Finite Group Databasebeta

← #16938459

Subgroups — #16938459

Order 4352.

386 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 77 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#14528958C211yesmaximal, characteristic, complemented
2#14527506C212yesmaximal, complemented
3#14527395C212yesmaximal, complemented
4#14526695C211yesmaximal, characteristic, complemented
5C17×#3253C211yesmaximal, characteristic
6#11762866C2212yes—
7C2×#10587493—22no—
8#11762833C2211yescharacteristic
9C2×#10587474C2211yescharacteristic
10#11762555—22no—
11#11762553—22no—
12#11762549—24no—
13C17×#532C2212yes—
14C17×#476—22no—
15C17×#469—22no—
16C17×#459—22no—
17C17×#423C2211yescharacteristic
18C2×#41×C17—22no—
19C2×D8×C17—22no—
20C2×M16×C17D412yes—
21C17×C4⋊Q8D412yes—
22C17×#127D412yes—
23C17×#124—22no—
24C17×#121—22no—
25C17×#121—22no—
26C4×D4×C17—22no—
27C4×D4×C17—22no—
28C2×C42×C17C2311yescharacteristic
29C2×#63223—21no—
30C22×#3622—21no—
31C17×#106—22no—
32C17×C4⋊C8—22no—
33C17×#102—24no—
34C22⋊#3622—22no—
35#10587493—44no—
36C4⋊#3622—22no—
37C4⋊#3622—22no—
38#10587474—22no—
39#10587474—21no—
40#10587474D412yes—
41#41×C17—84no—
42C2×Q8×C17—22no—
43C2×D4×C17—22no—
44C2×D4×C17—22no—
45C2×D4×C17—22no—
46C2×D4×C17—42no—
47C22×C4×C17—42no—
48C22×C4×C17C2×D411yescharacteristic
49C22×C4×C17#4112yes—
50D8×C17—82no—
51M16×C17—42no—
52C2×C8×C17—22no—
53C4⋊C4×C17—22no—
54C4⋊C4×C17—22no—
55C22⋊C4×C17—42no—
56C22⋊C4×C17—42no—
57C42×C17C2×D411yescharacteristic
58C42×C17C2×D412yes—
59C42×C17#4111yescharacteristic
60#63223—42no—
61C2×#3622—22no—
62C2×#3622—22no—
63C2×#3622—22no—
64C2×#3622—41no—
65C2×#3622—42no—
66#10524—171nomaximal, Sylow
67C23×C17—42no—
68C23×C17#12411yescharacteristic
69Q8×C17—82no—
70D4×C17—42no—
71D4×C17—42no—
72D4×C17—82no—
73D4×C17—82no—
74D4×C17—84no—
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17—42no—
78C2×C4×C17—42no—
79C2×C4×C17—84no—
80C2×C4×C17#12011yescharacteristic
81C2×C4×C17#12111yescharacteristic
82C2×C4×C17#12112yes—
83C2×C4×C17#12312yes—
84C8×C17—42no—
85#3622—24no—
86#3622—82no—
87#3622—81no—
88#3253D1711yescharacteristic
89#1849—171no—
90#1557—172no—
91#1530—172no—
92#1307—171no—
93C22×C17—22no—
94C22×C17—21no—
95C22×C17—82no—
96C22×C17—82no—
97C22×C17—82no—
98C22×C17#39411yescharacteristic
99C4×C17—22no—
100C4×C17—22no—
101C4×C17—21no—
102C4×C17—82no—
103C4×C17#45311yescharacteristic
104C4×C17#45611yescharacteristic
105#532C2×D1712yes—
106#476—22no—
107#469—22no—
108#459—22no—
109#432—172no—
110C2×#108—342no—
111#423—171no—
112#423C2×D1711yescharacteristic
113C2×#97—171no—
114#332—342no—
115#331—342no—
116#329—344no—
117C2×C17—41no—
118C2×C17—162no—
119C2×C17#203911yescharacteristic
120C2×C17#204812yes—
121C2×#41—22no—
122C2×D8—22no—
123C2×M16—341no—
124C2×M16C22⋊D1712yes—
125C22×C8—341no—
126C4⋊Q8C22⋊D1712yes—
127#127C22⋊D1712yes—
128#124—22no—
129#121—22no—
130#121—22no—
131C4×D4—22no—
132C4×D4—22no—
133C2×C42C22×D1711yescharacteristic
134#108—684no—
135#106—22no—
136C4⋊C8—22no—
137C4⋊C8—342no—
138C4⋊C8—342no—
139#102—24no—
140C22⋊C8—342no—
141#97—172no—
142#97—342no—
143#97—341no—
144C17#1052411yescharacteristic, complemented, Sylow
145#41—84no—
146C2×Q8—22no—
147C2×D4—22no—
148C2×D4—22no—
149C2×D4—22no—
150C2×D4—42no—
151C22×C4—42no—
152C22×C4#6325412yes—
153C22×C4C2×C22⋊D1711yescharacteristic
154D8—82no—
155M16—42no—
156M16—682no—
157C2×C8—22no—
158C2×C8—342no—
159C2×C8—342no—
160C2×C8—342no—
161C2×C8—682no—
162C2×C8—681no—
163C4⋊C4—22no—
164C4⋊C4—22no—
165C22⋊C4—42no—
166C22⋊C4—42no—
167C42D4×D1711yescharacteristic
168C42#6325411yescharacteristic
169C42C2×C22⋊D1712yes—
170C23—42no—
171C23#1058762211yescharacteristic
172Q8—82no—
173D4—42no—
174D4—42no—
175D4—82no—
176D4—82no—
177D4—84no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—84no—
183C2×C4#1058762112yes—
184C2×C4#1058762411yescharacteristic
185C2×C4#1058762512yes—
186C2×C4#1058763911yescharacteristic
187C8—42no—
188C8—344no—
189C8—1362no—
190C8—1361no—
191C22—22no—
192C22—21no—
193C22—82no—
194C22—82no—
195C22—82no—
196C22#1176272311yescharacteristic
197C4—22no—
198C4—22no—
199C4—21no—
200C4—82no—
201C4#1176297711yescharacteristic
202C4#1176299211yescharacteristic
203C2—41no—
204C2—162no—
205C2#1453000511yescharacteristic
206C2#1453005412yes—
subgroupG/H
centerC22#11762723
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
Fitting, prime radicalC17×#3253C2
socleC22×C17#394
hypercenter#3253D17
hypocenterC17#10524
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. #14528958C2semidirect
2. #14527506C2semidirect
3. #14527395C2semidirect
4. #14526695C2semidirect
144. C17#10524semidirect

Maximal subgroups

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

subgroupindex
#145289582
#145275062
#145273952
#145266952
C17×#32532
#1052417