Finite Group Databasebeta

← #17966514

Subgroups — #17966514

Order 4352.

588 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545480C211yesmaximal, characteristic
2#14545479C211yesmaximal, characteristic
3#14544362C211yesmaximal, characteristic, complemented
4#14544360C211yesmaximal, characteristic, complemented
5#14544359C211yesmaximal, characteristic, complemented
6#14544358C211yesmaximal, characteristic, complemented
7#14544355C211yesmaximal, characteristic, complemented
8#14544355C211yesmaximal, characteristic, complemented
9#14544349C211yesmaximal, characteristic, complemented
10#14544348C211yesmaximal, characteristic, complemented
11#14544346C211yesmaximal, characteristic, complemented
12#14544336C211yesmaximal, characteristic, complemented
13#14544335C211yesmaximal, characteristic, complemented
14#14544331C211yesmaximal, characteristic, complemented
15#14537744C211yesmaximal, characteristic
16#11763834—21no—
17#11763833—21no—
18#11763833—21no—
19#11763833—21no—
20#11763831C2211yescharacteristic
21#11763830C2211yescharacteristic
22#11763830C2211yescharacteristic
23#11763830C2211yescharacteristic
24#11763828C2211yescharacteristic
25#11763825C2211yescharacteristic
26#11763825C2211yescharacteristic
27#11763825C2211yescharacteristic
28#11763813C2211yescharacteristic
29#11763812C2211yescharacteristic
30#11763810C2211yescharacteristic
31C2×C4⋊#3624C2211yescharacteristic
32#11763783—21no—
33#11763782—21no—
34#11763774—21no—
35#11763773—21no—
36#11763673C2211yescharacteristic
37#11763673C2211yescharacteristic
38#11763672C2211yescharacteristic
39#11763672C2211yescharacteristic
40#11763672C2211yescharacteristic
41#11763672C2211yescharacteristic
42#11763672C2211yescharacteristic
43#11763672C2211yescharacteristic
44#11763671C2211yescharacteristic
45#11763671C2211yescharacteristic
46#11763671C2211yescharacteristic
47#11763671C2211yescharacteristic
48#11763670C2211yescharacteristic
49#11763670C2211yescharacteristic
50#11763670C2211yescharacteristic
51#11763670C2211yescharacteristic
52C4×#63254C2211yescharacteristic
53#11762938C411yescharacteristic
54#11762937C411yescharacteristic
55#11762885C411yescharacteristic
56#11762884C411yescharacteristic
57#11762881C411yescharacteristic
58#11762880C411yescharacteristic
59#11762877C411yescharacteristic
60#11762861C2211yescharacteristic
61#11762859C2211yescharacteristic
62#11762859C2211yescharacteristic
63#11762761C2211yescharacteristic
64M16×Dic17C2211yescharacteristic
65C2×C8×Dic17C2211yescharacteristic
66C17×#435C411yescharacteristic
67C2×#63254D411yescharacteristic
68C2×#63247—21no—
69C22×#3624—21no—
70C2×#63243—21no—
71C2×#63242—21no—
72C2×M16×C17C2×C411yescharacteristic
73C22×C8×C17C2×C411yescharacteristic
74C4×D4×C17C2×C411yescharacteristic
75D4×Dic17Q811yescharacteristic
76C4×C22⋊D17C2×C411yescharacteristic
77C4×C22⋊D17C2×C411yescharacteristic
