Finite Group Databasebeta

← #16957455

Subgroups — #16957455

Order 4352.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587564C211yesmaximal, characteristic
2C2×#11762713C211yesmaximal, characteristic, complemented
3C2×#11762713C211yesmaximal, characteristic, complemented
4C2×#11762706C211yesmaximal, characteristic, complemented
5C2×#11762667C211yesmaximal, characteristic
6C2×C4×#63225C211yesmaximal, characteristic, complemented
7C2×C22⋊C4×Dic17C211yesmaximal, characteristic
8#14527053C211yesmaximal, characteristic, complemented
9#14527050C211yesmaximal, characteristic, complemented
10#14527029C211yesmaximal, characteristic
11#14527027C211yesmaximal, characteristic
12#14527021C211yesmaximal, characteristic
13#14527014C211yesmaximal, characteristic, complemented
14#14527012C211yesmaximal, characteristic, complemented
15C17×#1437C211yesmaximal, characteristic
16C23×Dic34C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C2×#10587564—24no—
19C2×#10587564—24no—
20C2×#10587564C418yescomplemented
21C22×C4⋊Dic17C2211yescharacteristic
22C22×C4⋊Dic17C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×C22⋊Dic17C2211yescharacteristic
29C22×C22⋊Dic17C2211yescharacteristic
30C22×C22⋊Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34#11762713—24no—
35#11762713—24no—
36#11762706—24no—
37#11762667—24no—
38C4×#63225—24no—
39C22⋊C4×Dic17—24no—
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C22×C22⋊C4×C17C2211yescharacteristic
56C22×C42×C17C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C2×C17×#95C2211yescharacteristic
59C2×C17×#95C2211yescharacteristic
60C25×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×Dic17—22no—
68C23×Dic17—22no—
69C23×Dic17—22no—
70C23×Dic17—22no—
71C23×Dic17—22no—
72C23×Dic17—22no—
73C23×Dic17C2×C414yes—
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C22×Dic34—22no—
83C22×Dic34—22no—
84C22×Dic34—22no—
85C22×Dic34—22no—
86C22×Dic34—22no—
87C22×Dic34—22no—
88C22×Dic34C2×C414yes—
89C2×C22⋊C4×C17—22no—
90C2×C22⋊C4×C17—22no—
91C2×C22⋊C4×C17—22no—
92C2×C22⋊C4×C17—22no—
93C2×C22⋊C4×C17—22no—
94C2×C22⋊C4×C17—22no—
95C2×C22⋊C4×C17—41no—
96C2×C22⋊C4×C17C2×C414yes—
97C2×C22⋊C4×C17Q814yescomplemented
98C2×C42×C17—22no—
99C2×C42×C17—22no—
100C2×C42×C17—41no—
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⋊Dic17—41no—
109C2×C22⋊Dic17C2×C414yes—
110C2×C4⋊Dic17—22no—
111C2×C4⋊Dic17—22no—
112C2×C4⋊Dic17—22no—
113C2×C4⋊Dic17—22no—
114C2×C4⋊Dic17—41no—
115C2×C4⋊Dic17C2×C414yes—
116C2×#63225—22no—
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×#63225C2×C414yes—
127C2×#63225C2×C414yes—
128C2×#63225D414yes—
129C2×#63225D414yes—
130C2×#63225D414yes—
131C2×C4×Dic17—22no—
132C2×C4×Dic17—22no—
133C2×C4×Dic17—22no—
134C2×C4×Dic17—22no—
135C2×C4×Dic17—22no—
136C2×C4×Dic17—22no—
137C2×C4×Dic17—22no—
138C2×C4×Dic17—41no—
139C2×C4×Dic17D414yes—
140#10587564—232no—
141C17×#95—22no—
142C17×#95—22no—
143C17×#95—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—22no—
148#10587502—22no—
149#10587502—22no—
150#10587502—22no—
151#10587502—22no—
152#10587502—22no—
153#10587502—22no—
154#10587502—22no—
155#10587502—22no—
156#10587502—22no—
157C24×C17—21no—
158C24×C17—21no—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17—21no—
163C24×C17—21no—
164C24×C17—21no—
165C24×C17—21no—
166C24×C17—21no—
167C24×C17—21no—
168C24×C17—21no—
169C24×C17C22×C412yes—
170C24×C17C2×Q812yes—
