Finite Group Databasebeta

← #16950609

Subgroups — #16950609

Order 4352.

334 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 79 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#14537431C211yesmaximal, characteristic
2#14528889C212yesmaximal
3#14526914C212yesmaximal
4#14526905C211yesmaximal, characteristic
5C17×#1392C211yesmaximal, characteristic
6#41×Dic17C2211yescharacteristic
7#11762867—22no—
8#11762863—22no—
9#11762837C411yescharacteristic, complemented
10#11762835C411yescharacteristic, complemented
11#11762783C2212yes—
12#11762776C2211yescharacteristic
13M16×Dic17C411yescharacteristic, complemented
14C2×#10587486C411yescharacteristic, complemented
15#11762570—22no—
16#11762566—22no—
17C17×#413C2212yes—
18C17×#408C2211yescharacteristic
19C2×#41×C17C2311yescharacteristic
20C2×M16×C17—22no—
21C2×M16×C17C2×C411yescharacteristic
22C22×C8×C17C2×C411yescharacteristic
23Q8×Dic17—21no—
24D4×Dic17—22no—
25D4×Dic17—21no—
26#10587612—22no—
27#10587612C2×C411yescharacteristic
28#10587612D412yes—
29C2×C4×Dic17C2×C411yescharacteristic
30C2×C4×Dic17D412yes—
31C2×#63223C2×C411yescharacteristic
32C22×#3622C2×C411yescharacteristic
33C17×#101—22no—
34C17×#100—22no—
35C17×C22⋊C8—22no—
36#10587505—22no—
37#10587505—22no—
38C22⋊#3622—22no—
39#10587486—21no—
40#10587486—21no—
41#10587486—21no—
42#10587485—22no—
43#10587485—22no—
44C8×Dic17—21no—
45#41×C17—41no—
46#41×C17—41no—
47C2×Q8×C17#4111yescharacteristic
48C2×D4×C17#4112yes—
49C2×D4×C17#4111yescharacteristic
50C22×C4×C17C22×C411yescharacteristic
51C22×C4×C17C2×D412yes—
52C22×Dic17—21no—
53C22×Dic17—22no—
54M16×C17—41no—
55M16×C17—42no—
56M16×C17—42no—
57C2×C8×C17—21no—
58C2×C8×C17—21no—
59C2×C8×C17—41no—
60C2×C8×C17—42no—
61C22⋊Dic17—21no—
62C22⋊Dic17—22no—
63C22⋊Dic17—42no—
64C4⋊Dic17—21no—
65C4⋊Dic17—22no—
66C4⋊Dic17—42no—
67C4×Dic17—21no—
68C4×Dic17—22no—
69C4×Dic17—42no—
70C4×Dic17C22⋊C411yescharacteristic
71C4×Dic17C22⋊C412yes—
72C4×Dic17C22⋊C411yescharacteristic
73#63223—41no—
74C2×#3622—21no—
75C2×#3622—21no—
76C2×#3622—41no—
77#12865—171nomaximal, Sylow
78C23×C17#11711yescharacteristic
79C23×C17#12312yes—
80Q8×C17—41no—
81D4×C17—42no—
82D4×C17—41no—
83C2×C4×C17—21no—
84C2×C4×C17—22no—
85C2×C4×C17—21no—
86C2×C4×C17—22no—
87C2×C4×C17C2×C22⋊C411yescharacteristic
88C2×C4×C17#11711yescharacteristic
89C2×C4×C17#12312yes—
90C2×Dic17—22no—
91C2×Dic17—21no—
92C2×Dic17—21no—
93C2×Dic17—81no—
94C2×Dic17—82no—
95C2×Dic17—82no—
96C8×C17—41no—
97C8×C17—41no—
98C8×C17—82no—
99#3622—41no—
100#3622—41no—
101#2923—171no—
102#1827—172no—
103#1395—172no—
104#1392D1711yescharacteristic
105#1391—171no—
106C22×C17—22no—
107C22×C17—21no—
108C22×C17—41no—
109C22×C17—42no—
110C22×C17#38111yescharacteristic
111C4×C17—22no—
112C4×C17—21no—
113C4×C17#41011yescharacteristic
114C4×C17#41011yescharacteristic
