Finite Group Databasebeta

← #17018113

Subgroups — #17018113

Order 4352.

798 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14539363C211yesmaximal, characteristic, complemented
2#14538248C212yesmaximal, complemented
3#14528221C214yesmaximal, complemented
4#14528173C212yesmaximal, complemented
5#14528139C212yesmaximal, complemented
6#14527543C211yesmaximal, characteristic, complemented
7#14527459C212yesmaximal, complemented
8C2×C8×D4×C17C211yesmaximal, characteristic, complemented
9C2×#10587618—22no—
10#11763359C2212yes—
11#11763214C2211yescharacteristic, complemented
12#11763186C2211yescharacteristic, complemented
13#11763156C2212yescomplemented
14#11763045—21no—
15#11763045—21no—
16#11763024—24no—
17#11763014C2214yes—
18#11763004C2214yes—
19C4×D136—21no—
20C4×D136—21no—
21#11762833C2212yes—
22#11762808—22no—
23#11762562C2212yescomplemented
24#11762562C2212yescomplemented
25#11762554C2214yescomplemented
26#11762552C2214yescomplemented
27C23×C8×C17—21no—
28C2×C4×D4×C17C2211yescharacteristic
29C8×D4×C17—21no—
30C8×D4×C17—21no—
31C8×D4×C17C2212yes—
32C8×D4×C17C2212yes—
33C2×C17×C4⋊C8C2211yescharacteristic
34C2×C17×C22⋊C8—21no—
35C2×C4×C8×C17C2211yescharacteristic
36C22×D4×C17D411yescharacteristic
37C23×C4×C17—21no—
38C2×#63252—22no—
39C22×C8×C17—21no—
40C22×C8×C17—22no—
41C22×C8×C17—22no—
42C22×C8×C17—44no—
43C22×C8×C17D411yescharacteristic
44C22×C8×C17D411yescharacteristic
45C4×D4×C17—21no—
46C4×D4×C17—21no—
47C4×D4×C17D412yes—
48C4×D4×C17C2312yes—
49C2×C4⋊C4×C17D411yescharacteristic
50C2×C22⋊C4×C17—21no—
51C2×C42×C17C2311yescharacteristic
52C2×#63229—24no—
53#10587618—48no—
54C2×#63228—24no—
55#10587616—22no—
56#10587616—22no—
57C2×#63223—22no—
58C2×D136—21no—
59C2×D136—21no—
60#10587561—22no—
61#10587560C2312yes—
62C4×D68—22no—
63C4×D68—22no—
64#10587555C2312yes—
65C17×C4⋊C8—21no—
66C17×C4⋊C8C2312yes—
67C17×C22⋊C8—22no—
68C17×C22⋊C8—22no—
69C4×C8×C17D411yescharacteristic
70C4×C8×C17D411yescharacteristic
71C4×C8×C17C2311yescharacteristic
72C4×C8×C17C2311yescharacteristic
73#10587492—22no—
74#10587492—22no—
75#10587489—21no—
76#10587489—21no—
77#10587481—24no—
78#10587480—24no—
79C4⋊#3622—22no—
80C4⋊#3622C2314yes—
81C24×C17—21no—
82C2×D4×C17—21no—
83C2×D4×C17—22no—
84C2×D4×C17D814yescomplemented
85C2×D4×C17C2×D412yes—
86C22×C4×C17—21no—
87C22×C4×C17—22no—
88C22×C4×C17—22no—
89C22×C4×C17—42no—
90C22×C4×C17—42no—
91C22×C4×C17C2×D411yescharacteristic
92C22×C4×C17C2×D411yescharacteristic
93C22×C4×C17#4111yescharacteristic
94C2×C22⋊D17—42no—
95#63252—44no—
96#63252—44no—
97C2×D68—22no—
98C2×D68—22no—
99C2×D68—22no—
100C2×C4×D17—42no—
101C2×Dic34—22no—
102C2×C8×C17—22no—
103C2×C8×C17—22no—
104C2×C8×C17—41no—
105C2×C8×C17—44no—
106C2×C8×C17—42no—
107C2×C8×C17—44no—
108C2×C8×C17C2×D411yescharacteristic
109C2×C8×C17C2×D411yescharacteristic
110C2×C8×C17C2×D411yescharacteristic
111C2×C8×C17C2×D411yescharacteristic
112C4⋊C4×C17—21no—
113C4⋊C4×C17C2×D412yes—
114C22⋊C4×C17—22no—
115C22⋊C4×C17—22no—
116C42×C17C2×D411yescharacteristic
117C42×C17C2×D411yescharacteristic
118C42×C17#4111yescharacteristic
119C42×C17C2411yescharacteristic
120#63229—48no—
121#63228—48no—
122#63227—42no—
123#63227—42no—
124C4⋊Dic17—22no—
125C4⋊Dic17—22no—
126#63223—44no—
127C2×#3622—24no—
