Finite Group Databasebeta

← #16948607

Subgroups — #16948607

Order 4352.

228 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 63 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#14531039C211yesmaximal, characteristic
2#14530689C211yesmaximal, characteristic, complemented
3#14528155C211yesmaximal, characteristic, complemented
4#14528141C211yesmaximal, characteristic
5#14526855C211yesmaximal, characteristic, complemented
6#14526834C211yesmaximal, characteristic, complemented
7C17×#1361C211yesmaximal, characteristic
8C2×#10587498—21no—
9C2×#10587498—21no—
10#11763189C2211yescharacteristic
11#11763095—21no—
12#11763006—21no—
13C8×Dic34C2211yescharacteristic
14#11762627—21no—
15#11762584—21no—
16C4×#63214C2211yescharacteristic
17#11762562C2211yescharacteristic
18#11762554—21no—
19#11762553—21no—
20C17×#493C2211yescharacteristic
21C17×C4⋊C16C2211yescharacteristic
22C17×#335C2211yescharacteristic
23C2×D8×C17—21no—
24C2×D8×C17—21no—
25C17×#127—21no—
26C2×#63229—41no—
27C2×Dic68—21no—
28C2×Dic68—21no—
29#10587555—21no—
30C4×Dic34D411yescharacteristic
31C2×C16×C17—21no—
32C17×C4⋊C8—21no—
33C4×C8×C17C2311yescharacteristic
34#10587503—41no—
35#10587498—42no—
36#10587498—42no—
37#10587488—41no—
38#10587487—41no—
39#10587485—21no—
40C8×Dic17—21no—
41C2×#63214D411yescharacteristic
42C2×#63214D411yescharacteristic
43C4⋊#3622—21no—
44C4⋊#3622D411yescharacteristic
45C2×D4×C17—41no—
46C2×D4×C17—41no—
47C2×D4×C17—41no—
48C2×Dic34—41no—
49C2×Dic34D811yescharacteristic
50D8×C17—41no—
51D8×C17—41no—
52D8×C17—81no—
53C2×C8×C17—41no—
54C2×C8×C17C2×D411yescharacteristic
55C2×C8×C17#4111yescharacteristic
56C42×C17C2×D411yescharacteristic
57#63229—82no—
58C4⋊Dic17—41no—
59C4⋊Dic17—41no—
60C4⋊Dic17D811yescharacteristic
61#63225—21no—
62C4×Dic17—21no—
63C2×#3622—21no—
64C2×#3622—41no—
65Dic68—41no—
66Dic68—41no—
67Dic68—81no—
68C16×C17—41no—
69#63214—21no—
70#63214SD1612yescomplemented
71#12444—171nomaximal, Sylow
72C23×C17—81no—
73D4×C17—81no—
74D4×C17—81no—
75D4×C17—81no—
76D4×C17—81no—
77D4×C17—161no—
78C2×C4×C17#12111yescharacteristic
79C2×C4×C17C2×D811yescharacteristic
80C2×C4×C17#13511yescharacteristic
81C2×Dic17—21no—
82C2×Dic17—21no—
83C2×Dic17—81no—
84Dic34—21no—
85Dic34—21no—
86Dic34—81no—
87Dic34—81no—
88C8×C17—21no—
89C8×C17—81no—
90C8×C17C2×SD1611yescharacteristic
91C8×C17AGL(1,ℤ/8)11yescharacteristic
92#3622—41no—
93#3622—81no—
94#2248—171no—
95#2183—171no—
96#1670—171no—
97#1668—171no—
98#1371—171no—
99#1362—171no—
100#1361D1711yescharacteristic
101C22×C17—161no—
102C22×C17—161no—
103C22×C17—161no—
104C22×C17#46611yescharacteristic
105C4×C17—21no—
106C4×C17#46011yescharacteristic
107C4×C17#47211yescharacteristic
108C4×C17#50911yescharacteristic
109C4×C17#51011yescharacteristic
110Dic17—41no—
111Dic17—41no—
112Dic17—161no—
113C2×SD32—341no—
114C2×SD32—341no—
115#494—171no—
116#493C2×D1711yescharacteristic
117#475—341no—
118#460—341no—
119C8×Q8—171no—
120C4⋊C16—341no—
121C4⋊C16C2×D1711yescharacteristic
122#346—341no—
123C4×C16—171no—
124#335—171no—
125#335C2×D1711yescharacteristic
126#332—341no—
127#331—341no—
128C2×C17—321no—
129C2×C17#166811yescharacteristic
130C2×C17#222011yescharacteristic
131C2×C17#222311yescharacteristic
132C2×Q16—341no—
133C2×Q16—341no—
134C2×SD16—681no—
135C2×D8—21no—
136C2×D8—21no—
137C4⋊Q8—341no—
138#127—21no—
139C4×Q8—171no—
140SD32—682no—
141SD32—682no—
142C2×C16—21no—
143C2×C16—171no—
144C2×C16—171no—
145#106—681no—
146C4⋊C8—21no—
147C4⋊C8—171no—
148C4⋊C8—341no—
149C4⋊C8—341no—
150#103—681no—
151#102—681no—
152C4×C8—341no—
153C4×C8C22×D1711yescharacteristic
154C17#1244411yescharacteristic, complemented, Sylow
155C2×Q8—171no—
156C2×Q8—681no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160Q16—681no—
161Q16—681no—
162Q16—1361no—
163SD16—1362no—
164D8—41no—
165D8—41no—
166D8—81no—
167C2×C8—41no—
168C2×C8—341no—
169C2×C8—681no—
170C2×C8#6325211yescharacteristic
171C2×C8D4×D1711yescharacteristic
172C4⋊C4—171no—
173C4⋊C4—341no—
174C4⋊C4—681no—
175C4⋊C4—681no—
176C42—341no—
177C42D4×D1711yescharacteristic
178C16—41no—
179C16—172no—
180C16—341no—
181C23—81no—
182Q8—341no—
183Q8—341no—
184Q8—1361no—
185Q8—1361no—
186D4—81no—
187D4—81no—
188D4—81no—
189D4—81no—
190D4—161no—
191C2×C4—341no—
192C2×C4—341no—
193C2×C4—1361no—
194C2×C4#1058757011yescharacteristic
195C2×C4D8×D1711yescharacteristic
196C2×C4#1058760211yescharacteristic
197C8—21no—
198C8—81no—
199C8—681no—
200C8—1361no—
201C8#1058759711yescharacteristic
202C8SD16×D1711yescharacteristic
203C22—161no—
204C22—161no—
205C22—161no—
206C22#1176304411yescharacteristic
207C4—21no—
208C4—2721no—
209C4—681no—
210C4—681no—
211C4#1176300811yescharacteristic
212C4#1176307811yescharacteristic
213C4#1176324311yescharacteristic
214C4#1176324811yescharacteristic
215C2—321no—
216C2#1452814311yescharacteristic
217C2#1453089611yescharacteristic
218C2#1453091311yescharacteristic
subgroupG/H
centerC22#11763044
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#1361C2
socleC22×C17#466
prime radicalC17×#493C22
hypercenter#1361D17
hypocenterC17#12444
LCSG ▷ C4×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
2. #14530689C2semidirect
3. #14528155C2semidirect
5. #14526855C2semidirect
6. #14526834C2semidirect
70. #63214SD16semidirect
154. C17#12444semidirect

Maximal subgroups

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

subgroupindex
#145310392
#145306892
#145281552
#145281412
#145268552
#145268342
C17×#13612
#1244417