Finite Group Databasebeta

← #16957425

Subgroups — #16957425

Order 4352.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762707C211yesmaximal, characteristic, complemented
2C2×#11762697C212yesmaximal
3C2×#11762669C211yesmaximal, characteristic
4C2×#11762669C211yesmaximal, characteristic
5C2×C4×C4⋊Dic17C211yesmaximal, characteristic, complemented
6#14527039C212yesmaximal, complemented
7#14527031C212yesmaximal
8#14527014C211yesmaximal, characteristic, complemented
9#14527014C211yesmaximal, characteristic, complemented
10#14527008C212yesmaximal, complemented
11C2×C4×C22⋊C4×C17C211yesmaximal, characteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×C4⋊Dic17C2211yescharacteristic
14C22×C4⋊Dic17C2211yescharacteristic
15C22×C4⋊Dic17C2211yescharacteristic
16C22×#63225C2212yes—
17C22×C22⋊Dic17C2212yes—
18C22×C22⋊Dic17C2212yes—
19C22×C4×Dic17C2212yes—
20#11762707—24no—
21#11762697—28no—
22#11762669—24no—
23#11762669C418yescomplemented
24C4×C4⋊Dic17—24no—
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C24×C4×C17C2211yescharacteristic
34C22×C22⋊C4×C17C2211yescharacteristic
35C22×C22⋊C4×C17C2211yescharacteristic
36C22×C42×C17C2211yescharacteristic
37C22×C42×C17C2211yescharacteristic
38C4×C22⋊C4×C17—24no—
39C2×C17×#95C2211yescharacteristic
40C2×C17×#95C2211yescharacteristic
41C25×C17C2311yescharacteristic
42C23×C4×C17—22no—
43C23×C4×C17—22no—
44C23×C4×C17—22no—
45C23×C4×C17—22no—
46C23×C4×C17—22no—
47C23×C4×C17—22no—
48C23×C4×C17C2×C414yes—
49C23×C4×C17C2311yescharacteristic
50C23×C4×C17C2311yescharacteristic
51C23×C4×C17C2311yescharacteristic
52C23×C4×C17C2311yescharacteristic
53C23×C4×C17C2311yescharacteristic
54C23×C4×C17C2311yescharacteristic
55C23×Dic17C2312yes—
56C23×Dic17C2312yes—
57C23×Dic17C2312yes—
58C23×Dic17C2312yes—
59C2×C22⋊C4×C17—22no—
60C2×C22⋊C4×C17—22no—
61C2×C22⋊C4×C17—22no—
62C2×C22⋊C4×C17—22no—
63C2×C22⋊C4×C17—22no—
64C2×C22⋊C4×C17D414yes—
65C2×C42×C17—22no—
66C2×C42×C17—22no—
67C2×C42×C17—22no—
68C2×C42×C17—22no—
69C2×C42×C17—22no—
70C2×C42×C17D414yes—
71C2×C22⋊Dic17—24no—
72C2×C22⋊Dic17—24no—
73C2×C22⋊Dic17—24no—
74C2×C22⋊Dic17—24no—
75C2×C22⋊Dic17—42no—
76C2×C22⋊Dic17C2×C418yes—
77C2×C4⋊Dic17—22no—
78C2×C4⋊Dic17—22no—
79C2×C4⋊Dic17—22no—
80C2×C4⋊Dic17—22no—
81C2×C4⋊Dic17—22no—
82C2×C4⋊Dic17—22no—
83C2×C4⋊Dic17—22no—
84C2×C4⋊Dic17—22no—
85C2×C4⋊Dic17—22no—
86C2×C4⋊Dic17C2×C414yes—
87C2×C4⋊Dic17C2×C414yes—
88C2×C4⋊Dic17D414yes—
89C2×#63225—24no—
90C2×#63225—24no—
91C2×#63225—42no—
92C2×C4×Dic17—24no—
93C2×C4×Dic17—24no—
94C2×C4×Dic17—24no—
95C17×#95—22no—
96C17×#95—22no—
97#10587502—24no—
98#10587502—24no—
99#10587502—24no—
100#10587502—24no—
101#10587502—24no—
102#10587502—24no—
103#10587502—42no—
104#10587502C2×C418yes—
105C24×C17—21no—
106C24×C17—21no—
107C24×C17—21no—
108C24×C17—21no—
