Finite Group Databasebeta

← #16957708

Subgroups — #16957708

Order 4352.

1810 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587573C211yesmaximal, characteristic
2C2×#11762715C211yesmaximal, characteristic
3C2×#11762714C211yesmaximal, characteristic
4C2×C4×#63225C211yesmaximal, characteristic
5#14527047C212yesmaximal
6#14527042C212yesmaximal
7#14527016C212yesmaximal
8#14527015C212yesmaximal
9#14527013C211yesmaximal, characteristic
10#14527013C211yesmaximal, characteristic
11C2×C17×#389C211yesmaximal, characteristic
12C23×Dic34C2211yescharacteristic
13C2×#10587573—24no—
14C2×#10587573—24no—
15C2×#10587573—24no—
16C22×C4⋊Dic17C2211yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×#63225C2212yes—
19C22×#63225C2211yescharacteristic
20C22×C4×Dic17C2212yes—
21C22×C4×Dic17C2211yescharacteristic
22C22×C4×Dic17C2211yescharacteristic
23#11762715—24no—
24#11762714C418yescomplemented
25C4×#63225—24no—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2211yescharacteristic
30C2×#10587502C2212yes—
31C2×#10587502C2211yescharacteristic
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2212yes—
36C22×C4⋊C4×C17C2212yes—
37C22×C4⋊C4×C17C2211yescharacteristic
38C22×C4⋊C4×C17C2211yescharacteristic
39C22×C42×C17C2211yescharacteristic
40C17×#389—24no—
41C2×C17×#95C2212yes—
42C23×C4×C17C2312yes—
43C23×C4×C17C2312yes—
44C23×C4×C17C2311yescharacteristic
45C23×C4×C17C2311yescharacteristic
46C23×C4×C17C2311yescharacteristic
47C23×Dic17C2312yes—
48C23×Dic17C2311yescharacteristic
49C23×Dic17C2311yescharacteristic
50C23×Dic17C2312yes—
51C23×Dic17C2311yescharacteristic
52C23×Dic17C2311yescharacteristic
53C22×Dic34—22no—
54C22×Dic34—22no—
55C22×Dic34—22no—
56C22×Dic34—22no—
57C22×Dic34C2×C414yes—
58C22×Dic34D414yes—
59C22×Dic34Q814yes—
60C2×C4⋊C4×C17—22no—
61C2×C4⋊C4×C17—22no—
62C2×C4⋊C4×C17—22no—
63C2×C4⋊C4×C17—22no—
64C2×C4⋊C4×C17—24no—
65C2×C4⋊C4×C17—24no—
66C2×C4⋊C4×C17—42no—
67C2×C4⋊C4×C17C2×C414yes—
68C2×C4⋊C4×C17D414yes—
69C2×C42×C17—22no—
70C2×C42×C17—22no—
71C2×C42×C17—22no—
72C2×C4⋊Dic17—22no—
73C2×C4⋊Dic17—22no—
74C2×C4⋊Dic17—22no—
75C2×#63225—24no—
76C2×#63225—22no—
77C2×#63225—24no—
78C2×#63225—24no—
79C2×#63225—22no—
80C2×#63225—22no—
81C2×#63225—22no—
82C2×#63225—22no—
83C2×#63225Q814yescomplemented
84C2×C4×Dic17—24no—
85C2×C4×Dic17—22no—
86C2×C4×Dic17—22no—
87C2×C4×Dic17—22no—
88C2×C4×Dic17—22no—
89C2×C4×Dic17—24no—
90C2×C4×Dic17—24no—
91C2×C4×Dic17C2×C414yes—
92C2×C4×Dic17D414yes—
93#10587573—232no—
94C17×#95—24no—
95#10587502—24no—
96#10587502—24no—
97#10587502—22no—
98#10587502—22no—
99#10587502—24no—
100#10587502—24no—
101#10587502—42no—
102#10587502—42no—
