Finite Group Databasebeta

← #17005150

Subgroups — #17005150

Order 4352.

566 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14539391C211yesmaximal, characteristic
2#14537878C211yesmaximal, characteristic, complemented
3#14527660C211yesmaximal, characteristic, complemented
4#14527655C211yesmaximal, characteristic, complemented
5#14527653C211yesmaximal, characteristic, complemented
6#14527641C211yesmaximal, characteristic, complemented
7#14527634C211yesmaximal, characteristic, complemented
8#14527632C211yesmaximal, characteristic, complemented
9#14527625C211yesmaximal, characteristic, complemented
10#14527620C211yesmaximal, characteristic, complemented
11#14527549C211yesmaximal, characteristic, complemented
12#14527244C211yesmaximal, characteristic
13#14527238C211yesmaximal, characteristic, complemented
14#14527074C211yesmaximal, characteristic, complemented
15C17×#2993C211yesmaximal, characteristic
16#11763366C2211yescharacteristic
17#11763219C411yescharacteristic
18#11763204C411yescharacteristic
19#11763179C411yescharacteristic
20#11763168C411yescharacteristic
21#11763065C411yescharacteristic
22#11763065C411yescharacteristic
23#11763053C411yescharacteristic
24#11763053C411yescharacteristic
25#11762939C2211yescharacteristic
26#11762939C2211yescharacteristic
27#11762938—21no—
28#11762938—21no—
29C8×Dic34C2211yescharacteristic
30C8×Dic34C2211yescharacteristic
31C4×#63231C2211yescharacteristic
32C4×#63231C2211yescharacteristic
33C4×#63229C2211yescharacteristic
34C4×#63229C2211yescharacteristic
35#11762867—21no—
36#11762867—21no—
37#11762866C2211yescharacteristic
38C4×#63223C2211yescharacteristic
39C2×C4×#3622C2211yescharacteristic
40#11762561C2211yescharacteristic
41#11762561C2211yescharacteristic
42#11762559C2211yescharacteristic
43#11762559C2211yescharacteristic
44Q8⋊#3622C2211yescharacteristic
45Q8⋊#3622C2211yescharacteristic
46#11762539C2211yescharacteristic
47#11762539C2211yescharacteristic
48#11762539C2211yescharacteristic
49#11762539C2211yescharacteristic
50D4⋊#3622C2211yescharacteristic
51D4⋊#3622C2211yescharacteristic
52#11762531C2211yescharacteristic
53#11762531C2211yescharacteristic
54#11762530C2211yescharacteristic
55#11762530C2211yescharacteristic
56C17×#529C2211yescharacteristic
57C17×#446C2211yescharacteristic
58C8×Q8×C17C2211yescharacteristic
59C17×#436—21no—
60C17×#436C2211yescharacteristic
61C17×#435—21no—
62C8×D4×C17C2211yescharacteristic
63C17×#433—21no—
64C17×#431C2211yescharacteristic
65C17×#424—21no—
66C17×#423C2211yescharacteristic
67C2×M16×C17—21no—
68C2×M16×C17—21no—
69C22×C8×C17—21no—
70C17×#126—21no—
71C17×#125C2×C411yescharacteristic
72C17×#124C2×C411yescharacteristic
73C17×#123—21no—
74C17×C22⋊Q8C2×C411yescharacteristic
75C17×#121C2×C411yescharacteristic
76C4×Q8×C17C2311yescharacteristic
77C4×D4×C17—21no—
78C4×D4×C17C2311yescharacteristic
79C17×#117—21no—
80C2×C42×C17C2311yescharacteristic
81C2×#63231C2×C411yescharacteristic
82C2×#63231C2×C411yescharacteristic
83C2×#63229C2×C411yescharacteristic
84C2×#63229C2×C411yescharacteristic
85#10587612—21no—
86#10587610—21no—
87#10587610C2×C411yescharacteristic
88#10587610C2×C411yescharacteristic
89C2×#63223C2×C411yescharacteristic
90C2×#63223C2×C411yescharacteristic
91C22×#3622—21no—
92#10587556—21no—
93#10587555C2×C411yescharacteristic
94#10587555C2×C411yescharacteristic
95C4×Dic34—21no—
96C4×Dic34C2311yescharacteristic
97C4×Dic34C2311yescharacteristic
98C17×C4⋊C8—21no—
