Finite Group Databasebeta

← #16942189

Subgroups — #16942189

Order 4352.

1042 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×#11762772C211yesmaximal, characteristic
2C2×#11762772C211yesmaximal, characteristic
3C2×#11762666C211yesmaximal, characteristic
4C2×#11762578C211yesmaximal, characteristic, complemented
5C2×#11762577C211yesmaximal, characteristic, complemented
6C2×#11762577C211yesmaximal, characteristic, complemented
7C2×C17×#343C211yesmaximal, characteristic, complemented
8C23×C4×D17C2211yescharacteristic
9C22×#63223C2211yescharacteristic
10C22×#63223C2211yescharacteristic
11C22×C4⋊Dic17C2211yescharacteristic
12C22×#63227C412yes—
13#11762772—22no—
14#11762772—22no—
15#11762772—22no—
16#11762772—22no—
17C2×#10587491—21no—
18C2×#10587491—21no—
19C2×#10587491—21no—
20C2×#10587491—21no—
21#11762666—21no—
22#11762666—21no—
23#11762666—21no—
24#11762666—21no—
25C2×#10587502C412yes—
26#11762578—22no—
27#11762577—22no—
28#11762577—22no—
29C22×M16×C17C2211yescharacteristic
30C22×M16×C17C2211yescharacteristic
31C22×C4⋊C4×C17C2211yescharacteristic
32C17×#343—22no—
33C24×D17C2×C411yescharacteristic
34C23×C4×C17C2×C412yes—
35C23×C4×C17C2311yescharacteristic
36C23×Dic17C2×C411yescharacteristic
37C23×Dic17C2×C412yes—
38C22×C4×D17—21no—
39C22×C4×D17—21no—
40C22×C4×D17—21no—
41C22×C4×D17—21no—
42C22×C4×D17—21no—
43C22×C4×D17—21no—
44C22×C4×D17—21no—
45C22×C4×D17—21no—
46C22×C4×D17—21no—
47C22×C4×D17—21no—
48C22×C4×D17—21no—
49C22×C4×D17—21no—
50C22×C4×D17D411yescharacteristic
51C22×C4×D17D411yescharacteristic
52C22×C4×D17D411yescharacteristic
53C22×C4×D17D411yescharacteristic
54C2×M16×C17—21no—
55C2×M16×C17—21no—
56C2×M16×C17—21no—
57C2×M16×C17—21no—
58C2×M16×C17—21no—
59C2×M16×C17—21no—
60C2×M16×C17—21no—
61C2×M16×C17—21no—
62C2×M16×C17—21no—
63C2×M16×C17—21no—
64C2×M16×C17D412yes—
65C2×M16×C17D412yes—
66C22×C8×C17—21no—
67C22×C8×C17—21no—
68C2×C4⋊C4×C17—21no—
69C2×C4⋊C4×C17—21no—
70C2×C4⋊C4×C17—21no—
71C2×C4⋊C4×C17—21no—
72C2×C4⋊C4×C17—21no—
73C2×C4⋊C4×C17—21no—
74C2×#63227—22no—
75C2×#63227—22no—
76C2×#63227—44no—
77C2×C4⋊Dic17—21no—
78C2×C4⋊Dic17—21no—
79C2×C4⋊Dic17—21no—
80C2×C4⋊Dic17—21no—
81C2×C4⋊Dic17—21no—
82C2×C4⋊Dic17—21no—
83C2×#63223—21no—
84C2×#63223—21no—
85C2×#63223—21no—
86C2×#63223—21no—
87C2×#63223—21no—
88C2×#63223—21no—
89C2×#63223—21no—
90C2×#63223—21no—
91C2×#63223—21no—
92C2×#63223—21no—
93C2×#63223D412yes—
94C2×#63223D412yes—
95C22×#3622—21no—
96C22×#3622—21no—
97#10587502—22no—
98#10587502—22no—
99#10587491—24no—
100#10587491—24no—
101#10587491—24no—
102#10587491—24no—
103C24×C17C22×C411yescharacteristic
104C23×D17—21no—
105C23×D17—21no—
106C23×D17—22no—
107C23×D17—22no—
108C23×D17—21no—
109C23×D17—21no—
110C23×D17—21no—
111C23×D17—21no—
112C23×D17—41no—
113C23×D17—41no—
114C23×D17C22⋊C411yescharacteristic
115C23×D17C22⋊C411yescharacteristic
116C22×C4×C17—22no—
117C22×C4×C17—22no—
118C22×C4×C17—22no—
