Finite Group Databasebeta

← #17017444

Subgroups — #17017444

Order 4352.

638 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14540096C212yesmaximal
2#14537497C211yesmaximal, characteristic
3#14528304C212yesmaximal, complemented
4#14528294C212yesmaximal, complemented
5#14528156C214yesmaximal, complemented
6C2×#11762560C211yesmaximal, characteristic, complemented
7#14527474C212yesmaximal, complemented
8C17×#3160C211yesmaximal, characteristic, complemented
9C2×#10587587—21no—
10#11763359C2211yescharacteristic
11#11763096C2214yes—
12#11763094—22no—
13#11763040—24no—
14#11763011C2214yes—
15#11763009—22no—
16#11762888—21no—
17#11762888C2212yes—
18C8×D68—21no—
19C8×D68C2212yes—
20#11762833C2211yescharacteristic
21C2×C4⋊#3622C2212yes—
22#11762775—21no—
23#11762560C2212yes—
24#11762560C2212yes—
25#11762558C2214yes—
26#11762555C2214yes—
27C17×#533C2212yes—
28C17×#500C2211yescharacteristic
29C17×#500C2211yescharacteristic
30C17×#499—21no—
31C17×#499—21no—
32C17×#498C2212yes—
33C17×#427—21no—
34C17×#427—21no—
35C2×C4×C8×C17C2211yescharacteristic
36C2×#63252—21no—
37C22×C8×C17D411yescharacteristic
38C22×C8×C17D411yescharacteristic
39C17×C4⋊Q8C2312yes—
40C17×C4⋊Q8C2312yes—
41C17×#125—22no—
42C17×C22⋊Q8—22no—
43C17×C22⋊Q8—22no—
44C4×Q8×C17—22no—
45C4×Q8×C17—22no—
46C17×#117—22no—
47C2×C42×C17C2311yescharacteristic
48C2×#63230—24no—
49#10587616—21no—
50#10587616D412yes—
51C2×#63223—21no—
52C22×#3622—22no—
53#10587587—44no—
54C2×#63218—22no—
55C2×C8×D17—22no—
56#10587561—21no—
57#10587560D411yescharacteristic
58C4×D68—21no—
59C4×D68C2312yes—
60#10587555D411yescharacteristic
61C17×#107—21no—
62C17×#107—21no—
63C17×#107—21no—
64C17×#107—21no—
65C17×#106—22no—
66C17×#106—22no—
67C4×C8×C17D411yescharacteristic
68C4×C8×C17D411yescharacteristic
69C4×C8×C17C2311yescharacteristic
70C4×C8×C17C2311yescharacteristic
71#10587506—24no—
72#10587491—22no—
73#10587491—22no—
74#10587480—24no—
75#10587479—24no—
76C4⋊#3622—22no—
77C4⋊#3622—21no—
78C4⋊#3622C2314yes—
79C4⋊#3622C2312yes—
80C2×Q8×C17—22no—
81C2×Q8×C17—22no—
82C22×C4×C17C2×D411yescharacteristic
83C22×C4×C17C2×D411yescharacteristic
84C22×C4×C17#4111yescharacteristic
85C2×C22⋊D17—22no—
86#63252—42no—
87#63252—42no—
88C2×D68—21no—
89C2×D68—21no—
90C2×D68C2×D412yes—
91C2×C4×D17—22no—
92C2×Dic34—21no—
93C2×C8×C17—22no—
94C2×C8×C17SD1614yescomplemented
95C2×C8×C17C2×D411yescharacteristic
96C2×C8×C17C2×D411yescharacteristic
97C2×C8×C17C2×D411yescharacteristic
98C2×C8×C17C2×D411yescharacteristic
99C4⋊C4×C17—22no—
100C4⋊C4×C17—22no—
101C4⋊C4×C17—22no—
102C4⋊C4×C17—22no—
103C4⋊C4×C17—42no—
104C4⋊C4×C17—42no—
105C22⋊C4×C17—42no—
106C42×C17—42no—
107C42×C17C2×D411yescharacteristic
108C42×C17C2×D411yescharacteristic
109C42×C17#4111yescharacteristic
110C42×C17C2411yescharacteristic
111#63230—84no—
112#63227—22no—
