Finite Group Databasebeta

← #16955918

Subgroups — #16955918

Order 4352.

2022 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762702C211yesmaximal, characteristic
2C2×#11762684C211yesmaximal, characteristic
3C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊Dic17C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic17C211yesmaximal, characteristic
6C2×C22⋊C4×Dic17C211yesmaximal, characteristic
7#14527021C211yesmaximal, characteristic
8#14527021C211yesmaximal, characteristic
9#14527018C211yesmaximal, characteristic, complemented
10#14527018C211yesmaximal, characteristic, complemented
11#14527018C211yesmaximal, characteristic, complemented
12#14527016C211yesmaximal, characteristic, complemented
13C4×#10587502C211yesmaximal, characteristic, complemented
14#95×Dic17C211yesmaximal, characteristic, complemented
15C2×C17×#388C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C4×Dic17C2211yescharacteristic
24C22×C4×Dic17C2211yescharacteristic
25C22×C4×Dic17C2211yescharacteristic
26C22×C4×Dic17C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30#11762702C418yescomplemented
31#11762684C418yescomplemented
32C4⋊C4×Dic17—24no—
33C4×C4⋊Dic17—24no—
34C22⋊C4×Dic17—24no—
35C22⋊C4×Dic17—24no—
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C22×C4⋊C4×C17C2211yescharacteristic
51C22×C22⋊C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C42×C17C2211yescharacteristic
55C17×#388C418yescomplemented
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C25×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×Dic17—22no—
66C23×Dic17—22no—
67C23×Dic17—22no—
68C23×Dic17—22no—
69C23×Dic17—41no—
70C23×Dic17—41no—
71C23×Dic17C2×C414yes—
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C2×C4⋊C4×C17—22no—
81C2×C4⋊C4×C17—22no—
82C2×C4⋊C4×C17C2×C414yescomplemented
83C2×C22⋊C4×C17—22no—
84C2×C22⋊C4×C17—22no—
85C2×C22⋊C4×C17—22no—
86C2×C22⋊C4×C17—22no—
87C2×C22⋊C4×C17C2×C414yes—
88C2×C22⋊C4×C17C2×C414yes—
89C2×C22⋊C4×C17C2×C414yes—
90C2×C22⋊C4×C17C2×C414yes—
91C2×C22⋊C4×C17C2×C414yes—
92C2×C42×C17—22no—
93C2×C42×C17—22no—
94C2×C42×C17C2×C414yescomplemented
95C2×C22⋊Dic17—22no—
96C2×C22⋊Dic17—22no—
97C2×C22⋊Dic17—22no—
98C2×C22⋊Dic17—22no—
99C2×C22⋊Dic17—41no—
100C2×C22⋊Dic17—41no—
101C2×C22⋊Dic17C2×C414yes—
102C2×C22⋊Dic17C2×C414yes—
103C2×C22⋊Dic17C2×C414yes—
104C2×C4⋊Dic17—22no—
105C2×C4⋊Dic17—22no—
106C2×C4⋊Dic17—22no—
107C2×C4⋊Dic17—22no—
108C2×C4⋊Dic17—22no—
109C2×C4⋊Dic17—22no—
110C2×C4⋊Dic17C2×C414yes—
111C2×C4⋊Dic17C2×C414yes—
112C2×C4⋊Dic17C2×C414yescomplemented
113C2×C4×Dic17—22no—
114C2×C4×Dic17—22no—
115C2×C4×Dic17—22no—
116C2×C4×Dic17—22no—
117C2×C4×Dic17—22no—
118C2×C4×Dic17—22no—
119C2×C4×Dic17—22no—
120C2×C4×Dic17—22no—
121C2×C4×Dic17—22no—
122C2×C4×Dic17—22no—
123C2×C4×Dic17—22no—
124C2×C4×Dic17—22no—
