Finite Group Databasebeta

← #17966508

Subgroups — #17966508

Order 4352.

634 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545479C211yesmaximal, characteristic
2#14545429C211yesmaximal, characteristic
3#14544361C211yesmaximal, characteristic, complemented
4#14544360C211yesmaximal, characteristic, complemented
5#14544358C211yesmaximal, characteristic, complemented
6#14544357C211yesmaximal, characteristic, complemented
7#14544353C211yesmaximal, characteristic, complemented
8#14544351C211yesmaximal, characteristic, complemented
9#14544349C211yesmaximal, characteristic, complemented
10#14544348C211yesmaximal, characteristic, complemented
11#14544341C211yesmaximal, characteristic, complemented
12#14544336C211yesmaximal, characteristic, complemented
13#14544335C211yesmaximal, characteristic, complemented
14C2×#11763670C211yesmaximal, characteristic, complemented
15#14537744C211yesmaximal, characteristic
16C2×#10587678—21no—
17#11763834—21no—
18#11763833—21no—
19#11763831C2211yescharacteristic
20#11763830C2211yescharacteristic
21#11763828C2211yescharacteristic
22#11763825C2211yescharacteristic
23#11763816—21no—
24#11763815—21no—
25#11763815—21no—
26#11763813C2211yescharacteristic
27#11763812C2211yescharacteristic
28#11763812C2211yescharacteristic
29#11763812C2211yescharacteristic
30#11763810C2211yescharacteristic
31C2×C4⋊#3624C2211yescharacteristic
32C2×C4⋊#3624C2211yescharacteristic
33C2×C4⋊#3624C2211yescharacteristic
34#11763782—21no—
35#11763773—21no—
36#11763673C2211yescharacteristic
37#11763673C2211yescharacteristic
38#11763673C2211yescharacteristic
39#11763673C2211yescharacteristic
40#11763672C2211yescharacteristic
41#11763672C2211yescharacteristic
42#11763672C2211yescharacteristic
43#11763672C2211yescharacteristic
44#11763671C2211yescharacteristic
45#11763671C2211yescharacteristic
46#11763670C2211yescharacteristic
47#11763670C2211yescharacteristic
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—
69C2×#63247—21no—
70C2×#63247—21no—
71C22×#3624—21no—
72C22×#3624—21no—
73C22×#3624—21no—
74#10587678—44no—
75C2×#63243—21no—
76C2×#63242—21no—
77C2×M16×C17C2×C411yescharacteristic
78C22×C8×C17C2×C411yescharacteristic
79C4×D4×C17C2×C411yescharacteristic
80D4×Dic17Q811yescharacteristic
81C4×C22⋊D17C2×C411yescharacteristic
82C4×C22⋊D17C2×C411yescharacteristic
83C2×C4×Dic17C2311yescharacteristic
84C2×C4×Dic17C2311yescharacteristic
85C2×#63223C2×C411yescharacteristic
86C22×#3622C2×C411yescharacteristic
87C2×#63218C2×C411yescharacteristic
88C2×#63218C2×C411yescharacteristic
89#10587578D411yescharacteristic
90#10587573Q811yescharacteristic
91#10587567Q811yescharacteristic
92#10587567Q811yescharacteristic
93#10587563D411yescharacteristic
94#10587563D411yescharacteristic
95C42×D17C2311yescharacteristic
