Finite Group Databasebeta

← #16940489

Subgroups — #16940489

Order 4352.

958 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587479C211yesmaximal, characteristic
2C2×#11762571C211yesmaximal, characteristic
3C2×#11762571C211yesmaximal, characteristic
4C2×#11762571C211yesmaximal, characteristic
5C2×#11762564C211yesmaximal, characteristic
6#14527014C211yesmaximal, characteristic
7C2×C4×C4⋊C4×C17C211yesmaximal, characteristic
8C23×#3622C2211yescharacteristic
9C23×#3622C2211yescharacteristic
10C22×C4⋊Dic17C2211yescharacteristic
11C22×C4⋊Dic17C2211yescharacteristic
12C2×#10587479—22no—
13C2×#10587479—22no—
14C2×#10587479C414yescomplemented
15C2×#10587502—21no—
16C2×#10587502—21no—
17#11762571—22no—
18#11762571—22no—
19#11762571C414yescomplemented
20#11762564C414yescomplemented
21C22×C4⋊C4×C17C2211yescharacteristic
22C22×C4⋊C4×C17C2211yescharacteristic
23C22×C42×C17—21no—
24C22×C42×C17C2211yescharacteristic
25C4×C4⋊C4×C17—22no—
26C4×C4⋊C4×C17—22no—
27C2×C17×#95—21no—
28C23×C4×C17—21no—
29C23×C4×C17—21no—
30C23×C4×C17D411yescharacteristic
31C23×C4×C17D411yescharacteristic
32C23×C4×C17C2311yescharacteristic
33C23×Dic17—21no—
34C23×Dic17—21no—
35C2×C4⋊C4×C17—21no—
36C2×C4⋊C4×C17—21no—
37C2×C4⋊C4×C17—21no—
38C2×C4⋊C4×C17—21no—
39C2×C4⋊C4×C17—21no—
40C2×C4⋊C4×C17—21no—
41C2×C4⋊C4×C17C2×C412yes—
42C2×C4⋊C4×C17C2×C412yes—
43C2×C4⋊C4×C17D412yes—
44C2×C4⋊C4×C17D412yes—
45C2×C4⋊C4×C17D412yes—
46C2×C4⋊C4×C17Q812yes—
47C2×C42×C17—21no—
48C2×C42×C17—21no—
49C2×C42×C17—21no—
50C2×C42×C17—21no—
51C2×C42×C17—24no—
52C2×C42×C17—42no—
53C2×C42×C17—42no—
54C2×C42×C17C2×C412yes—
55C2×C42×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⋊Dic17—21no—
65C2×C4⋊Dic17—21no—
66C2×C4⋊Dic17C2×C412yes—
67C2×C4⋊Dic17C2×C412yes—
68C22×#3622—21no—
69C22×#3622—21no—
70C22×#3622—21no—
71C22×#3622—21no—
72C22×#3622—21no—
73C22×#3622—21no—
74C22×#3622—21no—
75C22×#3622—21no—
76C22×#3622—21no—
77C22×#3622—21no—
78C22×#3622C2×C412yes—
79C22×#3622C2×C412yes—
80C22×#3622C2×C412yes—
81C22×#3622C2×C412yes—
82C17×#95—24no—
83#10587502—42no—
84#10587502—42no—
85#10587479—28no—
86C24×C17C2×D411yescharacteristic
87C22×C4×C17—21no—
88C22×C4×C17—21no—
89C22×C4×C17—21no—
90C22×C4×C17—21no—
91C22×C4×C17—22no—
92C22×C4×C17—22no—
93C22×C4×C17—22no—
94C22×C4×C17—22no—
95C22×C4×C17—21no—
96C22×C4×C17—22no—
97C22×C4×C17—22no—
98C22×C4×C17—21no—
99C22×C4×C17—21no—
100C22×C4×C17—21no—
101C22×C4×C17—21no—
102C22×C4×C17—21no—
103C22×C4×C17—41no—
104C22×C4×C17—41no—
105C22×C4×C17—41no—
106C22×C4×C17—41no—
107C22×C4×C17—41no—
108C22×C4×C17—41no—
109C22×C4×C17—41no—
110C22×C4×C17—41no—
111C22×C4×C17C4⋊C412yes—
112C22×C4×C17C4⋊C412yes—
113C22×C4×C17SD1612yes—
114C22×C4×C17SD1612yes—
115C22×C4×C17C22×C411yescharacteristic