78C2×C4×Dic17C2311yescharacteristic
79C2×C4×Dic17C2311yescharacteristic
80C2×#63223C2×C411yescharacteristic
81C22×#3622C2×C411yescharacteristic
82C2×#63218C2×C411yescharacteristic
83C2×#63218C2×C411yescharacteristic
84#10587578D411yescharacteristic
85#10587573Q811yescharacteristic
86#10587567Q811yescharacteristic
87#10587567Q811yescharacteristic
88#10587563D411yescharacteristic
89#10587563D411yescharacteristic
90C42×D17C2311yescharacteristic
91C4×Dic34C2×C411yescharacteristic
92C22⋊#3624—21no—
93C22⋊#3624—21no—
94C22⋊#3624—21no—
95C22⋊#3624—21no—
96C22⋊#3624—21no—
97C22⋊#3624—21no—
98#10587544—21no—
99#10587544—21no—
100#10587543—21no—
101#10587543—21no—
102#10587542—21no—
103#10587542—21no—
104#10587542—21no—
105#10587542—21no—
106C4⋊#3624—21no—
107C4⋊#3624—21no—
108C4⋊#3624C2311yescharacteristic
109C4⋊#3624C2311yescharacteristic
110C4⋊#3624C2311yescharacteristic
111C4⋊#3624C2311yescharacteristic
112C4⋊#3624C2311yescharacteristic
113C4⋊#3624C2311yescharacteristic
114C4⋊#3624C2311yescharacteristic
115C4⋊#3624C2311yescharacteristic
116C4×#3624—21no—
117C4×#3624—21no—
118C4×#3624—21no—
119C4×#3624—21no—
120C17×C4⋊C8C2×C411yescharacteristic
121C17×C22⋊C8C2×C411yescharacteristic
122C17×C22⋊C8C2×C411yescharacteristic
123C17×#97C2×C411yescharacteristic
124C22⋊#3622C2×C411yescharacteristic
125C22⋊#3622C2×C411yescharacteristic
126#10587491C2×C411yescharacteristic
127#10587491C2×C411yescharacteristic
128#10587486C2×C411yescharacteristic
129#10587486C2×C411yescharacteristic
130#10587485C2×C411yescharacteristic
131#10587485C2×C411yescharacteristic
132#10587485C2×C411yescharacteristic
133#10587485C2×C411yescharacteristic
134C8×Dic17C2×C411yescharacteristic
135C8×Dic17C2×C411yescharacteristic
136C8×Dic17C2311yescharacteristic
137C8×Dic17C2311yescharacteristic
138C8×Dic17C2311yescharacteristic
139C8×Dic17C2311yescharacteristic
140C4⋊#3622C2×C411yescharacteristic
141#10587474C2×C411yescharacteristic
142C2×D4×C17C4⋊C411yescharacteristic
143C22×C4×C17C22×C411yescharacteristic
144C22×C4×C17C22×C411yescharacteristic
145C2×C22⋊D17C4⋊C411yescharacteristic
146C2×C22⋊D17C4⋊C411yescharacteristic
147C22×Dic17C2×D411yescharacteristic
148C22×Dic17C2×D411yescharacteristic
149C22×Dic17C2×Q811yescharacteristic
150C22×Dic17C2×Q811yescharacteristic
151#63254—41no—
152#63254—41no—
153C2×C4×D17C22×C411yescharacteristic
154C2×C4×D17C2×D411yescharacteristic
155C2×C4×D17C2×Q811yescharacteristic
156C2×Dic34C4⋊C411yescharacteristic
157#63247—42no—
158C2×#3624—21no—
159C2×#3624—21no—
160C2×#3624—21no—
161C2×#3624—21no—
162C2×#3624—21no—
163C2×#3624—21no—
164C2×#3624—21no—
165C2×#3624—21no—
166C2×#3624—42no—
167#63243—42no—
168#63242—42no—
169M16×C17—22no—
170C2×C8×C17—22no—
171C2×C8×C17C22×C411yescharacteristic
172C2×C8×C17C22×C411yescharacteristic
173C2×C8×C17C22×C411yescharacteristic
174C2×C8×C17C22×C411yescharacteristic
175C4⋊C4×C17C4⋊C411yescharacteristic