96C4×Dic34C2×C411yescharacteristic
97C22⋊#3624—21no—
98C22⋊#3624—21no—
99#10587544—21no—
100#10587544—21no—
101#10587544—21no—
102#10587544—21no—
103#10587543—21no—
104#10587543—21no—
105#10587542—21no—
106#10587542—21no—
107C4⋊#3624—21no—
108C4⋊#3624—21no—
109C4⋊#3624—21no—
110C4⋊#3624—21no—
111C4⋊#3624C2311yescharacteristic
112C4⋊#3624C2311yescharacteristic
113C4⋊#3624C2311yescharacteristic
114C4⋊#3624C2311yescharacteristic
115C4⋊#3624C2311yescharacteristic
116C4⋊#3624C2311yescharacteristic
117C4⋊#3624C2311yescharacteristic
118C4⋊#3624C2311yescharacteristic
119C4×#3624—21no—
120C4×#3624—21no—
121C17×C4⋊C8C2×C411yescharacteristic
122C17×C22⋊C8C2×C411yescharacteristic
123C17×C22⋊C8C2×C411yescharacteristic
124C17×#97C2×C411yescharacteristic
125C22⋊#3622C2×C411yescharacteristic
126C22⋊#3622C2×C411yescharacteristic
127#10587491C2×C411yescharacteristic
128#10587491C2×C411yescharacteristic
129#10587486C2×C411yescharacteristic
130#10587486C2×C411yescharacteristic
131#10587485C2×C411yescharacteristic
132#10587485C2×C411yescharacteristic
133#10587485C2×C411yescharacteristic
134#10587485C2×C411yescharacteristic
135C8×Dic17C2×C411yescharacteristic
136C8×Dic17C2×C411yescharacteristic
137C8×Dic17C2311yescharacteristic
138C8×Dic17C2311yescharacteristic
139C8×Dic17C2311yescharacteristic
140C8×Dic17C2311yescharacteristic
141C4⋊#3622C2×C411yescharacteristic
142#10587474C2×C411yescharacteristic
143C2×D4×C17C4⋊C411yescharacteristic
144C22×C4×C17C22×C411yescharacteristic
145C22×C4×C17C22×C411yescharacteristic
146C2×C22⋊D17C4⋊C411yescharacteristic
147C2×C22⋊D17C4⋊C411yescharacteristic
148C22×Dic17C2×D411yescharacteristic
149C22×Dic17C2×D411yescharacteristic
150C22×Dic17C2×Q811yescharacteristic
151C22×Dic17C2×Q811yescharacteristic
152#63254—22no—
153#63254—22no—
154C2×C4×D17C22×C411yescharacteristic
155C2×C4×D17C2×D411yescharacteristic
156C2×C4×D17C2×Q811yescharacteristic
157C2×Dic34C4⋊C411yescharacteristic
158#63247—42no—
159#63247—42no—
160#63247—42no—
161C2×#3624—21no—
162C2×#3624—21no—
163C2×#3624—21no—
164C2×#3624—21no—
165C2×#3624—21no—
166C2×#3624—21no—
167C2×#3624—21no—
168C2×#3624—21no—
169C2×#3624—42no—
170C2×#3624—42no—
171C2×#3624—42no—
172#63243—42no—
173#63242—42no—
174M16×C17—22no—
175C2×C8×C17—22no—
176C2×C8×C17C22×C411yescharacteristic
177C2×C8×C17C22×C411yescharacteristic
178C2×C8×C17C22×C411yescharacteristic
179C2×C8×C17C22×C411yescharacteristic
180C4⋊C4×C17C4⋊C411yescharacteristic
181C22⋊C4×C17C4⋊C411yescharacteristic
182C22⋊C4×C17C4⋊C411yescharacteristic
183C42×C17C22×C411yescharacteristic
184C22⋊Dic17C4⋊C411yescharacteristic
185C22⋊Dic17C4⋊C411yescharacteristic
186#63227C4⋊C411yescharacteristic
187#63227C4⋊C411yescharacteristic
188C4⋊Dic17C4⋊C411yescharacteristic
189#63225C4⋊C411yescharacteristic
190#63225C4⋊C411yescharacteristic