99C17×C4⋊C8—21no—
100C17×C4⋊C8—21no—
101C17×C4⋊C8D411yescharacteristic
102C17×C4⋊C8D411yescharacteristic
103C17×C4⋊C8C2311yescharacteristic
104C17×C4⋊C8C2311yescharacteristic
105C17×C22⋊C8—21no—
106C17×C22⋊C8—21no—
107C17×C22⋊C8D411yescharacteristic
108C17×C22⋊C8D411yescharacteristic
109C17×#97—21no—
110C4×C8×C17—21no—
111C4×C8×C17C2311yescharacteristic
112C4×C8×C17C2311yescharacteristic
113#10587506C2×C411yescharacteristic
114#10587506C2×C411yescharacteristic
115#10587503C2×C411yescharacteristic
116#10587503C2×C411yescharacteristic
117C22⋊#3622—21no—
118#10587486—21no—
119#10587486—21no—
120#10587485—21no—
121#10587485—21no—
122#10587485—21no—
123#10587485—21no—
124C8×Dic17—21no—
125C8×Dic17—21no—
126#10587481C2×C411yescharacteristic
127#10587481C2×C411yescharacteristic
128#10587481C2×C411yescharacteristic
129#10587481C2×C411yescharacteristic
130#10587479C2×C411yescharacteristic
131#10587479C2×C411yescharacteristic
132#10587478C2×C411yescharacteristic
133#10587478C2×C411yescharacteristic
134C4⋊#3622C2311yescharacteristic
135C4⋊#3622C2311yescharacteristic
136#10587474—21no—
137#10587474C2×C411yescharacteristic
138#10587474C2×C411yescharacteristic
139C4×#3622—21no—
140C4×#3622C2311yescharacteristic
141C4×#3622C2311yescharacteristic
142C4×#3622C2311yescharacteristic
143C4×#3622C2311yescharacteristic
144C2×Q8×C17C22×C411yescharacteristic
145C2×D4×C17—21no—
146C2×D4×C17C22×C411yescharacteristic
147C22×C4×C17—21no—
148C22×C4×C17C22×C411yescharacteristic
149C22×C4×C17C2×D411yescharacteristic
150C22×C4×C17#4111yescharacteristic
151C2×Dic34—21no—
152C2×Dic34C22×C411yescharacteristic
153C2×Dic34C22×C411yescharacteristic
154M16×C17—81no—
155M16×C17—81no—
156C2×C8×C17—21no—
157C2×C8×C17—21no—
158C2×C8×C17—81no—
159C2×C8×C17C2×D411yescharacteristic
160C2×C8×C17C2×D411yescharacteristic
161C2×C8×C17C2×D411yescharacteristic
162C2×C8×C17C2×D411yescharacteristic
163C4⋊C4×C17—21no—
164C4⋊C4×C17—21no—
165C4⋊C4×C17—21no—
166C4⋊C4×C17—21no—
167C4⋊C4×C17C22×C411yescharacteristic
168C4⋊C4×C17C22×C411yescharacteristic
169C22⋊C4×C17—21no—
170C22⋊C4×C17—21no—
171C22⋊C4×C17—21no—
172C22⋊C4×C17—21no—
173C22⋊C4×C17—21no—
174C42×C17—21no—
175C42×C17C22×C411yescharacteristic
176C42×C17C2×D411yescharacteristic
177C42×C17#4111yescharacteristic
178C42×C17C2411yescharacteristic
179C22⋊Dic17—21no—
180C22⋊Dic17—21no—
181#63231—41no—
182#63231—41no—
183#63229—41no—
184#63229—41no—
185C4⋊Dic17—21no—
186C4⋊Dic17—21no—
187C4⋊Dic17—21no—
188C4⋊Dic17C22×C411yescharacteristic
189C4⋊Dic17C22×C411yescharacteristic
190#63225—21no—
191#63225—21no—
192#63225—21no—
193#63225—21no—
194C4×Dic17—21no—
195C4×Dic17—21no—
196#63223—41no—
197#63223—41no—
198C2×#3622—21no—
199C2×#3622—21no—
200C2×#3622—21no—
201C2×#3622—21no—
202C2×#3622—42no—
203C2×#3622C22×C411yescharacteristic
204C2×#3622C22×C411yescharacteristic
205C2×#3622C22×C411yescharacteristic
206C2×#3622C22×C411yescharacteristic
207#17988—171nomaximal, Sylow
208C23×C17—21no—
209C23×C17C4×D411yescharacteristic
210Q8×C17—21no—
211Q8×C17—21no—
212D4×C17—21no—
213D4×C17—21no—
214D4×C17—81no—
215C2×C4×C17—21no—
216C2×C4×C17—21no—
217C2×C4×C17—21no—
218C2×C4×C17—21no—
219C2×C4×C17—21no—
220C2×C4×C17—21no—
221C2×C4×C17—21no—
222C2×C4×C17—41no—
223C2×C4×C17—41no—
224C2×C4×C17—41no—
225C2×C4×C17C4×D411yescharacteristic
226C2×C4×C17C4×D411yescharacteristic
227C2×C4×C17C4×D411yescharacteristic
228C2×C4×C17C23×C411yescharacteristic
