Finite Group Databasebeta

← #17973592

Subgroups — #17973592

Order 4352.

578 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545577C212yesmaximal
2#14544972C212yesmaximal
3#14544851C214yesmaximal
4#14544850C214yesmaximal
5#14544709C211yesmaximal, characteristic
6#14544502C211yesmaximal, characteristic
7#14539293C211yesmaximal, characteristic
8#11763861—24no—
9#11763860—24no—
10#11763816C2214yes—
11#11763814C2212yes—
12#11763774C2214yes—
13#11763768C2211yescharacteristic
14#11763745C2211yescharacteristic
15#11763685C2214yes—
16#11763679C2214yes—
17#11763679C2214yes—
18#11763674C2212yes—
19#11763674C2212yes—
20#11763364C2212yes—
21#11763212C412yescomplemented
22#11763209C414yescomplemented
23#11763207C411yescharacteristic, complemented
24#11762844C2214yes—
25C4×C8×D17C2211yescharacteristic
26C17×#498C411yescharacteristic, complemented
27C2×C4×#595C2311yescharacteristic
28C2×C4×#595C2311yescharacteristic
29C2×#63243C2314yes—
30C2×#63242C2312yes—
31C17×C4⋊Q8C2×C412yes—
32#10587632—22no—
33Q8×Dic17—22no—
34C2×C8×D17C2312yes—
35#10587583—22no—
36#10587578C2314yes—
37#10587576C2×C414yes—
38#10587573—22no—
39C42×D17C2311yescharacteristic
40#10587555C2×C412yes—
41(C2×#595)⋊C4—22no—
42#10587544—22no—
43#10587544—22no—
44#10587544—24no—
45#10587542—24no—
46#10587542D414yes—
47C4⋊#3624—24no—
48C4×#3624—24no—
49C17×#106C2×C414yes—
50C4×C8×C17C2×C411yescharacteristic
51#10587488C2×C414yes—
52C8×Dic17C2×C412yes—
53#10587478C2×C418yes—
54C4×#3622C2×C411yescharacteristic
55C22×#595—21no—
56C22×#595—21no—
57C2×Q8×C17—22no—
58C2×C4×D17#4112yes—
59C2×C4×D17C2411yescharacteristic
60C2×Dic34—22no—
61C2×#3624—24no—
62C2×#3624C2×D414yes—
63C4×#595—22no—
64C4×#595—22no—
65#63243—24no—
66#63243—24no—
67#63242—22no—
68#63242—22no—
69C2×C8×C17C22×C412yes—
70C4⋊C4×C17—22no—
71C4⋊C4×C17C22×C414yes—
72C42×C17C22×C411yescharacteristic
73#63227—24no—
74C4⋊Dic17—22no—
75C4⋊Dic17—24no—
76C4⋊Dic17C22×C414yes—
77#63225—24no—
78C4×Dic17—24no—
79C4×Dic17C22×C411yescharacteristic
80C4×Dic17C2×D412yes—
81C2×#3622C22×C412yes—
82C8×D17—22no—
83C8×D17—22no—
84#22258—171nomaximal, Sylow
85C22×D17C2×#4111yescharacteristic
86C2×#595—42no—
87C2×#595—42no—
88C2×#595—41no—
89C2×#595—41no—
90Q8×C17—82no—
91C2×C4×C17—24no—
92C2×C4×C17C4×D412yes—
93C2×C4×C17C23×C411yescharacteristic
94C2×Dic17—24no—
95C2×Dic17C4×D412yes—
96C2×Dic17C22×D411yescharacteristic
97C4×D17—42no—
98C4×D172−1+412yes—
99C4×D172−1+412yes—
100Dic34—82no—
101#3624—24no—
102#3624—44no—
103C8×C17—22no—
104#3622—22no—
105#3160—171no—
106#2961—172no—
107#1995—172no—
108#1922—174no—
109#1922—174no—
110#1837—171no—
111#1746—171no—
112C22×C17C2×C4×D411yescharacteristic
113C2×D17—22no—
114C2×D17#54111yescharacteristic
115C2×D17#54111yescharacteristic
