Finite Group Databasebeta

← #16955754

Subgroups — #16955754

Order 4352.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762666C211yesmaximal, characteristic
2C2×C4×#63227C211yesmaximal, characteristic
3C2×#11762656C211yesmaximal, characteristic
4C2×#11762656C211yesmaximal, characteristic
5C2×#95×D17C211yesmaximal, characteristic
6#14527018C211yesmaximal, characteristic, complemented
7#14527018C211yesmaximal, characteristic, complemented
8#14527016C211yesmaximal, characteristic, complemented
9#14527010C211yesmaximal, characteristic, complemented
10#14527008C211yesmaximal, characteristic, complemented
11#14527005C211yesmaximal, characteristic
12#14527005C211yesmaximal, characteristic
13C4×#10587502C211yesmaximal, characteristic, complemented
14#95×Dic17C211yesmaximal, characteristic, complemented
15C17×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×C4×Dic17C2211yescharacteristic
25C22×C4×Dic17C2211yescharacteristic
26C22×C4×Dic17C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29#11762666C418yescomplemented
30C4×#63227—24no—
31#11762656—24no—
32#11762656C418yescomplemented
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
48#95×D17C418yescomplemented
49C22×C4⋊C4×C17C2211yescharacteristic
50C22×C42×C17C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C24×D17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C22×C4×D17—22no—
72C22×C4×D17—22no—
73C22×C4×D17—22no—
74C22×C4×D17—22no—
75C22×C4×D17—22no—
76C22×C4×D17—22no—
77C22×C4×D17—22no—
78C22×C4×D17—22no—
79C22×C4×D17—41no—
80C22×C4×D17—41no—
81C22×C4×D17—41no—
82C22×C4×D17—41no—
83C22×C4×D17—41no—
84C22×C4×D17—41no—
85C22×C4×D17—41no—
86C22×C4×D17—41no—
87C22×C4×D17C2×C414yes—
88C22×C4×D17C2×C414yes—
89C22×C4×D17C2×C414yes—
90C22×C4×D17C2×C414yes—
91C22×C4×D17C2×C414yes—
92C2×C4⋊C4×C17—41no—
93C2×C4⋊C4×C17—41no—
94C2×C4⋊C4×C17C2×C414yescomplemented
95C2×C42×C17—22no—
96C2×C42×C17—22no—
97C2×C42×C17—41no—
98C2×#63227—22no—
99C2×#63227—22no—
100C2×#63227—22no—
101C2×#63227—22no—
102C2×#63227—22no—
103C2×#63227—22no—
104C2×#63227C2×C414yes—
105C2×#63227C2×C414yes—
106C2×#63227C2×C414yes—
107C2×#63227C2×C414yes—
108C2×#63227D414yes—
109C2×#63227Q814yes—
110C2×C4⋊Dic17—41no—
111C2×C4⋊Dic17—41no—
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—41no—
120C2×C4×Dic17—41no—
121C2×C4×Dic17—41no—
122C2×C4×Dic17—41no—
123C2×C4×Dic17—41no—
124C2×C4×Dic17—41no—
125C2×C4×Dic17—41no—
126C2×C4×Dic17C2×C414yescomplemented
127C2×C4×Dic17C2×C414yescomplemented
128C17×#95—22no—
129C17×#95—22no—
130C17×#95—41no—
131C17×#95C2×C414yes—
132C17×#95C2×C414yescomplemented
133#10587502—22no—
134#10587502—22no—
135#10587502—22no—
136#10587502—22no—
137#10587502—22no—
138#10587502—22no—
139#10587502—41no—
140#10587502—41no—
141#10587502—41no—
142#10587502C2×C414yes—
143#10587502C2×C414yes—
144#10587502C2×C414yes—
145#10587502C2×C414yescomplemented
146#10587502C2×C414yescomplemented
147#10587502C2×C414yescomplemented
148C24×C17C2411yescharacteristic
149C23×D17—21no—
150C23×D17—21no—
151C23×D17—21no—
152C23×D17—21no—
153C23×D17—21no—
