Finite Group Databasebeta

← #16958123

Subgroups — #16958123

Order 4352.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587610C211yesmaximal, characteristic
2C2×#11762713C211yesmaximal, characteristic, complemented
3C2×#11762682C211yesmaximal, characteristic
4C2×C4×C22⋊Dic17C211yesmaximal, characteristic
5#14527054C211yesmaximal, characteristic, complemented
6#14527050C211yesmaximal, characteristic, complemented
7#14527036C211yesmaximal, characteristic, complemented
8#14527035C211yesmaximal, characteristic, complemented
9#14527018C211yesmaximal, characteristic, complemented
10#14527015C211yesmaximal, characteristic, complemented
11#14527012C211yesmaximal, characteristic, complemented
12#14527007C211yesmaximal, characteristic
13#14527007C211yesmaximal, characteristic
14#14527007C211yesmaximal, characteristic
15C22×C17×#95C211yesmaximal, characteristic
16C23×Dic34C2211yescharacteristic
17C2×#10587610—24no—
18C2×#10587610—24no—
19C2×#10587610C418yescomplemented
20C22×C4⋊Dic17C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×C22⋊Dic17C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31#11762713—24no—
32#11762682—24no—
33C4×C22⋊Dic17—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
51C24×C4×C17C2211yescharacteristic
52C24×C4×C17C2211yescharacteristic
53C2×C17×#95—24no—
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
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—22no—
64C23×C4×C17—22no—
65C23×C4×C17—22no—
66C23×C4×C17—22no—
67C23×C4×C17—22no—
68C23×C4×C17—22no—
69C23×C4×C17—22no—
70C23×C4×C17—22no—
71C23×C4×C17—22no—
72C23×C4×C17—41no—
73C23×C4×C17—41no—
74C23×C4×C17—41no—
75C23×C4×C17—41no—
76C23×C4×C17—41no—
77C23×C4×C17—41no—
78C23×C4×C17C2×C414yes—
79C23×C4×C17Q814yescomplemented
80C23×C4×C17C2311yescharacteristic
81C23×C4×C17C2311yescharacteristic
82C23×C4×C17C2311yescharacteristic
83C23×C4×C17C2311yescharacteristic
84C23×C4×C17C2311yescharacteristic
85C23×C4×C17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
88C23×Dic17C2311yescharacteristic
89C23×Dic17C2311yescharacteristic
90C23×Dic17C2311yescharacteristic
91C23×Dic17C2311yescharacteristic
92C23×Dic17C2311yescharacteristic
93C23×Dic17C2311yescharacteristic
94C22×Dic34—22no—
95C22×Dic34—22no—
96C22×Dic34—22no—
97C22×Dic34—22no—
98C22×Dic34—41no—
99C22×Dic34—41no—
100C22×Dic34C2×C414yescomplemented
101C2×C22⋊Dic17—22no—
102C2×C22⋊Dic17—22no—
103C2×C22⋊Dic17—22no—
104C2×C22⋊Dic17—22no—
105C2×C22⋊Dic17—22no—
106C2×C22⋊Dic17—22no—
107C2×C22⋊Dic17—22no—
108C2×C22⋊Dic17C2×C414yes—
109C2×C22⋊Dic17C2×C414yes—
110C2×C22⋊Dic17D414yes—
111C2×C22⋊Dic17D414yes—
112C2×C22⋊Dic17Q814yescomplemented
113C2×C4⋊Dic17—22no—
114C2×C4⋊Dic17—22no—
115C2×C4⋊Dic17C2×C414yescomplemented
116#10587610—232no—
117C2×#63225—22no—
118C2×#63225—22no—
119C2×#63225—22no—
120C2×#63225—22no—
121C2×#63225—22no—
122C2×#63225—22no—
123C2×#63225—22no—
124C2×#63225—22no—
125C2×#63225—41no—
126C2×#63225—41no—
127C2×#63225C2×C414yescomplemented
128C2×#63225C2×C414yescomplemented
129C2×C4×Dic17—22no—
130C2×C4×Dic17—22no—
131C2×C4×Dic17—22no—
132C2×C4×Dic17—22no—