125C2×C4×Dic17—22no—
126C2×C4×Dic17—22no—
127C2×C4×Dic17—41no—
128C2×C4×Dic17—41no—
129C2×C4×Dic17—41no—
130C2×C4×Dic17—41no—
131C2×C4×Dic17—41no—
132C2×C4×Dic17—41no—
133C2×C4×Dic17C2×C414yescomplemented
134C17×#95C2×C414yescomplemented
135C17×#95C2×C414yescomplemented
136#10587502—22no—
137#10587502—22no—
138#10587502—22no—
139#10587502—22no—
140#10587502—22no—
141#10587502—22no—
142#10587502—41no—
143#10587502—41no—
144#10587502C2×C414yes—
145#10587502C2×C414yes—
146#10587502C2×C414yescomplemented
147#10587502C2×C414yescomplemented
148#10587502D414yes—
149#10587502D414yes—
150C24×C17—21no—
151C24×C17—21no—
152C24×C17—21no—
153C24×C17—21no—
154C24×C17—21no—
155C24×C17—21no—
156C24×C17—21no—
157C24×C17—21no—
158C24×C17—21no—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17C22×C412yes—
163C24×C17C22×C412yes—
164C24×C17C22×C412yes—
165C24×C17C2411yescharacteristic
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×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17C22×C412yes—
195C22×C4×C17C22×C412yes—
196C22×C4×C17C22×C412yes—
197C22×C4×C17C22×C412yes—
198C22×C4×C17C22×C412yes—
199C22×C4×C17C22×C412yes—
200C22×C4×C17C22×C412yes—
201C22×C4×C17C22×C412yes—
202C22×C4×C17C22×C412yes—
203C22×C4×C17C22×C412yes—
204C22×C4×C17C2×D412yes—
205C22×C4×C17C2×D412yes—
206C22×C4×C17#4112yes—
207C22×C4×C17#4112yes—
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—21no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17—21no—
246C22×Dic17—21no—
247C22×Dic17—21no—
248C22×Dic17—28no—
249C22×Dic17—28no—
250C22×Dic17—44no—
251C22×Dic17—44no—
252C22×Dic17—44no—
253C22×Dic17—44no—
254C22×Dic17—44no—
255C22×Dic17C22×C412yes—
256C22×Dic17C22×C412yes—
257C22×Dic17C22×C412yes—
258C22×Dic17C22×C412yes—
259C22×Dic17C22×C412yes—
260C22×Dic17C22×C412yes—
261C22×Dic17C22×C412yes—
262C22×Dic17C22×C412yes—
263C22×Dic17C2×D412yes—
264C22×Dic17C2×D412yes—
265C22×Dic17C2×D412yes—
266C22×Dic17C2×D412yes—
267C22×Dic17#4112yes—
268C22×Dic17#4112yes—
269C22×Dic17#4112yes—
270C22×Dic17#4112yes—
271C4⋊C4×C17—28no—
272C22⋊C4×C17—28no—
273C22⋊C4×C17—28no—
274C22⋊C4×C17C42116yescomplemented
275C42×C17—28no—
276C22⋊Dic17—28no—
277C22⋊Dic17—28no—
278C22⋊Dic17—44no—
279C4⋊Dic17—28no—
280C4⋊Dic17—28no—
281C4⋊Dic17—28no—
282C4×Dic17—28no—
283C4×Dic17—44no—
284C4×Dic17—44no—
285C4×Dic17—44no—
286C4×Dic17—44no—
287C4×Dic17—44no—
288C4×Dic17—44no—
289#13823—171nomaximal, Sylow
290C23×C17—22no—
291C23×C17—22no—
292C23×C17—22no—
293C23×C17—22no—
294C23×C17—22no—
295C23×C17—22no—
296C23×C17—22no—
297C23×C17—22no—
298C23×C17—22no—
299C23×C17—22no—
300C23×C17—22no—
301C23×C17—22no—
302C23×C17—22no—
303C23×C17—22no—
304C23×C17—22no—
305C23×C17—22no—
306C23×C17—22no—
307C23×C17—22no—
308C23×C17—41no—
309C23×C17—41no—
310C23×C17—41no—
311C23×C17—41no—
312C23×C17—41no—
