Finite Group Databasebeta

← #17962713

Subgroups — #17962713

Order 4352.

318 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 60 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#14545077C212yesmaximal
2#14543927C212yesmaximal, complemented
3#14543926C212yesmaximal, complemented
4#14539132C211yesmaximal, characteristic
5#11763795—22no—
6#11763720C2214yes—
7#11763718—22no—
8#11763359C2211yescharacteristic
9#11763179C2211yescharacteristic
10#11763179C2211yescharacteristic
11#11763175C411yescharacteristic
12#11763175C411yescharacteristic
13#11763171—22no—
14#11762803—22no—
15C2×#10587474C411yescharacteristic
16C17×#533C411yescharacteristic
17C2×#63252D412yes—
18D17⋊M16—42no—
19C17×C4⋊Q8—21no—
20C17×#125C2×C411yescharacteristic
21C17×#125C2×C411yescharacteristic
22C17×C22⋊Q8—41no—
23C4×Q8×C17—41no—
24C17×#117—21no—
25C2×C42×C17C2×C411yescharacteristic
26#10587616—41no—
27C22×#3622—21no—
28#10587561D412yes—
29#10587560C2×C411yescharacteristic
30C4×D68—41no—
31#10587555C2311yescharacteristic
32#10587553—42no—
33#10587545—24no—
34#10587481—22no—
35#10587481—22no—
36#10587480—22no—
37#10587480—22no—
38#10587474—21no—
39#10587474C2×C411yescharacteristic
40#10587474C2×C411yescharacteristic
41C2×Q8×C17—41no—
42C22×C4×C17—21no—
43C22×C4×C17C22⋊C411yescharacteristic
44C2×C22⋊D17—22no—
45#63252—42no—
46#63252—42no—
47C2×D68—41no—
48C2×D68C22⋊C412yes—
49C2×C4×D17—22no—
50C2×Dic34C2×D412yes—
51#63247—44no—
52#63243—82no—
53#63242—82no—
54C4⋊C4×C17—21no—
55C4⋊C4×C17—21no—
56C4⋊C4×C17—41no—
57C4⋊C4×C17—41no—
58C4⋊C4×C17—41no—
59C22⋊C4×C17—41no—
60C42×C17—21no—
61C42×C17—41no—
62C42×C17C22⋊C411yescharacteristic
63C42×C17C22×C411yescharacteristic
64#63227—42no—
65C4⋊Dic17—41no—
66C2×#3622—21no—
67C2×#3622—21no—
68C2×#3622—41no—
69C2×#3622—41no—
70#13598—171nomaximal, Sylow
71C23×C17#9911yescharacteristic
72C22×D17—22no—
73Q8×C17—82no—
74C2×C4×C17—21no—
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17—21no—
78C2×C4×C17—41no—
79C2×C4×C17—41no—
80C2×C4×C17—81no—
81C2×C4×C17#9911yescharacteristic
82C2×C4×C17C2×C22⋊C411yescharacteristic
83C22⋊D17—82no—
84C2×Dic17—22no—
85D68—42no—
86D68—82no—
87C4×D17—42no—
88C4×D17—42no—
89Dic34—42no—
90#3624—84no—
91#3622—41no—
92#3622—41no—
93#3135—171no—
94#2132—172no—
95#1413—172no—
96#1413—172no—
97C22×C17—21no—
98C22×C17—41no—
99C22×C17C2×#9911yescharacteristic
100C2×D17—42no—
101C2×D17—82no—
102C4×C17—21no—
103C4×C17—41no—
104C4×C17—41no—
105C4×C17—81no—
106C4×C17—81no—
107C4×C17#35411yescharacteristic
108C4×C17#35411yescharacteristic
109Dic17—42no—
110#533#59511yescharacteristic
111#532—171no—
112#491—171no—
113#491—171no—
114#490—171no—
115#490—171no—
116#489—342no—
117#416—342no—
118#413—342no—
119C2×#97—171no—
120#356—174no—
121#355—342no—
122C2×C17—21no—
123C2×C17—41no—
124C2×C17C2×#35411yescharacteristic
125D17—82no—
126C2×#41—172no—
127C2×M16—682no—
128C22×C8—341no—
129C4⋊Q8—21no—
130C4⋊Q8—171no—
131#127—171no—
132#125C2×#59511yescharacteristic
133#125C2×#59511yescharacteristic
134#124—172no—
135C22⋊Q8—41no—
136#121—681no—
137C4×Q8—41no—
138C4×D4—681no—
139#117—21no—
140C2×C42C2×#59511yescharacteristic
141#103—342no—
142#103—342no—
143#102—342no—
144#102—342no—
145#101—344no—
146#100—682no—
147#97—171no—
148#97—171no—
149#97—341no—
150C17#1359811yescharacteristic, complemented, Sylow
151#41—682no—
152#41—682no—
153C2×Q8—41no—
154C2×Q8—172no—
155C2×D4—172no—
156C2×D4—342no—
157C2×D4—681no—
158C22×C4—21no—
159C22×C4—342no—
160C22×C4C22⋊#59511yescharacteristic
161M16—684no—
162M16—1362no—
163C2×C8—341no—
164C2×C8—341no—
165C2×C8—681no—
166C2×C8—681no—
167C2×C8—1362no—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—681no—
174C22⋊C4—41no—
175C22⋊C4—682no—
176C42—21no—
177C42—41no—
178C42C22⋊#59511yescharacteristic
179C42C22×#59511yescharacteristic
180C23—342no—
181C23#1058755111yescharacteristic
182Q8—82no—
183Q8—682no—
184D4—682no—
185D4—1362no—
186D4—1362no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—81no—
194C2×C4—342no—
195C2×C4—682no—
196C2×C4—682no—
197C2×C4#1058755111yescharacteristic
198C2×C4C2×C22⋊#59511yescharacteristic
199C8—681no—
200C8—681no—
201C8—1364no—
202C22—21no—
203C22—41no—
204C22—682no—
205C22—1362no—
206C22C2×#1058755111yescharacteristic
207C4—21no—
208C4—41no—
209C4—41no—
210C4—81no—
211C4—81no—
212C4—682no—
213C4#1176371511yescharacteristic
214C4#1176371511yescharacteristic
215C2—21no—
216C2—41no—
217C2—1362no—
218C2C2×#1176371511yescharacteristic
subgroupG/H
centerC4#11763715
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC17×#533C4
socleC2×C17C2×#354
prime radical#11763359C22
cosocle#10587555C23
hypercenter#533#595
hypocenterC17#13598
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #14543927C2semidirect
3. #14543926C2semidirect
150. C17#13598semidirect

Maximal subgroups

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

subgroupindex
#145450772
#145439272
#145439262
#145391322
#1359817