Finite Group Databasebeta

← #16940171

Subgroups — #16940171

Order 4352.

998 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587485C211yesmaximal, characteristic
2C2×#11762674C211yesmaximal, characteristic
3C2×C4⋊C4×Dic17C211yesmaximal, characteristic
4C2×#11762572C211yesmaximal, characteristic
5C2×#11762571C211yesmaximal, characteristic
6C2×#11762571C211yesmaximal, characteristic
7C2×C17×#340C211yesmaximal, characteristic
8C23×#3622C2211yescharacteristic
9C22×C4⋊Dic17C2211yescharacteristic
10C22×C4⋊Dic17C2211yescharacteristic
11C22×C4×Dic17—21no—
12C22×C4×Dic17C2211yescharacteristic
13C2×#10587485—22no—
14C2×#10587485—22no—
15C2×#10587485C414yescomplemented
16#11762674—22no—
17#11762674C414yescomplemented
18C4⋊C4×Dic17—22no—
19C4⋊C4×Dic17C414yescomplemented
20C2×#10587502—21no—
21C2×#10587502—21no—
22C2×#10587502—21no—
23#11762572—22no—
24#11762571—22no—
25#11762571—22no—
26C23×C8×C17C2211yescharacteristic
27C22×C4⋊C4×C17C2211yescharacteristic
28C22×C4⋊C4×C17C2211yescharacteristic
29C17×#340—22no—
30C23×C4×C17—21no—
31C23×C4×C17—21no—
32C23×C4×C17C2311yescharacteristic
33C23×Dic17—21no—
34C23×Dic17—21no—
35C23×Dic17D411yescharacteristic
36C23×Dic17D411yescharacteristic
37C22×C8×C17—21no—
38C22×C8×C17—21no—
39C22×C8×C17—21no—
40C22×C8×C17—21no—
41C22×C8×C17—21no—
42C22×C8×C17—21no—
43C22×C8×C17C2×C412yes—
44C2×C4⋊C4×C17—21no—
45C2×C4⋊C4×C17—21no—
46C2×C4⋊C4×C17—21no—
47C2×C4⋊C4×C17—21no—
48C2×C4⋊C4×C17—21no—
49C2×C4⋊C4×C17—21no—
50C2×C4⋊C4×C17—21no—
51C2×C4⋊C4×C17—21no—
52C2×C4⋊C4×C17C2×C412yes—
53C2×C4⋊C4×C17C2×C412yes—
54C2×C4⋊C4×C17D412yes—
55C2×C4⋊C4×C17Q812yes—
56C2×C4⋊Dic17—21no—
57C2×C4⋊Dic17—21no—
58C2×C4⋊Dic17—21no—
59C2×C4⋊Dic17—21no—
60C2×C4⋊Dic17—21no—
61C2×C4⋊Dic17—21no—
62C2×C4⋊Dic17—21no—
63C2×C4⋊Dic17—21no—
64C2×C4⋊Dic17C2×C412yes—
65C2×C4⋊Dic17C2×C412yes—
66C2×C4⋊Dic17D412yes—
67C2×C4⋊Dic17Q812yes—
68C2×C4×Dic17—24no—
69C2×C4×Dic17—42no—
70C2×C4×Dic17—42no—
71C2×C4×Dic17C2×C412yes—
72C2×C4×Dic17C2×C412yes—
73C2×C4×Dic17C2×C412yes—
74C2×C4×Dic17D412yes—
75C2×C4×Dic17D412yes—
76C2×C4×Dic17Q812yes—
77C22×#3622—21no—
78C22×#3622—21no—
79C22×#3622—21no—
80C22×#3622—21no—
81C22×#3622—21no—
82C22×#3622—21no—
83C22×#3622C2×C412yes—
84#10587502—24no—
85#10587502—24no—
86#10587502—24no—
87#10587485—28no—
88C24×C17C2×D411yescharacteristic
89C22×C4×C17—22no—
90C22×C4×C17—22no—
91C22×C4×C17—22no—
92C22×C4×C17—22no—
93C22×C4×C17—41no—
94C22×C4×C17—41no—
95C22×C4×C17—41no—
96C22×C4×C17—41no—
97C22×C4×C17—41no—
98C22×C4×C17—41no—
99C22×C4×C17—41no—
100C22×C4×C17—41no—
101C22×C4×C17—41no—
102C22×C4×C17—41no—
103C22×C4×C17C22×C411yescharacteristic
104C22×C4×C17C22×C411yescharacteristic
105C22×C4×C17C22×C411yescharacteristic
106C22×C4×C17C2×D411yescharacteristic
107C22×C4×C17C2×D411yescharacteristic