103#10587502C2×C418yes—
104#10587502C2×C418yes—
105C24×C17C2411yescharacteristic
106C22×C4×C17—21no—
107C22×C4×C17—21no—
108C22×C4×C17—21no—
109C22×C4×C17—21no—
110C22×C4×C17—21no—
111C22×C4×C17—22no—
112C22×C4×C17—22no—
113C22×C4×C17—22no—
114C22×C4×C17—21no—
115C22×C4×C17—22no—
116C22×C4×C17—22no—
117C22×C4×C17—21no—
118C22×C4×C17—21no—
119C22×C4×C17—22no—
120C22×C4×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17—22no—
123C22×C4×C17—22no—
124C22×C4×C17—21no—
125C22×C4×C17—21no—
126C22×C4×C17—22no—
127C22×C4×C17—22no—
128C22×C4×C17—21no—
129C22×C4×C17—21no—
130C22×C4×C17C22×C414yes—
131C22×C4×C17C22×C412yes—
132C22×C4×C17C2×D412yes—
133C22×C4×C17C2×D412yes—
134C22×C4×C17C2×D414yes—
135C22×C4×C17C2×D412yes—
136C22×C4×C17C2×Q812yes—
137C22×C4×C17C2×Q812yes—
138C22×C4×C17#4112yes—
139C22×C4×C17#4112yes—
140C22×C4×C17#4112yes—
141C22×Dic17—22no—
142C22×Dic17—22no—
143C22×Dic17—21no—
144C22×Dic17—21no—
145C22×Dic17—21no—
146C22×Dic17—22no—
147C22×Dic17—22no—
148C22×Dic17—21no—
149C22×Dic17—21no—
150C22×Dic17—21no—
151C22×Dic17—21no—
152C22×Dic17—21no—
153C22×Dic17—21no—
154C22×Dic17—21no—
155C22×Dic17—21no—
156C22×Dic17—21no—
157C22×Dic17—21no—
158C22×Dic17—21no—
159C22×Dic17—21no—
160C22×Dic17—21no—
161C22×Dic17—21no—
162C22×Dic17—21no—
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×Dic17C22×C412yes—
173C22×Dic17C22×C414yes—
174C22×Dic17C22×C412yes—
175C22×Dic17C2×D412yes—
176C22×Dic17C2×D414yes—
177C22×Dic17C2×D412yes—
178C22×Dic17C2×Q814yes—
179C22×Dic17C2×Q812yes—
180C22×Dic17C2×Q812yes—
181C22×Dic17#4112yes—
182C22×Dic17#4112yes—
183C2×Dic34—28no—
184C2×Dic34—28no—
185C2×Dic34—28no—
186C2×Dic34—28no—
187C2×Dic34—28no—
188C2×Dic34—28no—
189C2×Dic34C4⋊C4116yescomplemented
190C4⋊C4×C17—28no—
191C4⋊C4×C17—28no—
192C4⋊C4×C17—48no—
193C42×C17—44no—
194C4⋊Dic17—44no—
195#63225—216no—
196#63225—28no—
197#63225—28no—
198C4×Dic17—216no—
199C4×Dic17—28no—
200C4×Dic17—28no—
201#14017—171nomaximal, Sylow
202C23×C17C23×C411yescharacteristic
203C23×C17C22×D411yescharacteristic
204C23×C17C22×D411yescharacteristic
205C23×C17C22×D411yescharacteristic
206C23×C17C22×Q811yescharacteristic
207C23×C17C22×Q811yescharacteristic
208C23×C17C2×#4111yescharacteristic
209C23×C17C2×#4111yescharacteristic
210C23×C17C2×#4111yescharacteristic
211C23×C17C2×#4111yescharacteristic
212C23×C17C2×#4111yescharacteristic
213C23×C17H(5,𝔽2)11yescharacteristic
214C23×C172−1+411yescharacteristic
215C23×C172−1+411yescharacteristic
216C23×C172−1+411yescharacteristic
217C2×C4×C17—24no—
218C2×C4×C17—24no—
219C2×C4×C17—24no—
220C2×C4×C17—24no—
221C2×C4×C17—22no—
222C2×C4×C17—22no—
