Finite Group Databasebeta

← #16964413

Subgroups — #16964413

Order 4352.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762722C211yesmaximal, characteristic
2C2×#11762714C211yesmaximal, characteristic, complemented
3C2×#11762713C211yesmaximal, characteristic, complemented
4C2×#11762680C211yesmaximal, characteristic
5C2×#11762680C211yesmaximal, characteristic
6#14527047C211yesmaximal, characteristic, complemented
7#14527043C211yesmaximal, characteristic, complemented
8#14527042C211yesmaximal, characteristic, complemented
9#14527026C211yesmaximal, characteristic
10#14527020C211yesmaximal, characteristic
11#14527020C211yesmaximal, characteristic
12#14527010C211yesmaximal, characteristic, complemented
13#14527009C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic
15C17×#1444C211yesmaximal, characteristic, complemented
16C23×Dic34C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×C4×Dic17C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28#11762722C418yescomplemented
29#11762714—24no—
30#11762713—24no—
31#11762680—24no—
32#11762680—24no—
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C22×C4⋊C4×C17C2211yescharacteristic
50C22×C4⋊C4×C17C2211yescharacteristic
51C22×C4⋊C4×C17C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C24×D17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C22×C4×D17—22no—
72C22×C4×D17—22no—
73C22×C4×D17—22no—
74C22×C4×D17—41no—
75C22×C4×D17—41no—
76C22×C4×D17—41no—
77C22×C4×D17—41no—
78C22×Dic34—22no—
79C22×Dic34—22no—
80C22×Dic34—22no—
81C22×Dic34—22no—
82C22×Dic34—41no—
83C22×Dic34—41no—
84C22×Dic34C2×C414yescomplemented
85C2×C4⋊C4×C17—22no—
86C2×C4⋊C4×C17—22no—
87C2×C4⋊C4×C17—22no—
88C2×C4⋊C4×C17—41no—
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×#63227—22no—
95C2×#63227—22no—
96C2×#63227—22no—
97C2×#63227—22no—
98C2×#63227—22no—
99C2×#63227—22no—
100C2×#63227—22no—
101C2×#63227—22no—
102C2×#63227—41no—
103C2×#63227—41no—
104C2×#63227—41no—
105C2×#63227—41no—
106C2×#63227—41no—
107C2×#63227—41no—
108C2×#63227C2×C414yes—
109C2×#63227C2×C414yes—
110C2×#63227C2×C414yes—
111C2×#63227Q814yescomplemented
112C2×#63225—22no—
113C2×#63225—22no—
114C2×#63225—22no—
115C2×#63225—41no—
116C2×#63225—41no—
117C2×#63225—41no—
118C2×C4×Dic17—22no—
119C2×C4×Dic17—22no—
120C2×C4×Dic17—22no—
121C2×C4×Dic17—22no—
122C2×C4×Dic17—41no—
123C2×C4×Dic17—41no—
124C17×#95—22no—
125C17×#95—41no—
126C17×#95—41no—
127C17×#95C2×C414yescomplemented
128#10587502—22no—
129#10587502—22no—
130#10587502—22no—
131#10587502—22no—
132#10587502—22no—
133#10587502—22no—
134#10587502—22no—
135#10587502—41no—
136#10587502—41no—
137#10587502—41no—
138#10587502—41no—
139#10587502—41no—
140#10587502C2×C414yescomplemented
141#10587502C2×C414yescomplemented
142#10587502D414yes—
143#10587502D414yes—
144C24×C17C2411yescharacteristic
145C23×D17—21no—
146C23×D17—21no—
147C23×D17—21no—
148C23×D17—21no—
149C23×D17—21no—
150C23×D17—21no—
151C23×D17—21no—
152C23×D17—21no—
153C23×D17—21no—
154C23×D17—21no—
155C23×D17—21no—
156C23×D17—21no—
157C23×D17C22×C412yes—
158C23×D17C2×Q812yes—
159C23×D17#4112yes—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17C22×C412yes—
203C22×C4×C17C22×C412yes—
