Finite Group Databasebeta

← #16955655

Subgroups — #16955655

Order 4352.

1710 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762702C211yesmaximal, characteristic
2C2×C22⋊C4×Dic17C211yesmaximal, characteristic
3#14527021C211yesmaximal, characteristic
4#14527021C211yesmaximal, characteristic
5#14527018C211yesmaximal, characteristic, complemented
6#14527016C211yesmaximal, characteristic, complemented
7#14527013C211yesmaximal, characteristic, complemented
8#14527011C211yesmaximal, characteristic, complemented
9#14527009C211yesmaximal, characteristic, complemented
10#14527009C211yesmaximal, characteristic, complemented
11#14527006C211yesmaximal, characteristic
12#14527006C211yesmaximal, characteristic
13C4×#10587502C211yesmaximal, characteristic, complemented
14#95×Dic17C211yesmaximal, characteristic, complemented
15C2×C17×#388C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C22⋊Dic17C2211yescharacteristic
19C22×C22⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C4×Dic17C2211yescharacteristic
22C22×C4×Dic17C2211yescharacteristic
23C22×C4×Dic17C2211yescharacteristic
24C22×C4×Dic17C2211yescharacteristic
25C22×C4×Dic17C2211yescharacteristic
26#11762702C418yescomplemented
27C22⋊C4×Dic17C418yescomplemented
28C2×#10587502C2211yescharacteristic
29C2×#10587502C2211yescharacteristic
30C2×#10587502C2211yescharacteristic
31C2×#10587502C2211yescharacteristic
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C22×C4⋊C4×C17C2211yescharacteristic
47C22×C22⋊C4×C17C2211yescharacteristic
48C22×C22⋊C4×C17C2211yescharacteristic
49C22×C22⋊C4×C17C2211yescharacteristic
50C22×C42×C17C2211yescharacteristic
51C17×#388C418yescomplemented
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C25×C17C2311yescharacteristic
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×Dic17—22no—
62C23×Dic17—22no—
63C23×Dic17—41no—
64C23×Dic17—41no—
65C23×Dic17—41no—
66C23×Dic17—41no—
67C23×Dic17C2×C414yes—
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C2×C4⋊C4×C17—41no—
77C2×C4⋊C4×C17—41no—
78C2×C4⋊C4×C17C2×C414yescomplemented
79C2×C22⋊C4×C17—41no—
80C2×C22⋊C4×C17—41no—
81C2×C22⋊C4×C17—41no—
82C2×C22⋊C4×C17—41no—
83C2×C22⋊C4×C17C2×C414yes—
84C2×C22⋊C4×C17C2×C414yes—
85C2×C22⋊C4×C17C2×C414yes—
86C2×C22⋊C4×C17C2×C414yes—
87C2×C22⋊C4×C17C2×C414yes—
88C2×C42×C17—41no—
89C2×C42×C17—41no—
90C2×C42×C17C2×C414yescomplemented
91C2×C22⋊Dic17—22no—
92C2×C22⋊Dic17—22no—
93C2×C22⋊Dic17—41no—
94C2×C22⋊Dic17—41no—
95C2×C22⋊Dic17—41no—
96C2×C22⋊Dic17—41no—
97C2×C22⋊Dic17C2×C414yes—
98C2×C22⋊Dic17C2×C414yes—
99C2×C22⋊Dic17C2×C414yes—
100C2×C4⋊Dic17—41no—
101C2×C4⋊Dic17—41no—
102C2×C4⋊Dic17C2×C414yescomplemented
103C2×C4×Dic17—22no—
104C2×C4×Dic17—22no—
105C2×C4×Dic17—41no—
106C2×C4×Dic17—41no—
107C2×C4×Dic17—41no—
108C2×C4×Dic17—41no—
109C2×C4×Dic17—41no—