133C2×C4×Dic17—41no—
134C2×C4×Dic17—41no—
135C17×#95—22no—
136C17×#95—22no—
137C17×#95—22no—
138C17×#95D414yes—
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—22no—
148#10587502—22no—
149#10587502—41no—
150#10587502—41no—
151#10587502—41no—
152#10587502—41no—
153#10587502—41no—
154#10587502—41no—
155C24×C17—21no—
156C24×C17—21no—
157C24×C17—21no—
158C24×C17—21no—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17—21no—
163C24×C17C22×C412yes—
164C24×C17C2×D412yes—
165C24×C17C2×D412yes—
166C24×C17C2×Q812yes—
167C24×C17C2×Q812yes—
168C24×C17#4112yes—
169C24×C17#4112yes—
170C24×C17C2411yescharacteristic
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—28no—
180C22×C4×C17—28no—
181C22×C4×C17—28no—
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×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—28no—
207C22×C4×C17—28no—
208C22×C4×C17—44no—
209C22×C4×C17—44no—
210C22×C4×C17—44no—
211C22×C4×C17—44no—
212C22×C4×C17—44no—
213C22×C4×C17—44no—
214C22×C4×C17—44no—
215C22×C4×C17—44no—
216C22×C4×C17—44no—
217C22×C4×C17—44no—
218C22×C4×C17—44no—
219C22×C4×C17—44no—
220C22×C4×C17—44no—
221C22×C4×C17—44no—
222C22×C4×C17—44no—
223C22×C4×C17—44no—
224C22×C4×C17C22×C412yes—
225C22×C4×C17C22×C412yes—
226C22×C4×C17C2×D412yes—
227C22×C4×C17C2×D412yes—
228C22×C4×C17C2×D412yes—
229C22×C4×C17C2×Q812yes—
230C22×C4×C17C2×Q812yes—
231C22×C4×C17#4112yes—
232C22×C4×C17#4112yes—
233C22×C4×C17#4112yes—
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×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—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17—21no—
268C22×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—21no—
271C22×Dic17—21no—
272C22×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17—21no—
275C22×Dic17—21no—
276C22×Dic17—21no—
277C22×Dic17—21no—
278C22×Dic17—21no—
279C22×Dic17—21no—
280C22×Dic17C22×C412yes—
281C22×Dic17C22×C412yes—
282C22×Dic17C22×C412yes—
283C22×Dic17C22×C412yes—
284C22×Dic17C2×D412yes—
285C22×Dic17C2×D412yes—
286C22×Dic17C2×D412yes—
287C22×Dic17C2×D412yes—
288C22×Dic17C2×Q812yes—
289C22×Dic17C2×Q812yes—
290C2×Dic34—28no—
291C2×Dic34—28no—
292C2×Dic34—44no—
293C2×Dic34—44no—
294C2×Dic34—44no—
295C2×Dic34—44no—
296C2×Dic34—44no—
297C22⋊Dic17—28no—
298C22⋊Dic17—28no—
299C22⋊Dic17—44no—
300C22⋊Dic17C22⋊C4116yes—
301C4⋊Dic17—28no—
302#63225—28no—
303#63225—28no—
304#63225—44no—
305#63225—44no—
306C4×Dic17—44no—
307C4×Dic17—44no—
308#14052—171nomaximal, Sylow
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×C17—22no—
333C23×C17—22no—
334C23×C17—22no—
335C23×C17—22no—
336C23×C17—22no—
337C23×C17C2×C22⋊C414yes—
338C23×C17C4×Q814yes—
339C23×C17C4×Q814yes—
340C23×C17C22⋊Q814yes—
341C23×C17C22⋊Q814yes—
342C23×C17#12414yes—
343C23×C17C4⋊Q814yes—
344C23×C17C23×C411yescharacteristic
345C23×C17C22×D411yescharacteristic
346C23×C17C22×D411yescharacteristic
347C23×C17C22×D411yescharacteristic
348C23×C17C22×Q811yescharacteristic
349C23×C17C22×Q811yescharacteristic
350C23×C17C2×#4111yescharacteristic
351C23×C17C2×#4111yescharacteristic
352C23×C17C2×#4111yescharacteristic
