Finite Group Databasebeta

← #17949681

Subgroups — #17949681

Order 4352.

516 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C4×#10587544C212yesmaximal
2#14543605C212yesmaximal
3#14543604C212yesmaximal
4C4×#10587630C211yesmaximal, characteristic
5C2×#10587544—22no—
6C2×C4×#3624—22no—
7#11763675C2214yes—
8C2×#10587630C411yescharacteristic
9C2×C4×Dic34C411yescharacteristic
10#11762716C2211yescharacteristic
11#11762714C2211yescharacteristic
12#11762704—22no—
13#11762678C411yescharacteristic
14C4×#63225—22no—
15C42×Dic17C2211yescharacteristic
16C2×C4×Q8×C17C411yescharacteristic
17C22×Q8×C17C2×C411yescharacteristic
18C22×Dic34C2×C411yescharacteristic
19C22×#3624—24no—
20C4×Q8×C17—42no—
21C2×C4⋊C4×C17—21no—
22C2×C4⋊C4×C17C2×C411yescharacteristic
23C2×C42×C17—21no—
24C2×C42×C17C2×C411yescharacteristic
25#10587630—22no—
26#10587630C814yescomplemented
27C2×C4⋊Dic17C2×C411yescharacteristic
28C2×#63225—21no—
29C2×#63225—22no—
30C2×#63225—22no—
31C2×C4×Dic17—21no—
32C2×C4×Dic17C2×C411yescharacteristic
33C2×C4×Dic17D412yes—
34C2×C4×Dic17D412yes—
35C2×C4×Dic17C2311yescharacteristic
36C4×Dic34—42no—
37#10587544—28no—
38C4×#3624—44no—
39#10587502—22no—
40#10587502—22no—
41C2×Q8×C17—21no—
42C2×Q8×C17—41no—
43C2×Q8×C17—41no—
44C2×Q8×C17C2×C812yes—
45C22×C4×C17—21no—
46C22×C4×C17—21no—
47C22×C4×C17C22⋊C411yescharacteristic
48C22×C4×C17C22⋊C411yescharacteristic
49C22×C4×C17C22×C411yescharacteristic
50C22×Dic17—21no—
51C22×Dic17—21no—
52C22×Dic17C22⋊C412yes—
53C22×Dic17C2×D412yes—
54C2×Dic34—21no—
55C2×Dic34—41no—
56C2×Dic34—41no—
57C2×Dic34C2×C812yes—
58C2×#3624—28no—
59C2×#3624—44no—
60C2×#3624—44no—
61C4⋊C4×C17—41no—
62C4⋊C4×C17—42no—
63C42×C17—22no—
64C42×C17—42no—
65C4⋊Dic17—41no—
66#63225—28no—
67#63225—42no—
68#63225—44no—
69C4×Dic17—24no—
70C4×Dic17—41no—
71C4×Dic17—42no—
72C4×Dic17C2×C812yes—
73C4×Dic17M1612yes—
74C4×Dic17SD1614yes—
75C4×Dic17Q1614yes—
76#7571—171nomaximal, Sylow
77C23×C17C2×C22⋊C411yescharacteristic
78Q8×C17—42no—
79Q8×C17—42no—
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—22no—
83C2×C4×C17—21no—
84C2×C4×C17—22no—
85C2×C4×C17—41no—
86C2×C4×C17—41no—
87C2×C4×C17—41no—
88C2×C4×C17—42no—
89C2×C4×C17#10012yes—
90C2×C4×C17#10314yes—
91C2×C4×C17C22×C811yescharacteristic
92C2×C4×C17C2×M1611yescharacteristic
93C2×Dic17—22no—
94C2×Dic17—22no—
95C2×Dic17—22no—
96C2×Dic17—41no—
97C2×Dic17—41no—
98C2×Dic17—41no—
99C2×Dic17—42no—
100C2×Dic17C22⋊C814yes—
101C2×Dic17#10314yes—
102C2×Dic17#10414yes—
103C2×Dic17C2×SD1612yes—
104C2×Dic17C2×Q1612yes—
105Dic34—42no—
106Dic34—42no—
107#3624—48no—
108C4×C4⋊Q8—171no—
109C4×C4⋊C8—172no—
110#1272—172no—
111#1272—172no—
112C22×C17C2×C22⋊C811yescharacteristic
113C22×C17#41011yescharacteristic
114C22×C17C2×#10011yescharacteristic
115C22×C17C2×#10312yes—
116C22×C17C2×#10412yes—
117C4×C17—21no—
118C4×C17—21no—
119C4×C17—42no—
120C4×C17—41no—
121C4×C17—81no—
122C4×C17#33314yes—
123Dic17—22no—
124Dic17—22no—