113#63227—22no—
114C4⋊Dic17—21no—
115C4⋊Dic17C2×D412yes—
116#63223—42no—
117C2×#3622—24no—
118C2×#3622—22no—
119C2×#3622—82no—
120#63218—44no—
121C8×D17—44no—
122#19194—171nomaximal, Sylow
123C23×C17#12111yescharacteristic
124C22×D17—22no—
125Q8×C17—42no—
126Q8×C17—42no—
127Q8×C17—82no—
128C2×C4×C17—22no—
129C2×C4×C17—41no—
130C2×C4×C17—42no—
131C2×C4×C17—42no—
132C2×C4×C17#12111yescharacteristic
133C2×C4×C17#12111yescharacteristic
134C2×C4×C17#12111yescharacteristic
135C2×C4×C17C2×SD1612yes—
136C2×C4×C17#13712yes—
137C2×C4×C17C22×D411yescharacteristic
138C2×C4×C17C22×D411yescharacteristic
139C2×C4×C17C2×#4111yescharacteristic
140C22⋊D17—44no—
141C2×Dic17—22no—
142D68—24no—
143D68—42no—
144D68—42no—
145C4×D17—42no—
146C4×D17—42no—
147Dic34—42no—
148C8×C17—21no—
149C8×C17—21no—
150C8×C17C2×SD1612yes—
151C8×C17C2×SD1612yes—
152#3622—42no—
153#3622—44no—
154#3246—172no—
155#3160D1711yescharacteristic, complemented
156#2931—171no—
157#1695—172no—
158#1693—172no—
159#1671—174no—
160C2×#334—171no—
161#1550—172no—
162C22×C17—21no—
163C22×C17—21no—
164C22×C17#46112yes—
165C22×C17C2×#12111yescharacteristic
166C2×D17—42no—
167C2×D17—42no—
168C2×D17—42no—
169C4×C17—21no—
170C4×C17—21no—
171C4×C17—21no—
172C4×C17—82no—
173C4×C17—82no—
174C4×C17#46112yes—
175C4×C17C22×SD1611yescharacteristic
176C4×C17C2×#13711yescharacteristic
177C4×C17#57712yes—
178Dic17—42no—
179C2×#131—341no—
180#533C2×D1712yes—
181#532—171no—
182#500C2×D1711yescharacteristic
183#500C2×D1711yescharacteristic
184#499—21no—
185#499—21no—
186#498C2×D1712yes—
187#476—174no—
188#475—342no—
189#465—344no—
190#461—174no—
191#460—342no—
192#436—172no—
193#436—341no—
194C8×D4—172no—
195C8×D4—341no—
196#427—21no—
197#427—21no—
198#423—171no—
199C2×C4⋊C8—172no—
200#408—341no—
201C2×C4×C8C2×D1711yescharacteristic
202#334—172no—
203#334—172no—
204#333—174no—
205#332—174no—
206C2×C17—22no—
207C2×C17C2×#46111yescharacteristic
208C2×C17#306011yescharacteristic
209C2×C17#306711yescharacteristic
210D17—82no—
211C2×#41—341no—
212C2×SD16—344no—
213#131—684no—
214C2×M16—341no—
215C2×M16—342no—
216C22×C8—342no—
217C22×C8—342no—
218C22×C8C22⋊D1711yescharacteristic
219C22×C8C22⋊D1711yescharacteristic
220C4⋊Q8—171no—
221C4⋊Q8C22×D1712yes—
222C4⋊Q8C22×D1712yes—
223#127—171no—
224#125—22no—
225#124—341no—
226C22⋊Q8—22no—
227C22⋊Q8—22no—
228#121—172no—
229#121—341no—
230C4×Q8—22no—
231C4×Q8—22no—
232C4×D4—172no—
233C4×D4—341no—
234#117—22no—
235C2×C42C22×D1711yescharacteristic
236#107—21no—
237#107—21no—
238#107—21no—
239#107—21no—
240#106—22no—
241#106—22no—
242#106—344no—
243C4⋊C8—172no—
244C4⋊C8—174no—
245C4⋊C8—342no—
246C4⋊C8—341no—
247#103—344no—
248#102—344no—
249C22⋊C8—342no—
250C22⋊C8—342no—
251C4×C8C22⋊D1711yescharacteristic
252C4×C8C22⋊D1711yescharacteristic
253C4×C8C22×D1711yescharacteristic