353C23×C17C2×#4111yescharacteristic
354C23×C17C2×#4111yescharacteristic
355C23×C17H(5,𝔽2)11yescharacteristic
356C23×C17H(5,𝔽2)11yescharacteristic
357C23×C17H(5,𝔽2)11yescharacteristic
358C23×C172−1+411yescharacteristic
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—22no—
382C2×C4×C17—22no—
383C2×C4×C17—416no—
384C2×C4×C17—416no—
385C2×C4×C17—416no—
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×C17—41no—
395C2×C4×C17—41no—
396C2×C4×C17—41no—
397C2×C4×C17—41no—
398C2×C4×C17—41no—
399C2×C4×C17—41no—
400C2×C4×C17—41no—
401C2×C4×C17—41no—
402C2×C4×C17C4×D414yes—
403C2×C4×C17C22⋊Q814yescomplemented
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—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×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×Dic17—41no—
452C2×Dic17—41no—
453C2×Dic17—41no—
454C2×Dic17—41no—
455C2×Dic17—41no—
456C2×Dic17—41no—
457C2×Dic17—41no—
458C2×Dic17C2×C22⋊C414yes—
459C2×Dic17C2×C22⋊C414yes—
460Dic34—416no—
461C22×C22⋊Q8—171no—
462C2×#391—171no—
463C2×#385—171no—
464C2×C4×C22⋊C4—171no—
465C22×#95D1711yescharacteristic
466#1446—171no—
467#1445—171no—
468#1441—171no—
469#1441—171no—
470#1436—171no—
471#1436—171no—
472C4⋊#95—171no—
473C22⋊#95—171no—
474C22⋊#95—171no—
475C22⋊#95—171no—
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×C17—24no—
485C22×C17—24no—
486C22×C17—24no—
487C22×C17—24no—
488C22×C17—24no—
489C22×C17—24no—
490C22×C17#39118yescomplemented
491C22×C17C22×C22⋊C411yescharacteristic
492C22×C17C2×C4×D411yescharacteristic
493C22×C17C2×C4×Q811yescharacteristic
494C22×C17C2×C4×Q811yescharacteristic
495C22×C17C4×#4111yescharacteristic
496C22×C17#51811yescharacteristic
497C22×C17#52011yescharacteristic
498C22×C17C2×C22⋊Q811yescharacteristic
499C22×C17C2×C22⋊Q811yescharacteristic
500C22×C17C2×C22⋊Q811yescharacteristic
501C22×C17#52511yescharacteristic
502C22×C17C2×#12411yescharacteristic
503C22×C17#52911yescharacteristic
504C22×C17C2×C4⋊Q811yescharacteristic
505C22×C17#53311yescharacteristic
506C22×C17#53811yescharacteristic
507C22×C17#53911yescharacteristic
508C22×C17#54311yescharacteristic
509C22×C17#54411yescharacteristic
510C22×C17D4211yescharacteristic
511C22×C17D4211yescharacteristic
512C22×C17#54611yescharacteristic
513C22×C17#54611yescharacteristic
514C22×C17#54611yescharacteristic
515C22×C17#54611yescharacteristic
516C22×C17#54611yescharacteristic
517C22×C17#54711yescharacteristic
518C22×C17#54711yescharacteristic
519C22×C17D4×Q811yescharacteristic
520C22×C17#55111yescharacteristic
521C22×C17#55111yescharacteristic
522C22×C17#55211yescharacteristic
523C22×C17#55411yescharacteristic
524C22×C17#55411yescharacteristic
525C22×C17#55411yescharacteristic
526C4×C17—24no—
527C4×C17—24no—
528C4×C17—42no—
529C4×C17—42no—
530C4×C17—42no—
531C4×C17—42no—
532Dic17—24no—
533Dic17—24no—
534Dic17—42no—
535Dic17—42no—
536Dic17—42no—
537Dic17—42no—
538Dic17—81no—
539Dic17—81no—
540C23×Q8—171no—
541C24×C4C2×D1711yescharacteristic
542C24×C4C2×D1711yescharacteristic
543C24×C4C2×D1711yescharacteristic
544C2×C22⋊Q8—178no—
545C2×C22⋊Q8—344no—
546C2×C22⋊Q8—344no—
547C22×C4⋊C4—171no—