110C2×C4×Dic17—41no—
111C2×C4×Dic17—41no—
112C2×C4×Dic17—41no—
113C2×C4×Dic17—41no—
114C2×C4×Dic17—41no—
115C2×C4×Dic17C2×C414yes—
116C2×C4×Dic17C2×C414yes—
117C2×C4×Dic17C2×C414yescomplemented
118C17×#95C2×C414yescomplemented
119C17×#95C2×C414yescomplemented
120#10587502—22no—
121#10587502—22no—
122#10587502—22no—
123#10587502—22no—
124#10587502—22no—
125#10587502—22no—
126#10587502—41no—
127#10587502—41no—
128#10587502—41no—
129#10587502—41no—
130#10587502—41no—
131#10587502—41no—
132#10587502—41no—
133#10587502—41no—
134#10587502C2×C414yes—
135#10587502C2×C414yes—
136#10587502C2×C414yescomplemented
137#10587502C2×C414yescomplemented
138C24×C17—21no—
139C24×C17—21no—
140C24×C17—21no—
141C24×C17—21no—
142C24×C17—21no—
143C24×C17—21no—
144C24×C17—21no—
145C24×C17—21no—
146C24×C17—21no—
147C24×C17—21no—
148C24×C17—21no—
149C24×C17—21no—
150C24×C17C22×C412yes—
151C24×C17C22×C412yes—
152C24×C17C22×C412yes—
153C24×C17C2411yescharacteristic
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17C22×C412yes—
187C22×C4×C17C22×C412yes—
188C22×C4×C17C22×C412yes—
189C22×C4×C17C22×C412yes—
190C22×C4×C17C22×C412yes—
191C22×C4×C17C22×C412yes—
192C22×C4×C17C22×C412yes—
193C22×C4×C17C22×C412yes—
194C22×C4×C17C22×C412yes—
195C22×C4×C17C22×C412yes—
196C22×Dic17—21no—
197C22×Dic17—21no—
198C22×Dic17—21no—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C22×Dic17—21no—
218C22×Dic17—21no—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—21no—
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—21no—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—28no—
241C22×Dic17—44no—
242C22×Dic17—44no—
243C22×Dic17—44no—
244C22×Dic17—44no—
245C22×Dic17—44no—
246C22×Dic17—44no—
247C22×Dic17C22×C412yes—
248C22×Dic17C22×C412yes—
249C22×Dic17C22×C412yes—
250C22×Dic17C22×C412yes—
251C22×Dic17C22×C412yes—
252C22×Dic17C22×C412yes—
253C22×Dic17C22×C412yes—
254C22×Dic17C22×C412yes—
255C22×Dic17#4112yes—
256C22×Dic17#4112yes—
257C22×Dic17#4112yes—
258C22×Dic17#4112yes—
259C4⋊C4×C17—44no—
260C22⋊C4×C17—44no—
261C22⋊C4×C17—44no—
262C22⋊C4×C17C42116yescomplemented
263C42×C17—44no—
264C22⋊Dic17—28no—
265C22⋊Dic17—44no—
266C22⋊Dic17—44no—
267C4⋊Dic17—44no—
268C4×Dic17—44no—
269C4×Dic17—44no—
270C4×Dic17—44no—
271C4×Dic17—44no—
272C4×Dic17—44no—
273#13788—171nomaximal, Sylow
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—22no—
277C23×C17—22no—
278C23×C17—22no—
279C23×C17—22no—
280C23×C17—22no—
281C23×C17—22no—
282C23×C17—22no—
283C23×C17—22no—
284C23×C17—22no—
285C23×C17—22no—
286C23×C17—22no—
287C23×C17—22no—
288C23×C17—22no—
289C23×C17—22no—
290C23×C17—22no—
291C23×C17—22no—
292C23×C17—41no—
293C23×C17—41no—
294C23×C17—41no—
295C23×C17—41no—
296C23×C17—41no—
297C23×C17—41no—
298C23×C17—41no—
299C23×C17—41no—
300C23×C17—41no—
301C23×C17—41no—
