Finite Group Databasebeta

← #16962291

Subgroups — #16962291

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×#11762707C211yesmaximal, characteristic, complemented
2C2×#11762702C211yesmaximal, characteristic
3C2×#11762684C211yesmaximal, characteristic
4C2×#11762681C211yesmaximal, characteristic
5C2×#11762681C211yesmaximal, characteristic
6C2×#11762678C211yesmaximal, characteristic, complemented
7#14527048C211yesmaximal, characteristic, complemented
8#14527047C211yesmaximal, characteristic, complemented
9#14527040C211yesmaximal, characteristic, complemented
10#14527036C211yesmaximal, characteristic, complemented
11#14527027C211yesmaximal, characteristic
12#14527027C211yesmaximal, characteristic
13#14527017C211yesmaximal, characteristic, complemented
14#14527010C211yesmaximal, characteristic, complemented
15C2×C17×#388C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×C22⋊Dic17C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30#11762707—24no—
31#11762702C418yescomplemented
32#11762684—24no—
33#11762681—24no—
34#11762681—24no—
35#11762678—24no—
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×C22⋊C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C42×C17C2211yescharacteristic
55C17×#388—24no—
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C25×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×Dic17—22no—
66C23×Dic17—22no—
67C23×Dic17—22no—
68C23×Dic17—41no—
69C23×Dic17—41no—
70C23×Dic17—41no—
71C23×Dic17—41no—
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C2×C4⋊C4×C17—22no—
81C2×C4⋊C4×C17—22no—
82C2×C4⋊C4×C17—41no—
83C2×C22⋊C4×C17—22no—
84C2×C22⋊C4×C17—22no—
85C2×C22⋊C4×C17—22no—
86C2×C22⋊C4×C17—22no—
87C2×C22⋊C4×C17—41no—
88C2×C22⋊C4×C17—41no—
89C2×C22⋊C4×C17C2×C414yes—
90C2×C22⋊C4×C17D414yes—
91C2×C22⋊C4×C17Q814yes—
92C2×C42×C17—22no—
93C2×C42×C17—22no—
94C2×C42×C17—41no—
95C2×C22⋊Dic17—22no—
96C2×C22⋊Dic17—22no—
97C2×C22⋊Dic17—22no—
98C2×C22⋊Dic17—22no—
99C2×C22⋊Dic17—22no—
100C2×C22⋊Dic17—41no—
101C2×C22⋊Dic17—41no—
102C2×C22⋊Dic17C2×C414yes—
103C2×C22⋊Dic17C2×C414yes—
104C2×C4⋊Dic17—22no—
105C2×C4⋊Dic17—22no—
106C2×C4⋊Dic17—22no—
107C2×C4⋊Dic17—22no—
108C2×C4⋊Dic17—22no—
109C2×C4⋊Dic17—22no—
110C2×C4⋊Dic17—41no—
111C2×C4⋊Dic17—41no—
112C2×C4⋊Dic17C2×C414yescomplemented
113C2×#63225—22no—
114C2×#63225—22no—
115C2×#63225—22no—
116C2×#63225—22no—
117C2×#63225—22no—
118C2×#63225—22no—
119C2×#63225—22no—
120C2×#63225—22no—
121C2×#63225—41no—
122C2×#63225—41no—
123C2×#63225—41no—
124C2×#63225—41no—
125C2×#63225—41no—
126C2×#63225—41no—
127C2×#63225—41no—
128C2×#63225—41no—
129C2×#63225—41no—
130C2×#63225D414yes—
131C2×C4×Dic17—22no—
132C2×C4×Dic17—22no—
133C2×C4×Dic17C2×C414yescomplemented
134C17×#95—22no—
135C17×#95—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×C17—21no—
151C24×C17—21no—
152C24×C17—21no—
153C24×C17—21no—
154C24×C17—21no—
155C24×C17—21no—
156C24×C17—21no—
157C24×C17—21no—
158C24×C17—21no—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17C22×C412yes—
163C24×C17C2×D412yes—