154C23×D17—21no—
155C23×D17—21no—
156C23×D17—21no—
157C23×D17C22×C412yes—
158C23×D17C22×C412yes—
159C23×D17C22×C412yes—
160C23×D17C2×D412yes—
161C23×D17C2×Q812yes—
162C23×D17#4112yes—
163C23×D17#4112yes—
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×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×C17C22×C412yes—
201C22×C4×C17C22×C412yes—
202C22×C4×C17C22×C412yes—
203C22×C4×C17C22×C412yes—
204C22×C4×C17C22×C412yes—
205C22×C4×C17C22×C412yes—
206C22×C4×C17C22×C412yes—
207C22×C4×C17C22×C412yes—
208C22×C4×C17C22×C412yes—
209C22×C4×C17C2×D412yes—
210C22×C4×C17C2×Q812yes—
211C22×C4×C17#4112yes—
212C22×C4×C17#4112yes—
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—21no—
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×Dic17C22×C412yes—
258C22×Dic17C2×D412yes—
259C22×Dic17C2×Q812yes—
260C22×Dic17#4112yes—
261C22×Dic17#4112yes—
262C2×C4×D17—28no—
263C2×C4×D17—28no—
264C2×C4×D17—28no—
265C2×C4×D17—28no—
266C2×C4×D17—44no—
267C2×C4×D17—44no—
268C2×C4×D17—44no—
269C2×C4×D17—44no—
270C2×C4×D17—44no—
271C2×C4×D17—44no—
272C2×C4×D17—44no—
273C2×C4×D17—44no—
274C2×C4×D17—44no—
275C2×C4×D17—44no—
276C2×C4×D17—44no—
277C2×C4×D17—44no—
278C2×C4×D17—44no—
279C2×C4×D17—44no—
280C2×C4×D17—44no—
281C2×C4×D17—44no—
282C2×C4×D17C42116yescomplemented
283C4⋊C4×C17—44no—
284C42×C17—44no—
285#63227—28no—
286#63227—28no—
287#63227—28no—
288#63227C4⋊C4116yescomplemented
289C4⋊Dic17—44no—
290C4×Dic17—44no—
291C4×Dic17—44no—
292C4×Dic17—44no—
293C4×Dic17—44no—
294C4×Dic17—44no—
295#13802—171nomaximal, Sylow
296C23×C17C23×C411yescharacteristic
297C23×C17C23×C411yescharacteristic
298C23×C17C23×C411yescharacteristic
299C23×C17C22×D411yescharacteristic
300C23×C17C22×Q811yescharacteristic
301C23×C17C2×#4111yescharacteristic
302C23×C17C2×#4111yescharacteristic
303C23×C17C2×#4111yescharacteristic
304C23×C17C2×#4111yescharacteristic
305C23×C17C2×#4111yescharacteristic
306C23×C17C2×#4111yescharacteristic
307C23×C17H(5,𝔽2)11yescharacteristic
308C23×C17H(5,𝔽2)11yescharacteristic
309C23×C17H(5,𝔽2)11yescharacteristic
310C23×C17H(5,𝔽2)11yescharacteristic
311C22×D17—22no—
312C22×D17—22no—
313C22×D17—22no—
314C22×D17—22no—
315C22×D17—22no—
316C22×D17—22no—
317C22×D17—22no—
318C22×D17—22no—
319C22×D17—22no—
320C22×D17—22no—
321C22×D17—22no—
322C22×D17—22no—
323C22×D17—22no—
324C22×D17—22no—
325C22×D17—22no—
326C22×D17—22no—
327C22×D17—22no—
328C22×D17—22no—
329C22×D17—22no—
330C22×D17—22no—
331C22×D17—22no—
332C22×D17—22no—
333C22×D17—22no—
334C22×D17—22no—
335C22×D17—22no—
336C22×D17—22no—
337C22×D17—22no—
338C22×D17—22no—
339C22×D17C2×C4214yes—
340C22×D17C2×C4⋊C414yes—
341C22×D17#11714yes—
342C22×D17C4×D414yes—
343C22×D17C4×D414yes—
344C22×D17C4×Q814yes—
345C22×D17C4×Q814yes—
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—22no—
371C2×C4×C17—22no—
372C2×C4×C17—22no—
373C2×C4×C17—22no—
374C2×C4×C17—22no—
375C2×C4×C17—22no—
376C2×C4×C17—41no—
377C2×C4×C17—41no—
378C2×C4×C17—41no—
379C2×C4×C17—41no—
380C2×C4×C17—41no—
381C2×C4×C17—41no—
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×C17C2×C4214yes—