204C22×C4×C17C22×C412yes—
205C22×C4×C17C2×D412yes—
206C22×C4×C17C2×D412yes—
207C22×C4×C17C2×Q812yes—
208C22×C4×C17#4112yes—
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×Dic17C22×C412yes—
250C22×Dic17C22×C412yes—
251C22×Dic17C22×C412yes—
252C22×Dic17C2×D412yes—
253C22×Dic17C2×D412yes—
254C22×Dic17C2×D412yes—
255C22×Dic17C2×D412yes—
256C22×Dic17C2×Q812yes—
257C22×Dic17#4112yes—
258C2×C4×D17—44no—
259C2×C4×D17—44no—
260C2×C4×D17—44no—
261C2×C4×D17—44no—
262C2×C4×D17—44no—
263C2×C4×D17—44no—
264C2×C4×D17—44no—
265C2×Dic34—28no—
266C2×Dic34—28no—
267C2×Dic34—44no—
268C2×Dic34—44no—
269C2×Dic34—44no—
270C2×Dic34—44no—
271C2×Dic34—44no—
272C4⋊C4×C17—44no—
273C4⋊C4×C17—44no—
274C4⋊C4×C17—44no—
275#63227—28no—
276#63227—28no—
277#63227—44no—
278#63227—44no—
279#63227—44no—
280#63227—44no—
281#63225—44no—
282#63225—44no—
283C4×Dic17—44no—
284C4×Dic17—44no—
285#14575—171nomaximal, Sylow
286C23×C17C23×C411yescharacteristic
287C23×C17C22×D411yescharacteristic
288C23×C17C22×D411yescharacteristic
289C23×C17C22×Q811yescharacteristic
290C23×C17C2×#4111yescharacteristic
291C23×C17C2×#4111yescharacteristic
292C23×C17C2×#4111yescharacteristic
293C23×C17H(5,𝔽2)11yescharacteristic
294C23×C17H(5,𝔽2)11yescharacteristic
295C23×C17H(5,𝔽2)11yescharacteristic
296C23×C17H(5,𝔽2)11yescharacteristic
297C23×C17H(5,𝔽2)11yescharacteristic
298C23×C172−1+411yescharacteristic
299C23×C172−1+411yescharacteristic
300C23×C172−1+411yescharacteristic
301C22×D17—22no—
302C22×D17—22no—
303C22×D17—22no—
304C22×D17—22no—
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—41no—
320C22×D17—41no—
321C22×D17—41no—
322C22×D17—41no—
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×D17C4×Q814yes—
336C2×C4×C17—22no—
337C2×C4×C17—22no—
338C2×C4×C17—22no—
339C2×C4×C17—22no—
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—41no—
355C2×C4×C17—41no—
356C2×C4×C17—41no—
357C2×C4×C17—41no—
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×C17—41no—
381C2×C4×C17—41no—
382C2×C4×C17—41no—
383C2×C4×C17—41no—
384C2×C4×C17C4×D414yes—
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—22no—
407C2×Dic17—22no—
408C2×Dic17—22no—
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×Dic17C4×D414yes—
434C4×D17—416no—
435Dic34—416no—
436C2×#393—171no—
437C2×#391—171no—
438C2×#391—171no—
439C2×#385—171no—
440C2×#385—171no—
441#1444—171no—
442#1444D1711yescharacteristic, complemented
443#1442—171no—
444#1442—171no—
445#1439—171no—
446#1437—171no—
447#1437—171no—
448#1434—171no—
449#1434—171no—
450C22⋊#95—171no—
451C22×C17C2×C4×D411yescharacteristic
452C22×C17C2×C4×D411yescharacteristic
453C22×C17C2×C4×Q811yescharacteristic
454C22×C17#51811yescharacteristic
455C22×C17#52011yescharacteristic
456C22×C17#52011yescharacteristic
457C22×C17#52011yescharacteristic
458C22×C17#53511yescharacteristic
459C22×C17#53511yescharacteristic
460C22×C17#53611yescharacteristic
461C22×C17#53611yescharacteristic
462C22×C17#53811yescharacteristic
463C22×C17#53911yescharacteristic
464C22×C17#54211yescharacteristic
465C22×C17#54211yescharacteristic
466C22×C17#54211yescharacteristic
467C22×C17#54211yescharacteristic
468C22×C17#54311yescharacteristic
469C22×C17#54411yescharacteristic
