Finite Group Databasebeta

← #16955835

Subgroups — #16955835

Order 4352.

2298 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762684C211yesmaximal, characteristic
2C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic17C211yesmaximal, characteristic
4C2×C22⋊C4×Dic17C211yesmaximal, characteristic
5C2×C4×C22⋊Dic17C211yesmaximal, characteristic
6C22×#10587502C211yesmaximal, characteristic
7#14527018C211yesmaximal, characteristic, complemented
8#14527018C211yesmaximal, characteristic, complemented
9#14527016C211yesmaximal, characteristic, complemented
10#14527016C211yesmaximal, characteristic, complemented
11#14527013C211yesmaximal, characteristic, complemented
12#14527009C211yesmaximal, characteristic, complemented
13#14527006C211yesmaximal, characteristic
14#95×Dic17C211yesmaximal, characteristic, complemented
15C2×C17×#385C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C4×Dic17C2211yescharacteristic
23C22×C4×Dic17C2211yescharacteristic
24C22×C4×Dic17C2211yescharacteristic
25C22×C4×Dic17C2211yescharacteristic
26C22×C4×Dic17C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28#11762684C418yescomplemented
29C4⋊C4×Dic17—24no—
30C22⋊C4×Dic17—24no—
31C22⋊C4×Dic17C418yescomplemented
32C4×C22⋊Dic17—24no—
33C2×#10587502—24no—
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
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C24×C4×C17C2211yescharacteristic
51C22×C4⋊C4×C17C2211yescharacteristic
52C22×C4⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C17×#385C418yescomplemented
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C25×C17C2311yescharacteristic
59C23×C4×C17—22no—
60C23×C4×C17—22no—
61C23×C4×C17—22no—
62C23×C4×C17—22no—
63C23×C4×C17—41no—
64C23×C4×C17—41no—
65C23×C4×C17C2×C414yes—
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×Dic17—22no—
73C23×Dic17—22no—
74C23×Dic17—22no—
75C23×Dic17—22no—
76C23×Dic17—22no—
77C23×Dic17—22no—
78C23×Dic17—22no—
79C23×Dic17—22no—
80C23×Dic17—41no—
81C23×Dic17—41no—
82C23×Dic17—41no—
83C23×Dic17—41no—
84C23×Dic17C2×C414yes—
85C23×Dic17C2×C414yes—
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
88C23×Dic17C2311yescharacteristic
89C23×Dic17C2311yescharacteristic
90C23×Dic17C2311yescharacteristic
91C23×Dic17C2311yescharacteristic
92C23×Dic17C2311yescharacteristic
93C23×Dic17C2311yescharacteristic
94C2×C4⋊C4×C17—22no—
95C2×C4⋊C4×C17—22no—
96C2×C4⋊C4×C17—41no—
97C2×C4⋊C4×C17—41no—
98C2×C4⋊C4×C17C2×C414yescomplemented
99C2×C4⋊C4×C17C2×C414yescomplemented
100C2×C22⋊C4×C17—22no—
101C2×C22⋊C4×C17—22no—
102C2×C22⋊C4×C17C2×C414yes—
103C2×C22⋊C4×C17C2×C414yes—
104C2×C22⋊C4×C17C2×C414yes—
105C2×C22⋊C4×C17C2×C414yes—
106C2×C22⋊Dic17—22no—
107C2×C22⋊Dic17—22no—
108C2×C22⋊Dic17C2×C414yes—
109C2×C22⋊Dic17C2×C414yes—
110C2×C22⋊Dic17D414yes—
111C2×C22⋊Dic17Q814yes—
112C2×C4⋊Dic17—22no—
113C2×C4⋊Dic17—22no—
114C2×C4⋊Dic17—41no—
115C2×C4⋊Dic17—41no—
116C2×C4⋊Dic17C2×C414yescomplemented
117C2×C4⋊Dic17C2×C414yescomplemented
