Finite Group Databasebeta

← #16955911

Subgroups — #16955911

Order 4352.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762702C211yesmaximal, characteristic
2C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic17C211yesmaximal, characteristic
4C2×C22⋊C4×Dic17C211yesmaximal, characteristic
5#14527021C211yesmaximal, characteristic
6#14527021C211yesmaximal, characteristic
7#14527018C211yesmaximal, characteristic, complemented
8#14527016C211yesmaximal, characteristic, complemented
9#14527009C211yesmaximal, characteristic, complemented
10#14527009C211yesmaximal, characteristic, complemented
11#14527006C211yesmaximal, characteristic
12C4×#10587502C211yesmaximal, characteristic, complemented
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
26C22×C4×Dic17C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28#11762702C418yescomplemented
29C4⋊C4×Dic17—24no—
30C22⋊C4×Dic17—24no—
31C22⋊C4×Dic17C418yescomplemented
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
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C22×C4⋊C4×C17C2211yescharacteristic
49C22×C22⋊C4×C17C2211yescharacteristic
50C22×C22⋊C4×C17C2211yescharacteristic
51C22×C22⋊C4×C17C2211yescharacteristic
52C22×C42×C17C2211yescharacteristic
53C17×#388C418yescomplemented
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C25×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×Dic17—22no—
64C23×Dic17—22no—
65C23×Dic17—22no—
66C23×Dic17—22no—
67C23×Dic17—41no—
68C23×Dic17—41no—
69C23×Dic17C2×C414yes—
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C2×C4⋊C4×C17—22no—
79C2×C4⋊C4×C17—22no—
80C2×C4⋊C4×C17C2×C414yescomplemented
81C2×C22⋊C4×C17—22no—
82C2×C22⋊C4×C17—22no—
83C2×C22⋊C4×C17—41no—
84C2×C22⋊C4×C17—41no—
85C2×C22⋊C4×C17C2×C414yes—
86C2×C22⋊C4×C17C2×C414yes—
87C2×C22⋊C4×C17C2×C414yes—
88C2×C22⋊C4×C17C2×C414yes—
89C2×C22⋊C4×C17C2×C414yes—
90C2×C42×C17—41no—
91C2×C42×C17—41no—
92C2×C42×C17C2×C414yescomplemented
93C2×C22⋊Dic17—22no—
94C2×C22⋊Dic17—22no—
95C2×C22⋊Dic17—22no—
96C2×C22⋊Dic17—22no—
97C2×C22⋊Dic17—41no—
98C2×C22⋊Dic17—41no—
99C2×C22⋊Dic17C2×C414yes—
100C2×C22⋊Dic17C2×C414yes—
101C2×C22⋊Dic17C2×C414yes—
102C2×C4⋊Dic17—22no—
103C2×C4⋊Dic17—22no—
104C2×C4⋊Dic17C2×C414yescomplemented
105C2×C4×Dic17—22no—
106C2×C4×Dic17—22no—
107C2×C4×Dic17—22no—
108C2×C4×Dic17—22no—
109C2×C4×Dic17—22no—
110C2×C4×Dic17—22no—
111C2×C4×Dic17—22no—
112C2×C4×Dic17—22no—
113C2×C4×Dic17—22no—
114C2×C4×Dic17—22no—
115C2×C4×Dic17—41no—
116C2×C4×Dic17—41no—
117C2×C4×Dic17—41no—
118C2×C4×Dic17—41no—
119C2×C4×Dic17—41no—
120C2×C4×Dic17—41no—
121C2×C4×Dic17—41no—
122C2×C4×Dic17—41no—
123C2×C4×Dic17C2×C414yes—
124C2×C4×Dic17C2×C414yes—
125C2×C4×Dic17C2×C414yescomplemented
126C17×#95C2×C414yescomplemented
127C17×#95C2×C414yescomplemented
128#10587502—22no—
129#10587502—22no—
130#10587502—22no—
131#10587502—22no—
132#10587502—22no—
133#10587502—22no—
