Finite Group Databasebeta

← #16962292

Subgroups — #16962292

Order 4352.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762704C211yesmaximal, characteristic, complemented
2C2×#11762700C211yesmaximal, characteristic
3C2×#11762699C211yesmaximal, characteristic
4C2×#11762680C211yesmaximal, characteristic
5C2×#11762680C211yesmaximal, characteristic
6C2×#11762680C211yesmaximal, characteristic
7#14527047C211yesmaximal, characteristic, complemented
8#14527047C211yesmaximal, characteristic, complemented
9#14527043C211yesmaximal, characteristic, complemented
10#14527034C211yesmaximal, characteristic, complemented
11#14527026C211yesmaximal, characteristic
12#14527026C211yesmaximal, characteristic
13#14527016C211yesmaximal, characteristic, complemented
14#14527011C211yesmaximal, characteristic, complemented
15C2×C17×#384C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28#11762704—24no—
29#11762700C418yescomplemented
30#11762699—24no—
31#11762680—24no—
32#11762680—24no—
33#11762680—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
50C22×C4⋊C4×C17C2211yescharacteristic
51C22×C4⋊C4×C17C2211yescharacteristic
52C22×C4⋊C4×C17C2211yescharacteristic
53C22×C4⋊C4×C17C2211yescharacteristic
54C22×C4⋊C4×C17C2211yescharacteristic
55C22×C4⋊C4×C17C2211yescharacteristic
56C22×C42×C17C2211yescharacteristic
57C17×#384—24no—
58C24×D17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C22×C4×D17—22no—
74C22×C4×D17—22no—
75C22×C4×D17—22no—
76C22×C4×D17—41no—
77C22×C4×D17—41no—
78C22×C4×D17—41no—
79C22×C4×D17—41no—
80C2×C4⋊C4×C17—22no—
81C2×C4⋊C4×C17—22no—
82C2×C4⋊C4×C17—22no—
83C2×C4⋊C4×C17—22no—
84C2×C4⋊C4×C17—22no—
85C2×C4⋊C4×C17—22no—
86C2×C4⋊C4×C17—22no—
87C2×C4⋊C4×C17—22no—
88C2×C4⋊C4×C17—22no—
89C2×C4⋊C4×C17—41no—
90C2×C4⋊C4×C17—41no—
91C2×C4⋊C4×C17—41no—
92C2×C4⋊C4×C17—41no—
93C2×C4⋊C4×C17—41no—
94C2×C4⋊C4×C17—41no—
95C2×C4⋊C4×C17—41no—
96C2×C4⋊C4×C17—41no—
97C2×C4⋊C4×C17D414yes—
98C2×C42×C17—22no—
99C2×C42×C17—22no—
100C2×C42×C17C2×C414yescomplemented
101C2×#63227—22no—
102C2×#63227—22no—
103C2×#63227—22no—
104C2×#63227—22no—
105C2×#63227—22no—
106C2×#63227—22no—
107C2×#63227—22no—
108C2×#63227—22no—
109C2×#63227—22no—
110C2×#63227—41no—
111C2×#63227—41no—
112C2×#63227—41no—
113C2×#63227—41no—
114C2×#63227C2×C414yes—
115C2×#63227C2×C414yes—
116C2×#63227C2×C414yes—
117C2×#63227D414yes—
118C2×#63227Q814yes—
119C2×#63225—22no—
120C2×#63225—22no—
121C2×#63225—22no—
122C2×#63225—22no—
123C2×#63225—22no—
124C2×#63225—22no—
125C2×#63225—22no—
126C2×#63225—41no—
127C2×#63225—41no—
128C2×#63225—41no—
129C2×#63225—41no—
130C2×#63225C2×C414yescomplemented
131C2×C4×Dic17—22no—
132C2×C4×Dic17—22no—
133C2×C4×Dic17—41no—
134#10587502—22no—
135#10587502—22no—
136#10587502—22no—
137#10587502—22no—
138#10587502—22no—
139#10587502—22no—
140#10587502—22no—
141#10587502—22no—
142#10587502—22no—
143#10587502—22no—
144#10587502—41no—
145#10587502—41no—
146#10587502—41no—
147#10587502C2×C414yescomplemented
148#10587502C2×C414yescomplemented
149#10587502D414yes—
150C24×C17C2411yescharacteristic
151C23×D17—21no—
152C23×D17—21no—
153C23×D17—21no—