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—22no—
128C2×C4×Dic17—41no—
129C2×C4×Dic17—41no—
130C2×C4×Dic17—41no—
131C2×C4×Dic17—41no—
132C2×C4×Dic17—41no—
133C2×C4×Dic17—41no—
134C2×C4×Dic17C2×C414yescomplemented
135C2×C4×Dic17C2×C414yescomplemented
136C17×#95C2×C414yescomplemented
137C17×#95C2×C414yescomplemented
138#10587502—22no—
139#10587502—22no—
140#10587502—22no—
141#10587502—22no—
142#10587502—22no—
143#10587502—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—41no—
148#10587502—41no—
149#10587502C2×C414yescomplemented
150#10587502C2×C414yescomplemented
151#10587502C2×C414yescomplemented
152#10587502C2×C414yescomplemented
153#10587502D414yes—
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×C17C2×D412yes—
166C24×C17C2×Q812yes—
167C24×C17#4112yes—
168C24×C17#4112yes—
169C24×C17C2411yescharacteristic
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—28no—
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×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—28no—
202C22×C4×C17—44no—
203C22×C4×C17—44no—
204C22×C4×C17—44no—
205C22×C4×C17—44no—
206C22×C4×C17—44no—
207C22×C4×C17C22×C412yes—
208C22×C4×C17C22×C412yes—
209C22×C4×C17C22×C412yes—
210C22×C4×C17C22×C412yes—
211C22×C4×C17C22×C412yes—
212C22×C4×C17C22×C412yes—
213C22×C4×C17C22×C412yes—
214C22×C4×C17C22×C412yes—
215C22×C4×C17C22×C412yes—
216C22×C4×C17C22×C412yes—
217C22×C4×C17C2×D412yes—
218C22×C4×C17#4112yes—
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—28no—
236C22×Dic17—28no—
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—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—21no—
260C22×Dic17—21no—
261C22×Dic17—28no—
262C22×Dic17—28no—
263C22×Dic17—44no—
264C22×Dic17—44no—
265C22×Dic17—44no—
266C22×Dic17—44no—
267C22×Dic17—44no—
268C22×Dic17—44no—
269C22×Dic17—44no—
270C22×Dic17—44no—
271C22×Dic17—44no—
272C22×Dic17—44no—
273C22×Dic17C22×C412yes—
274C22×Dic17C22×C412yes—
275C22×Dic17C22×C412yes—
276C22×Dic17C22×C412yes—
277C22×Dic17C22×C412yes—
278C22×Dic17C22×C412yes—
279C22×Dic17C22×C412yes—
280C22×Dic17C22×C412yes—
281C22×Dic17C2×D412yes—
282C22×Dic17C2×D412yes—
283C22×Dic17C2×D412yes—
284C22×Dic17C2×D412yes—
285C22×Dic17C2×Q812yes—
286C22×Dic17C2×Q812yes—
287C22×Dic17#4112yes—
288C22×Dic17#4112yes—
289C4⋊C4×C17—28no—
290C4⋊C4×C17—44no—
291C22⋊C4×C17—28no—
292C22⋊C4×C17C42116yescomplemented
293C22⋊Dic17—28no—
294C22⋊Dic17C4⋊C4116yescomplemented
295C4⋊Dic17—28no—
296C4⋊Dic17—44no—
297C4×Dic17—28no—
298C4×Dic17—44no—
299C4×Dic17—44no—
300C4×Dic17—44no—
301C4×Dic17—44no—
302C4×Dic17—44no—
303#13814—171nomaximal, Sylow
304C23×C17—22no—
305C23×C17—22no—
306C23×C17—22no—
307C23×C17—22no—
308C23×C17—22no—
309C23×C17—22no—
310C23×C17—22no—
311C23×C17—22no—
312C23×C17—22no—
313C23×C17—22no—
314C23×C17—22no—
315C23×C17—22no—
316C23×C17—22no—
317C23×C17—22no—
318C23×C17—22no—
319C23×C17—22no—
320C23×C17—22no—
321C23×C17—22no—
322C23×C17—22no—
323C23×C17—22no—
324C23×C17—22no—
