Finite Group Databasebeta

← #17962699

Subgroups — #17962699

Order 4352.

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

normal subgroups only

This group has 326 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#14545057C212yesmaximal
2#14543924C212yesmaximal, complemented
3#14543923C212yesmaximal, complemented
4#14539132C211yesmaximal, characteristic
5#11763788—22no—
6#11763716—22no—
7#11763714C2214yes—
8#11763359C2211yescharacteristic
9#11763179C411yescharacteristic, complemented
10#11763179C411yescharacteristic, complemented
11#11763175C2211yescharacteristic
12#11763175C2211yescharacteristic
13#11763171—22no—
14#11762803—22no—
15C2×#10587474C411yescharacteristic, complemented
16C17×#533C411yescharacteristic, complemented
17C2×#63252D412yes—
18#10587677—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#10587560C2311yescharacteristic
30C4×D68—41no—
31#10587555C2×C411yescharacteristic
32#10587551—42no—
33#10587539—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×D68C2×D412yes—
49C2×C4×D17—22no—
50C2×Dic34C22⋊C412yes—
51C22⋊#595—44no—
52C4⋊#595—82no—
53C4×#595—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#13594—171nomaximal, Sylow
71C23×C17#9911yescharacteristic
72C22×D17—22no—
73C2×#595—84no—
74Q8×C17—82no—
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17—41no—
80C2×C4×C17—41no—
81C2×C4×C17—81no—
82C2×C4×C17#9911yescharacteristic
83C2×C4×C17C2×C22⋊C411yescharacteristic
84C22⋊D17—82no—
85C2×Dic17—22no—
86D68—42no—
87D68—82no—
88C4×D17—42no—
89C4×D17—42no—
90Dic34—42no—
91#3622—41no—
92#3622—41no—
93#3135—171no—
94#2126—172no—
95#1412—172no—
96#1412—172no—
97C22×C17—21no—
98C22×C17—41no—
99C22×C17C2×#9911yescharacteristic
100C2×D17—42no—
101C2×D17—82no—
102#595—164no—
103C4×C17—21no—
104C4×C17—41no—
105C4×C17—41no—
106C4×C17—81no—
107C4×C17—81no—
108C4×C17#35411yescharacteristic
109C4×C17#35411yescharacteristic
110Dic17—42no—
111#533#59511yescharacteristic, complemented
112#532—171no—
113#491—171no—
114#491—171no—
115#490—171no—
116#490—171no—
117#489—342no—
118#416—342no—
119#410—342no—
120C2×#97—171no—
121#354—342no—
122#353—174no—
123C2×C17—21no—
124C2×C17—41no—
125C2×C17C2×#35411yescharacteristic
126D17—82no—
127C2×#41—172no—
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—
140#117—682no—
141C2×C42C2×#59511yescharacteristic
142#103—342no—
143#103—342no—
144#102—342no—
145#102—342no—
146#99—344no—
147#99—682no—
148#97—171no—
149#97—171no—
150#97—341no—
151C17#1359411yescharacteristic, complemented, Sylow
152#41—682no—
153#41—682no—
154C2×Q8—41no—
155C2×Q8—172no—
156C2×D4—172no—
157C2×D4—342no—
158C2×D4—681no—
159C22×C4—21no—
160C22×C4—342no—
161C22×C4C22⋊#59511yescharacteristic
162C2×C8—341no—
163C2×C8—341no—
164C2×C8—681no—
165C2×C8—681no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—681no—
172C4⋊C4—1362no—
173C22⋊C4—41no—
174C22⋊C4—682no—
175C22⋊C4—684no—
176C42—21no—
177C42—41no—
178C42—1362no—
179C42C22⋊#59511yescharacteristic
180C42C22×#59511yescharacteristic
181C23—342no—
182C23#1058755111yescharacteristic
183Q8—82no—
184Q8—682no—
185D4—682no—
186D4—1362no—
187D4—1362no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4—342no—
196C2×C4—682no—
197C2×C4—682no—
198C2×C4—1364no—
199C2×C4#1058755111yescharacteristic
200C2×C4C2×C22⋊#59511yescharacteristic
201C8—681no—
202C8—681no—
203C22—21no—
204C22—41no—
205C22—682no—
206C22—1362no—
207C22C2×#1058755111yescharacteristic
208C4—21no—
209C4—41no—
210C4—41no—
211C4—81no—
212C4—81no—
213C4—2724no—
214C4—682no—
215C4#1176371511yescharacteristic
216C4#1176371511yescharacteristic
217C2—21no—
218C2—41no—
219C2—1362no—
220C2C2×#1176371511yescharacteristic
subgroupG/H
centerC4#11763715
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC17×#533C4
socleC2×C17C2×#354
prime radical#11763359C22
cosocle#10587560C23
hypercenter#533#595
hypocenterC17#13594
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. #14543924C2semidirect
3. #14543923C2semidirect
9. #11763179C4semidirect
10. #11763179C4semidirect
15. C2×#10587474C4semidirect
16. C17×#533C4semidirect
111. #533#595semidirect
151. C17#13594semidirect

Maximal subgroups

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

subgroupindex
#145450572
#145439242
#145439232
#145391322
#1359417