Finite Group Databasebeta

← #16942212

Subgroups — #16942212

Order 4352.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762681C211yesmaximal, characteristic
2C2×#11762667C211yesmaximal, characteristic
3C2×#11762576C211yesmaximal, characteristic
4C2×#11762575C211yesmaximal, characteristic
5C2×#11762575C211yesmaximal, characteristic
6#14527006C211yesmaximal, characteristic
7C2×C17×#342C211yesmaximal, characteristic
8C24×Dic17C2211yescharacteristic
9C22×#63225—21no—
10C22×#63225C412yescomplemented
11C22×C22⋊Dic17C2211yescharacteristic
12C22×C22⋊Dic17C2211yescharacteristic
13C22×C22⋊Dic17C2211yescharacteristic
14#11762681—21no—
15#11762681—22no—
16#11762681—21no—
17#11762667—22no—
18#11762667—22no—
19C2×#10587502—21no—
20C2×#10587502—22no—
21C2×#10587502C412yescomplemented
22#11762576—22no—
23#11762575—22no—
24#11762575—22no—
25C22×C22⋊C4×C17C2211yescharacteristic
26C22×C22⋊C4×C17C2211yescharacteristic
27C22×C22⋊C4×C17C2211yescharacteristic
28C17×#342—22no—
29C25×C17C2311yescharacteristic
30C23×C4×C17—21no—
31C23×C4×C17—21no—
32C23×C4×C17C2×C411yescharacteristic
33C23×C4×C17C2×C411yescharacteristic
34C23×Dic17—21no—
35C23×Dic17—21no—
36C23×Dic17—21no—
37C23×Dic17—21no—
38C23×Dic17—21no—
39C23×Dic17—21no—
40C23×Dic17—44no—
41C23×Dic17C2×C412yes—
42C23×Dic17C2×C412yes—
43C23×Dic17D411yescharacteristic
44C23×Dic17D412yes—
45C23×Dic17D411yescharacteristic
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×C17—21no—
54C2×C22⋊C4×C17—21no—
55C2×C22⋊C4×C17—21no—
56C2×C22⋊C4×C17—21no—
57C2×C22⋊C4×C17—21no—
58C2×C22⋊C4×C17—21no—
59C2×C22⋊C4×C17—21no—
60C2×C22⋊C4×C17—21no—
61C2×C22⋊C4×C17—21no—
62C2×C22⋊C4×C17D412yes—
63C2×C22⋊C4×C17Q812yes—
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⋊Dic17—21no—
73C2×C22⋊Dic17—21no—
74C2×C22⋊Dic17—21no—
75C2×C22⋊Dic17—21no—
76C2×C22⋊Dic17—21no—
77C2×C22⋊Dic17—21no—
78C2×C22⋊Dic17D412yes—
79C2×C22⋊Dic17D412yes—
80C2×C22⋊Dic17Q812yes—
81C2×C22⋊Dic17Q812yes—
82C2×#63225—24no—
83C2×#63225—22no—
84C2×#63225—22no—
85C2×#63225—44no—
86C2×#63225—44no—
87#10587502—24no—
88#10587502—22no—
89#10587502—22no—
90#10587502—44no—
91C24×C17—42no—
92C24×C17—42no—
93C24×C17C22×C411yescharacteristic
94C24×C17C2×D411yescharacteristic
95C24×C17C2×D411yescharacteristic
96C24×C17C2×D411yescharacteristic
97C24×C17C2×D411yescharacteristic
98C24×C17C2×D411yescharacteristic
99C24×C17C2×Q811yescharacteristic
100C24×C17C2×Q811yescharacteristic
101C24×C17C2×Q811yescharacteristic
102C24×C17#4111yescharacteristic
103C24×C17#4111yescharacteristic
104C24×C17#4111yescharacteristic
105C24×C17#4111yescharacteristic
106C24×C17#4111yescharacteristic
107C24×C17#4111yescharacteristic
108C22×C4×C17—21no—
109C22×C4×C17—21no—
110C22×C4×C17—22no—
111C22×C4×C17—22no—
112C22×C4×C17—21no—
113C22×C4×C17—21no—
114C22×C4×C17—21no—
115C22×C4×C17—21no—
116C22×C4×C17—42no—
117C22×C4×C17—42no—
118C22×C4×C17—42no—
119C22×C4×C17—42no—
120C22×C4×C17—41no—
121C22×C4×C17—41no—
122C22×C4×C17—41no—
123C22×C4×C17—41no—
124C22×C4×C17—42no—
125C22×C4×C17—42no—
