Finite Group Databasebeta

← #16958061

Subgroups — #16958061

Order 4352.

1586 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762707C211yesmaximal, characteristic
2C2×#11762707C211yesmaximal, characteristic
3C2×#11762707C211yesmaximal, characteristic
4C2×#11762704C212yesmaximal
5C2×C4×C4⋊Dic17C211yesmaximal, characteristic
6#14527039C212yesmaximal
7#14527034C212yesmaximal
8#14527019C212yesmaximal
9#14527014C211yesmaximal, characteristic
10#14527014C211yesmaximal, characteristic
11C2×C4×C4⋊C4×C17C211yesmaximal, characteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×C4⋊Dic17C2211yescharacteristic
14C22×C4⋊Dic17C2211yescharacteristic
15C22×C4⋊Dic17C2211yescharacteristic
16C22×#63225C2212yes—
17C22×#63225C2212yes—
18C22×#63225C2212yes—
19C22×C4×Dic17C2212yes—
20#11762707—24no—
21#11762707—24no—
22#11762707C418yescomplemented
23#11762704—28no—
24C4×C4⋊Dic17—24no—
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C22×C4⋊C4×C17C2211yescharacteristic
34C22×C4⋊C4×C17C2211yescharacteristic
35C22×C42×C17C2211yescharacteristic
36C22×C42×C17C2211yescharacteristic
37C22×C42×C17C2211yescharacteristic
38C4×C4⋊C4×C17—24no—
39C2×C17×#95C2211yescharacteristic
40C2×C17×#95C2211yescharacteristic
41C23×C4×C17C2311yescharacteristic
42C23×C4×C17C2311yescharacteristic
43C23×C4×C17C2311yescharacteristic
44C23×C4×C17C2311yescharacteristic
45C23×C4×C17C2311yescharacteristic
46C23×C4×C17C2311yescharacteristic
47C23×C4×C17C2311yescharacteristic
48C23×Dic17C2312yes—
49C23×Dic17C2312yes—
50C23×Dic17C2312yes—
51C23×Dic17C2312yes—
52C2×C4⋊C4×C17—22no—
53C2×C4⋊C4×C17—22no—
54C2×C4⋊C4×C17—22no—
55C2×C4⋊C4×C17—22no—
56C2×C4⋊C4×C17—22no—
57C2×C4⋊C4×C17D414yes—
58C2×C42×C17—22no—
59C2×C42×C17—22no—
60C2×C42×C17—22no—
61C2×C42×C17—22no—
62C2×C42×C17—22no—
63C2×C42×C17—22no—
64C2×C42×C17—22no—
65C2×C42×C17C2×C414yes—
66C2×C42×C17D414yes—
67C2×C4⋊Dic17—22no—
68C2×C4⋊Dic17—22no—
69C2×C4⋊Dic17—22no—
70C2×C4⋊Dic17—22no—
71C2×C4⋊Dic17—22no—
72C2×C4⋊Dic17—22no—
73C2×C4⋊Dic17—22no—
74C2×C4⋊Dic17C2×C414yes—
75C2×C4⋊Dic17C2×C414yes—
76C2×C4⋊Dic17D414yes—
77C2×C4⋊Dic17Q814yes—
78C2×C4⋊Dic17Q814yes—
79C2×#63225—24no—
80C2×#63225—24no—
81C2×#63225—24no—
82C2×#63225—24no—
83C2×#63225—24no—
84C2×#63225—24no—
85C2×#63225—24no—
86C2×#63225—42no—
87C2×#63225C2×C418yes—
88C2×C4×Dic17—24no—
89C2×C4×Dic17—24no—
90C2×C4×Dic17—42no—
91C17×#95—22no—
92C17×#95—22no—
93#10587502—24no—
94#10587502—24no—
95#10587502—24no—
96#10587502—24no—
97#10587502—24no—
98#10587502—24no—
99#10587502—42no—
100#10587502C2×C418yes—
101C24×C17C2411yescharacteristic
102C22×C4×C17—21no—
103C22×C4×C17—21no—
104C22×C4×C17—21no—
105C22×C4×C17—21no—
106C22×C4×C17—21no—
107C22×C4×C17—21no—
108C22×C4×C17—21no—
109C22×C4×C17—21no—
110C22×C4×C17—21no—
111C22×C4×C17—21no—
112C22×C4×C17—21no—
113C22×C4×C17—21no—
114C22×C4×C17—21no—
115C22×C4×C17—21no—
116C22×C4×C17—21no—
117C22×C4×C17—21no—
118C22×C4×C17—21no—
119C22×C4×C17—21no—
120C22×C4×C17—21no—