116#595—81no—
117#595—81no—
118C4×C17—22no—
119C4×C17—44no—
120C4×C17#51912yes—
121Dic17—22no—
122Dic17—44no—
123Dic17#53612yes—
124#533—172no—
125#500—172no—
126#499—174no—
127#498—171no—
128#498#59511yescharacteristic, complemented
129#446—344no—
130#446—344no—
131#427—174no—
132#424—174no—
133#423—172no—
134#405—174no—
135C2×#97—171no—
136C2×C4×C8—171no—
137#376—171no—
138#341—174no—
139#339—174no—
140#339—174no—
141#336—172no—
142#336—172no—
143C2×C17#232711yescharacteristic
144C2×C17#295712yes—
145D17—21no—
146D17—21no—
147C2×M16—174no—
148C22×C8—172no—
149C22×C8—172no—
150C4⋊Q8—172no—
151C4⋊Q8C2×#59512yes—
152#125—174no—
153C22⋊Q8—342no—
154C22⋊Q8—342no—
155C4×Q8—342no—
156C4×Q8—342no—
157#117—174no—
158C2×C42—171no—
159C2×C42—171no—
160C2×C42—171no—
161#107—178no—
162#106—174no—
163#106C2×#59514yes—
164C4⋊C8—342no—
165C4⋊C8—342no—
166C4⋊C8—344no—
167C4⋊C8—344no—
168#97—174no—
169#97—344no—
170C4×C8—172no—
171C4×C8—171no—
172C4×C8—344no—
173C4×C8C2×#59511yescharacteristic
174#95—342no—
175C17#2225811yescharacteristic, complemented, Sylow
176C2×Q8—22no—
177C2×Q8—342no—
178C22×C4—171no—
179C22×C4—172no—
180C22×C4—341no—
181C22×C4—341no—
182M16—344no—
183M16—344no—
184C2×C8—174no—
185C2×C8—172no—
186C2×C8—342no—
187C2×C8—342no—
188C2×C8—342no—
189C2×C8—342no—
190C2×C8—344no—
191C2×C8C22×#59512yes—
192C4⋊C4—22no—
193C4⋊C4—174no—
194C4⋊C4—344no—
195C4⋊C4—344no—
196C4⋊C4—342no—
197C4⋊C4C22×#59514yes—
198C22⋊C4—344no—
199C42—172no—
200C42—171no—
201C42—344no—
202C42—342no—
203C42—342no—
204C42C22×#59511yescharacteristic
205C23—171no—
206Q8—82no—
207Q8—1362no—
208C2×C4—24no—
209C2×C4—171no—
210C2×C4—172no—
211C2×C4—172no—
212C2×C4—172no—
213C2×C4—344no—
214C2×C4—682no—
215C2×C4—681no—
216C2×C4—681no—
217C2×C4—682no—
218C2×C4—682no—
219C2×C4D4×#59512yes—
220C2×C4C23×#59511yescharacteristic
221C8—22no—
222C8—344no—
223C8—342no—
224C8—684no—
225C22—171no—
226C22—171no—
227C22—342no—
228C22C2×D4×#59511yescharacteristic
229C4—22no—
230C4—44no—
231C4—172no—
232C4—342no—
233C4—684no—
234C4—1361no—
235C4—1361no—
236C4#1176387712yes—
237C2—341no—
238C2—341no—
239C2#1454527511yescharacteristic
240C2#1454556212yes—
subgroupG/H
centerC22C2×D4×#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC17×#498C4
socleC22×C17C2×C4×D4
prime radicalC22×D17C2×#41
cosocleC2×C4×D17C24
hypercenter#498#595
hypocenterC17#22258
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
21. #11763212C4semidirect
22. #11763209C4semidirect
23. #11763207C4semidirect
26. C17×#498C4semidirect
128. #498#595semidirect
175. C17#22258semidirect

Maximal subgroups

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

subgroupindex
#145455772
#145449722
#145448512
#145448502
#145447092
#145445022
#145392932
#2225817