Finite Group Databasebeta

← #16939624

Subgroups — #16939624

Order 4352.

1510 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
1C22×#10587563C211yesmaximal, characteristic
2C2×#11762670C211yesmaximal, characteristic
3C2×#11762670C211yesmaximal, characteristic
4C2×#11762576C211yesmaximal, characteristic
5C2×#11762575C211yesmaximal, characteristic
6C2×#11762575C211yesmaximal, characteristic
7C2×C17×#342C211yesmaximal, characteristic
8C24×Dic17C2211yescharacteristic
9C2×#10587563—22no—
10C2×#10587563—22no—
11C2×#10587563—22no—
12C2×#10587563—22no—
13C2×#10587563—22no—
14C2×#10587563C414yescomplemented
15C22×#63225—21no—
16C22×C22⋊Dic17C2211yescharacteristic
17C22×C22⋊Dic17C2211yescharacteristic
18C22×C22⋊Dic17C2211yescharacteristic
19C22×C4×Dic17—21no—
20#11762670—21no—
21#11762670—21no—
22#11762670—22no—
23#11762670—22no—
24#11762670C414yescomplemented
25C2×#10587502—22no—
26C2×#10587502C414yescomplemented
27#11762576—22no—
28#11762575—22no—
29#11762575—22no—
30C22×C22⋊C4×C17C2211yescharacteristic
31C22×C22⋊C4×C17C2211yescharacteristic
32C22×C22⋊C4×C17C2211yescharacteristic
33C17×#342—22no—
34C25×C17C2311yescharacteristic
35C23×C4×C17—21no—
36C23×C4×C17—21no—
37C23×C4×C17C2×C412yes—
38C23×Dic17—21no—
39C23×Dic17—21no—
40C23×Dic17—21no—
41C23×Dic17—21no—
42C23×Dic17—21no—
43C23×Dic17—21no—
44C23×Dic17—21no—
45C23×Dic17—21no—
46C23×Dic17—21no—
47C23×Dic17—21no—
48C23×Dic17C2×C412yes—
49C23×Dic17C2×C412yes—
50C23×Dic17C2×C412yes—
51C23×Dic17C2×C412yes—
52C23×Dic17D411yescharacteristic
53C23×Dic17D411yescharacteristic
54C23×Dic17D412yes—
55C23×Dic17D412yes—
56C23×Dic17Q812yes—
57C2×C22⋊C4×C17—21no—
58C2×C22⋊C4×C17—21no—
59C2×C22⋊C4×C17—21no—
60C2×C22⋊C4×C17—21no—
61C2×C22⋊C4×C17—21no—
62C2×C22⋊C4×C17—21no—
63C2×C22⋊C4×C17—21no—
64C2×C22⋊C4×C17—21no—
65C2×C22⋊C4×C17—21no—
66C2×C22⋊C4×C17—21no—
67C2×C22⋊C4×C17—21no—
68C2×C22⋊C4×C17—21no—
69C2×C22⋊C4×C17—21no—
70C2×C22⋊C4×C17—21no—
71C2×C22⋊C4×C17C2×C412yes—
72C2×C22⋊C4×C17C2×C412yes—
73C2×C22⋊C4×C17D412yes—
74C2×C22⋊C4×C17D412yes—
75C2×C22⋊Dic17—21no—
76C2×C22⋊Dic17—21no—
77C2×C22⋊Dic17—21no—
78C2×C22⋊Dic17—21no—
79C2×C22⋊Dic17—21no—
80C2×C22⋊Dic17—21no—
81C2×C22⋊Dic17—21no—
82C2×C22⋊Dic17—21no—
83C2×C22⋊Dic17—21no—
84C2×C22⋊Dic17—21no—
85C2×C22⋊Dic17—21no—
86C2×C22⋊Dic17—21no—
87C2×C22⋊Dic17—21no—
88C2×C22⋊Dic17—21no—
89C2×C22⋊Dic17C2×C412yes—
90C2×C22⋊Dic17C2×C412yes—
91C2×C22⋊Dic17D412yes—
92C2×C22⋊Dic17D412yes—
93C2×#63225—24no—
94C2×#63225—24no—
95C2×#63225—24no—
96C2×C4×Dic17—24no—
97C2×C4×Dic17—24no—
98C2×C4×Dic17—24no—
99#10587563—28no—
100#10587563—28no—
101#10587563—28no—
102#10587563—28no—
103#10587502—28no—
104#10587502—24no—
105#10587502—24no—
106C24×C17—44no—