108C22×C4×C17C2×D411yescharacteristic
109C22×C4×C17C2×D411yescharacteristic
110C22×C4×C17C2×Q811yescharacteristic
111C22×C4×C17C2×Q811yescharacteristic
112C22×C4×C17C2×Q811yescharacteristic
113C22×C4×C17#4111yescharacteristic
114C22×C4×C17#4111yescharacteristic
115C22×C4×C17#4111yescharacteristic
116C22×C4×C17#4111yescharacteristic
117C22×Dic17—21no—
118C22×Dic17—21no—
119C22×Dic17—21no—
120C22×Dic17—21no—
121C22×Dic17—21no—
122C22×Dic17—21no—
123C22×Dic17—21no—
124C22×Dic17—21no—
125C22×Dic17—22no—
126C22×Dic17—22no—
127C22×Dic17—22no—
128C22×Dic17—22no—
129C22×Dic17—41no—
130C22×Dic17—41no—
131C22×Dic17—41no—
132C22×Dic17—41no—
133C22×Dic17—41no—
134C22×Dic17—41no—
135C22×Dic17—41no—
136C22×Dic17—41no—
137C22×Dic17—41no—
138C22×Dic17—41no—
139C22×Dic17C22⋊C412yes—
140C22×Dic17C22⋊C412yes—
141C22×Dic17C22⋊C412yes—
142C22×Dic17C22⋊C412yes—
143C22×Dic17C4⋊C412yes—
144C22×Dic17C4⋊C412yes—
145C2×C8×C17—22no—
146C2×C8×C17—22no—
147C2×C8×C17—22no—
148C2×C8×C17—41no—
149C2×C8×C17—41no—
150C2×C8×C17—41no—
151C2×C8×C17—41no—
152C4⋊C4×C17—22no—
153C4⋊C4×C17—22no—
154C4⋊C4×C17—22no—
155C4⋊C4×C17—22no—
156C4⋊C4×C17—22no—
157C4⋊C4×C17—41no—
158C4⋊C4×C17—41no—
159C4⋊C4×C17C4⋊C414yes—
160C4⋊Dic17—22no—
161C4⋊Dic17—22no—
162C4⋊Dic17—22no—
163C4⋊Dic17—22no—
164C4⋊Dic17—22no—
165C4⋊Dic17—41no—
166C4⋊Dic17—41no—
167C4⋊Dic17C4⋊C414yes—
168C4×Dic17—48no—
169C4×Dic17C4214yes—
170C4×Dic17C22⋊C414yes—
171C4×Dic17C4⋊C414yes—
172C4×Dic17C4⋊C414yes—
173C2×#3622—22no—
174C2×#3622—22no—
175C2×#3622—22no—
176C2×#3622—41no—
177C2×#3622—41no—
178C2×#3622—41no—
179C2×#3622—41no—
180#10850—171nomaximal, Sylow
181C23×C17C2×C22⋊C411yescharacteristic
182C23×C17C2×C22⋊C411yescharacteristic
183C23×C17C2×C4⋊C411yescharacteristic
184C23×C17#12111yescharacteristic
185C23×C17#12111yescharacteristic
186C23×C17C22⋊Q811yescharacteristic
187C23×C17C22⋊Q811yescharacteristic
188C23×C17#13511yescharacteristic
189C23×C17#13511yescharacteristic
190C23×C17#13511yescharacteristic
191C23×C17#13511yescharacteristic
192C23×C17AGL(1,ℤ/8)11yescharacteristic
193C23×C17AGL(1,ℤ/8)11yescharacteristic
194C23×C17#13711yescharacteristic
195C23×C17#13711yescharacteristic
196C2×C4×C17—24no—
197C2×C4×C17—42no—
198C2×C4×C17—42no—
199C2×C4×C17—42no—
200C2×C4×C17—42no—
201C2×C4×C17—42no—
202C2×C4×C17—42no—
203C2×C4×C17—42no—
204C2×C4×C17—42no—
205C2×C4×C17—42no—
206C2×C4×C17—81no—
207C2×C4×C17—81no—
208C2×C4×C17—81no—
209C2×C4×C17—81no—
210C2×C4×C17C2×C4211yescharacteristic
211C2×C4×C17C2×C22⋊C411yescharacteristic
212C2×C4×C17C2×C4⋊C411yescharacteristic
213C2×C4×C17C2×C4⋊C411yescharacteristic
214C2×C4×C17C2×C4⋊C411yescharacteristic
215C2×C4×C17C2×C4⋊C411yescharacteristic
216C2×C4×C17#11711yescharacteristic
217C2×C4×C17#11711yescharacteristic
218C2×C4×C17C4×D411yescharacteristic