229C2×C4×C17C22×D411yescharacteristic
230C2×C4×C17C2×#4111yescharacteristic
231C2×Dic17—21no—
232C2×Dic17—21no—
233C2×Dic17—21no—
234C2×Dic17—21no—
235Dic34—21no—
236Dic34—21no—
237Dic34—21no—
238Dic34—21no—
239Dic34—81no—
240C8×C17—21no—
241C8×C17—21no—
242C8×C17—21no—
243C8×C17—21no—
244C8×C17—41no—
245C8×C17—41no—
246#3622—22no—
247#3622—21no—
248#3622—21no—
249#3622—21no—
250#3622—21no—
251#3622—41no—
252#3622—41no—
253#3622—41no—
254#3172—171no—
255#2993D1711yescharacteristic
256#2985—171no—
257#1588—171no—
258#1587—171no—
259#1587—171no—
260#1585—171no—
261#1584—171no—
262#1584—171no—
263#1583—171no—
264#1582—171no—
265#1569—171no—
266#1494—171no—
267#1493—171no—
268#1451—171no—
269C22×C17—21no—
270C22×C17—21no—
271C22×C17—21no—
272C22×C17—41no—
273C22×C17—41no—
274C22×C17—41no—
275C22×C17C2×C4×D411yescharacteristic
276C4×C17—21no—
277C4×C17—21no—
278C4×C17—21no—
279C4×C17—21no—
280C4×C17—41no—
281C4×C17—41no—
282C4×C17—41no—
283C4×C17#56811yescharacteristic
284C4×C17#56811yescharacteristic
285C4×C17#57711yescharacteristic
286C4×C17#57811yescharacteristic
287Dic17—41no—
288Dic17—41no—
289Dic17—41no—
290Dic17—41no—
291#533—171no—
292#529C2×D1711yescharacteristic
293#501—171no—
294#497—171no—
295#491—171no—
296#489—171no—
297#470—171no—
298#470—171no—
299#468—171no—
300#468—171no—
301#446—171no—
302#446—171no—
303#446—341no—
304#446—341no—
305#446C2×D1711yescharacteristic
306C8×Q8—171no—
307C8×Q8—171no—
308C8×Q8C2×D1711yescharacteristic
309C4×Q16—171no—
310C4×Q16—171no—
311C4×SD16—171no—
312C4×SD16—171no—
313#436—21no—
314#436C2×D1711yescharacteristic
315#435—21no—
316C8×D4C2×D1711yescharacteristic
317#433—21no—
318#433—341no—
319#433—341no—
320#432—171no—
321#431C2×D1711yescharacteristic
322#424—21no—
323#423C2×D1711yescharacteristic
324C4×M16—171no—
325C2×C4×C8—171no—
326#335—171no—
327#335—171no—
328#334—171no—
329#334—171no—
330Q8⋊C8—171no—
331Q8⋊C8—171no—
332Q8⋊C8—171no—
333Q8⋊C8—171no—
334Q8⋊C8—171no—
335Q8⋊C8—171no—
336D4⋊C8—171no—
337D4⋊C8—171no—
338#322—171no—
339#322—171no—
340#322—171no—
341#322—171no—
342C2×C17—41no—
343C2×C17—81no—
344C2×C17#293211yescharacteristic
345C2×C17#294711yescharacteristic
346C2×C17#295611yescharacteristic
347C2×Q16—171no—
348C2×Q16—171no—
349C2×SD16—171no—
350C2×SD16—171no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—171no—
354C2×M16—171no—
355C22×C8—21no—
356C22×C8—341no—
357C4⋊Q8—171no—
358C4⋊Q8—171no—
359#126—21no—
360#125—341no—
361#125C4×D1711yescharacteristic
362#124C4×D1711yescharacteristic
363#123—21no—
364C22⋊Q8—171no—
365C22⋊Q8—171no—
366C22⋊Q8—341no—
367C22⋊Q8C4×D1711yescharacteristic
368#121C4×D1711yescharacteristic
369C4×Q8—171no—
370C4×Q8—171no—
371C4×Q8—341no—
372C4×Q8C22×D1711yescharacteristic
373C4×D4—21no—
374C4×D4C22×D1711yescharacteristic
375#117—21no—
376#117—341no—
377C2×C42C22×D1711yescharacteristic
378#107—171no—
379#107—171no—
380#106—171no—
381#106—171no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—171no—
386C4⋊C8—171no—
387C4⋊C8—341no—
388C4⋊C8—341no—
389C4⋊C8—341no—
390C4⋊C8—341no—
391C4⋊C8C22⋊D1711yescharacteristic
392C4⋊C8C22⋊D1711yescharacteristic
393C4⋊C8C22×D1711yescharacteristic
394C4⋊C8C22×D1711yescharacteristic
395#103—171no—
396#103—171no—
397#103—171no—
398#103—171no—
399#103—171no—
400#103—171no—
401#102—171no—
402#102—171no—
403C22⋊C8—21no—
404C22⋊C8—21no—
405C22⋊C8—341no—
406C22⋊C8C22⋊D1711yescharacteristic
407C22⋊C8C22⋊D1711yescharacteristic
408#97—21no—