119C22×C4×C17—42no—
120C22×C4×C17—42no—
121C22×C4×C17C2×D411yescharacteristic
122C22×C4×C17C2×D411yescharacteristic
123C22×C4×C17C2×D411yescharacteristic
124C22×C4×C17C2×D411yescharacteristic
125C22×C4×C17C2×D411yescharacteristic
126C22×C4×C17C2×D411yescharacteristic
127C22×C4×C17#4111yescharacteristic
128C22×C4×C17#4111yescharacteristic
129C22×C4×C17#4111yescharacteristic
130C22×C4×C17#4111yescharacteristic
131C22×C4×C17#4111yescharacteristic
132C22×C4×C17#4111yescharacteristic
133C22×C4×C17#4111yescharacteristic
134C22×C4×C17#4111yescharacteristic
135C22×Dic17—21no—
136C22×Dic17—21no—
137C22×Dic17—21no—
138C22×Dic17—21no—
139C22×Dic17—21no—
140C22×Dic17—21no—
141C22×Dic17—22no—
142C22×Dic17—22no—
143C22×Dic17—22no—
144C22×Dic17—42no—
145C22×Dic17—42no—
146C22×Dic17C22⋊C411yescharacteristic
147C22×Dic17C22⋊C411yescharacteristic
148C2×C4×D17—21no—
149C2×C4×D17—21no—
150C2×C4×D17—21no—
151C2×C4×D17—21no—
152C2×C4×D17—21no—
153C2×C4×D17—21no—
154C2×C4×D17—21no—
155C2×C4×D17—21no—
156C2×C4×D17—21no—
157C2×C4×D17—21no—
158C2×C4×D17—21no—
159C2×C4×D17—21no—
160C2×C4×D17—21no—
161C2×C4×D17—21no—
162C2×C4×D17—21no—
163C2×C4×D17—21no—
164C2×C4×D17—21no—
165C2×C4×D17—21no—
166C2×C4×D17—21no—
167C2×C4×D17—21no—
168C2×C4×D17—21no—
169C2×C4×D17—21no—
170C2×C4×D17—21no—
171C2×C4×D17—21no—
172C2×C4×D17—41no—
173C2×C4×D17—41no—
174C2×C4×D17—41no—
175C2×C4×D17—41no—
176C2×C4×D17—41no—
177C2×C4×D17—41no—
178C2×C4×D17—41no—
179C2×C4×D17—41no—
180C2×C4×D17—41no—
181C2×C4×D17—41no—
182C2×C4×D17—41no—
183C2×C4×D17—41no—
184C2×C4×D17—41no—
185C2×C4×D17—41no—
186C2×C4×D17—41no—
187C2×C4×D17—41no—
188M16×C17—22no—
189M16×C17—22no—
190M16×C17—22no—
191M16×C17—22no—
192M16×C17—41no—
193M16×C17—41no—
194M16×C17—41no—
195M16×C17—41no—
196C2×C8×C17—22no—
197C2×C8×C17—22no—
198C2×C8×C17—41no—
199C2×C8×C17—41no—
200C2×C8×C17—41no—
201C2×C8×C17—41no—
202C4⋊C4×C17—41no—
203C4⋊C4×C17—41no—
204C4⋊C4×C17—41no—
205C4⋊C4×C17—41no—
206#63227—44no—
207#63227—44no—
208C4⋊Dic17—41no—
209C4⋊Dic17—41no—
210C4⋊Dic17—41no—
211C4⋊Dic17—41no—
212#63223—22no—
213#63223—22no—
214#63223—22no—
215#63223—22no—
216#63223—41no—
217#63223—41no—
218#63223—41no—
219#63223—41no—
220C2×#3622—22no—
221C2×#3622—22no—
222C2×#3622—41no—
223C2×#3622—41no—
224C2×#3622—41no—
225C2×#3622—41no—
226#11198—171nomaximal, Sylow
227C23×C17—21no—
228C23×C17—21no—
229C23×C17—21no—
230C23×C17—21no—
231C23×C17C2×C22⋊C411yescharacteristic
232C23×C17#11711yescharacteristic
233C23×C17#11711yescharacteristic
234C23×C17C4×D411yescharacteristic
235C23×C17C4×D411yescharacteristic
236C23×C17C4×D411yescharacteristic
237C23×C17C4×D411yescharacteristic
238C22×D17—24no—
239C22×D17—24no—
240C22×D17—21no—
241C22×D17—21no—
242C22×D17—21no—
243C22×D17—21no—
244C22×D17—21no—
245C22×D17—21no—
246C22×D17—21no—
247C22×D17—21no—
248C22×D17—21no—
249C22×D17—21no—
250C22×D17—21no—
251C22×D17—21no—
252C22×D17—42no—