126C22×Dic17—21no—
127C22×Dic17—21no—
128C22×Dic17—24no—
129C22×Dic17—22no—
130C22×Dic17—22no—
131C22×Dic17—22no—
132C22×Dic17—22no—
133C22×Dic17—21no—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—21no—
137C22×Dic17—24no—
138C22×Dic17—24no—
139C22×Dic17—22no—
140C22×Dic17—22no—
141C22×Dic17—42no—
142C22×Dic17—42no—
143C22×Dic17—42no—
144C22×Dic17—44no—
145C22×Dic17—44no—
146C22×Dic17—44no—
147C22×Dic17—44no—
148C22×Dic17—42no—
149C22×Dic17—42no—
150C22×Dic17—42no—
151C22×Dic17—42no—
152C22×Dic17—42no—
153C22×Dic17—42no—
154C22×Dic17—41no—
155C22×Dic17—41no—
156C22×Dic17—41no—
157C22×Dic17—41no—
158C22×Dic17C22⋊C412yes—
159C22×Dic17C22⋊C412yes—
160C22×Dic17C4⋊C414yescomplemented
161C22⋊C4×C17—22no—
162C22⋊C4×C17—22no—
163C22⋊C4×C17—22no—
164C22⋊C4×C17—22no—
165C22⋊C4×C17—41no—
166C22⋊C4×C17—41no—
167C22⋊C4×C17—41no—
168C22⋊C4×C17—41no—
169C22⋊C4×C17—41no—
170C22⋊C4×C17—41no—
171C22⋊C4×C17—41no—
172C22⋊C4×C17—41no—
173C22⋊Dic17—22no—
174C22⋊Dic17—22no—
175C22⋊Dic17—22no—
176C22⋊Dic17—22no—
177C22⋊Dic17—22no—
178C22⋊Dic17—22no—
179C22⋊Dic17—22no—
180C22⋊Dic17—22no—
181C22⋊Dic17—41no—
182C22⋊Dic17—41no—
183C22⋊Dic17—41no—
184C22⋊Dic17—41no—
185#63225—48no—
186#63225—44no—
187#63225—44no—
188#11203—171nomaximal, Sylow
189C23×C17—22no—
190C23×C17—22no—
191C23×C17—22no—
192C23×C17—22no—
193C23×C17—22no—
194C23×C17—22no—
195C23×C17—41no—
196C23×C17—41no—
197C23×C17—41no—
198C23×C17—41no—
199C23×C17—42no—
200C23×C17—41no—
201C23×C17—41no—
202C23×C17—42no—
203C23×C17—42no—
204C23×C17—42no—
205C23×C17—42no—
206C23×C17—42no—
207C23×C17—41no—
208C23×C17—42no—
209C23×C17—41no—
210C23×C17—42no—
211C23×C17C2×C22⋊C411yescharacteristic
212C23×C17C2×C4⋊C411yescharacteristic
213C23×C17#11711yescharacteristic
214C23×C17C4×D411yescharacteristic
215C23×C17C4×D411yescharacteristic
216C23×C17C4×Q811yescharacteristic
217C23×C17C4×Q811yescharacteristic
218C23×C17#12011yescharacteristic
219C23×C17#12111yescharacteristic
220C23×C17#12111yescharacteristic
221C23×C17#12111yescharacteristic
222C23×C17#12111yescharacteristic
223C23×C17#12111yescharacteristic
224C23×C17#12111yescharacteristic
225C23×C17C22⋊Q811yescharacteristic
226C23×C17C22⋊Q811yescharacteristic
227C23×C17C22⋊Q811yescharacteristic
228C23×C17C22⋊Q811yescharacteristic
229C23×C17C22⋊Q811yescharacteristic
230C23×C17C22⋊Q811yescharacteristic
231C23×C17C22⋊Q811yescharacteristic
232C23×C17C22⋊Q811yescharacteristic
233C23×C17#12311yescharacteristic
234C23×C17#12311yescharacteristic
235C23×C17#12311yescharacteristic
236C23×C17#12411yescharacteristic
237C23×C17#12511yescharacteristic
238C23×C17#12511yescharacteristic
239C23×C17#12511yescharacteristic
240C23×C17#12511yescharacteristic
241C23×C17#12611yescharacteristic
242C23×C17#12611yescharacteristic
243C23×C17C4⋊Q811yescharacteristic
244C23×C17C4⋊Q811yescharacteristic
245C23×C17C4⋊Q811yescharacteristic
246C2×C4×C17—42no—
247C2×C4×C17—44no—
248C2×C4×C17—42no—
249C2×C4×C17—41no—
250C2×C4×C17—41no—
251C2×C4×C17—42no—
252C2×C4×C17—42no—
253C2×C4×C17—42no—