164C24×C17C2×Q812yes—
165C24×C17C2411yescharacteristic
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×C17C2×D412yes—
203C22×C4×C17C2×D412yes—
204C22×C4×C17C2×D412yes—
205C22×C4×C17C2×D412yes—
206C22×C4×C17C2×Q812yes—
207C22×C4×C17C2×Q812yes—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17—21no—
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×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—44no—
255C22×Dic17—44no—
256C22×Dic17—44no—
257C22×Dic17—44no—
258C22×Dic17—44no—
259C22×Dic17—44no—
260C22×Dic17—44no—
261C22×Dic17C22×C412yes—
262C22×Dic17C22×C412yes—
263C22×Dic17C22×C412yes—
264C22×Dic17C22×C412yes—
265C22×Dic17C2×D412yes—
266C22×Dic17C2×D412yes—
267C22×Dic17C2×D412yes—
268C22×Dic17C2×D412yes—
269C22×Dic17#4112yes—
270C22×Dic17#4112yes—
271C4⋊C4×C17—44no—
272C22⋊C4×C17—44no—
273C22⋊C4×C17—44no—
274C22⋊C4×C17C4⋊C4116yescomplemented
275C42×C17—44no—
276C22⋊Dic17—28no—
277C22⋊Dic17—28no—
278C22⋊Dic17—44no—
279C4⋊Dic17—28no—
280C4⋊Dic17—44no—
281C4⋊Dic17—44no—
282#63225—44no—
283#63225—44no—
284#63225—44no—
285#63225—44no—
286#63225—44no—
287#63225—44no—
288C4×Dic17—28no—
289#14405—171nomaximal, Sylow
290C23×C17—22no—
291C23×C17—22no—
292C23×C17—22no—
293C23×C17—22no—
294C23×C17—22no—
295C23×C17—22no—
296C23×C17—22no—
297C23×C17—22no—
298C23×C17—22no—
299C23×C17—22no—
300C23×C17—22no—
301C23×C17—22no—
302C23×C17—22no—
303C23×C17—22no—
304C23×C17—22no—
305C23×C17—22no—
306C23×C17—22no—
307C23×C17—22no—
308C23×C17—41no—
309C23×C17—41no—
310C23×C17—41no—
311C23×C17—41no—
312C23×C17—41no—
313C23×C17—41no—
314C23×C17—41no—
315C23×C17—41no—
316C23×C17—41no—
317C23×C17—41no—
318C23×C17—41no—
319C23×C17—41no—
320C23×C17—41no—
321C23×C17—41no—
322C23×C17—41no—
323C23×C17—41no—
324C23×C17C2×C4⋊C414yes—
325C23×C17C23×C411yescharacteristic
326C23×C17C22×D411yescharacteristic
327C23×C17C22×D411yescharacteristic
328C23×C17C22×D411yescharacteristic
329C23×C17C22×Q811yescharacteristic
330C23×C17C2×#4111yescharacteristic
331C23×C17C2×#4111yescharacteristic
332C23×C17H(5,𝔽2)11yescharacteristic
333C23×C17H(5,𝔽2)11yescharacteristic
334C23×C17H(5,𝔽2)11yescharacteristic
335C23×C17H(5,𝔽2)11yescharacteristic
336C23×C172−1+411yescharacteristic
337C23×C172−1+411yescharacteristic
338C23×C172−1+411yescharacteristic
339C23×C172−1+411yescharacteristic
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—41no—
359C2×C4×C17—41no—
360C2×C4×C17—41no—
361C2×C4×C17—41no—
362C2×C4×C17—41no—
363C2×C4×C17—41no—
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×C17C2×C4⋊C414yes—
381C2×C4×C17C2×C4⋊C414yes—
382C2×Dic17—22no—
383C2×Dic17—22no—
384C2×Dic17—22no—
385C2×Dic17—22no—
386C2×Dic17—22no—
387C2×Dic17—22no—
388C2×Dic17—22no—
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—416no—
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×Dic17C4×D414yes—
438C2×Dic17C4×D414yes—
439C2×#389—171no—
440C2×#388—171no—
441C2×#388D1711yescharacteristic
442C2×#385—171no—
443C2×#385—171no—
444C2×#385—171no—
445C2×#384—171no—
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×C17—24no—