134#10587502—22no—
135#10587502—22no—
136#10587502—22no—
137#10587502—41no—
138#10587502—41no—
139#10587502C2×C414yes—
140#10587502C2×C414yes—
141#10587502C2×C414yescomplemented
142#10587502C2×C414yescomplemented
143#10587502D414yes—
144C24×C17—21no—
145C24×C17—21no—
146C24×C17—21no—
147C24×C17—21no—
148C24×C17—21no—
149C24×C17—21no—
150C24×C17—21no—
151C24×C17—21no—
152C24×C17—21no—
153C24×C17—21no—
154C24×C17—21no—
155C24×C17—21no—
156C24×C17C22×C412yes—
157C24×C17C22×C412yes—
158C24×C17C22×C412yes—
159C24×C17C2411yescharacteristic
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×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
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×C4×C17C22×C412yes—
197C22×C4×C17C22×C412yes—
198C22×C4×C17C22×C412yes—
199C22×C4×C17C22×C412yes—
200C22×C4×C17C2×D412yes—
201C22×C4×C17#4112yes—
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—21no—
241C22×Dic17—21no—
242C22×Dic17—28no—
243C22×Dic17—28no—
244C22×Dic17—44no—
245C22×Dic17—44no—
246C22×Dic17—44no—
247C22×Dic17—44no—
248C22×Dic17—44no—
249C22×Dic17C22×C412yes—
250C22×Dic17C22×C412yes—
251C22×Dic17C22×C412yes—
252C22×Dic17C22×C412yes—
253C22×Dic17C22×C412yes—
254C22×Dic17C22×C412yes—
255C22×Dic17C22×C412yes—
256C22×Dic17C22×C412yes—
257C22×Dic17C2×D412yes—
258C22×Dic17C2×D412yes—
259C22×Dic17#4112yes—
260C22×Dic17#4112yes—
261C22×Dic17#4112yes—
262C22×Dic17#4112yes—
263C22×Dic17#4112yes—
264C22×Dic17#4112yes—
265C4⋊C4×C17—28no—
266C22⋊C4×C17—28no—
267C22⋊C4×C17—44no—
268C22⋊C4×C17C42116yescomplemented
269C42×C17—44no—
270C22⋊Dic17—28no—
271C22⋊Dic17—28no—
272C22⋊Dic17—44no—
273C4⋊Dic17—28no—
274C4×Dic17—28no—
275C4×Dic17—44no—
276C4×Dic17—44no—
277C4×Dic17—44no—
278C4×Dic17—44no—
279C4×Dic17—44no—
280C4×Dic17—44no—
281#13822—171nomaximal, Sylow
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—22no—
293C23×C17—22no—
294C23×C17—22no—
295C23×C17—22no—
296C23×C17—22no—
297C23×C17—22no—
298C23×C17—22no—
299C23×C17—22no—
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×C17—41no—
309C23×C17—41no—
310C23×C17—41no—
311C23×C17—41no—
312C23×C17—41no—
313C23×C17—41no—
314C23×C17—41no—
315C23×C17—41no—
316C23×C17C2×C4214yes—
317C23×C17C23×C411yescharacteristic
318C23×C17C23×C411yescharacteristic
319C23×C17C23×C411yescharacteristic
320C23×C17C22×D411yescharacteristic
321C23×C17C2×#4111yescharacteristic
322C23×C17C2×#4111yescharacteristic
323C23×C17C2×#4111yescharacteristic
324C23×C17C2×#4111yescharacteristic
325C23×C17C2×#4111yescharacteristic
326C23×C17C2×#4111yescharacteristic
327C23×C17C2×#4111yescharacteristic
328C23×C17H(5,𝔽2)11yescharacteristic
329C23×C17H(5,𝔽2)11yescharacteristic
330C23×C17H(5,𝔽2)11yescharacteristic
331C23×C172−1+411yescharacteristic
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—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—41no—
360C2×C4×C17—41no—