115Dic17—42no—
116Dic17—41no—
117Dic17—41no—
118Dic17—162no—
119C4×#41—171no—
120#433—342no—
121#432—342no—
122#424—171no—
123#424—171no—
124#413C2×D1712yes—
125#410—172no—
126#408—171no—
127#408C2×D1711yescharacteristic
128C4×M16—171no—
129C2×#97—171no—
130#339—342no—
131H(3,ℤ/4)—342no—
132C2×C17—21no—
133C2×C17—42no—
134C2×C17—41no—
135C2×C17#182011yescharacteristic
136C2×#41C22×D1711yescharacteristic
137C2×M16—22no—
138C2×M16—171no—
139C2×M16C4×D1711yescharacteristic
140C22×C8—171no—
141C22×C8C4×D1711yescharacteristic
142C4×Q8—341no—
143C4×D4—342no—
144C4×D4—341no—
145#117—171no—
146#117—172no—
147#117—342no—
148C2×C42—171no—
149C2×C42—172no—
150C4⋊C8—342no—
151C4⋊C8—342no—
152#101—22no—
153#100—22no—
154#99—342no—
155#99—342no—
156C22⋊C8—22no—
157C22⋊C8—342no—
158#97—341no—
159#97—341no—
160#97—341no—
161C4×C8—341no—
162C17#1286511yescharacteristic, complemented, Sylow
163#41—41no—
164#41—41no—
165C2×Q8#6325411yescharacteristic
166C2×D4#6325212yes—
167C2×D4#6325611yescharacteristic
168C22×C4—341no—
169C22×C4—342no—
170C22×C4C2×C4×D1711yescharacteristic
171C22×C4D4×D1712yes—
172M16—41no—
173M16—42no—
174M16—42no—
175M16—681no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—41no—
179C2×C8—42no—
180C2×C8—341no—
181C2×C8—341no—
182C2×C8—681no—
183C4⋊C4—342no—
184C4⋊C4—341no—
185C4⋊C4—682no—
186C22⋊C4—341no—
187C22⋊C4—342no—
188C22⋊C4—682no—
189C42—171no—
190C42—171no—
191C42—172no—
192C42—342no—
193C42—341no—
194C42—682no—
195C23#1058755811yescharacteristic
196C23#1058758012yes—
197Q8—41no—
198D4—42no—
199D4—41no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—341no—
205C2×C4—341no—
206C2×C4—342no—
207C2×C4—1362no—
208C2×C4—1361no—
209C2×C4—1362no—
210C2×C4C22⋊C4×D1711yescharacteristic
211C2×C4#1058756912yes—
212C2×C4#1058757811yescharacteristic
213C8—41no—
214C8—41no—
215C8—82no—
216C8—681no—
217C8—681no—
218C22—22no—
219C22—21no—
220C22—41no—
221C22—42no—
222C22#1176267111yescharacteristic
223C4—22no—
224C4—21no—
225C4—2722no—
226C4—681no—
227C4—681no—
228C4—682no—
229C4#1176278111yescharacteristic
230C4#1176278111yescharacteristic
231C2—21no—
232C2—42no—
233C2—41no—
234C2#1452886011yescharacteristic
subgroupG/H
centerC4#11762781
commutatorC22×C4×C17C22×C4
FrattiniC2×#41C22×D17
FittingC17×#1392C2
socleC2×C17#1820
prime radical, cosocleC2×#41×C17C23
hypercenter#1392D17
hypocenterC17#12865
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1392

Complements

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

NH ≅ G/Ntype
9. #11762837C4semidirect
10. #11762835C4semidirect
13. M16×Dic17C4semidirect
14. C2×#10587486C4semidirect
162. C17#12865semidirect

Maximal subgroups

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

subgroupindex
#145374312
#145288892
#145269142
#145269052
C17×#13922
#1286517