Finite Group Databasebeta

← #16938452

Subgroups — #16938452

Order 4352.

402 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 99 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#14529761C212yesmaximal
3#14527472C212yesmaximal
4#14526659C211yesmaximal, characteristic
5C17×#1842C211yesmaximal, characteristic
6#11763366C2212yes—
7#11763105—22no—
8#11763050—22no—
9#11763020—22no—
10#11762833C2212yes—
11#11762569—22no—
12#11762569—22no—
13#11762557—22no—
14#11762556—22no—
15C2×C17×C4⋊C8—22no—
16C2×C17×C4⋊C8C2211yescharacteristic
17C2×C17×C4⋊C8C2211yescharacteristic
18C43×C17C2211yescharacteristic
19C22×C8×C17—21no—
20C22×C8×C17D412yes—
21C2×C42×C17—21no—
22C2×C42×C17—21no—
23C2×C42×C17D411yescharacteristic
24C2×C42×C17D411yescharacteristic
25C2×C42×C17C2311yescharacteristic
26#10587612—22no—
27#10587610—22no—
28#10587610—22no—
29C2×#63223—22no—
30C2×Dic68—22no—
31#10587556—22no—
32#10587555D412yes—
33#10587555D412yes—
34C4×Dic34—22no—
35C4×Dic34—22no—
36C17×C4⋊C8—22no—
37C17×C4⋊C8—22no—
38C17×C4⋊C8—44no—
39#10587489—22no—
40#10587487—24no—
41C4⋊#3622—22no—
42C4⋊#3622—22no—
43C22×C4×C17—21no—
44C22×C4×C17—21no—
45C22×C4×C17C2×D411yescharacteristic
46C22×C4×C17C2×D411yescharacteristic
47C22×C4×C17#4111yescharacteristic
48C2×Dic34—22no—
49C2×Dic34—22no—
50C2×C8×C17—22no—
51C2×C8×C17—42no—
52C2×C8×C17—42no—
53C2×C8×C17—41no—
54C42×C17—22no—
55C42×C17—22no—
56C42×C17—21no—
57C42×C17—22no—
58C42×C17—42no—
59C42×C17Q1612yescomplemented
60C42×C17C2×D412yes—
61C42×C17#4112yes—
62C22⋊Dic17—42no—
63C4⋊Dic17—22no—
64C4⋊Dic17—22no—
65C4⋊Dic17—22no—
66C4⋊Dic17—22no—
67#63225—42no—
68#63225—42no—
69C4×Dic17—42no—
70#63223—42no—
71#63223—42no—
72C2×#3622—42no—
73Dic68—82no—
74#10522—171nomaximal, Sylow
75C23×C17#12111yescharacteristic
76C2×C4×C17—22no—
77C2×C4×C17—22no—
78C2×C4×C17—22no—
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—22no—
82C2×C4×C17—41no—
83C2×C4×C17—41no—
84C2×C4×C17—41no—
85C2×C4×C17#12011yescharacteristic
86C2×C4×C17#12112yes—
87C2×C4×C17#12312yes—
88C2×C4×C17#12411yescharacteristic
89C2×C4×C17C2×Q1611yescharacteristic
90C2×C4×C17#13511yescharacteristic
91C2×C4×C17#13712yes—
92C2×Dic17—42no—
93C2×Dic17—42no—
94Dic34—42no—
95Dic34—42no—
96Dic34—82no—
97C8×C17—42no—
98C8×C17—81no—
99#3622—82no—
100#3249—171no—
101#1994—172no—
102#1842D1711yescharacteristic
103#1550—172no—
104#1292—171no—
105C22×C17—21no—
106C22×C17—21no—
107C22×C17#39411yescharacteristic
108C22×C17#46711yescharacteristic
109C22×C17#47011yescharacteristic
110C4×C17—24no—
111C4×C17—22no—
112C4×C17—21no—
113C4×C17—42no—
114C4×C17#45311yescharacteristic
115C4×C17#45611yescharacteristic
116C4×C17#46212yes—
117C4×C17#46412yes—
118Dic17—82no—
119Dic17—82no—
120#533—172no—
121#477—342no—
122#467—342no—
123#462—342no—
124#423—172no—
125C2×C4⋊C8—22no—