154C23×D17—21no—
155C23×D17—21no—
156C23×D17—21no—
157C23×D17—21no—
158C23×D17—21no—
159C23×D17—21no—
160C23×D17—21no—
161C23×D17—21no—
162C23×D17—21no—
163C23×D17C22×C412yes—
164C23×D17C2×D412yes—
165C23×D17C2×Q812yes—
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×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17C22×C412yes—
205C22×C4×C17C22×C412yes—
206C22×C4×C17C22×C412yes—
207C22×C4×C17C2×D412yes—
208C22×C4×C17C2×D412yes—
209C22×C4×C17C2×D412yes—
210C22×C4×C17C2×D412yes—
211C22×C4×C17C2×D412yes—
212C22×C4×C17C2×Q812yes—
213C22×C4×C17#4112yes—
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—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17C22×C412yes—
258C22×Dic17C22×C412yes—
259C22×Dic17C22×C412yes—
260C22×Dic17C2×D412yes—
261C22×Dic17C2×D412yes—
262C22×Dic17C2×D412yes—
263C22×Dic17C2×Q812yes—
264C2×C4×D17—44no—
265C2×C4×D17—44no—
266C2×C4×D17—44no—
267C2×C4×D17—44no—
268C2×C4×D17—44no—
269C2×C4×D17—44no—
270C2×C4×D17—44no—
271C4⋊C4×C17—44no—
272C4⋊C4×C17—44no—
273C4⋊C4×C17—44no—
274C4⋊C4×C17—44no—
275C4⋊C4×C17—44no—
276C4⋊C4×C17—44no—
277C42×C17—28no—
278#63227—28no—
279#63227—28no—
280#63227—44no—
281#63227—44no—
282#63227—44no—
283#63227C4⋊C4116yescomplemented
284#63225—28no—
285#63225—44no—
286#63225—44no—
287#63225—44no—
288C4×Dic17—44no—
289#14405—171nomaximal, Sylow
290C23×C17C23×C411yescharacteristic
291C23×C17C22×D411yescharacteristic
292C23×C17C22×D411yescharacteristic
293C23×C17C22×D411yescharacteristic
294C23×C17C22×Q811yescharacteristic
295C23×C17C2×#4111yescharacteristic
296C23×C17C2×#4111yescharacteristic
297C23×C17H(5,𝔽2)11yescharacteristic
298C23×C17H(5,𝔽2)11yescharacteristic
299C23×C17H(5,𝔽2)11yescharacteristic
300C23×C17H(5,𝔽2)11yescharacteristic
301C23×C172−1+411yescharacteristic
302C23×C172−1+411yescharacteristic
303C23×C172−1+411yescharacteristic
304C23×C172−1+411yescharacteristic
305C22×D17—22no—
306C22×D17—22no—
307C22×D17—22no—
308C22×D17—22no—
309C22×D17—22no—
310C22×D17—22no—
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—41no—
324C22×D17—41no—
325C22×D17—41no—
326C22×D17—41no—
327C22×D17—41no—
328C22×D17—41no—
329C22×D17—41no—
330C22×D17—41no—
331C22×D17—41no—
332C22×D17—41no—
333C22×D17—41no—
334C22×D17—41no—
335C22×D17—41no—
336C22×D17—41no—
337C22×D17—41no—
338C22×D17—41no—
339C22×D17C2×C4⋊C414yes—
340C2×C4×C17—22no—
341C2×C4×C17—22no—
342C2×C4×C17—22no—
343C2×C4×C17—22no—
344C2×C4×C17—22no—
345C2×C4×C17—22no—
346C2×C4×C17—22no—
347C2×C4×C17—22no—
348C2×C4×C17—22no—
349C2×C4×C17—22no—
350C2×C4×C17—22no—
351C2×C4×C17—22no—
352C2×C4×C17—22no—
353C2×C4×C17—22no—
354C2×C4×C17—22no—
355C2×C4×C17—22no—
356C2×C4×C17—22no—
357C2×C4×C17—22no—
358C2×C4×C17—22no—
359C2×C4×C17—22no—
360C2×C4×C17—22no—
361C2×C4×C17—22no—
362C2×C4×C17—22no—
363C2×C4×C17—22no—
364C2×C4×C17—41no—
365C2×C4×C17—41no—
366C2×C4×C17—41no—
367C2×C4×C17—41no—
368C2×C4×C17—41no—
369C2×C4×C17—41no—
370C2×C4×C17—41no—
371C2×C4×C17—41no—
372C2×C4×C17—41no—
373C2×C4×C17—41no—
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×C17C2×C4⋊C414yes—
387C2×C4×C17C4×D414yes—
388C2×C4×C17C4×D414yes—
389C2×Dic17—22no—