219C2×C4×C17C4×D411yescharacteristic
220C2×C4×C17C4×D411yescharacteristic
221C2×C4×C17C4×D411yescharacteristic
222C2×C4×C17C4×Q811yescharacteristic
223C2×C4×C17C4×Q811yescharacteristic
224C2×C4×C17C4×Q811yescharacteristic
225C2×C4×C17C4×Q811yescharacteristic
226C2×C4×C17#12111yescharacteristic
227C2×C4×C17#12111yescharacteristic
228C2×C4×C17C22⋊Q811yescharacteristic
229C2×C4×C17C22⋊Q811yescharacteristic
230C2×C4×C17#12411yescharacteristic
231C2×C4×C17#12411yescharacteristic
232C2×C4×C17#12511yescharacteristic
233C2×C4×C17#12511yescharacteristic
234C2×C4×C17#12711yescharacteristic
235C2×C4×C17C4⋊Q811yescharacteristic
236C2×C4×C17C4⋊Q811yescharacteristic
237C2×C4×C17C4⋊Q811yescharacteristic
238C2×Dic17—22no—
239C2×Dic17—22no—
240C2×Dic17—22no—
241C2×Dic17—22no—
242C2×Dic17—22no—
243C2×Dic17—22no—
244C2×Dic17—22no—
245C2×Dic17—22no—
246C2×Dic17—22no—
247C2×Dic17—22no—
248C2×Dic17—22no—
249C2×Dic17—22no—
250C2×Dic17—24no—
251C2×Dic17—42no—
252C2×Dic17—42no—
253C2×Dic17—42no—
254C2×Dic17—42no—
255C2×Dic17—42no—
256C2×Dic17—42no—
257C2×Dic17—42no—
258C2×Dic17—42no—
259C2×Dic17—42no—
260C2×Dic17—81no—
261C2×Dic17—81no—
262C2×Dic17—81no—
263C2×Dic17—81no—
264C2×Dic17#9514yes—
265C2×Dic17#9514yes—
266C8×C17—42no—
267#3622—42no—
268C22×C4⋊C8—171no—
269C2×#382—171no—
270C2×C4×C4⋊C4—171no—
271C2×#340—171no—
272C2×#340—171no—
273C2×#340—171no—
274C2×#340D1711yescharacteristic
275C22×C17C2×#9511yescharacteristic
276C22×C17#38011yescharacteristic
277C22×C17#38011yescharacteristic
278C22×C17#38911yescharacteristic
279C22×C17#38911yescharacteristic
280C22×C17#39011yescharacteristic
281C22×C17#39111yescharacteristic
282C22×C17#41611yescharacteristic
283C22×C17#41611yescharacteristic
284C22×C17#41611yescharacteristic
285C22×C17#41611yescharacteristic
286C22×C17#41711yescharacteristic
287C22×C17#41711yescharacteristic
288C22×C17#41811yescharacteristic
289C22×C17#41911yescharacteristic
290C22×C17#42711yescharacteristic
291C22×C17#42711yescharacteristic
292C22×C17#42811yescharacteristic
293C22×C17#42811yescharacteristic
294C22×C17#46311yescharacteristic
295C22×C17#46311yescharacteristic
296C22×C17#46311yescharacteristic
297C22×C17#46311yescharacteristic
298C22×C17#46411yescharacteristic
299C22×C17#46411yescharacteristic
300C22×C17#46411yescharacteristic
301C22×C17#46411yescharacteristic
302C22×C17#47811yescharacteristic
303C22×C17#47811yescharacteristic
304C22×C17#47811yescharacteristic
305C22×C17#47811yescharacteristic
306C22×C17#47911yescharacteristic
307C22×C17#47911yescharacteristic
308C22×C17#47911yescharacteristic
309C22×C17#47911yescharacteristic
310C4×C17—44no—
311C4×C17—82no—
312C4×C17C4×C4⋊C411yescharacteristic
313C4×C17C4×C4⋊C411yescharacteristic
314C4×C17#38211yescharacteristic
315C4×C17#38411yescharacteristic
316C4×C17#38911yescharacteristic