361C2×C4×C17—41no—
362C2×C4×C17—41no—
363C2×C4×C17—41no—
364C2×C4×C17—41no—
365C2×C4×C17—41no—
366C2×C4×C17—41no—
367C2×C4×C17—41no—
368C2×C4×C17—41no—
369C2×C4×C17—41no—
370C2×C4×C17—41no—
371C2×C4×C17C2×C4214yes—
372C2×C4×C17C2×C4214yes—
373C2×C4×C17C4×D414yes—
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—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—416no—
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—41no—
422C2×Dic17—41no—
423C2×Dic17—41no—
424C2×Dic17—41no—
425C2×Dic17—41no—
426C2×Dic17—41no—
427C2×Dic17#11714yes—
428C2×Dic17#11714yes—
429C2×Dic17C4×D414yes—
430C2×Dic17C4×D414yes—
431C2×#388—171no—
432C2×#388D1711yescharacteristic
433C2×C4×C4⋊C4—171no—
434C2×C4×C22⋊C4—171no—
435C2×C4×C22⋊C4—171no—
436#1437—171no—
437#1437—171no—
438#1436—171no—
439#1436—171no—
440#1434—171no—
441#1434—171no—
442C22⋊#95—171no—
443C4×#95—171no—
444C4×#95—171no—
445C4×#95—171no—
446C22×C17—24no—
447C22×C17—24no—
448C22×C17—24no—
449C22×C17—42no—
450C22×C17—42no—
451C22×C17—42no—
452C22×C17—42no—
453C22×C17—42no—
454C22×C17—42no—
455C22×C17—42no—
456C22×C17—42no—
457C22×C17—42no—
458C22×C17—42no—
459C22×C17—42no—
460C22×C17—42no—
461C22×C17C22×C4211yescharacteristic
462C22×C17C2×#11711yescharacteristic
463C22×C17C2×#11711yescharacteristic
464C22×C17C2×C4×D411yescharacteristic
465C22×C17C2×C4×D411yescharacteristic
466C22×C17C2×C4×D411yescharacteristic
467C22×C17C4×#4111yescharacteristic
468C22×C17C4×#4111yescharacteristic
469C22×C17C4×#4111yescharacteristic
470C22×C17C4×#4111yescharacteristic
471C22×C17C4×#4111yescharacteristic
472C22×C17C4×#4111yescharacteristic
473C22×C17C4×#4111yescharacteristic
474C22×C17#51811yescharacteristic
475C22×C17#51811yescharacteristic
476C22×C17#51811yescharacteristic
477C22×C17#52011yescharacteristic
478C22×C17#52011yescharacteristic
479C22×C17#52011yescharacteristic
480C22×C17#54611yescharacteristic
481C22×C17#54611yescharacteristic
482C22×C17#54611yescharacteristic
483C22×C17#54811yescharacteristic
484C22×C17#55111yescharacteristic
485C22×C17#55111yescharacteristic
486C22×C17#55211yescharacteristic
487C22×C17#55311yescharacteristic
488C22×C17#55311yescharacteristic
489C22×C17#55311yescharacteristic
490C22×C17#55311yescharacteristic
491C22×C17#55311yescharacteristic
492C22×C17#55611yescharacteristic
493C22×C17#55611yescharacteristic
494C22×C17#55911yescharacteristic
495C22×C17#55911yescharacteristic
496C4×C17—24no—
497C4×C17—24no—
498C4×C17—24no—
499C4×C17—42no—
500C4×C17—42no—
501C4×C17—42no—
502Dic17—24no—
503Dic17—24no—
504Dic17—24no—
505Dic17—24no—
506Dic17—42no—
507Dic17—42no—
508Dic17—42no—
509Dic17—42no—
510C24×C4—171no—
511C22×C4⋊C4—171no—
512C22×C4⋊C4C2×D1711yescharacteristic
513C22×C22⋊C4—171no—
514C22×C22⋊C4—171no—
515C22×C22⋊C4—171no—
516C22×C22⋊C4C2×D1711yescharacteristic
517C22×C22⋊C4C2×D1711yescharacteristic
518C22×C22⋊C4C2×D1711yescharacteristic