191#63225C4⋊C411yescharacteristic
192#63225C4⋊C411yescharacteristic
193C4×Dic17C22×C411yescharacteristic
194C4×Dic17C22×C411yescharacteristic
195C4×Dic17C2×D411yescharacteristic
196C4×Dic17C2×D411yescharacteristic
197C4×Dic17C2×D411yescharacteristic
198C4×Dic17C2×Q811yescharacteristic
199C4×Dic17C2×Q811yescharacteristic
200C4×Dic17C2×Q811yescharacteristic
201C4×Dic17C2411yescharacteristic
202#63223—41no—
203C2×#3622—41no—
204C2×#3622C22×C411yescharacteristic
205C2×#3622C22×C411yescharacteristic
206C2×#3622C22×C411yescharacteristic
207C2×#3622C22×C411yescharacteristic
208#63218—22no—
209#63218—41no—
210#17830—171nomaximal, Sylow
211C23×C17C2×C4⋊C411yescharacteristic
212C23×C17C2×C4⋊C411yescharacteristic
213C22×D17C2×C4⋊C411yescharacteristic
214D4×C17—22no—
215C2×C4×C17—21no—
216C2×C4×C17—21no—
217C2×C4×C17—21no—
218C2×C4×C17—21no—
219C2×C4×C17C2×C4⋊C411yescharacteristic
220C2×C4×C17C2×C4⋊C411yescharacteristic
221C2×C4×C17C2×C4⋊C411yescharacteristic
222C2×C4×C17C2×C4⋊C411yescharacteristic
223C2×C4×C17C23×C411yescharacteristic
224C22⋊D17—22no—
225C22⋊D17—22no—
226C2×Dic17—21no—
227C2×Dic17—21no—
228C2×Dic17—41no—
229C2×Dic17—41no—
230C2×Dic17C2×C4⋊C411yescharacteristic
231C2×Dic17C2×C4⋊C411yescharacteristic
232C2×Dic17C2×C4⋊C411yescharacteristic
233C2×Dic17C2×C4⋊C411yescharacteristic
234C2×Dic17C2×C4⋊C411yescharacteristic
235C2×Dic17AGL(1,ℤ/8)12yes—
236C2×Dic17#13712yes—
237C2×Dic17C22×D411yescharacteristic
238C2×Dic17C22×Q811yescharacteristic
239C4×D17—21no—
240C4×D17—21no—
241C4×D17—21no—
242C4×D17—21no—
243C4×D17—41no—
244Dic34—22no—
245#3624—41no—
246#3624—41no—
247#3624—41no—
248#3624—41no—
249#3624—41no—
250#3624—41no—
251#3624—41no—
252#3624—41no—
253C8×C17—21no—
254C8×C17—21no—
255C8×C17—21no—
256C8×C17#13112yescomplemented
257#3622—21no—
258#3622—21no—
259#3622—21no—
260#3622—21no—
261#2965—171no—
262#2925—171no—
263#2906—171no—
264#1574—171no—
265#1574—171no—
266#1573—171no—
267#1573—171no—
268#1571—171no—
269#1570—171no—
270#1569—171no—
271#1569—171no—
272#1567—171no—
273#1565—171no—
274#1565—171no—
275C2×#334—171no—
276C22×C17—21no—
277C22×C17—21no—
278C22×C17—21no—
279C22×C17—21no—
280C22×C17—21no—
281C22×C17#42812yes—
282C22×C17C22×C4⋊C411yescharacteristic
283C2×D17—21no—
284C2×D17—21no—
285C2×D17—21no—
286C4×C17—21no—
287C4×C17—21no—
288C4×C17—21no—
289C4×C17—21no—
290C4×C17C2×#13111yescharacteristic
291C4×C17#56811yescharacteristic
292Dic17—21no—
293Dic17—21no—
294Dic17—21no—
295Dic17—21no—
296Dic17—21no—
297Dic17#42812yes—
298Dic17C2×AGL(1,ℤ/8)11yescharacteristic
299Dic17C2×#13711yescharacteristic
300C2×#131—341no—
301C4×#41—171no—
302#446—171no—
303#446—171no—
304#436—171no—
305#436—171no—
306#435—171no—
307#435—171no—
308#435—171no—
309#435#59511yescharacteristic
310#433—341no—
311#433—341no—
312#432—171no—