317C4×C17#38911yescharacteristic
318C4×C17#39011yescharacteristic
319C4×C17#39111yescharacteristic
320Dic17—24no—
321Dic17—24no—
322Dic17—44no—
323Dic17—82no—
324C23×C8—171no—
325C23×C8C2×D1711yescharacteristic
326C22×C4⋊C4—171no—
327C22×C4⋊C4—171no—
328C22×C4⋊C4C2×D1711yescharacteristic
329C22×C4⋊C4C2×D1711yescharacteristic
330C22×C42—171no—
331C22×C42—341no—
332C2×C4⋊C8—174no—
333C2×C4⋊C8—342no—
334C2×C4⋊C8—342no—
335#382—174no—
336#382—342no—
337C4×C4⋊C4—174no—
338C4×C4⋊C4—342no—
339C2×#95—341no—
340C2×#95—341no—
341C2×#95—341no—
342#340—22no—
343#340—342no—
344#340—342no—
345#340—342no—
346C2×C17C4⋊#9511yescharacteristic
347C2×C17#173511yescharacteristic
348C2×C17#173611yescharacteristic
349C2×C17#180411yescharacteristic
350C2×C17#180411yescharacteristic
351C2×C17#180511yescharacteristic
352C2×C17#180511yescharacteristic
353C2×C17#194911yescharacteristic
354C2×C17#194911yescharacteristic
355C2×C17#194911yescharacteristic
356C2×C17#194911yescharacteristic
357C2×C17#198311yescharacteristic
358C2×C17#198311yescharacteristic
359C2×C17#198911yescharacteristic
360C2×C17#198911yescharacteristic
361C23×C4—21no—
362C23×C4—21no—
363C23×C4—171no—
364C23×C4—171no—
365C23×C4—341no—
366C23×C4—341no—
367C23×C4C22×D1711yescharacteristic
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—172no—
375C22×C8—341no—
376C22×C8—341no—
377C22×C8—341no—
378C22×C8—341no—
379C22×C8—341no—
380C22×C8—341no—
381C22×C8C4×D1712yes—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—172no—
391C2×C4⋊C4—172no—
392C2×C4⋊C4—172no—
393C2×C4⋊C4—172no—
394C2×C4⋊C4—341no—
395C2×C4⋊C4—341no—
396C2×C4⋊C4—341no—
397C2×C4⋊C4—341no—
398C2×C4⋊C4—341no—
399C2×C4⋊C4—341no—
400C2×C4⋊C4—341no—
401C2×C4⋊C4—341no—
402C2×C4⋊C4Dic3412yes—
403C2×C4⋊C4C4×D1712yes—
404C2×C4⋊C4C4×D1712yes—
405C2×C4⋊C4C22⋊D1712yes—
406C2×C42—172no—
407C2×C42—172no—
408C2×C42—172no—
409C2×C42—172no—
410C2×C42—172no—
411C2×C42—172no—
412C2×C42—344no—
413C2×C42—682no—
414C2×C42—682no—
415C4⋊C8—348no—
416#95—344no—
417#95—344no—
418#95—344no—
419C17#1085011yescharacteristic, complemented, Sylow
420C24D4×D1711yescharacteristic
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—172no—
436C22×C4—172no—
437C22×C4—172no—
438C22×C4—172no—
439C22×C4—172no—
440C22×C4—172no—
441C22×C4—341no—
442C22×C4—341no—
443C22×C4—341no—
444C22×C4—341no—
445C22×C4—341no—
446C22×C4—341no—
447C22×C4—341no—
448C22×C4—341no—
449C22×C4—342no—
450C22×C4—342no—
451C22×C4—342no—
452C22×C4—342no—
453C22×C4—681no—
454C22×C4—681no—
455C22×C4—681no—
456C22×C4—681no—
457C22×C4—681no—
458C22×C4—681no—
459C22×C4—681no—
460C22×C4—681no—
461C22×C4—681no—
462C22×C4—681no—
463C22×C4C2×Dic3411yescharacteristic
464C22×C4C2×C4×D1711yescharacteristic
465C22×C4C2×C4×D1711yescharacteristic
466C22×C4C2×C4×D1711yescharacteristic
