Finite Group Databasebeta

← #16947603

Subgroups — #16947603

Order 4352.

354 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 67 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#14540094C211yesmaximal, characteristic
2#14530969C212yesmaximal, complemented
3#14526792C212yesmaximal, complemented
4#14526724C211yesmaximal, characteristic, complemented
5C17×#2087C211yesmaximal, characteristic, complemented
6#11763359—21no—
7#11763090—22no—
8#11763045—21no—
9#11763045C2212yes—
10#11763005—22no—
11#11762636—22no—
12#11762609—22no—
13C22⋊#63214C2212yes—
14C2×C17×#107C2211yescharacteristic
15C2×C17×C4⋊C8C2211yescharacteristic
16C17×#389—21no—
17C17×#340—21no—
18C17×#340C2211yescharacteristic
19C2×#63252—41no—
20C22×C8×C17D411yescharacteristic
21C22×C8×C17C2311yescharacteristic
22C2×C4⋊C4×C17—21no—
23C2×C4⋊C4×C17—21no—
24C2×C4⋊C4×C17—41no—
25C2×C42×C17D411yescharacteristic
26#10587616—22no—
27#10587616—41no—
28C2×D136—21no—
29C2×D136D412yes—
30#10587561—41no—
31#10587560—21no—
32C4×D68—22no—
33C4×D68—41no—
34#10587555—21no—
35C17×#107—22no—
36C17×C4⋊C8—22no—
37C17×#95—41no—
38#10587492—22no—
39#10587492—22no—
40#10587489—21no—
41#10587489D412yes—
42C2×#63214—22no—
43C22×C4×C17—41no—
44C22×C4×C17—41no—
45C22×C4×C17D811yescharacteristic
46C22×C4×C17D811yescharacteristic
47C22×C4×C17C2×D411yescharacteristic
48C2×C22⋊D17—42no—
49#63252—82no—
50#63252—82no—
51C2×D68—22no—
52C2×D68—41no—
53C2×D68—41no—
54C2×C4×D17—42no—
55C2×Dic34—41no—
56C2×C8×C17—21no—
57C2×C8×C17—41no—
58C2×C8×C17—41no—
59C2×C8×C17C2×D412yes—
60C4⋊C4×C17—22no—
61C4⋊C4×C17—41no—
62C4⋊C4×C17—41no—
63C4⋊C4×C17—41no—
64C4⋊C4×C17—82no—
65C42×C17—21no—
66C42×C17—21no—
67#63227—42no—
68#63227—42no—
69C4⋊Dic17—22no—
70C4⋊Dic17—41no—
71D136—42no—
72D136—81no—
73#63214—42no—
74#12291—171nomaximal, Sylow
75C23×C17C2×D811yescharacteristic
76C22×D17—42no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—41no—
83C2×C4×C17—42no—
84C2×C4×C17—81no—
85C2×C4×C17—81no—
86C2×C4×C17—81no—
87C2×C4×C17—81no—
88C2×C4×C17—81no—
89C2×C4×C17SD3212yes—
90C2×C4×C17#12011yescharacteristic
91C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
92C22⋊D17—82no—
93C22⋊D17—82no—
94C2×Dic17—42no—
95D68—42no—
96D68—42no—
97D68—82no—
98D68—82no—
99C4×D17—84no—
100Dic34—82no—
101C8×C17—22no—
102C8×C17—41no—
103#3245—171no—
104#2233—172no—
105#2087D1711yescharacteristic, complemented
106#1347—172no—
107#1322—171no—
108C22×C17—21no—
109C22×C17—21no—
110C22×C17#44711yescharacteristic
111C22×C17C2×SD3211yescharacteristic
112C22×C17#50911yescharacteristic
113C2×D17—82no—
114C2×D17—82no—
115C2×D17—82no—
116C4×C17—21no—
117C4×C17—22no—
118C4×C17—41no—
119C4×C17—82no—
120C4×C17—161no—
121C4×C17#45611yescharacteristic
122C4×C17#45811yescharacteristic
123Dic17—82no—
124#532—341no—
125#474—342no—
126#466—172no—
127#466—341no—
128#459—342no—
129C2×#107C2×D1711yescharacteristic