171C24×C17#4112yes—
172C24×C17C2411yescharacteristic
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×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17C22×C412yes—
207C22×C4×C17C22×C412yes—
208C22×C4×C17C2×D412yes—
209C22×C4×C17C2×D412yes—
210C22×C4×C17C2×D412yes—
211C22×C4×C17C2×D412yes—
212C22×C4×C17C2×Q812yes—
213C22×C4×C17C2×Q812yes—
214C22×C4×C17#4112yes—
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×Dic17—28no—
250C22×Dic17—28no—
251C22×Dic17—28no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—44no—
260C22×Dic17—44no—
261C22×Dic17—44no—
262C22×Dic17—44no—
263C22×Dic17C22×C412yes—
264C22×Dic17C22×C412yes—
265C22×Dic17C22×C412yes—
266C22×Dic17C22×C412yes—
267C22×Dic17C2×D412yes—
268C22×Dic17C2×D412yes—
269C22×Dic17C2×D412yes—
270C22×Dic17C2×D412yes—
271C22×Dic17C2×D412yes—
272C22×Dic17C2×D412yes—
273C22×Dic17C2×D412yes—
274C22×Dic17C2×D412yes—
275C22×Dic17#4112yes—
276C22×Dic17#4112yes—
277C22×Dic17#4112yes—
278C2×Dic34—28no—
279C2×Dic34—28no—
280C2×Dic34—28no—
281C2×Dic34—44no—
282C2×Dic34—44no—
283C2×Dic34—44no—
284C2×Dic34—44no—
285C22⋊C4×C17—28no—
286C22⋊C4×C17—28no—
287C22⋊C4×C17—44no—
288C42×C17—44no—
289C22⋊Dic17—28no—
290C22⋊Dic17—28no—
291C22⋊Dic17—44no—
292C4⋊Dic17—28no—
293C4⋊Dic17—44no—
294#63225—28no—
295#63225—28no—
296#63225—44no—
297#63225—44no—
298#63225C22⋊C4116yescomplemented
299C4×Dic17—28no—
300C4×Dic17—44no—
301C4×Dic17—44no—
302#13997—171nomaximal, Sylow
303C23×C17—22no—
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—41no—
322C23×C17—41no—
323C23×C17—41no—
324C23×C17—41no—
325C23×C17—41no—
326C23×C17—41no—
327C23×C17—41no—
328C23×C17—41no—
329C23×C17—41no—
330C23×C17—41no—
331C23×C17—41no—
332C23×C17—41no—
333C23×C17—41no—
334C23×C17—41no—
335C23×C17—41no—
336C23×C17—41no—
337C23×C17C4×Q814yes—
338C23×C17C23×C411yescharacteristic
339C23×C17C22×D411yescharacteristic
340C23×C17C22×D411yescharacteristic
341C23×C17C22×D411yescharacteristic
342C23×C17C22×D411yescharacteristic
343C23×C17C22×Q811yescharacteristic
344C23×C17C2×#4111yescharacteristic
345C23×C17C2×#4111yescharacteristic
346C23×C17C2×#4111yescharacteristic
347C23×C17C2×#4111yescharacteristic
348C23×C17C2×#4111yescharacteristic
349C23×C17H(5,𝔽2)11yescharacteristic
350C23×C172−1+411yescharacteristic
351C23×C172−1+411yescharacteristic
352C23×C172−1+411yescharacteristic
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—41no—
375C2×C4×C17—41no—
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×C17—41no—
393C2×C4×C17C2×C22⋊C414yes—
394C2×C4×C17C22⋊Q814yescomplemented
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—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—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—416no—
437C2×Dic17—41no—
438C2×Dic17—41no—
439C2×Dic17—41no—
440C2×Dic17—41no—
441C2×Dic17—41no—
442C2×Dic17—41no—
443C2×Dic17—41no—
444C2×Dic17C2×C22⋊C414yes—
445C2×Dic17C2×C22⋊C414yes—
446C2×Dic17C4×D414yes—
447C2×Dic17C4×D414yes—
448C2×Dic17#12114yes—
449C2×Dic17#12114yes—
450C2×Dic17#12414yes—
451C2×Dic17#12714yes—
452Dic34—416no—
453C22×C22⋊Q8—171no—
454C2×#391—171no—
455C2×#391—171no—
456C2×#389—171no—
457C2×#380—171no—
458C2×C4×C4⋊C4—171no—
459C2×C4×C22⋊C4—171no—
460#1445—171no—
461#1445—171no—
462#1439—171no—
463#1439—171no—
464#1437—171no—
465#1437D1711yescharacteristic
466C4⋊#95—171no—
467C4⋊#95—171no—
468C22×C17—24no—
469C22×C17—24no—
470C22×C17—24no—
471C22×C17—42no—