455C22×C17—24no—
456C22×C17—24no—
457C22×C17—42no—
458C22×C17—42no—
459C22×C17—42no—
460C22×C17—42no—
461C22×C17—42no—
462C22×C17—42no—
463C22×C17—42no—
464C22×C17—42no—
465C22×C17—42no—
466C22×C17—42no—
467C22×C17—42no—
468C22×C17—42no—
469C22×C17C22×C4⋊C411yescharacteristic
470C22×C17C2×C4×D411yescharacteristic
471C22×C17C2×C4×D411yescharacteristic
472C22×C17#52011yescharacteristic
473C22×C17#52011yescharacteristic
474C22×C17#52011yescharacteristic
475C22×C17#52011yescharacteristic
476C22×C17#53411yescharacteristic
477C22×C17#53511yescharacteristic
478C22×C17#53511yescharacteristic
479C22×C17#53611yescharacteristic
480C22×C17#53611yescharacteristic
481C22×C17#53611yescharacteristic
482C22×C17#53911yescharacteristic
483C22×C17#53911yescharacteristic
484C22×C17#54211yescharacteristic
485C22×C17#54211yescharacteristic
486C22×C17#54411yescharacteristic
487C22×C17#54411yescharacteristic
488C22×C17D4211yescharacteristic
489C22×C17D4211yescharacteristic
490C22×C17D4211yescharacteristic
491C22×C17#54711yescharacteristic
492C22×C17#54711yescharacteristic
493C22×C17#54711yescharacteristic
494C22×C17#54811yescharacteristic
495C22×C17D4×Q811yescharacteristic
496C22×C17D4×Q811yescharacteristic
497C22×C17#55311yescharacteristic
498C22×C17#55411yescharacteristic
499C22×C17#55411yescharacteristic
500C22×C17#56011yescharacteristic
501C22×C17#56311yescharacteristic
502C22×C17#56311yescharacteristic
503C22×C17#56311yescharacteristic
504C4×C17—24no—
505C4×C17—24no—
506C4×C17—42no—
507C4×C17—42no—
508C4×C17—81no—
509C4×C17—81no—
510Dic17—24no—
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⋊C4—171no—
524C22×C4⋊C4—171no—
525C22×C4⋊C4—171no—
526C22×C4⋊C4—171no—
527C22×C4⋊C4—171no—
528C22×C4⋊C4C2×D1711yescharacteristic
529C22×C22⋊C4—171no—
530C22×C22⋊C4—171no—
531C22×C22⋊C4—171no—
532C22×C22⋊C4C2×D1711yescharacteristic
533C22×C22⋊C4C2×D1711yescharacteristic
534C22×C22⋊C4C2×D1711yescharacteristic
535C22×C42—171no—
536C22×C42C2×D1711yescharacteristic
537#389—344no—
538#388—24no—
539#388—178no—
540#385—344no—
541#385—344no—
542#385—344no—
543#384—344no—
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×#95C2×D1711yescharacteristic
559C2×#95C2×D1711yescharacteristic
560C2×C17—44no—
561C2×C17#231711yescharacteristic
562C2×C17#232211yescharacteristic
563C2×C17#232611yescharacteristic
564C2×C17D4×C4⋊C411yescharacteristic
565C2×C17D4×C4⋊C411yescharacteristic
566C2×C17#236111yescharacteristic
567C2×C17#238311yescharacteristic
568C2×C17#266911yescharacteristic
569C2×C17#267411yescharacteristic
570C2×C17#267711yescharacteristic
571C2×C17#268011yescharacteristic
572C2×C17#271811yescharacteristic
573C2×C17#272011yescharacteristic
574C2×C17#272911yescharacteristic
575C2×C17#279011yescharacteristic
576C25C22×D1711yescharacteristic
577C23×C4—171no—
578C23×C4—171no—
579C23×C4—171no—
580C23×C4—171no—
581C23×C4—171no—
582C23×C4—171no—
583C23×C4—171no—
584C23×C4—171no—
585C23×C4—342no—
586C23×C4—342no—
587C23×C4—342no—
588C23×C4—681no—
589C23×C4—681no—