325C23×C17—22no—
326C23×C17—22no—
327C23×C17—22no—
328C23×C17—22no—
329C23×C17—22no—
330C23×C17—22no—
331C23×C17—22no—
332C23×C17C2×C4214yes—
333C23×C17C2×C4⋊C414yes—
334C23×C17#11714yes—
335C23×C17C4×D414yes—
336C23×C17C4×D414yes—
337C23×C17C4×Q814yes—
338C23×C17C4×Q814yes—
339C23×C17C23×C411yescharacteristic
340C23×C17C23×C411yescharacteristic
341C23×C17C23×C411yescharacteristic
342C23×C17C22×D411yescharacteristic
343C23×C17C22×D411yescharacteristic
344C23×C17C22×Q811yescharacteristic
345C23×C17C2×#4111yescharacteristic
346C23×C17C2×#4111yescharacteristic
347C23×C17C2×#4111yescharacteristic
348C23×C17C2×#4111yescharacteristic
349C23×C17C2×#4111yescharacteristic
350C23×C17H(5,𝔽2)11yescharacteristic
351C23×C17H(5,𝔽2)11yescharacteristic
352C23×C17H(5,𝔽2)11yescharacteristic
353C23×C172−1+411yescharacteristic
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—22no—
371C2×C4×C17—22no—
372C2×C4×C17—22no—
373C2×C4×C17—22no—
374C2×C4×C17—22no—
375C2×C4×C17—22no—
376C2×C4×C17—22no—
377C2×C4×C17—22no—
378C2×C4×C17—22no—
379C2×C4×C17—22no—
380C2×C4×C17—22no—
381C2×C4×C17—416no—
382C2×C4×C17—41no—
383C2×C4×C17—41no—
384C2×C4×C17—41no—
385C2×C4×C17—41no—
386C2×C4×C17—41no—
387C2×C4×C17—41no—
388C2×C4×C17—41no—
389C2×C4×C17—41no—
390C2×C4×C17—41no—
391C2×C4×C17—41no—
392C2×C4×C17—41no—
393C2×C4×C17—41no—
394C2×C4×C17C2×C4214yes—
395C2×C4×C17C2×C4214yes—
396C2×C4×C17C4×D414yes—
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—22no—
419C2×Dic17—22no—
420C2×Dic17—22no—
421C2×Dic17—22no—
422C2×Dic17—22no—
423C2×Dic17—22no—
424C2×Dic17—22no—
425C2×Dic17—22no—
426C2×Dic17—22no—
427C2×Dic17—22no—
428C2×Dic17—22no—
429C2×Dic17—22no—
430C2×Dic17—22no—
431C2×Dic17—22no—
432C2×Dic17—22no—
433C2×Dic17—416no—
434C2×Dic17—416no—
435C2×Dic17—41no—
436C2×Dic17—41no—
437C2×Dic17—41no—
438C2×Dic17—41no—
439C2×Dic17—41no—
440C2×Dic17—41no—
441C2×Dic17—41no—
442C2×Dic17—41no—
443C2×Dic17—41no—
444C2×Dic17—41no—
445C2×Dic17—41no—
446C2×Dic17—41no—
447C2×Dic17—41no—
448C2×Dic17—41no—
449C2×Dic17—41no—
450C2×Dic17—41no—
451C2×Dic17C2×C4⋊C414yes—
452C2×Dic17C2×C4⋊C414yes—
453C2×Dic17C4×D414yes—
454C2×Dic17C4×D414yes—
455C2×#385—171no—
456C2×#385D1711yescharacteristic
457C2×C4×C4⋊C4—171no—
458C2×C4×C22⋊C4—171no—
459C2×C4×C22⋊C4—171no—
460C2×C4×C22⋊C4—171no—
461C22×#95—171no—
462#1436—171no—
463#1436—171no—
464#1436—171no—
465#1436—171no—
466C4⋊#95—171no—
467#1434—171no—
468C22⋊#95—171no—
469C4×#95—171no—
470C22×C17—24no—
471C22×C17—24no—
472C22×C17—24no—
473C22×C17—24no—
474C22×C17—24no—
475C22×C17—24no—
476C22×C17—24no—
477C22×C17—24no—
478C22×C17—24no—
479C22×C17—24no—
480C22×C17—24no—
481C22×C17—24no—
482C22×C17—24no—
483C22×C17—24no—
484C22×C17C4×C4⋊C418yescomplemented
485C22×C17C22×C4211yescharacteristic
486C22×C17C22×C4⋊C411yescharacteristic
487C22×C17C2×#11711yescharacteristic
488C22×C17C2×C4×D411yescharacteristic
489C22×C17C2×C4×D411yescharacteristic
490C22×C17C2×C4×D411yescharacteristic