548C22×C4⋊C4—171no—
549C22×C4⋊C4—171no—
550C22×C4⋊C4—171no—
551C22×C4⋊C4—171no—
552C22×C22⋊C4—171no—
553C22×C22⋊C4—171no—
554C22×C22⋊C4—171no—
555C22×C22⋊C4—171no—
556C22×C42—171no—
557C22×C42—171no—
558#391—344no—
559#385—344no—
560C4×C22⋊C4—344no—
561C2×#95—24no—
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—171no—
574C2×#95—171no—
575C2×#95—171no—
576C2×#95—171no—
577C2×#95—171no—
578C2×#95C2×D1711yescharacteristic
579C2×#95C2×D1711yescharacteristic
580C2×#95C2×D1711yescharacteristic
581C2×#95C2×D1711yescharacteristic
582C2×C17—28no—
583C2×C17C2×#39111yescharacteristic
584C2×C17C4×C22⋊Q811yescharacteristic
585C2×C17#232911yescharacteristic
586C2×C17D4×C22⋊C411yescharacteristic
587C2×C17#233911yescharacteristic
588C2×C17#236011yescharacteristic
589C2×C17#236811yescharacteristic
590C2×C17#243711yescharacteristic
591C2×C17#243811yescharacteristic
592C2×C17#244011yescharacteristic
593C2×C17#244911yescharacteristic
594C2×C17#245011yescharacteristic
595C2×C17#247211yescharacteristic
596C2×C17#248811yescharacteristic
597C2×C17#254911yescharacteristic
598C25C22×D1711yescharacteristic
599C22×Q8—174no—
600C22×Q8—342no—
601C22×Q8—342no—
602C22×Q8—342no—
603C22×Q8—342no—
604C22×Q8—681no—
605C22×Q8—681no—
606C23×C4—22no—
607C23×C4—22no—
608C23×C4—22no—
609C23×C4—22no—
610C23×C4—22no—
611C23×C4—22no—
612C23×C4—22no—
613C23×C4—22no—
614C23×C4—22no—
615C23×C4—22no—
616C23×C4—22no—
617C23×C4—22no—
618C23×C4—22no—
619C23×C4—41no—
620C23×C4—41no—
621C23×C4—41no—
622C23×C4—41no—
623C23×C4—41no—
624C23×C4—41no—
625C23×C4—171no—
626C23×C4—171no—
627C23×C4—171no—
628C23×C4—171no—
629C23×C4—171no—
630C23×C4—171no—
631C23×C4—171no—
632C23×C4—171no—
633C23×C4Dic3414yescomplemented
634C23×C4C4×D1714yes—
635C23×C4C22×D1711yescharacteristic
636C23×C4C22×D1711yescharacteristic
637C23×C4C22×D1711yescharacteristic
638C23×C4C22×D1711yescharacteristic
639C23×C4C22×D1711yescharacteristic
640C23×C4C22×D1711yescharacteristic
641C22⋊Q8—3432no—
642C2×C4⋊C4—174no—
643C2×C4⋊C4—174no—
644C2×C4⋊C4—174no—
645C2×C4⋊C4—342no—
646C2×C4⋊C4—342no—
647C2×C4⋊C4—342no—
648C2×C4⋊C4—342no—
649C2×C4⋊C4—342no—
650C2×C4⋊C4—342no—
651C2×C4⋊C4—342no—
652C2×C4⋊C4—342no—
653C2×C4⋊C4—342no—
654C2×C4⋊C4—342no—
655C2×C4⋊C4—681no—
656C2×C4⋊C4—681no—
657C2×C22⋊C4—174no—
658C2×C22⋊C4—174no—
659C2×C22⋊C4—174no—
660C2×C22⋊C4—174no—
661C2×C22⋊C4—174no—
662C2×C22⋊C4—342no—
663C2×C22⋊C4—342no—
664C2×C22⋊C4—342no—
665C2×C22⋊C4—342no—
666C2×C22⋊C4—342no—
667C2×C22⋊C4—342no—
668C2×C22⋊C4—342no—
669C2×C42—342no—
670C2×C42—342no—
671C2×C42—342no—
672C2×C42—342no—
673C2×C42—681no—
674C2×C42—681no—
675#95—22no—
676#95—22no—
677#95—22no—
678#95—342no—
679#95—342no—
680#95—342no—
681#95—342no—
682#95—342no—
683#95—342no—
684#95—342no—
685#95—342no—
686#95—342no—
687#95—342no—
688#95—681no—
689#95—681no—
690#95—681no—
691#95—681no—
692#95—681no—
693#95—681no—
694#95C22⋊D1714yes—
695C17#1405211yescharacteristic, complemented, Sylow
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24C2×Dic3412yes—
705C24C2×C4×D1712yes—
706C24#6325212yes—
707C24D4×D1712yes—
708C24D4×D1712yes—
