Finite Group Databasebeta

← #17962716

Subgroups — #17962716

Order 4352.

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

normal subgroups only

This group has 312 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
1C2×#11763720C212yesmaximal
2#14543927C212yesmaximal, complemented
3#14543926C212yesmaximal, complemented
4#14539166C211yesmaximal, characteristic
5C2×#10587545—22no—
6#11763720—22no—
7#11763720C2214yes—
8C2×#10587555C2211yescharacteristic
9#11763179C411yescharacteristic
10#11763179C411yescharacteristic
11#11763179C2211yescharacteristic
12#11763179C2211yescharacteristic
13#11763161—22no—
14#11762817—22no—
15C4×#63223C411yescharacteristic
16C17×#533C411yescharacteristic
17C22×Dic34D412yes—
18C2×#63247—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
26C2×C4⋊Dic17—41no—
27C2×#63223—21no—
28#10587555—41no—
29#10587555C2×C411yescharacteristic
30#10587555D412yes—
31#10587555C2311yescharacteristic
32#10587545—24no—
33#10587545—42no—
34#10587481—22no—
35#10587481—22no—
36#10587481—22no—
37#10587481—22no—
38#10587474C2×C411yescharacteristic
39#10587474C2×C411yescharacteristic
40C4×#3622—21no—
41C2×Q8×C17—41no—
42C22×C4×C17—21no—
43C22×C4×C17C22⋊C411yescharacteristic
44C22×Dic17—22no—
45C2×Dic34—22no—
46C2×Dic34—42no—
47C2×Dic34—42no—
48C2×Dic34C22⋊C412yes—
49C2×Dic34C2×D412yes—
50#63247—44no—
51#63247—82no—
52C2×#3624—82no—
53C4⋊C4×C17—21no—
54C4⋊C4×C17—21no—
55C4⋊C4×C17—41no—
56C4⋊C4×C17—41no—
57C4⋊C4×C17—41no—
58C22⋊C4×C17—41no—
59C42×C17—21no—
60C42×C17—41no—
61C42×C17C22⋊C411yescharacteristic
62C42×C17C22×C411yescharacteristic
63C4⋊Dic17—41no—
64C4⋊Dic17—42no—
65C4⋊Dic17—41no—
66#63223—42no—
67C2×#3622—21no—
68C2×#3622—21no—
69#13599—171nomaximal, Sylow
70C23×C17#9911yescharacteristic
71Q8×C17—82no—
72C2×C4×C17—22no—
73C2×C4×C17—21no—
74C2×C4×C17—21no—
75C2×C4×C17—42no—
76C2×C4×C17—41no—
77C2×C4×C17—41no—
78C2×C4×C17#9911yescharacteristic
79C2×C4×C17C2×C22⋊C411yescharacteristic
80C2×Dic17—22no—
81C2×Dic17—22no—
82C2×Dic17—42no—
83C2×Dic17—42no—
84Dic34—42no—
85Dic34—42no—
86Dic34—82no—
87#3624—84no—
88#3622—41no—
89#3622—41no—
90#3139—171no—
91C2×#356—172no—
92#1413—172no—
93#1413—172no—
94C22×C17—41no—
95C22×C17#35412yes—
96C22×C17C2×#9911yescharacteristic
97C4×C17—22no—
98C4×C17—21no—
99C4×C17—21no—
100C4×C17—41no—
101C4×C17—81no—
102C4×C17—81no—
103Dic17—42no—
104Dic17—42no—
105#533#59511yescharacteristic
106C2×C4⋊Q8—171no—
107#491—171no—
108#491—171no—
109#491—171no—
110#491—171no—
111#487—342no—
112#419—342no—
113C2×#101—342no—
114C4×M16—171no—
115#356—174no—
116#356—342no—
117C2×C17—21no—
118C2×C17—22no—
119C2×C17C2×#35411yescharacteristic
120C22×Q8—172no—
121C2×M16—341no—
122C2×M16—682no—
123C4⋊Q8—21no—
124C4⋊Q8—172no—
125C4⋊Q8—171no—
126C4⋊Q8—171no—
127C4⋊Q8—681no—
128#125C2×#59511yescharacteristic
129#125C2×#59511yescharacteristic
130C22⋊Q8—41no—
131C4×Q8—41no—
132#117—21no—
133C2×C4⋊C4—681no—
134C2×C42C2×#59511yescharacteristic
135#103—342no—
136#103—342no—
137#103—342no—
138#103—342no—
139#101—344no—
140#101—682no—
141#97—171no—
142#97—171no—
143C4×C8—341no—
144C17#1359911yescharacteristic, complemented, Sylow
145C2×Q8—41no—
146C2×Q8—172no—
147C2×Q8—172no—
148C2×Q8—342no—
149C2×Q8—682no—
150C2×Q8—682no—
151C22×C4—21no—
152C22×C4—342no—
153C22×C4C22⋊#59511yescharacteristic
154M16—682no—
155M16—684no—
156M16—1362no—
157C2×C8—341no—
158C2×C8—341no—
159C2×C8—1362no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—682no—
166C4⋊C4—681no—
167C4⋊C4—681no—
168C22⋊C4—41no—
169C42—21no—
170C42—41no—
171C42C22⋊#59511yescharacteristic
172C42C22×#59511yescharacteristic
173C23#1058755111yescharacteristic
174Q8—82no—
175Q8—682no—
176Q8—682no—
177Q8—1362no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—42no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—342no—
185C2×C4—342no—
186C2×C4—682no—
187C2×C4—682no—
188C2×C4#1058755111yescharacteristic
189C2×C4C2×C22⋊#59511yescharacteristic
190C8—681no—
191C8—681no—
192C8—1364no—
193C22—41no—
194C22#1176371512yes—
195C22C2×#1058755111yescharacteristic
196C4—22no—
197C4—21no—
198C4—21no—
199C4—41no—
200C4—81no—
201C4—81no—
202C4—682no—
203C4—682no—
204C2—21no—
205C2—22no—
206C2C2×#1176371511yescharacteristic
subgroupG/H
centerC2C2×#11763715
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC17×#533C4
socleC2×C17C2×#354
prime radicalC23×C17#99
cosocle#10587555C23
hypercenter#533#595
hypocenterC17#13599
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #14543927C2semidirect
3. #14543926C2semidirect
144. C17#13599semidirect

Maximal subgroups

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

subgroupindex
C2×#117637202
#145439272
#145439262
#145391662
#1359917