491C22×C17C2×C4×D411yescharacteristic
492C22×C17C2×C4×D411yescharacteristic
493C22×C17C2×C4×Q811yescharacteristic
494C22×C17C2×C4×Q811yescharacteristic
495C22×C17C4×#4111yescharacteristic
496C22×C17C4×#4111yescharacteristic
497C22×C17C4×#4111yescharacteristic
498C22×C17#51811yescharacteristic
499C22×C17#51811yescharacteristic
500C22×C17#51811yescharacteristic
501C22×C17#52011yescharacteristic
502C22×C17#52011yescharacteristic
503C22×C17#52011yescharacteristic
504C22×C17D4211yescharacteristic
505C22×C17#54611yescharacteristic
506C22×C17#54611yescharacteristic
507C22×C17#54611yescharacteristic
508C22×C17#54611yescharacteristic
509C22×C17#54711yescharacteristic
510C22×C17D4×Q811yescharacteristic
511C22×C17#55111yescharacteristic
512C22×C17#55111yescharacteristic
513C22×C17#55111yescharacteristic
514C22×C17#55111yescharacteristic
515C22×C17#55211yescharacteristic
516C22×C17#55211yescharacteristic
517C22×C17#55411yescharacteristic
518C22×C17#55411yescharacteristic
519C22×C17#55411yescharacteristic
520C4×C17—24no—
521C4×C17—24no—
522C4×C17—24no—
523C4×C17—42no—
524C4×C17—42no—
525C4×C17—42no—
526Dic17—24no—
527Dic17—24no—
528Dic17—24no—
529Dic17—24no—
530Dic17—42no—
531Dic17—42no—
532Dic17—42no—
533Dic17—42no—
534C24×C4—171no—
535C24×C4—171no—
536C24×C4C2×D1711yescharacteristic
537C22×C4⋊C4—171no—
538C22×C4⋊C4—171no—
539C22×C4⋊C4C2×D1711yescharacteristic
540C22×C4⋊C4C2×D1711yescharacteristic
541C22×C22⋊C4—171no—
542C22×C22⋊C4—171no—
543C22×C22⋊C4C2×D1711yescharacteristic
544C22×C22⋊C4C2×D1711yescharacteristic
545C22×C42—171no—
546C22×C42—171no—
547C22×C42—171no—
548C22×C42—171no—
549C22×C42—171no—
550C22×C42—171no—
551#385—178no—
552#385Dic1718yescomplemented
553C4×C4⋊C4—344no—
554C4×C22⋊C4—178no—
555C4×C22⋊C4—344no—
556C4×C22⋊C4—344no—
557C2×#95—171no—
558C2×#95—171no—
559C2×#95—171no—
560C2×#95—171no—
561C2×#95—171no—
562C2×#95—171no—
563C2×#95—171no—
564C2×#95—171no—
565C2×#95—171no—
566C2×#95—171no—
567C2×#95—171no—
568C2×#95—171no—
569C2×#95—171no—
570C2×#95—171no—
571C2×#95—171no—
572C2×#95—171no—
573C2×#95—344no—
574C2×#95C2×D1711yescharacteristic
575C2×#95C2×D1711yescharacteristic
576C2×C17—28no—
577C2×C17C2×C4×C4⋊C411yescharacteristic
578C2×C17C42×D411yescharacteristic
579C2×C17#227511yescharacteristic
580C2×C17#234211yescharacteristic
581C2×C17#234311yescharacteristic
582C2×C17D4×C4⋊C411yescharacteristic
583C2×C17#234911yescharacteristic
584C2×C17#235811yescharacteristic
585C2×C17#235811yescharacteristic
586C2×C17#235911yescharacteristic
587C2×C17#235911yescharacteristic
588C2×C17#236011yescharacteristic
589C2×C17#236011yescharacteristic
590C2×C17#236811yescharacteristic
591C2×C17#236811yescharacteristic
592C25C22×D1711yescharacteristic
593C23×C4—22no—
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—41no—
598C23×C4—41no—
599C23×C4—171no—
600C23×C4—171no—
601C23×C4—171no—
602C23×C4—171no—
603C23×C4—171no—
604C23×C4—171no—
605C23×C4—171no—
606C23×C4—171no—
607C23×C4—174no—
