Finite Group Databasebeta

← #17958653

Subgroups — #17958653

Order 4352.

358 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 74 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#14544046C211yesmaximal, characteristic
2#14544026C211yesmaximal, characteristic
3#14543724C214yesmaximal
4#14533999C211yesmaximal, characteristic
5#11763830—21no—
6#11763826—21no—
7#11763655—21no—
8#11763655—21no—
9#11763654C2212yes—
10#11763654C2212yes—
11C2×#10587555C411yescharacteristic
12C2×C4×Dic34C2211yescharacteristic
13#11762749—21no—
14#11762749—21no—
15#11762715C412yes—
16#11762714—21no—
17#11762714—21no—
18#11762675C2212yes—
19C4×C4⋊C4×C17C411yescharacteristic
20C22×Dic34—21no—
21C22×Dic34C2×C411yescharacteristic
22C2×C4⋊C4×C17—21no—
23C2×C42×C17C2×C412yes—
24C2×C42×C17C2×C411yescharacteristic
25C2×C4⋊Dic17—21no—
26C2×C4⋊Dic17C2×C412yes—
27C2×C4⋊Dic17C2311yescharacteristic
28C2×#63225D411yescharacteristic
29C2×#63225D411yescharacteristic
30C2×C4×Dic17D411yescharacteristic
31C2×C4×Dic17D411yescharacteristic
32#10587555—41no—
33#10587555—41no—
34C4×Dic34—41no—
35C4×Dic34—41no—
36C22⋊#3624—22no—
37C22⋊#3624—22no—
38#10587544—41no—
39#10587542—41no—
40C4⋊#3624—41no—
41C4×#3624—41no—
42C17×#95—21no—
43#10587502—22no—
44#10587502—22no—
45#10587502—22no—
46#10587502—22no—
47C22×C4×C17—22no—
48C22×C4×C17C22⋊C411yescharacteristic
49C22×C4×C17C22⋊C411yescharacteristic
50C22×C4×C17C22×C411yescharacteristic
51C22×Dic17—22no—
52C22×Dic17C22⋊C411yescharacteristic
53C22×Dic17C22⋊C411yescharacteristic
54C22×Dic17C2×D411yescharacteristic
55C22×Dic17C2×D411yescharacteristic
56C2×Dic34—22no—
57C2×Dic34—22no—
58C2×Dic34—41no—
59C2×Dic34—44no—
60C2×Dic34—41no—
61C2×Dic34—41no—
62C2×#3624—42no—
63C2×#3624—42no—
64C4⋊C4×C17—42no—
65C42×C17—21no—
66C42×C17—21no—
67C42×C17—24no—
68C4⋊Dic17—41no—
69C4⋊Dic17—42no—
70C4⋊Dic17—42no—
71#63225—41no—
72#63225—41no—
73C4×Dic17—21no—
74C4×Dic17—21no—
75C4×Dic17—21no—
76C4×Dic17—21no—
77#11573—171nomaximal, Sylow
78C23×C17C2×C22⋊C411yescharacteristic
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—22no—
82C2×C4×C17—21no—
83C2×C4×C17—41no—
84C2×C4×C17—42no—
85C2×C4×C17—42no—
86C2×C4×C17—42no—
87C2×C4×C17#9911yescharacteristic
88C2×C4×C17#9911yescharacteristic
89C2×C4×C17#13112yes—
90C2×Dic17—21no—
91C2×Dic17—21no—
92C2×Dic17—21no—
93C2×Dic17—21no—
94C2×Dic17—21no—
95C2×Dic17—21no—
96C2×Dic17—21no—
97C2×Dic17—41no—
98C2×Dic17—41no—
99C2×Dic17—44no—
100C2×Dic17—42no—
101C2×Dic17#10112yes—
102Dic34—44no—
103Dic34—82no—
104Dic34—82no—
105#3624—82no—
106#3624—82no—
107#2568—171no—
108#1467—171no—
109#1461—171no—
110#1324—174no—
111C22×C17—21no—
112C22×C17—21no—
113C22×C17#40811yescharacteristic
114C22×C17C2×#9911yescharacteristic
115C22×C17C2×#10111yescharacteristic
116C4×C17—21no—