313C23×C17—41no—
314C23×C17—41no—
315C23×C17—41no—
316C23×C17—41no—
317C23×C17—41no—
318C23×C17—41no—
319C23×C17—41no—
320C23×C17—41no—
321C23×C17—41no—
322C23×C17—41no—
323C23×C17—41no—
324C23×C17C2×C4214yes—
325C23×C17C23×C411yescharacteristic
326C23×C17C23×C411yescharacteristic
327C23×C17C23×C411yescharacteristic
328C23×C17C22×D411yescharacteristic
329C23×C17C22×D411yescharacteristic
330C23×C17C2×#4111yescharacteristic
331C23×C17C2×#4111yescharacteristic
332C23×C17C2×#4111yescharacteristic
333C23×C17C2×#4111yescharacteristic
334C23×C17C2×#4111yescharacteristic
335C23×C17C2×#4111yescharacteristic
336C23×C17H(5,𝔽2)11yescharacteristic
337C23×C17H(5,𝔽2)11yescharacteristic
338C23×C172−1+411yescharacteristic
339C23×C172−1+411yescharacteristic
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—22no—
349C2×C4×C17—22no—
350C2×C4×C17—22no—
351C2×C4×C17—22no—
352C2×C4×C17—22no—
353C2×C4×C17—22no—
354C2×C4×C17—22no—
355C2×C4×C17—22no—
356C2×C4×C17—22no—
357C2×C4×C17—22no—
358C2×C4×C17—22no—
359C2×C4×C17—22no—
360C2×C4×C17—22no—
361C2×C4×C17—22no—
362C2×C4×C17—22no—
363C2×C4×C17—22no—
364C2×C4×C17—22no—
365C2×C4×C17—22no—
366C2×C4×C17—22no—
367C2×C4×C17—22no—
368C2×C4×C17—22no—
369C2×C4×C17—22no—
370C2×C4×C17—41no—
371C2×C4×C17—41no—
372C2×C4×C17—41no—
373C2×C4×C17—41no—
374C2×C4×C17—41no—
375C2×C4×C17—41no—
376C2×C4×C17—41no—
377C2×C4×C17—41no—
378C2×C4×C17C2×C4214yes—
379C2×C4×C17C2×C4214yes—
380C2×C4×C17C4×D414yes—
381C2×C4×C17C4×D414yes—
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—22no—
397C2×Dic17—22no—
398C2×Dic17—22no—
399C2×Dic17—22no—
400C2×Dic17—22no—
401C2×Dic17—22no—
402C2×Dic17—22no—
403C2×Dic17—22no—
404C2×Dic17—22no—
405C2×Dic17—22no—
406C2×Dic17—22no—
407C2×Dic17—22no—
408C2×Dic17—22no—
409C2×Dic17—22no—
410C2×Dic17—22no—
411C2×Dic17—22no—
412C2×Dic17—22no—
413C2×Dic17—22no—
414C2×Dic17—22no—
415C2×Dic17—22no—
416C2×Dic17—22no—
417C2×Dic17—22no—
418C2×Dic17—416no—
419C2×Dic17—41no—
420C2×Dic17—41no—
421C2×Dic17—41no—
422C2×Dic17—41no—
423C2×Dic17—41no—
424C2×Dic17—41no—
425C2×Dic17—41no—
426C2×Dic17—41no—
427C2×Dic17—41no—
428C2×Dic17—41no—
429C2×Dic17—41no—
430C2×Dic17—41no—
431C2×Dic17—41no—
432C2×Dic17—41no—
433C2×Dic17—41no—
434C2×Dic17—41no—
435C2×Dic17C4×D414yes—
436C2×Dic17C4×D414yes—
437C2×Dic17C4×D414yes—
438C2×Dic17C4×D414yes—
439C2×#388—171no—
440C2×#388D1711yescharacteristic
441C2×#385—171no—
442C2×C4×C4⋊C4—171no—
443C2×C4×C4⋊C4—171no—
444C2×C4×C22⋊C4—171no—
445C2×C4×C22⋊C4—171no—
446#1437—171no—
447#1437—171no—
448#1436—171no—
449#1436—171no—
450#1436—171no—
451#1436—171no—
452C4×#95—171no—
453C4×#95—171no—
454C22×C17—24no—
455C22×C17—24no—
456C22×C17—24no—
457C22×C17—42no—
458C22×C17—42no—
459C22×C17—42no—
460C22×C17—42no—
461C22×C17—42no—
462C22×C17—42no—
463C22×C17—42no—
464C22×C17—42no—