472C22×C17—42no—
473C22×C17—42no—
474C22×C17—42no—
475C22×C17—42no—
476C22×C17—42no—
477C22×C17—42no—
478C22×C17—42no—
479C22×C17—42no—
480C22×C17—42no—
481C22×C17—42no—
482C22×C17—42no—
483C22×C17C22×C22⋊C411yescharacteristic
484C22×C17C2×C4×D411yescharacteristic
485C22×C17C2×C4×D411yescharacteristic
486C22×C17C2×C4×Q811yescharacteristic
487C22×C17C4×#4111yescharacteristic
488C22×C17#51911yescharacteristic
489C22×C17#52011yescharacteristic
490C22×C17C2×#12111yescharacteristic
491C22×C17C2×#12111yescharacteristic
492C22×C17C2×C22⋊Q811yescharacteristic
493C22×C17#52511yescharacteristic
494C22×C17C2×#12411yescharacteristic
495C22×C17#52911yescharacteristic
496C22×C17C2×#12711yescharacteristic
497C22×C17#53311yescharacteristic
498C22×C17#53611yescharacteristic
499C22×C17#53711yescharacteristic
500C22×C17#54111yescharacteristic
501C22×C17#54211yescharacteristic
502C22×C17#54611yescharacteristic
503C22×C17#54611yescharacteristic
504C22×C17#54611yescharacteristic
505C22×C17#54711yescharacteristic
506C22×C17#54711yescharacteristic
507C22×C17#54711yescharacteristic
508C22×C17#54811yescharacteristic
509C22×C17#54811yescharacteristic
510C22×C17#54811yescharacteristic
511C22×C17D4×Q811yescharacteristic
512C22×C17D4×Q811yescharacteristic
513C22×C17D4×Q811yescharacteristic
514C22×C17#55211yescharacteristic
515C22×C17#55211yescharacteristic
516C22×C17#55411yescharacteristic
517C22×C17#55611yescharacteristic
518C4×C17—24no—
519C4×C17—24no—
520C4×C17—42no—
521C4×C17—42no—
522C4×C17—42no—
523C4×C17—81no—
524Dic17—24no—
525Dic17—42no—
526Dic17—42no—
527Dic17—42no—
528Dic17—42no—
529Dic17—42no—
530Dic17—81no—
531Dic17#39018yes—
532C23×Q8—171no—
533C24×C4—171no—
534C2×C22⋊Q8—178no—
535C2×C22⋊Q8—344no—
536C2×C22⋊Q8—344no—
537C22×C4⋊C4—171no—
538C22×C4⋊C4—171no—
539C22×C4⋊C4—171no—
540C22×C4⋊C4—171no—
541C22×C4⋊C4—171no—
542C22×C4⋊C4—171no—
543C22×C4⋊C4—171no—
544C22×C22⋊C4—171no—
545C22×C22⋊C4—171no—
546C22×C22⋊C4—171no—
547C22×C22⋊C4C2×D1711yescharacteristic
548C22×C22⋊C4C2×D1711yescharacteristic
549C22×C22⋊C4C2×D1711yescharacteristic
550C22×C42—171no—
551C22×C42—171no—
552C22×C42—171no—
553C22×C42C2×D1711yescharacteristic
554#391—344no—
555#391—344no—
556#389—344no—
557#380—344no—
558C4×C4⋊C4—344no—
559C4×C22⋊C4—344no—
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×#95C2×D1711yescharacteristic
574C2×#95C2×D1711yescharacteristic
575C2×#95C2×D1711yescharacteristic
576C2×C17—44no—
577C2×C17C2×#39011yescharacteristic
578C2×C17C4×C22⋊Q811yescharacteristic
579C2×C17#232311yescharacteristic
580C2×C17#233911yescharacteristic
581C2×C17Q8×C22⋊C411yescharacteristic
582C2×C17#236011yescharacteristic
583C2×C17#236211yescharacteristic
584C2×C17#241511yescharacteristic
585C2×C17#241711yescharacteristic
586C2×C17#242711yescharacteristic
587C2×C17#242911yescharacteristic
588C2×C17#248911yescharacteristic
589C2×C17#249211yescharacteristic
590C2×C17#254011yescharacteristic
591C2×C17#254211yescharacteristic
592C25C22×D1711yescharacteristic
593C22×Q8—174no—
594C22×Q8—342no—
595C22×Q8—342no—
596C22×Q8—342no—
597C22×Q8—342no—
598C22×Q8—342no—
599C22×Q8—342no—
600C23×C4—171no—
601C23×C4—171no—
602C23×C4—174no—
603C23×C4—171no—
604C23×C4—171no—
605C23×C4—171no—
606C23×C4—171no—
607C23×C4—171no—
608C23×C4—171no—
609C23×C4—342no—
610C23×C4—342no—
611C23×C4—342no—
612C23×C4—342no—
613C23×C4—342no—
614C23×C4—342no—
615C23×C4C22×D1711yescharacteristic