128D136—42no—
129D136—42no—
130#19255—171nomaximal, Sylow
131C23×C17—22no—
132C23×C17—24no—
133C23×C17—42no—
134C23×C17—42no—
135C23×C17#12111yescharacteristic
136C22×D17—42no—
137D4×C17—22no—
138D4×C17—24no—
139D4×C17C2×D814yes—
140C2×C4×C17—21no—
141C2×C4×C17—21no—
142C2×C4×C17—22no—
143C2×C4×C17—41no—
144C2×C4×C17—44no—
145C2×C4×C17—42no—
146C2×C4×C17—42no—
147C2×C4×C17—42no—
148C2×C4×C17#12111yescharacteristic
149C2×C4×C17#12111yescharacteristic
150C2×C4×C17#12111yescharacteristic
151C2×C4×C17C2×D812yes—
152C2×C4×C17#13512yes—
153C2×C4×C17C22×D411yescharacteristic
154C2×C4×C17C22×D411yescharacteristic
155C2×C4×C17C2×#4111yescharacteristic
156C22⋊D17—84no—
157C2×Dic17—42no—
158D68—42no—
159D68—42no—
160D68—42no—
161D68—42no—
162D68—82no—
163C4×D17—84no—
164Dic34—42no—
165Dic34—42no—
166C8×C17—21no—
167C8×C17—21no—
168C8×C17—21no—
169C8×C17—42no—
170C8×C17AGL(1,ℤ/8)12yescomplemented
171#3622—44no—
172#3169—171no—
173#3036—172no—
174C2×C8×D4D1711yescharacteristic, complemented
175#1681—174no—
176#1673—172no—
177#1667—172no—
178#1567—171no—
179#1547—172no—
180C22×C17—21no—
181C22×C17—21no—
182C22×C17—24no—
183C22×C17—48no—
184C22×C17—42no—
185C22×C17—42no—
186C22×C17#46612yes—
187C22×C17C2×#12111yescharacteristic
188C2×D17—82no—
189C2×D17—82no—
190C2×D17—82no—
191C4×C17—21no—
192C4×C17—21no—
193C4×C17—21no—
194C4×C17—42no—
195C4×C17#46612yes—
196C4×C17C22×D811yescharacteristic
197C4×C17C2×#13511yescharacteristic
198C4×C17C2×AGL(1,ℤ/8)11yescharacteristic
199C4×C17#57511yescharacteristic
200Dic17—82no—
201C2×AGL(1,ℤ/8)—342no—
202C23×C8—21no—
203#532—172no—
204C2×C4×D4C2×D1711yescharacteristic
205#500—171no—
206#493—171no—
207#486—172no—
208#466—341no—
209#466—341no—
210#463—344no—
211#461—174no—
212#459—174no—
213C4×D8—341no—
214C4×D8—341no—
215C8×D4—21no—
216C8×D4—21no—
217C8×D4C2×D1712yes—
218C8×D4C2×D1712yes—
219#423—172no—
220C2×C4⋊C8C2×D1711yescharacteristic
221#417—342no—
222C2×C22⋊C8—21no—
223C2×C4×C8C2×D1711yescharacteristic
224#335—172no—
225#335—172no—
226#332—174no—
227#331—174no—
228C2×C17—22no—
229C2×C17—44no—
230C2×C17#303611yescharacteristic
231C2×C17C2×#46611yescharacteristic
232C2×C17#306711yescharacteristic
233D17—162no—
234C2×#41—342no—
235C22×D4D6811yescharacteristic
236C23×C4—21no—
237AGL(1,ℤ/8)—688no—
238C2×SD16—344no—
239C2×D8—344no—
240C2×D8—341no—
241C2×D8—341no—
242C2×M16—342no—
243C22×C8—21no—
244C22×C8—22no—
245C22×C8—22no—
246C22×C8—44no—
247C22×C8C22⋊D1711yescharacteristic
248C22×C8C22⋊D1711yescharacteristic
249C4⋊Q8—172no—
250#127—172no—
251#124—342no—
252#121—342no—
253#121—342no—
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—342no—
257C4×D4—342no—
258C4×D4D6812yes—
259C4×D4C22×D1712yes—
260C2×C4⋊C4D6811yescharacteristic
261C2×C22⋊C4—21no—
262C2×C42C22×D1711yescharacteristic
263#107—341no—
264#107—341no—
265C4⋊C8—21no—
266C4⋊C8—174no—
267C4⋊C8—342no—
268C4⋊C8C22×D1712yes—
269#103—344no—
270#102—342no—
271#102—342no—
272#102—344no—
273C22⋊C8—22no—
274C22⋊C8—22no—
275C4×C8C22⋊D1711yescharacteristic
276C4×C8C22⋊D1711yescharacteristic
277C4×C8C22×D1711yescharacteristic
278C4×C8C22×D1711yescharacteristic
279C17#1925511yescharacteristic, complemented, Sylow
280C24—21no—
281#41—684no—
282#41—684no—
283C2×Q8—342no—