465C22×C17—42no—
466C22×C17—42no—
467C22×C17—42no—
468C22×C17—42no—
469C22×C17C22×C4211yescharacteristic
470C22×C17C2×C4×D411yescharacteristic
471C22×C17C2×C4×D411yescharacteristic
472C22×C17C2×C4×D411yescharacteristic
473C22×C17C2×C4×D411yescharacteristic
474C22×C17C2×C4×D411yescharacteristic
475C22×C17C2×C4×D411yescharacteristic
476C22×C17C4×#4111yescharacteristic
477C22×C17C4×#4111yescharacteristic
478C22×C17C4×#4111yescharacteristic
479C22×C17C4×#4111yescharacteristic
480C22×C17C4×#4111yescharacteristic
481C22×C17C4×#4111yescharacteristic
482C22×C17#51811yescharacteristic
483C22×C17#51911yescharacteristic
484C22×C17#52011yescharacteristic
485C22×C17#52011yescharacteristic
486C22×C17#52011yescharacteristic
487C22×C17#52011yescharacteristic
488C22×C17D4211yescharacteristic
489C22×C17#54611yescharacteristic
490C22×C17#54611yescharacteristic
491C22×C17#54711yescharacteristic
492C22×C17#54711yescharacteristic
493C22×C17#54811yescharacteristic
494C22×C17#54811yescharacteristic
495C22×C17#55111yescharacteristic
496C22×C17#55111yescharacteristic
497C22×C17#55211yescharacteristic
498C22×C17#55211yescharacteristic
499C22×C17#55311yescharacteristic
500C22×C17#55311yescharacteristic
501C22×C17#55611yescharacteristic
502C22×C17#55611yescharacteristic
503C22×C17#55911yescharacteristic
504C4×C17—24no—
505C4×C17—24no—
506C4×C17—24no—
507C4×C17—24no—
508C4×C17—42no—
509C4×C17—42no—
510Dic17—24no—
511Dic17—24no—
512Dic17—24no—
513Dic17—24no—
514Dic17—42no—
515Dic17—42no—
516Dic17—42no—
517Dic17—42no—
518C24×C4—171no—
519C22×C4⋊C4—171no—
520C22×C4⋊C4—171no—
521C22×C4⋊C4—171no—
522C22×C4⋊C4C2×D1711yescharacteristic
523C22×C22⋊C4—171no—
524C22×C22⋊C4—171no—
525C22×C22⋊C4—171no—
526C22×C22⋊C4C2×D1711yescharacteristic
527C22×C22⋊C4C2×D1711yescharacteristic
528C22×C22⋊C4C2×D1711yescharacteristic
529C22×C42—171no—
530C22×C42—171no—
531C22×C42—171no—
532C22×C42—171no—
533C22×C42—171no—
534C22×C42—171no—
535C22×C42—171no—
536C22×C42C2×D1711yescharacteristic
537#388—178no—
538#388Dic1718yescomplemented
539#385—178no—
540C4×C4⋊C4—344no—
541C4×C4⋊C4—344no—
542C4×C22⋊C4—344no—
543C4×C22⋊C4—344no—
544C2×#95—171no—
545C2×#95—171no—
546C2×#95—171no—
547C2×#95—171no—
548C2×#95—171no—
549C2×#95—171no—
550C2×#95—171no—
551C2×#95—171no—
552C2×#95—171no—
553C2×#95—171no—
554C2×#95—171no—
555C2×#95—171no—
556C2×#95—171no—
557C2×#95—171no—
558C2×#95C2×D1711yescharacteristic
559C2×#95C2×D1711yescharacteristic
560C2×C17—44no—
561C2×C17C42×D411yescharacteristic
562C2×C17C42×D411yescharacteristic
563C2×C17#227411yescharacteristic
564C2×C17#235811yescharacteristic
565C2×C17#235911yescharacteristic
566C2×C17#235911yescharacteristic
567C2×C17#236111yescharacteristic
568C2×C17#236111yescharacteristic
569C2×C17#236211yescharacteristic
570C2×C17#236211yescharacteristic