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×C17C22×C412yes—
135C22×C4×C17C22×C412yes—
136C22×C4×C17C22×C412yes—
137C22×C4×C17C2×D412yes—
138C22×C4×C17C2×D412yes—
139C22×C4×C17C2×D412yes—
140C22×C4×C17C2×D412yes—
141C22×C4×C17C2×D412yes—
142C22×C4×C17C2×D412yes—
143C22×C4×C17C2×D412yes—
144C22×C4×C17C2×Q812yes—
145C22×C4×C17C2×Q812yes—
146C22×C4×C17#4112yes—
147C22×C4×C17#4112yes—
148C22×C4×C17#4112yes—
149C22×C4×C17#4112yes—
150C22×C4×C17#4112yes—
151C22×Dic17—22no—
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—22no—
161C22×Dic17—22no—
162C22×Dic17—22no—
163C22×Dic17—22no—
164C22×Dic17—22no—
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—22no—
174C22×Dic17C22×C414yes—
175C22×Dic17C22×C414yes—
176C22×Dic17C2×D414yes—
177C22×Dic17C2×Q814yes—
178C22×Dic17C2×Q814yes—
179C4⋊C4×C17—28no—
180C4⋊C4×C17—28no—
181C42×C17—28no—
182C42×C17—28no—
183C42×C17—44no—
184C4⋊Dic17—28no—
185C4⋊Dic17—28no—
186C4⋊Dic17—44no—
187C4⋊Dic17C4⋊C4116yescomplemented
188#63225—216no—
189#63225—48no—
190#63225—48no—
191C4×Dic17—48no—
192#14046—171nomaximal, Sylow
193C23×C17C23×C411yescharacteristic
194C23×C17C22×D411yescharacteristic
195C23×C17C22×D411yescharacteristic
196C23×C17C22×D411yescharacteristic
197C23×C17C22×Q811yescharacteristic
198C23×C17C22×Q811yescharacteristic
199C23×C17C2×#4111yescharacteristic
200C23×C17C2×#4111yescharacteristic
201C23×C17C2×#4111yescharacteristic
202C23×C17C2×#4111yescharacteristic
203C23×C17C2×#4111yescharacteristic
204C23×C17H(5,𝔽2)11yescharacteristic
205C23×C172−1+411yescharacteristic
206C23×C172−1+411yescharacteristic
207C23×C172−1+411yescharacteristic
208C2×C4×C17—22no—
209C2×C4×C17—22no—
210C2×C4×C17—22no—
211C2×C4×C17—22no—
212C2×C4×C17—22no—
213C2×C4×C17—22no—
214C2×C4×C17—22no—
215C2×C4×C17—22no—
216C2×C4×C17—22no—
217C2×C4×C17—22no—
218C2×C4×C17—22no—
219C2×C4×C17—22no—
220C2×C4×C17—22no—
221C2×C4×C17—22no—
222C2×C4×C17—22no—
223C2×C4×C17—22no—
224C2×C4×C17—22no—
225C2×C4×C17—22no—
226C2×C4×C17—22no—
227C2×C4×C17—22no—
228C2×C4×C17—22no—
229C2×C4×C17—22no—
230C2×C4×C17—22no—
231C2×C4×C17—22no—
232C2×C4×C17—41no—
233C2×C4×C17—41no—
234C2×C4×C17—41no—
235C2×C4×C17—41no—
236C2×C4×C17—41no—
237C2×C4×C17—41no—
238C2×C4×C17—41no—
239C2×C4×C17—41no—
240C2×C4×C17—41no—
241C2×C4×C17—41no—
242C2×C4×C17—41no—
243C2×C4×C17—41no—
244C2×C4×C17—41no—
245C2×C4×C17—41no—
246C2×C4×C17—41no—
247C2×C4×C17—41no—
248C2×C4×C17C2×C4⋊C414yes—
249C2×C4×C17C4×D414yes—
250C2×C4×C17C4×D414yes—
251C2×C4×C17C4×Q814yes—
252C2×C4×C17#12114yes—
253C2×C4×C17#12114yes—
254C2×C4×C17C22⋊Q814yes—
255C2×C4×C17#12514yes—
256C2×C4×C17C4⋊Q814yes—
257C2×Dic17—24no—
258C2×Dic17—24no—
259C2×Dic17—24no—
260C2×Dic17—24no—
261C2×Dic17—24no—
262C2×Dic17—24no—
263C2×Dic17—24no—
264C2×Dic17—24no—
265C2×Dic17—24no—
266C2×Dic17—24no—
267C2×Dic17—24no—
268C2×Dic17—24no—
269C2×Dic17—42no—
270C2×Dic17—42no—
271C2×Dic17—42no—
272C2×Dic17—42no—
273C2×Dic17—42no—
274C2×Dic17—42no—
275C2×Dic17—42no—
276C2×Dic17—42no—
277C2×Dic17—42no—