116C22×C4×C17C22×C411yescharacteristic
117C22×C4×C17C22×C411yescharacteristic
118C22×C4×C17C2×D411yescharacteristic
119C22×C4×C17C2×D411yescharacteristic
120C22×C4×C17C2×D411yescharacteristic
121C22×C4×C17C2×Q811yescharacteristic
122C22×C4×C17C2×Q811yescharacteristic
123C22×C4×C17#4111yescharacteristic
124C22×C4×C17#4111yescharacteristic
125C22×C4×C17#4111yescharacteristic
126C22×C4×C17#4111yescharacteristic
127C22×C4×C17#4111yescharacteristic
128C22×C4×C17#4111yescharacteristic
129C22×Dic17—22no—
130C22×Dic17—22no—
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×Dic17—41no—
140C22×Dic17—41no—
141C22×Dic17—41no—
142C22×Dic17—41no—
143C4⋊C4×C17—22no—
144C4⋊C4×C17—22no—
145C4⋊C4×C17—22no—
146C4⋊C4×C17—22no—
147C4⋊C4×C17—22no—
148C4⋊C4×C17—22no—
149C4⋊C4×C17C22⋊C414yes—
150C4⋊C4×C17C4⋊C414yes—
151C42×C17—22no—
152C42×C17—22no—
153C42×C17—22no—
154C42×C17—22no—
155C42×C17—48no—
156C4⋊Dic17—22no—
157C4⋊Dic17—22no—
158C4⋊Dic17—22no—
159C4⋊Dic17—22no—
160C4⋊Dic17—41no—
161C4⋊Dic17—41no—
162C4⋊Dic17—41no—
163C4⋊Dic17—41no—
164C2×#3622—22no—
165C2×#3622—22no—
166C2×#3622—22no—
167C2×#3622—22no—
168C2×#3622—22no—
169C2×#3622—22no—
170C2×#3622—22no—
171C2×#3622—22no—
172C2×#3622—22no—
173C2×#3622—41no—
174C2×#3622—41no—
175C2×#3622—41no—
176C2×#3622—41no—
177C2×#3622C4214yescomplemented
178#10908—171nomaximal, Sylow
179C23×C17C2×C4⋊C411yescharacteristic
180C23×C17C4×D411yescharacteristic
181C23×C17C4×D411yescharacteristic
182C23×C17#12011yescharacteristic
183C23×C17#12111yescharacteristic
184C23×C17C22⋊Q811yescharacteristic
185C23×C17#12311yescharacteristic
186C23×C17C2×SD1611yescharacteristic
187C23×C17C2×SD1611yescharacteristic
188C23×C17#13511yescharacteristic
189C23×C17#13511yescharacteristic
190C23×C17AGL(1,ℤ/8)11yescharacteristic
191C23×C17AGL(1,ℤ/8)11yescharacteristic
192C23×C17#13711yescharacteristic
193C23×C17#13711yescharacteristic
194C2×C4×C17—22no—
195C2×C4×C17—22no—
196C2×C4×C17—22no—
197C2×C4×C17—22no—
198C2×C4×C17—22no—
199C2×C4×C17—22no—
200C2×C4×C17—22no—
201C2×C4×C17—24no—
202C2×C4×C17—24no—
203C2×C4×C17—22no—
204C2×C4×C17—22no—
205C2×C4×C17—42no—
206C2×C4×C17—42no—
207C2×C4×C17—42no—
208C2×C4×C17—42no—
209C2×C4×C17—41no—
210C2×C4×C17—42no—
211C2×C4×C17—42no—
212C2×C4×C17—42no—
213C2×C4×C17—41no—
214C2×C4×C17—42no—
215C2×C4×C17—42no—
216C2×C4×C17—42no—
217C2×C4×C17—42no—
218C2×C4×C17—42no—
219C2×C4×C17—41no—
220C2×C4×C17—41no—
221C2×C4×C17#10614yescomplemented
222C2×C4×C17C2×C4211yescharacteristic
223C2×C4×C17C2×C22⋊C411yescharacteristic
224C2×C4×C17C2×C4⋊C411yescharacteristic
225C2×C4×C17#11711yescharacteristic
226C2×C4×C17#11711yescharacteristic
227C2×C4×C17#11711yescharacteristic
228C2×C4×C17C4×D411yescharacteristic