302C23×C17—41no—
303C23×C17—41no—
304C23×C17—41no—
305C23×C17—41no—
306C23×C17—41no—
307C23×C17—41no—
308C23×C17C2×C4214yes—
309C23×C17C23×C411yescharacteristic
310C23×C17C23×C411yescharacteristic
311C23×C17C23×C411yescharacteristic
312C23×C17C2×#4111yescharacteristic
313C23×C17C2×#4111yescharacteristic
314C23×C17C2×#4111yescharacteristic
315C23×C17C2×#4111yescharacteristic
316C23×C17H(5,𝔽2)11yescharacteristic
317C23×C17H(5,𝔽2)11yescharacteristic
318C23×C17H(5,𝔽2)11yescharacteristic
319C23×C17H(5,𝔽2)11yescharacteristic
320C23×C17H(5,𝔽2)11yescharacteristic
321C23×C17H(5,𝔽2)11yescharacteristic
322C23×C172−1+411yescharacteristic
323C23×C172−1+411yescharacteristic
324C2×C4×C17—22no—
325C2×C4×C17—22no—
326C2×C4×C17—22no—
327C2×C4×C17—22no—
328C2×C4×C17—22no—
329C2×C4×C17—22no—
330C2×C4×C17—22no—
331C2×C4×C17—22no—
332C2×C4×C17—22no—
333C2×C4×C17—22no—
334C2×C4×C17—22no—
335C2×C4×C17—22no—
336C2×C4×C17—22no—
337C2×C4×C17—22no—
338C2×C4×C17—22no—
339C2×C4×C17—22no—
340C2×C4×C17—22no—
341C2×C4×C17—22no—
342C2×C4×C17—22no—
343C2×C4×C17—22no—
344C2×C4×C17—22no—
345C2×C4×C17—22no—
346C2×C4×C17—22no—
347C2×C4×C17—22no—
348C2×C4×C17—41no—
349C2×C4×C17—41no—
350C2×C4×C17—41no—
351C2×C4×C17—41no—
352C2×C4×C17—41no—
353C2×C4×C17—41no—
354C2×C4×C17—41no—
355C2×C4×C17—41no—
356C2×C4×C17—41no—
357C2×C4×C17—41no—
358C2×C4×C17—41no—
359C2×C4×C17—41no—
360C2×C4×C17—41no—
361C2×C4×C17—41no—
362C2×C4×C17—41no—
363C2×C4×C17—41no—
364C2×C4×C17C2×C4214yes—
365C2×C4×C17C2×C4214yes—
366C2×Dic17—22no—
367C2×Dic17—22no—
368C2×Dic17—22no—
369C2×Dic17—22no—
370C2×Dic17—22no—
371C2×Dic17—22no—
372C2×Dic17—22no—
373C2×Dic17—22no—
374C2×Dic17—22no—
375C2×Dic17—22no—
376C2×Dic17—22no—
377C2×Dic17—22no—
378C2×Dic17—22no—
379C2×Dic17—22no—
380C2×Dic17—22no—
381C2×Dic17—22no—
382C2×Dic17—22no—
383C2×Dic17—22no—
384C2×Dic17—22no—
385C2×Dic17—22no—
386C2×Dic17—22no—
387C2×Dic17—22no—
388C2×Dic17—22no—
389C2×Dic17—22no—
390C2×Dic17—22no—
391C2×Dic17—22no—
392C2×Dic17—22no—
393C2×Dic17—22no—
394C2×Dic17—22no—
395C2×Dic17—22no—
396C2×Dic17—416no—
397C2×Dic17—41no—
398C2×Dic17—41no—
399C2×Dic17—41no—
400C2×Dic17—41no—
401C2×Dic17—41no—
402C2×Dic17—41no—
403C2×Dic17—41no—
404C2×Dic17—41no—
405C2×Dic17—41no—
406C2×Dic17—41no—
407C2×Dic17—41no—
408C2×Dic17—41no—
409C2×Dic17—41no—
410C2×Dic17—41no—
411C2×Dic17—41no—
412C2×Dic17—41no—
413C2×Dic17—41no—
414C2×Dic17—41no—
415C2×Dic17—41no—
416C2×Dic17—41no—
417C2×Dic17—41no—
418C2×Dic17—41no—
419C2×Dic17—41no—
420C2×Dic17—41no—
421C2×Dic17#11714yes—
422C2×Dic17#11714yes—
423C2×#388—171no—
424C2×#388D1711yescharacteristic
425C2×C4×C22⋊C4—171no—
426#1437—171no—
427#1437—171no—
428#1436—171no—
429#1436—171no—
430C4⋊#95—171no—
431#1434—171no—
432#1434—171no—
433#1434—171no—
434C22⋊#95—171no—
435C22⋊#95—171no—
436C4×#95—171no—
