Finite Group Databasebeta

← #16940187

Subgroups — #16940187

Order 4352.

1338 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762667C211yesmaximal, characteristic
2C2×#11762667C211yesmaximal, characteristic
3C2×C22⋊C4×Dic17C211yesmaximal, characteristic
4C2×#11762576C211yesmaximal, characteristic
5C2×#11762575C211yesmaximal, characteristic
6C2×#11762575C211yesmaximal, characteristic
7C2×C17×#342C211yesmaximal, characteristic
8C24×Dic17C2211yescharacteristic
9C22×#63225—21no—
10C22×#63225C412yescomplemented
11C22×C22⋊Dic17C2211yescharacteristic
12C22×C22⋊Dic17C2211yescharacteristic
13C22×C22⋊Dic17C2211yescharacteristic
14C22×C4×Dic17—21no—
15#11762667—21no—
16#11762667—21no—
17#11762667—21no—
18#11762667—21no—
19#11762667—22no—
20#11762667C414yescomplemented
21C22⋊C4×Dic17—22no—
22C22⋊C4×Dic17C414yescomplemented
23C2×#10587502—21no—
24C2×#10587502—21no—
25C2×#10587502C412yescomplemented
26#11762576—22no—
27#11762575—22no—
28#11762575—22no—
29C22×C22⋊C4×C17C2211yescharacteristic
30C22×C22⋊C4×C17C2211yescharacteristic
31C22×C22⋊C4×C17C2211yescharacteristic
32C17×#342—22no—
33C25×C17C2311yescharacteristic
34C23×C4×C17—21no—
35C23×C4×C17—21no—
36C23×C4×C17C2×C412yes—
37C23×Dic17—21no—
38C23×Dic17—21no—
39C23×Dic17—44no—
40C23×Dic17C2×C411yescharacteristic
41C23×Dic17C2×C412yes—
42C23×Dic17C2×C411yescharacteristic
43C23×Dic17C2×C412yes—
44C23×Dic17C2×C412yes—
45C23×Dic17D411yescharacteristic
46C23×Dic17D411yescharacteristic
47C23×Dic17D411yescharacteristic
48C23×Dic17D411yescharacteristic
49C23×Dic17D412yes—
50C23×Dic17Q812yes—
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×C17—21no—
63C2×C22⋊C4×C17—21no—
64C2×C22⋊C4×C17—21no—
65C2×C22⋊C4×C17C2×C412yes—
66C2×C22⋊C4×C17C2×C412yes—
67C2×C22⋊C4×C17D412yes—
68C2×C22⋊C4×C17Q812yes—
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⋊Dic17—21no—
79C2×C22⋊Dic17—21no—
80C2×C22⋊Dic17—21no—
81C2×C22⋊Dic17—21no—
82C2×C22⋊Dic17—21no—
83C2×C22⋊Dic17C2×C412yes—
84C2×C22⋊Dic17C2×C412yes—
85C2×C22⋊Dic17D412yes—
86C2×C22⋊Dic17Q812yes—
87C2×#63225—24no—
88C2×#63225—22no—
89C2×#63225—22no—
90C2×#63225—44no—
91C2×#63225—44no—
92C2×C4×Dic17—24no—
93C2×C4×Dic17—44no—
94#10587502—24no—
95#10587502—24no—
96#10587502—22no—
97#10587502—22no—
98C24×C17—42no—
99C24×C17—42no—
100C24×C17C22×C411yescharacteristic
101C24×C17C22×C411yescharacteristic
102C24×C17C22×C411yescharacteristic
103C24×C17C2×D411yescharacteristic
104C24×C17C2×D411yescharacteristic
105C24×C17C2×D411yescharacteristic
106C24×C17C2×D411yescharacteristic
107C24×C17C2×D411yescharacteristic
108C24×C17C2×Q811yescharacteristic
109C24×C17C2×Q811yescharacteristic
110C24×C17C2×Q811yescharacteristic
