Finite Group Databasebeta

← #17949293

Subgroups — #17949293

Order 4352.

228 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 36 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#14543727C211yesmaximal, characteristic, complemented
2#14543662C211yesmaximal, characteristic, complemented
3#14530005C211yesmaximal, characteristic
4C2×#10587544—21no—
5#11763654—21no—
6C2×#10587508—21no—
7#11762810—21no—
8#11762678C2211yescharacteristic
9#11762578C411yescharacteristic
10C17×#537C411yescharacteristic
11C2×#41×C17—21no—
12C22×#3624—41no—
13C17×C22⋊Q8—41no—
14C17×#121—41no—
15C17×#121—41no—
16C2×C4⋊C4×C17C2×C411yescharacteristic
17C2×C4⋊Dic17D411yescharacteristic
18C2×#63225—41no—
19C2×C4×Dic17D411yescharacteristic
20C2×#63223—21no—
21C22⋊#3624—41no—
22#10587544—22no—
23#10587544—41no—
24#10587508—41no—
25#10587508—41no—
26#10587506—41no—
27#10587503—41no—
28#41×C17—41no—
29#41×C17—41no—
30#41×C17—41no—
31#41×C17—41no—
32C2×Q8×C17—21no—
33C2×D4×C17—21no—
34C2×D4×C17—41no—
35C2×D4×C17—41no—
36C22×C4×C17—21no—
37C22×C4×C17—41no—
38C22×C4×C17C22⋊C411yescharacteristic
39C22×Dic17—21no—
40C22×Dic17—21no—
41C2×#3624—42no—
42C2×#3624—81no—
43C2×#3624—81no—
44C2×#3624—81no—
45C4⋊C4×C17—41no—
46C4⋊C4×C17—41no—
47C22⋊C4×C17—42no—
48C4⋊Dic17—41no—
49#63225—81no—
50#63225—81no—
51C4×Dic17—21no—
52C4×Dic17D811yescharacteristic
53C4×Dic17SD1611yescharacteristic
54#63223—41no—
55#63223—41no—
56C2×#3622—41no—
57#7417—171nomaximal, Sylow
58C23×C17—41no—
59C23×C17#9911yescharacteristic
60Q8×C17—41no—
61Q8×C17—41no—
62D4×C17—41no—
63D4×C17—41no—
64D4×C17—81no—
65D4×C17—81no—
66D4×C17—161no—
67C2×C4×C17—21no—
68C2×C4×C17—21no—
69C2×C4×C17—41no—
70C2×C4×C17—41no—
71C2×C4×C17—81no—
72C2×C4×C17—81no—
73C2×C4×C17—81no—
74C2×C4×C17#10211yescharacteristic
75C2×C4×C17#10411yescharacteristic
76C2×Dic17—21no—
77C2×Dic17—21no—
78C2×Dic17—21no—
79C2×Dic17—21no—
80C2×Dic17—21no—
81C2×Dic17—21no—
82C2×Dic17—41no—
83C2×Dic17—81no—
84#3624—82no—
85#3624—161no—
86#3622—81no—
87#2039—171no—
88#1325—171no—
89#1296—171no—
90C22×C17—21no—
91C22×C17—21no—
92C22×C17—81no—
93C22×C17—81no—
94C22×C17—81no—
95C22×C17#32711yescharacteristic
96C22×C17AΣL(1,𝔽16)11yescharacteristic
97C22×C17#35511yescharacteristic
98C4×C17—21no—
99C4×C17—21no—
100C4×C17—81no—
101C4×C17—81no—
102Dic17—21no—
103Dic17—21no—
104Dic17—21no—
105Dic17—21no—
106Dic17—81no—
107#537#59511yescharacteristic
108C2×C4⋊C8—341no—
109C2×#104—341no—
110#417—341no—
111#384—171no—
112#343—171no—
113#324—341no—
114C2×C17—21no—
115C2×C17—21no—
116C2×C17—161no—
117C2×C17#134511yescharacteristic
118C2×C17#140211yescharacteristic
119C2×C17#140511yescharacteristic
120C2×#41—21no—
121C2×M16—341no—
122C22×C8—681no—
123C22⋊Q8—41no—
124#121—41no—
125#121—41no—
126C2×C4⋊C4—171no—
127C2×C4⋊C4—681no—
128C2×C4⋊C4C2×#59511yescharacteristic
129C2×C42—171no—
130C4⋊C8—342no—
131C4⋊C8—681no—
132#104—681no—
133#104—681no—
134#103—681no—
135#102—681no—
136C22⋊C8—681no—
137C17#741711yescharacteristic, complemented, Sylow
138#41—41no—
139#41—41no—
140#41—41no—
141#41—41no—
142C2×Q8—21no—
143C2×D4—21no—
144C2×D4—41no—
145C2×D4—41no—
146C22×C4—21no—
147C22×C4—41no—
148C22×C4—341no—
149C22×C4—341no—
150C22×C4C22⋊#59511yescharacteristic
151M16—681no—
152M16—681no—
153C2×C8—681no—
154C2×C8—682no—
155C2×C8—1361no—
156C2×C8—1361no—
157C2×C8—1361no—
158C4⋊C4—41no—
159C4⋊C4—41no—
160C4⋊C4—681no—
161C4⋊C4—1361no—
162C4⋊C4—1361no—
163C22⋊C4—42no—
164C42—171no—
165C42—171no—
166C42—341no—
167C23—41no—
168C23#1058755111yescharacteristic
169Q8—41no—
170Q8—41no—
171D4—41no—
172D4—41no—
173D4—81no—
174D4—81no—
175D4—161no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4—81no—
183C2×C4—341no—
184C2×C4—341no—
185C2×C4—341no—
186C2×C4—341no—
187C2×C4—341no—
188C2×C4—341no—
189C2×C4—681no—
190C2×C4—1361no—
191C2×C4#1058754711yescharacteristic
192C2×C4#1058754811yescharacteristic
193C8—2721no—
194C8—1361no—
195C8—1362no—
196C22—21no—
197C22—21no—
198C22—81no—
199C22—81no—
200C22—81no—
201C22#1176366011yescharacteristic
202C22#1176370911yescharacteristic
203C22#1176371711yescharacteristic
204C4—21no—
205C4—21no—
206C4—81no—
207C4—81no—
208C4—341no—
209C4—341no—
210C4—341no—
211C4—341no—
212C4—1361no—
213C2—21no—
214C2—21no—
215C2—161no—
216C2#1454376611yescharacteristic
217C2#1454390311yescharacteristic
218C2#1454390911yescharacteristic
subgroupG/H
centerC22#11763709
commutatorC2×C4⋊C4×C17C2×C4
FrattiniC2×C4⋊C4C2×#595
Fitting, prime radicalC17×#537C4
socleC22×C17AΣL(1,𝔽16)
cosocle#11762678C22
hypercenter#537#595
hypocenterC17#7417
LCSG ▷ C2×C4⋊C4×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #14543727C2semidirect
2. #14543662C2semidirect
137. C17#7417semidirect

Maximal subgroups

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

subgroupindex
#145437272
#145436622
#145300052
#741717