278C2×Dic17—42no—
279C2×Dic17—42no—
280C2×Dic17—42no—
281C2×Dic17—42no—
282C2×Dic17—42no—
283C2×Dic17—42no—
284C2×Dic17C2×C4⋊C418yes—
285C2×#389—171no—
286C2×#389—171no—
287C2×#389—171no—
288C2×#389—172no—
289C2×C4×C4⋊C4—171no—
290C2×C4×C4⋊C4D1711yescharacteristic
291#1442—172no—
292#1441—172no—
293#1436—172no—
294C4⋊#95—171no—
295C4⋊#95—171no—
296C22×C17C22×C4⋊C411yescharacteristic
297C22×C17C2×C4×D411yescharacteristic
298C22×C17C2×C4×D411yescharacteristic
299C22×C17C2×C4×Q811yescharacteristic
300C22×C17C4×#4111yescharacteristic
301C22×C17#51911yescharacteristic
302C22×C17#52011yescharacteristic
303C22×C17C2×#12111yescharacteristic
304C22×C17C2×#12111yescharacteristic
305C22×C17C2×C22⋊Q811yescharacteristic
306C22×C17#52511yescharacteristic
307C22×C17C2×#12511yescharacteristic
308C22×C17#52911yescharacteristic
309C22×C17C2×C4⋊Q811yescharacteristic
310C22×C17#53211yescharacteristic
311C22×C17#53611yescharacteristic
312C22×C17#53711yescharacteristic
313C22×C17#54111yescharacteristic
314C22×C17#54211yescharacteristic
315C22×C17D4211yescharacteristic
316C22×C17#54711yescharacteristic
317C22×C17#54711yescharacteristic
318C22×C17#54811yescharacteristic
319C22×C17#54811yescharacteristic
320C22×C17D4×Q811yescharacteristic
321C22×C17D4×Q811yescharacteristic
322C22×C17#55211yescharacteristic
323C22×C17#55311yescharacteristic
324C22×C17#55411yescharacteristic
325C22×C17#55411yescharacteristic
326C22×C17#55611yescharacteristic
327C22×C17#55711yescharacteristic
328C22×C17#55711yescharacteristic
329C22×C17#55711yescharacteristic
330C22×C17#55711yescharacteristic
331C4×C17—24no—
332C4×C17—24no—
333C4×C17—42no—
334C4×C17—42no—
335C4×C17—42no—
336C4×C17—42no—
337C4×C17#38918yescomplemented
338Dic17—28no—
339Dic17—44no—
340Dic17—44no—
341Dic17—82no—
342C22×C4⋊C4—171no—
343C22×C4⋊C4—172no—
344C22×C4⋊C4—171no—
345C22×C4⋊C4—171no—
346C22×C4⋊C4—172no—
347C22×C4⋊C4—171no—
348C22×C4⋊C4—172no—
349C22×C4⋊C4C2×D1711yescharacteristic
350C22×C4⋊C4C2×D1711yescharacteristic
351C22×C42—172no—
352C22×C42C2×D1711yescharacteristic
353C22×C42C2×D1711yescharacteristic
354C22×C42C2×D1711yescharacteristic
355#389—178no—
356#389—344no—
357#389—348no—
358#389—344no—
359C4×C4⋊C4—24no—
360C4×C4⋊C4—344no—
361C2×#95—172no—
362C2×#95—172no—
363C2×#95—172no—
364C2×#95—172no—
365C2×#95—172no—
366C2×#95—172no—
367C2×#95—172no—
368C2×#95—172no—
369C2×#95C2×D1711yescharacteristic
370C2×#95C2×D1711yescharacteristic
371C2×C17C2×#38911yescharacteristic
372C2×C17C4×#12111yescharacteristic
373C2×C17#232311yescharacteristic
374C2×C17D4×C4⋊C411yescharacteristic
375C2×C17#235111yescharacteristic
376C2×C17#236511yescharacteristic
377C2×C17#237011yescharacteristic
378C2×C17#241511yescharacteristic
379C2×C17#241611yescharacteristic
380C2×C17#245211yescharacteristic
381C2×C17#245311yescharacteristic
382C2×C17#250611yescharacteristic
383C2×C17#250911yescharacteristic
384C2×C17#254611yescharacteristic
385C2×C17#258411yescharacteristic
386C23×C4—172no—
387C23×C4—172no—