109C24×C17—21no—
110C24×C17—21no—
111C24×C17—21no—
112C24×C17—21no—
113C24×C17—21no—
114C24×C17—21no—
115C24×C17—21no—
116C24×C17—21no—
117C24×C17C22×C412yes—
118C24×C17C2×D412yes—
119C24×C17#4112yes—
120C24×C17C2411yescharacteristic
121C22×C4×C17—21no—
122C22×C4×C17—21no—
123C22×C4×C17—21no—
124C22×C4×C17—21no—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17—21no—
128C22×C4×C17—21no—
129C22×C4×C17—21no—
130C22×C4×C17—21no—
131C22×C4×C17—21no—
132C22×C4×C17—21no—
133C22×C4×C17—21no—
134C22×C4×C17—21no—
135C22×C4×C17—21no—
136C22×C4×C17—21no—
137C22×C4×C17—21no—
138C22×C4×C17—21no—
139C22×C4×C17—21no—
140C22×C4×C17—21no—
141C22×C4×C17—21no—
142C22×C4×C17—21no—
143C22×C4×C17—21no—
144C22×C4×C17—21no—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—21no—
148C22×C4×C17—21no—
149C22×C4×C17—28no—
150C22×C4×C17—28no—
151C22×C4×C17—28no—
152C22×C4×C17—44no—
153C22×C4×C17—44no—
154C22×C4×C17—44no—
155C22×C4×C17—44no—
156C22×C4×C17C22×C412yes—
157C22×C4×C17C22×C412yes—
158C22×C4×C17C2×D412yes—
159C22×C4×C17C2×D412yes—
160C22×C4×C17C2×D412yes—
161C22×C4×C17C2×D412yes—
162C22×C4×C17C2×D412yes—
163C22×C4×C17C2×D412yes—
164C22×C4×C17#4112yes—
165C22×C4×C17#4112yes—
166C22×C4×C17#4112yes—
167C22×C4×C17#4112yes—
168C22×C4×C17#4112yes—
169C22×C4×C17#4112yes—
170C22×Dic17—22no—
171C22×Dic17—22no—
172C22×Dic17—22no—
173C22×Dic17—22no—
174C22×Dic17—22no—
175C22×Dic17—22no—
176C22×Dic17—22no—
177C22×Dic17—22no—
178C22×Dic17—22no—
179C22×Dic17—22no—
180C22×Dic17—22no—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—22no—
189C22×Dic17—22no—
190C22×Dic17—22no—
191C22×Dic17—22no—
192C22×Dic17—22no—
193C22×Dic17—22no—
194C22×Dic17—22no—
195C22×Dic17C22×C414yes—
196C22×Dic17C22×C414yes—
197C22×Dic17C2×D414yes—
198C22⋊C4×C17—28no—
199C22⋊C4×C17—28no—
200C42×C17—28no—
201C42×C17—44no—
202C22⋊Dic17—216no—
203C22⋊Dic17—48no—
204C4⋊Dic17—28no—
205C4⋊Dic17—28no—
206C4⋊Dic17—28no—
207C4⋊Dic17—44no—
208#63225—48no—
209C4×Dic17—48no—
210#13994—171nomaximal, Sylow
211C23×C17—22no—
212C23×C17—22no—
213C23×C17—22no—
214C23×C17—22no—
215C23×C17—22no—
216C23×C17—22no—
217C23×C17—22no—
218C23×C17—22no—
219C23×C17—22no—
220C23×C17—22no—
221C23×C17—22no—
222C23×C17—22no—
223C23×C17—22no—
224C23×C17—22no—
225C23×C17—22no—
226C23×C17—22no—
227C23×C17—22no—
228C23×C17—22no—
229C23×C17—41no—
230C23×C17—41no—
231C23×C17—41no—
232C23×C17—41no—
233C23×C17—41no—
234C23×C17—41no—
235C23×C17—41no—
236C23×C17—41no—
237C23×C17—41no—
238C23×C17—41no—
239C23×C17—41no—
240C23×C17—41no—
241C23×C17—41no—
242C23×C17—41no—
243C23×C17—41no—
244C23×C17—41no—
245C23×C17C4×D414yes—
246C23×C17C23×C411yescharacteristic
247C23×C17C22×D411yescharacteristic
248C23×C17C22×D411yescharacteristic
249C23×C17C22×D411yescharacteristic
250C23×C17C2×#4111yescharacteristic