253C22×D17—42no—
254C22×D17—42no—
255C22×D17—42no—
256C22×D17—42no—
257C22×D17—42no—
258C22×D17—42no—
259C22×D17—42no—
260C22×D17—42no—
261C22×D17—42no—
262C22×D17—41no—
263C22×D17—41no—
264C22×D17—41no—
265C22×D17—41no—
266C22×D17#10012yes—
267C22×D17#10112yes—
268C2×C4×C17—42no—
269C2×C4×C17—42no—
270C2×C4×C17—42no—
271C2×C4×C17—82no—
272C2×C4×C17—82no—
273C2×C4×C17#12011yescharacteristic
274C2×C4×C17#12011yescharacteristic
275C2×C4×C17#12111yescharacteristic
276C2×C4×C17#12111yescharacteristic
277C2×C4×C17#12111yescharacteristic
278C2×C4×C17#12111yescharacteristic
279C2×C4×C17#12111yescharacteristic
280C2×C4×C17#12111yescharacteristic
281C2×C4×C17#12111yescharacteristic
282C2×C4×C17#12111yescharacteristic
283C2×C4×C17#12311yescharacteristic
284C2×C4×C17#12311yescharacteristic
285C2×C4×C17#12311yescharacteristic
286C2×C4×C17#12311yescharacteristic
287C2×C4×C17#12311yescharacteristic
288C2×C4×C17#12311yescharacteristic
289C2×C4×C17#12311yescharacteristic
290C2×C4×C17#12311yescharacteristic
291C2×C4×C17#12311yescharacteristic
292C2×C4×C17#12311yescharacteristic
293C2×C4×C17#12411yescharacteristic
294C2×C4×C17#12411yescharacteristic
295C2×C4×C17#12411yescharacteristic
296C2×C4×C17#12411yescharacteristic
297C2×C4×C17#12611yescharacteristic
298C2×C4×C17#12611yescharacteristic
299C2×C4×C17#12611yescharacteristic
300C2×C4×C17#12611yescharacteristic
301C2×Dic17—21no—
302C2×Dic17—21no—
303C2×Dic17—21no—
304C2×Dic17—21no—
305C2×Dic17—21no—
306C2×Dic17—21no—
307C2×Dic17—41no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17—42no—
312C2×Dic17—42no—
313C2×Dic17—42no—
314C2×Dic17—82no—
315C2×Dic17—82no—
316C4×D17—41no—
317C4×D17—41no—
318C4×D17—41no—
319C4×D17—41no—
320C4×D17—41no—
321C4×D17—41no—
322C4×D17—41no—
323C4×D17—41no—
324C4×D17—41no—
325C4×D17—41no—
326C4×D17—41no—
327C4×D17—41no—
328C4×D17—41no—
329C4×D17—41no—
330C4×D17—41no—
331C4×D17—41no—
332C8×C17—42no—
333C8×C17—42no—
334#3622—42no—
335#3622—42no—
336C2×#407—171no—
337C2×#407—171no—
338C2×#380—171no—
339C2×#343—171no—
340C2×#343—171no—
341C2×#343—171no—
342C2×#343D1711yescharacteristic, complemented
343C22×C17—21no—
344C22×C17—21no—
345C22×C17—21no—
346C22×C17—21no—
347C22×C17—21no—
348C22×C17—21no—
349C22×C17—21no—
350C22×C17—21no—
351C22×C17—21no—
352C22×C17—21no—
353C22×C17—21no—
354C22×C17—21no—
355C22×C17#38111yescharacteristic
356C22×C17#38611yescharacteristic
357C22×C17#38611yescharacteristic
358C22×C17#38811yescharacteristic
359C22×C17#38811yescharacteristic
360C22×C17#38811yescharacteristic
361C22×C17#38811yescharacteristic
362C22×C17C2×#10011yescharacteristic
363C22×C17C2×#10111yescharacteristic
364C22×C17#41311yescharacteristic
365C22×C17#41311yescharacteristic
366C2×D17—22no—
367C2×D17—22no—
368C2×D17—22no—
369C2×D17—22no—
370C2×D17—22no—
371C2×D17—22no—
372C2×D17—44no—
373C2×D17—44no—
374C2×D17—44no—
375C2×D17—44no—
376C2×D17—41no—