470C22×C17D4211yescharacteristic
471C22×C17#54611yescharacteristic
472C22×C17#54611yescharacteristic
473C22×C17#54611yescharacteristic
474C22×C17#54611yescharacteristic
475C22×C17D4×Q811yescharacteristic
476C22×C17D4×Q811yescharacteristic
477C22×C17#55111yescharacteristic
478C22×C17#55211yescharacteristic
479C22×C17#55211yescharacteristic
480C22×C17#55411yescharacteristic
481C22×C17#55411yescharacteristic
482C22×C17H(3,𝔽4)11yescharacteristic
483C22×C17#56211yescharacteristic
484C22×C17#56211yescharacteristic
485C22×C17#56311yescharacteristic
486C2×D17—24no—
487C2×D17—24no—
488C2×D17—24no—
489C2×D17—42no—
490C2×D17—42no—
491C2×D17—42no—
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—
501C4×C17—24no—
502C4×C17—42no—
503C4×C17—42no—
504C4×C17—42no—
505C4×C17—42no—
506C4×C17—81no—
507C4×C17—81no—
508Dic17—24no—
509Dic17—42no—
510Dic17—42no—
511Dic17—42no—
512Dic17—42no—
513Dic17—42no—
514Dic17—42no—
515C23×Q8—171no—
516C24×C4—171no—
517C22×C4⋊C4—171no—
518C22×C4⋊C4—171no—
519C22×C4⋊C4C2×D1711yescharacteristic
520C22×C4⋊C4C2×D1711yescharacteristic
521C22×C4⋊C4C2×D1711yescharacteristic
522C22×C22⋊C4—171no—
523C22×C22⋊C4—171no—
524C22×C22⋊C4—171no—
525C22×C22⋊C4—171no—
526C22×C22⋊C4—171no—
527C22×C22⋊C4—171no—
528C22×C42—171no—
529C22×C42—171no—
530#393—178no—
531#391—344no—
532#391—344no—
533#385—344no—
534#385—344no—
535C2×#95—171no—
536C2×#95—171no—
537C2×#95—171no—
538C2×#95—171no—
539C2×#95—171no—
540C2×#95—171no—
541C2×#95—171no—
542C2×#95—171no—
543C2×#95—171no—
544C2×#95—171no—
545C2×#95—171no—
546C2×#95—171no—
547C2×#95—171no—
548C2×#95—171no—
549C2×#95—171no—
550C2×#95—171no—
551C2×#95C2×D1711yescharacteristic
552C2×#95C2×D1711yescharacteristic
553C2×#95C2×D1711yescharacteristic
554C2×#95C2×D1711yescharacteristic
555C2×C17#232611yescharacteristic
556C2×C17#232611yescharacteristic
557C2×C17#232911yescharacteristic
558C2×C17#235811yescharacteristic
559C2×C17#236011yescharacteristic
560C2×C17#236011yescharacteristic
561C2×C17#237911yescharacteristic
562C2×C17#267011yescharacteristic
563C2×C17#267711yescharacteristic
564C2×C17#268711yescharacteristic
565C2×C17#268711yescharacteristic
566C2×C17#269211yescharacteristic
567C2×C17#269211yescharacteristic
568C2×C17#276311yescharacteristic
569C2×C17#276411yescharacteristic
570D17—44no—
571C25—171no—
572C22×Q8—174no—
573C22×Q8—342no—
574C22×Q8—342no—
575C22×Q8—342no—
576C22×Q8—342no—
577C22×Q8—681no—
578C22×Q8—681no—
579C23×C4—171no—
580C23×C4—171no—
581C23×C4—171no—
582C23×C4—171no—
583C23×C4—171no—
584C23×C4—171no—
585C23×C4—171no—
586C23×C4—342no—
587C23×C4—342no—
588C23×C4—342no—
589C23×C4—681no—
590C23×C4—681no—
591C23×C4—681no—
592C23×C4—681no—
593C23×C4C22×D1711yescharacteristic
594C23×C4C22×D1711yescharacteristic
595C23×C4C22×D1711yescharacteristic
596C23×C4C22×D1711yescharacteristic
597C23×C4C22×D1711yescharacteristic
598C23×C4C22×D1711yescharacteristic
599C23×C4C22×D1711yescharacteristic
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—342no—
610C2×C4⋊C4—342no—
611C2×C4⋊C4—342no—
612C2×C4⋊C4—681no—
613C2×C4⋊C4—681no—
614C2×C4⋊C4—681no—
615C2×C22⋊C4—174no—
616C2×C22⋊C4—174no—
617C2×C22⋊C4—174no—
618C2×C22⋊C4—174no—
619C2×C22⋊C4—342no—