223C2×C4×C17—22no—
224C2×C4×C17—24no—
225C2×C4×C17—24no—
226C2×C4×C17—22no—
227C2×C4×C17—22no—
228C2×C4×C17—22no—
229C2×C4×C17—41no—
230C2×C4×C17—41no—
231C2×C4×C17—42no—
232C2×C4×C17—41no—
233C2×C4×C17—41no—
234C2×C4×C17—42no—
235C2×C4×C17—42no—
236C2×C4×C17—41no—
237C2×C4×C17—42no—
238C2×C4×C17—42no—
239C2×C4×C17—41no—
240C2×C4×C17—41no—
241C2×C4×C17—41no—
242C2×C4×C17—42no—
243C2×C4×C17—42no—
244C2×C4×C17—42no—
245C2×C4×C17C2×C4⋊C414yes—
246C2×C4×C17C4×D414yes—
247C2×C4×C17C4×D414yes—
248C2×C4×C17#12014yes—
249C2×C4×C17C22⋊Q814yes—
250C2×C4×C17C22⋊Q814yes—
251C2×C4×C17#12314yes—
252C2×Dic17—24no—
253C2×Dic17—24no—
254C2×Dic17—22no—
255C2×Dic17—22no—
256C2×Dic17—24no—
257C2×Dic17—22no—
258C2×Dic17—24no—
259C2×Dic17—24no—
260C2×Dic17—22no—
261C2×Dic17—24no—
262C2×Dic17—22no—
263C2×Dic17—22no—
264C2×Dic17—22no—
265C2×Dic17—22no—
266C2×Dic17—22no—
267C2×Dic17—22no—
268C2×Dic17—22no—
269C2×Dic17—22no—
270C2×Dic17—22no—
271C2×Dic17—22no—
272C2×Dic17—22no—
273C2×Dic17—22no—
274C2×Dic17—22no—
275C2×Dic17—22no—
276C2×Dic17—41no—
277C2×Dic17—41no—
278C2×Dic17—41no—
279C2×Dic17—41no—
280C2×Dic17—41no—
281C2×Dic17—41no—
282C2×Dic17—41no—
283C2×Dic17—41no—
284C2×Dic17—42no—
285C2×Dic17—42no—
286C2×Dic17—42no—
287C2×Dic17—42no—
288C2×Dic17—42no—
289C2×Dic17—42no—
290C2×Dic17—42no—
291C2×Dic17C2×C4⋊C418yes—
292C2×Dic17C4×Q814yescomplemented
293C2×Dic17C22⋊Q814yes—
294Dic34—232no—
295C22×C4×Q8—171no—
296C2×#391—171no—
297C2×#391—171no—
298C2×#389D1711yescharacteristic
299C2×C4×C4⋊C4—171no—
300#1444—172no—
301#1442—172no—
302#1436—172no—
303#1436—172no—
304C4⋊#95—171no—
305C4⋊#95—171no—
306C22×C17C22×C4⋊C411yescharacteristic
307C22×C17C2×C4×D411yescharacteristic
308C22×C17C2×C4×D411yescharacteristic
309C22×C17C2×C4×Q811yescharacteristic
310C22×C17C4×#4111yescharacteristic
311C22×C17#51911yescharacteristic
312C22×C17#52011yescharacteristic
313C22×C17C2×#12011yescharacteristic
314C22×C17C2×C22⋊Q811yescharacteristic
315C22×C17C2×C22⋊Q811yescharacteristic
316C22×C17C2×C22⋊Q811yescharacteristic
317C22×C17C2×#12311yescharacteristic
318C22×C17#52511yescharacteristic
319C22×C17#52911yescharacteristic
320C22×C17#53311yescharacteristic
321C22×C17#53611yescharacteristic
322C22×C17#53711yescharacteristic
323C22×C17#54111yescharacteristic
324C22×C17#54211yescharacteristic
325C22×C17#54611yescharacteristic
326C22×C17#54711yescharacteristic
327C22×C17#54811yescharacteristic
328C22×C17#54811yescharacteristic
329C22×C17#54811yescharacteristic
330C22×C17D4×Q811yescharacteristic
331C22×C17D4×Q811yescharacteristic
332C22×C17#55011yescharacteristic
333C22×C17#55611yescharacteristic
334C22×C17#55611yescharacteristic