229C2×C4×C17C4×D411yescharacteristic
230C2×C4×C17C4×D411yescharacteristic
231C2×C4×C17C4×D411yescharacteristic
232C2×C4×C17C4×D411yescharacteristic
233C2×C4×C17C4×D411yescharacteristic
234C2×C4×C17C4×Q811yescharacteristic
235C2×C4×C17C4×Q811yescharacteristic
236C2×C4×C17C4×Q811yescharacteristic
237C2×C4×C17C4×Q811yescharacteristic
238C2×C4×C17#12111yescharacteristic
239C2×C4×C17C22⋊Q811yescharacteristic
240C2×C4×C17C22⋊Q811yescharacteristic
241C2×C4×C17C22⋊Q811yescharacteristic
242C2×C4×C17#12311yescharacteristic
243C2×C4×C17#12311yescharacteristic
244C2×C4×C17#12411yescharacteristic
245C2×C4×C17#12511yescharacteristic
246C2×C4×C17#12511yescharacteristic
247C2×C4×C17#12611yescharacteristic
248C2×C4×C17#12611yescharacteristic
249C2×C4×C17C4⋊Q811yescharacteristic
250C2×Dic17—42no—
251C2×Dic17—42no—
252C2×Dic17—42no—
253C2×Dic17—42no—
254C2×Dic17—42no—
255C2×Dic17—42no—
256C2×Dic17—81no—
257C2×Dic17—81no—
258C2×Dic17—81no—
259C2×Dic17—81no—
260C2×Dic17—81no—
261C2×Dic17—81no—
262C2×Dic17—81no—
263C2×Dic17—81no—
264#3622—24no—
265#3622—42no—
266C22×#106—171no—
267C2×C4×C4⋊C4D1711yescharacteristic
268C2×#340—171no—
269C2×#340—171no—
270C2×#340—171no—
271C2×#336—171no—
272C4⋊#95—171no—
273C22×C17C4×C4⋊C411yescharacteristic
274C22×C17#38511yescharacteristic
275C22×C17#38511yescharacteristic
276C22×C17#38611yescharacteristic
277C22×C17#38711yescharacteristic
278C22×C17#38811yescharacteristic
279C22×C17#38911yescharacteristic
280C22×C17C2×#10611yescharacteristic
281C22×C17#42711yescharacteristic
282C22×C17#42811yescharacteristic
283C22×C17#42811yescharacteristic
284C22×C17C4×SD1611yescharacteristic
285C22×C17C4×SD1611yescharacteristic
286C22×C17C4×SD1611yescharacteristic
287C22×C17C4×SD1611yescharacteristic
288C22×C17#44011yescharacteristic
289C22×C17#44011yescharacteristic
290C22×C17#44111yescharacteristic
291C22×C17#44211yescharacteristic
292C22×C17#44811yescharacteristic
293C22×C17#44911yescharacteristic
294C22×C17#45011yescharacteristic
295C22×C17#45211yescharacteristic
296C22×C17#46011yescharacteristic
297C22×C17#46111yescharacteristic
298C22×C17#46311yescharacteristic
299C22×C17#46411yescharacteristic
300C22×C17#47511yescharacteristic
301C22×C17#47611yescharacteristic
302C22×C17#47811yescharacteristic
303C22×C17#47911yescharacteristic
304C22×C17#48111yescharacteristic
305C22×C17#48211yescharacteristic
306C22×C17#48311yescharacteristic
307C22×C17#48511yescharacteristic
308C4×C17—24no—
309C4×C17—42no—
310C4×C17—44no—
311C4×C17—44no—
312C4×C17C4×C22⋊C411yescharacteristic
313C4×C17C4×C4⋊C411yescharacteristic
314C4×C17#38711yescharacteristic
315C4×C17#38711yescharacteristic
316C4×C17#38711yescharacteristic
317C4×C17#38811yescharacteristic
318C4×C17#38911yescharacteristic