388C23×C4—172no—
389C23×C4—172no—
390C23×C4C22×D1711yescharacteristic
391C23×C4C22×D1711yescharacteristic
392C23×C4C22×D1711yescharacteristic
393C23×C4C22×D1711yescharacteristic
394C23×C4C22×D1711yescharacteristic
395C23×C4C22×D1711yescharacteristic
396C23×C4C22×D1711yescharacteristic
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—174no—
403C2×C4⋊C4—174no—
404C2×C4⋊C4—174no—
405C2×C4⋊C4—178no—
406C2×C4⋊C4—174no—
407C2×C4⋊C4—174no—
408C2×C4⋊C4—344no—
409C2×C4⋊C4—344no—
410C2×C4⋊C4—342no—
411C2×C4⋊C4—342no—
412C2×C4⋊C4—342no—
413C2×C4⋊C4—342no—
414C2×C4⋊C4—344no—
415C2×C4⋊C4—344no—
416C2×C4⋊C4—344no—
417C2×C4⋊C4—344no—
418C2×C4⋊C4—342no—
419C2×C4⋊C4—342no—
420C2×C4⋊C4—344no—
421C2×C4⋊C4—342no—
422C2×C4⋊C4—682no—
423C2×C4⋊C4D6814yes—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—344no—
432C2×C42—344no—
433C2×C42—682no—
434C2×C42C4×D1714yes—
435C2×C42C22⋊D1714yes—
436#95—22no—
437#95—22no—
438#95—178no—
439#95—344no—
440#95—344no—
441#95—344no—
442#95—344no—
443#95—344no—
444#95—344no—
445#95—682no—
446C17#1404611yescharacteristic, complemented, Sylow
447C24C23×D1711yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—174no—
481C22×C4—174no—
482C22×C4—174no—
483C22×C4—174no—
484C22×C4—174no—
485C22×C4—342no—
486C22×C4—342no—
487C22×C4—342no—
488C22×C4—342no—
489C22×C4—342no—
490C22×C4—342no—
491C22×C4—342no—
492C22×C4—342no—
493C22×C4—342no—
494C22×C4—342no—
495C22×C4—342no—
496C22×C4—342no—
497C22×C4—342no—
498C22×C4—342no—
499C22×C4—342no—
500C22×C4—342no—
501C22×C4—342no—
502C22×C4—342no—
503C22×C4—342no—
504C22×C4—342no—
505C22×C4—342no—
506C22×C4—342no—
507C22×C4—342no—
508C22×C4C2×C4×D1712yes—
509C22×C4C2×C4×D1712yes—
510C22×C4C2×C4×D1712yes—
511C22×C4C2×D6812yes—
512C22×C4C2×D6812yes—
513C22×C4C2×D6812yes—
514C22×C4#6325212yes—
515C22×C4#6325212yes—
516C22×C4#6325212yes—
517C22×C4#6325212yes—
518C22×C4D4×D1712yes—
519C22×C4#6325412yes—
520C22×C4Q8×D1712yes—
521C22×C4Q8×D1712yes—
522C22×C4C2×C22⋊D1712yes—
523C22×C4C2×C22⋊D1712yes—
524C22×C4C2×C22⋊D1712yes—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—1716no—
528C4⋊C4—3416no—
529C4⋊C4—348no—
530C4⋊C4—348no—
531C4⋊C4—688no—
532C4⋊C4—688no—
533C4⋊C4—684no—
534C42—28no—
535C42—28no—
536C42—44no—
537C42—688no—
538C23C22×C4×D1711yescharacteristic
539C23C22×D6811yescharacteristic
540C23C2×#6325211yescharacteristic
541C23C2×#6325211yescharacteristic
542C23C2×#6325211yescharacteristic
543C23C2×#6325211yescharacteristic
544C23C2×D4×D1711yescharacteristic
545C23C2×#6325411yescharacteristic
546C23C2×Q8×D1711yescharacteristic
547C23C2×Q8×D1711yescharacteristic
548C23#1058769611yescharacteristic
549C23#1058769711yescharacteristic
550C23#1058769711yescharacteristic
551C23#1058769711yescharacteristic
552C23C22×C22⋊D1711yescharacteristic
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—178no—
594C2×C4—344no—
595C2×C4—344no—
596C2×C4—344no—
597C2×C4—344no—
598C2×C4—344no—
599C2×C4—344no—
600C2×C4—344no—
601C2×C4—344no—
602C2×C4—344no—