251C23×C17C2×#4111yescharacteristic
252C23×C17C2×#4111yescharacteristic
253C23×C17C2×#4111yescharacteristic
254C23×C17C2×#4111yescharacteristic
255C23×C17C2×#4111yescharacteristic
256C23×C17C2×#4111yescharacteristic
257C23×C17H(5,𝔽2)11yescharacteristic
258C23×C172−1+411yescharacteristic
259C23×C172−1+411yescharacteristic
260C23×C172−1+411yescharacteristic
261C2×C4×C17—22no—
262C2×C4×C17—22no—
263C2×C4×C17—22no—
264C2×C4×C17—22no—
265C2×C4×C17—22no—
266C2×C4×C17—22no—
267C2×C4×C17—22no—
268C2×C4×C17—22no—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—22no—
279C2×C4×C17—41no—
280C2×C4×C17—41no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—41no—
284C2×C4×C17—41no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—41no—
288C2×C4×C17—41no—
289C2×C4×C17—41no—
290C2×C4×C17—41no—
291C2×C4×C17—41no—
292C2×C4×C17—41no—
293C2×C4×C17—41no—
294C2×C4×C17—41no—
295C2×C4×C17—416no—
296C2×C4×C17#11714yes—
297C2×C4×C17C4×D414yes—
298C2×C4×C17C4×D414yes—
299C2×C4×C17#12114yes—
300C2×C4×C17#12114yes—
301C2×C4×C17#12314yes—
302C2×C4×C17#12414yes—
303C2×C4×C17#12614yes—
304C2×Dic17—24no—
305C2×Dic17—24no—
306C2×Dic17—24no—
307C2×Dic17—24no—
308C2×Dic17—24no—
309C2×Dic17—24no—
310C2×Dic17—24no—
311C2×Dic17—24no—
312C2×Dic17—24no—
313C2×Dic17—42no—
314C2×Dic17—42no—
315C2×Dic17—42no—
316C2×Dic17—42no—
317C2×Dic17—42no—
318C2×Dic17—42no—
319C2×Dic17—42no—
320C2×Dic17—42no—
321C2×Dic17—42no—
322C2×Dic17—42no—
323C2×Dic17—42no—
324C2×Dic17—42no—
325C2×Dic17—42no—
326C2×Dic17—42no—
327C2×Dic17—42no—
328C2×Dic17—42no—
329C2×Dic17—42no—
330C2×Dic17—42no—
331C2×Dic17—42no—
332C2×#389—171no—
333C2×#388—172no—
334C2×#380—171no—
335C2×#380—171no—
336C2×C4×C4⋊C4—171no—
337C2×C4×C22⋊C4D1711yescharacteristic
338#1442—172no—
339#1440—172no—
340C4⋊#95—171no—
341C4⋊#95—171no—
342#1434—172no—
343C22×C17—24no—
344C22×C17—24no—
345C22×C17—24no—
346C22×C17—42no—
347C22×C17—42no—
348C22×C17—42no—
349C22×C17—42no—
350C22×C17—42no—
351C22×C17—42no—
352C22×C17—42no—
353C22×C17—42no—
354C22×C17—42no—
355C22×C17—42no—
356C22×C17—42no—
357C22×C17—42no—
358C22×C17C2×#11711yescharacteristic
359C22×C17C2×C4×D411yescharacteristic
360C22×C17C2×C4×D411yescharacteristic
361C22×C17C2×C4×D411yescharacteristic
362C22×C17C4×#4111yescharacteristic
363C22×C17#51911yescharacteristic
364C22×C17#52011yescharacteristic
365C22×C17C2×#12111yescharacteristic
366C22×C17C2×#12111yescharacteristic
367C22×C17C2×#12311yescharacteristic
368C22×C17#52511yescharacteristic
369C22×C17C2×#12411yescharacteristic
370C22×C17C2×#12611yescharacteristic
371C22×C17#52911yescharacteristic
372C22×C17#53211yescharacteristic
373C22×C17#53611yescharacteristic
374C22×C17#53711yescharacteristic
375C22×C17#54111yescharacteristic
376C22×C17#54211yescharacteristic