125Dic17—42no—
126Dic17—81no—
127Dic17Q8⋊C818yes—
128C2×C4⋊Q8—171no—
129C2×C4×Q8—171no—
130C2×C4×Q8#59511yescharacteristic
131C2×C4⋊C8—342no—
132C2×C4×C8—342no—
133#391—171no—
134#391—171no—
135#389—342no—
136#384—171no—
137C4×C4⋊C4—342no—
138C43—171no—
139#336—174no—
140C2×C17#146011yescharacteristic
141C2×C17C2×Q8⋊C812yes—
142C2×C17#150312yes—
143C2×C17#152511yescharacteristic
144C2×C17C2×#33311yescharacteristic
145C22×Q8—171no—
146C22×Q8C2×#59511yescharacteristic
147C22×C8—344no—
148C4⋊Q8—174no—
149C4⋊Q8—342no—
150C4×Q8—42no—
151C4×Q8—682no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—171no—
154C2×C4⋊C4—342no—
155C2×C4⋊C4—342no—
156C2×C4⋊C4—341no—
157C2×C4⋊C4C2×#59511yescharacteristic
158C2×C42—21no—
159C2×C42—172no—
160C2×C42—171no—
161C2×C42—172no—
162C2×C42—171no—
163C2×C42—341no—
164C2×C42C2×#59511yescharacteristic
165C4⋊C8—348no—
166C4×C8—684no—
167#95—342no—
168#95—342no—
169C17#757111yescharacteristic, complemented, Sylow
170C2×Q8—21no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—172no—
174C2×Q8—341no—
175C2×Q8—681no—
176C2×Q8—681no—
177C2×Q8#6324212yes—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—172no—
181C22×C4—172no—
182C22×C4—341no—
183C22×C4—341no—
184C22×C4C22⋊#59511yescharacteristic
185C22×C4C22⋊#59511yescharacteristic
186C22×C4C22×#59511yescharacteristic
187C2×C8—348no—
188C2×C8—684no—
189C2×C8—684no—
190C4⋊C4—41no—
191C4⋊C4—42no—
192C4⋊C4—348no—
193C4⋊C4—681no—
194C4⋊C4—682no—
195C4⋊C4—684no—
196C42—22no—
197C42—42no—
198C42—172no—
199C42—172no—
200C42—174no—
201C42—174no—
202C42—344no—
203C42—681no—
204C42—682no—
205C23C2×C22⋊#59511yescharacteristic
206Q8—42no—
207Q8—42no—
208Q8—682no—
209Q8—682no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—174no—
220C2×C4—174no—
221C2×C4—174no—
222C2×C4—172no—
223C2×C4—172no—
224C2×C4—342no—
225C2×C4—342no—
226C2×C4—342no—
227C2×C4—681no—
228C2×C4—681no—
229C2×C4—681no—
230C2×C4—682no—
231C2×C4#1058754914yes—
232C2×C4#1058755312yes—
233C2×C4C2×#6324211yescharacteristic
234C2×C4D17⋊M1611yescharacteristic
235C8—688no—
236C22#1176377711yescharacteristic
237C22#1176378811yescharacteristic
238C22C2×#1058755311yescharacteristic
239C22C2×#1058754912yes—
240C22D17⋊#10412yes—
241C4—21no—
242C4—21no—
243C4—41no—
244C4—42no—
245C4—81no—
246C4—178no—
247C4—342no—
248C4—342no—
249C4—682no—
250C4—1361no—
251C4#1176366914yes—
252C2#1454402311yescharacteristic
253C2#1454407312yes—
254C2#1454416612yes—
255C2#1454423811yescharacteristic
256C2C2×#1176366911yescharacteristic
subgroupG/H
centerC22×C4C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC2×C4×Q8×C17C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4×Q8#595
hypocenterC17#7571
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
26. #10587630C8semidirect
169. C17#7571semidirect

Maximal subgroups

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

subgroupindex
C4×#105875442
#145436052
#145436042
C4×#105876302
#757117