126C2×C4⋊C8C2×D1711yescharacteristic
127C2×C4⋊C8C2×D1711yescharacteristic
128C43C2×D1711yescharacteristic
129#339—342no—
130#339—342no—
131#333—342no—
132#332—342no—
133C2×C17—21no—
134C2×C17—21no—
135C2×C17#203911yescharacteristic
136C2×C17#205011yescharacteristic
137C2×C17#205611yescharacteristic
138C2×Q16—342no—
139C2×M16—342no—
140C22×C8—21no—
141C22×C8C22⋊D1712yes—
142C4⋊Q8—172no—
143C4⋊Q8—172no—
144#125—342no—
145C22⋊Q8—342no—
146C22⋊Q8—342no—
147C4×Q8—342no—
148C4×Q8—342no—
149#117—342no—
150C2×C42—21no—
151C2×C42—21no—
152C2×C42D6811yescharacteristic
153C2×C42D6811yescharacteristic
154C2×C42C22×D1711yescharacteristic
155#107—342no—
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8—44no—
159C4⋊C8—342no—
160C4⋊C8—342no—
161#103—344no—
162C17#1052211yescharacteristic, complemented, Sylow
163C2×Q8—342no—
164C2×Q8—342no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4C2×D6811yescharacteristic
168C22×C4#6325211yescharacteristic
169C22×C4C2×C22⋊D1711yescharacteristic
170Q16—1362no—
171M16—682no—
172M16—682no—
173C2×C8—22no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—41no—
177C2×C8—682no—
178C4⋊C4—342no—
179C4⋊C4—342no—
180C4⋊C4—342no—
181C4⋊C4—342no—
182C4⋊C4—682no—
183C4⋊C4—682no—
184C22⋊C4—682no—
185C42—22no—
186C42—22no—
187C42—21no—
188C42—22no—
189C42—42no—
190C42—682no—
191C42Dic6812yescomplemented
192C42D4×D1712yes—
193C42#6325612yes—
194C23#1058761611yescharacteristic
195Q8—682no—
196Q8—682no—
197Q8—1362no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—682no—
208C2×C4—682no—
209C2×C4#1058758012yes—
210C2×C4#1058758112yes—
211C2×C4#1058759011yescharacteristic
212C2×C4C2×Dic6811yescharacteristic
213C2×C4#1058759512yes—
214C2×C4#1058762311yescharacteristic
215C2×C4#1058763311yescharacteristic
216C8—42no—
217C8—81no—
218C8—1362no—
219C22—21no—
220C22—21no—
221C22#1176272611yescharacteristic
222C22#1176305011yescharacteristic
223C22#1176306711yescharacteristic
224C4—24no—
225C4—22no—
226C4—21no—
227C4—42no—
228C4—1362no—
229C4—1362no—
230C4#1176297611yescharacteristic
231C4#1176299111yescharacteristic
232C4#1176302012yes—
233C4#1176303212yes—
234C2—21no—
235C2—21no—
236C2#1453000811yescharacteristic
237C2#1453007111yescharacteristic
238C2#1453010711yescharacteristic
subgroupG/H
centerC22#11762726
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1842C2
socleC22×C17#394
prime radicalC23×C17#121
hypercenter#1842D17
hypocenterC17#10522
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1842

Complements

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

NH ≅ G/Ntype
59. C42×C17Q16semidirect
162. C17#10522semidirect
191. C42Dic68semidirect

Maximal subgroups

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

subgroupindex
#145401292
#145297612
#145274722
#145266592
C17×#18422
#1052217