Finite Group Databasebeta

← #16947611

Subgroups — #16947611

Order 4352.

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

normal subgroups only

This group has 310 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#14540129C211yesmaximal, characteristic
2#14530987C212yesmaximal
3#14530277C211yesmaximal, characteristic
4#14526797C212yesmaximal
5C17×#1322C211yesmaximal, characteristic
6#11763366—21no—
7#11763105—22no—
8#11763050—21no—
9#11763050C2212yes—
10#11763020—22no—
11C2×#10587489C2211yescharacteristic
12#11762707—21no—
13#11762635—22no—
14#11762614—22no—
15#11762572—21no—
16#11762572C2211yescharacteristic
17C2×C17×C4⋊C8C2211yescharacteristic
18C17×C22⋊C16C2212yes—
19C22×C8×C17D411yescharacteristic
20C22×C8×C17C2311yescharacteristic
21C2×C42×C17D411yescharacteristic
22#10587612—41no—
23C2×C4⋊Dic17—21no—
24C2×C4⋊Dic17—21no—
25#10587610—22no—
26#10587610—41no—
27C2×#63225—41no—
28C2×Dic68—21no—
29C2×Dic68D412yes—
30#10587556—41no—
31#10587555—21no—
32#10587555—21no—
33C4×Dic34—22no—
34C4×Dic34—41no—
35C2×C16×C17—22no—
36C17×C4⋊C8—22no—
37#10587502—41no—
38#10587489—21no—
39#10587489—22no—
40#10587489D412yes—
41#10587487—22no—
42#10587487—22no—
43C22×C4×C17D811yescharacteristic
44C22×C4×C17D811yescharacteristic
45C22×C4×C17C2×D411yescharacteristic
46C22×Dic17—41no—
47C22×Dic17—41no—
48C2×Dic34—22no—
49C2×Dic34—41no—
50C2×C8×C17—21no—
51C2×C8×C17—41no—
52C2×C8×C17—41no—
53C2×C8×C17C2×D412yes—
54C42×C17—21no—
55C42×C17—21no—
56C22⋊Dic17—42no—
57C4⋊Dic17—22no—
58C4⋊Dic17—22no—
59C4⋊Dic17—41no—
60C4⋊Dic17—41no—
61C4⋊Dic17—41no—
62C4⋊Dic17—41no—
63C4⋊Dic17—41no—
64C4⋊Dic17—41no—
65#63225—42no—
66#63225—42no—
67#63225—82no—
68C4×Dic17—42no—
69Dic68—42no—
70Dic68—81no—
71C16×C17—42no—
72#12292—171nomaximal, Sylow
73C23×C17C2×D811yescharacteristic
74C2×C4×C17—21no—
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17—41no—
80C2×C4×C17Q3212yes—
81C2×C4×C17#12011yescharacteristic
82C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
83C2×Dic17—42no—
84C2×Dic17—42no—
85C2×Dic17—42no—
86C2×Dic17—81no—
87C2×Dic17—81no—
88C2×Dic17—81no—
89C2×Dic17—81no—
90C2×Dic17—81no—
91Dic34—42no—
92Dic34—42no—
93Dic34—82no—
94C8×C17—22no—
95C8×C17—41no—
96#3249—171no—
97#2236—172no—
98#2087—171no—
99#1348—172no—
100#1322D1711yescharacteristic
101C22×C17—21no—
102C22×C17—21no—
103C22×C17#44711yescharacteristic
104C22×C17C2×Q3211yescharacteristic
105C22×C17#51011yescharacteristic
106C4×C17—21no—
107C4×C17—22no—
108C4×C17—41no—
109C4×C17#45611yescharacteristic
110C4×C17#45811yescharacteristic
111Dic17—82no—
112Dic17—82no—
113Dic17—82no—
114Dic17—161no—
115#533—341no—
116#477—342no—
117#467—172no—
118#467—341no—
119#462—342no—
120C2×#107—171no—
121C2×C4⋊C8C2×D1711yescharacteristic
122#389—341no—
123#366—342no—
124#358—342no—
125C22⋊C16C2×D1712yes—
126#340—171no—
127#340—341no—
128C2×C17—21no—
129C2×C17—21no—
130C2×C17#161011yescharacteristic
131C2×C17#218811yescharacteristic
132C2×C17#219011yescharacteristic
133C2×Q16—172no—
134C2×Q16—341no—
135C22×C8D6811yescharacteristic
136C22×C8C22×D1711yescharacteristic
137C4⋊Q8—341no—
138C4⋊Q8—341no—
139#125—681no—
140C22⋊Q8—342no—
141C22⋊Q8—681no—
142C4×Q8—342no—
143C4×Q8—681no—
144#117—681no—
145C2×C4⋊C4—341no—
146C2×C4⋊C4—341no—
147C2×C4⋊C4—681no—
148C2×C42D6811yescharacteristic
149C2×C16—22no—
150#107—172no—
151#107—341no—
152#107—342no—
153C4⋊C8—22no—
154#103—342no—
155#103—342no—
156#95—681no—
157C17#1229211yescharacteristic, complemented, Sylow
158C2×Q8—342no—
159C2×Q8—681no—
160C22×C4—681no—
161C22×C4—681no—
162C22×C4D13611yescharacteristic
163C22×C4D13611yescharacteristic
164C22×C4C2×D6811yescharacteristic
165Q16—682no—
166Q16—1361no—
167C2×C8—21no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8D4×D1712yes—
171C4⋊C4—342no—
172C4⋊C4—342no—
173C4⋊C4—681no—
174C4⋊C4—681no—
175C4⋊C4—681no—
176C4⋊C4—682no—
177C4⋊C4—681no—
178C4⋊C4—682no—
179C4⋊C4—681no—
180C4⋊C4—681no—
181C4⋊C4—1362no—
182C22⋊C4—682no—
183C42—21no—
184C42—21no—
185C42—682no—
186C16—42no—
187C23C2×D13611yescharacteristic
188Q8—682no—
189Q8—682no—
190Q8—1362no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—682no—
198C2×C4—682no—
199C2×C4—682no—
200C2×C4—1361no—
201C2×C4—1361no—
202C2×C4—1361no—
203C2×C4—1361no—
204C2×C4—1361no—
205C2×C4Dic13612yes—
206C2×C4#1058756811yescharacteristic
207C2×C4#1058759411yescharacteristic
208C8—22no—
209C8—41no—
210C22—21no—
211C22—21no—
212C22#1176294511yescharacteristic
213C22C2×Dic13611yescharacteristic
214C22#1176325211yescharacteristic
215C4—21no—
216C4—22no—
217C4—41no—
218C4—2721no—
219C4—1362no—
220C4—1362no—
221C4—1362no—
222C4#1176299411yescharacteristic
223C4#1176300011yescharacteristic
224C2—21no—
225C2—21no—
226C2#1452778911yescharacteristic
227C2#1453072011yescharacteristic
228C2#1453073211yescharacteristic
subgroupG/H
centerC22#11762945
commutator, cosocleC22×C8×C17C23
FrattiniC22×C8C22×D17
FittingC17×#1322C2
socleC22×C17#447
prime radicalC23×C17C2×D8
hypercenter#1322D17
hypocenterC17#12292
LCSG ▷ C22×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
157. C17#12292semidirect

Maximal subgroups

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

subgroupindex
#145401292
#145309872
#145302772
#145267972
C17×#13222
#1229217