377C22×C17D4211yescharacteristic
378C22×C17#54711yescharacteristic
379C22×C17#54711yescharacteristic
380C22×C17#54711yescharacteristic
381C22×C17#54711yescharacteristic
382C22×C17#54811yescharacteristic
383C22×C17#54811yescharacteristic
384C22×C17#55211yescharacteristic
385C22×C17#55211yescharacteristic
386C22×C17#55211yescharacteristic
387C22×C17#55211yescharacteristic
388C22×C17#55211yescharacteristic
389C22×C17#55311yescharacteristic
390C22×C17#55511yescharacteristic
391C22×C17#55511yescharacteristic
392C22×C17#55611yescharacteristic
393C4×C17—24no—
394C4×C17—42no—
395C4×C17—42no—
396C4×C17—42no—
397C4×C17—42no—
398C4×C17#38818yescomplemented
399Dic17—44no—
400Dic17—44no—
401Dic17—44no—
402Dic17—82no—
403C24×C4C2×D1711yescharacteristic
404C22×C4⋊C4—171no—
405C22×C4⋊C4—171no—
406C22×C4⋊C4—171no—
407C22×C4⋊C4—171no—
408C22×C4⋊C4—172no—
409C22×C22⋊C4—172no—
410C22×C22⋊C4—172no—
411C22×C22⋊C4C2×D1711yescharacteristic
412C22×C22⋊C4C2×D1711yescharacteristic
413C22×C42—172no—
414C22×C42C2×D1711yescharacteristic
415C22×C42C2×D1711yescharacteristic
416#389—344no—
417#388—348no—
418#380—178no—
419#380—344no—
420C4×C4⋊C4—344no—
421C4×C22⋊C4—24no—
422C2×#95—172no—
423C2×#95—172no—
424C2×#95—172no—
425C2×#95—172no—
426C2×#95—172no—
427C2×#95—172no—
428C2×#95—172no—
429C2×#95—172no—
430C2×#95C2×D1711yescharacteristic
431C2×#95C2×D1711yescharacteristic
432C2×C17—44no—
433C2×C17C2×#38811yescharacteristic
434C2×C17C4×#12111yescharacteristic
435C2×C17#232311yescharacteristic
436C2×C17#234411yescharacteristic
437C2×C17#234611yescharacteristic
438C2×C17#236111yescharacteristic
439C2×C17#236211yescharacteristic
440C2×C17#248511yescharacteristic
441C2×C17#248611yescharacteristic
442C2×C17#248911yescharacteristic
443C2×C17#249111yescharacteristic
444C2×C17#249511yescharacteristic
445C2×C17#249611yescharacteristic
446C2×C17#253611yescharacteristic
447C2×C17#253711yescharacteristic
448C25C22×D1711yescharacteristic
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—172no—
456C23×C4—172no—
457C23×C4—172no—
458C23×C4—172no—
459C23×C4C4×D1714yes—
460C23×C4C22×D1711yescharacteristic
461C23×C4C22×D1711yescharacteristic
462C23×C4C22×D1711yescharacteristic
463C23×C4C22×D1711yescharacteristic
464C23×C4C22×D1711yescharacteristic
465C23×C4C22×D1711yescharacteristic
466C2×C4⋊C4—174no—
467C2×C4⋊C4—174no—
468C2×C4⋊C4—174no—
469C2×C4⋊C4—342no—
470C2×C4⋊C4—342no—
471C2×C4⋊C4—342no—
472C2×C4⋊C4—342no—
473C2×C4⋊C4—342no—
474C2×C4⋊C4—342no—
475C2×C4⋊C4—344no—
476C2×C4⋊C4—344no—
477C2×C4⋊C4—342no—
478C2×C4⋊C4—342no—
479C2×C4⋊C4—342no—
480C2×C4⋊C4—682no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—178no—
487C2×C22⋊C4—344no—
488C2×C22⋊C4—344no—
489C2×C22⋊C4—344no—
490C2×C22⋊C4—344no—
491C2×C22⋊C4—682no—
492C2×C22⋊C4D6814yes—
493C2×C42—22no—