390C2×Dic17—22no—
391C2×Dic17—22no—
392C2×Dic17—22no—
393C2×Dic17—22no—
394C2×Dic17—22no—
395C2×Dic17—22no—
396C2×Dic17—22no—
397C2×Dic17—22no—
398C2×Dic17—22no—
399C2×Dic17—22no—
400C2×Dic17—22no—
401C2×Dic17—22no—
402C2×Dic17—22no—
403C2×Dic17—22no—
404C2×Dic17—22no—
405C2×Dic17—22no—
406C2×Dic17—22no—
407C2×Dic17—41no—
408C2×Dic17—41no—
409C2×Dic17—41no—
410C2×Dic17—41no—
411C2×Dic17—41no—
412C2×Dic17—41no—
413C2×Dic17—41no—
414C2×Dic17—41no—
415C2×Dic17—41no—
416C2×Dic17—41no—
417C2×Dic17—41no—
418C2×Dic17—41no—
419C2×Dic17—41no—
420C2×Dic17—41no—
421C2×Dic17—41no—
422C2×Dic17—41no—
423C2×Dic17—41no—
424C2×Dic17—41no—
425C2×Dic17—41no—
426C2×Dic17—41no—
427C2×Dic17—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×Dic17C2×C4⋊C414yes—
438C4×D17—416no—
439C2×#389—171no—
440C2×#388—171no—
441C2×#388—171no—
442C2×#385—171no—
443C2×#385—171no—
444C2×#385—171no—
445C2×#384D1711yescharacteristic, complemented
446#1444—171no—
447#1444—171no—
448#1442—171no—
449#1441—171no—
450#1439—171no—
451#1439—171no—
452#1436—171no—
453#1434—171no—
454C22×C17C22×C4⋊C411yescharacteristic
455C22×C17C2×C4×D411yescharacteristic
456C22×C17C2×C4×D411yescharacteristic
457C22×C17#52011yescharacteristic
458C22×C17#52011yescharacteristic
459C22×C17#52011yescharacteristic
460C22×C17#52011yescharacteristic
461C22×C17#53411yescharacteristic
462C22×C17#53511yescharacteristic
463C22×C17#53511yescharacteristic
464C22×C17#53611yescharacteristic
465C22×C17#53611yescharacteristic
466C22×C17#53611yescharacteristic
467C22×C17#53911yescharacteristic
468C22×C17#53911yescharacteristic
469C22×C17#54211yescharacteristic
470C22×C17#54211yescharacteristic
471C22×C17#54411yescharacteristic
472C22×C17#54411yescharacteristic
473C22×C17D4211yescharacteristic
474C22×C17D4211yescharacteristic
475C22×C17D4211yescharacteristic
476C22×C17#54711yescharacteristic
477C22×C17#54711yescharacteristic
478C22×C17#54711yescharacteristic
479C22×C17#54811yescharacteristic
480C22×C17D4×Q811yescharacteristic
481C22×C17D4×Q811yescharacteristic
482C22×C17#55311yescharacteristic
483C22×C17#55411yescharacteristic
484C22×C17#55411yescharacteristic
485C22×C17#56011yescharacteristic
486C22×C17#56311yescharacteristic
487C22×C17#56311yescharacteristic
488C22×C17#56311yescharacteristic
489C2×D17—24no—
490C2×D17—24no—
491C2×D17—24no—
492C2×D17—42no—
493C2×D17—42no—
494C2×D17—42no—
495C2×D17—42no—
496C2×D17—42no—
497C2×D17—42no—
498C2×D17—42no—
499C2×D17—42no—
500C2×D17—42no—
501C2×D17—42no—
502C2×D17—42no—
503C2×D17—42no—
504C4×C17—24no—
505C4×C17—24no—
506C4×C17—24no—
507C4×C17—42no—
508C4×C17—42no—
509C4×C17—81no—
510C4×C17—81no—
511Dic17—24no—
512Dic17—42no—
513Dic17—42no—
514Dic17—42no—
515Dic17—42no—
516Dic17—81no—
517Dic17—81no—
518C24×C4—171no—
519C22×C4⋊C4—171no—
520C22×C4⋊C4—171no—
521C22×C4⋊C4—171no—
522C22×C4⋊C4—171no—
523C22×C4⋊C4C2×D1711yescharacteristic
524C22×C4⋊C4C2×D1711yescharacteristic
525C22×C4⋊C4C2×D1711yescharacteristic
526C22×C4⋊C4C2×D1711yescharacteristic
527C22×C4⋊C4C2×D1711yescharacteristic
528C22×C4⋊C4C2×D1711yescharacteristic
529C22×C22⋊C4—171no—
530C22×C22⋊C4—171no—