608C23×C4—174no—
609C23×C4—342no—
610C23×C4—342no—
611C23×C4—342no—
612C23×C4—342no—
613C23×C4—342no—
614C23×C4—342no—
615C23×C4—342no—
616C23×C4—342no—
617C23×C4—681no—
618C23×C4—681no—
619C23×C4—681no—
620C23×C4—681no—
621C23×C4C2×Dic1714yes—
622C23×C4C22×D1711yescharacteristic
623C23×C4C22×D1711yescharacteristic
624C23×C4C22×D1711yescharacteristic
625C23×C4C22×D1711yescharacteristic
626C23×C4C22×D1711yescharacteristic
627C23×C4C22×D1711yescharacteristic
628C2×C4⋊C4—22no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—174no—
633C2×C4⋊C4—174no—
634C2×C4⋊C4—342no—
635C2×C4⋊C4—342no—
636C2×C4⋊C4—681no—
637C2×C4⋊C4—681no—
638C2×C4⋊C4C2×Dic1714yescomplemented
639C2×C4⋊C4C2×Dic1714yescomplemented
640C2×C22⋊C4—22no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—174no—
643C2×C22⋊C4—174no—
644C2×C22⋊C4—174no—
645C2×C22⋊C4—174no—
646C2×C22⋊C4—342no—
647C2×C22⋊C4—342no—
648C2×C22⋊C4C4×D1714yes—
649C2×C22⋊C4C4×D1714yes—
650C2×C22⋊C4C2×Dic1714yes—
651C2×C22⋊C4C2×Dic1714yes—
652C2×C42—174no—
653C2×C42—174no—
654C2×C42—342no—
655C2×C42—342no—
656C2×C42—342no—
657C2×C42—342no—
658C2×C42—342no—
659C2×C42—342no—
660C2×C42—342no—
661C2×C42—342no—
662C2×C42—342no—
663C2×C42—342no—
664C2×C42—681no—
665C2×C42—681no—
666C2×C42—681no—
667C2×C42—681no—
668C2×C42—681no—
669C2×C42—681no—
670#95—174no—
671#95—174no—
672#95—174no—
673#95—174no—
674#95—174no—
675#95—342no—
676#95—342no—
677#95—342no—
678#95—342no—
679#95—342no—
680#95—342no—
681#95—342no—
682#95—342no—
683#95—342no—
684#95—681no—
685#95—681no—
686#95C2×Dic1714yescomplemented
687#95C2×Dic1714yescomplemented
688C17#1381411yescharacteristic, complemented, Sylow
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C2×C4×D1712yes—
698C24C2×C4×D1712yes—
699C24D4×D1712yes—
700C24#6325412yes—
701C24Q8×D1712yes—
702C24#6325612yes—
703C24C22×Dic1712yes—
704C24C23×D1711yescharacteristic
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—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—172no—
743C22×C4—172no—
744C22×C4—172no—
745C22×C4—172no—
746C22×C4—172no—
747C22×C4—172no—
748C22×C4—172no—
749C22×C4—172no—
750C22×C4—172no—
751C22×C4—172no—
752C22×C4—172no—
753C22×C4—172no—
754C22×C4—172no—
755C22×C4—172no—
756C22×C4—172no—
757C22×C4—172no—
758C22×C4—348no—
759C22×C4—348no—
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—341no—
772C22×C4—341no—
773C22×C4—341no—
774C22×C4—341no—
775C22×C4—341no—
776C22×C4—341no—
777C22×C4—341no—
778C22×C4—341no—
779C22×C4—341no—
780C22×C4—341no—
781C22×C4—341no—
782C22×C4—341no—
783C22×C4—341no—
784C22×C4—341no—
785C22×C4—341no—
786C22×C4—341no—
787C22×C4—341no—
788C22×C4—341no—
789C22×C4—341no—
790C22×C4—341no—
791C22×C4—341no—
792C22×C4—341no—
793C22×C4—341no—
794C22×C4—341no—
795C22×C4—341no—
796C22×C4—341no—
797C22×C4—341no—
798C22×C4—341no—
799C22×C4—341no—
800C22×C4—348no—
801C22×C4—348no—
802C22×C4—684no—
803C22×C4—684no—
804C22×C4—684no—
805C22×C4—684no—
806C22×C4—684no—
807C22×C4—684no—