107C24×C17C22×C411yescharacteristic
108C24×C17C22×C411yescharacteristic
109C24×C17C22×C411yescharacteristic
110C24×C17C2×D411yescharacteristic
111C24×C17C2×D411yescharacteristic
112C24×C17C2×D411yescharacteristic
113C24×C17C2×D411yescharacteristic
114C24×C17C2×D411yescharacteristic
115C24×C17C2×D411yescharacteristic
116C24×C17C2×D411yescharacteristic
117C24×C17C2×Q811yescharacteristic
118C24×C17#4111yescharacteristic
119C24×C17#4111yescharacteristic
120C24×C17#4111yescharacteristic
121C24×C17#4111yescharacteristic
122C22×C4×C17—22no—
123C22×C4×C17—22no—
124C22×C4×C17—22no—
125C22×C4×C17—22no—
126C22×C4×C17—22no—
127C22×C4×C17—22no—
128C22×C4×C17—22no—
129C22×C4×C17—44no—
130C22×C4×C17—44no—
131C22×C4×C17—41no—
132C22×C4×C17—41no—
133C22×C4×C17—44no—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—22no—
137C22×Dic17—22no—
138C22×Dic17—22no—
139C22×Dic17—22no—
140C22×Dic17—22no—
141C22×Dic17—22no—
142C22×Dic17—22no—
143C22×Dic17—22no—
144C22×Dic17—22no—
145C22×Dic17—22no—
146C22×Dic17—22no—
147C22×Dic17—22no—
148C22×Dic17—21no—
149C22×Dic17—21no—
150C22×Dic17—21no—
151C22×Dic17—21no—
152C22×Dic17—22no—
153C22×Dic17—22no—
154C22×Dic17—22no—
155C22×Dic17—22no—
156C22×Dic17—22no—
157C22×Dic17—22no—
158C22×Dic17—22no—
159C22×Dic17—22no—
160C22×Dic17—21no—
161C22×Dic17—21no—
162C22×Dic17—22no—
163C22×Dic17—21no—
164C22×Dic17—21no—
165C22×Dic17—22no—
166C22×Dic17—22no—
167C22×Dic17—22no—
168C22×Dic17—22no—
169C22×Dic17—22no—
170C22×Dic17—22no—
171C22×Dic17—22no—
172C22×Dic17—22no—
173C22×Dic17—44no—
174C22×Dic17—44no—
175C22×Dic17—41no—
176C22×Dic17—41no—
177C22×Dic17—44no—
178C22×Dic17C4214yes—
179C22×Dic17C22⋊C414yes—
180C22×Dic17C22⋊C412yes—
181C22×Dic17C22⋊C412yes—
182C22×Dic17C22⋊C412yes—
183C22×Dic17C22⋊C412yes—
184C22×Dic17C4⋊C414yes—
185C22×Dic17C4⋊C414yes—
186C22×Dic17C4⋊C412yes—
187C22×Dic17C4⋊C412yes—
188C22⋊C4×C17—22no—
189C22⋊C4×C17—22no—
190C22⋊C4×C17—22no—
191C22⋊C4×C17—22no—
192C22⋊C4×C17—22no—
193C22⋊C4×C17—41no—
194C22⋊C4×C17—41no—
195C22⋊C4×C17—41no—
196C22⋊C4×C17—41no—
197C22⋊C4×C17—41no—
198C22⋊C4×C17—41no—
199C22⋊C4×C17C22⋊C414yes—
200C22⋊Dic17—22no—
201C22⋊Dic17—22no—
202C22⋊Dic17—22no—
203C22⋊Dic17—22no—
204C22⋊Dic17—22no—
205C22⋊Dic17—41no—
206C22⋊Dic17—41no—
207C22⋊Dic17—41no—
208C22⋊Dic17—41no—
209C22⋊Dic17—41no—
210C22⋊Dic17—41no—
211C22⋊Dic17C22⋊C414yes—
212#63225—216no—
213C4×Dic17—216no—
214#10736—171nomaximal, Sylow
215C23×C17—24no—
216C23×C17—24no—
217C23×C17—24no—
218C23×C17—42no—
219C23×C17—42no—
220C23×C17—42no—
221C23×C17—42no—
222C23×C17—42no—
223C23×C17—42no—
224C23×C17—42no—
225C23×C17—42no—
226C23×C17—42no—
227C23×C17—42no—
228C23×C17—42no—
229C23×C17—42no—
230C23×C17C2×C4211yescharacteristic
