Finite Group Databasebeta

← #17050995

Subgroups — #17050995

Order 4352.

1066 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762940C211yesmaximal, characteristic, complemented
2#14531741C211yesmaximal, characteristic, complemented
3#14529758C211yesmaximal, characteristic, complemented
4#14529754C211yesmaximal, characteristic, complemented
5#14529750C211yesmaximal, characteristic, complemented
6#14529742C211yesmaximal, characteristic, complemented
7#14529742C211yesmaximal, characteristic, complemented
8#14529737C211yesmaximal, characteristic, complemented
9#14528794C211yesmaximal, characteristic
10#14528794C211yesmaximal, characteristic
11#14528784C211yesmaximal, characteristic
12#14528609C211yesmaximal, characteristic
13#14528609C211yesmaximal, characteristic
14C4×#10587503C211yesmaximal, characteristic
15C2×C17×#554C211yesmaximal, characteristic
16#11762940—24no—
17C2×C4⋊#3622C2211yescharacteristic
18C2×C4⋊#3622C2211yescharacteristic
19C2×C4⋊#3622C2211yescharacteristic
20C2×#10587503C2211yescharacteristic
21C2×#10587503C2211yescharacteristic
22C2×#10587503C2211yescharacteristic
23C2×#10587503C2211yescharacteristic
24C2×#10587474C2211yescharacteristic
25C2×#10587474C2211yescharacteristic
26C2×C4×#3622C2211yescharacteristic
27#11762716—21no—
28#11762695—21no—
29#11762695—21no—
30#11762679C2211yescharacteristic
31#11762675C2211yescharacteristic
32#11762675C2211yescharacteristic
33C4⋊C4×Dic17—21no—
34C4×C4⋊Dic17C2211yescharacteristic
35C4×C4⋊Dic17C2211yescharacteristic
36C4×C4⋊Dic17C2211yescharacteristic
37#11762571C2211yescharacteristic
38#11762571C2211yescharacteristic
39#11762571C2211yescharacteristic
40#11762571C2211yescharacteristic
41#11762571C2211yescharacteristic
42#11762571C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49C17×#554—24no—
50C17×#554C418yescomplemented
51C2×C17×C4⋊Q8C2211yescharacteristic
52C2×C17×#125C2211yescharacteristic
53C2×C17×#125C2211yescharacteristic
54C2×C17×C22⋊Q8—21no—
55C2×C17×C22⋊Q8—21no—
56C2×C17×C22⋊Q8—21no—
57C2×C4×Q8×C17C2211yescharacteristic
58C2×C4×D4×C17C2211yescharacteristic
59C2×C4×D4×C17C2211yescharacteristic
60C2×C4×D4×C17C2211yescharacteristic
61C22×C4⋊C4×C17—21no—
62C22×Q8×C17—21no—
63C22×Q8×C17D411yescharacteristic
64C22×D4×C17C2311yescharacteristic
65C23×C4×C17—21no—
66C23×C4×C17—21no—
67C23×C4×C17—21no—
68C17×C4⋊Q8—22no—
69C17×C4⋊Q8C2×C414yes—
70C17×#125—22no—
71C17×#125—22no—
72C17×#125C2×C414yes—
73C17×#125C2×C414yes—
74C17×C22⋊Q8—28no—
75C17×C22⋊Q8—28no—
76C17×C22⋊Q8—28no—
77C4×Q8×C17C2×C414yes—
78C4×Q8×C17D414yes—
79C4×D4×C17—22no—
80C4×D4×C17—22no—
81C4×D4×C17—22no—
82C4×D4×C17C2×C414yes—
83C4×D4×C17C2×C414yes—
84C4×D4×C17C2×C414yes—
85C2×C4⋊C4×C17—21no—
86C2×C4⋊C4×C17—21no—
87C2×C4⋊C4×C17—21no—
88C2×C4⋊C4×C17—21no—
89C2×C4⋊C4×C17—21no—
90C2×C4⋊C4×C17—28no—
91C2×C4⋊C4×C17D411yescharacteristic
92C2×C4⋊C4×C17D411yescharacteristic
93C2×C4⋊C4×C17D411yescharacteristic
94C2×C4⋊C4×C17C2311yescharacteristic
95C2×C4⋊C4×C17C2311yescharacteristic