808C22×C4—684no—
809C22×C4—684no—
810C22×C4—684no—
811C22×C4—684no—
812C22×C4C2×C4×D1712yes—
813C22×C4C2×C4×D1712yes—
814C22×C4C2×C4×D1712yes—
815C22×C4C2×C4×D1712yes—
816C22×C4D4×D1712yes—
817C22×C4#6325412yes—
818C22×C4C22×Dic1712yes—
819C22×C4C22×Dic1712yes—
820C22×C4C22×Dic1712yes—
821C22×C4C22×Dic1712yes—
822C22×C4C22×Dic1712yes—
823C22×C4C22×Dic1712yes—
824C4⋊C4—28no—
825C4⋊C4—44no—
826C4⋊C4—348no—
827C4⋊C4—684no—
828C22⋊C4—28no—
829C22⋊C4—1716no—
830C22⋊C4—348no—
831C22⋊C4C4×Dic17116yescomplemented
832C42—348no—
833C42—684no—
834C42—684no—
835C42—684no—
836C42—684no—
837C42—684no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23#1058757314yes—
867C23C4⋊C4×D1714yes—
868C23#1058757814yes—
869C23#1058757914yes—
870C23C2×C4×Dic1714yes—
871C23D4×Dic1714yes—
872C23Q8×Dic1714yes—
873C23C22×C4×D1711yescharacteristic
874C23C22×C4×D1711yescharacteristic
875C23C2×D4×D1711yescharacteristic
876C23C2×D4×D1711yescharacteristic
877C23C2×#6325411yescharacteristic
878C23C2×#6325411yescharacteristic
879C23#1058769111yescharacteristic
880C23#1058769111yescharacteristic
881C23C2×Q8×D1711yescharacteristic
882C23C2×#6325611yescharacteristic
883C23#41×D1711yescharacteristic
884C23#41×D1711yescharacteristic
885C23#1058769611yescharacteristic
886C23#1058769711yescharacteristic
887C23C23×Dic1711yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—416no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—174no—
929C2×C4—174no—
930C2×C4—174no—
931C2×C4—174no—
932C2×C4—342no—
933C2×C4—342no—
934C2×C4—342no—
935C2×C4—342no—
936C2×C4—342no—
937C2×C4—342no—
938C2×C4—342no—
939C2×C4—342no—
940C2×C4—342no—
941C2×C4—342no—
942C2×C4—342no—
943C2×C4—342no—
944C2×C4—342no—
945C2×C4—342no—
946C2×C4—342no—
947C2×C4—342no—
948C2×C4—342no—
949C2×C4—342no—
950C2×C4—342no—
951C2×C4—342no—
952C2×C4—342no—
953C2×C4—342no—
954C2×C4—342no—
955C2×C4—342no—
956C2×C4—342no—
957C2×C4—342no—
958C2×C4—342no—
959C2×C4—342no—
960C2×C4—342no—
961C2×C4—342no—
962C2×C4—342no—
963C2×C4—342no—
964C2×C4—342no—
965C2×C4—342no—
966C2×C4—342no—
967C2×C4—342no—
968C2×C4—6816no—
969C2×C4—6816no—
970C2×C4—681no—
971C2×C4—681no—
972C2×C4—681no—
973C2×C4—681no—
974C2×C4—681no—
975C2×C4—681no—
976C2×C4—681no—
977C2×C4—681no—
978C2×C4—681no—
979C2×C4—681no—
980C2×C4—681no—
981C2×C4—681no—
982C2×C4—681no—
983C2×C4—681no—
984C2×C4—681no—
985C2×C4—681no—
986C2×C4C2×C4×Dic1714yes—
987C2×C4C2×C4×Dic1714yes—
988C2×C4D4×Dic1714yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22C4⋊C4×Dic1718yescomplemented
1004C22C22×C4×Dic1711yescharacteristic
1005C22C2×C4⋊C4×D1711yescharacteristic
1006C22C2×#1058757811yescharacteristic
1007C22C4×D4×D1711yescharacteristic
1008C22C4×D4×D1711yescharacteristic
1009C22C2×#1058757911yescharacteristic
1010C22C2×D4×Dic1711yescharacteristic
1011C22C2×D4×Dic1711yescharacteristic
1012C22C2×#1058757311yescharacteristic
1013C22C2×Q8×Dic1711yescharacteristic
1014C22C4×#6325411yescharacteristic
1015C22C4×#6325411yescharacteristic
