Finite Group Databasebeta

← #16955108

Subgroups — #16955108

Order 4352.

220 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C2×#11762648C211yesmaximal, characteristic, complemented
2C2×#11762647C211yesmaximal, characteristic, complemented
3#14531032C211yesmaximal, characteristic
4#14530642C211yesmaximal, characteristic, complemented
5#14526979C211yesmaximal, characteristic, complemented
6#14526961C211yesmaximal, characteristic, complemented
7C17×#1415C211yesmaximal, characteristic, complemented
8C2×Dic136C2211yescharacteristic
9C2×D272C2211yescharacteristic
10C2×#10587497—21no—
11#11763184—21no—
12#11762903—21no—
13#11762648—22no—
14#11762647—22no—
15C2×#10587465C2211yescharacteristic
16#11762612—21no—
17C16×Dic17C2211yescharacteristic
18C2×C17×D16C2211yescharacteristic
19C2×C17×C32C2211yescharacteristic
20C17×#366C2211yescharacteristic
21C2×D8×C17—21no—
22#10587626—41no—
23C2×#63228—41no—
24C2×Dic68—21no—
25C2×D136—21no—
26#10587573—41no—
27C17×D16—21no—
28C17×D16—21no—
29C2×C16×C17C2311yescharacteristic
30C17×#107—21no—
31#10587497—42no—
32C8×Dic17D411yescharacteristic
33C2×#63214D411yescharacteristic
34#10587481—41no—
35Dic136—21no—
36Dic136D412yescomplemented
37D272—21no—
38D272—21no—
39C17×C32—21no—
40#10587465—21no—
41C2×D4×C17—41no—
42C2×C22⋊D17—81no—
43C2×C22⋊D17—81no—
44C2×D68—41no—
45C2×Dic34—41no—
46D8×C17—41no—
47D8×C17—41no—
48C2×C8×C17C2×D411yescharacteristic
49C4⋊C4×C17—41no—
50#63228—82no—
51#63225—81no—
52C4×Dic17—81no—
53C4×Dic17D811yescharacteristic
54C2×#3622D811yescharacteristic
55Dic68—22no—
56Dic68—41no—
57D136—41no—
58D136—41no—
59C16×C17C2×D411yescharacteristic
60C16×C17#4111yescharacteristic
61#63214—21no—
62#13686—171nomaximal, Sylow
63C23×C17—81no—
64C22×D17—81no—
65D4×C17—81no—
66D4×C17—81no—
67C2×C4×C17—81no—
68C2×C4×C17C2×D811yescharacteristic
69C22⋊D17—162no—
70C22⋊D17—162no—
71C2×Dic17—81no—
72C2×Dic17D1611yescharacteristic
73C2×Dic17D1611yescharacteristic
74D68—81no—
75D68—81no—
76Dic34—42no—
77Dic34—81no—
78C8×C17#12111yescharacteristic
79C8×C17AGL(1,ℤ/8)11yescharacteristic
80#3622—21no—
81C2×SD64—171no—
82C2×SD64—171no—
83#2246—171no—
84C4×Q32—171no—
85C4⋊C32—171no—
86#1415—171no—
87#1415D1711yescharacteristic, complemented
88C22×C17—161no—
89C22×C17—161no—
90C22×C17—161no—
91C22×C17C2×D1611yescharacteristic
92C2×D17—161no—
93C2×D17—161no—
94C2×D17—161no—
95C4×C17—161no—
96C4×C17#45911yescharacteristic
97C4×C17#50911yescharacteristic
98Dic17—21no—
99Dic17—82no—
100Dic17SD6412yescomplemented
101C2×Q32—171no—
102C2×D16—171no—
103C2×D16—341no—
104C2×D16C2×D1711yescharacteristic
105#493—341no—
106C4×Q16—341no—
107SD64—342no—
108SD64—342no—
109C2×C32—171no—
110C2×C32C2×D1711yescharacteristic
111#366C2×D1711yescharacteristic
112#358—341no—
113C4×C16—171no—
114C2×C17—321no—
115C2×C17#220611yescharacteristic
116C2×C17C2×SD6411yescharacteristic
117C2×C17#226311yescharacteristic
118D17—321no—
119C2×Q16—341no—
120C2×D8—21no—
121C2×D8—341no—
122C2×D8—681no—
123#127—681no—
124C4×Q8—681no—
125Q32—172no—
126Q32—341no—
127D16—21no—
128D16—21no—
129D16—341no—
130D16—341no—
131D16—682no—
132C2×C16—171no—
133C2×C16C22×D1711yescharacteristic
134#107—21no—
135#103—681no—
136C4×C8—171no—
137C32—21no—
138C32—341no—
139C17#1368611yescharacteristic, complemented, Sylow
140C2×Q8—681no—
141C2×D4—41no—
142C2×D4—681no—
143C2×D4—1361no—
144C2×D4—1361no—
145Q16—342no—
146Q16—681no—
147D8—41no—
148D8—41no—
149D8—681no—
150D8—681no—
151D8—1362no—
152C2×C8—171no—
153C2×C8D4×D1711yescharacteristic
154C4⋊C4—41no—
155C4⋊C4—1361no—
156C42—171no—
157C42—1361no—
158C16—341no—
159C16#6325211yescharacteristic
160C16D4×D1711yescharacteristic
161C23—81no—
162C23—1361no—
163Q8—682no—
164Q8—1361no—
165D4—81no—
166D4—81no—
167D4—2722no—
168D4—2722no—
169D4—1361no—
170D4—1361no—
171C2×C4—81no—
172C2×C4—171no—
173C2×C4—171no—
174C2×C4—1361no—
175C2×C4D8×D1711yescharacteristic
176C8—341no—
177C8#1058757011yescharacteristic
178C8#1058760011yescharacteristic
179C22—161no—
180C22—161no—
181C22—161no—
182C22—2721no—
183C22—2721no—
184C22—2721no—
185C22D16×D1711yescharacteristic
186C4—161no—
187C4—172no—
188C4—341no—
189C4—1362no—
190C4#1176300311yescharacteristic
191C4#1176324611yescharacteristic
192C2—321no—
193C2—5441no—
194C2#1453081811yescharacteristic
195C2D17×SD6411yescharacteristic
196C2#1453109511yescharacteristic
subgroupG/H
centerC22D16×D17
commutator, cosocleC2×C16×C17C23
FrattiniC2×C16C22×D17
FittingC17×#1415C2
socleC22×C17C2×D16
prime radical#14531032C2
hypercenter#1415D17
hypocenterC17#13686
LCSG ▷ C2×C16×C17 ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1415

Complements

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

NH ≅ G/Ntype
1. C2×#11762648C2semidirect
2. C2×#11762647C2semidirect
4. #14530642C2semidirect
5. #14526979C2semidirect
6. #14526961C2semidirect
7. C17×#1415C2semidirect
36. Dic136D4semidirect
87. #1415D17semidirect
100. Dic17SD64semidirect
139. C17#13686semidirect

Maximal subgroups

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

subgroupindex
C2×#117626482
C2×#117626472
#145310322
#145306422
#145269792
#145269612
C17×#14152
#1368617