437C4×#95—171no—
438C22×C17—24no—
439C22×C17—24no—
440C22×C17—24no—
441C22×C17—42no—
442C22×C17—42no—
443C22×C17—42no—
444C22×C17—42no—
445C22×C17—42no—
446C22×C17—42no—
447C22×C17—42no—
448C22×C17—42no—
449C22×C17—42no—
450C22×C17—42no—
451C22×C17—42no—
452C22×C17—42no—
453C22×C17C22×C4211yescharacteristic
454C22×C17C2×#11711yescharacteristic
455C22×C17C2×#11711yescharacteristic
456C22×C17C4×#4111yescharacteristic
457C22×C17C4×#4111yescharacteristic
458C22×C17C4×#4111yescharacteristic
459C22×C17C4×#4111yescharacteristic
460C22×C17#51811yescharacteristic
461C22×C17#51811yescharacteristic
462C22×C17#51811yescharacteristic
463C22×C17#51811yescharacteristic
464C22×C17#51811yescharacteristic
465C22×C17#51811yescharacteristic
466C22×C17#52011yescharacteristic
467C22×C17#52011yescharacteristic
468C22×C17#52011yescharacteristic
469C22×C17#52011yescharacteristic
470C22×C17#52011yescharacteristic
471C22×C17#52011yescharacteristic
472C22×C17#53811yescharacteristic
473C22×C17#53811yescharacteristic
474C22×C17#53811yescharacteristic
475C22×C17#53811yescharacteristic
476C22×C17#53811yescharacteristic
477C22×C17#53811yescharacteristic
478C22×C17#53911yescharacteristic
479C22×C17#53911yescharacteristic
480C22×C17#54011yescharacteristic
481C22×C17#54011yescharacteristic
482C22×C17#54011yescharacteristic
483C22×C17#54111yescharacteristic
484C22×C17#54211yescharacteristic
485C22×C17#54211yescharacteristic
486C22×C17#54211yescharacteristic
487C22×C17#54211yescharacteristic
488C4×C17—24no—
489C4×C17—24no—
490C4×C17—42no—
491C4×C17—42no—
492C4×C17—42no—
493C4×C17—42no—
494Dic17—24no—
495Dic17—24no—
496Dic17—42no—
497Dic17—42no—
498Dic17—42no—
499Dic17—42no—
500Dic17—42no—
501Dic17—42no—
502C24×C4—171no—
503C22×C4⋊C4—171no—
504C22×C4⋊C4C2×D1711yescharacteristic
505C22×C22⋊C4—171no—
506C22×C22⋊C4—171no—
507C22×C22⋊C4—171no—
508C22×C22⋊C4C2×D1711yescharacteristic
509C22×C22⋊C4C2×D1711yescharacteristic
510C22×C22⋊C4C2×D1711yescharacteristic
511C22×C42—171no—
512C22×C42—171no—
513C22×C42—171no—
514C22×C42—171no—
515C22×C42—171no—
516C22×C42C2×D1711yescharacteristic
517#388—178no—
518#388Dic1718yescomplemented
519C4×C22⋊C4—178no—
520C2×#95—171no—
521C2×#95—171no—
522C2×#95—171no—
523C2×#95—171no—
524C2×#95—171no—
525C2×#95—171no—
526C2×#95—171no—
527C2×#95—171no—
528C2×#95—171no—
529C2×#95—171no—
530C2×#95—171no—
531C2×#95—171no—
532C2×#95—171no—
533C2×#95—171no—
534C2×#95—171no—
535C2×#95—171no—
536C2×#95—171no—
537C2×#95—171no—
538C2×#95C2×D1711yescharacteristic
539C2×#95C2×D1711yescharacteristic
540C2×C17—44no—
541C2×C17C4×#11711yescharacteristic
542C2×C17#227511yescharacteristic
543C2×C17#227511yescharacteristic
544C2×C17#231211yescharacteristic
545C2×C17#231411yescharacteristic
546C2×C17#231811yescharacteristic
547C2×C17#231911yescharacteristic