96C2×C4⋊C4×C17C2311yescharacteristic
97C2×C22⋊C4×C17—21no—
98C2×C22⋊C4×C17—21no—
99C2×C22⋊C4×C17—21no—
100C2×C42×C17C2311yescharacteristic
101C2×C42×C17C2311yescharacteristic
102C2×C42×C17C2311yescharacteristic
103C2×C4⋊Dic17—21no—
104C2×C4⋊Dic17—21no—
105C2×C4⋊Dic17C2311yescharacteristic
106C2×C4⋊Dic17C2311yescharacteristic
107C2×C4⋊Dic17C2311yescharacteristic
108C2×C4⋊Dic17C2311yescharacteristic
109C2×C4×Dic17—21no—
110C2×C4×Dic17—21no—
111C2×C4×Dic17—21no—
112C22×#3622C2311yescharacteristic
113C22×#3622C2311yescharacteristic
114C22×#3622C2311yescharacteristic
115C22×#3622C2311yescharacteristic
116#10587503—22no—
117#10587503—22no—
118#10587503—22no—
119#10587503Q814yescomplemented
120#10587502—21no—
121#10587502—21no—
122#10587502—21no—
123#10587502—21no—
124#10587502—21no—
125#10587502—21no—
126#10587502—21no—
127C4⋊#3622—22no—
128C4⋊#3622—22no—
129C4⋊#3622—22no—
130#10587474—22no—
131#10587474—22no—
132C4×#3622—22no—
133C24×C17—21no—
134C2×Q8×C17—24no—
135C2×Q8×C17—41no—
136C2×Q8×C17—41no—
137C2×Q8×C17—81no—
138C2×Q8×C17—81no—
139C2×Q8×C17C22⋊C414yes—
140C2×D4×C17—21no—
141C2×D4×C17—21no—
142C2×D4×C17—21no—
143C2×D4×C17C22×C412yes—
144C2×D4×C17C2×Q812yes—
145C2×D4×C17#4112yes—
146C22×C4×C17—21no—
147C22×C4×C17—21no—
148C22×C4×C17—21no—
149C22×C4×C17—24no—
150C22×C4×C17—24no—
151C22×C4×C17—24no—
152C22×C4×C17—42no—
153C22×C4×C17—42no—
154C22×C4×C17—81no—
155C22×C4×C17—81no—
156C22×C4×C17—81no—
157C22×C4×C17—81no—
158C22×C4×C17C2×D411yescharacteristic
159C22×C4×C17C2×D411yescharacteristic
160C22×C4×C17C2×D411yescharacteristic
161C22×C4×C17C2×D411yescharacteristic
162C22×C4×C17C2×D411yescharacteristic
163C22×C4×C17C2×D411yescharacteristic
164C22×C4×C17C2411yescharacteristic
165C22×Dic17—21no—
166C22×Dic17—21no—
167C22×Dic17—21no—
168C22×Dic17—21no—
169C4⋊C4×C17—24no—
170C4⋊C4×C17—24no—
171C4⋊C4×C17—24no—
172C4⋊C4×C17—24no—
173C4⋊C4×C17—24no—
174C4⋊C4×C17—21no—
175C4⋊C4×C17—21no—
176C4⋊C4×C17—21no—
177C4⋊C4×C17C22⋊C414yes—
178C4⋊C4×C17C22⋊C414yes—
179C4⋊C4×C17C22⋊C414yes—
180C4⋊C4×C17C22×C412yes—
181C4⋊C4×C17C22×C412yes—
182C4⋊C4×C17C22×C412yes—
183C22⋊C4×C17—24no—
184C22⋊C4×C17—24no—
185C22⋊C4×C17—24no—
186C42×C17C22×C412yes—
187C42×C17C22×C412yes—
188C42×C17C22×C412yes—
189C42×C17C2×D412yes—
190C42×C17C2×D412yes—
191C42×C17C2×D412yes—
192C4⋊Dic17—21no—
193C4⋊Dic17—21no—
194C4⋊Dic17—21no—
195C4⋊Dic17—21no—
196C4⋊Dic17—21no—
197C4⋊Dic17—21no—
198C4⋊Dic17—21no—
199C4⋊Dic17—42no—
200C4⋊Dic17—81no—
201C4⋊Dic17C2×Q812yes—
202C4×Dic17—42no—
203C4×Dic17—81no—
204C4×Dic17—81no—
205C2×#3622—21no—
206C2×#3622—21no—
207C2×#3622—21no—
208C2×#3622—21no—
209C2×#3622—21no—
210C2×#3622—21no—
211C2×#3622—21no—
212C2×#3622—21no—
213C2×#3622—21no—
214C2×#3622—21no—
215C2×#3622—21no—
216C2×#3622C2×Q812yes—
217#22526—171nomaximal, Sylow
218C23×C17—22no—
219C23×C17—22no—
220C23×C17—22no—
221C23×C17—41no—
222C23×C17—41no—
223C23×C17—41no—
224C23×C17—41no—
225C23×C17C22×D411yescharacteristic
226Q8×C17—44no—