709C24#6325412yes—
710C24Q8×D1712yes—
711C24C23×D1711yescharacteristic
712C2×Q8—348no—
713C2×Q8—348no—
714C2×Q8—684no—
715C2×Q8—684no—
716C2×Q8—684no—
717C2×Q8—684no—
718C2×Q8—684no—
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—28no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—28no—
753C22×C4—28no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—172no—
773C22×C4—172no—
774C22×C4—172no—
775C22×C4—172no—
776C22×C4—172no—
777C22×C4—172no—
778C22×C4—172no—
779C22×C4—172no—
780C22×C4—172no—
781C22×C4—172no—
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—341no—
801C22×C4—341no—
802C22×C4—341no—
803C22×C4—341no—
804C22×C4—341no—
805C22×C4—341no—
806C22×C4—341no—
807C22×C4—341no—
808C22×C4—341no—
809C22×C4—341no—
810C22×C4—341no—
811C22×C4—341no—
812C22×C4—341no—
813C22×C4—341no—
814C22×C4—341no—
815C22×C4—341no—
816C22×C4—341no—
817C22×C4—341no—
818C22×C4—341no—
819C22×C4—341no—
820C22×C4—341no—
821C22×C4—341no—
822C22×C4—341no—
823C22×C4—341no—
824C22×C4—341no—
825C22×C4—341no—
826C22×C4—341no—
827C22×C4—341no—
828C22×C4C2×Dic3412yes—
829C22×C4C2×Dic3412yes—
830C22×C4C2×C4×D1712yes—
831C22×C4C2×C4×D1712yes—
832C22×C4#6325212yes—
833C22×C4#6325212yes—
834C22×C4#6325212yes—
835C22×C4C2×C22⋊D1712yes—
836C22×C4C2×C22⋊D1712yes—
837C22×C4C2×C22⋊D1712yes—
838C4⋊C4—348no—
839C4⋊C4—348no—
840C4⋊C4—348no—
841C4⋊C4—684no—
842C4⋊C4—684no—
843C22⋊C4—1716no—
844C22⋊C4—348no—
845C22⋊C4—348no—
846C22⋊C4—684no—
847C42—684no—
848C42—684no—
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—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23C4×Dic3414yes—
878C23#1058756414yes—
879C23C22⋊C4×D1714yes—
880C23#1058757114yes—
881C23#1058757314yes—
882C23#1058757414yes—
883C23#1058758214yes—
884C23C22×Dic3411yescharacteristic
885C23C22×C4×D1711yescharacteristic
886C23C2×#6325211yescharacteristic
887C23C2×#6325211yescharacteristic
888C23C2×#6325211yescharacteristic
889C23C2×#6325211yescharacteristic
890C23C2×D4×D1711yescharacteristic
891C23C2×D4×D1711yescharacteristic
892C23C2×#6325411yescharacteristic
893C23#1058769111yescharacteristic
894C23#1058769111yescharacteristic
895C23#1058769111yescharacteristic
896C23C2×Q8×D1711yescharacteristic
897C23#1058769411yescharacteristic
898C23C22×C22⋊D1711yescharacteristic
899Q8—6816no—
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—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—416no—
925C2×C4—416no—
926C2×C4—416no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—174no—
944C2×C4—174no—
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—342no—
969C2×C4—681no—
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×C4—681no—
987C2×C4—681no—
988C2×C4—681no—
989C2×C4—681no—
990C2×C4—681no—
991C2×C4—681no—
992C2×C4—681no—
993C2×C4—681no—
994C2×C4—681no—
995C2×C4—681no—
996C2×C4—681no—
997C2×C4—681no—
998C2×C4—681no—
999C2×C4#1058761014yescomplemented
1000C2×C4C4×C22⋊D1714yes—
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—24no—
1005C22—24no—
1006C22—24no—
1007C22—24no—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22#1176271318yescomplemented