548C2×C17#233311yescharacteristic
549C2×C17#233311yescharacteristic
550C2×C17#233411yescharacteristic
551C2×C17#233411yescharacteristic
552C2×C17#233511yescharacteristic
553C2×C17#233511yescharacteristic
554C2×C17#233711yescharacteristic
555C2×C17#233711yescharacteristic
556C25C22×D1711yescharacteristic
557C23×C4—171no—
558C23×C4—171no—
559C23×C4—171no—
560C23×C4—171no—
561C23×C4—171no—
562C23×C4—171no—
563C23×C4—171no—
564C23×C4—171no—
565C23×C4—174no—
566C23×C4—342no—
567C23×C4—342no—
568C23×C4—681no—
569C23×C4—681no—
570C23×C4—681no—
571C23×C4—681no—
572C23×C4C22×D1711yescharacteristic
573C23×C4C22×D1711yescharacteristic
574C23×C4C22×D1711yescharacteristic
575C23×C4C22×D1711yescharacteristic
576C23×C4C22×D1711yescharacteristic
577C23×C4C22×D1711yescharacteristic
578C2×C4⋊C4—41no—
579C2×C4⋊C4—41no—
580C2×C4⋊C4—174no—
581C2×C4⋊C4—681no—
582C2×C4⋊C4—681no—
583C2×C4⋊C4C2×Dic1714yescomplemented
584C2×C22⋊C4—41no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—174no—
589C2×C22⋊C4—174no—
590C2×C22⋊C4—174no—
591C2×C22⋊C4—342no—
592C2×C22⋊C4—342no—
593C2×C22⋊C4—681no—
594C2×C22⋊C4—681no—
595C2×C22⋊C4—681no—
596C2×C22⋊C4—681no—
597C2×C22⋊C4C4×D1714yes—
598C2×C22⋊C4C4×D1714yes—
599C2×C22⋊C4C2×Dic1714yes—
600C2×C22⋊C4C2×Dic1714yes—
601C2×C22⋊C4C2×Dic1714yes—
602C2×C42—41no—
603C2×C42—41no—
604C2×C42—174no—
605C2×C42—174no—
606C2×C42—174no—
607C2×C42—342no—
608C2×C42—342no—
609C2×C42—681no—
610C2×C42—681no—
611C2×C42—681no—
612C2×C42—681no—
613C2×C42—681no—
614C2×C42—681no—
615C2×C42—681no—
616C2×C42—681no—
617C2×C42—681no—
618C2×C42—681no—
619C2×C42C2×Dic1714yescomplemented
620#95—174no—
621#95—174no—
622#95—174no—
623#95—174no—
624#95—342no—
625#95—342no—
626#95—342no—
627#95—342no—
628#95—342no—
629#95—342no—
630#95—681no—
631#95—681no—
632#95—681no—
633#95—681no—
634#95—681no—
635#95—681no—
636#95—681no—
637#95—681no—
638#95C2×Dic1714yescomplemented
639#95C2×Dic1714yescomplemented
640C17#1378811yescharacteristic, complemented, Sylow
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×C4×D1712yes—
654C24C2×C4×D1712yes—
655C24C22×Dic1712yes—
656C24C23×D1711yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—172no—
690C22×C4—172no—
691C22×C4—172no—
692C22×C4—172no—
693C22×C4—172no—
694C22×C4—172no—
695C22×C4—172no—
696C22×C4—172no—
697C22×C4—172no—
698C22×C4—172no—
699C22×C4—172no—
700C22×C4—172no—
701C22×C4—348no—
702C22×C4—341no—
703C22×C4—341no—
704C22×C4—341no—
705C22×C4—341no—
706C22×C4—341no—
707C22×C4—341no—
708C22×C4—341no—
709C22×C4—341no—
710C22×C4—341no—
711C22×C4—341no—
712C22×C4—341no—
713C22×C4—341no—
714C22×C4—341no—
715C22×C4—341no—
716C22×C4—341no—
717C22×C4—341no—
718C22×C4—341no—
719C22×C4—341no—
720C22×C4—341no—
721C22×C4—341no—
722C22×C4—341no—
723C22×C4—341no—
724C22×C4—341no—
725C22×C4—341no—