467C22×C4#6325211yescharacteristic
468C22×C4#6325211yescharacteristic
469C22×C4D4×D1711yescharacteristic
470C22×C4D4×D1711yescharacteristic
471C22×C4D4×D1711yescharacteristic
472C22×C4#6325411yescharacteristic
473C22×C4#6325411yescharacteristic
474C22×C4Q8×D1711yescharacteristic
475C22×C4Q8×D1711yescharacteristic
476C22×C4C2×C22⋊D1711yescharacteristic
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—342no—
485C2×C8—342no—
486C2×C8—342no—
487C2×C8—681no—
488C2×C8—681no—
489C2×C8—681no—
490C2×C8—681no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—174no—
499C4⋊C4—342no—
500C4⋊C4—342no—
501C4⋊C4—342no—
502C4⋊C4—342no—
503C4⋊C4—342no—
504C4⋊C4—681no—
505C4⋊C4—681no—
506C4⋊C4#6322514yes—
507C42—174no—
508C42—174no—
509C42—174no—
510C42—174no—
511C42—688no—
512C23#1058756411yescharacteristic
513C23C22⋊C4×D1711yescharacteristic
514C23C22⋊C4×D1711yescharacteristic
515C23#1058757011yescharacteristic
516C23C4⋊C4×D1711yescharacteristic
517C23#1058758211yescharacteristic
518C23#1058759711yescharacteristic
519C23#1058759811yescharacteristic
520C23#1058760011yescharacteristic
521C23#1058760111yescharacteristic
522C23#1058760211yescharacteristic
523C23#1058760211yescharacteristic
524C23#1058760411yescharacteristic
525C23#1058760511yescharacteristic
526C23#1058762511yescharacteristic
527C2×C4—24no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4—81no—
540C2×C4—81no—
541C2×C4—174no—
542C2×C4—174no—
543C2×C4—342no—
544C2×C4—342no—
545C2×C4—342no—
546C2×C4—342no—
547C2×C4—342no—
548C2×C4—342no—
549C2×C4—342no—
550C2×C4—342no—
551C2×C4—342no—
552C2×C4—342no—
553C2×C4—342no—
554C2×C4—342no—
555C2×C4—344no—
556C2×C4—682no—
557C2×C4—682no—
558C2×C4—682no—
559C2×C4—682no—
560C2×C4—682no—
561C2×C4—682no—
562C2×C4—682no—
563C2×C4—682no—
564C2×C4—682no—
565C2×C4—1361no—
566C2×C4—1361no—
567C2×C4—1361no—
568C2×C4—1361no—
569C2×C4C4×Dic3411yescharacteristic
570C2×C4C4×Dic3411yescharacteristic
571C2×C4C42×D1711yescharacteristic
572C2×C4#1058755811yescharacteristic
573C2×C4#1058756311yescharacteristic
574C2×C4#1058756411yescharacteristic
575C2×C4C22⋊C4×D1711yescharacteristic
576C2×C4#1058756711yescharacteristic
577C2×C4#1058756711yescharacteristic
578C2×C4#1058757011yescharacteristic
579C2×C4#1058757111yescharacteristic
580C2×C4#1058757111yescharacteristic
581C2×C4#1058757311yescharacteristic
582C2×C4#1058757311yescharacteristic
583C2×C4#1058757411yescharacteristic
584C2×C4#1058757411yescharacteristic
585C2×C4#1058757511yescharacteristic
586C2×C4#1058757511yescharacteristic
587C2×C4C4⋊C4×D1711yescharacteristic
588C2×C4C4⋊C4×D1711yescharacteristic
589C2×C4C4⋊C4×D1711yescharacteristic
590C2×C4#1058758211yescharacteristic
591C2×C4C2×#6322511yescharacteristic
592C2×C4C4×C22⋊D1711yescharacteristic
593C2×C4C4×C22⋊D1711yescharacteristic