531C22×C22⋊C4—171no—
532C22×C22⋊C4—171no—
533C22×C22⋊C4—171no—
534C22×C22⋊C4—171no—
535C22×C42—171no—
536C22×C42C2×D1711yescharacteristic
537#389—344no—
538#388—178no—
539#388—344no—
540#385—344no—
541#385—344no—
542#385—344no—
543#384—24no—
544C2×#95—171no—
545C2×#95—171no—
546C2×#95—171no—
547C2×#95—171no—
548C2×#95—171no—
549C2×#95—171no—
550C2×#95—171no—
551C2×#95—171no—
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×C17#231711yescharacteristic
561C2×C17#232211yescharacteristic
562C2×C17#232611yescharacteristic
563C2×C17D4×C4⋊C411yescharacteristic
564C2×C17D4×C4⋊C411yescharacteristic
565C2×C17#236111yescharacteristic
566C2×C17#238311yescharacteristic
567C2×C17#266911yescharacteristic
568C2×C17#267411yescharacteristic
569C2×C17#267711yescharacteristic
570C2×C17#268011yescharacteristic
571C2×C17#271811yescharacteristic
572C2×C17#272011yescharacteristic
573C2×C17#272911yescharacteristic
574C2×C17#279011yescharacteristic
575D17—44no—
576C25—171no—
577C23×C4—171no—
578C23×C4—171no—
579C23×C4—171no—
580C23×C4—171no—
581C23×C4—171no—
582C23×C4—171no—
583C23×C4—171no—
584C23×C4—342no—
585C23×C4—342no—
586C23×C4—342no—
587C23×C4—681no—
588C23×C4—681no—
589C23×C4—681no—
590C23×C4—681no—
591C23×C4C22×D1711yescharacteristic
592C23×C4C22×D1711yescharacteristic
593C23×C4C22×D1711yescharacteristic
594C23×C4C22×D1711yescharacteristic
595C23×C4C22×D1711yescharacteristic
596C23×C4C22×D1711yescharacteristic
597C23×C4C22×D1711yescharacteristic
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4—41no—
615C2×C4⋊C4—174no—
616C2×C4⋊C4—342no—
617C2×C4⋊C4—342no—
618C2×C4⋊C4—342no—
619C2×C4⋊C4—342no—
620C2×C4⋊C4—342no—
621C2×C4⋊C4—342no—
622C2×C4⋊C4—342no—
623C2×C4⋊C4—681no—
624C2×C4⋊C4—681no—
625C2×C4⋊C4—681no—
626C2×C4⋊C4—681no—
627C2×C4⋊C4C22⋊D1714yes—
628C2×C22⋊C4—174no—
629C2×C22⋊C4—174no—
630C2×C22⋊C4—174no—
631C2×C22⋊C4—174no—
632C2×C22⋊C4—174no—
633C2×C22⋊C4—342no—
634C2×C22⋊C4—342no—
635C2×C22⋊C4—342no—
636C2×C22⋊C4—342no—
637C2×C22⋊C4—342no—
638C2×C22⋊C4—342no—
639C2×C22⋊C4—342no—
640C2×C22⋊C4—342no—
641C2×C22⋊C4—342no—
642C2×C22⋊C4—681no—
643C2×C22⋊C4—681no—
644C2×C22⋊C4—681no—
645C2×C22⋊C4—681no—
646C2×C42—22no—
647C2×C42—22no—
648C2×C42—342no—
649C2×C42—342no—
650C2×C42—681no—
651C2×C42C4×D1714yescomplemented
652#95—174no—
653#95—174no—
654#95—174no—
655#95—342no—
656#95—342no—
657#95—342no—
658#95—342no—
659#95—342no—
660#95—342no—
661#95—342no—
662#95—342no—
663#95—342no—
664#95—342no—
665#95—681no—
666#95—681no—
667#95—681no—
668C17#1440511yescharacteristic, complemented, Sylow
669C24—172no—
670C24—172no—
671C24—172no—
672C24—341no—
673C24—341no—
674C24—341no—
675C24—341no—
676C24—341no—
677C24—341no—
678C24—341no—
679C24—341no—
680C24—341no—
681C24—341no—
682C24—341no—
683C24—341no—
684C24C23×D1711yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—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—172no—
724C22×C4—172no—
725C22×C4—172no—
726C22×C4—172no—
727C22×C4—172no—
728C22×C4—172no—
729C22×C4—172no—
730C22×C4—341no—
731C22×C4—341no—
732C22×C4—341no—
733C22×C4—341no—
734C22×C4—341no—
735C22×C4—341no—