319C4×C17#39111yescharacteristic
320Dic17—82no—
321Dic17—82no—
322C23×C8—171no—
323C23×C8—171no—
324C22×C4⋊C4—171no—
325C22×C4⋊C4—171no—
326C22×C4⋊C4C2×D1711yescharacteristic
327C22×C4⋊C4C2×D1711yescharacteristic
328C22×C42—21no—
329C22×C42C2×D1711yescharacteristic
330C2×#106—174no—
331C2×#106—342no—
332C2×#106—342no—
333C4×C4⋊C4—22no—
334C4×C4⋊C4—22no—
335C2×#95—21no—
336C2×#95—341no—
337C2×#95—341no—
338#340—174no—
339#340—342no—
340#340—342no—
341#336—174no—
342C2×C17#143611yescharacteristic
343C2×C17C4×#10611yescharacteristic
344C2×C17#177611yescharacteristic
345C2×C17#185311yescharacteristic
346C2×C17#185411yescharacteristic
347C2×C17#186411yescharacteristic
348C2×C17#186511yescharacteristic
349C2×C17#187711yescharacteristic
350C2×C17#188011yescharacteristic
351C2×C17#191911yescharacteristic
352C2×C17#192011yescharacteristic
353C2×C17#192611yescharacteristic
354C2×C17#192711yescharacteristic
355C2×C17#194811yescharacteristic
356C2×C17#194911yescharacteristic
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—341no—
360C23×C4—341no—
361C23×C4C22⋊D1711yescharacteristic
362C23×C4C22⋊D1711yescharacteristic
363C23×C4C22×D1711yescharacteristic
364C22×C8—172no—
365C22×C8—172no—
366C22×C8—172no—
367C22×C8—172no—
368C22×C8—341no—
369C22×C8—341no—
370C22×C8—341no—
371C22×C8—341no—
372C22×C8—341no—
373C22×C8—341no—
374C22×C8—341no—
375C22×C8—341no—
376C22×C8—341no—
377C22×C8—341no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—172no—
385C2×C4⋊C4—172no—
386C2×C4⋊C4—341no—
387C2×C4⋊C4—341no—
388C2×C4⋊C4—341no—
389C2×C4⋊C4—341no—
390C2×C4⋊C4—341no—
391C2×C4⋊C4—341no—
392C2×C4⋊C4—341no—
393C2×C4⋊C4—341no—
394C2×C4⋊C4—341no—
395C2×C4⋊C4—341no—
396C2×C4⋊C4Dic3412yes—
397C2×C4⋊C4C4×D1712yes—
398C2×C4⋊C4C4×D1712yes—
399C2×C4⋊C4D6812yes—
400C2×C4⋊C4C22⋊D1712yes—
401C2×C4⋊C4C22⋊D1712yes—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—24no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42Dic3412yes—
410C2×C42C4×D1712yes—
411#106—348no—
412#95—24no—
413#95—682no—
414#95—682no—
415C17#1090811yescharacteristic, complemented, Sylow
416C24C2×C22⋊D1711yescharacteristic
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—342no—
442C22×C4—342no—
443C22×C4—681no—
444C22×C4—681no—
445C22×C4—681no—
446C22×C4—681no—
447C22×C4—681no—
448C22×C4—681no—
449C22×C4—681no—
450C22×C4—681no—
451C22×C4—681no—
452C22×C4—681no—
453C22×C4—681no—
454C22×C4—681no—
455C22×C4#6322512yes—
456C22×C4#6322512yes—
457C22×C4#6322912yes—
458C22×C4#6323012yes—
459C22×C4C2×Dic3411yescharacteristic
460C22×C4C2×Dic3411yescharacteristic
461C22×C4C2×C4×D1711yescharacteristic
462C22×C4C2×C4×D1711yescharacteristic
463C22×C4C2×C4×D1711yescharacteristic
464C22×C4C2×D6811yescharacteristic