594C2×C4#1058762511yescharacteristic
595C2×C4#1058762611yescharacteristic
596C2×C4#1058763011yescharacteristic
597C8—42no—
598C8—682no—
599C22#95×D1711yescharacteristic
600C22#1176266711yescharacteristic
601C22#1176266811yescharacteristic
602C22#1176270411yescharacteristic
603C22#1176270611yescharacteristic
604C22#1176270911yescharacteristic
605C22#1176271311yescharacteristic
606C22#1176280211yescharacteristic
607C22#1176280211yescharacteristic
608C22#1176280411yescharacteristic
609C22#1176280411yescharacteristic
610C22#1176280711yescharacteristic
611C22#1176280911yescharacteristic
612C22#1176281211yescharacteristic
613C22#1176281611yescharacteristic
614C22#1176284411yescharacteristic
615C22#1176284611yescharacteristic
616C22#1176284811yescharacteristic
617C22#1176285011yescharacteristic
618C22#1176302211yescharacteristic
619C22#1176302311yescharacteristic
620C22#1176302611yescharacteristic
621C22#1176302711yescharacteristic
622C22#1176302911yescharacteristic
623C22#1176303011yescharacteristic
624C22#1176303311yescharacteristic
625C22#1176303411yescharacteristic
626C22#1176310711yescharacteristic
627C22#1176310811yescharacteristic
628C22#1176311111yescharacteristic
629C22#1176311211yescharacteristic
630C22#1176311411yescharacteristic
631C22#1176311511yescharacteristic
632C22#1176311811yescharacteristic
633C22#1176311911yescharacteristic
634C4—44no—
635C4—82no—
636C4—344no—
637C4—344no—
638C4—684no—
639C4—1362no—
640C4#1176266011yescharacteristic
641C4C4×#6322511yescharacteristic
642C4#1176267311yescharacteristic
643C4#1176267811yescharacteristic
644C4#1176270411yescharacteristic
645C4#1176270611yescharacteristic
646C4#1176270911yescharacteristic
647C4#1176271311yescharacteristic
648C2#1452701211yescharacteristic
649C2#1452849911yescharacteristic
650C2#1452850211yescharacteristic
651C2#1452879211yescharacteristic
652C2#1452879311yescharacteristic
653C2#1452879711yescharacteristic
654C2#1452879811yescharacteristic
655C2#1452954911yescharacteristic
656C2#1452955111yescharacteristic
657C2#1452955311yescharacteristic
658C2#1452955511yescharacteristic
659C2#1452971311yescharacteristic
660C2#1452971511yescharacteristic
661C2#1452973811yescharacteristic
662C2#1452974011yescharacteristic
subgroupG/H
centerC24D4×D17
commutatorC2×C4×C17C2×C42
FrattiniC23×C4C22×D17
FittingC2×C17×#340C2
socle, prime radicalC24×C17C2×D4
cosocleC23×C4×C17C23
hypercenterC2×#340D17
hypocenterC17#10850
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
15. C2×#10587485C4semidirect
17. #11762674C4semidirect
19. C4⋊C4×Dic17C4semidirect
419. C17#10850semidirect

Maximal subgroups

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

subgroupindex
C22×#105874852
C2×#117626742
C2×C4⋊C4×Dic172
C2×#117625722
C2×#117625712
C2×C17×#3402
#1085017