111C24×C17#4111yescharacteristic
112C24×C17#4111yescharacteristic
113C24×C17#4111yescharacteristic
114C24×C17#4111yescharacteristic
115C22×C4×C17—22no—
116C22×C4×C17—22no—
117C22×C4×C17—22no—
118C22×C4×C17—22no—
119C22×C4×C17—22no—
120C22×C4×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17—42no—
123C22×C4×C17—42no—
124C22×C4×C17—42no—
125C22×C4×C17—42no—
126C22×C4×C17—41no—
127C22×C4×C17—41no—
128C22×C4×C17—42no—
129C22×C4×C17—42no—
130C22×Dic17—24no—
131C22×Dic17—24no—
132C22×Dic17—24no—
133C22×Dic17—22no—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—22no—
137C22×Dic17—22no—
138C22×Dic17—22no—
139C22×Dic17—22no—
140C22×Dic17—44no—
141C22×Dic17—44no—
142C22×Dic17—44no—
143C22×Dic17—44no—
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×Dic17—42no—
154C22×Dic17—42no—
155C22×Dic17C4212yes—
156C22×Dic17C4212yes—
157C22×Dic17C22⋊C411yescharacteristic
158C22×Dic17C22⋊C411yescharacteristic
159C22×Dic17C22⋊C412yes—
160C22×Dic17C22⋊C412yes—
161C22×Dic17C22⋊C411yescharacteristic
162C22×Dic17C22⋊C412yes—
163C22×Dic17C22⋊C412yes—
164C22×Dic17C22⋊C411yescharacteristic
165C22×Dic17C4⋊C412yes—
166C22×Dic17C4⋊C412yes—
167C22×Dic17C4⋊C412yes—
168C22×Dic17C4⋊C412yes—
169C22×Dic17C4⋊C412yes—
170C22×Dic17C4⋊C412yes—
171C22⋊C4×C17—22no—
172C22⋊C4×C17—22no—
173C22⋊C4×C17—22no—
174C22⋊C4×C17—22no—
175C22⋊C4×C17—22no—
176C22⋊C4×C17—41no—
177C22⋊C4×C17—41no—
178C22⋊C4×C17—41no—
179C22⋊C4×C17—41no—
180C22⋊C4×C17—41no—
181C22⋊C4×C17—41no—
182C22⋊C4×C17C4⋊C414yescomplemented
183C22⋊Dic17—22no—
184C22⋊Dic17—22no—
185C22⋊Dic17—22no—
186C22⋊Dic17—22no—
187C22⋊Dic17—22no—
188C22⋊Dic17—41no—
189C22⋊Dic17—41no—
190C22⋊Dic17—41no—
191C22⋊Dic17—41no—
192C22⋊Dic17—41no—
193C22⋊Dic17—41no—
194C22⋊Dic17C4⋊C414yescomplemented
195#63225—44no—
196#63225—48no—
197#63225—44no—
198C4×Dic17—48no—
199#10854—171nomaximal, Sylow
200C23×C17—22no—
201C23×C17—22no—
202C23×C17—22no—
203C23×C17—22no—
204C23×C17—22no—
205C23×C17—22no—
206C23×C17—41no—
207C23×C17—41no—
208C23×C17—41no—
209C23×C17—41no—
210C23×C17—41no—
211C23×C17—41no—
212C23×C17—42no—
213C23×C17—41no—
214C23×C17—42no—
215C23×C17—42no—
216C23×C17—41no—
217C23×C17—42no—
218C23×C17—42no—
219C23×C17—42no—
220C23×C17—42no—
221C23×C17—42no—
222C23×C17C2×C4211yescharacteristic
223C23×C17C2×C22⋊C411yescharacteristic
224C23×C17C2×C22⋊C411yescharacteristic
225C23×C17C2×C22⋊C411yescharacteristic
226C23×C17C2×C4⋊C411yescharacteristic
227C23×C17C2×C4⋊C411yescharacteristic
228C23×C17C2×C4⋊C411yescharacteristic
229C23×C17C2×C4⋊C411yescharacteristic
230C23×C17C2×C4⋊C411yescharacteristic
231C23×C17#11711yescharacteristic
232C23×C17#11711yescharacteristic