571C2×C17#236711yescharacteristic
572C2×C17#236711yescharacteristic
573C2×C17#237311yescharacteristic
574C2×C17#237311yescharacteristic
575C2×C17#237411yescharacteristic
576C25C22×D1711yescharacteristic
577C23×C4—171no—
578C23×C4—171no—
579C23×C4—171no—
580C23×C4—171no—
581C23×C4—171no—
582C23×C4—171no—
583C23×C4—171no—
584C23×C4—171no—
585C23×C4—174no—
586C23×C4—342no—
587C23×C4—342no—
588C23×C4—342no—
589C23×C4—342no—
590C23×C4—681no—
591C23×C4—681no—
592C23×C4C22×D1711yescharacteristic
593C23×C4C22×D1711yescharacteristic
594C23×C4C22×D1711yescharacteristic
595C23×C4C22×D1711yescharacteristic
596C23×C4C22×D1711yescharacteristic
597C23×C4C22×D1711yescharacteristic
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—174no—
601C2×C4⋊C4—174no—
602C2×C4⋊C4—174no—
603C2×C4⋊C4—342no—
604C2×C4⋊C4—342no—
605C2×C4⋊C4—342no—
606C2×C4⋊C4—342no—
607C2×C4⋊C4—342no—
608C2×C4⋊C4—342no—
609C2×C4⋊C4C2×Dic1714yescomplemented
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—174no—
615C2×C22⋊C4—174no—
616C2×C22⋊C4—174no—
617C2×C22⋊C4—342no—
618C2×C22⋊C4—342no—
619C2×C22⋊C4—342no—
620C2×C22⋊C4—342no—
621C2×C22⋊C4—681no—
622C2×C22⋊C4—681no—
623C2×C22⋊C4C4×D1714yes—
624C2×C22⋊C4C4×D1714yes—
625C2×C22⋊C4C2×Dic1714yes—
626C2×C22⋊C4C2×Dic1714yes—
627C2×C22⋊C4C2×Dic1714yes—
628C2×C42—22no—
629C2×C42—22no—
630C2×C42—174no—
631C2×C42—342no—
632C2×C42—342no—
633C2×C42—342no—
634C2×C42—342no—
635C2×C42—342no—
636C2×C42—342no—
637C2×C42—342no—
638C2×C42—342no—
639C2×C42—342no—
640C2×C42—342no—
641C2×C42—342no—
642C2×C42—342no—
643C2×C42—342no—
644C2×C42—342no—
645C2×C42—681no—
646C2×C42—681no—
647C2×C42—681no—
648C2×C42—681no—
649C2×C42—681no—
650C2×C42—681no—
651C2×C42C2×Dic1714yescomplemented
652#95—174no—
653#95—174no—
654#95—174no—
655#95—174no—
656#95—174no—
657#95—174no—
658#95—342no—
659#95—342no—
660#95—342no—
661#95—342no—
662#95—342no—
663#95—342no—
664#95—681no—
665#95—681no—
666#95C2×Dic1714yescomplemented
667#95C2×Dic1714yescomplemented
668C17#1382311yescharacteristic, complemented, Sylow
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C2×C4×D1712yes—
682C24C2×C4×D1712yes—
683C24C22×Dic1712yes—
684C24C23×D1711yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—172no—
714C22×C4—172no—
715C22×C4—172no—
716C22×C4—172no—
717C22×C4—172no—
718C22×C4—172no—
719C22×C4—172no—
720C22×C4—172no—
721C22×C4—172no—
722C22×C4—172no—
723C22×C4—172no—
724C22×C4—172no—
725C22×C4—172no—
726C22×C4—172no—
727C22×C4—172no—
728C22×C4—172no—
729C22×C4—348no—
730C22×C4—348no—
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—341no—
747C22×C4—341no—
748C22×C4—341no—
749C22×C4—341no—
750C22×C4—341no—
751C22×C4—341no—
752C22×C4—341no—
753C22×C4—341no—
754C22×C4—341no—
755C22×C4—341no—
756C22×C4—341no—
757C22×C4—341no—
758C22×C4—341no—
