Finite Group Databasebeta

← #17948754

Subgroups — #17948754

Order 4352.

276 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 52 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#14544685C211yesmaximal, characteristic
2#14544037C211yesmaximal, characteristic
3#14528551C211yesmaximal, characteristic
4#11763829—21no—
5#11763781—21no—
6#11763689—21no—
7#11763689C412yes—
8#11763655—21no—
9#11763653C412yes—
10C2×#10587558C2211yescharacteristic
11C2×#10587491—21no—
12C2×#10587474C411yescharacteristic
13#11762563—21no—
14C2×C4×C8×C17C411yescharacteristic
15C22×C4×D17D411yescharacteristic
16C2×#63247—22no—
17C22×C8×C17—21no—
18C2×C42×C17C2×C411yescharacteristic
19C2×#63227C2×C411yescharacteristic
20C2×#63227Q811yescharacteristic
21C2×#63225C2×C411yescharacteristic
22C2×#63225D411yescharacteristic
23C2×C4×Dic17D411yescharacteristic
24C22×#3622—21no—
25#10587558—41no—
26#10587558—41no—
27C22⋊#3624—22no—
28#10587544—41no—
29#10587543—41no—
30#10587543—41no—
31#10587542—41no—
32C4×C8×C17—41no—
33#10587491—24no—
34#10587474—41no—
35C23×D17C4⋊C411yescharacteristic
36C22×C4×C17C4211yescharacteristic
37C22×C4×C17C22⋊C411yescharacteristic
38C22×C4×C17C4⋊C411yescharacteristic
39C22×Dic17C22⋊C411yescharacteristic
40C22×Dic17C22⋊C411yescharacteristic
41C22×Dic17C4⋊C411yescharacteristic
42C2×C4×D17—21no—
43C2×C4×D17—21no—
44C2×C4×D17—22no—
45C2×C4×D17—41no—
46#63247—42no—
47#63247—42no—
48C2×#3624—42no—
49C2×#3624—42no—
50C2×C8×C17—22no—
51C2×C8×C17—41no—
52C2×C8×C17—41no—
53C42×C17—21no—
54C42×C17—21no—
55#63227—41no—
56#63227—41no—
57#63225—41no—
58#63225—41no—
59C4×Dic17—21no—
60C4×Dic17—21no—
61C2×#3622—22no—
62C2×#3622—41no—
63C2×#3622—41no—
64#7216—171nomaximal, Sylow
65C23×C17#9511yescharacteristic
66C22×D17—21no—
67C22×D17—21no—
68C22×D17—21no—
69C22×D17—41no—
70C22×D17—41no—
71C2×C4×C17—21no—
72C2×C4×C17—21no—
73C2×C4×C17—21no—
74C2×C4×C17—21no—
75C2×C4×C17—41no—
76C2×C4×C17—41no—
77C2×C4×C17#9911yescharacteristic
78C2×C4×C17#9911yescharacteristic
79C2×Dic17—21no—
80C2×Dic17—21no—
81C2×Dic17—21no—
82C2×Dic17—21no—
83C2×Dic17—41no—
84C2×Dic17—41no—
85C2×Dic17#10412yes—
86C4×D17—42no—
87C4×D17—42no—
88#3624—82no—
89#3624—82no—
90C8×C17—42no—
91#3622—42no—
92#1822—171no—
93#1750—171no—
94#1464—171no—
95C22×C17—21no—
96C22×C17—21no—
97C22×C17H(3,ℤ/4)11yescharacteristic
98C22×C17#33911yescharacteristic
99C22×C17#34211yescharacteristic
100C2×D17—42no—
101C2×D17—41no—
102C2×D17—41no—
103C2×D17—41no—
104C2×D17—81no—
105C4×C17—21no—
106C4×C17—21no—
107C4×C17—41no—
108C4×C17—41no—
109Dic17—22no—
110Dic17—41no—
111Dic17—41no—
112C2×#117—171no—
113#432—341no—
114#407—341no—
115C2×C22⋊C8—341no—
116C2×#97—171no—
117C2×C4×C8#59511yescharacteristic
118#343—172no—
119#343—341no—
120#336—341no—
121#324—341no—
122#323—172no—
123C2×C17—21no—
124C2×C17—21no—
125C2×C17#128411yescharacteristic
126C2×C17#139211yescharacteristic
127C2×C17#139511yescharacteristic
128D17—81no—
129C23×C4—171no—
130C2×M16—342no—
131C22×C8—21no—
132C22×C8—341no—
133#117—681no—
134#117—681no—
135C2×C4⋊C4—171no—
136C2×C4⋊C4—171no—
137C2×C22⋊C4—171no—
138C2×C22⋊C4—171no—
139C2×C42—171no—
140C2×C42C2×#59511yescharacteristic
141C4⋊C8—681no—
142C22⋊C8—344no—
143C22⋊C8—342no—
144C22⋊C8—681no—
145C22⋊C8—681no—
146#97—681no—
147#97—681no—
148C4×C8—41no—
149C17#721611yescharacteristic, complemented, Sylow
150C24—171no—
151C22×C4—171no—
152C22×C4—171no—
153C22×C4—171no—
154C22×C4—342no—
155C22×C4—341no—
156C22×C4—341no—
157C22×C4—681no—
158C22×C4C4×#59511yescharacteristic
159C22×C4C4⋊#59511yescharacteristic
160C22×C4C22⋊#59511yescharacteristic
161M16—682no—
162M16—682no—
163C2×C8—22no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—342no—
167C2×C8—681no—
168C2×C8—681no—
169C2×C8—682no—
170C2×C8—682no—
171C4⋊C4—681no—
172C4⋊C4—681no—
173C22⋊C4—681no—
174C22⋊C4—681no—
175C42—21no—
176C42—21no—
177C42—341no—
178C42—341no—
179C23—341no—
180C23—341no—
181C23—341no—
182C23—681no—
183C23—681no—
184C23(C2×#595)⋊C411yescharacteristic
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—172no—
192C2×C4—341no—
193C2×C4—341no—
194C2×C4—341no—
195C2×C4—341no—
196C2×C4—682no—
197C2×C4—682no—
198C2×C4—681no—
199C2×C4—681no—
200C2×C4#1058753911yescharacteristic
201C2×C4#1058755111yescharacteristic
202C8—42no—
203C8—682no—
204C8—1362no—
205C8—1362no—
206C22—21no—
207C22—21no—
208C22—682no—
209C22—681no—
210C22—681no—
211C22—681no—
212C22—1361no—
213C22#1176367611yescharacteristic
214C22#1176368011yescharacteristic
215C22#1176368711yescharacteristic
216C4—21no—
217C4—21no—
218C4—41no—
219C4—41no—
220C4—342no—
221C4—681no—
222C4—681no—
223C2—21no—
224C2—21no—
225C2—1361no—
226C2#1454363211yescharacteristic
227C2#1454387511yescharacteristic
228C2#1454388411yescharacteristic
subgroupG/H
centerC22#11763687
commutatorC22×C4×C17C42
FrattiniC2×C42C2×#595
FittingC2×C4×C8×C17C4
socleC22×C17#342
prime radicalC23×D17C4⋊C4
cosocleC2×#10587558C22
hypercenterC2×C4×C8#595
hypocenterC17#7216
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
149. C17#7216semidirect

Maximal subgroups

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

subgroupindex
#145446852
#145440372
#145285512
#721617