335C22×C17#55711yescharacteristic
336C22×C17#55711yescharacteristic
337C22×C17#55711yescharacteristic
338C22×C17#55711yescharacteristic
339C22×C17Q8211yescharacteristic
340C22×C17#55911yescharacteristic
341C4×C17—44no—
342C4×C17—44no—
343C4×C17—42no—
344C4×C17—42no—
345C4×C17#38518yes—
346Dic17—24no—
347Dic17—28no—
348Dic17—24no—
349Dic17—42no—
350Dic17—42no—
351Dic17—82no—
352C23×Q8—171no—
353C2×C4×Q8—344no—
354C2×C4×Q8—344no—
355C2×C4×Q8—344no—
356C22×C4⋊C4—171no—
357C22×C4⋊C4—172no—
358C22×C4⋊C4—171no—
359C22×C4⋊C4—171no—
360C22×C4⋊C4C2×D1712yes—
361C22×C4⋊C4C2×D1711yescharacteristic
362C22×C4⋊C4C2×D1711yescharacteristic
363C22×C42—171no—
364C22×C42—171no—
365C22×C42—172no—
366C22×C42C2×D1711yescharacteristic
367#391—178no—
368#391—344no—
369#389—24no—
370C4×C4⋊C4—344no—
371C2×#95—172no—
372C2×#95—172no—
373C2×#95—172no—
374C2×#95—172no—
375C2×#95—171no—
376C2×#95—172no—
377C2×#95—172no—
378C2×#95—171no—
379C2×#95—172no—
380C2×#95—172no—
381C2×#95C2×D1712yes—
382C2×C17C2×#38511yescharacteristic
383C2×C17C4×C22⋊Q811yescharacteristic
384C2×C17#232311yescharacteristic
385C2×C17Q8×C4⋊C411yescharacteristic
386C2×C17#235111yescharacteristic
387C2×C17#236511yescharacteristic
388C2×C17#236711yescharacteristic
389C2×C17#240711yescharacteristic
390C2×C17#240911yescharacteristic
391C2×C17#244611yescharacteristic
392C2×C17#244811yescharacteristic
393C2×C17#245111yescharacteristic
394C2×C17#245311yescharacteristic
395C2×C17#258111yescharacteristic
396C2×C17#258211yescharacteristic
397C22×Q8—174no—
398C22×Q8—174no—
399C22×Q8—174no—
400C22×Q8—342no—
401C22×Q8—342no—
402C22×Q8—342no—
403C22×Q8—342no—
404C23×C4—171no—
405C23×C4—172no—
406C23×C4—171no—
407C23×C4—171no—
408C23×C4—171no—
409C23×C4—172no—
410C23×C4C22×D1712yes—
411C23×C4C22×D1711yescharacteristic
412C23×C4C22×D1711yescharacteristic
413C23×C4C22×D1712yes—
414C23×C4C22×D1711yescharacteristic
415C4×Q8—3432no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—174no—
424C2×C4⋊C4—344no—
425C2×C4⋊C4—344no—
426C2×C4⋊C4—342no—
427C2×C4⋊C4—342no—
428C2×C4⋊C4—342no—
429C2×C4⋊C4—342no—
430C2×C4⋊C4—342no—
431C2×C4⋊C4—344no—
432C2×C4⋊C4—342no—
433C2×C4⋊C4—342no—
434C2×C4⋊C4—342no—
435C2×C4⋊C4C4×D1714yes—
436C2×C4⋊C4C22⋊D1714yes—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—174no—
441C2×C42—174no—
442C2×C42—344no—
443C2×C42—344no—
444C2×C42—342no—
445C2×C42—342no—
446C2×C42—342no—
447C2×C42—344no—
448C2×C42—342no—
449#95—24no—
450#95—178no—
451#95—178no—
452#95—344no—
453#95—344no—
454#95—342no—
455#95—342no—
456#95—344no—
457#95—344no—
458#95—682no—
459#95—682no—
460C17#1401711yescharacteristic, complemented, Sylow