465C22×C4#6325211yescharacteristic
466C22×C4#6325211yescharacteristic
467C22×C4#6325211yescharacteristic
468C22×C4#6325211yescharacteristic
469C22×C4#6325211yescharacteristic
470C22×C4#6325211yescharacteristic
471C22×C4C2×C22⋊D1711yescharacteristic
472C22×C4C2×C22⋊D1711yescharacteristic
473C2×C8—174no—
474C2×C8—342no—
475C2×C8—342no—
476C2×C8—342no—
477C2×C8—342no—
478C2×C8—342no—
479C2×C8—342no—
480C2×C8—342no—
481C2×C8—342no—
482C2×C8—342no—
483C2×C8—681no—
484C2×C8—681no—
485C2×C8—681no—
486C2×C8—681no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—342no—
494C4⋊C4—342no—
495C4⋊C4—342no—
496C4⋊C4—342no—
497C4⋊C4—681no—
498C4⋊C4—681no—
499C4⋊C4—681no—
500C4⋊C4—681no—
501C4⋊C4#6322514yes—
502C4⋊C4#6322714yes—
503C42—22no—
504C42—22no—
505C42—22no—
506C42—22no—
507C42—48no—
508C23C2×#6322511yescharacteristic
509C23#1058761011yescharacteristic
510C23C4×C22⋊D1711yescharacteristic
511C23C4×C22⋊D1711yescharacteristic
512C23#1058761511yescharacteristic
513C23#1058761611yescharacteristic
514C23#1058761811yescharacteristic
515C23C2×#6322911yescharacteristic
516C23C2×#6323011yescharacteristic
517C23#1058762811yescharacteristic
518C23#1058763511yescharacteristic
519C23#1058763611yescharacteristic
520C23#1058763611yescharacteristic
521C23#1058763711yescharacteristic
522C23#1058763911yescharacteristic
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—682no—
551C2×C4—682no—
552C2×C4—682no—
553C2×C4—682no—
554C2×C4—682no—
555C2×C4—682no—
556C2×C4—1361no—
557C2×C4—1361no—
558C2×C4—1361no—
559C2×C4—1361no—
560C2×C4—1361no—
561C2×C4—1361no—
562C2×C4—1361no—
563C2×C4—1361no—
564C2×C4#1058747914yescomplemented
565C2×C4C4×Dic3411yescharacteristic
566C2×C4C4×Dic3411yescharacteristic
567C2×C4C4×Dic3411yescharacteristic
568C2×C4C4×Dic3411yescharacteristic
569C2×C4#1058755511yescharacteristic
570C2×C4#1058755611yescharacteristic
571C2×C4#1058755611yescharacteristic
572C2×C4C42×D1711yescharacteristic
573C2×C4#1058755811yescharacteristic
574C2×C4#1058755811yescharacteristic
575C2×C4#1058755811yescharacteristic
576C2×C4C4×D6811yescharacteristic
577C2×C4C4×D6811yescharacteristic
578C2×C4#1058756111yescharacteristic
579C2×C4#1058756211yescharacteristic
580C2×C4#1058756211yescharacteristic
581C2×C4C2×#6322511yescharacteristic
582C2×C4#1058761011yescharacteristic
583C2×C4#1058761011yescharacteristic
584C2×C4#1058761011yescharacteristic
585C2×C4C2×#6322711yescharacteristic
586C2×C4C4×C22⋊D1711yescharacteristic
587C2×C4C4×C22⋊D1711yescharacteristic
588C2×C4C4×C22⋊D1711yescharacteristic
589C2×C4C4×C22⋊D1711yescharacteristic
590C2×C4#1058761511yescharacteristic
591C2×C4#1058761511yescharacteristic
592C2×C4#1058761611yescharacteristic
593C8—344no—
594C8—682no—