377C2×D17—41no—
378C2×D17—41no—
379C2×D17—41no—
380C2×D17—41no—
381C2×D17—41no—
382C2×D17—41no—
383C2×D17—41no—
384C4×C17—82no—
385C4×C17#39411yescharacteristic
386C4×C17#39411yescharacteristic
387C4×C17#39411yescharacteristic
388C4×C17#39411yescharacteristic
389C4×C17#39711yescharacteristic
390C4×C17#39711yescharacteristic
391C4×C17#39711yescharacteristic
392C4×C17#39711yescharacteristic
393Dic17—41no—
394Dic17—41no—
395Dic17—82no—
396C24×C4—171no—
397C22×M16—171no—
398C22×M16—171no—
399C22×M16C2×D1711yescharacteristic
400C22×M16C2×D1711yescharacteristic
401C22×C4⋊C4—171no—
402C22×C4⋊C4C2×D1711yescharacteristic
403C22×C22⋊C4—172no—
404#407—342no—
405#407—342no—
406#407—342no—
407#407—342no—
408C2×C22⋊C8—341no—
409C2×C22⋊C8—341no—
410C2×C22⋊C8—341no—
411C2×C22⋊C8—341no—
412#380—341no—
413#380—341no—
414#380—341no—
415#380—341no—
416C2×#95—172no—
417#343—22no—
418#343—342no—
419#343—342no—
420#343—342no—
421C2×C17—21no—
422C2×C17—21no—
423C2×C17—21no—
424C2×C17—21no—
425C2×C17#144011yescharacteristic
426C2×C17#182111yescharacteristic
427C2×C17#182211yescharacteristic
428C2×C17#190011yescharacteristic
429C2×C17#190011yescharacteristic
430C2×C17#190111yescharacteristic
431C2×C17#190111yescharacteristic
432D17—42no—
433D17—42no—
434C25—171no—
435C23×C4—171no—
436C23×C4—171no—
437C23×C4—171no—
438C23×C4—171no—
439C23×C4—171no—
440C23×C4—172no—
441C23×C4—341no—
442C23×C4—341no—
443C23×C4—341no—
444C23×C4—341no—
445C23×C4—341no—
446C23×C4—341no—
447C23×C4—341no—
448C23×C4—341no—
449C23×C4—341no—
450C23×C4—341no—
451C23×C4—341no—
452C23×C4—341no—
453C23×C4C4×D1712yes—
454C23×C4C22×D1711yescharacteristic
455C2×M16—21no—
456C2×M16—21no—
457C2×M16—21no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—172no—
466C2×M16—172no—
467C2×M16—341no—
468C2×M16—341no—
469C2×M16—341no—
470C2×M16—341no—
471C2×M16—341no—
472C2×M16—341no—
473C2×M16—341no—
474C2×M16—341no—
475C2×M16—341no—
476C2×M16—341no—
477C2×M16D6812yes—
478C2×M16C22⋊D1712yes—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—341no—
482C22×C8—341no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—341no—
490C2×C4⋊C4—341no—
491C2×C4⋊C4—341no—
492C2×C4⋊C4—341no—
493C2×C4⋊C4—341no—
494C2×C4⋊C4—341no—
495C2×C22⋊C4—342no—
496C2×C22⋊C4—342no—
497C2×C22⋊C4—684no—
498C22⋊C8—344no—
499C22⋊C8—344no—
500C22⋊C8—344no—
501C22⋊C8—344no—
502#95—342no—
503#95—342no—
504C17#1119811yescharacteristic, complemented, Sylow
505C24—171no—
506C24—171no—
507C24—342no—
508C24—342no—
509C24—341no—
510C24—341no—
511C24—341no—
512C24—341no—
513C24—341no—
514C24—341no—
515C24—681no—
516C24—681no—
517C24C2×C4×D1711yescharacteristic
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—171no—
524C22×C4—171no—
525C22×C4—341no—
526C22×C4—341no—
527C22×C4—341no—
528C22×C4—341no—
529C22×C4—341no—
530C22×C4—341no—
531C22×C4—341no—
532C22×C4—341no—
533C22×C4—341no—
534C22×C4—341no—
535C22×C4—341no—