736C22×C4—341no—
737C22×C4—341no—
738C22×C4—341no—
739C22×C4—341no—
740C22×C4—341no—
741C22×C4—341no—
742C22×C4—341no—
743C22×C4—341no—
744C22×C4—341no—
745C22×C4—341no—
746C22×C4—341no—
747C22×C4—341no—
748C22×C4—341no—
749C22×C4—341no—
750C22×C4—341no—
751C22×C4—341no—
752C22×C4—341no—
753C22×C4—341no—
754C22×C4—341no—
755C22×C4—341no—
756C22×C4—341no—
757C22×C4—341no—
758C22×C4—341no—
759C22×C4—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—684no—
773C22×C4—684no—
774C22×C4—684no—
775C22×C4—684no—
776C22×C4—684no—
777C22×C4—684no—
778C22×C4—684no—
779C22×C4C2×C4×D1712yes—
780C22×C4C2×C4×D1712yes—
781C22×C4C2×C4×D1712yes—
782C22×C4#6325212yes—
783C22×C4D4×D1712yes—
784C22×C4D4×D1712yes—
785C22×C4Q8×D1712yes—
786C22×C4#6325612yes—
787C22×C4C2×C22⋊D1712yes—
788C22×C4C2×C22⋊D1712yes—
789C22×C4C2×C22⋊D1712yes—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—348no—
797C4⋊C4—684no—
798C4⋊C4—684no—
799C4⋊C4—684no—
800C22⋊C4—1716no—
801C22⋊C4—348no—
802C22⋊C4—348no—
803C22⋊C4—684no—
804C22⋊C4—684no—
805C22⋊C4—684no—
806C42—28no—
807C42—684no—
808C23—174no—
809C23—342no—
810C23—342no—
811C23—342no—
812C23—342no—
813C23—342no—
814C23—342no—
815C23—342no—
816C23—342no—
817C23—342no—
818C23—342no—
819C23—342no—
820C23—342no—
821C23—342no—
822C23—342no—
823C23—342no—
824C23—342no—
825C23—342no—
826C23—342no—
827C23—681no—
828C23—681no—
829C23—681no—
830C23—681no—
831C23—681no—
832C23—681no—
833C23—681no—
834C23—681no—
835C23—681no—
836C23—681no—
837C23—681no—
838C23—681no—
839C23—681no—
840C23—681no—
841C23—681no—
842C23—681no—
843C23C22×C4×D1711yescharacteristic
844C23C2×#6325211yescharacteristic
845C23C2×D4×D1711yescharacteristic
846C23C2×D4×D1711yescharacteristic
847C23#1058769111yescharacteristic
848C23#1058769111yescharacteristic
849C23#1058769111yescharacteristic
850C23#1058769111yescharacteristic
851C23C2×Q8×D1711yescharacteristic
852C23C2×#6325611yescharacteristic
853C23#1058769411yescharacteristic
854C23#1058769411yescharacteristic
855C23#1058769411yescharacteristic
856C23#1058769411yescharacteristic
857C23C22×C22⋊D1711yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
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—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—174no—
905C2×C4—342no—
906C2×C4—342no—
907C2×C4—342no—
908C2×C4—342no—
909C2×C4—342no—
910C2×C4—342no—
911C2×C4—342no—
912C2×C4—342no—
913C2×C4—342no—
914C2×C4—342no—
915C2×C4—342no—
916C2×C4—342no—
917C2×C4—342no—
918C2×C4—342no—
919C2×C4—342no—
920C2×C4—342no—
921C2×C4—342no—
922C2×C4—342no—
923C2×C4—6816no—
924C2×C4—681no—
925C2×C4—681no—
926C2×C4—681no—
927C2×C4—681no—
928C2×C4—681no—
929C2×C4—681no—
930C2×C4—681no—
931C2×C4—681no—
932C2×C4—681no—
933C2×C4—681no—
934C2×C4—681no—
935C2×C4—681no—
936C2×C4—681no—
937C2×C4—681no—
938C2×C4—681no—
939C2×C4—681no—
940C2×C4—681no—
941C2×C4—681no—
942C2×C4—681no—
943C2×C4—681no—
944C2×C4—681no—
945C2×C4—681no—
946C2×C4—681no—
947C2×C4—681no—
948C2×C4—681no—
949C2×C4—681no—
950C2×C4—681no—
951C2×C4—681no—
952C2×C4—681no—
953C2×C4—681no—
954C2×C4C4⋊C4×D1714yes—
955C2×C4#1058757914yes—