1016C22C2×C22⋊C4×D1711yescharacteristic
1017C22C2×C4×C22⋊D1711yescharacteristic
1018C22C2×#1058757311yescharacteristic
1019C22C2×C4×Dic3411yescharacteristic
1020C22C4×#6325211yescharacteristic
1021C22#1176328211yescharacteristic
1022C22#1176329011yescharacteristic
1023C22C2×#1058756411yescharacteristic
1024C22C2×#1058758211yescharacteristic
1025C22C2×#1058761011yescharacteristic
1026C22#1176332011yescharacteristic
1027C22C2×#1058757111yescharacteristic
1028C22#1176334311yescharacteristic
1029C22C2×#1058757411yescharacteristic
1030C22#1176336611yescharacteristic
1031C22#1176339711yescharacteristic
1032C22#1176340611yescharacteristic
1033C22#1176343511yescharacteristic
1034C22#1176344011yescharacteristic
1035C22D4×C22⋊D1711yescharacteristic
1036C22D4×C22⋊D1711yescharacteristic
1037C22#1176344911yescharacteristic
1038C22#1176344911yescharacteristic
1039C22#1176344911yescharacteristic
1040C22#1176344911yescharacteristic
1041C22#1176345311yescharacteristic
1042C22#1176346011yescharacteristic
1043C22#1176346011yescharacteristic
1044C22Q8×C22⋊D1711yescharacteristic
1045C22#1176348511yescharacteristic
1046C22#1176348511yescharacteristic
1047C22#1176349411yescharacteristic
1048C22#1176351411yescharacteristic
1049C22#1176351411yescharacteristic
1050C22#1176351411yescharacteristic
1051C4—24no—
1052C4—24no—
1053C4—42no—
1054C4—42no—
1055C4—42no—
1056C4—42no—
1057C4—344no—
1058C4—344no—
1059C4—682no—
1060C4—682no—
1061C4—682no—
1062C4—682no—
1063C4—1361no—
1064C4—1361no—
1065C2—28no—
1066C2C2×#1176271311yescharacteristic
1067C2C4×#1058761011yescharacteristic
1068C2#1453151711yescharacteristic
1069C2C22⋊C4×C22⋊D1711yescharacteristic
1070C2#1453161111yescharacteristic
1071C2#1453178911yescharacteristic
1072C2#1453186411yescharacteristic
1073C2#1453244511yescharacteristic
1074C2#1453246011yescharacteristic
1075C2#1453248011yescharacteristic
1076C2#1453259311yescharacteristic
1077C2#1453260811yescharacteristic
1078C2#1453290411yescharacteristic
1079C2#1453311011yescharacteristic
1080C2#1453379511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC22×C17×#95C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC22×#95D17
hypocenterC17#14052
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
2. C2×#11762713C2semidirect
5. #14527054C2semidirect
6. #14527050C2semidirect
7. #14527036C2semidirect
8. #14527035C2semidirect
9. #14527018C2semidirect
10. #14527015C2semidirect
11. #14527012C2semidirect
19. C2×#10587610C4semidirect
79. C23×C4×C17Q8semidirect
100. C22×Dic34C2×C4semidirect
112. C2×C22⋊Dic17Q8semidirect
115. C2×C4⋊Dic17C2×C4semidirect
127. C2×#63225C2×C4semidirect
128. C2×#63225C2×C4semidirect
403. C2×C4×C17C22⋊Q8semidirect
490. C22×C17#391semidirect
633. C23×C4Dic34semidirect
695. C17#14052semidirect
999. C2×C4#10587610semidirect
1015. C22#11762713semidirect

Maximal subgroups

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

subgroupindex
C22×#105876102
C2×#117627132
C2×#117626822
C2×C4×C22⋊Dic172
#145270542
#145270502
#145270362
#145270352
#145270182
#145270152
#145270122
#145270072
C22×C17×#952
#1405217