536C22×C4—341no—
537C22×C4—341no—
538C22×C4—341no—
539C22×C4—341no—
540C22×C4—341no—
541C22×C4—341no—
542C22×C4—341no—
543C22×C4—341no—
544C22×C4—341no—
545C22×C4—341no—
546C22×C4—341no—
547C22×C4—341no—
548C22×C4—341no—
549C22×C4—341no—
550C22×C4—341no—
551C22×C4—341no—
552C22×C4—341no—
553C22×C4—341no—
554C22×C4—341no—
555C22×C4—342no—
556C22×C4—342no—
557C22×C4—342no—
558C22×C4—681no—
559C22×C4—681no—
560C22×C4—681no—
561C22×C4—681no—
562C22×C4—681no—
563C22×C4—681no—
564C22×C4—681no—
565C22×C4—681no—
566C22×C4—681no—
567C22×C4—681no—
568C22×C4—681no—
569C22×C4—681no—
570C22×C4—681no—
571C22×C4—681no—
572C22×C4—681no—
573C22×C4—681no—
574C22×C4—682no—
575C22×C4—682no—
576C22×C4C2×D6811yescharacteristic
577C22×C4#6325211yescharacteristic
578C22×C4#6325211yescharacteristic
579C22×C4#6325211yescharacteristic
580C22×C4#6325211yescharacteristic
581C22×C4D4×D1711yescharacteristic
582C22×C4D4×D1711yescharacteristic
583C22×C4D4×D1711yescharacteristic
584C22×C4D4×D1711yescharacteristic
585C22×C4#6325411yescharacteristic
586C22×C4#6325411yescharacteristic
587C22×C4#6325611yescharacteristic
588C22×C4#6325611yescharacteristic
589C22×C4C2×C22⋊D1711yescharacteristic
590M16—22no—
591M16—22no—
592M16—22no—
593M16—22no—
594M16—41no—
595M16—41no—
596M16—41no—
597M16—41no—
598M16—342no—
599M16—342no—
600M16—342no—
601M16—342no—
602M16—681no—
603M16—681no—
604M16—681no—
605M16—681no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—342no—
613C2×C8—342no—
614C2×C8—681no—
615C2×C8—681no—
616C2×C8—681no—
617C2×C8—681no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—681no—
623C4⋊C4—681no—
624C4⋊C4—681no—
625C4⋊C4—681no—
626C22⋊C4—684no—
627C22⋊C4—684no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—172no—
633C23—172no—
634C23—344no—
635C23—344no—
636C23—341no—
637C23—341no—
638C23—341no—
639C23—341no—
640C23—341no—
641C23—341no—
642C23—341no—
643C23—341no—
644C23—341no—
645C23—341no—
646C23—341no—
647C23—341no—
648C23—682no—
649C23—682no—
650C23—682no—
651C23—682no—
652C23—682no—
653C23—682no—
654C23—682no—
655C23—682no—
656C23—682no—
657C23—682no—
658C23—681no—
659C23—681no—
660C23—681no—
661C23—681no—
662C23#1058755811yescharacteristic
663C23C4×D6811yescharacteristic
664C23C22⋊C4×D1711yescharacteristic
665C23#1058756711yescharacteristic
666C23#1058757811yescharacteristic
667C23#1058757911yescharacteristic
668C23C4×C22⋊D1711yescharacteristic
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—82no—
673C2×C4—82no—
674C2×C4—341no—
675C2×C4—341no—
676C2×C4—341no—
677C2×C4—341no—
678C2×C4—341no—
679C2×C4—341no—
680C2×C4—681no—
681C2×C4—681no—
682C2×C4—681no—
683C2×C4—681no—
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—682no—
701C2×C4—682no—
702C2×C4—682no—
703C2×C4—1362no—
704C2×C4—1362no—
705C2×C4#1058756111yescharacteristic
706C2×C4#1058756211yescharacteristic
707C2×C4#1058756811yescharacteristic
708C2×C4#1058756911yescharacteristic