759C22×C4—341no—
760C22×C4—341no—
761C22×C4—341no—
762C22×C4—341no—
763C22×C4—341no—
764C22×C4—341no—
765C22×C4—341no—
766C22×C4—341no—
767C22×C4—341no—
768C22×C4—341no—
769C22×C4—341no—
770C22×C4—341no—
771C22×C4—684no—
772C22×C4—684no—
773C22×C4—684no—
774C22×C4—684no—
775C22×C4—684no—
776C22×C4C2×C4×D1712yes—
777C22×C4C2×C4×D1712yes—
778C22×C4C2×C4×D1712yes—
779C22×C4C2×C4×D1712yes—
780C22×C4D4×D1712yes—
781C22×C4D4×D1712yes—
782C22×C4#6325412yes—
783C22×C4#6325412yes—
784C22×C4C22×Dic1712yes—
785C22×C4C22×Dic1712yes—
786C22×C4C22×Dic1712yes—
787C22×C4C22×Dic1712yes—
788C22×C4C22×Dic1712yes—
789C22×C4C22×Dic1712yes—
790C4⋊C4—28no—
791C4⋊C4—348no—
792C4⋊C4—348no—
793C4⋊C4—348no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—348no—
797C22⋊C4—348no—
798C22⋊C4—684no—
799C22⋊C4C4×Dic17116yescomplemented
800C42—28no—
801C42—348no—
802C42—684no—
803C42—684no—
804C42—684no—
805C42—684no—
806C42—684no—
807C42—684no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×C4×Dic1714yes—
843C23C22×C4×D1711yescharacteristic
844C23C22×C4×D1711yescharacteristic
845C23C2×D4×D1711yescharacteristic
846C23C2×D4×D1711yescharacteristic
847C23C2×#6325411yescharacteristic
848C23C2×#6325411yescharacteristic
849C23#41×D1711yescharacteristic
850C23#41×D1711yescharacteristic
851C23#41×D1711yescharacteristic
852C23#41×D1711yescharacteristic
853C23#1058769611yescharacteristic
854C23#1058769611yescharacteristic
855C23#1058769711yescharacteristic
856C23#1058769711yescharacteristic
857C23C23×Dic1711yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—174no—
897C2×C4—174no—
898C2×C4—174no—
899C2×C4—174no—
900C2×C4—342no—
901C2×C4—342no—
902C2×C4—342no—
903C2×C4—342no—
904C2×C4—342no—
905C2×C4—342no—
906C2×C4—342no—
907C2×C4—342no—
908C2×C4—342no—
909C2×C4—342no—
910C2×C4—342no—
911C2×C4—342no—
912C2×C4—342no—
913C2×C4—342no—
914C2×C4—342no—
915C2×C4—342no—
916C2×C4—342no—
917C2×C4—342no—
918C2×C4—342no—
919C2×C4—342no—
920C2×C4—342no—
921C2×C4—342no—
922C2×C4—342no—
923C2×C4—342no—
924C2×C4—342no—
925C2×C4—342no—
926C2×C4—342no—
927C2×C4—342no—
928C2×C4—342no—
929C2×C4—342no—
930C2×C4—342no—
931C2×C4—342no—
932C2×C4—342no—
933C2×C4—342no—
934C2×C4—342no—
935C2×C4—342no—
936C2×C4—6816no—
937C2×C4—681no—
938C2×C4—681no—
939C2×C4—681no—
940C2×C4—681no—
941C2×C4—681no—
942C2×C4—681no—
943C2×C4—681no—
944C2×C4—681no—
945C2×C4—681no—
946C2×C4—681no—
947C2×C4—681no—
948C2×C4—681no—
949C2×C4—681no—
950C2×C4—681no—
951C2×C4—681no—
952C2×C4—681no—
953C2×C4C2×C4×Dic1714yes—
954C2×C4C2×C4×Dic1714yes—
955C2×C4D4×Dic1714yes—
956C2×C4D4×Dic1714yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C4×Dic1711yescharacteristic
973C22C4×D4×D1711yescharacteristic
974C22C4×D4×D1711yescharacteristic
975C22C4×D4×D1711yescharacteristic
976C22C4×D4×D1711yescharacteristic