233C23×C17C4×D411yescharacteristic
234C23×C17C4×D411yescharacteristic
235C23×C17C4×D411yescharacteristic
236C23×C17C4×D411yescharacteristic
237C23×C17C4×Q811yescharacteristic
238C23×C17C4×Q811yescharacteristic
239C23×C17C4×Q811yescharacteristic
240C23×C17C4×Q811yescharacteristic
241C23×C17#12111yescharacteristic
242C23×C17#12111yescharacteristic
243C23×C17#12111yescharacteristic
244C23×C17#12111yescharacteristic
245C23×C17C22⋊Q811yescharacteristic
246C23×C17C22⋊Q811yescharacteristic
247C23×C17C22⋊Q811yescharacteristic
248C23×C17C22⋊Q811yescharacteristic
249C23×C17#12411yescharacteristic
250C23×C17#12411yescharacteristic
251C23×C17#12511yescharacteristic
252C23×C17#12511yescharacteristic
253C23×C17#12711yescharacteristic
254C23×C17C4⋊Q811yescharacteristic
255C23×C17C4⋊Q811yescharacteristic
256C23×C17C4⋊Q811yescharacteristic
257C2×C4×C17—24no—
258C2×C4×C17—44no—
259C2×C4×C17—42no—
260C2×C4×C17—44no—
261C2×C4×C17—42no—
262C2×C4×C17—42no—
263C2×C4×C17—42no—
264C2×C4×C17—42no—
265C2×C4×C17—42no—
266C2×C4×C17—42no—
267C2×C4×C17—42no—
268C2×C4×C17—82no—
269C2×C4×C17—82no—
270C2×C4×C17—82no—
271C2×C4×C17—82no—
272C2×Dic17—22no—
273C2×Dic17—22no—
274C2×Dic17—22no—
275C2×Dic17—24no—
276C2×Dic17—24no—
277C2×Dic17—24no—
278C2×Dic17—24no—
279C2×Dic17—24no—
280C2×Dic17—24no—
281C2×Dic17—24no—
282C2×Dic17—42no—
283C2×Dic17—42no—
284C2×Dic17—42no—
285C2×Dic17—42no—
286C2×Dic17—42no—
287C2×Dic17—42no—
288C2×Dic17—44no—
289C2×Dic17—42no—
290C2×Dic17—44no—
291C2×Dic17—42no—
292C2×Dic17—42no—
293C2×Dic17—42no—
294C2×Dic17—42no—
295C2×Dic17—42no—
296C2×Dic17—42no—
297C2×Dic17—42no—
298C2×Dic17—82no—
299C2×Dic17—82no—
300C2×Dic17—82no—
301C2×Dic17—82no—
302C2×Dic17#9512yes—
303C2×Dic17#9512yes—
304C2×Dic17#9512yes—
305C2×Dic17#9512yes—
306C2×Dic17#9914yes—
307C2×#380—171no—
308C2×#380—171no—
309C2×C4×C22⋊C4—171no—
310C2×#342—171no—
311C2×#342—171no—
312C2×#342—171no—
313C2×#342D1711yescharacteristic
314C22×C17—22no—
315C22×C17—22no—
316C22×C17—22no—
317C22×C17—22no—
318C22×C17—22no—
319C22×C17—22no—
320C22×C17—21no—
321C22×C17—21no—
322C22×C17—21no—
323C22×C17—21no—
324C22×C17—21no—
325C22×C17—21no—
326C22×C17—21no—
327C22×C17—21no—
328C22×C17—21no—
329C22×C17—21no—
330C22×C17—21no—
331C22×C17—21no—
332C22×C17—22no—
333C22×C17—22no—
334C22×C17—22no—
335C22×C17—22no—
336C22×C17—22no—
337C22×C17—22no—
338C22×C17—41no—
339C22×C17—41no—
340C22×C17—41no—
341C22×C17—41no—
342C22×C17—41no—
343C22×C17—41no—
344C22×C17—41no—
345C22×C17—41no—
346C22×C17—41no—
347C22×C17—41no—
348C22×C17—41no—
349C22×C17—41no—
350C22×C17—41no—
351C22×C17—41no—
352C22×C17—41no—
353C22×C17—41no—
354C22×C17C2×#9511yescharacteristic
355C22×C17C4×C4⋊C411yescharacteristic