409#97—171no—
410#97—171no—
411#97—341no—
412#97—341no—
413#97—341no—
414C4×C8—21no—
415C4×C8—171no—
416C4×C8—171no—
417C4×C8—171no—
418C4×C8—171no—
419C4×C8—341no—
420C4×C8—341no—
421C4×C8—341no—
422C4×C8C22×D1711yescharacteristic
423C4×C8C22×D1711yescharacteristic
424C17#1798811yescharacteristic, complemented, Sylow
425C2×Q8—171no—
426C2×Q8—171no—
427C2×Q8—341no—
428C2×Q8C2×C4×D1711yescharacteristic
429C2×D4—21no—
430C2×D4C2×C4×D1711yescharacteristic
431C22×C4—21no—
432C22×C4C2×C4×D1711yescharacteristic
433C22×C4#6325211yescharacteristic
434C22×C4C2×C22⋊D1711yescharacteristic
435Q16—681no—
436Q16—681no—
437SD16—681no—
438SD16—681no—
439M16—81no—
440M16—81no—
441M16—681no—
442M16—681no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—81no—
446C2×C8—171no—
447C2×C8—171no—
448C2×C8—171no—
449C2×C8—171no—
450C2×C8—341no—
451C2×C8—341no—
452C2×C8—341no—
453C2×C8—341no—
454C2×C8—682no—
455C2×C8C2×C22⋊D1711yescharacteristic
456C2×C8C2×C22⋊D1711yescharacteristic
457C2×C8C2×C22⋊D1711yescharacteristic
458C2×C8C2×C22⋊D1711yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—171no—
464C4⋊C4—171no—
465C4⋊C4—341no—
466C4⋊C4—341no—
467C4⋊C4—341no—
468C4⋊C4—341no—
469C4⋊C4—341no—
470C4⋊C4—341no—
471C4⋊C4—341no—
472C4⋊C4C2×C4×D1711yescharacteristic
473C4⋊C4C2×C4×D1711yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—341no—
480C22⋊C4—341no—
481C42—21no—
482C42—341no—
483C42—341no—
484C42C2×C4×D1711yescharacteristic
485C42#6325211yescharacteristic
486C42C2×C22⋊D1711yescharacteristic
487C42C23×D1711yescharacteristic
488C23—21no—
489C23C4×C22⋊D1711yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—341no—
493Q8—341no—
494Q8—341no—
495Q8—341no—
496Q8—1361no—
497D4—21no—
498D4—21no—
499D4—81no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—341no—
511C2×C4—341no—
512C2×C4—341no—
513C2×C4—341no—
514C2×C4C4×C22⋊D1711yescharacteristic
515C2×C4C4×C22⋊D1711yescharacteristic
516C2×C4C4×C22⋊D1711yescharacteristic
517C2×C4C22×C4×D1711yescharacteristic
518C2×C4C2×#6325211yescharacteristic
519C2×C4C22×C22⋊D1711yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—342no—
527C8—341no—
528C8—341no—
529C8—341no—
530C8—341no—
531C8—681no—
532C8—681no—
533C8—681no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22C2×C4×C22⋊D1711yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—681no—
549C4—681no—
550C4—681no—
551C4—681no—
552C4#1176357411yescharacteristic
553C4#1176357411yescharacteristic
554C4#1176362011yescharacteristic
555C4#1176362411yescharacteristic
556C2—41no—
557C2—81no—
558C2#1453750011yescharacteristic
559C2#1453762311yescharacteristic
560C2#1453769111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#2993C2
socleC22×C17C2×C4×D4
prime radicalC17×#121C2×C4
cosocleC42×C17C24
hypercenter#2993D17
hypocenterC17#17988
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #14537878C2semidirect
3. #14527660C2semidirect
4. #14527655C2semidirect
5. #14527653C2semidirect
6. #14527641C2semidirect
7. #14527634C2semidirect
8. #14527632C2semidirect
9. #14527625C2semidirect
10. #14527620C2semidirect
11. #14527549C2semidirect
13. #14527238C2semidirect
14. #14527074C2semidirect
424. C17#17988semidirect

Maximal subgroups

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

subgroupindex
#145393912
#145378782
#145276602
#145276552
#145276532
#145276412
#145276342
#145276322
#145276252
#145276202
#145275492
#145272442
#145272382
#145270742
C17×#29932
#1798817