313#432—171no—
314#431—171no—
315#431—171no—
316#431—171no—
317#431—171no—
318#431—171no—
319#424—341no—
320#424—341no—
321#424—341no—
322#423—171no—
323#423—171no—
324#423—171no—
325#423—171no—
326C2×C4⋊C8—171no—
327C2×C4⋊C8—171no—
328C2×C4⋊C8—171no—
329C2×C4⋊C8—171no—
330#408—341no—
331#405—341no—
332C4×M16—171no—
333C4×M16—171no—
334C2×C4×C8—171no—
335#335—171no—
336#335—171no—
337#335—171no—
338#335—171no—
339#335—171no—
340#335—171no—
341#335—171no—
342#335—171no—
343#334—171no—
344#334—171no—
345#334—171no—
346#334—171no—
347#334—171no—
348#334—171no—
349#334—171no—
350#334—171no—
351C2×C17—22no—
352C2×C17—41no—
353C2×C17#290611yescharacteristic
354C2×C17C2×#42811yescharacteristic
355C2×C17#291611yescharacteristic
356D17—41no—
357C2×#41—171no—
358#131—684no—
359C2×M16—171no—
360C2×M16—171no—
361C2×M16—171no—
362C2×M16—341no—
363C2×M16—341no—
364C2×M16—341no—
365C2×M16—341no—
366C2×M16C2×#59511yescharacteristic
367C22×C8—171no—
368C22×C8—341no—
369C22×C8—341no—
370C22×C8—341no—
371C22×C8—341no—
372C22×C8C2×#59511yescharacteristic
373C4×Q8—171no—
374C4×Q8—171no—
375C4×D4—171no—
376C4×D4—171no—
377C4×D4—171no—
378C4×D4—171no—
379C4×D4—171no—
380C4×D4C2×#59511yescharacteristic
381#117—171no—
382#117—171no—
383#117—171no—
384C2×C42—171no—
385C2×C42—171no—
386C2×C42—171no—
387C4⋊C8—171no—
388C4⋊C8—171no—
389C4⋊C8—171no—
390C4⋊C8—171no—
391C4⋊C8—171no—
392C4⋊C8—171no—
393C4⋊C8—171no—
394C4⋊C8—171no—
395C4⋊C8—171no—
396C4⋊C8—171no—
397C4⋊C8—171no—
398C4⋊C8—171no—
399C4⋊C8—171no—
400C4⋊C8—341no—
401C4⋊C8—341no—
402C4⋊C8—341no—
403C4⋊C8—341no—
404C4⋊C8—341no—
405C4⋊C8—341no—
406C4⋊C8—341no—
407C4⋊C8—341no—
408C4⋊C8C2×#59511yescharacteristic
409C22⋊C8—171no—
410C22⋊C8—171no—
411C22⋊C8—171no—
412C22⋊C8—171no—
413C22⋊C8—341no—
414C22⋊C8—341no—
415C22⋊C8—341no—
416C22⋊C8—341no—
417C22⋊C8C2×#59511yescharacteristic
418C22⋊C8C2×#59511yescharacteristic
419#97—171no—
420#97—171no—
421#97—171no—
422#97—341no—
423#97—341no—
424#97C2×#59511yescharacteristic
425C4×C8—171no—
426C4×C8—171no—
427C4×C8—171no—
428C4×C8—171no—
429C4×C8—171no—
430C4×C8—171no—
431C4×C8—341no—
432C4×C8—341no—
433C17#1783011yescharacteristic, complemented, Sylow
434#41—342no—
435#41—342no—
436C2×Q8—171no—
437C2×D4—171no—
438C2×D4—171no—
439C2×D4C4⋊#59511yescharacteristic
440C22×C4—171no—
441C22×C4—171no—
442C22×C4—171no—
443C22×C4—171no—
444C22×C4—171no—
445C22×C4—171no—
446C22×C4—171no—
447C22×C4C22×#59511yescharacteristic
448C22×C4C22×#59511yescharacteristic
449M16—22no—
450M16—342no—
451M16—681no—
452M16—681no—
453M16—682no—
454M16—682no—
455M16—682no—
456M16—682no—
457C2×C8—22no—
458C2×C8—171no—
459C2×C8—171no—
460C2×C8—171no—
461C2×C8—171no—
462C2×C8—341no—
463C2×C8—341no—
464C2×C8—341no—
465C2×C8—341no—
466C2×C8—341no—
467C2×C8—341no—
468C2×C8—341no—