603C2×C4—344no—
604C2×C4—344no—
605C2×C4—344no—
606C2×C4—682no—
607C2×C4—682no—
608C2×C4—682no—
609C2×C4—682no—
610C2×C4—682no—
611C2×C4—682no—
612C2×C4—682no—
613C2×C4—682no—
614C2×C4—682no—
615C2×C4—682no—
616C2×C4—682no—
617C2×C4—682no—
618C2×C4—682no—
619C2×C4—682no—
620C2×C4—682no—
621C2×C4C4×D6814yes—
622C2×C4#1058757314yes—
623C2×C4#1058757514yes—
624C2×C4C4⋊C4×D1714yes—
625C2×C4#1058758214yes—
626C2×C4C4×C22⋊D1714yes—
627C2×C4#1058761614yes—
628C2×C4#1058762514yes—
629C2×C4#1058763014yes—
630C22C2×C4⋊C4×D1711yescharacteristic
631C22C2×C4×C22⋊D1711yescharacteristic
632C22C2×C4×D6811yescharacteristic
633C22C2×#1058757311yescharacteristic
634C22C4×#6325211yescharacteristic
635C22#1176328611yescharacteristic
636C22#1176328911yescharacteristic
637C22C2×#1058762511yescharacteristic
638C22C2×#1058761611yescharacteristic
639C22C2×#1058758211yescharacteristic
640C22#1176332011yescharacteristic
641C22C2×#1058757511yescharacteristic
642C22#1176334311yescharacteristic
643C22C2×#1058763011yescharacteristic
644C22#1176335911yescharacteristic
645C22#1176338011yescharacteristic
646C22#1176338711yescharacteristic
647C22#1176342111yescharacteristic
648C22#1176343011yescharacteristic
649C22D4×D6811yescharacteristic
650C22#1176346311yescharacteristic
651C22#1176346411yescharacteristic
652C22#1176346811yescharacteristic
653C22#1176346811yescharacteristic
654C22Q8×D6811yescharacteristic
655C22Q8×D6811yescharacteristic
656C22#1176349911yescharacteristic
657C22#1176350511yescharacteristic
658C22#1176351911yescharacteristic
659C22#1176351911yescharacteristic
660C22#1176352911yescharacteristic
661C22#1176353711yescharacteristic
662C22#1176353711yescharacteristic
663C22#1176353711yescharacteristic
664C22#1176353711yescharacteristic
665C4—24no—
666C4—24no—
667C4—42no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—348no—
672C4—684no—
673C4—684no—
674C4—1362no—
675C4#1176270418yescomplemented
676C2C2×#1176270411yescharacteristic
677C2C4×#1058761611yescharacteristic
678C2#1453146611yescharacteristic
679C2C4⋊C4×D6811yescharacteristic
680C2#1453170411yescharacteristic
681C2#1453184211yescharacteristic
682C2#1453187811yescharacteristic
683C2#1453221311yescharacteristic
684C2#1453222411yescharacteristic
685C2#1453263411yescharacteristic
686C2#1453264511yescharacteristic
687C2#1453330011yescharacteristic
688C2#1453333311yescharacteristic
689C2#1453376911yescharacteristic
690C2#1453417211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C4×C4⋊C4×C17C2
socle, prime radical, cosocleC24×C17C24
hypercenterC2×C4×C4⋊C4D17
hypocenterC17#14046
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
22. #11762707C4semidirect
187. C4⋊Dic17C4⋊C4semidirect
337. C4×C17#389semidirect
446. C17#14046semidirect
675. C4#11762704semidirect

Maximal subgroups

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

subgroupindex
C2×#117627072
C2×#117627042
C2×C4×C4⋊Dic172
#145270392
#145270342
#145270192
#145270142
C2×C4×C4⋊C4×C172
#1404617