590C23×C4—681no—
591C23×C4—681no—
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—41no—
601C2×C4⋊C4—174no—
602C2×C4⋊C4—174no—
603C2×C4⋊C4—342no—
604C2×C4⋊C4—342no—
605C2×C4⋊C4—342no—
606C2×C4⋊C4—342no—
607C2×C4⋊C4—342no—
608C2×C4⋊C4—342no—
609C2×C4⋊C4—342no—
610C2×C4⋊C4—342no—
611C2×C4⋊C4—342no—
612C2×C4⋊C4—342no—
613C2×C4⋊C4—342no—
614C2×C4⋊C4—342no—
615C2×C4⋊C4—342no—
616C2×C4⋊C4—342no—
617C2×C4⋊C4—681no—
618C2×C4⋊C4—681no—
619C2×C4⋊C4—681no—
620C2×C4⋊C4—681no—
621C2×C4⋊C4—681no—
622C2×C4⋊C4—681no—
623C2×C4⋊C4—681no—
624C2×C4⋊C4—681no—
625C2×C4⋊C4—681no—
626C2×C4⋊C4—681no—
627C2×C4⋊C4—681no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—41no—
633C2×C22⋊C4—41no—
634C2×C22⋊C4—174no—
635C2×C22⋊C4—174no—
636C2×C22⋊C4—342no—
637C2×C22⋊C4—342no—
638C2×C22⋊C4—342no—
639C2×C22⋊C4—342no—
640C2×C22⋊C4—342no—
641C2×C22⋊C4—681no—
642C2×C22⋊C4—681no—
643C2×C22⋊C4Dic3414yes—
644C2×C22⋊C4C4×D1714yes—
645C2×C22⋊C4C22⋊D1714yes—
646C2×C42—22no—
647C2×C42—22no—
648C2×C42—41no—
649C2×C42—174no—
650C2×C42—342no—
651C2×C42—342no—
652#95—22no—
653#95—22no—
654#95—174no—
655#95—174no—
656#95—174no—
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—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C2×Dic3412yes—
682C24C2×C4×D1712yes—
683C24C2×C22⋊D1712yes—
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—172no—
720C22×C4—172no—
721C22×C4—172no—
722C22×C4—172no—
723C22×C4—172no—
724C22×C4—172no—
725C22×C4—172no—
726C22×C4—172no—
727C22×C4—172no—
728C22×C4—172no—
729C22×C4—341no—
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—341no—
773C22×C4—341no—
774C22×C4—341no—
775C22×C4—684no—
776C22×C4—684no—
777C22×C4—684no—
778C22×C4—684no—
779C22×C4—684no—
780C22×C4—684no—
781C22×C4—684no—
782C22×C4C2×Dic3412yes—
783C22×C4C2×Dic3412yes—
784C22×C4C2×C4×D1712yes—
785C22×C4C2×C4×D1712yes—
786C22×C4D4×D1712yes—
787C22×C4D4×D1712yes—
788C22×C4C2×C22⋊D1712yes—
789C22×C4C2×C22⋊D1712yes—
790C4⋊C4—44no—
791C4⋊C4—348no—
792C4⋊C4—684no—
793C4⋊C4—684no—
794C4⋊C4—684no—
795C4⋊C4—684no—
796C4⋊C4—684no—
797C4⋊C4—684no—
798C4⋊C4—684no—
799C4⋊C4—684no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—348no—
803C22⋊C4—348no—
804C22⋊C4—684no—
805C22⋊C4#63225116yescomplemented
806C42—44no—
807C42—348no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×#6322514yes—
843C23C22×Dic3411yescharacteristic
844C23C22×C4×D1711yescharacteristic
845C23C2×D4×D1711yescharacteristic
846C23C2×D4×D1711yescharacteristic
847C23#1058769111yescharacteristic
848C23#1058769111yescharacteristic
849C23#41×D1711yescharacteristic
850C23#41×D1711yescharacteristic
851C23#1058769611yescharacteristic
852C23#1058769611yescharacteristic
853C23#1058769711yescharacteristic
854C23#1058769711yescharacteristic
855C23#1058769711yescharacteristic
856C23#1058769711yescharacteristic
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—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
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—174no—
899C2×C4—174no—
900C2×C4—342no—
901C2×C4—342no—