393C2×C4×C17C2×C4⋊C414yes—
394C2×C4×C17#11714yes—
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—22no—
419C2×Dic17—22no—
420C2×Dic17—22no—
421C2×Dic17—22no—
422C2×Dic17—22no—
423C2×Dic17—22no—
424C2×Dic17—22no—
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×Dic17—41no—
436C2×Dic17—41no—
437C2×Dic17—41no—
438C2×Dic17—41no—
439C2×Dic17—41no—
440C2×Dic17—41no—
441C2×Dic17C2×C4214yes—
442C2×Dic17C2×C4⋊C414yes—
443C2×Dic17#11714yes—
444C4×D17—416no—
445C4×D17—416no—
446C4×D17—416no—
447C2×#380—171no—
448C2×C4×C22⋊C4—171no—
449C2×C4×C22⋊C4—171no—
450C2×C4×C22⋊C4—171no—
451C22×#95—171no—
452#1436—171no—
453#1436—171no—
454#1436—171no—
455#1436D1711yescharacteristic, complemented
456#1434—171no—
457#1434—171no—
458C22⋊#95—171no—
459C22⋊#95—171no—
460C4×#95—171no—
461C4×#95—171no—
462C22×C17C22×C4211yescharacteristic
463C22×C17C22×C4⋊C411yescharacteristic
464C22×C17C2×#11711yescharacteristic
465C22×C17C2×#11711yescharacteristic
466C22×C17C2×#11711yescharacteristic
467C22×C17C2×C4×D411yescharacteristic
468C22×C17C2×C4×D411yescharacteristic
469C22×C17C2×C4×Q811yescharacteristic
470C22×C17C2×C4×Q811yescharacteristic
471C22×C17C4×#4111yescharacteristic
472C22×C17C4×#4111yescharacteristic
473C22×C17C4×#4111yescharacteristic
474C22×C17C4×#4111yescharacteristic
475C22×C17#51811yescharacteristic
476C22×C17#51811yescharacteristic
477C22×C17#51811yescharacteristic
478C22×C17#51811yescharacteristic
479C22×C17#51811yescharacteristic
480C22×C17#51811yescharacteristic
481C22×C17#54611yescharacteristic
482C22×C17#54611yescharacteristic
483C22×C17#54611yescharacteristic
484C22×C17#54611yescharacteristic
485C22×C17#55111yescharacteristic
486C22×C17#55111yescharacteristic
487C22×C17#55111yescharacteristic
488C22×C17#55111yescharacteristic
489C22×C17#55311yescharacteristic
490C22×C17#55311yescharacteristic
491C22×C17#55311yescharacteristic
492C22×C17#55311yescharacteristic
493C22×C17#55411yescharacteristic
494C22×C17#55411yescharacteristic
495C22×C17#55411yescharacteristic
496C22×C17#55411yescharacteristic
497C2×D17—24no—
498C2×D17—24no—
499C2×D17—24no—
500C2×D17—24no—
501C2×D17—24no—
502C2×D17—24no—
503C2×D17—24no—
504C2×D17—24no—
505C2×D17—24no—
506C2×D17—24no—
507C2×D17—24no—
508C2×D17—24no—
509C2×D17—24no—
510C2×D17—24no—
511C2×D17C4×C4⋊C418yes—
512C4×C17—24no—
513C4×C17—24no—
514C4×C17—24no—
515C4×C17—42no—
516C4×C17—42no—
517C4×C17—42no—
518C4×C17—42no—
519Dic17—24no—
520Dic17—24no—
521Dic17—24no—
522Dic17—42no—
523Dic17—42no—
524Dic17—42no—
525Dic17—42no—
526C24×C4—171no—
527C24×C4—171no—
528C24×C4—171no—
529C22×C4⋊C4—171no—
530C22×C4⋊C4C2×D1711yescharacteristic
531C22×C22⋊C4—171no—
532C22×C22⋊C4—171no—
533C22×C22⋊C4—171no—
534C22×C22⋊C4—171no—
535C22×C42—171no—
536C22×C42—171no—
537C22×C42—171no—
538C22×C42—171no—
539C22×C42—171no—
540C22×C42C2×D1711yescharacteristic
541#380—178no—
542C4×C22⋊C4—178no—
543C4×C22⋊C4—344no—
544C4×C22⋊C4—344no—
545C2×#95—171no—
546C2×#95—171no—
547C2×#95—171no—
548C2×#95—171no—
549C2×#95—171no—
550C2×#95—171no—
551C2×#95—178no—
552C2×#95—171no—
553C2×#95—171no—