356C22×C17C4×C4⋊C411yescharacteristic
357C22×C17#38011yescharacteristic
358C22×C17#38011yescharacteristic
359C22×C17#38211yescharacteristic
360C22×C17#38411yescharacteristic
361C22×C17#38911yescharacteristic
362C22×C17#38911yescharacteristic
363C22×C17#38911yescharacteristic
364C22×C17#38911yescharacteristic
365C22×C17#39011yescharacteristic
366C22×C17#39011yescharacteristic
367C22×C17#39111yescharacteristic
368C22×C17#39111yescharacteristic
369C22×C17C2×#9912yes—
370C22×C17#41012yes—
371C4×C17—44no—
372C4×C17—82no—
373C4×C17—82no—
374Dic17—22no—
375Dic17—22no—
376Dic17—22no—
377Dic17—44no—
378Dic17—82no—
379Dic17—82no—
380Dic17#34214yescomplemented
381C24×C4—171no—
382C22×C4⋊C4—172no—
383C22×C4⋊C4—341no—
384C22×C22⋊C4—171no—
385C22×C22⋊C4—171no—
386C22×C22⋊C4—171no—
387C22×C22⋊C4C2×D1711yescharacteristic
388C22×C22⋊C4C2×D1711yescharacteristic
389C22×C22⋊C4C2×D1711yescharacteristic
390C22×C42—341no—
391#380—174no—
392#380—341no—
393#380—341no—
394#380—341no—
395#380—341no—
396#380—342no—
397C4×C22⋊C4—174no—
398C4×C22⋊C4—342no—
399C2×#95—172no—
400C2×#95—341no—
401C2×#95—341no—
402#342—22no—
403#342—342no—
404#342—342no—
405#342—342no—
406C2×C17—21no—
407C2×C17—21no—
408C2×C17—21no—
409C2×C17—21no—
410C2×C17—21no—
411C2×C17—21no—
412C2×C17—21no—
413C2×C17—21no—
414C2×C17—21no—
415C2×C17—21no—
416C2×C17—21no—
417C2×C17—21no—
418C2×C17C4⋊#9511yescharacteristic
419C2×C17C2×#34211yescharacteristic
420C2×C17#174011yescharacteristic
421C2×C17#196412yes—
422C2×C17#199612yes—
423C25C22×D1711yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—171no—
427C23×C4—171no—
428C23×C4—171no—
429C23×C4—171no—
430C23×C4—172no—
431C23×C4—172no—
432C23×C4—171no—
433C23×C4—171no—
434C23×C4—172no—
435C23×C4—172no—
436C23×C4—172no—
437C23×C4—341no—
438C23×C4—341no—
439C23×C4—684no—
440C23×C4C4×D1712yes—
441C2×C4⋊C4—342no—
442C2×C4⋊C4—342no—
443C2×C4⋊C4—344no—
444C2×C4⋊C4—684no—
445C2×C4⋊C4—684no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—172no—
461C2×C22⋊C4—172no—
462C2×C22⋊C4—172no—
463C2×C22⋊C4—172no—
464C2×C22⋊C4—341no—
465C2×C22⋊C4—341no—
466C2×C22⋊C4—341no—
467C2×C22⋊C4—341no—
468C2×C22⋊C4—341no—
469C2×C22⋊C4—341no—
470C2×C22⋊C4—341no—
471C2×C22⋊C4—341no—
472C2×C22⋊C4—341no—
473C2×C22⋊C4—341no—
474C2×C22⋊C4—341no—
475C2×C22⋊C4—341no—
476C2×C22⋊C4—341no—
477C2×C22⋊C4—341no—
478C2×C22⋊C4Dic3412yes—
479C2×C22⋊C4C4×D1712yes—
480C2×C22⋊C4C4×D1712yes—
481C2×C22⋊C4C22⋊D1712yes—
482C2×C42—344no—
483C2×C42—684no—
484#95—342no—
485#95—342no—
486#95—344no—
487#95—344no—
488C17#1085411yescharacteristic, complemented, Sylow
489C24—42no—
490C24—42no—
491C24C2×Dic3411yescharacteristic