902C2×C4—342no—
903C2×C4—342no—
904C2×C4—342no—
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—342no—
924C2×C4—6816no—
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×C4—681no—
955C2×C4C2×#6322514yes—
956C2×C4C2×#6322514yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×#6322511yescharacteristic
973C22C4×D4×D1711yescharacteristic
974C22C4×D4×D1711yescharacteristic
975C22#1176328811yescharacteristic
976C22#1176328811yescharacteristic
977C22#1176328911yescharacteristic
978C22#1176328911yescharacteristic
979C22#1176336711yescharacteristic
980C22#1176337311yescharacteristic
981C22#1176337511yescharacteristic
982C22#1176337911yescharacteristic
983C22#1176338011yescharacteristic
984C22#1176338111yescharacteristic
985C22#1176340011yescharacteristic
986C22#1176340211yescharacteristic
987C22#1176342311yescharacteristic
988C22#1176342511yescharacteristic
989C22#1176343711yescharacteristic
990C22#1176343711yescharacteristic
991C22D4×C22⋊D1711yescharacteristic
992C22D4×C22⋊D1711yescharacteristic
993C22#1176344311yescharacteristic
994C22#1176345711yescharacteristic
995C22#1176345811yescharacteristic
996C22#1176345811yescharacteristic
997C22#1176346711yescharacteristic
998C22D4×Dic3411yescharacteristic
999C22D4×Dic3411yescharacteristic
1000C22#1176351011yescharacteristic
1001C22#1176351811yescharacteristic
1002C22#1176351811yescharacteristic
1003C22#1176354711yescharacteristic
1004C22#1176355911yescharacteristic
1005C22#1176356111yescharacteristic
1006C22#1176356211yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—344no—
1014C4—344no—
1015C4—682no—
1016C4—682no—
1017C4—682no—
1018C4—682no—
1019C4—1361no—
1020C4—1361no—
1021C2—44no—
1022C2#1453140411yescharacteristic
1023C2#1453145411yescharacteristic
1024C2#1453149311yescharacteristic
1025C2D4×#6322511yescharacteristic
1026C2D4×#6322511yescharacteristic
1027C2#1453179711yescharacteristic
1028C2#1453197111yescharacteristic
1029C2#1453499611yescharacteristic
1030C2#1453505911yescharacteristic
1031C2#1453509611yescharacteristic
1032C2#1453512111yescharacteristic
1033C2#1453562811yescharacteristic
1034C2#1453566811yescharacteristic
1035C2#1453576311yescharacteristic
1036C2#1453654911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#388D17
hypocenterC17#14405
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×#11762707C2semidirect
6. C2×#11762678C2semidirect
7. #14527048C2semidirect
8. #14527047C2semidirect
9. #14527040C2semidirect
10. #14527036C2semidirect
13. #14527017C2semidirect
14. #14527010C2semidirect
31. #11762702C4semidirect
112. C2×C4⋊Dic17C2×C4semidirect
133. C2×C4×Dic17C2×C4semidirect
147. #10587502C2×C4semidirect
148. #10587502C2×C4semidirect
274. C22⋊C4×C17C4⋊C4semidirect
668. C17#14405semidirect
805. C22⋊C4#63225semidirect

Maximal subgroups

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

subgroupindex
C2×#117627072
C2×#117627022
C2×#117626842
C2×#117626812
C2×#117626782
#145270482
#145270472
#145270402
#145270362
#145270272
#145270172
#145270102
C2×C17×#3882
#1440517