616C23×C4C22×D1711yescharacteristic
617C23×C4C22×D1711yescharacteristic
618C23×C4C22×D1711yescharacteristic
619C23×C4C22×D1711yescharacteristic
620C23×C4C22×D1711yescharacteristic
621C22⋊Q8—3432no—
622C2×C4⋊C4—174no—
623C2×C4⋊C4—174no—
624C2×C4⋊C4—174no—
625C2×C4⋊C4—174no—
626C2×C4⋊C4—174no—
627C2×C4⋊C4—174no—
628C2×C4⋊C4—342no—
629C2×C4⋊C4—342no—
630C2×C4⋊C4—342no—
631C2×C4⋊C4—342no—
632C2×C4⋊C4—342no—
633C2×C4⋊C4—342no—
634C2×C4⋊C4—342no—
635C2×C4⋊C4—342no—
636C2×C4⋊C4—342no—
637C2×C4⋊C4—342no—
638C2×C4⋊C4—342no—
639C2×C4⋊C4—342no—
640C2×C4⋊C4—342no—
641C2×C4⋊C4—681no—
642C2×C4⋊C4—681no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—41no—
650C2×C22⋊C4—174no—
651C2×C22⋊C4—342no—
652C2×C22⋊C4—342no—
653C2×C22⋊C4—342no—
654C2×C22⋊C4—342no—
655C2×C22⋊C4—342no—
656C2×C22⋊C4—342no—
657C2×C22⋊C4—342no—
658C2×C22⋊C4—681no—
659C2×C22⋊C4Dic3414yescomplemented
660C2×C22⋊C4C4×D1714yes—
661C2×C42—22no—
662C2×C42—22no—
663C2×C42—41no—
664C2×C42—174no—
665C2×C42—342no—
666C2×C42—342no—
667C2×C42—342no—
668C2×C42—342no—
669C2×C42—342no—
670C2×C42—342no—
671C2×C42—342no—
672C2×C42—681no—
673#95—22no—
674#95—22no—
675#95—22no—
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—342no—
685#95—342no—
686#95—342no—
687#95—342no—
688#95—342no—
689C17#1399711yescharacteristic, complemented, Sylow
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24C2×Dic3412yes—
703C24C2×C4×D1712yes—
704C24#6325212yes—
705C24C23×D1711yescharacteristic
706C2×Q8—348no—
707C2×Q8—348no—
708C2×Q8—348no—
709C2×Q8—684no—
710C2×Q8—684no—
711C2×Q8—684no—
712C2×Q8—684no—
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—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—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—172no—
759C22×C4—172no—
760C22×C4—172no—
761C22×C4—348no—
762C22×C4—348no—
763C22×C4—348no—
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—341no—
801C22×C4—341no—
802C22×C4—341no—
803C22×C4—341no—
804C22×C4—341no—
805C22×C4—684no—
806C22×C4—684no—
807C22×C4—684no—
808C22×C4—684no—
809C22×C4C2×Dic3412yes—
810C22×C4C2×Dic3412yes—
811C22×C4C2×C4×D1712yes—
812C22×C4C2×C4×D1712yes—
813C22×C4D4×D1712yes—
814C22×C4D4×D1712yes—
815C22×C4D4×D1712yes—
816C22×C4D4×D1712yes—
817C22×C4#6325412yes—
818C4⋊C4—1716no—
819C4⋊C4—348no—
820C4⋊C4—348no—
821C4⋊C4—348no—
822C4⋊C4—684no—
823C4⋊C4—684no—
824C4⋊C4—684no—
825C22⋊C4—28no—
826C22⋊C4—28no—
827C22⋊C4—44no—
828C22⋊C4—348no—
829C22⋊C4—348no—
830C22⋊C4—684no—
831C42—44no—
832C42—348no—
833C42—684no—
834C42—684no—
835C23—22no—
836C23—22no—
837C23—22no—
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—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23C4×Dic3414yes—
870C23C22×Dic3411yescharacteristic
871C23C22×C4×D1711yescharacteristic
872C23C2×#6325211yescharacteristic
873C23C2×D4×D1711yescharacteristic
874C23C2×D4×D1711yescharacteristic
875C23C2×D4×D1711yescharacteristic
876C23C2×D4×D1711yescharacteristic
877C23C2×#6325411yescharacteristic
878C23#1058769111yescharacteristic
879C23#41×D1711yescharacteristic
880C23#41×D1711yescharacteristic
881C23#41×D1711yescharacteristic
882C23#1058769711yescharacteristic
883C23#1058769711yescharacteristic
884C23#1058769711yescharacteristic
885Q8—6816no—
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—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
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—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—174no—