554C2×#95—171no—
555C2×#95—171no—
556C2×#95—171no—
557C2×#95—171no—
558C2×#95—171no—
559C2×#95—171no—
560C2×#95—171no—
561C2×#95C2×D1711yescharacteristic
562C2×#95C2×D1711yescharacteristic
563C2×#95C2×D1711yescharacteristic
564C2×#95C2×D1711yescharacteristic
565C2×#95C2×D1711yescharacteristic
566C2×C17C2×C4×C4⋊C411yescharacteristic
567C2×C17C4×#11711yescharacteristic
568C2×C17#227311yescharacteristic
569C2×C17#234211yescharacteristic
570C2×C17#234211yescharacteristic
571C2×C17#234511yescharacteristic
572C2×C17#234511yescharacteristic
573C2×C17#234911yescharacteristic
574C2×C17#234911yescharacteristic
575C2×C17#235311yescharacteristic
576C2×C17#235311yescharacteristic
577C2×C17#236411yescharacteristic
578C2×C17#236411yescharacteristic
579C2×C17#236811yescharacteristic
580C2×C17#236811yescharacteristic
581D17—28no—
582C25—171no—
583C23×C4—171no—
584C23×C4—171no—
585C23×C4—171no—
586C23×C4—174no—
587C23×C4—174no—
588C23×C4—174no—
589C23×C4—171no—
590C23×C4—171no—
591C23×C4—171no—
592C23×C4—171no—
593C23×C4—174no—
594C23×C4—174no—
595C23×C4—342no—
596C23×C4—342no—
597C23×C4—342no—
598C23×C4—342no—
599C23×C4—342no—
600C23×C4—342no—
601C23×C4—342no—
602C23×C4—342no—
603C23×C4—681no—
604C23×C4—681no—
605C23×C4—681no—
606C23×C4—681no—
607C23×C4—681no—
608C23×C4—681no—
609C23×C4—681no—
610C23×C4—681no—
611C23×C4C22×D1711yescharacteristic
612C23×C4C22×D1711yescharacteristic
613C23×C4C22×D1711yescharacteristic
614C23×C4C22×D1711yescharacteristic
615C23×C4C22×D1711yescharacteristic
616C23×C4C22×D1711yescharacteristic
617C23×C4C22×D1711yescharacteristic
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—174no—
621C2×C4⋊C4—681no—
622C2×C4⋊C4—681no—
623C2×C4⋊C4C4×D1714yescomplemented
624C2×C22⋊C4—174no—
625C2×C22⋊C4—174no—
626C2×C22⋊C4—174no—
627C2×C22⋊C4—174no—
628C2×C22⋊C4—174no—
629C2×C22⋊C4—174no—
630C2×C22⋊C4—342no—
631C2×C22⋊C4—342no—
632C2×C22⋊C4—342no—
633C2×C22⋊C4—342no—
634C2×C22⋊C4—342no—
635C2×C22⋊C4—342no—
636C2×C42—22no—
637C2×C42—22no—
638C2×C42—41no—
639C2×C42—174no—
640C2×C42—174no—
641C2×C42—342no—
642C2×C42—342no—
643C2×C42—342no—
644C2×C42—342no—
645C2×C42—342no—
646C2×C42—342no—
647C2×C42—681no—
648C2×C42—681no—
649C2×C42—681no—
650C2×C42—681no—
651C2×C42—681no—
652C2×C42—681no—
653C2×C42—681no—
654#95—22no—
655#95—22no—
656#95—41no—
657#95—174no—
658#95—174no—
659#95—174no—
660#95—174no—
661#95—174no—
662#95—174no—
663#95—342no—
664#95—342no—
665#95—342no—
666#95—342no—
667#95—342no—
668#95—342no—
669#95—681no—
670#95—681no—
671#95—681no—
672#95C4×D1714yes—
673#95C4×D1714yescomplemented
674C17#1380211yescharacteristic, complemented, Sylow
675C24—172no—
676C24—172no—
677C24—172no—
678C24—172no—
679C24—172no—
680C24—172no—
681C24—172no—
682C24—341no—
683C24—341no—
684C24—341no—
685C24—341no—
686C24—341no—
687C24—341no—
688C24—341no—
689C24—341no—
690C24C23×D1711yescharacteristic
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—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—172no—
728C22×C4—172no—
729C22×C4—172no—
730C22×C4—172no—
731C22×C4—172no—