130C2×C4⋊C8C2×D1711yescharacteristic
131#389—21no—
132#367—342no—
133#357—342no—
134C22⋊C16—172no—
135#340—21no—
136#340C2×D1711yescharacteristic
137C2×C17—21no—
138C2×C17—21no—
139C2×C17#161011yescharacteristic
140C2×C17#218711yescharacteristic
141C2×C17#219011yescharacteristic
142D17—162no—
143C2×#41—681no—
144C2×D8—172no—
145C2×D8—341no—
146C22×C8C22⋊D1711yescharacteristic
147C22×C8C22×D1711yescharacteristic
148C4⋊Q8—341no—
149#127—341no—
150#124—681no—
151#121—342no—
152#121—681no—
153C4×D4—342no—
154C4×D4—681no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—41no—
158C2×C42C22⋊D1711yescharacteristic
159C2×C16—342no—
160#107—22no—
161#107—172no—
162#107—341no—
163C4⋊C8—22no—
164#102—342no—
165#102—342no—
166#95—41no—
167C17#1229111yescharacteristic, complemented, Sylow
168#41—1362no—
169#41—1362no—
170C2×Q8—681no—
171C2×D4—342no—
172C2×D4—681no—
173C2×D4—681no—
174C2×D4—682no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—682no—
178C22×C4#6322811yescharacteristic
179C22×C4#6322811yescharacteristic
180C22×C4C2×C22⋊D1711yescharacteristic
181D8—682no—
182D8—1361no—
183C2×C8—21no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8D4×D1712yes—
187C4⋊C4—22no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—82no—
192C4⋊C4—342no—
193C4⋊C4—681no—
194C22⋊C4—682no—
195C22⋊C4—682no—
196C42—21no—
197C42—21no—
198C16—682no—
199C23—682no—
200C23C2×#6322811yescharacteristic
201Q8—1362no—
202D4—682no—
203D4—682no—
204D4—1362no—
205D4—1362no—
206D4—1362no—
207D4—1362no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—81no—
216C2×C4—81no—
217C2×C4—81no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—682no—
221C2×C4—1364no—
222C2×C4#1058749912yes—
223C2×C4#1058762311yescharacteristic
224C2×C4#1058763511yescharacteristic
225C8—22no—
226C8—41no—
227C22—21no—
228C22—21no—
229C22—1362no—
230C22—1362no—
231C22—1362no—
232C22#1176294211yescharacteristic
233C22C2×#1058749911yescharacteristic
234C22#1176324411yescharacteristic
235C4—21no—
236C4—22no—
237C4—41no—
238C4—82no—
239C4—161no—
240C4—1362no—
241C4#1176299111yescharacteristic
242C4#1176299811yescharacteristic
243C2—21no—
244C2—21no—
245C2—2722no—
246C2#1452778611yescharacteristic
247C2#1453071211yescharacteristic
248C2#1453072911yescharacteristic
subgroupG/H
centerC22#11762942
commutator, cosocleC22×C8×C17C23
FrattiniC22×C8C22×D17
FittingC17×#2087C2
socleC22×C17#447
prime radical#14540094C2
hypercenter#2087D17
hypocenterC17#12291
LCSG ▷ C22×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2087

Complements

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

NH ≅ G/Ntype
2. #14530969C2semidirect
3. #14526792C2semidirect
4. #14526724C2semidirect
5. C17×#2087C2semidirect
105. #2087D17semidirect
167. C17#12291semidirect

Maximal subgroups

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

subgroupindex
#145400942
#145309692
#145267922
#145267242
C17×#20872
#1229117