Finite Group Databasebeta

← #16940548

Subgroups — #16940548

Order 4352.

1246 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762682C211yesmaximal, characteristic
2#14531137C211yesmaximal, characteristic
3C2×#11762576C211yesmaximal, characteristic
4C2×#11762575C211yesmaximal, characteristic
5C2×#11762575C211yesmaximal, characteristic
6#14527007C211yesmaximal, characteristic
7C17×C22⋊#95C211yesmaximal, characteristic
8C22×#63225—21no—
9C22×C22⋊Dic17C2211yescharacteristic
10C22×C22⋊Dic17C2211yescharacteristic
11C22×C22⋊Dic17C2211yescharacteristic
12C22×C22⋊Dic17C2211yescharacteristic
13#11762682—22no—
14#11762682C414yescomplemented
15C22⋊C4×Dic17—21no—
16C22⋊C4×Dic17—21no—
17C22⋊C4×Dic17—22no—
18C4×C22⋊Dic17—22no—
19C2×#10587502—21no—
20C2×#10587502—22no—
21#11762576C414yescomplemented
22#11762575—22no—
23#11762575C414yescomplemented
24C24×C4×C17C2211yescharacteristic
25C22×C22⋊C4×C17C2211yescharacteristic
26C22×C22⋊C4×C17C2211yescharacteristic
27C2×C17×#95—22no—
28C25×C17C2311yescharacteristic
29C23×C4×C17—21no—
30C23×C4×C17—21no—
31C23×C4×C17—21no—
32C23×C4×C17—21no—
33C23×C4×C17—21no—
34C23×C4×C17—21no—
35C23×C4×C17—21no—
36C23×C4×C17—44no—
37C23×C4×C17C2×C412yes—
38C23×C4×C17D412yes—
39C23×Dic17—21no—
40C23×Dic17—21no—
41C23×Dic17D411yescharacteristic
42C23×Dic17D411yescharacteristic
43C23×Dic17D412yes—
44C2×C22⋊C4×C17—21no—
45C2×C22⋊C4×C17—21no—
46C2×C22⋊C4×C17—21no—
47C2×C22⋊C4×C17—21no—
48C2×C22⋊C4×C17—21no—
49C2×C22⋊C4×C17—21no—
50C2×C22⋊C4×C17—21no—
51C2×C22⋊C4×C17—21no—
52C2×C22⋊C4×C17—21no—
53C2×C22⋊C4×C17C2×C412yes—
54C2×C22⋊C4×C17C2×C412yes—
55C2×C22⋊C4×C17Q812yes—
56C2×C22⋊Dic17—21no—
57C2×C22⋊Dic17—21no—
58C2×C22⋊Dic17—21no—
59C2×C22⋊Dic17—21no—
60C2×C22⋊Dic17—21no—
61C2×C22⋊Dic17—21no—
62C2×C22⋊Dic17—21no—
63C2×C22⋊Dic17—21no—
64C2×C22⋊Dic17—21no—
65C2×C22⋊Dic17—21no—
66C2×C22⋊Dic17—21no—
67C2×C22⋊Dic17—21no—
68C2×C22⋊Dic17—21no—
69C2×C22⋊Dic17—21no—
70C2×C22⋊Dic17—21no—
71C2×C22⋊Dic17—21no—
72C2×C22⋊Dic17C2×C412yes—
73C2×C22⋊Dic17C2×C412yes—
74C2×C22⋊Dic17C2×C412yes—
75C2×C22⋊Dic17C2×C412yes—
76C2×C22⋊Dic17C2×C412yes—
77C2×C22⋊Dic17C2×C412yes—
78C2×C22⋊Dic17D412yes—
79C2×C22⋊Dic17Q812yes—
80C2×#63225—24no—
81C2×#63225—44no—
82C2×C4×Dic17—22no—
83C2×C4×Dic17—22no—
84C17×#95—44no—
85#10587502—22no—
86#10587502—22no—
87#10587502—24no—
88#10587502—44no—
89C24×C17—42no—
90C24×C17—42no—
91C24×C17C22×C411yescharacteristic
92C24×C17C22×C411yescharacteristic
93C24×C17C22×C411yescharacteristic
94C24×C17C2×D411yescharacteristic
95C24×C17C2×D411yescharacteristic
96C24×C17C2×D411yescharacteristic
97C24×C17C2×D411yescharacteristic
98C24×C17C2×Q811yescharacteristic
99C24×C17C2×Q811yescharacteristic
100C24×C17#4111yescharacteristic
101C24×C17#4111yescharacteristic
102C24×C17#4111yescharacteristic
103C24×C17#4111yescharacteristic
104C24×C17#4111yescharacteristic
105C24×C17#4111yescharacteristic
106C22×C4×C17—24no—
107C22×C4×C17—24no—
108C22×C4×C17—24no—
109C22×C4×C17—22no—
110C22×C4×C17—22no—
111C22×C4×C17—22no—
112C22×C4×C17—22no—
113C22×C4×C17—22no—
114C22×C4×C17—22no—