461C24C23×D1711yescharacteristic
462C2×Q8—1716no—
463C2×Q8—348no—
464C2×Q8—348no—
465C2×Q8—348no—
466C2×Q8—348no—
467C2×Q8—348no—
468C2×Q8—348no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—172no—
494C22×C4—174no—
495C22×C4—174no—
496C22×C4—172no—
497C22×C4—172no—
498C22×C4—172no—
499C22×C4—174no—
500C22×C4—172no—
501C22×C4—172no—
502C22×C4—172no—
503C22×C4—172no—
504C22×C4—342no—
505C22×C4—341no—
506C22×C4—341no—
507C22×C4—342no—
508C22×C4—341no—
509C22×C4—341no—
510C22×C4—342no—
511C22×C4—341no—
512C22×C4—341no—
513C22×C4—341no—
514C22×C4—341no—
515C22×C4—342no—
516C22×C4—341no—
517C22×C4—341no—
518C22×C4—341no—
519C22×C4—341no—
520C22×C4—341no—
521C22×C4—341no—
522C22×C4—341no—
523C22×C4—341no—
524C22×C4—341no—
525C22×C4—341no—
526C22×C4—341no—
527C22×C4—341no—
528C22×C4—342no—
529C22×C4—342no—
530C22×C4—342no—
531C22×C4—342no—
532C22×C4—342no—
533C22×C4—342no—
534C22×C4—342no—
535C22×C4C2×C4×D1714yes—
536C22×C4C2×C4×D1712yes—
537C22×C4#6325212yes—
538C22×C4D4×D1712yes—
539C22×C4D4×D1712yes—
540C22×C4#6325412yes—
541C22×C4Q8×D1712yes—
542C22×C4Q8×D1712yes—
543C22×C4#6325612yes—
544C22×C4C2×C22⋊D1714yes—
545C22×C4C2×C22⋊D1712yes—
546C4⋊C4—28no—
547C4⋊C4—28no—
548C4⋊C4—48no—
549C4⋊C4—348no—
550C4⋊C4—3416no—
551C4⋊C4—348no—
552C4⋊C4—684no—
553C42—44no—
554C42—3416no—
555C42—348no—
556C42—348no—
557C23C22×C4×D1711yescharacteristic
558C23C2×#6325211yescharacteristic
559C23C2×D4×D1711yescharacteristic
560C23C2×D4×D1711yescharacteristic
561C23C2×#6325411yescharacteristic
562C23#1058769111yescharacteristic
563C23C2×Q8×D1711yescharacteristic
564C23C2×Q8×D1711yescharacteristic
565C23C2×#6325611yescharacteristic
566C23#1058769411yescharacteristic
567C23#41×D1711yescharacteristic
568C23#41×D1711yescharacteristic
569C23#1058769711yescharacteristic
570C23#1058769711yescharacteristic
571C23C22×C22⋊D1711yescharacteristic
572Q8—3432no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—178no—
602C2×C4—174no—
603C2×C4—174no—
604C2×C4—342no—
605C2×C4—342no—
606C2×C4—342no—
607C2×C4—342no—
608C2×C4—344no—
609C2×C4—342no—
610C2×C4—344no—
611C2×C4—342no—
612C2×C4—342no—
613C2×C4—344no—
614C2×C4—342no—
615C2×C4—344no—
616C2×C4—344no—
617C2×C4—344no—
618C2×C4—342no—
619C2×C4—342no—
620C2×C4—342no—
621C2×C4—342no—
622C2×C4—342no—
623C2×C4—342no—
624C2×C4—342no—
625C2×C4—342no—
626C2×C4—342no—
627C2×C4—342no—
628C2×C4—681no—
629C2×C4—681no—
630C2×C4—681no—
631C2×C4—681no—
632C2×C4—681no—
633C2×C4—681no—
634C2×C4—681no—
635C2×C4—681no—
636C2×C4—682no—
637C2×C4—682no—
638C2×C4—682no—
639C2×C4—682no—
640C2×C4—682no—
641C2×C4—682no—
642C2×C4—682no—