227Q8×C17—84no—
228D4×C17—22no—
229D4×C17—22no—
230D4×C17—22no—
231D4×C17C4×Q814yes—
232C2×C4×C17—21no—
233C2×C4×C17—21no—
234C2×C4×C17—21no—
235C2×C4×C17—21no—
236C2×C4×C17—21no—
237C2×C4×C17—21no—
238C2×C4×C17—21no—
239C2×C4×C17—21no—
240C2×C4×C17—21no—
241C2×C4×C17—21no—
242C2×C4×C17—21no—
243C2×C4×C17—21no—
244C2×C4×C17—22no—
245C2×C4×C17—22no—
246C2×C4×C17—22no—
247C2×C4×C17—48no—
248C2×C4×C17—41no—
249C2×C4×C17—41no—
250C2×C4×C17—41no—
251C2×C4×C17—41no—
252C2×C4×C17—41no—
253C2×C4×C17—41no—
254C2×C4×C17—84no—
255C2×C4×C17—84no—
256C2×C4×C17C2×C22⋊C412yes—
257C2×C4×C17C2×C22⋊C412yes—
258C2×C4×C17C2×C22⋊C412yes—
259C2×C4×C17C2×C22⋊C412yes—
260C2×C4×C17C2×C22⋊C412yes—
261C2×C4×C17C2×C22⋊C412yes—
262C2×C4×C17C23×C411yescharacteristic
263C2×C4×C17C22×D411yescharacteristic
264C2×C4×C17C22×Q811yescharacteristic
265C2×C4×C17C2×#4111yescharacteristic
266C2×C4×C172−1+411yescharacteristic
267C2×C4×C172−1+411yescharacteristic
268C2×Dic17—22no—
269C2×Dic17—41no—
270C2×Dic17—41no—
271C2×Dic17—41no—
272C2×Dic17—41no—
273C2×Dic17—41no—
274C2×Dic17—41no—
275C2×Dic17—41no—
276C2×Dic17—41no—
277C2×Dic17—41no—
278C2×Dic17—41no—
279C2×Dic17—41no—
280#3622—22no—
281#3622—41no—
282#3622—41no—
283#3622—41no—
284C2×#554D1711yescharacteristic
285C2×#446—171no—
286#2355—171no—
287#1993—171no—
288#1992—171no—
289#1991—171no—
290#1989—171no—
291#1989—171no—
292#1988—171no—
293#1804—171no—
294#1804—171no—
295#1802—171no—
296#1762—171no—
297#1762—171no—
298C4×#102—171no—
299C22×C17—24no—
300C22×C17—42no—
301C22×C17—42no—
302C22×C17—42no—
303C22×C17—42no—
304C22×C17—42no—
305C22×C17—42no—
306C22×C17C22×C22⋊C411yescharacteristic
307C22×C17#54811yescharacteristic
308C22×C17D4×Q811yescharacteristic
309C22×C17#57511yescharacteristic
310C22×C17#57511yescharacteristic
311C22×C17#57611yescharacteristic
312C22×C17#57711yescharacteristic
313C4×C17—22no—
314C4×C17—22no—
315C4×C17—22no—
316C4×C17—22no—
317C4×C17—22no—
318C4×C17—22no—
319C4×C17—42no—
320C4×C17—42no—
321C4×C17—42no—
322C4×C17C2×C4×Q811yescharacteristic
323C4×C17#51911yescharacteristic
324C4×C17#54811yescharacteristic
325C4×C17D4×Q811yescharacteristic
326Dic17—42no—
327Dic17—81no—
328Dic17—81no—
329Dic17—81no—
330#554—24no—
331#554Dic1718yescomplemented
332C2×C4⋊Q8C2×D1711yescharacteristic
333C2×#125C2×D1711yescharacteristic
334C2×#125C2×D1711yescharacteristic
335C2×C22⋊Q8—21no—
336C2×C22⋊Q8—21no—
337C2×C22⋊Q8—21no—
338C2×C4×Q8C2×D1711yescharacteristic
339C2×C4×D4C2×D1711yescharacteristic
340C2×C4×D4C2×D1711yescharacteristic
341C2×C4×D4C2×D1711yescharacteristic
342C22×C4⋊C4—21no—
343#446—344no—
344C2×C4⋊C8—171no—
345C2×C4⋊C8—171no—
346C2×C4⋊C8—171no—
347C2×#102—171no—
348C2×#102—171no—
349C2×#102—171no—
350C2×#102—171no—
351C2×#97—171no—
352C2×#97—171no—
353C2×C4×C8—171no—
354#391—341no—
355#387—341no—
356#387—341no—
357#384—171no—
358#382—171no—
359#382—171no—
360C4×C4⋊C4—171no—
361C4×C4⋊C4—171no—
362C4×C4⋊C4—171no—
363C4×C4⋊C4—341no—
364#340—171no—
365#340—171no—