927C2×C4—174no—
928C2×C4—174no—
929C2×C4—174no—
930C2×C4—174no—
931C2×C4—174no—
932C2×C4—174no—
933C2×C4—174no—
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—6816no—
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×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#1058756414yescomplemented
984C2×C4C22⋊C4×D1714yes—
985C22—24no—
986C22—24no—
987C22—24no—
988C22—42no—
989C22—42no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22—42no—
1000C22C2×C22⋊C4×D1711yescharacteristic
1001C22C4×D4×D1711yescharacteristic
1002C22C4×D4×D1711yescharacteristic
1003C22C2×C4×Dic3411yescharacteristic
1004C22C4×#6325411yescharacteristic
1005C22#1176328611yescharacteristic
1006C22#1176328811yescharacteristic
1007C22#121×D1711yescharacteristic
1008C22#121×D1711yescharacteristic
1009C22C2×#1058756411yescharacteristic
1010C22#1176331811yescharacteristic
1011C22#124×D1711yescharacteristic
1012C22#1176333911yescharacteristic
1013C22#127×D1711yescharacteristic
1014C22#1176336211yescharacteristic
1015C22#1176337911yescharacteristic
1016C22#1176338611yescharacteristic
1017C22#1176341611yescharacteristic
1018C22#1176342711yescharacteristic
1019C22#1176344611yescharacteristic
1020C22#1176344811yescharacteristic
1021C22#1176344911yescharacteristic
1022C22#1176345711yescharacteristic
1023C22#1176345911yescharacteristic
1024C22#1176345911yescharacteristic
1025C22#1176346711yescharacteristic
1026C22#1176346811yescharacteristic
1027C22#1176346811yescharacteristic
1028C22D4×Dic3411yescharacteristic
1029C22D4×Dic3411yescharacteristic
1030C22D4×Dic3411yescharacteristic
1031C22#1176349211yescharacteristic
1032C22#1176349611yescharacteristic
1033C22#1176351811yescharacteristic
1034C22#1176352611yescharacteristic
1035C4—24no—
1036C4—24no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—81no—
1041C4—178no—
1042C4—344no—
1043C4—682no—
1044C4—682no—
1045C4—682no—
1046C4—682no—
1047C4—682no—
1048C4—1361no—
1049C2—44no—
1050C2D17×#39011yescharacteristic
1051C2C4×#1058756411yescharacteristic
1052C2#1453145911yescharacteristic
1053C2#1453161011yescharacteristic
1054C2C22⋊C4×Dic3411yescharacteristic
1055C2#1453179011yescharacteristic
1056C2#1453180811yescharacteristic
1057C2#1453221011yescharacteristic
1058C2#1453223211yescharacteristic
1059C2#1453235811yescharacteristic
1060C2#1453238011yescharacteristic
1061C2#1453312211yescharacteristic
1062C2#1453315511yescharacteristic
1063C2#1453372111yescharacteristic
1064C2#1453373511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1437C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenter#1437D17
hypocenterC17#13997
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#11762713C2semidirect
3. C2×#11762713C2semidirect
4. C2×#11762706C2semidirect
6. C2×C4×#63225C2semidirect
8. #14527053C2semidirect
9. #14527050C2semidirect
13. #14527014C2semidirect
14. #14527012C2semidirect
20. C2×#10587564C4semidirect
97. C2×C22⋊C4×C17Q8semidirect
298. #63225C22⋊C4semidirect
394. C2×C4×C17C22⋊Q8semidirect
659. C2×C22⋊C4Dic34semidirect
689. C17#13997semidirect
983. C2×C4#10587564semidirect

Maximal subgroups

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

subgroupindex
C22×#105875642
C2×#117627132
C2×#117627062
C2×#117626672
C2×C4×#632252
C2×C22⋊C4×Dic172
#145270532
#145270502
#145270292
#145270272
#145270212
#145270142
#145270122
C17×#14372
#1399717