231C23×C17C2×C22⋊C411yescharacteristic
232C23×C17C2×C22⋊C411yescharacteristic
233C23×C17C2×C22⋊C411yescharacteristic
234C23×C17C2×C22⋊C411yescharacteristic
235C23×C17C2×C22⋊C411yescharacteristic
236C23×C17C2×C4⋊C411yescharacteristic
237C23×C17C2×C4⋊C411yescharacteristic
238C23×C17C2×C4⋊C411yescharacteristic
239C23×C17#11711yescharacteristic
240C23×C17#11711yescharacteristic
241C23×C17C4×D411yescharacteristic
242C23×C17C4×D411yescharacteristic
243C23×C17C4×D411yescharacteristic
244C23×C17C4×D411yescharacteristic
245C23×C17C4×D411yescharacteristic
246C23×C17C4×D411yescharacteristic
247C23×C17C4×D411yescharacteristic
248C23×C17C4×D411yescharacteristic
249C23×C17#12011yescharacteristic
250C23×C17#12011yescharacteristic
251C23×C17#12011yescharacteristic
252C23×C17#12011yescharacteristic
253C23×C17#12111yescharacteristic
254C23×C17#12111yescharacteristic
255C23×C17#12111yescharacteristic
256C23×C17#12111yescharacteristic
257C23×C17C22⋊Q811yescharacteristic
258C23×C17C22⋊Q811yescharacteristic
259C23×C17C22⋊Q811yescharacteristic
260C23×C17C22⋊Q811yescharacteristic
261C23×C17#12311yescharacteristic
262C23×C17#12311yescharacteristic
263C23×C17#12311yescharacteristic
264C23×C17#12311yescharacteristic
265C2×C4×C17—24no—
266C2×C4×C17—44no—
267C2×C4×C17—44no—
268C2×C4×C17—44no—
269C2×C4×C17—44no—
270C2×C4×C17—42no—
271C2×C4×C17—42no—
272C2×C4×C17—44no—
273C2×C4×C17—82no—
274C2×C4×C17—82no—
275C2×C4×C17—82no—
276C2×C4×C17—82no—
277C2×Dic17—24no—
278C2×Dic17—24no—
279C2×Dic17—22no—
280C2×Dic17—22no—
281C2×Dic17—24no—
282C2×Dic17—24no—
283C2×Dic17—22no—
284C2×Dic17—22no—
285C2×Dic17—24no—
286C2×Dic17—22no—
287C2×Dic17—22no—
288C2×Dic17—24no—
289C2×Dic17—22no—
290C2×Dic17—22no—
291C2×Dic17—24no—
292C2×Dic17—22no—
293C2×Dic17—22no—
294C2×Dic17—24no—
295C2×Dic17—22no—
296C2×Dic17—22no—
297C2×Dic17—24no—
298C2×Dic17—44no—
299C2×Dic17—44no—
300C2×Dic17—44no—
301C2×Dic17—44no—
302C2×Dic17—42no—
303C2×Dic17—42no—
304C2×Dic17—44no—
305C2×Dic17—82no—
306C2×Dic17—82no—
307C2×Dic17—82no—
308C2×Dic17—82no—
309C2×Dic17#9514yes—
310C2×Dic17#9514yes—
311C22×#117—171no—
312C2×#381—171no—
313C2×#381—171no—
314C2×#342—171no—
315C2×#342—171no—
316C2×#342—171no—
317C2×#342D1711yescharacteristic
318C22×C17—22no—
319C22×C17—22no—
320C22×C17—22no—
321C22×C17—22no—
322C22×C17—22no—
323C22×C17—22no—
324C22×C17—22no—
325C22×C17—22no—
326C22×C17—22no—
327C22×C17—22no—
328C22×C17—22no—
329C22×C17—22no—
330C22×C17—22no—
331C22×C17—22no—
332C22×C17—22no—
333C22×C17—22no—
334C22×C17—22no—
335C22×C17—22no—
336C22×C17—41no—
337C22×C17—41no—
338C22×C17—41no—
339C22×C17—41no—
340C22×C17—41no—
341C22×C17—41no—
342C22×C17—41no—
343C22×C17—41no—
344C22×C17—41no—