643C2×C4C4⋊C4×D1714yes—
644C2×C4#1058757914yes—
645C2×C4#1058758014yes—
646C2×C4#1058758214yes—
647C2×C4C4×C22⋊D1714yes—
648C2×C4#1058762314yes—
649C2×C4#1058763214yes—
650C22C2×C4⋊C4×D1711yescharacteristic
651C22C2×C4×C22⋊D1711yescharacteristic
652C22C2×#1058757911yescharacteristic
653C22C4×Q8×D1711yescharacteristic
654C22C4×#6325411yescharacteristic
655C22#1176328511yescharacteristic
656C22#1176328811yescharacteristic
657C22C2×#1058762311yescharacteristic
658C22C22⋊Q8×D1711yescharacteristic
659C22C2×#1058763211yescharacteristic
660C22C2×#1058758211yescharacteristic
661C22C2×#1058758011yescharacteristic
662C22#1176331911yescharacteristic
663C22#1176334411yescharacteristic
664C22#1176336411yescharacteristic
665C22#1176338211yescharacteristic
666C22#1176338811yescharacteristic
667C22#1176342211yescharacteristic
668C22#1176343311yescharacteristic
669C22#1176345311yescharacteristic
670C22#1176345811yescharacteristic
671C22#1176346511yescharacteristic
672C22#1176346611yescharacteristic
673C22#1176346911yescharacteristic
674C22#1176347211yescharacteristic
675C22Q8×C22⋊D1711yescharacteristic
676C22#1176347711yescharacteristic
677C22#1176352911yescharacteristic
678C22#1176353111yescharacteristic
679C22#1176353411yescharacteristic
680C22#1176353611yescharacteristic
681C22#1176353611yescharacteristic
682C22#1176353711yescharacteristic
683C22#1176353911yescharacteristic
684C22#1176354211yescharacteristic
685C4—44no—
686C4—44no—
687C4—42no—
688C4—42no—
689C4—344no—
690C4—348no—
691C4—344no—
692C4—682no—
693C4—682no—
694C4—1362no—
695C4#1176268018yes—
696C2C2×#1176268011yescharacteristic
697C2#1453131411yescharacteristic
698C2#1453146411yescharacteristic
699C2#1453169811yescharacteristic
700C2#1453170311yescharacteristic
701C2#1453183811yescharacteristic
702C2#1453185711yescharacteristic
703C2#1453212511yescharacteristic
704C2#1453214511yescharacteristic
705C2#1453256211yescharacteristic
706C2#1453258411yescharacteristic
707C2#1453261911yescharacteristic
708C2#1453264111yescharacteristic
709C2#1453415211yescharacteristic
710C2#1453415611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#389C2
socle, prime radical, cosocleC24×C17C24
hypercenterC2×#389D17
hypocenterC17#14017
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
24. #11762714C4semidirect
83. C2×#63225Q8semidirect
189. C2×Dic34C4⋊C4semidirect
292. C2×Dic17C4×Q8semidirect
460. C17#14017semidirect

Maximal subgroups

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

subgroupindex
C22×#105875732
C2×#117627152
C2×#117627142
C2×C4×#632252
#145270472
#145270422
#145270162
#145270152
#145270132
C2×C17×#3892
#1401717