595C22C4×#6322511yescharacteristic
596C22#1176268211yescharacteristic
597C22#1176268211yescharacteristic
598C22#1176268811yescharacteristic
599C22#1176269311yescharacteristic
600C22#1176270011yescharacteristic
601C22#1176270711yescharacteristic
602C22C2×#1058747911yescharacteristic
603C22#1176284511yescharacteristic
604C22#1176284911yescharacteristic
605C22#1176285211yescharacteristic
606C22C4×#6322911yescharacteristic
607C22C4×#6322911yescharacteristic
608C22C4×#6323011yescharacteristic
609C22C4×#6323011yescharacteristic
610C22#1176290711yescharacteristic
611C22#1176290911yescharacteristic
612C22#1176291411yescharacteristic
613C22#1176291911yescharacteristic
614C22#1176294811yescharacteristic
615C22#1176295411yescharacteristic
616C22#1176296011yescharacteristic
617C22#1176297111yescharacteristic
618C22#1176300911yescharacteristic
619C22#1176301411yescharacteristic
620C22#1176302411yescharacteristic
621C22#1176303111yescharacteristic
622C22#1176309411yescharacteristic
623C22#1176309911yescharacteristic
624C22#1176310911yescharacteristic
625C22#1176311611yescharacteristic
626C22#1176312711yescharacteristic
627C22#1176313311yescharacteristic
628C22#1176313911yescharacteristic
629C22#1176315011yescharacteristic
630C4—24no—
631C4—44no—
632C4—44no—
633C4—42no—
634C4—1362no—
635C4—1362no—
636C4C4×#6322711yescharacteristic
637C4C4×#6322511yescharacteristic
638C4#1176269311yescharacteristic
639C4#1176269311yescharacteristic
640C4#1176269311yescharacteristic
641C4#1176270011yescharacteristic
642C4#1176270711yescharacteristic
643C4#1176271511yescharacteristic
644C2#1452701711yescharacteristic
645C2C4×#1058747911yescharacteristic
646C2#1452868211yescharacteristic
647C2#1452897711yescharacteristic
648C2#1452898311yescharacteristic
649C2#1452904511yescharacteristic
650C2#1452905211yescharacteristic
651C2#1452911811yescharacteristic
652C2#1452913911yescharacteristic
653C2#1452936211yescharacteristic
654C2#1452936911yescharacteristic
655C2#1452941111yescharacteristic
656C2#1452941811yescharacteristic
657C2#1452954711yescharacteristic
658C2#1452955211yescharacteristic
subgroupG/H
centerC24C2×C22⋊D17
commutatorC2×C4×C17C2×C42
FrattiniC23×C4C22×D17
FittingC2×C4×C4⋊C4×C17C2
socle, prime radicalC24×C17C2×D4
cosocleC23×C4×C17C23
hypercenterC2×C4×C4⋊C4D17
hypocenterC17#10908
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
14. C2×#10587479C4semidirect
19. #11762571C4semidirect
20. #11762564C4semidirect
177. C2×#3622C42semidirect
221. C2×C4×C17#106semidirect
415. C17#10908semidirect
564. C2×C4#10587479semidirect

Maximal subgroups

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

subgroupindex
C22×#105874792
C2×#117625712
C2×#117625642
#145270142
C2×C4×C4⋊C4×C172
#1090817