Finite Group Databasebeta

← #16956515

Subgroups — #16956515

Order 4352.

2690 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D68C211yesmaximal, characteristic
2C2×#11762687C212yesmaximal
3C2×#11762680C212yesmaximal, complemented
4C2×#11762668C211yesmaximal, characteristic, complemented
5C2×#95×D17C211yesmaximal, characteristic, complemented
6#14527036C212yesmaximal, complemented
7#14527026C212yesmaximal, complemented
8#14527011C211yesmaximal, characteristic, complemented
9#14527005C211yesmaximal, characteristic, complemented
10#14527005C211yesmaximal, characteristic, complemented
11C17×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D68C2211yescharacteristic
13C23×C4×D17C2212yes—
14C23×C4×D17C2211yescharacteristic
15C23×C4×D17C2211yescharacteristic
16C2×C4×D68—28no—
17C2×C4×D68C418yescomplemented
18C22×C4⋊Dic17C2211yescharacteristic
19C22×#63225C2212yes—
20C22×#63227C2212yes—
21C22×#63227C2212yes—
22C22×#63227C2212yes—
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25#11762687—28no—
26#11762680—28no—
27#11762668—24no—
28C2×#10587502C2211yescharacteristic
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2211yescharacteristic
35#95×D17—24no—
36C22×C4⋊C4×C17C2212yes—
37C22×C42×C17C2211yescharacteristic
38C2×C17×#95C2211yescharacteristic
39C2×C17×#95C2211yescharacteristic
40C2×C17×#95C2212yes—
41C24×D17C2311yescharacteristic
42C24×D17C2311yescharacteristic
43C23×C4×C17C2312yes—
44C23×C4×C17C2312yes—
45C23×C4×C17C2311yescharacteristic
46C23×C4×C17C2311yescharacteristic
47C23×C4×C17C2311yescharacteristic
48C23×Dic17C2312yes—
49C23×Dic17C2311yescharacteristic
50C23×Dic17C2312yes—
51C23×Dic17C2311yescharacteristic
52C22×D68—24no—
53C22×D68—24no—
54C22×D68C2×C414yes—
55C22×D68D414yes—
56C22×D68Q814yes—
57C22×C4×D17—24no—
58C22×C4×D17—24no—
59C22×C4×D17—22no—
60C22×C4×D17—22no—
61C22×C4×D17—24no—
62C22×C4×D17—22no—
63C22×C4×D17—22no—
64C22×C4×D17—24no—
65C22×C4×D17—24no—
66C22×C4×D17—24no—
67C22×C4×D17—24no—
68C22×C4×D17—42no—
69C22×C4×D17—42no—
70C22×C4×D17—42no—
71C22×C4×D17—42no—
72C22×C4×D17C2×C414yes—
73C22×C4×D17C2×C414yescomplemented
74C2×C4⋊C4×C17—24no—
75C2×C4⋊C4×C17—24no—
76C2×C4⋊C4×C17—42no—
77C2×C42×C17—24no—
78C2×C42×C17C2×C414yescomplemented
79C2×#63227—24no—
80C2×#63227—24no—
81C2×#63227—24no—
82C2×#63227—24no—
83C2×#63227—24no—
84C2×#63227—24no—
85C2×#63227—24no—
86C2×#63227—24no—
87C2×#63227—42no—
88C2×#63227—42no—
89C2×#63227C2×C414yes—
90C2×#63227C2×C414yescomplemented
91C2×#63227D418yes—
92C2×C4⋊Dic17—24no—
93C2×C4⋊Dic17C2×C414yescomplemented
94C2×#63225—24no—
95C2×#63225—24no—
96C2×#63225—42no—
97C4×D68—232no—
98C17×#95—22no—
99C17×#95—22no—