494C2×C42—22no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42—22no—
498C2×C42—344no—
499C2×C42—344no—
500C2×C42—344no—
501C2×C42C22⋊D1714yes—
502#95—22no—
503#95—22no—
504#95—178no—
505#95—344no—
506#95—344no—
507#95—344no—
508#95—344no—
509#95—344no—
510#95—344no—
511#95—682no—
512C17#1399411yescharacteristic, complemented, Sylow
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24C2×C4×D1712yes—
526C24C2×D6812yes—
527C24#6325212yes—
528C24C23×D1711yescharacteristic
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—174no—
565C22×C4—174no—
566C22×C4—174no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4—342no—
570C22×C4—342no—
571C22×C4—342no—
572C22×C4—342no—
573C22×C4—342no—
574C22×C4—342no—
575C22×C4—342no—
576C22×C4—342no—
577C22×C4—342no—
578C22×C4—342no—
579C22×C4—342no—
580C22×C4—342no—
581C22×C4—342no—
582C22×C4—342no—
583C22×C4—342no—
584C22×C4—342no—
585C22×C4—342no—
586C22×C4—342no—
587C22×C4—342no—
588C22×C4—342no—
589C22×C4—342no—
590C22×C4—342no—
591C22×C4—342no—
592C22×C4C2×C4×D1712yes—
593C22×C4C2×C4×D1712yes—
594C22×C4C2×D6812yes—
595C22×C4C2×D6812yes—
596C22×C4#6325212yes—
597C22×C4#6325212yes—
598C22×C4#6325212yes—
599C22×C4D4×D1712yes—
600C22×C4#6325412yes—
601C22×C4#6325412yes—
602C22×C4#6325412yes—
603C22×C4C2×C22⋊D1712yes—
604C22×C4C2×C22⋊D1712yes—
605C22×C4C2×C22⋊D1712yes—
606C4⋊C4—348no—
607C4⋊C4—348no—
608C4⋊C4—348no—
609C4⋊C4—688no—
610C4⋊C4—684no—
611C22⋊C4—28no—
612C22⋊C4—28no—
613C22⋊C4—3416no—
614C22⋊C4—688no—
615C42—28no—
616C42—44no—
617C42—688no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23C4×D6814yes—
653C23C22×C4×D1711yescharacteristic
654C23C22×D6811yescharacteristic
655C23C2×#6325211yescharacteristic
656C23C2×#6325211yescharacteristic
657C23C2×#6325211yescharacteristic
658C23C2×#6325211yescharacteristic
659C23C2×D4×D1711yescharacteristic
660C23C2×#6325411yescharacteristic
661C23C2×#6325411yescharacteristic
662C23C2×#6325411yescharacteristic
663C23#1058769611yescharacteristic
664C23#1058769711yescharacteristic
665C23#1058769711yescharacteristic
666C23#1058769711yescharacteristic
667C23C22×C22⋊D1711yescharacteristic
668C2×C4—22no—
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—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—416no—
703C2×C4—344no—
704C2×C4—344no—
705C2×C4—344no—
706C2×C4—344no—
707C2×C4—344no—
708C2×C4—344no—
709C2×C4—344no—
710C2×C4—344no—
711C2×C4—344no—
712C2×C4—682no—
713C2×C4—682no—
714C2×C4—682no—
715C2×C4—682no—
716C2×C4—682no—
717C2×C4—682no—
718C2×C4—682no—
719C2×C4—682no—
720C2×C4—682no—
721C2×C4—682no—
722C2×C4—682no—
723C2×C4—682no—
724C2×C4—682no—
725C2×C4—682no—
726C2×C4—682no—
727C2×C4—682no—
728C2×C4—682no—
729C2×C4—682no—
730C2×C4—682no—
731C2×C4#1058756314yes—
732C2×C4#1058756514yes—
733C2×C4#1058756714yes—