519C22×C42—171no—
520C22×C42—171no—
521C22×C42—171no—
522C22×C42—171no—
523C22×C42—171no—
524C22×C42—171no—
525C22×C42—171no—
526C22×C42C2×D1711yescharacteristic
527#388—178no—
528#388Dic1718yescomplemented
529C4×C4⋊C4—344no—
530C4×C22⋊C4—178no—
531C4×C22⋊C4—344no—
532C2×#95—171no—
533C2×#95—171no—
534C2×#95—171no—
535C2×#95—171no—
536C2×#95—171no—
537C2×#95—171no—
538C2×#95—171no—
539C2×#95—171no—
540C2×#95—171no—
541C2×#95—171no—
542C2×#95—171no—
543C2×#95—171no—
544C2×#95—171no—
545C2×#95—171no—
546C2×#95—171no—
547C2×#95—171no—
548C2×#95C2×D1711yescharacteristic
549C2×#95C2×D1711yescharacteristic
550C2×C17—44no—
551C2×C17C4×#11711yescharacteristic
552C2×C17C42×D411yescharacteristic
553C2×C17#227511yescharacteristic
554C2×C17#234211yescharacteristic
555C2×C17#234711yescharacteristic
556C2×C17#235211yescharacteristic
557C2×C17#235711yescharacteristic
558C2×C17#236411yescharacteristic
559C2×C17#236411yescharacteristic
560C2×C17#236711yescharacteristic
561C2×C17#236711yescharacteristic
562C2×C17#237311yescharacteristic
563C2×C17#237311yescharacteristic
564C2×C17#237411yescharacteristic
565C2×C17#237411yescharacteristic
566C25C22×D1711yescharacteristic
567C23×C4—171no—
568C23×C4—171no—
569C23×C4—171no—
570C23×C4—171no—
571C23×C4—171no—
572C23×C4—171no—
573C23×C4—171no—
574C23×C4—171no—
575C23×C4—174no—
576C23×C4—342no—
577C23×C4—342no—
578C23×C4—342no—
579C23×C4—342no—
580C23×C4—681no—
581C23×C4—681no—
582C23×C4C22×D1711yescharacteristic
583C23×C4C22×D1711yescharacteristic
584C23×C4C22×D1711yescharacteristic
585C23×C4C22×D1711yescharacteristic
586C23×C4C22×D1711yescharacteristic
587C23×C4C22×D1711yescharacteristic
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—174no—
591C2×C4⋊C4—342no—
592C2×C4⋊C4—342no—
593C2×C4⋊C4C2×Dic1714yescomplemented
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—41no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4—174no—
599C2×C22⋊C4—174no—
600C2×C22⋊C4—174no—
601C2×C22⋊C4—342no—
602C2×C22⋊C4—342no—
603C2×C22⋊C4—342no—
604C2×C22⋊C4—342no—
605C2×C22⋊C4—681no—
606C2×C22⋊C4—681no—
607C2×C22⋊C4C4×D1714yes—
608C2×C22⋊C4C4×D1714yes—
609C2×C22⋊C4C2×Dic1714yes—
610C2×C22⋊C4C2×Dic1714yes—
611C2×C22⋊C4C2×Dic1714yes—
612C2×C42—41no—
613C2×C42—41no—
614C2×C42—174no—
615C2×C42—174no—
616C2×C42—174no—
617C2×C42—342no—
618C2×C42—342no—
619C2×C42—342no—
620C2×C42—342no—
621C2×C42—342no—
622C2×C42—342no—
623C2×C42—342no—
624C2×C42—342no—
625C2×C42—342no—
626C2×C42—342no—
627C2×C42—681no—
628C2×C42—681no—
629C2×C42—681no—
630C2×C42—681no—
631C2×C42—681no—
632C2×C42—681no—
633C2×C42—681no—
634C2×C42—681no—
635C2×C42C2×Dic1714yescomplemented
636#95—174no—
637#95—174no—
638#95—174no—
639#95—174no—
640#95—174no—
641#95—342no—
642#95—342no—
643#95—342no—
644#95—342no—
645#95—342no—
646#95—342no—
647#95—342no—
648#95—342no—
649#95—342no—
650#95—681no—
651#95—681no—