100C17×#95—24no—
101#10587502—24no—
102#10587502—24no—
103#10587502—22no—
104#10587502—24no—
105#10587502—24no—
106#10587502—42no—
107#10587502D414yescomplemented
108C24×C17C2411yescharacteristic
109C23×D17—21no—
110C23×D17—22no—
111C23×D17—21no—
112C23×D17—21no—
113C23×D17—22no—
114C23×D17—21no—
115C23×D17—22no—
116C23×D17—21no—
117C23×D17—21no—
118C23×D17—22no—
119C23×D17—22no—
120C23×D17—22no—
121C23×D17—21no—
122C23×D17—21no—
123C23×D17C22×C412yes—
124C23×D17C22×C412yes—
125C23×D17C2×D412yes—
126C23×D17C2×D414yes—
127C23×D17C2×D412yes—
128C23×D17C2×Q812yes—
129C23×D17C2×Q812yes—
130C23×D17#4114yes—
131C22×C4×C17—22no—
132C22×C4×C17—22no—
133C22×C4×C17—22no—
134C22×C4×C17—22no—
135C22×C4×C17—22no—
136C22×C4×C17—21no—
137C22×C4×C17—21no—
138C22×C4×C17—22no—
139C22×C4×C17—22no—
140C22×C4×C17—22no—
141C22×C4×C17—22no—
142C22×C4×C17—22no—
143C22×C4×C17—22no—
144C22×C4×C17—22no—
145C22×C4×C17—22no—
146C22×C4×C17—22no—
147C22×C4×C17—22no—
148C22×C4×C17—22no—
149C22×C4×C17—22no—
150C22×C4×C17—22no—
151C22×C4×C17C22×C412yes—
152C22×C4×C17C22×C412yes—
153C22×C4×C17C22×C412yes—
154C22×C4×C17C2×D414yes—
155C22×C4×C17C2×D412yes—
156C22×C4×C17C2×D412yes—
157C22×C4×C17C2×Q812yes—
158C22×C4×C17#4114yes—
159C22×C4×C17#4112yes—
160C22×Dic17—21no—
161C22×Dic17—21no—
162C22×Dic17—22no—
163C22×Dic17—21no—
164C22×Dic17—22no—
165C22×Dic17—22no—
166C22×Dic17—22no—
167C22×Dic17—22no—
168C22×Dic17—21no—
169C22×Dic17—22no—
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×Dic17C22×C412yes—
181C22×Dic17C22×C412yes—
182C22×Dic17C2×D414yes—
183C22×Dic17C2×D414yes—
184C2×D68—28no—
185C2×D68—28no—
186C2×D68—216no—
187C2×D68—216no—
188C2×D68C4⋊C4116yescomplemented
189C2×C4×D17—216no—
190C2×C4×D17—28no—
191C2×C4×D17—28no—
192C2×C4×D17—28no—
193C2×C4×D17—28no—
194C2×C4×D17—44no—
195C2×C4×D17—44no—
196C2×C4×D17—48no—
197C2×C4×D17—48no—
198C2×C4×D17—48no—
199C2×C4×D17—48no—
200C2×C4×D17—48no—
201C2×C4×D17—48no—
202C2×C4×D17—48no—
203C2×C4×D17—48no—
204C2×C4×D17—48no—
205C2×C4×D17—48no—
206C4⋊C4×C17—48no—
207C42×C17—28no—
208#63227—28no—
209#63227—48no—
210#63227—48no—
211#63227—48no—
212#63227C22⋊C4116yescomplemented
213C4⋊Dic17—28no—
214#63225—48no—
215#13899—171nomaximal, Sylow
216C23×C17C23×C411yescharacteristic
217C23×C17C22×D412yes—
218C23×C17C22×D411yescharacteristic
219C23×C17C22×D411yescharacteristic
220C23×C17C22×Q811yescharacteristic
221C23×C17C2×#4112yes—
222C23×C17C2×#4111yescharacteristic
223C23×C17C2×#4112yes—
224C23×C17H(5,𝔽2)11yescharacteristic
225C23×C17H(5,𝔽2)12yes—
226C23×C172−1+411yescharacteristic
227C22×D17—22no—
228C22×D17—22no—
229C22×D17—22no—
230C22×D17—22no—