176C22⋊C4×C17C4⋊C411yescharacteristic
177C22⋊C4×C17C4⋊C411yescharacteristic
178C42×C17C22×C411yescharacteristic
179C22⋊Dic17C4⋊C411yescharacteristic
180C22⋊Dic17C4⋊C411yescharacteristic
181#63227C4⋊C411yescharacteristic
182#63227C4⋊C411yescharacteristic
183C4⋊Dic17C4⋊C411yescharacteristic
184#63225C4⋊C411yescharacteristic
185#63225C4⋊C411yescharacteristic
186#63225C4⋊C411yescharacteristic
187#63225C4⋊C411yescharacteristic
188C4×Dic17C22×C411yescharacteristic
189C4×Dic17C22×C411yescharacteristic
190C4×Dic17C2×D411yescharacteristic
191C4×Dic17C2×D411yescharacteristic
192C4×Dic17C2×D411yescharacteristic
193C4×Dic17C2×Q811yescharacteristic
194C4×Dic17C2×Q811yescharacteristic
195C4×Dic17C2×Q811yescharacteristic
196C4×Dic17C2411yescharacteristic
197#63223—41no—
198C2×#3622—41no—
199C2×#3622C22×C411yescharacteristic
200C2×#3622C22×C411yescharacteristic
201C2×#3622C22×C411yescharacteristic
202C2×#3622C22×C411yescharacteristic
203#63218—22no—
204#63218—41no—
205#17831—171nomaximal, Sylow
206C23×C17C2×C4⋊C411yescharacteristic
207C23×C17C2×C4⋊C411yescharacteristic
208C22×D17C2×C4⋊C411yescharacteristic
209D4×C17—41no—
210C2×C4×C17—21no—
211C2×C4×C17—21no—
212C2×C4×C17—21no—
213C2×C4×C17—21no—
214C2×C4×C17C2×C4⋊C411yescharacteristic
215C2×C4×C17C2×C4⋊C411yescharacteristic
216C2×C4×C17C2×C4⋊C411yescharacteristic
217C2×C4×C17C2×C4⋊C411yescharacteristic
218C2×C4×C17C23×C411yescharacteristic
219C22⋊D17—41no—
220C22⋊D17—41no—
221C2×Dic17—21no—
222C2×Dic17—21no—
223C2×Dic17—21no—
224C2×Dic17—21no—
225C2×Dic17—41no—
226C2×Dic17—41no—
227C2×Dic17C2×C4⋊C411yescharacteristic
228C2×Dic17C2×C4⋊C411yescharacteristic
229C2×Dic17C2×C4⋊C411yescharacteristic
230C2×Dic17C2×C4⋊C411yescharacteristic
231C2×Dic17C2×C4⋊C411yescharacteristic
232C2×Dic17C22×D411yescharacteristic
233C2×Dic17C22×Q811yescharacteristic
234C4×D17—21no—
235C4×D17—21no—
236C4×D17—21no—
237C4×D17—21no—
238C4×D17—41no—
239Dic34—41no—
240#3624—41no—
241#3624—41no—
242#3624—41no—
243#3624—41no—
244#3624—41no—
245#3624—41no—
246#3624—41no—
247#3624—41no—
248C8×C17—21no—
249C8×C17—21no—
250C8×C17—21no—
251C8×C17#13112yes—
252#3622—21no—
253#3622—21no—
254#3622—21no—
255#3622—21no—
256#2965—171no—
257#2925—171no—
258#2925—171no—
259#1574—171no—
260#1574—171no—
261#1573—171no—
262#1573—171no—
263#1572—171no—
264#1572—171no—
265#1569—171no—
266#1569—171no—
267#1568—171no—
268#1565—171no—
269#1565—171no—
270#1564—171no—
271C22×C17—21no—
272C22×C17—21no—
273C22×C17—21no—
274C22×C17—21no—
275C22×C17—21no—
276C22×C17—21no—
277C22×C17C22×C4⋊C411yescharacteristic
278C2×D17—21no—
279C2×D17—21no—
280C2×D17—21no—
281C4×C17—21no—
282C4×C17—21no—
283C4×C17—21no—
284C4×C17—21no—
285C4×C17C2×#13111yescharacteristic
286C4×C17#56811yescharacteristic
287Dic17—21no—
288Dic17—21no—
289Dic17—21no—
290Dic17—21no—
291Dic17—21no—
292Dic17—21no—
293Dic17#57511yescharacteristic
294Dic17#57511yescharacteristic
