
767C2#1454122611yescharacteristic
768C2#1454125611yescharacteristic
subgroupG/H
centerC23C22×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#435C2
socleC23×C17C22×D4
prime radicalC2×#11763463C2
cosocleC22×C4×C17C24
hypercenterC2×#435D17
hypocenterC17#22495
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #14531713C2semidirect
3. #14529757C2semidirect
4. #14529731C2semidirect
5. #14529222C2semidirect
6. #14529212C2semidirect
7. #14529104C2semidirect
8. #14529099C2semidirect
9. #14528875C2semidirect
10. #14528871C2semidirect
11. #14528795C2semidirect
12. #14528610C2semidirect
13. #14528504C2semidirect
14. C2×#11762572C2semidirect
15. C2×C17×#435C2semidirect
18. #11763463C4semidirect
98. #10587616C2×C4semidirect
113. C2×C4⋊Dic17C2×C4semidirect
127. C4×D68C2×C4semidirect
129. #10587555C2×C4semidirect
214. C2×C8×C17#41semidirect
243. C4⋊Dic17#41semidirect
333. C2×#435D17semidirect
527. C17#22495semidirect
599. C2×C8#63254semidirect

Maximal subgroups

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

subgroupindex
C2×#117634632
#145317132
#145297572
#145297312
#145292222
#145292122
#145291042
#145290992
#145288752
#145288712
#145287952
#145286102
#145285042
C2×#117625722
C2×C17×#4352
#2249517