231C22×D17—24no—
232C22×D17—24no—
233C22×D17—24no—
234C22×D17—24no—
235C22×D17—24no—
236C22×D17—22no—
237C22×D17—24no—
238C22×D17—24no—
239C22×D17—24no—
240C22×D17—24no—
241C22×D17—22no—
242C22×D17—22no—
243C22×D17—24no—
244C22×D17—22no—
245C22×D17—22no—
246C22×D17—22no—
247C22×D17—22no—
248C22×D17—22no—
249C22×D17—22no—
250C22×D17—22no—
251C22×D17—24no—
252C22×D17—24no—
253C22×D17—22no—
254C22×D17—24no—
255C22×D17—22no—
256C22×D17—22no—
257C22×D17—24no—
258C22×D17—22no—
259C22×D17—42no—
260C22×D17—42no—
261C22×D17—42no—
262C22×D17—42no—
263C22×D17—42no—
264C22×D17—42no—
265C22×D17—42no—
266C22×D17—42no—
267C22×D17C2×C22⋊C414yes—
268C22×D17C2×C4⋊C414yes—
269C22×D17C2×C4⋊C414yes—
270C22×D17#11714yes—
271C22×D17#12118yes—
272C22×D17C22⋊Q818yes—
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—24no—
280C2×C4×C17—24no—
281C2×C4×C17—24no—
282C2×C4×C17—24no—
283C2×C4×C17—24no—
284C2×C4×C17—24no—
285C2×C4×C17—24no—
286C2×C4×C17—24no—
287C2×C4×C17—24no—
288C2×C4×C17—42no—
289C2×C4×C17—42no—
290C2×C4×C17—42no—
291C2×C4×C17—42no—
292C2×C4×C17—42no—
293C2×C4×C17—42no—
294C2×C4×C17—42no—
295C2×C4×C17—42no—
296C2×C4×C17—42no—
297C2×C4×C17—42no—
298C2×C4×C17—42no—
299C2×C4×C17C2×C22⋊C414yes—
300C2×C4×C17C2×C4⋊C414yes—
301C2×C4×C17C4×D414yes—
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—24no—
305C2×Dic17—24no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—24no—
310C2×Dic17—24no—
311C2×Dic17—24no—
312C2×Dic17—42no—
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×Dic17C2×C22⋊C414yes—
326D68—232no—
327C4×D17—416no—
328C4×D17—416no—
329C4×D17—432no—
330C22×C4×D4—171no—
331C2×#386—172no—
332C2×#385—172no—
333C2×#380—171no—
334C22×#95—171no—
335#1441—172no—
336#1439—172no—
337C4⋊#95D1711yescharacteristic, complemented
338#1434—171no—
339C22⋊#95—171no—
340C22⋊#95—171no—
341C22×C17C22×C22⋊C411yescharacteristic
342C22×C17C22×C4⋊C411yescharacteristic
343C22×C17C2×#11711yescharacteristic
344C22×C17C2×C4×D411yescharacteristic
345C22×C17C4×#4111yescharacteristic
346C22×C17#51811yescharacteristic
347C22×C17#52011yescharacteristic
348C22×C17C2×#12112yes—
349C22×C17C2×C22⋊Q812yes—
350C22×C17#52512yes—
351C22×C17#52912yes—
352C22×C17#53812yes—
353C22×C17#53912yes—
354C22×C17D4212yes—
355C22×C17D4211yescharacteristic
356C22×C17#54612yes—
357C22×C17#54612yes—
358C22×C17#54612yes—
359C22×C17#54712yes—
360C22×C17#54711yescharacteristic
361C22×C17D4×Q811yescharacteristic
362C22×C17#55412yes—
363C22×C17#55411yescharacteristic
364C2×D17—24no—
365C2×D17—24no—
366C2×D17—24no—
367C2×D17—24no—
368C2×D17—24no—
369C2×D17—28no—
370C2×D17—28no—
371C2×D17—28no—
372C2×D17—28no—
373C2×D17—24no—