117C4×C17—22no—
118C4×C17—41no—
119C4×C17—82no—
120C4×C17#35512yes—
121Dic17—22no—
122Dic17—41no—
123Dic17—41no—
124Dic17—41no—
125Dic17—82no—
126C2×C4⋊Q8—171no—
127C2×C4×Q8—171no—
128#432—341no—
129#431—341no—
130#400—341no—
131#400—341no—
132#391—172no—
133#391—341no—
134#391—341no—
135#382—172no—
136C4×C4⋊C4#59511yescharacteristic
137#324—172no—
138#324—172no—
139#324—341no—
140#324—341no—
141C2×C17—21no—
142C2×C17—21no—
143C2×C17#147211yescharacteristic
144C2×C17#212911yescharacteristic
145C2×C17C2×#35511yescharacteristic
146C22×Q8—171no—
147C22×Q8—341no—
148C4⋊Q8—681no—
149C4⋊Q8—681no—
150C4×Q8—681no—
151C4×Q8—681no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—171no—
154C2×C4⋊C4—171no—
155C2×C4⋊C4—171no—
156C2×C4⋊C4—172no—
157C2×C4⋊C4—341no—
158C2×C42—171no—
159C2×C42—171no—
160C2×C42C2×#59512yes—
161C2×C42C2×#59511yescharacteristic
162C4⋊C8—681no—
163C4⋊C8—681no—
164C22⋊C8—342no—
165C22⋊C8—342no—
166#97—681no—
167C4×C8—681no—
168#95—21no—
169#95—342no—
170#95—342no—
171#95—342no—
172#95—342no—
173C17#1157311yescharacteristic, complemented, Sylow
174C2×Q8—342no—
175C2×Q8—342no—
176C2×Q8—681no—
177C2×Q8—684no—
178C2×Q8—681no—
179C2×Q8—681no—
180C22×C4—22no—
181C22×C4—171no—
182C22×C4—171no—
183C22×C4—171no—
184C22×C4—171no—
185C22×C4—342no—
186C22×C4C22⋊#59511yescharacteristic
187C22×C4C22⋊#59511yescharacteristic
188C22×C4C22×#59511yescharacteristic
189C2×C8—682no—
190C2×C8—682no—
191C4⋊C4—42no—
192C4⋊C4—681no—
193C4⋊C4—681no—
194C4⋊C4—681no—
195C4⋊C4—682no—
196C4⋊C4—682no—
197C42—21no—
198C42—21no—
199C42—24no—
200C42—341no—
201C42—341no—
202C42—341no—
203C42—341no—
204C23C2×C22⋊#59511yescharacteristic
205Q8—684no—
206Q8—1362no—
207Q8—1362no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—172no—
217C2×C4—341no—
218C2×C4—341no—
219C2×C4—341no—
220C2×C4—341no—
221C2×C4—341no—
222C2×C4—341no—
223C2×C4—341no—
224C2×C4—681no—
225C2×C4—681no—
226C2×C4—684no—
227C2×C4—682no—
228C2×C4#1058753911yescharacteristic
229C2×C4#1058753911yescharacteristic
230C2×C4#1058767812yes—
231C8—1362no—
232C8—1362no—
233C22—21no—
234C22—21no—
235C22#1176378311yescharacteristic
236C22C2×#1058753911yescharacteristic
237C22D17⋊#10111yescharacteristic
238C4—21no—
239C4—22no—
240C4—41no—
241C4—82no—
242C4—342no—
243C4—681no—
244C4—681no—
245C4—681no—
246C4—1362no—
247C4#1176371812yes—
248C2—21no—
249C2—21no—
250C2#1454406211yescharacteristic
251C2#1454506811yescharacteristic
252C2C2×#1176371811yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenterC4×C4⋊C4#595
hypocenterC17#11573
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
173. C17#11573semidirect

Maximal subgroups

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

subgroupindex
#145440462
#145440262
#145437242
#145339992
#1157317