254C4×C8C22×D1711yescharacteristic
255C17#1919411yescharacteristic, complemented, Sylow
256#41—682no—
257#41—682no—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—341no—
261C2×D4—172no—
262C2×D4—342no—
263C2×D4—341no—
264C2×D4—341no—
265C22×C4—342no—
266C22×C4D4×D1711yescharacteristic
267C22×C4#6325411yescharacteristic
268C22×C4C2×C22⋊D1711yescharacteristic
269SD16—1364no—
270M16—682no—
271M16—684no—
272C2×C8—22no—
273C2×C8—344no—
274C2×C8—342no—
275C2×C8—684no—
276C2×C8—1362no—
277C2×C8#6323014yescomplemented
278C2×C8C2×C22⋊D1711yescharacteristic
279C2×C8C2×C22⋊D1711yescharacteristic
280C2×C8C2×C22⋊D1711yescharacteristic
281C2×C8C2×C22⋊D1711yescharacteristic
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—172no—
289C4⋊C4—341no—
290C22⋊C4—42no—
291C22⋊C4—342no—
292C22⋊C4—342no—
293C42—42no—
294C42D4×D1711yescharacteristic
295C42#6325411yescharacteristic
296C42C2×C22⋊D1711yescharacteristic
297C42C23×D1711yescharacteristic
298C23—342no—
299C23#1058762411yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—82no—
303Q8—682no—
304D4—344no—
305D4—682no—
306D4—684no—
307D4—682no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—342no—
313C2×C4—682no—
314C2×C4—682no—
315C2×C4#1058762411yescharacteristic
316C2×C4#1058762411yescharacteristic
317C2×C4#1058762411yescharacteristic
318C2×C4C2×#6323012yes—
319C2×C4#1058762812yes—
320C2×C4C2×D4×D1711yescharacteristic
321C2×C4C2×#6325411yescharacteristic
322C2×C4C22×C22⋊D1711yescharacteristic
323C8—21no—
324C8—21no—
325C8—682no—
326C8—684no—
327C8C2×#6323012yes—
328C8C2×#6323012yes—
329C22—21no—
330C22—21no—
331C22—682no—
332C22—682no—
333C22—682no—
334C22#1176301112yes—
335C22C2×#1058762411yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—82no—
340C4—82no—
341C4—682no—
342C4#1176301112yes—
343C4C22×#6323011yescharacteristic
344C4C2×#1058762811yescharacteristic
345C4#1176361612yes—
346C2—22no—
347C2—1362no—
348C2C2×#1176301111yescharacteristic
349C2#1453844211yescharacteristic
350C2#1453850011yescharacteristic
subgroupG/H
centerC22C2×#10587624
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
FittingC17×#3160C2
socleC22×C17C2×#121
prime radical#11763359C22
hypercenter#3160D17
hypocenterC17#19194
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3160

Complements

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

NH ≅ G/Ntype
3. #14528304C2semidirect
4. #14528294C2semidirect
5. #14528156C2semidirect
6. C2×#11762560C2semidirect
7. #14527474C2semidirect
8. C17×#3160C2semidirect
94. C2×C8×C17SD16semidirect
155. #3160D17semidirect
255. C17#19194semidirect
277. C2×C8#63230semidirect

Maximal subgroups

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

subgroupindex
#145400962
#145374972
#145283042
#145282942
#145281562
C2×#117625602
#145274742
C17×#31602
#1919417