295C4×#41—171no—
296#446—171no—
297#446—171no—
298#436—171no—
299#436—171no—
300#435—171no—
301#435—171no—
302#435—171no—
303#435#59511yescharacteristic
304#433—341no—
305#433—341no—
306#433—341no—
307#433—341no—
308#432—171no—
309#432—171no—
310#432—171no—
311#432—171no—
312#431—171no—
313#431—171no—
314#431—171no—
315#431—171no—
316#431—171no—
317#431—171no—
318#431—171no—
319#423—171no—
320#423—171no—
321C2×C4⋊C8—171no—
322C2×C4⋊C8—171no—
323#408—341no—
324#408—341no—
325#405—341no—
326#405—341no—
327C4×M16—171no—
328C4×M16—171no—
329C2×C4×C8—171no—
330#335—171no—
331#335—171no—
332#335—171no—
333#335—171no—
334#335—171no—
335#335—171no—
336#335—171no—
337#335—171no—
338#334—171no—
339#334—171no—
340#334—171no—
341#334—171no—
342#334—171no—
343#334—171no—
344#334—171no—
345#334—171no—
346C2×C17—41no—
347C2×C17—41no—
348C2×C17#290611yescharacteristic
349C2×C17#291111yescharacteristic
350C2×C17#291611yescharacteristic
351D17—41no—
352C2×#41—171no—
353C2×M16—171no—
354C2×M16—171no—
355C2×M16—171no—
356C2×M16—341no—
357C2×M16—341no—
358C2×M16C2×#59511yescharacteristic
359C22×C8—171no—
360C22×C8—341no—
361C22×C8—341no—
362C22×C8C2×#59511yescharacteristic
363C4×Q8—171no—
364C4×Q8—171no—
365C4×D4—171no—
366C4×D4—171no—
367C4×D4—171no—
368C4×D4—171no—
369C4×D4—171no—
370C4×D4C2×#59511yescharacteristic
371#117—171no—
372#117—171no—
373#117—171no—
374C2×C42—171no—
375C2×C42—171no—
376C2×C42—171no—
377C4⋊C8—171no—
378C4⋊C8—171no—
379C4⋊C8—171no—
380C4⋊C8—171no—
381C4⋊C8—171no—
382C4⋊C8—171no—
383C4⋊C8—171no—
384C4⋊C8—171no—
385C4⋊C8—171no—
386C4⋊C8—171no—
387C4⋊C8—171no—
388C4⋊C8—171no—
389C4⋊C8—171no—
390C4⋊C8—341no—
391C4⋊C8—341no—
392C4⋊C8—341no—
393C4⋊C8—341no—
394C4⋊C8C2×#59511yescharacteristic
395C22⋊C8—171no—
396C22⋊C8—171no—
397C22⋊C8—171no—
398C22⋊C8—171no—
399C22⋊C8—341no—
400C22⋊C8—341no—
401C22⋊C8—341no—
402C22⋊C8—341no—
403C22⋊C8—341no—
404C22⋊C8—341no—
405C22⋊C8—341no—
406C22⋊C8—341no—
407C22⋊C8C2×#59511yescharacteristic
408C22⋊C8C2×#59511yescharacteristic
409#97—171no—
410#97—171no—
411#97—171no—
412#97—341no—
413#97—341no—
414#97—341no—
415#97—341no—
416#97C2×#59511yescharacteristic
417C4×C8—171no—
418C4×C8—171no—
419C4×C8—171no—
420C4×C8—171no—
421C4×C8—171no—
422C4×C8—171no—
423C4×C8—341no—
424C4×C8—341no—
425C4×C8—341no—
426C4×C8—341no—
427C17#1783111yescharacteristic, complemented, Sylow
428#41—681no—
429#41—681no—
430C2×Q8—171no—
431C2×D4—171no—
432C2×D4—171no—
433C2×D4C4⋊#59511yescharacteristic
434C22×C4—171no—
435C22×C4—171no—
436C22×C4—171no—
437C22×C4—171no—
438C22×C4—171no—
439C22×C4—171no—
440C22×C4—171no—
441C22×C4C22×#59511yescharacteristic
442C22×C4C22×#59511yescharacteristic
443M16—22no—
444M16—342no—
445M16—681no—
446M16—681no—
447M16—682no—
448M16—682no—
449C2×C8—22no—
450C2×C8—171no—
451C2×C8—171no—
452C2×C8—171no—
453C2×C8—171no—
454C2×C8—341no—
455C2×C8—341no—
456C2×C8—341no—
