Finite Group Databasebeta

← #17962894

Subgroups — #17962894

Order 4352.

194 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 50 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#14545187C211yesmaximal, characteristic, complemented
2#14545182C211yesmaximal, characteristic, complemented
3#14543949C211yesmaximal, characteristic, complemented
4#14543939C211yesmaximal, characteristic, complemented
5#14543938C211yesmaximal, characteristic, complemented
6#14543894C211yesmaximal, characteristic, complemented
7#14531098C211yesmaximal, characteristic
8#11763853—21no—
9D8×#595—21no—
10#11763742C2211yescharacteristic
11#11763738C2211yescharacteristic
12#11763736C2211yescharacteristic
13#11763724—21no—
14#11763721—21no—
15#11763696C2211yescharacteristic
16#11763242C2211yescharacteristic
17D16×D17C2211yescharacteristic
18#11762646C411yescharacteristic, complemented
19D544C411yescharacteristic, complemented
20#11762644C411yescharacteristic, complemented
21#11762642C2211yescharacteristic
22C17×SD64C411yescharacteristic, complemented
23#10587680—41no—
24D4×#595—41no—
25#10587605—21no—
26D8×D17—21no—
27#10587550—41no—
28#10587547—41no—
29#10587536—21no—
30#10587534—21no—
31C8×#595D411yescharacteristic
32#10587529D411yescharacteristic
33C17×Q32C2×C411yescharacteristic, complemented
34C17×D16C2×C411yescharacteristic
35#10587499—21no—
36#10587497—21no—
37D272C2×C411yescharacteristic
38D272C2×C411yescharacteristic, complemented
39C16×D17C2311yescharacteristic
40#10587467—21no—
41C17×C32C2×C411yescharacteristic, complemented
42#10587465C2×C411yescharacteristic, complemented
43C22×#595—81no—
44#63256—41no—
45D4×D17—41no—
46C22⋊#595—81no—
47C4⋊#595—41no—
48C4×#595D811yescharacteristic
49#63243—41no—
50#63243—81no—
51#63242—81no—
52#63242D811yescharacteristic
53Q16×C17—21no—
54D8×C17—21no—
55#63230—41no—
56#63228—41no—
57D136—21no—
58D136—21no—
59C8×D17C2×D411yescharacteristic
60#63216—21no—
61C16×C17C22×C411yescharacteristic
62#63214#4111yescharacteristic
63#13658—171nomaximal, Sylow
64C22×D17—81no—
65C2×#595—21no—
66C2×#595—81no—
67C2×#595—162no—
68Q8×C17—41no—
69D4×C17—41no—
70C22⋊D17—81no—
71D68—41no—
72D68—41no—
73D68—81no—
74C4×D17—81no—
75C4×D17C2×D811yescharacteristic
76#3624—21no—
77#3624—81no—
78C8×C17C4×D411yescharacteristic
79#3622#13511yescharacteristic
80#2263—171no—
81#2179—171no—
82#2177—171no—
83#1426—171no—
84#1419—171no—
85#1418—171no—
86#1398—171no—
87C22×C17—81no—
88C2×D17—81no—
89C2×D17—81no—
90C2×D17—161no—
91C2×D17—161no—
92C2×D17#50911yescharacteristic
93#595—41no—
94#595—161no—
95C4×C17—81no—
96C4×C17C4×D811yescharacteristic
97Dic17#50911yescharacteristic
98#508—171no—
99C2×D16—171no—
100#443—341no—
101C4×D8—341no—
102SD64—171no—
103SD64#59511yescharacteristic, complemented
104D32—171no—
105D32—171no—
106M64—171no—
107M64—171no—
108#368—171no—
109#367—171no—
110#359—341no—
111#357—341no—
112#346—171no—
113C2×C17—161no—
114C2×C17#217711yescharacteristic
115D17—21no—
116D17—161no—
117D17—161no—
118#135—341no—
119C2×D8—341no—
120#131—681no—
121C4×D4—681no—
122Q32C2×#59511yescharacteristic, complemented
123SD32—341no—
124D16—171no—
125D16—171no—
126D16—341no—
127D16C2×#59511yescharacteristic
128C2×C16—171no—
129C2×C16—171no—
130#108—341no—
131#107—341no—
132#104—681no—
133#102—681no—
134C4×C8—171no—
135C32—171no—
136C32—341no—
137C32C2×#59511yescharacteristic, complemented
138C17#1365811yescharacteristic, complemented, Sylow
139#41—681no—
140C2×D4—681no—
141C22×C4—1361no—
142Q16—21no—
143SD16—681no—
144D8—21no—
145D8—341no—
146D8—341no—
147D8—681no—
148M16—681no—
149M16—1361no—
150C2×C8—171no—
151C2×C8—171no—
152C2×C8—1361no—
153C4⋊C4—681no—
154C22⋊C4—1361no—
155C42—171no—
156C16—171no—
157C16—341no—
158C16C22×#59511yescharacteristic
159C23—1361no—
160Q8—41no—
161D4—41no—
162D4—681no—
163D4—681no—
164D4—1361no—
165D4—1361no—
166C2×C4—2722no—
167C2×C4—171no—
168C2×C4—341no—
169C2×C4—1361no—
170C2×C4—1361no—
171C8—171no—
172C8—341no—
173C8—1361no—
174C8D4×#59511yescharacteristic
175C22—81no—
176C22—2721no—
177C22—2721no—
178C22—171no—
179C22—1361no—
180C22—1361no—
181C4—81no—
182C4—2721no—
183C4—171no—
184C4—681no—
185C4D8×#59511yescharacteristic
186C2—161no—
187C2—2721no—
188C2—2721no—
189C2—341no—
190C2#1454518211yescharacteristic
subgroupG/H
centerC2#14545182
commutatorC16×C17C22×C4
FrattiniC16C22×#595
FittingC17×SD64C4
socleC2×C17#2177
prime radical#14531098C2
cosocleC16×D17C23
hypercenterSD64#595
hypocenterC17#13658
LCSG ▷ C16×C17 ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ SD64

Complements

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

NH ≅ G/Ntype
1. #14545187C2semidirect
2. #14545182C2semidirect
3. #14543949C2semidirect
4. #14543939C2semidirect
5. #14543938C2semidirect
6. #14543894C2semidirect
18. #11762646C4semidirect
19. D544C4semidirect
20. #11762644C4semidirect
22. C17×SD64C4semidirect
33. C17×Q32C2×C4semidirect
38. D272C2×C4semidirect
41. C17×C32C2×C4semidirect
42. #10587465C2×C4semidirect
103. SD64#595semidirect
122. Q32C2×#595semidirect
137. C32C2×#595semidirect
138. C17#13658semidirect

Maximal subgroups

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

subgroupindex
#145451872
#145451822
#145439492
#145439392
#145439382
#145438942
#145310982
#1365817