374C2×D17—24no—
375C2×D17—24no—
376C2×D17—24no—
377C2×D17—42no—
378C2×D17—42no—
379C2×D17—42no—
380C2×D17—44no—
381C2×D17—44no—
382C2×D17—44no—
383C2×D17—44no—
384C2×D17—42no—
385C2×D17#38018yescomplemented
386C4×C17—24no—
387C4×C17—24no—
388C4×C17—24no—
389C4×C17—44no—
390C4×C17—82no—
391Dic17—24no—
392Dic17—42no—
393Dic17—44no—
394Dic17—82no—
395C23×D4—171no—
396C24×C4—171no—
397C24×C4—171no—
398C24×C4—172no—
399C2×C4×D4—178no—
400C2×C4×D4—348no—
401C22×C4⋊C4—171no—
402C22×C4⋊C4—172no—
403C22×C4⋊C4C2×D1712yes—
404C22×C22⋊C4—171no—
405C22×C22⋊C4—171no—
406C22×C22⋊C4—172no—
407C22×C22⋊C4—172no—
408C22×C22⋊C4—172no—
409C22×C42C2×D1711yescharacteristic
410#386—348no—
411#385—348no—
412#380—344no—
413C2×#95—171no—
414C2×#95—171no—
415C2×#95—172no—
416C2×#95—172no—
417C2×#95—172no—
418C2×#95—172no—
419C2×#95—172no—
420C2×#95—344no—
421C2×#95C2×D1711yescharacteristic
422C2×#95C2×D1711yescharacteristic
423C2×#95C2×D1712yes—
424C2×C17C2×#38011yescharacteristic
425C2×C17#229011yescharacteristic
426C2×C17#231811yescharacteristic
427C2×C17D4×C22⋊C411yescharacteristic
428C2×C17#233911yescharacteristic
429C2×C17D4×C4⋊C411yescharacteristic
430C2×C17#234911yescharacteristic
431C2×C17#242412yes—
432C2×C17#242512yes—
433C2×C17#244912yes—
434C2×C17#245012yes—
435D17—28no—
436D17—44no—
437C25—171no—
438C25—171no—
439C22×D4—174no—
440C22×D4—174no—
441C22×D4—174no—
442C22×D4—344no—
443C22×D4—344no—
444C23×C4—171no—
445C23×C4—171no—
446C23×C4—172no—
447C23×C4—174no—
448C23×C4—174no—
449C23×C4—172no—
450C23×C4—344no—
451C23×C4—344no—
452C23×C4—344no—
453C23×C4—344no—
454C23×C4—344no—
455C23×C4—344no—
456C23×C4—344no—
457C23×C4—342no—
458C23×C4—342no—
459C23×C4—342no—
460C23×C4—342no—
461C23×C4—682no—
462C23×C4—682no—
463C23×C4—682no—
464C23×C4—682no—
465C23×C4C22×D1712yes—
466C23×C4C22×D1712yes—
467C23×C4C22×D1711yescharacteristic
468C23×C4C22×D1711yescharacteristic
469C23×C4C22×D1711yescharacteristic
470C4×D4—3432no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—174no—
475C2×C4⋊C4—344no—
476C2×C4⋊C4—344no—
477C2×C4⋊C4—344no—
478C2×C4⋊C4—682no—
479C2×C22⋊C4—174no—
480C2×C22⋊C4—178no—
481C2×C22⋊C4—174no—
482C2×C22⋊C4—344no—
483C2×C22⋊C4—344no—
484C2×C22⋊C4—344no—
485C2×C22⋊C4—344no—
486C2×C22⋊C4—344no—
487C2×C22⋊C4—344no—
488C2×C22⋊C4—344no—
489C2×C22⋊C4—344no—
490C2×C22⋊C4—682no—
491C2×C22⋊C4—682no—
492C2×C42—24no—
493C2×C42C4×D1714yescomplemented
494#95—22no—
495#95—22no—
496#95—24no—
497#95—174no—
498#95—344no—
499#95—344no—
500#95—344no—
501#95—344no—
502#95—342no—
503#95—682no—
504C17#1389911yescharacteristic, complemented, Sylow
505C24—172no—
506C24—174no—
507C24—172no—
508C24—172no—