709C2×C4#1058756911yescharacteristic
710C2×C4#1058756911yescharacteristic
711C2×C4#1058757011yescharacteristic
712C2×C4#1058757011yescharacteristic
713C2×C4#1058757011yescharacteristic
714C2×C4#1058757111yescharacteristic
715C2×C4#1058757111yescharacteristic
716C2×C4#1058757211yescharacteristic
717C2×C4#1058758011yescharacteristic
718C2×C4#1058758011yescharacteristic
719C2×C4#1058758011yescharacteristic
720C2×C4#1058758011yescharacteristic
721C2×C4#1058758011yescharacteristic
722C2×C4#1058758111yescharacteristic
723C2×C4#1058758111yescharacteristic
724C2×C4#1058758411yescharacteristic
725C2×C4#1058758411yescharacteristic
726C2×C4#1058758411yescharacteristic
727C2×C4#1058761511yescharacteristic
728C2×C4#1058761611yescharacteristic
729C2×C4#1058762311yescharacteristic
730C2×C4#1058762411yescharacteristic
731C2×C4#1058762511yescharacteristic
732C2×C4#1058763311yescharacteristic
733C8—42no—
734C8—42no—
735C8—682no—
736C8—682no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—342no—
750C22—342no—
751C22—342no—
752C22—342no—
753C22—342no—
754C22—342no—
755C22—684no—
756C22—684no—
757C22—684no—
758C22—684no—
759C22—681no—
760C22—681no—
761C22—681no—
762C22—681no—
763C22—681no—
764C22—681no—
765C22—681no—
766C22—681no—
767C22#1176267111yescharacteristic
768C22#1176268511yescharacteristic
769C22#1176268711yescharacteristic
770C22#1176269811yescharacteristic
771C22#1176269911yescharacteristic
772C22#1176270011yescharacteristic
773C22#1176270111yescharacteristic
774C22#100×D1711yescharacteristic
775C22#101×D1711yescharacteristic
776C22#1176279011yescharacteristic
777C22#1176279211yescharacteristic
778C4—82no—
779C4—681no—
780C4—681no—
781C4—1362no—
782C4#1176272411yescharacteristic
783C4#1176272511yescharacteristic
784C4#1176272611yescharacteristic
785C4#1176272711yescharacteristic
786C4#1176273511yescharacteristic
787C4#1176273611yescharacteristic
788C4#1176273811yescharacteristic
789C4#1176273811yescharacteristic
790C2—21no—
791C2—21no—
792C2—21no—
793C2—21no—
794C2—682no—
795C2—682no—
796C2#1452703211yescharacteristic
797C2#1452886311yescharacteristic
798C2#1452886611yescharacteristic
799C2#1452924411yescharacteristic
800C2#1452924611yescharacteristic
801C2#1452924911yescharacteristic
802C2#1452925111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D17
commutatorC24×C17C22×C4
FrattiniC23×C4C22×D17
FittingC2×C17×#343C2
socleC23×C17C2×C22⋊C4
prime radicalC24×D17C2×C4
cosocleC23×C4×C17C23
hypercenterC2×#343D17
hypocenterC17#11198
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
4. C2×#11762578C2semidirect
5. C2×#11762577C2semidirect
6. C2×#11762577C2semidirect
7. C2×C17×#343C2semidirect
342. C2×#343D17semidirect
504. C17#11198semidirect

Maximal subgroups

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

subgroupindex
C2×#117627722
C2×#117626662
C2×#117625782
C2×#117625772
C2×C17×#3432
#1119817