254C2×C4×C17—42no—
255C2×C4×C17—82no—
256C2×C4×C17—82no—
257C2×C4×C17—81no—
258C2×C4×C17—81no—
259C2×C4×C17—82no—
260C2×C4×C17—81no—
261C2×C4×C17—81no—
262C2×C4×C17—81no—
263C2×C4×C17—81no—
264C2×Dic17—24no—
265C2×Dic17—24no—
266C2×Dic17—22no—
267C2×Dic17—22no—
268C2×Dic17—24no—
269C2×Dic17—22no—
270C2×Dic17—22no—
271C2×Dic17—22no—
272C2×Dic17—44no—
273C2×Dic17—44no—
274C2×Dic17—44no—
275C2×Dic17—44no—
276C2×Dic17—44no—
277C2×Dic17—42no—
278C2×Dic17—42no—
279C2×Dic17—42no—
280C2×Dic17—42no—
281C2×Dic17—44no—
282C2×Dic17—42no—
283C2×Dic17—44no—
284C2×Dic17—42no—
285C2×Dic17—42no—
286C2×Dic17—42no—
287C2×Dic17—82no—
288C2×Dic17—82no—
289C2×Dic17—81no—
290C2×Dic17—81no—
291C2×Dic17—82no—
292C2×Dic17#9914yes—
293C2×#385—171no—
294C2×#380—171no—
295C2×#342—171no—
296C2×#342—171no—
297C2×#342—171no—
298C2×#342D1711yescharacteristic
299C22⋊#95—171no—
300C22×C17—22no—
301C22×C17—22no—
302C22×C17—22no—
303C22×C17—22no—
304C22×C17—22no—
305C22×C17—22no—
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—21no—
317C22×C17—21no—
318C22×C17—22no—
319C22×C17—22no—
320C22×C17—22no—
321C22×C17—22no—
322C22×C17—22no—
323C22×C17—22no—
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×C17—41no—
333C22×C17—41no—
334C22×C17—41no—
335C22×C17—41no—
336C22×C17—41no—
337C22×C17—41no—
338C22×C17—41no—
339C22×C17—41no—
340C22×C17#38011yescharacteristic
341C22×C17#38611yescharacteristic
342C22×C17#38711yescharacteristic
343C22×C17#38711yescharacteristic
344C22×C17#38911yescharacteristic
345C22×C17#38911yescharacteristic
346C22×C17#39111yescharacteristic
347C22×C17#39411yescharacteristic
348C22×C17#39511yescharacteristic
349C22×C17#39611yescharacteristic
350C22×C17#39611yescharacteristic
351C22×C17#39811yescharacteristic
352C22×C17#39811yescharacteristic
353C22×C17#39811yescharacteristic
354C22×C17#40011yescharacteristic
355C22×C17C2×#9912yes—
356C22×C17#41012yes—
357C4×C17—82no—
358C4×C17—82no—
359C4×C17—81no—
360C4×C17—81no—
361Dic17—24no—
362Dic17—44no—
363Dic17—42no—
364Dic17—82no—
365Dic17—82no—
366C24×C4—171no—
367C22×C4⋊C4—172no—
368C22×C4⋊C4—341no—
369C22×C22⋊C4—171no—
370C22×C22⋊C4—171no—
371C22×C22⋊C4—171no—
372C22×C22⋊C4C2×D1711yescharacteristic
373C22×C22⋊C4C2×D1711yescharacteristic
374C22×C22⋊C4C2×D1711yescharacteristic
375#385—341no—
376#385—342no—
377#385—341no—
378#380—342no—
379#380—342no—
380C2×#95—172no—
381C2×#95—341no—
382C2×#95—342no—
383#342—22no—
384#342—342no—
385#342—342no—
386#342—342no—
387C2×C17—21no—
388C2×C17—21no—
389C2×C17—21no—
390C2×C17—21no—
391C2×C17—21no—
392C2×C17—21no—
393C2×C17—21no—
394C2×C17—21no—
395C2×C17—21no—
396C2×C17—21no—
397C2×C17—21no—
398C2×C17—21no—
399C2×C17#144111yescharacteristic
400C2×C17#179912yes—
401C2×C17#189811yescharacteristic
402C2×C17#189911yescharacteristic
403C2×C17#199612yes—
404C25C22×D1711yescharacteristic
405C23×C4—21no—
406C23×C4—21no—
407C23×C4—171no—
408C23×C4—172no—
409C23×C4—172no—
410C23×C4—172no—
411C23×C4—171no—
412C23×C4—341no—
413C23×C4—341no—
414C23×C4—341no—
415C23×C4—341no—
416C23×C4—341no—