732C22×C4—172no—
733C22×C4—172no—
734C22×C4—172no—
735C22×C4—172no—
736C22×C4—1716no—
737C22×C4—172no—
738C22×C4—172no—
739C22×C4—172no—
740C22×C4—172no—
741C22×C4—348no—
742C22×C4—348no—
743C22×C4—348no—
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—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—348no—
781C22×C4—684no—
782C22×C4—684no—
783C22×C4—684no—
784C22×C4—684no—
785C22×C4—684no—
786C22×C4—684no—
787C22×C4—684no—
788C22×C4—684no—
789C22×C4—684no—
790C22×C4—684no—
791C22×C4—684no—
792C22×C4—684no—
793C22×C4—684no—
794C22×C4—684no—
795C22×C4—684no—
796C22×C4—684no—
797C22×C4C2×C4×D1712yes—
798C22×C4C2×C4×D1712yes—
799C22×C4C2×C4×D1712yes—
800C22×C4C2×C4×D1712yes—
801C22×C4C2×C4×D1712yes—
802C22×C4C2×C4×D1712yes—
803C22×C4C2×C4×D1712yes—
804C22×C4C2×C4×D1712yes—
805C22×C4C2×C4×D1712yes—
806C22×C4D4×D1712yes—
807C22×C4#6325412yes—
808C22×C4Q8×D1712yes—
809C22×C4#6325612yes—
810C4⋊C4—44no—
811C4⋊C4—684no—
812C22⋊C4—1716no—
813C22⋊C4—348no—
814C22⋊C4—348no—
815C22⋊C4—348no—
816C42—44no—
817C42—684no—
818C42—684no—
819C42—684no—
820C42—684no—
821C42—684no—
822C23—174no—
823C23—174no—
824C23—174no—
825C23—174no—
826C23—174no—
827C23—174no—
828C23—174no—
829C23—342no—
830C23—342no—
831C23—342no—
832C23—342no—
833C23—342no—
834C23—342no—
835C23—342no—
836C23—342no—
837C23—342no—
838C23—342no—
839C23—342no—
840C23—342no—
841C23—342no—
842C23—342no—
843C23—342no—
844C23—342no—
845C23—342no—
846C23—342no—
847C23—342no—
848C23—342no—
849C23—342no—
850C23—342no—
851C23—342no—
852C23—342no—
853C23—342no—
854C23—342no—
855C23—342no—
856C23—342no—
857C23C22×C4×D1711yescharacteristic
858C23C22×C4×D1711yescharacteristic
859C23C22×C4×D1711yescharacteristic
860C23C2×D4×D1711yescharacteristic
861C23C2×#6325411yescharacteristic
862C23#1058769111yescharacteristic
863C23#1058769111yescharacteristic
864C23C2×Q8×D1711yescharacteristic
865C23C2×#6325611yescharacteristic
866C23#41×D1711yescharacteristic
867C23#41×D1711yescharacteristic
868C23#41×D1711yescharacteristic
869C23#41×D1711yescharacteristic
870C23#1058769611yescharacteristic
871C23#1058769611yescharacteristic
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—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—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—174no—
919C2×C4—174no—
920C2×C4—174no—
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—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—6816no—
952C2×C4—6816no—
953C2×C4—6816no—
954C2×C4—681no—
955C2×C4—681no—
956C2×C4—681no—
957C2×C4—681no—
958C2×C4—681no—
959C2×C4—681no—
960C2×C4—681no—
961C2×C4—681no—
962C2×C4—681no—
963C2×C4—681no—
964C2×C4—681no—
965C2×C4—681no—
966C2×C4—681no—
967C2×C4—681no—
968C2×C4—681no—
969C2×C4—681no—
970C2×C4C42×D1714yes—
971C2×C4C4⋊C4×D1714yes—
972C2×C4#1058757814yes—
973C22—178no—
974C22—344no—
975C22—344no—
976C22—344no—
977C22—344no—
978C22—344no—
979C22—344no—
980C22—344no—
981C22—344no—
982C22—344no—
983C22—344no—
984C22—344no—
985C22—344no—
986C22—344no—
987C22—344no—
988C22C2×C42×D1711yescharacteristic
989C22C2×C4⋊C4×D1711yescharacteristic