115C22×C4×C17—44no—
116C22×C4×C17—44no—
117C22×C4×C17—44no—
118C22×C4×C17—44no—
119C22×C4×C17—42no—
120C22×C4×C17—42no—
121C22×C4×C17—42no—
122C22×C4×C17—41no—
123C22×C4×C17—41no—
124C22×C4×C17—41no—
125C22×C4×C17—41no—
126C22×C4×C17—42no—
127C22×C4×C17—42no—
128C22×C4×C17—42no—
129C22×C4×C17—42no—
130C22×C4×C17—41no—
131C22×C4×C17—41no—
132C22×C4×C17C4⋊C414yescomplemented
133C22×Dic17—22no—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—22no—
137C22×Dic17—21no—
138C22×Dic17—21no—
139C22×Dic17—21no—
140C22×Dic17—21no—
141C22×Dic17—22no—
142C22×Dic17—22no—
143C22×Dic17—42no—
144C22×Dic17—42no—
145C22×Dic17—42no—
146C22×Dic17—42no—
147C22×Dic17—42no—
148C22×Dic17—42no—
149C22×Dic17—42no—
150C22×Dic17—42no—
151C22×Dic17—41no—
152C22×Dic17—41no—
153C22×Dic17C22⋊C412yes—
154C22×Dic17C22⋊C412yes—
155C22×Dic17C4⋊C414yescomplemented
156C22⋊C4×C17—22no—
157C22⋊C4×C17—22no—
158C22⋊C4×C17—22no—
159C22⋊C4×C17—22no—
160C22⋊C4×C17—22no—
161C22⋊C4×C17—22no—
162C22⋊C4×C17—41no—
163C22⋊C4×C17—41no—
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⋊Dic17—22no—
175C22⋊Dic17—22no—
176C22⋊Dic17—22no—
177C22⋊Dic17—41no—
178C22⋊Dic17—41no—
179C22⋊Dic17C4214yescomplemented
180#63225—48no—
181C4×Dic17—82no—
182C4×Dic17—82no—
183#10918—171nomaximal, Sylow
184C23×C17—22no—
185C23×C17—22no—
186C23×C17—22no—
187C23×C17—22no—
188C23×C17—22no—
189C23×C17—22no—
190C23×C17—41no—
191C23×C17—41no—
192C23×C17—41no—
193C23×C17—41no—
194C23×C17—42no—
195C23×C17—42no—
196C23×C17—41no—
197C23×C17—41no—
198C23×C17—42no—
199C23×C17—42no—
200C23×C17—42no—
201C23×C17—41no—
202C23×C17—42no—
203C23×C17—42no—
204C23×C17—41no—
205C23×C17—42no—
206C23×C17C2×C4211yescharacteristic
207C23×C17C2×C22⋊C411yescharacteristic
208C23×C17C2×C4⋊C411yescharacteristic
209C23×C17C2×C4⋊C411yescharacteristic
210C23×C17#11711yescharacteristic
211C23×C17#11711yescharacteristic
212C23×C17#11711yescharacteristic
213C23×C17C4×D411yescharacteristic
214C23×C17C4×D411yescharacteristic
215C23×C17C4×D411yescharacteristic
216C23×C17C4×D411yescharacteristic
217C23×C17C4×D411yescharacteristic
218C23×C17C4×D411yescharacteristic
219C23×C17C4×D411yescharacteristic
220C23×C17C4×D411yescharacteristic
221C23×C17C4×Q811yescharacteristic
222C23×C17C4×Q811yescharacteristic
223C23×C17C4×Q811yescharacteristic
224C23×C17C4×Q811yescharacteristic
225C23×C17#12011yescharacteristic
226C23×C17#12111yescharacteristic
227C23×C17#12111yescharacteristic
228C23×C17C22⋊Q811yescharacteristic
229C23×C17C22⋊Q811yescharacteristic
230C23×C17C22⋊Q811yescharacteristic
231C23×C17C22⋊Q811yescharacteristic
232C23×C17#12311yescharacteristic
233C23×C17#12311yescharacteristic
234C23×C17#12311yescharacteristic
235C23×C17#12411yescharacteristic
236C23×C17#12511yescharacteristic
237C23×C17#12511yescharacteristic
238C23×C17#12611yescharacteristic
239C23×C17#12611yescharacteristic
240C23×C17C4⋊Q811yescharacteristic
241C2×C4×C17—24no—
242C2×C4×C17—24no—
243C2×C4×C17—24no—
244C2×C4×C17—24no—
245C2×C4×C17—42no—
246C2×C4×C17—44no—
247C2×C4×C17—44no—
248C2×C4×C17—42no—
249C2×C4×C17—42no—