734C2×C4#1058757114yes—
735C2×C4C4×C22⋊D1714yes—
736C2×C4#1058761614yes—
737C2×C4#1058762114yes—
738C2×C4#1058762414yes—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22C2×#1058756311yescharacteristic
755C22C2×#1058756711yescharacteristic
756C22C2×C4×C22⋊D1711yescharacteristic
757C22C2×C4×D6811yescharacteristic
758C22C4×#6325211yescharacteristic
759C22#1176328611yescharacteristic
760C22#1176328911yescharacteristic
761C22C2×#1058762411yescharacteristic
762C22C2×#1058761611yescharacteristic
763C22C2×#1058762111yescharacteristic
764C22#1176332011yescharacteristic
765C22C2×#1058757111yescharacteristic
766C22C2×#1058756511yescharacteristic
767C22#1176334311yescharacteristic
768C22#1176335911yescharacteristic
769C22#1176338011yescharacteristic
770C22#1176338711yescharacteristic
771C22#1176342111yescharacteristic
772C22#1176343011yescharacteristic
773C22D4×D6811yescharacteristic
774C22#1176346311yescharacteristic
775C22#1176346311yescharacteristic
776C22#1176346311yescharacteristic
777C22#1176346411yescharacteristic
778C22#1176346811yescharacteristic
779C22#1176346811yescharacteristic
780C22#1176349911yescharacteristic
781C22#1176349911yescharacteristic
782C22#1176349911yescharacteristic
783C22#1176349911yescharacteristic
784C22#1176349911yescharacteristic
785C22#1176350511yescharacteristic
786C22#1176352411yescharacteristic
787C22#1176352411yescharacteristic
788C22#1176352911yescharacteristic
789C4—24no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—684no—
795C4—684no—
796C4—684no—
797C4—1362no—
798C4#1176269718yescomplemented
799C2—44no—
800C2C2×#1176269711yescharacteristic
801C2C4×#1058761611yescharacteristic
802C2#1453146611yescharacteristic
803C2#1453165111yescharacteristic
804C2#1453166711yescharacteristic
805C2#1453179811yescharacteristic
806C2#1453180911yescharacteristic
807C2#1453308111yescharacteristic
808C2#1453309211yescharacteristic
809C2#1453312511yescharacteristic
810C2#1453314711yescharacteristic
811C2#1453319511yescharacteristic
812C2#1453320611yescharacteristic
813C2#1453369311yescharacteristic
814C2#1453369711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C4×C22⋊C4×C17C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×C4×C22⋊C4D17
hypocenterC17#13994
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11762707C2semidirect
5. C2×C4×C4⋊Dic17C2semidirect
6. #14527039C2semidirect
8. #14527014C2semidirect
9. #14527014C2semidirect
10. #14527008C2semidirect
23. #11762669C4semidirect
398. C4×C17#388semidirect
512. C17#13994semidirect
798. C4#11762697semidirect

Maximal subgroups

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

subgroupindex
C2×#117627072
C2×#117626972
C2×#117626692
C2×C4×C4⋊Dic172
#145270392
#145270312
#145270142
#145270082
C2×C4×C22⋊C4×C172
#1399417