492C24C2×C4×D1711yescharacteristic
493C24C2×C4×D1711yescharacteristic
494C24C2×C4×D1711yescharacteristic
495C24#6325211yescharacteristic
496C24#6325211yescharacteristic
497C24D4×D1711yescharacteristic
498C24D4×D1711yescharacteristic
499C24D4×D1711yescharacteristic
500C24D4×D1711yescharacteristic
501C24#6325411yescharacteristic
502C24#6325411yescharacteristic
503C24Q8×D1711yescharacteristic
504C24Q8×D1711yescharacteristic
505C24C2×C22⋊D1711yescharacteristic
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—171no—
522C22×C4—172no—
523C22×C4—172no—
524C22×C4—172no—
525C22×C4—171no—
526C22×C4—171no—
527C22×C4—171no—
528C22×C4—172no—
529C22×C4—172no—
530C22×C4—172no—
531C22×C4—172no—
532C22×C4—172no—
533C22×C4—172no—
534C22×C4—172no—
535C22×C4—172no—
536C22×C4—172no—
537C22×C4—344no—
538C22×C4—344no—
539C22×C4—344no—
540C22×C4—342no—
541C22×C4—342no—
542C22×C4—342no—
543C22×C4—342no—
544C22×C4—342no—
545C22×C4—342no—
546C22×C4—342no—
547C22×C4—684no—
548C22×C4—684no—
549C22×C4—684no—
550C22×C4—684no—
551C22×C4—682no—
552C22×C4—682no—
553C22×C4—682no—
554C22×C4—682no—
555C22×C4—682no—
556C22×C4—682no—
557C22×C4—682no—
558C22×C4—681no—
559C22×C4—681no—
560C22×C4—682no—
561C22×C4—682no—
562C4⋊C4—684no—
563C4⋊C4—688no—
564C4⋊C4—684no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—174no—
577C22⋊C4—342no—
578C22⋊C4—342no—
579C22⋊C4—342no—
580C22⋊C4—342no—
581C22⋊C4—342no—
582C22⋊C4—681no—
583C22⋊C4—681no—
584C22⋊C4—681no—
585C22⋊C4—681no—
586C22⋊C4—681no—
587C22⋊C4—681no—
588C22⋊C4#6322514yescomplemented
589C42—688no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—42no—
601C23—41no—
602C23—41no—
603C23—42no—
604C23—42no—
605C23—41no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—41no—
610C23—42no—
611C23—42no—
612C23C4×Dic3411yescharacteristic
613C23C4×Dic3411yescharacteristic
614C23C42×D1711yescharacteristic
615C23#1058755811yescharacteristic
616C23#1058756311yescharacteristic
617C23#1058756411yescharacteristic
618C23#1058756411yescharacteristic
619C23C22⋊C4×D1711yescharacteristic
620C23C22⋊C4×D1711yescharacteristic
621C23C22⋊C4×D1711yescharacteristic
622C23#1058756711yescharacteristic
623C23#1058756711yescharacteristic
624C23#1058757011yescharacteristic
625C23#1058757011yescharacteristic
626C23#1058757111yescharacteristic
627C23#1058757111yescharacteristic
628C23#1058757311yescharacteristic
629C23#1058757311yescharacteristic
630C23#1058757411yescharacteristic
631C23#1058757411yescharacteristic
632C23#1058757511yescharacteristic
633C23#1058757511yescharacteristic
634C23C4⋊C4×D1711yescharacteristic
635C23C4⋊C4×D1711yescharacteristic
636C23C4⋊C4×D1711yescharacteristic
637C23C4⋊C4×D1711yescharacteristic