977C22C2×D4×Dic1711yescharacteristic
978C22C2×D4×Dic1711yescharacteristic
979C22C4×#6325411yescharacteristic
980C22C4×#6325411yescharacteristic
981C22C4×#6325411yescharacteristic
982C22C4×#6325411yescharacteristic
983C22#41×Dic1711yescharacteristic
984C22#41×Dic1711yescharacteristic
985C22#1176328311yescharacteristic
986C22#1176328611yescharacteristic
987C22#1176328911yescharacteristic
988C22#1176328911yescharacteristic
989C22#1176329211yescharacteristic
990C22#1176329211yescharacteristic
991C22#1176344311yescharacteristic
992C22#1176345111yescharacteristic
993C22#1176345211yescharacteristic
994C22#1176345711yescharacteristic
995C22#1176345911yescharacteristic
996C22#1176346511yescharacteristic
997C22#1176346711yescharacteristic
998C22#1176348211yescharacteristic
999C22#1176348411yescharacteristic
1000C22#1176349511yescharacteristic
1001C22#1176349611yescharacteristic
1002C22#1176351011yescharacteristic
1003C22#1176351111yescharacteristic
1004C22#1176352611yescharacteristic
1005C22#1176352811yescharacteristic
1006C22#1176354111yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—344no—
1014C4—344no—
1015C4—344no—
1016C4—344no—
1017C4—682no—
1018C4—682no—
1019C4—682no—
1020C4—682no—
1021C2—44no—
1022C2C4×D4×Dic1711yescharacteristic
1023C2C4×D4×Dic1711yescharacteristic
1024C2#1453114011yescharacteristic
1025C2#1453176211yescharacteristic
1026C2#1453177511yescharacteristic
1027C2#1453178011yescharacteristic
1028C2#1453179711yescharacteristic
1029C2#1453180411yescharacteristic
1030C2#1453180811yescharacteristic
1031C2#1453181411yescharacteristic
1032C2#1453185811yescharacteristic
1033C2#1453185911yescharacteristic
1034C2#1453190811yescharacteristic
1035C2#1453191111yescharacteristic
1036C2#1453191411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#388D17
hypocenterC17#13823
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic17C2semidirect
4. C2×C4×C4⋊Dic17C2semidirect
9. #14527018C2semidirect
10. #14527018C2semidirect
11. #14527018C2semidirect
12. #14527016C2semidirect
13. C4×#10587502C2semidirect
14. #95×Dic17C2semidirect
30. #11762702C4semidirect
31. #11762684C4semidirect
55. C17×#388C4semidirect
82. C2×C4⋊C4×C17C2×C4semidirect
94. C2×C42×C17C2×C4semidirect
112. C2×C4⋊Dic17C2×C4semidirect
133. C2×C4×Dic17C2×C4semidirect
134. C17×#95C2×C4semidirect
135. C17×#95C2×C4semidirect
146. #10587502C2×C4semidirect
147. #10587502C2×C4semidirect
274. C22⋊C4×C17C42semidirect
538. #388Dic17semidirect
609. C2×C4⋊C4C2×Dic17semidirect
651. C2×C42C2×Dic17semidirect
666. #95C2×Dic17semidirect
667. #95C2×Dic17semidirect
668. C17#13823semidirect
799. 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×#117626842
C2×C4⋊C4×Dic172
C2×C4×C4⋊Dic172
C2×C22⋊C4×Dic172
#145270212
#145270182
#145270162
C4×#105875022
#95×Dic172
C2×C17×#3882
#1382317