345C22×C17—41no—
346C22×C17—41no—
347C22×C17—41no—
348C22×C17—41no—
349C22×C17—41no—
350C22×C17—41no—
351C22×C17—41no—
352C22×C17C2×#9511yescharacteristic
353C22×C17C4×C22⋊C411yescharacteristic
354C22×C17C4×C22⋊C411yescharacteristic
355C22×C17#37911yescharacteristic
356C22×C17#38011yescharacteristic
357C22×C17#38011yescharacteristic
358C22×C17#38111yescharacteristic
359C22×C17#38511yescharacteristic
360C22×C17#38511yescharacteristic
361C22×C17#38511yescharacteristic
362C22×C17#38511yescharacteristic
363C22×C17#38611yescharacteristic
364C22×C17#38611yescharacteristic
365C22×C17#38611yescharacteristic
366C22×C17#38611yescharacteristic
367C22×C17#41014yes—
368C4×C17—44no—
369C4×C17—82no—
370C4×C17—82no—
371Dic17—24no—
372Dic17—24no—
373Dic17—44no—
374Dic17—82no—
375Dic17—82no—
376C24×C4—171no—
377C2×#117—174no—
378C2×#117—342no—
379C2×#117—342no—
380C2×#117—342no—
381C2×#117—342no—
382C2×#117—342no—
383C22×C4⋊C4—341no—
384C22×C22⋊C4—171no—
385C22×C22⋊C4—171no—
386C22×C22⋊C4—171no—
387C22×C22⋊C4C2×D1711yescharacteristic
388C22×C22⋊C4C2×D1711yescharacteristic
389C22×C22⋊C4C2×D1711yescharacteristic
390C22×C42—341no—
391#381—174no—
392#381—341no—
393#381—342no—
394#381—341no—
395#381—342no—
396C2×#95—174no—
397C2×#95—342no—
398#342—22no—
399#342—342no—
400#342—342no—
401#342—342no—
402C2×C17—21no—
403C2×C17—21no—
404C2×C17—21no—
405C2×C17—21no—
406C2×C17—21no—
407C2×C17—21no—
408C2×C17—21no—
409C2×C17—21no—
410C2×C17—21no—
411C2×C17—21no—
412C2×C17—21no—
413C2×C17—21no—
414C2×C17C22⋊#9511yescharacteristic
415C2×C17#174012yes—
416C2×C17#189912yes—
417C2×C17#189912yes—
418C25C22×D1711yescharacteristic
419C23×C4—21no—
420C23×C4—21no—
421C23×C4—172no—
422C23×C4—172no—
423C23×C4—172no—
424C23×C4—171no—
425C23×C4—172no—
426C23×C4—172no—
427C23×C4—171no—
428C23×C4—172no—
429C23×C4—172no—
430C23×C4—341no—
431C23×C4—341no—
432C23×C4—341no—
433C23×C4—341no—
434C23×C4—341no—
435C23×C4—341no—
436C23×C4—341no—
437C23×C4—341no—
438C23×C4—341no—
439C23×C4—341no—
440C23×C4C4×D1712yes—
441#117—348no—
442#117—348no—
443#117—348no—
444#117—348no—
445C2×C4⋊C4—344no—
446C2×C4⋊C4—344no—
447C2×C4⋊C4—344no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—172no—
463C2×C22⋊C4—172no—
464C2×C22⋊C4—172no—
465C2×C22⋊C4—172no—
466C2×C22⋊C4—341no—
467C2×C22⋊C4—341no—
468C2×C22⋊C4—341no—
469C2×C22⋊C4—341no—
470C2×C22⋊C4—341no—
471C2×C22⋊C4—341no—
472C2×C22⋊C4—341no—
473C2×C22⋊C4—341no—
474C2×C22⋊C4—341no—
475C2×C22⋊C4—341no—
476C2×C22⋊C4—341no—
477C2×C22⋊C4—341no—
478C2×C22⋊C4—341no—
479C2×C22⋊C4—341no—
480C2×C22⋊C4C4×D1712yes—
481C2×C22⋊C4C4×D1712yes—
482C2×C22⋊C4D6812yes—
483C2×C22⋊C4C22⋊D1712yes—
484C2×C42—344no—
485C2×C42—344no—
486C2×C42—344no—
487#95—344no—