726C22×C4—341no—
727C22×C4—341no—
728C22×C4—341no—
729C22×C4—341no—
730C22×C4—341no—
731C22×C4—341no—
732C22×C4—341no—
733C22×C4—341no—
734C22×C4—341no—
735C22×C4—341no—
736C22×C4—341no—
737C22×C4—341no—
738C22×C4—341no—
739C22×C4—341no—
740C22×C4—341no—
741C22×C4—341no—
742C22×C4—341no—
743C22×C4—341no—
744C22×C4—341no—
745C22×C4—341no—
746C22×C4—684no—
747C22×C4—684no—
748C22×C4—684no—
749C22×C4—684no—
750C22×C4—684no—
751C22×C4—684no—
752C22×C4C2×C4×D1712yes—
753C22×C4C2×C4×D1712yes—
754C22×C4C2×C4×D1712yes—
755C22×C4C2×C4×D1712yes—
756C22×C4C22×Dic1712yes—
757C22×C4C22×Dic1712yes—
758C22×C4C22×Dic1712yes—
759C22×C4C22×Dic1712yes—
760C22×C4C22×Dic1712yes—
761C22×C4C22×Dic1712yes—
762C4⋊C4—44no—
763C4⋊C4—684no—
764C22⋊C4—44no—
765C22⋊C4—44no—
766C22⋊C4—348no—
767C22⋊C4—684no—
768C22⋊C4—684no—
769C22⋊C4C4×Dic17116yescomplemented
770C42—44no—
771C42—684no—
772C42—684no—
773C42—684no—
774C42—684no—
775C42—684no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×C4×Dic1714yes—
811C23C22×C4×D1711yescharacteristic
812C23C22×C4×D1711yescharacteristic
813C23#1058769111yescharacteristic
814C23#1058769111yescharacteristic
815C23#1058769111yescharacteristic
816C23#1058769111yescharacteristic
817C23#41×D1711yescharacteristic
818C23#41×D1711yescharacteristic
819C23#41×D1711yescharacteristic
820C23#41×D1711yescharacteristic
821C23#1058769611yescharacteristic
822C23#1058769611yescharacteristic
823C23#1058769711yescharacteristic
824C23#1058769711yescharacteristic
825C23C23×Dic1711yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—174no—
867C2×C4—174no—
868C2×C4—342no—
869C2×C4—342no—
870C2×C4—342no—
871C2×C4—342no—
872C2×C4—342no—
873C2×C4—342no—
874C2×C4—342no—
875C2×C4—342no—
876C2×C4—342no—
877C2×C4—342no—
878C2×C4—342no—
879C2×C4—342no—
880C2×C4—342no—
881C2×C4—342no—
882C2×C4—342no—
883C2×C4—342no—
884C2×C4—342no—
885C2×C4—342no—
886C2×C4—342no—
887C2×C4—342no—
888C2×C4—342no—
889C2×C4—342no—
890C2×C4—342no—
891C2×C4—342no—
892C2×C4—342no—
893C2×C4—342no—
894C2×C4—342no—
895C2×C4—342no—
896C2×C4—342no—
897C2×C4—342no—
898C2×C4—6816no—
899C2×C4—681no—
900C2×C4—681no—
901C2×C4—681no—
902C2×C4—681no—
903C2×C4—681no—
904C2×C4—681no—
905C2×C4—681no—
906C2×C4—681no—
907C2×C4—681no—
908C2×C4—681no—
909C2×C4—681no—
910C2×C4—681no—
911C2×C4—681no—
912C2×C4—681no—
913C2×C4—681no—
914C2×C4—681no—
915C2×C4—681no—
916C2×C4—681no—
917C2×C4—681no—
918C2×C4—681no—
919C2×C4—681no—
920C2×C4—681no—
921C2×C4—681no—
922C2×C4—681no—
923C2×C4C2×C4×Dic1714yes—
924C2×C4C2×C4×Dic1714yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×C4×Dic1711yescharacteristic
941C22#117×D1711yescharacteristic
942C22#117×D1711yescharacteristic
943C22#1176327711yescharacteristic
944C22#1176327711yescharacteristic
945C22#41×Dic1711yescharacteristic
946C22#41×Dic1711yescharacteristic