250C2×C4×C17—44no—
251C2×C4×C17—42no—
252C2×C4×C17—44no—
253C2×C4×C17—42no—
254C2×C4×C17—42no—
255C2×C4×C17—44no—
256C2×C4×C17—44no—
257C2×C4×C17—42no—
258C2×C4×C17—82no—
259C2×C4×C17—82no—
260C2×C4×C17—81no—
261C2×C4×C17—81no—
262C2×Dic17—24no—
263C2×Dic17—24no—
264C2×Dic17—22no—
265C2×Dic17—22no—
266C2×Dic17—44no—
267C2×Dic17—44no—
268C2×Dic17—42no—
269C2×Dic17—42no—
270C2×Dic17—42no—
271C2×Dic17—42no—
272C2×Dic17—42no—
273C2×Dic17—42no—
274C2×Dic17—42no—
275C2×Dic17—42no—
276C2×Dic17—44no—
277C2×Dic17—44no—
278C2×Dic17—42no—
279C2×Dic17—82no—
280C2×Dic17—81no—
281C2×Dic17—81no—
282C2×Dic17—82no—
283C2×Dic17—81no—
284C2×Dic17—81no—
285C2×#385—171no—
286#2273—171no—
287C2×#342—171no—
288C2×#342—171no—
289C2×#342—171no—
290C22⋊#95—171no—
291C22⋊#95D1711yescharacteristic
292C22×C17—22no—
293C22×C17—22no—
294C22×C17—22no—
295C22×C17—22no—
296C22×C17—22no—
297C22×C17—22no—
298C22×C17—22no—
299C22×C17—22no—
300C22×C17—22no—
301C22×C17—22no—
302C22×C17—22no—
303C22×C17—22no—
304C22×C17—21no—
305C22×C17—21no—
306C22×C17—21no—
307C22×C17—21no—
308C22×C17—21no—
309C22×C17—21no—
310C22×C17—21no—
311C22×C17—21no—
312C22×C17—21no—
313C22×C17—21no—
314C22×C17—21no—
315C22×C17—21no—
316C22×C17—41no—
317C22×C17—41no—
318C22×C17—41no—
319C22×C17—41no—
320C22×C17—41no—
321C22×C17—41no—
322C22×C17—41no—
323C22×C17—41no—
324C22×C17—41no—
325C22×C17—41no—
326C22×C17—41no—
327C22×C17—41no—
328C22×C17—41no—
329C22×C17—41no—
330C22×C17—41no—
331C22×C17—41no—
332C22×C17C4×C22⋊C411yescharacteristic
333C22×C17C4×C4⋊C411yescharacteristic
334C22×C17C4×C4⋊C411yescharacteristic
335C22×C17#38511yescharacteristic
336C22×C17#38511yescharacteristic
337C22×C17#38611yescharacteristic
338C22×C17#38711yescharacteristic
339C22×C17#38711yescharacteristic
340C22×C17#38711yescharacteristic
341C22×C17#38711yescharacteristic
342C22×C17#38811yescharacteristic
343C22×C17#38811yescharacteristic
344C22×C17#38911yescharacteristic
345C22×C17#38911yescharacteristic
346C22×C17#39111yescharacteristic
347C22×C17B(4,𝔽2)12yes—
348C22×C17#45812yes—
349C4×C17—44no—
350C4×C17—44no—
351C4×C17—82no—
352Dic17—44no—
353Dic17—44no—
354Dic17—42no—
355Dic17—42no—
356Dic17—82no—
357C24×C4C2×D1711yescharacteristic
358C22×C4⋊C4—341no—
359C22×C22⋊C4—171no—
360C22×C22⋊C4—171no—
361C22×C22⋊C4—171no—
362C22×C22⋊C4—171no—
363C22×C22⋊C4C2×D1711yescharacteristic
364C22×C22⋊C4C2×D1711yescharacteristic
365#385—174no—
366#385—342no—
367C4×C22⋊C4—341no—
368C4×C22⋊C4—341no—
369C4×C22⋊C4—342no—
370C4×C22⋊C4—342no—
371C2×#95—22no—
372C2×#95—341no—
373C2×#95—342no—
374#342—174no—
375#342—174no—
376#342—342no—
377C2×C17—21no—
378C2×C17—21no—
379C2×C17—21no—
380C2×C17—21no—
381C2×C17—21no—
382C2×C17—21no—
383C2×C17—21no—
384C2×C17—21no—
385C2×C17—21no—
386C2×C17—21no—
387C2×C17—21no—
388C2×C17—21no—
389C2×C17#143611yescharacteristic
390C2×C17#186712yes—
391C2×C17#186712yes—
392C2×C17#188911yescharacteristic
393C2×C17#189011yescharacteristic
394C25C22×D1711yescharacteristic
395C23×C4—21no—
396C23×C4—21no—
397C23×C4—21no—