488#95—344no—
489#95—348no—
490C17#1073611yescharacteristic, complemented, Sylow
491C24—44no—
492C24C2×C4×D1711yescharacteristic
493C24C2×C4×D1711yescharacteristic
494C24C2×C4×D1711yescharacteristic
495C24C2×D6811yescharacteristic
496C24#6325211yescharacteristic
497C24#6325211yescharacteristic
498C24D4×D1711yescharacteristic
499C24D4×D1711yescharacteristic
500C24D4×D1711yescharacteristic
501C24D4×D1711yescharacteristic
502C24D4×D1711yescharacteristic
503C24#6325411yescharacteristic
504C24Q8×D1711yescharacteristic
505C24#6325611yescharacteristic
506C24C2×C22⋊D1711yescharacteristic
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—44no—
519C22×C4—174no—
520C22×C4—174no—
521C22×C4—172no—
522C22×C4—172no—
523C22×C4—172no—
524C22×C4—172no—
525C22×C4—174no—
526C22×C4—174no—
527C22×C4—172no—
528C22×C4—172no—
529C22×C4—342no—
530C22×C4—342no—
531C22×C4—342no—
532C22×C4—342no—
533C22×C4—342no—
534C22×C4—342no—
535C22×C4—341no—
536C22×C4—341no—
537C22×C4—342no—
538C22×C4—341no—
539C22×C4—341no—
540C22×C4—342no—
541C22×C4—342no—
542C22×C4—342no—
543C22×C4—342no—
544C22×C4—342no—
545C22×C4—342no—
546C22×C4—341no—
547C22×C4—341no—
548C22×C4—342no—
549C22×C4—342no—
550C22×C4—342no—
551C22×C4—342no—
552C22×C4—342no—
553C22×C4—342no—
554C22×C4—342no—
555C22×C4—342no—
556C22×C4—341no—
557C22×C4—341no—
558C22×C4—342no—
559C22×C4—342no—
560C22×C4—342no—
561C22×C4—342no—
562C22×C4—342no—
563C22×C4—342no—
564C22×C4—342no—
565C22×C4—342no—
566C22×C4—342no—
567C22×C4—342no—
568C22×C4—684no—
569C22×C4—684no—
570C22×C4—681no—
571C22×C4—681no—
572C22×C4—684no—
573C4⋊C4—3416no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—41no—
584C22⋊C4—41no—
585C22⋊C4—174no—
586C22⋊C4—342no—
587C22⋊C4—342no—
588C22⋊C4—342no—
589C22⋊C4—342no—
590C22⋊C4—342no—
591C22⋊C4—681no—
592C22⋊C4—681no—
593C22⋊C4—681no—
594C22⋊C4—681no—
595C22⋊C4—681no—
596C22⋊C4—681no—
597C22⋊C4#6322714yes—
598C42—3416no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23C42×D1711yescharacteristic
615C23#1058755811yescharacteristic
616C23C4×D6811yescharacteristic
617C23C4×D6811yescharacteristic
618C23C22⋊C4×D1711yescharacteristic
619C23C22⋊C4×D1711yescharacteristic
620C23C22⋊C4×D1711yescharacteristic
621C23C22⋊C4×D1711yescharacteristic
622C23#1058756711yescharacteristic
623C23#1058756711yescharacteristic
624C23#1058756811yescharacteristic
625C23#1058756811yescharacteristic
626C23#1058756911yescharacteristic
627C23#1058756911yescharacteristic
628C23#1058757011yescharacteristic
629C23#1058757011yescharacteristic
630C23C4⋊C4×D1711yescharacteristic
631C23C4⋊C4×D1711yescharacteristic
632C23C4⋊C4×D1711yescharacteristic
633C23#1058757811yescharacteristic
634C23#1058757911yescharacteristic