366#340—171no—
367#340—171no—
368#340—171no—
369#340—171no—
370#340—171no—
371#340—171no—
372#340—171no—
373#340—171no—
374#340—171no—
375#340—171no—
376C2×C17—44no—
377C2×C17Q8×C22⋊C411yescharacteristic
378C2×C17#289611yescharacteristic
379C2×C17#289711yescharacteristic
380C2×C17#337011yescharacteristic
381C2×C17#337611yescharacteristic
382C2×C17#338811yescharacteristic
383C2×C17#338911yescharacteristic
384C22×Q8—21no—
385C22×Q8C22⋊D1711yescharacteristic
386C22×D4C22×D1711yescharacteristic
387C23×C4—21no—
388C23×C4—21no—
389C23×C4—21no—
390C22×C8—171no—
391C22×C8—171no—
392C22×C8—171no—
393C22×C8—171no—
394C4⋊Q8—22no—
395C4⋊Q8C2×Dic1714yes—
396#125—22no—
397#125—22no—
398#125C2×Dic1714yes—
399#125C2×Dic1714yes—
400C22⋊Q8—28no—
401C22⋊Q8—28no—
402C22⋊Q8—28no—
403C4×Q8C2×Dic1714yes—
404C4×Q8C22⋊D1714yes—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4C2×Dic1714yes—
409C4×D4C2×Dic1714yes—
410C4×D4C2×Dic1714yes—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—28no—
417C2×C4⋊C4—171no—
418C2×C4⋊C4—171no—
419C2×C4⋊C4—171no—
420C2×C4⋊C4—171no—
421C2×C4⋊C4—341no—
422C2×C4⋊C4—341no—
423C2×C4⋊C4C22⋊D1711yescharacteristic
424C2×C4⋊C4C22⋊D1711yescharacteristic
425C2×C4⋊C4C22⋊D1711yescharacteristic
426C2×C4⋊C4C22×D1711yescharacteristic
427C2×C4⋊C4C22×D1711yescharacteristic
428C2×C4⋊C4C22×D1711yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C42—341no—
433C2×C42—341no—
434C2×C42—341no—
435C2×C42C22×D1711yescharacteristic
436C2×C42C22×D1711yescharacteristic
437C2×C42C22×D1711yescharacteristic
438C4⋊C8—342no—
439C4⋊C8—342no—
440C4⋊C8—342no—
441#102—174no—
442#102—342no—
443#102—342no—
444#102—342no—
445#97—342no—
446#97—342no—
447C4×C8—342no—
448#95—341no—
449#95—341no—
450#95—341no—
451#95—341no—
452#95—341no—
453#95—341no—
454#95—341no—
455C17#2252611yescharacteristic, complemented, Sylow
456C24—21no—
457C2×Q8—24no—
458C2×Q8—41no—
459C2×Q8—41no—
460C2×Q8—81no—
461C2×Q8—81no—
462C2×Q8C22⋊Dic1714yes—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4Q8×D1712yes—
467C2×D4#6325612yes—
468C2×D4C22×Dic1712yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—81no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4—81no—
481C22×C4—341no—
482C22×C4—341no—
483C22×C4—341no—
484C22×C4—341no—
485C22×C4C2×C22⋊D1711yescharacteristic
486C22×C4C2×C22⋊D1711yescharacteristic
487C22×C4C2×C22⋊D1711yescharacteristic
488C22×C4C2×C22⋊D1711yescharacteristic
489C22×C4C2×C22⋊D1711yescharacteristic
490C22×C4C2×C22⋊D1711yescharacteristic
491C22×C4C23×D1711yescharacteristic
492C2×C8—172no—
493C2×C8—341no—
494C2×C8—341no—
495C2×C8—341no—
496C2×C8—341no—
497C2×C8—341no—
498C2×C8—341no—
499C2×C8—341no—
500C2×C8—341no—
501C2×C8—341no—
502C2×C8—341no—
503C2×C8—341no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—24no—
508C4⋊C4—24no—
509C4⋊C4—24no—
510C4⋊C4—24no—
511C4⋊C4—24no—
512C4⋊C4—172no—
513C4⋊C4—341no—
514C4⋊C4—341no—
515C4⋊C4—341no—
516C4⋊C4—341no—
517C4⋊C4—341no—
518C4⋊C4—341no—
519C4⋊C4—341no—