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—21no—
401C23×C4—21no—
402C23×C4—44no—
403C23×C4—171no—
404C23×C4—171no—
405C23×C4—172no—
406C23×C4—341no—
407C23×C4—341no—
408C23×C4C4×D1712yes—
409C23×C4C22⋊D1712yes—
410C2×C4⋊C4—344no—
411C2×C4⋊C4—684no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—172no—
422C2×C22⋊C4—172no—
423C2×C22⋊C4—172no—
424C2×C22⋊C4—172no—
425C2×C22⋊C4—172no—
426C2×C22⋊C4—172no—
427C2×C22⋊C4—172no—
428C2×C22⋊C4—172no—
429C2×C22⋊C4—341no—
430C2×C22⋊C4—341no—
431C2×C22⋊C4—341no—
432C2×C22⋊C4—341no—
433C2×C22⋊C4—341no—
434C2×C22⋊C4—341no—
435C2×C22⋊C4—341no—
436C2×C22⋊C4—341no—
437C2×C22⋊C4—341no—
438C2×C22⋊C4—341no—
439C2×C22⋊C4—341no—
440C2×C22⋊C4—341no—
441C2×C22⋊C4—341no—
442C2×C22⋊C4—341no—
443C2×C22⋊C4—341no—
444C2×C22⋊C4—341no—
445C2×C22⋊C4Dic3412yes—
446C2×C22⋊C4C4×D1712yes—
447C2×C22⋊C4C4×D1712yes—
448C2×C42—342no—
449C2×C42—342no—
450#95—44no—
451#95—344no—
452#95—342no—
453#95—342no—
454#95—684no—
455C17#1091811yescharacteristic, complemented, Sylow
456C24—42no—
457C24—42no—
458C24C2×Dic3411yescharacteristic
459C24C2×C4×D1711yescharacteristic
460C24C2×C4×D1711yescharacteristic
461C24C2×C4×D1711yescharacteristic
462C24#6325211yescharacteristic
463C24#6325211yescharacteristic
464C24D4×D1711yescharacteristic
465C24D4×D1711yescharacteristic
466C24D4×D1711yescharacteristic
467C24#6325411yescharacteristic
468C24#6325411yescharacteristic
469C24#6325411yescharacteristic
470C24Q8×D1711yescharacteristic
471C24#6325611yescharacteristic
472C24C2×C22⋊D1711yescharacteristic
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—44no—
485C22×C4—44no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—172no—
500C22×C4—172no—
501C22×C4—174no—
502C22×C4—342no—
503C22×C4—342no—
504C22×C4—342no—
505C22×C4—342no—
506C22×C4—341no—
507C22×C4—341no—
508C22×C4—341no—
509C22×C4—341no—
510C22×C4—342no—
511C22×C4—342no—
512C22×C4—682no—
513C22×C4—682no—
514C22×C4—682no—
515C22×C4—682no—
516C22×C4—682no—
517C22×C4—682no—
518C22×C4—682no—
519C22×C4—682no—
520C22×C4—681no—
521C22×C4—681no—
522C22×C4#6322514yescomplemented
523C4⋊C4—688no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4—174no—
533C22⋊C4—342no—
534C22⋊C4—342no—
535C22⋊C4—342no—
536C22⋊C4—342no—
537C22⋊C4—342no—
538C22⋊C4—342no—
539C22⋊C4—342no—
540C22⋊C4—342no—
541C22⋊C4—342no—
542C22⋊C4—342no—
543C22⋊C4—342no—
544C22⋊C4—342no—
545C22⋊C4—342no—
546C22⋊C4—681no—
547C22⋊C4—681no—
548C42—1362no—
549C42—1362no—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—41no—
564C23—42no—
565C23—41no—
566C23—41no—
567C23—42no—
568C23—42no—
569C23—41no—
570C23—42no—
571C23—42no—
572C23C4×Dic3411yescharacteristic
573C23C4×Dic3411yescharacteristic
574C23C42×D1711yescharacteristic
575C23#1058755811yescharacteristic
576C23#1058756311yescharacteristic
577C23#1058756411yescharacteristic
578C23#1058756411yescharacteristic
579C23#1058756511yescharacteristic
580C23C22⋊C4×D1711yescharacteristic
581C23#1058756711yescharacteristic
582C23#1058756711yescharacteristic
583C23#1058756711yescharacteristic
584C23#1058756711yescharacteristic