284C2×D4—22no—
285C2×D4—21no—
286C2×D4—342no—
287C2×D4—342no—
288C2×D4—342no—
289C2×D4—682no—
290C2×D4D13614yescomplemented
291C2×D4C2×D6812yes—
292C22×C4—21no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—682no—
298C22×C4C2×D6811yescharacteristic
299C22×C4#6325211yescharacteristic
300C22×C4C2×C22⋊D1711yescharacteristic
301SD16—688no—
302D8—682no—
303D8—688no—
304D8—682no—
305M16—684no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—44no—
310C2×C8—42no—
311C2×C8—44no—
312C2×C8—344no—
313C2×C8C2×C22⋊D1711yescharacteristic
314C2×C8C2×C22⋊D1711yescharacteristic
315C2×C8C2×C22⋊D1711yescharacteristic
316C2×C8C2×C22⋊D1711yescharacteristic
317C4⋊C4—21no—
318C4⋊C4—342no—
319C4⋊C4—342no—
320C4⋊C4C2×D6812yes—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—682no—
324C22⋊C4—682no—
325C42C2×D6811yescharacteristic
326C42#6325211yescharacteristic
327C42C2×C22⋊D1711yescharacteristic
328C42C23×D1711yescharacteristic
329C23—24no—
330C23—22no—
331C23—42no—
332C23—42no—
333C23—682no—
334C23#1058761611yescharacteristic
335Q8—682no—
336Q8—682no—
337D4—24no—
338D4—22no—
339D4—682no—
340D4—682no—
341D4—682no—
342D4—682no—
343D4—1362no—
344D4—1364no—
345D4C2×D13614yes—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—41no—
350C2×C4—44no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—682no—
355C2×C4—1364no—
356C2×C4C2×D13612yes—
357C2×C4#1058759012yes—
358C2×C4#1058761611yescharacteristic
359C2×C4#1058761611yescharacteristic
360C2×C4#1058761611yescharacteristic
361C2×C4C22×D6811yescharacteristic
362C2×C4C2×#6325211yescharacteristic
363C2×C4C22×C22⋊D1711yescharacteristic
364C8—21no—
365C8—21no—
366C8—21no—
367C8—42no—
368C8—684no—
369C8#1058761812yescomplemented
370C22—21no—
371C22—21no—
372C22—24no—
373C22—48no—
374C22—42no—
375C22—42no—
376C22—1362no—
377C22—1362no—
378C22—1362no—
379C22#1176304512yes—
380C22C2×#1058761611yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—42no—
385C4—1362no—
386C4#1176304512yes—
387C4C22×D13611yescharacteristic
388C4C2×#1058759011yescharacteristic
389C4C2×#1058761811yescharacteristic
390C4#1176360711yescharacteristic
391C2—22no—
392C2—44no—
393C2—2722no—
394C2#1453824811yescharacteristic
395C2C2×#1176304511yescharacteristic
396C2#1453850411yescharacteristic
subgroupG/H
centerC22C2×#10587616
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
FittingC2×C8×D4×C17C2
socleC22×C17C2×#121
hypercenterC2×C8×D4D17
hypocenterC17#19255
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. #14539363C2semidirect
2. #14538248C2semidirect
3. #14528221C2semidirect
4. #14528173C2semidirect
5. #14528139C2semidirect
6. #14527543C2semidirect
7. #14527459C2semidirect
8. C2×C8×D4×C17C2semidirect
11. #11763214C22semidirect
12. #11763186C22semidirect
13. #11763156C22semidirect
23. #11762562C22semidirect
24. #11762562C22semidirect
25. #11762554C22semidirect
26. #11762552C22semidirect
84. C2×D4×C17D8semidirect
170. C8×C17AGL(1,ℤ/8)semidirect
174. C2×C8×D4D17semidirect
279. C17#19255semidirect
290. C2×D4D136semidirect
369. C8#10587618semidirect

Maximal subgroups

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

subgroupindex
#145393632
#145382482
#145282212
#145281732
#145281392
#145275432
#145274592
C2×C8×D4×C172
#1925517