417C23×C4—341no—
418C23×C4—684no—
419C23×C4C4×D1711yescharacteristic
420C23×C4C4×D1711yescharacteristic
421C2×C4⋊C4—342no—
422C2×C4⋊C4—342no—
423C2×C4⋊C4—344no—
424C2×C4⋊C4—684no—
425C2×C4⋊C4—684no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—172no—
443C2×C22⋊C4—172no—
444C2×C22⋊C4—172no—
445C2×C22⋊C4—172no—
446C2×C22⋊C4—341no—
447C2×C22⋊C4—341no—
448C2×C22⋊C4—341no—
449C2×C22⋊C4—341no—
450C2×C22⋊C4—341no—
451C2×C22⋊C4—341no—
452C2×C22⋊C4—341no—
453C2×C22⋊C4—341no—
454C2×C22⋊C4—341no—
455C2×C22⋊C4—341no—
456C2×C22⋊C4—341no—
457C2×C22⋊C4—341no—
458C2×C22⋊C4—341no—
459C2×C22⋊C4—341no—
460C2×C22⋊C4Dic3412yes—
461C2×C22⋊C4C22⋊D1712yes—
462#95—342no—
463#95—342no—
464#95—344no—
465#95—684no—
466C17#1120311yescharacteristic, complemented, Sylow
467C24—42no—
468C24—42no—
469C24C2×Dic3411yescharacteristic
470C24C2×C4×D1711yescharacteristic
471C24#6325211yescharacteristic
472C24#6325211yescharacteristic
473C24#6325211yescharacteristic
474C24#6325211yescharacteristic
475C24D4×D1711yescharacteristic
476C24D4×D1711yescharacteristic
477C24D4×D1711yescharacteristic
478C24D4×D1711yescharacteristic
479C24#6325411yescharacteristic
480C24#6325411yescharacteristic
481C24Q8×D1711yescharacteristic
482C24Q8×D1711yescharacteristic
483C24C2×C22⋊D1711yescharacteristic
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—172no—
503C22×C4—172no—
504C22×C4—174no—
505C22×C4—344no—
506C22×C4—344no—
507C22×C4—344no—
508C22×C4—341no—
509C22×C4—341no—
510C22×C4—342no—
511C22×C4—342no—
512C22×C4—342no—
513C22×C4—341no—
514C22×C4—342no—
515C22×C4—342no—
516C22×C4—341no—
517C22×C4—342no—
518C22×C4—342no—
519C22×C4—342no—
520C22×C4—682no—
521C22×C4—682no—
522C22×C4—682no—
523C22×C4—684no—
524C22×C4—684no—
525C22×C4—684no—
526C22×C4—684no—
527C22×C4—682no—
528C22×C4—682no—
529C22×C4—682no—
530C22×C4—682no—
531C22×C4—682no—
532C22×C4—682no—
533C22×C4—681no—
534C22×C4—681no—
535C22×C4—681no—
536C22×C4—681no—
537C4⋊C4—684no—
538C4⋊C4—688no—
539C4⋊C4—684no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C22⋊C4—41no—
552C22⋊C4—342no—
553C22⋊C4—342no—
554C22⋊C4—342no—
555C22⋊C4—342no—
556C22⋊C4—342no—
557C22⋊C4—342no—
558C22⋊C4—342no—
559C22⋊C4—342no—
560C22⋊C4—681no—
561C22⋊C4—681no—
562C22⋊C4—681no—
563C22⋊C4—681no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—41no—
578C23—42no—
579C23—42no—
580C23—41no—
581C23—41no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—41no—
586C23C4×Dic3411yescharacteristic
587C23#1058755611yescharacteristic
588C23#1058755811yescharacteristic
589C23#1058756211yescharacteristic
590C23#1058756411yescharacteristic
591C23#1058756411yescharacteristic
592C23#1058756511yescharacteristic
593C23C22⋊C4×D1711yescharacteristic
594C23#1058756711yescharacteristic
595C23#1058756911yescharacteristic
596C23#1058756911yescharacteristic
597C23#1058757011yescharacteristic
598C23#1058757011yescharacteristic
599C23#1058757011yescharacteristic
600C23#1058757011yescharacteristic
601C23#1058757111yescharacteristic
602C23#1058757311yescharacteristic