1016C22#41×Dic1711yescharacteristic
1017C22#1176328111yescharacteristic
1018C22#1176328111yescharacteristic
1019C22#1176328411yescharacteristic
1020C22#1176328811yescharacteristic
1021C22#1176328811yescharacteristic
1022C22#1176329211yescharacteristic
1023C22#1176344111yescharacteristic
1024C22#1176344611yescharacteristic
1025C22#1176344611yescharacteristic
1026C22#1176345011yescharacteristic
1027C22#1176345111yescharacteristic
1028C22#1176345711yescharacteristic
1029C22#1176347211yescharacteristic
1030C22#1176348211yescharacteristic
1031C22#1176348611yescharacteristic
1032C22#1176348611yescharacteristic
1033C22#1176349011yescharacteristic
1034C22#1176349611yescharacteristic
1035C22#1176350111yescharacteristic
1036C22#1176351311yescharacteristic
1037C22#1176351311yescharacteristic
1038C22#1176351711yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—344no—
1046C4—344no—
1047C4—344no—
1048C4—344no—
1049C4—682no—
1050C4—682no—
1051C4—682no—
1052C4—682no—
1053C2—28no—
1054C2C2×C4⋊C4×Dic1711yescharacteristic
1055C2C4×D4×Dic1711yescharacteristic
1056C2#1453114511yescharacteristic
1057C2#1453163111yescharacteristic
1058C2#1453164211yescharacteristic
1059C2#1453168211yescharacteristic
1060C2#1453169011yescharacteristic
1061C2#1453176011yescharacteristic
1062C2#1453176811yescharacteristic
1063C2#1453177411yescharacteristic
1064C2#1453178011yescharacteristic
1065C2#1453178411yescharacteristic
1066C2#1453179311yescharacteristic
1067C2#1453186511yescharacteristic
1068C2#1453186911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC2×C17×#385C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#385D17
hypocenterC17#13814
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic17C2semidirect
7. #14527018C2semidirect
8. #14527018C2semidirect
9. #14527016C2semidirect
10. #14527016C2semidirect
11. #14527013C2semidirect
12. #14527009C2semidirect
14. #95×Dic17C2semidirect
28. #11762684C4semidirect
31. C22⋊C4×Dic17C4semidirect
55. C17×#385C4semidirect
98. C2×C4⋊C4×C17C2×C4semidirect
99. C2×C4⋊C4×C17C2×C4semidirect
116. C2×C4⋊Dic17C2×C4semidirect
117. C2×C4⋊Dic17C2×C4semidirect
134. C2×C4×Dic17C2×C4semidirect
135. C2×C4×Dic17C2×C4semidirect
136. C17×#95C2×C4semidirect
137. C17×#95C2×C4semidirect
149. #10587502C2×C4semidirect
150. #10587502C2×C4semidirect
151. #10587502C2×C4semidirect
152. #10587502C2×C4semidirect
292. C22⋊C4×C17C42semidirect
294. C22⋊Dic17C4⋊C4semidirect
484. C22×C17C4×C4⋊C4semidirect
552. #385Dic17semidirect
638. C2×C4⋊C4C2×Dic17semidirect
639. C2×C4⋊C4C2×Dic17semidirect
686. #95C2×Dic17semidirect
687. #95C2×Dic17semidirect
688. C17#13814semidirect
831. C22⋊C4C4×Dic17semidirect
1003. C22C4⋊C4×Dic17semidirect

Maximal subgroups

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

subgroupindex
C2×#117626842
C2×C4⋊C4×Dic172
C2×C22⋊C4×Dic172
C2×C4×C22⋊Dic172
C22×#105875022
#145270182
#145270162
#145270132
#145270092
#145270062
#95×Dic172
C2×C17×#3852
#1381417