652#95C2×Dic1714yescomplemented
653#95C2×Dic1714yescomplemented
654C17#1382211yescharacteristic, complemented, Sylow
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C2×C4×D1712yes—
668C24C2×C4×D1712yes—
669C24C22×Dic1712yes—
670C24C23×D1711yescharacteristic
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—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—172no—
702C22×C4—172no—
703C22×C4—172no—
704C22×C4—172no—
705C22×C4—172no—
706C22×C4—172no—
707C22×C4—172no—
708C22×C4—172no—
709C22×C4—172no—
710C22×C4—172no—
711C22×C4—172no—
712C22×C4—172no—
713C22×C4—172no—
714C22×C4—172no—
715C22×C4—172no—
716C22×C4—172no—
717C22×C4—348no—
718C22×C4—348no—
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—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—684no—
760C22×C4—684no—
761C22×C4—684no—
762C22×C4—684no—
763C22×C4—684no—
764C22×C4C2×C4×D1712yes—
765C22×C4C2×C4×D1712yes—
766C22×C4C2×C4×D1712yes—
767C22×C4C2×C4×D1712yes—
768C22×C4D4×D1712yes—
769C22×C4#6325412yes—
770C22×C4C22×Dic1712yes—
771C22×C4C22×Dic1712yes—
772C22×C4C22×Dic1712yes—
773C22×C4C22×Dic1712yes—
774C22×C4C22×Dic1712yes—
775C22×C4C22×Dic1712yes—
776C4⋊C4—28no—
777C4⋊C4—348no—
778C22⋊C4—28no—
779C22⋊C4—44no—
780C22⋊C4—348no—
781C22⋊C4—348no—
782C22⋊C4—684no—
783C22⋊C4C4×Dic17116yescomplemented
784C42—44no—
785C42—348no—
786C42—684no—
787C42—684no—
788C42—684no—
789C42—684no—
790C42—684no—
791C42—684no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4×Dic1714yes—
827C23C22×C4×D1711yescharacteristic
828C23C22×C4×D1711yescharacteristic
829C23C2×D4×D1711yescharacteristic
830C23C2×#6325411yescharacteristic
831C23#1058769111yescharacteristic
832C23#1058769111yescharacteristic
833C23#41×D1711yescharacteristic
834C23#41×D1711yescharacteristic
835C23#41×D1711yescharacteristic
836C23#41×D1711yescharacteristic
837C23#41×D1711yescharacteristic
838C23#41×D1711yescharacteristic
839C23#1058769611yescharacteristic
840C23#1058769711yescharacteristic
841C23C23×Dic1711yescharacteristic
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—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
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—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—174no—
882C2×C4—174no—
883C2×C4—174no—
884C2×C4—174no—
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—342no—
899C2×C4—342no—
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—6816no—
922C2×C4—681no—
923C2×C4—681no—
924C2×C4—681no—
925C2×C4—681no—
926C2×C4—681no—
927C2×C4—681no—
928C2×C4—681no—
929C2×C4—681no—
930C2×C4—681no—
931C2×C4—681no—
932C2×C4—681no—
933C2×C4—681no—
934C2×C4—681no—
935C2×C4—681no—
936C2×C4—681no—
937C2×C4—681no—
938C2×C4C2×C4×Dic1714yes—
939C2×C4C2×C4×Dic1714yes—
940C2×C4D4×Dic1714yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4×Dic1711yescharacteristic
957C22#117×D1711yescharacteristic