469C2×C8—341no—
470C2×C8—681no—
471C2×C8—682no—
472C2×C8—682no—
473C2×C8—682no—
474C2×C8—682no—
475C2×C8C22×#59511yescharacteristic
476C2×C8C22×#59511yescharacteristic
477C2×C8C22×#59511yescharacteristic
478C2×C8C22×#59511yescharacteristic
479C4⋊C4—171no—
480C4⋊C4—171no—
481C4⋊C4—171no—
482C4⋊C4—171no—
483C4⋊C4—171no—
484C4⋊C4C4⋊#59511yescharacteristic
485C22⋊C4—171no—
486C22⋊C4—171no—
487C22⋊C4—171no—
488C22⋊C4—171no—
489C22⋊C4C4⋊#59511yescharacteristic
490C22⋊C4C4⋊#59511yescharacteristic
491C42—171no—
492C42—171no—
493C42—171no—
494C42—171no—
495C42—171no—
496C42—171no—
497C42—171no—
498C42—171no—
499C42—171no—
500C42C22×#59511yescharacteristic
501C23—171no—
502C23C2×C4⋊#59511yescharacteristic
503C23C2×C4⋊#59511yescharacteristic
504Q8—342no—
505D4—22no—
506D4—342no—
507D4—342no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—172no—
513C2×C4—172no—
514C2×C4—171no—
515C2×C4—171no—
516C2×C4—171no—
517C2×C4—171no—
518C2×C4—171no—
519C2×C4—171no—
520C2×C4—171no—
521C2×C4—341no—
522C2×C4—341no—
523C2×C4—341no—
524C2×C4—341no—
525C2×C4—341no—
526C2×C4—341no—
527C2×C4—681no—
528C2×C4—681no—
529C2×C4—681no—
530C2×C4C2×C4⋊#59511yescharacteristic
531C2×C4C2×C4⋊#59511yescharacteristic
532C2×C4C2×C4⋊#59511yescharacteristic
533C2×C4C2×C4⋊#59511yescharacteristic
534C2×C4C23×#59511yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—341no—
539C8—341no—
540C8—341no—
541C8—341no—
542C8—681no—
543C8—681no—
544C8—681no—
545C8—681no—
546C8—681no—
547C8—681no—
548C8—681no—
549C8—681no—
550C8#1058767812yescomplemented
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—341no—
557C22—341no—
558C22—341no—
559C22#1176382012yes—
560C22C22×C4⋊#59511yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—171no—
566C4—171no—
567C4—172no—
568C4—341no—
569C4—341no—
570C4—341no—
571C4—341no—
572C4—341no—
573C4C2×#1058767811yescharacteristic
574C4#1176388811yescharacteristic
575C2—22no—
576C2—41no—
577C2—681no—
578C2#1454542911yescharacteristic
579C2C2×#1176382011yescharacteristic
580C2#1454544511yescharacteristic
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#17830
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. #14544361C2semidirect
4. #14544360C2semidirect
5. #14544358C2semidirect
6. #14544357C2semidirect
7. #14544353C2semidirect
8. #14544351C2semidirect
9. #14544349C2semidirect
10. #14544348C2semidirect
11. #14544341C2semidirect
12. #14544336C2semidirect
13. #14544335C2semidirect
14. C2×#11763670C2semidirect
256. C8×C17#131semidirect
433. C17#17830semidirect
550. C8#10587678semidirect

Maximal subgroups

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

subgroupindex
#145454792
#145454292
#145443612
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C2×#117636702
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