520C4⋊C4—682no—
521C4⋊C4—1361no—
522C4⋊C4C22⋊Dic1714yes—
523C4⋊C4C22⋊Dic1714yes—
524C4⋊C4C22⋊Dic1714yes—
525C4⋊C4C22×Dic1712yes—
526C4⋊C4C22×Dic1712yes—
527C4⋊C4C22×Dic1712yes—
528C22⋊C4—24no—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C42—682no—
532C42—1361no—
533C42—1361no—
534C42C22×Dic1712yes—
535C42C22×Dic1712yes—
536C42C22×Dic1712yes—
537C42C2×C22⋊D1712yes—
538C42C2×C22⋊D1712yes—
539C42C2×C22⋊D1712yes—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23C22×C22⋊D1711yescharacteristic
548Q8—44no—
549Q8—84no—
550D4—22no—
551D4—22no—
552D4—22no—
553D4Q8×Dic1714yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—48no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—84no—
577C2×C4—84no—
578C2×C4—342no—
579C2×C4—681no—
580C2×C4—681no—
581C2×C4—681no—
582C2×C4—681no—
583C2×C4—681no—
584C2×C4—681no—
585C2×C4—681no—
586C2×C4—681no—
587C2×C4—681no—
588C2×C4—681no—
589C2×C4—681no—
590C2×C4C2×C22⋊Dic1712yes—
591C2×C4C2×C22⋊Dic1712yes—
592C2×C4C2×C22⋊Dic1712yes—
593C2×C4C2×C22⋊Dic1712yes—
594C2×C4C2×C22⋊Dic1712yes—
595C2×C4C2×C22⋊Dic1712yes—
596C2×C4C2×Q8×D1711yescharacteristic
597C2×C4C2×#6325611yescharacteristic
598C2×C4#1058769411yescharacteristic
599C2×C4#1058769411yescharacteristic
600C2×C4C23×Dic1711yescharacteristic
601C2×C4C22×C22⋊D1711yescharacteristic
602C8—342no—
603C8—681no—
604C8—681no—
605C8—681no—
606C22—24no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22C22×C22⋊Dic1711yescharacteristic
614C22#1176347011yescharacteristic
615C22Q8×C22⋊D1711yescharacteristic
616C22#1176360711yescharacteristic
617C22#1176360711yescharacteristic
618C22#1176361211yescharacteristic
619C22#1176362011yescharacteristic
620C4—22no—
621C4—22no—
622C4—22no—
623C4—22no—
624C4—22no—
625C4—22no—
626C4—42no—
627C4—42no—
628C4—42no—
629C4—682no—
630C4—1361no—
631C4—1361no—
632C4—1361no—
633C4C2×Q8×Dic1711yescharacteristic
634C4#1176328711yescharacteristic
635C4#1176347011yescharacteristic
636C4Q8×C22⋊D1711yescharacteristic
637C2—44no—
638C2Q8×C22⋊Dic1711yescharacteristic
639C2#1453730311yescharacteristic
640C2#1453731011yescharacteristic
641C2#1454153711yescharacteristic
642C2#1454161111yescharacteristic
643C2#1454172911yescharacteristic
644C2#1454173811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#554C2
socleC23×C17C22×D4
prime radicalC22×D4×C17C23
cosocleC22×C4×C17C24
hypercenterC2×#554D17
hypocenterC17#22526
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#11762940C2semidirect
2. #14531741C2semidirect
3. #14529758C2semidirect
4. #14529754C2semidirect
5. #14529750C2semidirect
6. #14529742C2semidirect
7. #14529742C2semidirect
8. #14529737C2semidirect
50. C17×#554C4semidirect
119. #10587503Q8semidirect
331. #554Dic17semidirect
455. C17#22526semidirect

Maximal subgroups

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

subgroupindex
C2×#117629402
#145317412
#145297582
#145297542
#145297502
#145297422
#145297372
#145287942
#145287842
#145286092
C4×#105875032
C2×C17×#5542
#2252617