956C2×C4C4×C22⋊D1714yes—
957C22—344no—
958C22—344no—
959C22—344no—
960C22—682no—
961C22—682no—
962C22—682no—
963C22—682no—
964C22—682no—
965C22—682no—
966C22—682no—
967C22—682no—
968C22—682no—
969C22—682no—
970C22—682no—
971C22—682no—
972C22C2×C4⋊C4×D1711yescharacteristic
973C22C2×C4×C22⋊D1711yescharacteristic
974C22C2×#1058757911yescharacteristic
975C22#1176329011yescharacteristic
976C22#1176329011yescharacteristic
977C22#1176329011yescharacteristic
978C22#1176329011yescharacteristic
979C22#1176336811yescharacteristic
980C22#1176337211yescharacteristic
981C22#1176337211yescharacteristic
982C22#1176338311yescharacteristic
983C22#1176338411yescharacteristic
984C22#1176338411yescharacteristic
985C22#1176340611yescharacteristic
986C22#1176340611yescharacteristic
987C22#1176343311yescharacteristic
988C22#1176343311yescharacteristic
989C22#1176343611yescharacteristic
990C22#1176343611yescharacteristic
991C22D4×C22⋊D1711yescharacteristic
992C22D4×C22⋊D1711yescharacteristic
993C22#1176344411yescharacteristic
994C22#1176346011yescharacteristic
995C22#1176346011yescharacteristic
996C22#1176346211yescharacteristic
997C22#1176347011yescharacteristic
998C22Q8×C22⋊D1711yescharacteristic
999C22#1176347411yescharacteristic
1000C22#1176350711yescharacteristic
1001C22#1176351411yescharacteristic
1002C22#1176352011yescharacteristic
1003C22#1176354611yescharacteristic
1004C22#1176355811yescharacteristic
1005C22#1176355811yescharacteristic
1006C22#1176355811yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—42no—
1011C4—42no—
1012C4—81no—
1013C4—81no—
1014C4—344no—
1015C4—682no—
1016C4—682no—
1017C4—682no—
1018C4—682no—
1019C4—1361no—
1020C4—1361no—
1021C2—684no—
1022C2#1453140511yescharacteristic
1023C2#1453145311yescharacteristic
1024C2#1453149211yescharacteristic
1025C2C4⋊C4×C22⋊D1711yescharacteristic
1026C2#1453168411yescharacteristic
1027C2#1453180011yescharacteristic
1028C2#1453197711yescharacteristic
1029C2#1453499711yescharacteristic
1030C2#1453506011yescharacteristic
1031C2#1453509411yescharacteristic
1032C2#1453512411yescharacteristic
1033C2#1453562911yescharacteristic
1034C2#1453565911yescharacteristic
1035C2#1453576011yescharacteristic
1036C2#1453655011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#384C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenterC2×#384D17
hypocenterC17#14405
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
1. C2×#11762704C2semidirect
7. #14527047C2semidirect
8. #14527047C2semidirect
9. #14527043C2semidirect
10. #14527034C2semidirect
13. #14527016C2semidirect
14. #14527011C2semidirect
15. C2×C17×#384C2semidirect
29. #11762700C4semidirect
100. C2×C42×C17C2×C4semidirect
130. C2×#63225C2×C4semidirect
147. #10587502C2×C4semidirect
148. #10587502C2×C4semidirect
283. #63227C4⋊C4semidirect
445. C2×#384D17semidirect
651. C2×C42C4×D17semidirect
668. C17#14405semidirect

Maximal subgroups

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

subgroupindex
C2×#117627042
C2×#117627002
C2×#117626992
C2×#117626802
#145270472
#145270432
#145270342
#145270262
#145270162
#145270112
C2×C17×#3842
#1440517