603C23#1058757411yescharacteristic
604C23#1058757411yescharacteristic
605C23#1058757511yescharacteristic
606C23#1058757511yescharacteristic
607C23#1058757511yescharacteristic
608C23C4⋊C4×D1711yescharacteristic
609C23#1058758211yescharacteristic
610C23#1058758211yescharacteristic
611C23#1058758211yescharacteristic
612C23#1058758211yescharacteristic
613C23#1058758211yescharacteristic
614C23#1058761011yescharacteristic
615C23C4×C22⋊D1711yescharacteristic
616C23#1058761511yescharacteristic
617C23#1058762311yescharacteristic
618C23#1058762411yescharacteristic
619C23#1058762511yescharacteristic
620C23#1058763011yescharacteristic
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—44no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—82no—
631C2×C4—82no—
632C2×C4—81no—
633C2×C4—81no—
634C2×C4—82no—
635C2×C4—81no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4—81no—
639C2×C4—174no—
640C2×C4—344no—
641C2×C4—344no—
642C2×C4—342no—
643C2×C4—342no—
644C2×C4—342no—
645C2×C4—342no—
646C2×C4—344no—
647C2×C4—342no—
648C2×C4—684no—
649C2×C4—684no—
650C2×C4—684no—
651C2×C4—684no—
652C2×C4—682no—
653C2×C4—682no—
654C2×C4—684no—
655C2×C4—682no—
656C2×C4—682no—
657C2×C4—684no—
658C2×C4—682no—
659C2×C4—682no—
660C2×C4—684no—
661C2×C4—682no—
662C2×C4—682no—
663C2×C4—1362no—
664C2×C4—1362no—
665C2×C4—1361no—
666C2×C4—1361no—
667C2×C4—1362no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—21no—
681C22—21no—
682C22—21no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22#1176266811yescharacteristic
709C22#1176268511yescharacteristic
710C22#1176269111yescharacteristic
711C22#1176269311yescharacteristic
712C22#1176270411yescharacteristic
713C22#1176270611yescharacteristic
714C22#1176271311yescharacteristic
715C22#1176272411yescharacteristic
716C22#1176272911yescharacteristic
717C22#1176273211yescharacteristic
718C22#1176273311yescharacteristic
719C22#1176274011yescharacteristic
720C22#1176274311yescharacteristic
721C22#1176274311yescharacteristic
722C22#1176275011yescharacteristic
723C22#99×D1712yes—
724C22#1176278112yes—
725C4—82no—
726C4—82no—
727C4—81no—
728C4—81no—
729C4—344no—
730C4—684no—
731C4—682no—
732C4—1362no—
733C4—1362no—
734C2—21no—
735C2—21no—
736C2—21no—
737C2—21no—
738C2—21no—
739C2—21no—
740C2—21no—
741C2—21no—
742C2—21no—
743C2—21no—
744C2—21no—
745C2—21no—
746C2#1452703511yescharacteristic
747C2#1452877112yes—
748C2#1452923411yescharacteristic
749C2#1452923911yescharacteristic
750C2#1452976712yes—
subgroupG/H
centerC23C22⋊C4×D17
commutatorC24×C17C22×C4
FrattiniC25C22×D17
FittingC2×C17×#342C2
socleC23×C17C2×C22⋊C4
prime radical, cosocleC25×C17C23
hypercenterC2×#342D17
hypocenterC17#11203
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
10. C22×#63225C4semidirect
21. C2×#10587502C4semidirect
160. C22×Dic17C4⋊C4semidirect
466. C17#11203semidirect

Maximal subgroups

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

subgroupindex
C2×#117626812
C2×#117626672
C2×#117625762
C2×#117625752
#145270062
C2×C17×#3422
#1120317