947C22#1176328111yescharacteristic
948C22#1176328111yescharacteristic
949C22#1176328111yescharacteristic
950C22#1176328111yescharacteristic
951C22#1176328411yescharacteristic
952C22#1176328411yescharacteristic
953C22#1176328811yescharacteristic
954C22#1176328811yescharacteristic
955C22#1176328811yescharacteristic
956C22#1176328811yescharacteristic
957C22#1176329211yescharacteristic
958C22#1176329211yescharacteristic
959C22#1176339111yescharacteristic
960C22#1176339111yescharacteristic
961C22#1176339311yescharacteristic
962C22#1176339311yescharacteristic
963C22#1176339511yescharacteristic
964C22#1176339811yescharacteristic
965C22#1176340011yescharacteristic
966C22#1176340211yescharacteristic
967C22#1176340911yescharacteristic
968C22#1176340911yescharacteristic
969C22#1176341111yescharacteristic
970C22#1176341611yescharacteristic
971C22#1176342311yescharacteristic
972C22#1176342311yescharacteristic
973C22#1176342511yescharacteristic
974C22#1176342711yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—344no—
982C4—344no—
983C4—682no—
984C4—682no—
985C4—682no—
986C4—682no—
987C4—682no—
988C4—682no—
989C2—44no—
990C2#117×Dic1711yescharacteristic
991C2#1453114511yescharacteristic
992C2#1453114511yescharacteristic
993C2#1453137811yescharacteristic
994C2#1453138811yescharacteristic
995C2#1453141411yescharacteristic
996C2#1453142511yescharacteristic
997C2#1453154711yescharacteristic
998C2#1453155111yescharacteristic
999C2#1453155711yescharacteristic
1000C2#1453156311yescharacteristic
1001C2#1453157211yescharacteristic
1002C2#1453157811yescharacteristic
1003C2#1453159511yescharacteristic
1004C2#1453159911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#388D17
hypocenterC17#13788
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
5. #14527018C2semidirect
6. #14527016C2semidirect
7. #14527013C2semidirect
8. #14527011C2semidirect
9. #14527009C2semidirect
10. #14527009C2semidirect
13. C4×#10587502C2semidirect
14. #95×Dic17C2semidirect
26. #11762702C4semidirect
27. C22⋊C4×Dic17C4semidirect
51. C17×#388C4semidirect
78. C2×C4⋊C4×C17C2×C4semidirect
90. C2×C42×C17C2×C4semidirect
102. C2×C4⋊Dic17C2×C4semidirect
117. C2×C4×Dic17C2×C4semidirect
118. C17×#95C2×C4semidirect
119. C17×#95C2×C4semidirect
136. #10587502C2×C4semidirect
137. #10587502C2×C4semidirect
262. C22⋊C4×C17C42semidirect
518. #388Dic17semidirect
583. C2×C4⋊C4C2×Dic17semidirect
619. C2×C42C2×Dic17semidirect
638. #95C2×Dic17semidirect
639. #95C2×Dic17semidirect
640. C17#13788semidirect
769. C22⋊C4C4×Dic17semidirect

Maximal subgroups

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

subgroupindex
C2×#117627022
C2×C22⋊C4×Dic172
#145270212
#145270182
#145270162
#145270132
#145270112
#145270092
#145270062
C4×#105875022
#95×Dic172
C2×C17×#3882
#1378817