585C23#1058756911yescharacteristic
586C23#1058757011yescharacteristic
587C23#1058757111yescharacteristic
588C23#1058757311yescharacteristic
589C23#1058757311yescharacteristic
590C23#1058757411yescharacteristic
591C23#1058757511yescharacteristic
592C23#1058757611yescharacteristic
593C23C4⋊C4×D1711yescharacteristic
594C23#1058757811yescharacteristic
595C23#1058757911yescharacteristic
596C23#1058757911yescharacteristic
597C23#1058758011yescharacteristic
598C23#1058758211yescharacteristic
599C23#1058758411yescharacteristic
600C23C2×#6322511yescharacteristic
601C23C4×C22⋊D1711yescharacteristic
602C23C4×C22⋊D1711yescharacteristic
603C23#1058762111yescharacteristic
604C23#1058762311yescharacteristic
605C23#1058762411yescharacteristic
606C23#1058763211yescharacteristic
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—44no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—42no—
618C2×C4—44no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—42no—
624C2×C4—82no—
625C2×C4—82no—
626C2×C4—81no—
627C2×C4—81no—
628C2×C4—344no—
629C2×C4—344no—
630C2×C4—342no—
631C2×C4—342no—
632C2×C4—682no—
633C2×C4—684no—
634C2×C4—684no—
635C2×C4—682no—
636C2×C4—682no—
637C2×C4—682no—
638C2×C4—682no—
639C2×C4—682no—
640C2×C4—682no—
641C2×C4—684no—
642C2×C4—682no—
643C2×C4—684no—
644C2×C4—682no—
645C2×C4—1362no—
646C2×C4—1361no—
647C2×C4—1361no—
648C2×C4—1362no—
649C2×C4—1361no—
650C2×C4—1361no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22#1176265611yescharacteristic
692C22#1176266011yescharacteristic
693C22C4×#6322511yescharacteristic
694C22#1176268011yescharacteristic
695C22#1176268111yescharacteristic
696C22#1176268511yescharacteristic
697C22#1176269011yescharacteristic
698C22#1176269111yescharacteristic
699C22#1176269211yescharacteristic
700C22#1176269611yescharacteristic
701C22#1176269711yescharacteristic
702C22#1176269811yescharacteristic
703C22#1176270511yescharacteristic
704C22#1176270611yescharacteristic
705C22#1176271311yescharacteristic
706C22#1176299512yes—
707C22#1176299812yes—
708C4—44no—
709C4—44no—
710C4—82no—
711C4—684no—
712C4—684no—
713C4—682no—
714C4—682no—
715C4—1362no—
716C2—21no—
717C2—21no—
718C2—21no—
719C2—21no—
720C2—21no—
721C2—21no—
722C2—21no—
723C2—21no—
724C2—21no—
725C2—21no—
726C2—21no—
727C2—21no—
728C2#1452701511yescharacteristic
729C2#1452906312yes—
730C2#1452906412yes—
731C2#1452918911yescharacteristic
732C2#1452919411yescharacteristic
subgroupG/H
centerC23#10587623
commutatorC23×C17C2×C42
FrattiniC25C22×D17
FittingC17×C22⋊#95C2
socleC23×C17#120
prime radical, cosocleC25×C17C23
hypercenterC22⋊#95D17
hypocenterC17#10918
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
14. #11762682C4semidirect
21. #11762576C4semidirect
23. #11762575C4semidirect
132. C22×C4×C17C4⋊C4semidirect
155. C22×Dic17C4⋊C4semidirect
179. C22⋊Dic17C42semidirect
455. C17#10918semidirect
522. C22×C4#63225semidirect

Maximal subgroups

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

subgroupindex
C2×#117626822
#145311372
C2×#117625762
C2×#117625752
#145270072
C17×C22⋊#952
#1091817