620C2×C22⋊C4—342no—
621C2×C22⋊C4—342no—
622C2×C22⋊C4—342no—
623C2×C22⋊C4—342no—
624C2×C22⋊C4—342no—
625C2×C22⋊C4—342no—
626C2×C22⋊C4—342no—
627C2×C22⋊C4—681no—
628C2×C22⋊C4—681no—
629C2×C22⋊C4—681no—
630C2×C22⋊C4—681no—
631C2×C22⋊C4—681no—
632C2×C22⋊C4—681no—
633C2×C42—342no—
634C2×C42—342no—
635C2×C42—342no—
636C2×C42—342no—
637C2×C42—681no—
638C2×C42—681no—
639#95—22no—
640#95—41no—
641#95—41no—
642#95—174no—
643#95—174no—
644#95—174no—
645#95—174no—
646#95—342no—
647#95—342no—
648#95—342no—
649#95—342no—
650#95—342no—
651#95—342no—
652#95—342no—
653#95—681no—
654#95—681no—
655#95—681no—
656#95—681no—
657#95—681no—
658#95C4×D1714yescomplemented
659C17#1457511yescharacteristic, complemented, Sylow
660C24—172no—
661C24—172no—
662C24—172no—
663C24—341no—
664C24—341no—
665C24—341no—
666C24—341no—
667C24—341no—
668C24—341no—
669C24—341no—
670C24—341no—
671C24—341no—
672C24—341no—
673C24—341no—
674C24—341no—
675C24C23×D1711yescharacteristic
676C2×Q8—348no—
677C2×Q8—348no—
678C2×Q8—684no—
679C2×Q8—684no—
680C2×Q8—684no—
681C2×Q8—684no—
682C2×Q8—684no—
683C22×C4—21no—
684C22×C4—21no—
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—21no—
724C22×C4—21no—
725C22×C4—172no—
726C22×C4—172no—
727C22×C4—172no—
728C22×C4—172no—
729C22×C4—172no—
730C22×C4—172no—
731C22×C4—172no—
732C22×C4—172no—
733C22×C4—172no—
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—684no—
775C22×C4—684no—
776C22×C4—684no—
777C22×C4—684no—
778C22×C4—684no—
779C22×C4—684no—
780C22×C4—684no—
781C22×C4C2×C4×D1712yes—
782C22×C4C2×C4×D1712yes—
783C22×C4C2×C4×D1712yes—
784C22×C4D4×D1712yes—
785C22×C4D4×D1712yes—
786C22×C4Q8×D1712yes—
787C22×C4#6325612yes—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—684no—
792C4⋊C4—684no—
793C22⋊C4—348no—
794C22⋊C4—348no—
795C22⋊C4—684no—
796C22⋊C4—684no—
797C22⋊C4—684no—
798C22⋊C4—684no—
799C42—684no—
800C42—684no—
801C23—174no—
802C23—342no—
803C23—342no—
804C23—342no—
805C23—342no—
806C23—342no—
807C23—342no—
808C23—342no—
809C23—342no—
810C23—342no—
811C23—342no—
812C23—342no—
813C23—342no—
814C23—342no—
815C23—342no—
816C23—342no—
817C23—342no—
818C23—342no—
819C23—342no—
820C23—681no—
821C23—681no—
822C23—681no—
823C23—681no—
824C23—681no—
825C23—681no—
826C23—681no—
827C23—681no—
828C23—681no—
829C23—681no—
830C23—681no—
831C23—681no—
832C23—681no—
833C23—681no—
834C23—681no—
835C23—681no—
836C23C22×C4×D1711yescharacteristic
837C23C2×D4×D1711yescharacteristic
838C23C2×D4×D1711yescharacteristic
839C23#1058769111yescharacteristic
840C23#1058769111yescharacteristic
841C23#1058769111yescharacteristic
842C23#1058769111yescharacteristic
843C23C2×Q8×D1711yescharacteristic
844C23C2×#6325611yescharacteristic
845C23#1058769411yescharacteristic
846C23#1058769411yescharacteristic
847C23#41×D1711yescharacteristic
848C23#41×D1711yescharacteristic
849C23#1058769611yescharacteristic
850C23#1058769711yescharacteristic
851Q8—6816no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
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—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
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—41no—
899C2×C4—41no—
900C2×C4—174no—
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—342no—