457C2×C8—341no—
458C2×C8—341no—
459C2×C8—341no—
460C2×C8—341no—
461C2×C8—341no—
462C2×C8—681no—
463C2×C8—682no—
464C2×C8—682no—
465C2×C8C22×#59511yescharacteristic
466C2×C8C22×#59511yescharacteristic
467C2×C8C22×#59511yescharacteristic
468C2×C8C22×#59511yescharacteristic
469C4⋊C4—171no—
470C4⋊C4—171no—
471C4⋊C4—171no—
472C4⋊C4—171no—
473C4⋊C4—171no—
474C4⋊C4C4⋊#59511yescharacteristic
475C22⋊C4—171no—
476C22⋊C4—171no—
477C22⋊C4—171no—
478C22⋊C4—171no—
479C22⋊C4C4⋊#59511yescharacteristic
480C22⋊C4C4⋊#59511yescharacteristic
481C42—171no—
482C42—171no—
483C42—171no—
484C42—171no—
485C42—171no—
486C42—171no—
487C42—171no—
488C42—171no—
489C42—171no—
490C42C22×#59511yescharacteristic
491C23—171no—
492C23C2×C4⋊#59511yescharacteristic
493C23C2×C4⋊#59511yescharacteristic
494Q8—681no—
495D4—41no—
496D4—681no—
497D4—681no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—171no—
503C2×C4—171no—
504C2×C4—171no—
505C2×C4—171no—
506C2×C4—171no—
507C2×C4—171no—
508C2×C4—171no—
509C2×C4—341no—
510C2×C4—341no—
511C2×C4—341no—
512C2×C4—341no—
513C2×C4—341no—
514C2×C4—341no—
515C2×C4—341no—
516C2×C4—341no—
517C2×C4—681no—
518C2×C4—681no—
519C2×C4—681no—
520C2×C4C2×C4⋊#59511yescharacteristic
521C2×C4C2×C4⋊#59511yescharacteristic
522C2×C4C2×C4⋊#59511yescharacteristic
523C2×C4C2×C4⋊#59511yescharacteristic
524C2×C4C23×#59511yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—341no—
529C8—341no—
530C8—341no—
531C8—341no—
532C8—681no—
533C8—681no—
534C8—681no—
535C8—681no—
536C8—681no—
537C8—681no—
538C8—681no—
539C8—681no—
540C8#1058767812yes—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—341no—
548C22—341no—
549C22—341no—
550C22C22×C4⋊#59511yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—171no—
556C4—171no—
557C4—341no—
558C4—341no—
559C4—341no—
560C4—341no—
561C4—341no—
562C4—341no—
563C4C2×#1058767811yescharacteristic
564C4#1176388811yescharacteristic
565C2—41no—
566C2—41no—
567C2—681no—
568C2#1454542911yescharacteristic
569C2#1454543711yescharacteristic
570C2#1454544611yescharacteristic
subgroupG/H
centerC22C22×C4⋊#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC17×#435C4
socleC22×C17C22×C4⋊C4
prime radicalC2×#63254D4
cosocleC4×Dic17C24
hypercenter#435#595
hypocenterC17#17831
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
3. #14544362C2semidirect
4. #14544360C2semidirect
5. #14544359C2semidirect
6. #14544358C2semidirect
7. #14544355C2semidirect
8. #14544355C2semidirect
9. #14544349C2semidirect
10. #14544348C2semidirect
11. #14544346C2semidirect
12. #14544336C2semidirect
13. #14544335C2semidirect
14. #14544331C2semidirect
427. C17#17831semidirect

Maximal subgroups

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

subgroupindex
#145454802
#145454792
#145443622
#145443602
#145443592
#145443582
#145443552
#145443492
#145443482
#145443462
#145443362
#145443352
#145443312
#145377442
#1783117