638C23#1058758211yescharacteristic
639C23#1058758211yescharacteristic
640C23C2×#6322511yescharacteristic
641C23C4×C22⋊D1711yescharacteristic
642C23C4×C22⋊D1711yescharacteristic
643C23#1058762511yescharacteristic
644C23#1058762511yescharacteristic
645C23#1058762611yescharacteristic
646C23#1058763011yescharacteristic
647C2×C4—24no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—82no—
659C2×C4—82no—
660C2×C4—82no—
661C2×C4—82no—
662C2×C4—174no—
663C2×C4—172no—
664C2×C4—172no—
665C2×C4—172no—
666C2×C4—172no—
667C2×C4—344no—
668C2×C4—344no—
669C2×C4—344no—
670C2×C4—344no—
671C2×C4—344no—
672C2×C4—344no—
673C2×C4—342no—
674C2×C4—342no—
675C2×C4—342no—
676C2×C4—344no—
677C2×C4—682no—
678C2×C4—682no—
679C2×C4—682no—
680C2×C4—682no—
681C2×C4—682no—
682C2×C4—682no—
683C2×C4—682no—
684C2×C4—682no—
685C2×C4—684no—
686C2×C4—684no—
687C2×C4—682no—
688C2×C4—682no—
689C2×C4—682no—
690C2×C4—682no—
691C2×C4—682no—
692C2×C4—682no—
693C2×C4—1362no—
694C2×C4—1362no—
695C2×C4—1362no—
696C2×C4—1362no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22#95×D1711yescharacteristic
738C22#1176266011yescharacteristic
739C22C4×#6322511yescharacteristic
740C22#1176266711yescharacteristic
741C22#1176266811yescharacteristic
742C22#1176267311yescharacteristic
743C22#1176267811yescharacteristic
744C22#1176270411yescharacteristic
745C22#1176270411yescharacteristic
746C22#1176270611yescharacteristic
747C22#1176270611yescharacteristic
748C22#1176270911yescharacteristic
749C22#1176270911yescharacteristic
750C22#1176271311yescharacteristic
751C22#1176271311yescharacteristic
752C22#99×D1712yes—
753C22#1176278112yes—
754C4—44no—
755C4—82no—
756C4—82no—
757C4—174no—
758C4—342no—
759C4—342no—
760C4—342no—
761C4—684no—
762C4—1362no—
763C4—1362no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—21no—
773C2—21no—
774C2—21no—
775C2—21no—
776C2#1452701211yescharacteristic
777C2D17×#34211yescharacteristic
778C2#1452851511yescharacteristic
779C2#1452961812yes—
780C2#1452976712yes—
subgroupG/H
centerC23C22⋊C4×D17
commutatorC23×C17C2×C42
FrattiniC25C22×D17
FittingC2×C17×#342C2
socleC23×C17C2×C22⋊C4
prime radical, cosocleC25×C17C23
hypercenterC2×#342D17
hypocenterC17#10854
LCSG ▷ C23×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
20. #11762667C4semidirect
22. C22⋊C4×Dic17C4semidirect
25. C2×#10587502C4semidirect
182. C22⋊C4×C17C4⋊C4semidirect
194. C22⋊Dic17C4⋊C4semidirect
380. Dic17#342semidirect
488. C17#10854semidirect
588. C22⋊C4#63225semidirect

Maximal subgroups

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

subgroupindex
C2×#117626672
C2×C22⋊C4×Dic172
C2×#117625762
C2×#117625752
C2×C17×#3422
#1085417