990C22#117×D1711yescharacteristic
991C22#117×D1711yescharacteristic
992C22C2×#1058757811yescharacteristic
993C22C4×D4×D1711yescharacteristic
994C22C4×D4×D1711yescharacteristic
995C22C4×Q8×D1711yescharacteristic
996C22C4×Q8×D1711yescharacteristic
997C22C4×#6325411yescharacteristic
998C22C4×#6325411yescharacteristic
999C22C4×#6325611yescharacteristic
1000C22C4×#6325611yescharacteristic
1001C22#1176328111yescharacteristic
1002C22#1176328111yescharacteristic
1003C22#1176328111yescharacteristic
1004C22#1176328111yescharacteristic
1005C22#1176328211yescharacteristic
1006C22#1176328311yescharacteristic
1007C22#1176344611yescharacteristic
1008C22#1176345011yescharacteristic
1009C22#1176345111yescharacteristic
1010C22#1176345611yescharacteristic
1011C22#1176348211yescharacteristic
1012C22#1176348411yescharacteristic
1013C22#1176348611yescharacteristic
1014C22#1176348911yescharacteristic
1015C22#1176350411yescharacteristic
1016C22#1176350611yescharacteristic
1017C22#1176351011yescharacteristic
1018C22#1176351211yescharacteristic
1019C22#1176351311yescharacteristic
1020C22#1176351511yescharacteristic
1021C22#1176351711yescharacteristic
1022C22#1176352011yescharacteristic
1023C4—24no—
1024C4—24no—
1025C4—24no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4—344no—
1031C4—344no—
1032C4—344no—
1033C4—682no—
1034C4—682no—
1035C4—682no—
1036C4—682no—
1037C2—348no—
1038C2C4×C4⋊C4×D1711yescharacteristic
1039C2C4×#1058757811yescharacteristic
1040C2#1453113611yescharacteristic
1041C2#1453162811yescharacteristic
1042C2#1453163111yescharacteristic
1043C2#1453165811yescharacteristic
1044C2#1453166011yescharacteristic
1045C2#1453169011yescharacteristic
1046C2#1453169311yescharacteristic
1047C2#1453171911yescharacteristic
1048C2#1453172311yescharacteristic
1049C2#1453183011yescharacteristic
1050C2#1453183311yescharacteristic
1051C2#1453186311yescharacteristic
1052C2#1453186611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC17×#1436C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenter#1436D17
hypocenterC17#13802
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
6. #14527018C2semidirect
7. #14527018C2semidirect
8. #14527016C2semidirect
9. #14527010C2semidirect
10. #14527008C2semidirect
13. C4×#10587502C2semidirect
14. #95×Dic17C2semidirect
15. C17×#1436C2semidirect
29. #11762666C4semidirect
32. #11762656C4semidirect
48. #95×D17C4semidirect
94. C2×C4⋊C4×C17C2×C4semidirect
112. C2×C4⋊Dic17C2×C4semidirect
126. C2×C4×Dic17C2×C4semidirect
127. C2×C4×Dic17C2×C4semidirect
132. C17×#95C2×C4semidirect
145. #10587502C2×C4semidirect
146. #10587502C2×C4semidirect
147. #10587502C2×C4semidirect
282. C2×C4×D17C42semidirect
288. #63227C4⋊C4semidirect
455. #1436D17semidirect
623. C2×C4⋊C4C4×D17semidirect
673. #95C4×D17semidirect
674. C17#13802semidirect

Maximal subgroups

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

subgroupindex
C2×#117626662
C2×C4×#632272
C2×#117626562
C2×#95×D172
#145270182
#145270162
#145270102
#145270082
#145270052
C4×#105875022
#95×Dic172
C17×#14362
#1380217