635C23#1058757911yescharacteristic
636C23#1058758011yescharacteristic
637C23#1058758011yescharacteristic
638C23#1058758111yescharacteristic
639C23#1058758211yescharacteristic
640C23#1058758211yescharacteristic
641C23#1058758311yescharacteristic
642C23C2×#6322711yescharacteristic
643C23C4×C22⋊D1711yescharacteristic
644C23C4×C22⋊D1711yescharacteristic
645C23#1058762311yescharacteristic
646C23#1058762311yescharacteristic
647C23#1058762411yescharacteristic
648C23#1058763211yescharacteristic
649C2×C4—24no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—44no—
654C2×C4—44no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—82no—
658C2×C4—82no—
659C2×C4—82no—
660C2×C4—82no—
661C2×C4—174no—
662C2×C4—174no—
663C2×C4—344no—
664C2×C4—344no—
665C2×C4—342no—
666C2×C4—342no—
667C2×C4—344no—
668C2×C4—344no—
669C2×C4—342no—
670C2×C4—342no—
671C2×C4—342no—
672C2×C4—342no—
673C2×C4—344no—
674C2×C4—342no—
675C2×C4—342no—
676C2×C4—344no—
677C2×C4—344no—
678C2×C4—342no—
679C2×C4—342no—
680C2×C4—344no—
681C2×C4—342no—
682C2×C4—342no—
683C2×C4—344no—
684C2×C4—684no—
685C2×C4—684no—
686C2×C4—684no—
687C2×C4—684no—
688C2×C4—684no—
689C2×C4—682no—
690C2×C4—682no—
691C2×C4—1362no—
692C2×C4—1362no—
693C2×C4—1362no—
694C2×C4—1362no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22#95×D1711yescharacteristic
730C22#1176265611yescharacteristic
731C22C4×#6322711yescharacteristic
732C22#1176266411yescharacteristic
733C22#1176266611yescharacteristic
734C22#1176266811yescharacteristic
735C22#1176267111yescharacteristic
736C22#1176268011yescharacteristic
737C22#1176268011yescharacteristic
738C22#1176268311yescharacteristic
739C22#1176268311yescharacteristic
740C22#1176268511yescharacteristic
741C22#1176268511yescharacteristic
742C22#1176268711yescharacteristic
743C22#1176268711yescharacteristic
744C22#1176278114yes—
745C4—44no—
746C4—82no—
747C4—82no—
748C4—344no—
749C4—344no—
750C4—684no—
751C4—1362no—
752C4—1362no—
753C2—21no—
754C2—21no—
755C2—21no—
756C2—21no—
757C2—21no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—21no—
765C2#1452700511yescharacteristic
766C2#1452851512yes—
767C2#1452923912yes—
768C2#1452924112yes—
subgroupG/H
centerC23C22⋊C4×D17
commutatorC23×C17C2×C42
FrattiniC25C22×D17
FittingC2×C17×#342C2
socleC23×C17C2×C22⋊C4
prime radical, cosocleC25×C17C23
hypercenterC2×#342D17
hypocenterC17#10736
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
14. C2×#10587563C4semidirect
24. #11762670C4semidirect
26. C2×#10587502C4semidirect
490. C17#10736semidirect

Maximal subgroups

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

subgroupindex
C22×#105875632
C2×#117626702
C2×#117625762
C2×#117625752
C2×C17×#3422
#1073617