509C24—174no—
510C24—172no—
511C24—172no—
512C24—172no—
513C24—342no—
514C24—341no—
515C24—341no—
516C24—341no—
517C24—341no—
518C24—342no—
519C24—342no—
520C24—341no—
521C24—342no—
522C24—341no—
523C24—341no—
524C24—341no—
525C24—342no—
526C24—342no—
527C24C23×D1711yescharacteristic
528C2×D4—1716no—
529C2×D4—348no—
530C2×D4—348no—
531C2×D4—3416no—
532C2×D4—3416no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—172no—
554C22×C4—174no—
555C22×C4—172no—
556C22×C4—174no—
557C22×C4—348no—
558C22×C4—348no—
559C22×C4—3416no—
560C22×C4—341no—
561C22×C4—341no—
562C22×C4—342no—
563C22×C4—342no—
564C22×C4—341no—
565C22×C4—342no—
566C22×C4—342no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4—341no—
570C22×C4—342no—
571C22×C4—342no—
572C22×C4—342no—
573C22×C4—348no—
574C22×C4—348no—
575C22×C4—342no—
576C22×C4—342no—
577C22×C4—342no—
578C22×C4—342no—
579C22×C4—342no—
580C22×C4—342no—
581C22×C4—342no—
582C22×C4—684no—
583C22×C4—684no—
584C22×C4—688no—
585C22×C4—688no—
586C22×C4—688no—
587C22×C4—688no—
588C22×C4—688no—
589C22×C4—688no—
590C22×C4—688no—
591C22×C4—688no—
592C22×C4—688no—
593C22×C4—688no—
594C22×C4C2×C4×D1712yes—
595C22×C4C2×C4×D1712yes—
596C22×C4C2×C4×D1712yes—
597C22×C4#6325214yes—
598C22×C4D4×D1714yes—
599C22×C4D4×D1712yes—
600C22×C4D4×D1712yes—
601C22×C4Q8×D1712yes—
602C22×C4#6325612yes—
603C4⋊C4—48no—
604C4⋊C4—348no—
605C4⋊C4—688no—
606C22⋊C4—1716no—
607C22⋊C4—348no—
608C22⋊C4—688no—
609C22⋊C4—688no—
610C22⋊C4—688no—
611C42—28no—
612C23—174no—
613C23—174no—
614C23—174no—
615C23—178no—
616C23—178no—
617C23—174no—
618C23—344no—
619C23—342no—
620C23—342no—
621C23—344no—
622C23—342no—
623C23—342no—
624C23—342no—
625C23—342no—
626C23—342no—
627C23—344no—
628C23—344no—
629C23—344no—
630C23—344no—
631C23—344no—
632C23—342no—
633C23—344no—
634C23—344no—
635C23—344no—
636C23—342no—
637C23—342no—
638C23—342no—
639C23—342no—
640C23—344no—
641C23—342no—
642C23—342no—
643C23—342no—
644C23—342no—
645C23—342no—
646C23—344no—
647C23—344no—
648C23—342no—
649C23—344no—
650C23—682no—
651C23—682no—
652C23—682no—
653C23—682no—
654C23—682no—
655C23—682no—
656C23—682no—
657C23—682no—
658C23C22×C4×D1711yescharacteristic
659C23C2×#6325212yes—
660C23C2×D4×D1712yes—
661C23C2×D4×D1711yescharacteristic
662C23C2×D4×D1711yescharacteristic
663C23#1058769111yescharacteristic
664C23C2×Q8×D1711yescharacteristic
665C23C2×#6325611yescharacteristic
666C23#1058769411yescharacteristic
667C23#41×D1712yes—
668C23#1058769612yes—
669D4—3432no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—174no—
697C2×C4—342no—
698C2×C4—342no—
699C2×C4—344no—
700C2×C4—344no—
701C2×C4—342no—
702C2×C4—342no—