958C22#117×D1711yescharacteristic
959C22C4×D4×D1711yescharacteristic
960C22C4×D4×D1711yescharacteristic
961C22C2×D4×Dic1711yescharacteristic
962C22C4×#6325411yescharacteristic
963C22C4×#6325411yescharacteristic
964C22#1176327711yescharacteristic
965C22#1176327711yescharacteristic
966C22#41×Dic1711yescharacteristic
967C22#41×Dic1711yescharacteristic
968C22#41×Dic1711yescharacteristic
969C22#1176328111yescharacteristic
970C22#1176328111yescharacteristic
971C22#1176328411yescharacteristic
972C22#1176328811yescharacteristic
973C22#1176328811yescharacteristic
974C22#1176329211yescharacteristic
975C22#1176344811yescharacteristic
976C22#1176344811yescharacteristic
977C22#1176345211yescharacteristic
978C22#1176346711yescharacteristic
979C22#1176348411yescharacteristic
980C22#1176348711yescharacteristic
981C22#1176349511yescharacteristic
982C22#1176350211yescharacteristic
983C22#1176350211yescharacteristic
984C22#1176350411yescharacteristic
985C22#1176350411yescharacteristic
986C22#1176351011yescharacteristic
987C22#1176352611yescharacteristic
988C22#1176352811yescharacteristic
989C22#1176354111yescharacteristic
990C22#1176354311yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—344no—
998C4—344no—
999C4—344no—
1000C4—344no—
1001C4—682no—
1002C4—682no—
1003C4—682no—
1004C4—682no—
1005C2—44no—
1006C2#117×Dic1711yescharacteristic
1007C2C4×D4×Dic1711yescharacteristic
1008C2#1453114511yescharacteristic
1009C2#1453163211yescharacteristic
1010C2#1453167411yescharacteristic
1011C2#1453171211yescharacteristic
1012C2#1453175411yescharacteristic
1013C2#1453182811yescharacteristic
1014C2#1453183611yescharacteristic
1015C2#1453185011yescharacteristic
1016C2#1453185911yescharacteristic
1017C2#1453190211yescharacteristic
1018C2#1453190811yescharacteristic
1019C2#1453191211yescharacteristic
1020C2#1453192011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#388D17
hypocenterC17#13822
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic17C2semidirect
7. #14527018C2semidirect
8. #14527016C2semidirect
9. #14527009C2semidirect
10. #14527009C2semidirect
12. C4×#10587502C2semidirect
13. C4×#10587502C2semidirect
14. #95×Dic17C2semidirect
28. #11762702C4semidirect
31. C22⋊C4×Dic17C4semidirect
53. C17×#388C4semidirect
80. C2×C4⋊C4×C17C2×C4semidirect
92. C2×C42×C17C2×C4semidirect
104. C2×C4⋊Dic17C2×C4semidirect
125. C2×C4×Dic17C2×C4semidirect
126. C17×#95C2×C4semidirect
127. C17×#95C2×C4semidirect
141. #10587502C2×C4semidirect
142. #10587502C2×C4semidirect
268. C22⋊C4×C17C42semidirect
528. #388Dic17semidirect
593. C2×C4⋊C4C2×Dic17semidirect
635. C2×C42C2×Dic17semidirect
652. #95C2×Dic17semidirect
653. #95C2×Dic17semidirect
654. C17#13822semidirect
783. 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×C4⋊C4×Dic172
C2×C22⋊C4×Dic172
#145270212
#145270182
#145270162
#145270092
#145270062
C4×#105875022
#95×Dic172
C2×C17×#3882
#1382217