925C2×C4—6816no—
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#1058757914yes—
951C22—344no—
952C22—344no—
953C22—344no—
954C22—682no—
955C22—682no—
956C22—682no—
957C22—682no—
958C22—682no—
959C22—682no—
960C22—682no—
961C22—682no—
962C22—682no—
963C22—682no—
964C22—682no—
965C22—682no—
966C22C4×D4×D1711yescharacteristic
967C22C2×#1058757911yescharacteristic
968C22C4×Q8×D1711yescharacteristic
969C22#1176328111yescharacteristic
970C22#1176328811yescharacteristic
971C22#1176329011yescharacteristic
972C22#1176329011yescharacteristic
973C22#1176337211yescharacteristic
974C22#1176337411yescharacteristic
975C22#1176338211yescharacteristic
976C22#1176338411yescharacteristic
977C22#1176339111yescharacteristic
978C22#1176340711yescharacteristic
979C22#1176342711yescharacteristic
980C22#1176342911yescharacteristic
981C22#1176343311yescharacteristic
982C22#1176343311yescharacteristic
983C22#1176343411yescharacteristic
984C22#1176343611yescharacteristic
985C22#1176344111yescharacteristic
986C22#1176344811yescharacteristic
987C22#1176345011yescharacteristic
988C22#1176345111yescharacteristic
989C22#1176345611yescharacteristic
990C22#1176347211yescharacteristic
991C22#1176347411yescharacteristic
992C22#1176348611yescharacteristic
993C22#1176349111yescharacteristic
994C22#1176349711yescharacteristic
995C22#1176351311yescharacteristic
996C22#1176352011yescharacteristic
997C22#1176355211yescharacteristic
998C22#1176355511yescharacteristic
999C22#1176355611yescharacteristic
1000C22#1176356011yescharacteristic
1001C4—24no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—81no—
1007C4—81no—
1008C4—344no—
1009C4—682no—
1010C4—682no—
1011C4—682no—
1012C4—682no—
1013C4—682no—
1014C4—682no—
1015C2—684no—
1016C2#1453149011yescharacteristic
1017C2#1453149211yescharacteristic
1018C2#1453151811yescharacteristic
1019C2#1453176011yescharacteristic
1020C2#1453178611yescharacteristic
1021C2#1453178811yescharacteristic
1022C2#1453195711yescharacteristic
1023C2#1453500911yescharacteristic
1024C2#1453509811yescharacteristic
1025C2#1453519811yescharacteristic
1026C2#1453521211yescharacteristic
1027C2#1453527311yescharacteristic
1028C2#1453528711yescharacteristic
1029C2#1453619411yescharacteristic
1030C2#1453620311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1444C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenter#1444D17
hypocenterC17#14575
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
2. C2×#11762714C2semidirect
3. C2×#11762713C2semidirect
6. #14527047C2semidirect
7. #14527043C2semidirect
8. #14527042C2semidirect
12. #14527010C2semidirect
13. #14527009C2semidirect
15. C17×#1444C2semidirect
28. #11762722C4semidirect
84. C22×Dic34C2×C4semidirect
111. C2×#63227Q8semidirect
127. C17×#95C2×C4semidirect
140. #10587502C2×C4semidirect
141. #10587502C2×C4semidirect
442. #1444D17semidirect
658. #95C4×D17semidirect
659. C17#14575semidirect

Maximal subgroups

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

subgroupindex
C2×#117627222
C2×#117627142
C2×#117627132
C2×#117626802
#145270472
#145270432
#145270422
#145270262
#145270202
#145270102
#145270092
#145270052
C17×#14442
#1457517