703C2×C4—342no—
704C2×C4—344no—
705C2×C4—344no—
706C2×C4—344no—
707C2×C4—6816no—
708C2×C4—6816no—
709C2×C4—6832no—
710C2×C4—682no—
711C2×C4—682no—
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×C4C22⋊C4×D1714yes—
724C2×C4C4⋊C4×D1714yes—
725C2×C4#1058757914yes—
726C22—178no—
727C22—344no—
728C22—344no—
729C22—344no—
730C22—344no—
731C22—344no—
732C22—344no—
733C22—348no—
734C22—348no—
735C22—348no—
736C22—348no—
737C22—344no—
738C22—344no—
739C22—344no—
740C22—682no—
741C22—682no—
742C22—682no—
743C22—682no—
744C22—684no—
745C22—684no—
746C22—684no—
747C22—684no—
748C22C2×C22⋊C4×D1711yescharacteristic
749C22C2×C4⋊C4×D1711yescharacteristic
750C22#117×D1711yescharacteristic
751C22C2×#1058757911yescharacteristic
752C22C4×#6325211yescharacteristic
753C22#1176328311yescharacteristic
754C22#1176329011yescharacteristic
755C22#121×D1712yes—
756C22C22⋊Q8×D1712yes—
757C22#1176331812yes—
758C22#1176334612yes—
759C22#1176339312yes—
760C22#1176340712yes—
761C22#1176344312yes—
762C22#1176344411yescharacteristic
763C22#1176344912yes—
764C22#1176345012yes—
765C22#1176345512yes—
766C22#1176346012yes—
767C22#1176346211yescharacteristic
768C22#1176347411yescharacteristic
769C22#1176351912yes—
770C22#1176352011yescharacteristic
771C4—24no—
772C4—24no—
773C4—24no—
774C4—44no—
775C4—82no—
776C4—344no—
777C4—682no—
778C4—684no—
779C4—1362no—
780C2—348no—
781C2—684no—
782C2D17×#38011yescharacteristic
783C2#1453122511yescharacteristic
784C2#1453142011yescharacteristic
785C2#1453160411yescharacteristic
786C2#1453161111yescharacteristic
787C2#1453168411yescharacteristic
788C2#1453169511yescharacteristic
789C2#1453232712yes—
790C2#1453234212yes—
791C2#1453260012yes—
792C2#1453260512yes—
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C4⋊#95C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenterC4⋊#95D17
hypocenterC17#13899
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#11762680C2semidirect
4. C2×#11762668C2semidirect
5. C2×#95×D17C2semidirect
6. #14527036C2semidirect
7. #14527026C2semidirect
8. #14527011C2semidirect
9. #14527005C2semidirect
10. #14527005C2semidirect
11. C17×C4⋊#95C2semidirect
17. C2×C4×D68C4semidirect
73. C22×C4×D17C2×C4semidirect
78. C2×C42×C17C2×C4semidirect
90. C2×#63227C2×C4semidirect
93. C2×C4⋊Dic17C2×C4semidirect
107. #10587502D4semidirect
188. C2×D68C4⋊C4semidirect
212. #63227C22⋊C4semidirect
337. C4⋊#95D17semidirect
385. C2×D17#380semidirect
493. C2×C42C4×D17semidirect
504. C17#13899semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D682
C2×#117626872
C2×#117626802
C2×#117626682
C2×#95×D172
#145270362
#145270262
#145270112
#145270052
C17×C4⋊#952
#1389917