Finite Group Databasebeta

← #16835507

Subgroups — #16835507

Order 3712.

360 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 78 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×D29⋊M16C211yesmaximal, characteristic
2C2×#11745225C212yesmaximal, complemented
3#14272105C211yesmaximal, characteristic
4#14272036C212yesmaximal, complemented
5C22⋊Q8×D29C211yesmaximal, characteristic
6C2×Q8×D29C2211yescharacteristic
7C22×C4×D29C2211yescharacteristic
8C2×C22⋊#1181—21no—
9C2×#90800—21no—
10C2×C4⋊#1181C2212yes—
11D29⋊M16—24no—
12C2×#90796—21no—
13C2×D29⋊C8C2212yes—
14C29×C22⋊Q8C411yescharacteristic, complemented
15#11745308C411yescharacteristic, complemented
16#11745286C411yescharacteristic, complemented
17#11745259C411yescharacteristic, complemented
18#11745258—21no—
19C4⋊C4×D29—21no—
20C4⋊C4×D29C2211yescharacteristic
21C22⋊C4×D29—21no—
22#11745240—21no—
23#11745225—24no—
24(C2×#1181)⋊C4—21no—
25C23×D29D411yescharacteristic
26C22×#1181—22no—
27C2×Q8×C29C2×C411yescharacteristic
28C22×C4×C29C2×C411yescharacteristic
29C22×Dic29D411yescharacteristic
30Q8×D29—22no—
31Q8×D29—22no—
32C2×C4×D29—22no—
33C2×C4×D29—22no—
34C2×C4×D29—21no—
35C2×C4×D29—21no—
36C2×C4×D29C2×C411yescharacteristic
37C2×C4×D29D411yescharacteristic
38C2×C4×D29D411yescharacteristic
39C2×C4×D29C2311yescharacteristic
40C2×Dic58—21no—
41C2×Dic58C2×C411yescharacteristic
42C22⋊#1181—42no—
43#90800—24no—
44C2×#6599—22no—
45C4⋊#1181—22no—
46C4⋊#1181—22no—
47#90796—24no—
48D29⋊C8—22no—
49D29⋊C8D414yes—
50C4⋊C4×C29—21no—
51C4⋊C4×C29C2×C411yescharacteristic
52C22⋊C4×C29—21no—
53C22⋊Dic29—21no—
54#90781—21no—
55#90781—21no—
56C4⋊Dic29—21no—
57C4⋊Dic29C2×C411yescharacteristic
58#90779—21no—
59#90779—21no—
60#90779—21no—
61C23×C29C22⋊C411yescharacteristic
62C22×D29—22no—
63C22×D29—21no—
64C22×D29—21no—
65C22×D29—22no—
66C22×D29C22⋊C411yescharacteristic
67C22×D29C2×D411yescharacteristic
68C2×#1181—42no—
69C2×#1181—42no—
70C2×#1181—42no—
71Q8×C29—22no—
72C2×C4×C29—22no—
73C2×C4×C29—21no—
74C2×C4×C29—21no—
75C2×C4×C29C22⋊C411yescharacteristic
76C2×C4×C29C22×C411yescharacteristic
77C2×Dic29—21no—
78C2×Dic29—21no—
79C2×Dic29—21no—
80C2×Dic29—21no—
81C2×Dic29C22⋊C411yescharacteristic
82C2×Dic29C2×D411yescharacteristic
83C4×D29—22no—
84C4×D29—22no—
85C4×D29—21no—
86C4×D29—21no—
87C4×D29—42no—
88C4×D29—41no—
89C4×D29—41no—
90C4×D29C2×D412yes—
91C4×D29#4112yes—
92Dic58—22no—
93Dic58—41no—
94Dic58—41no—
95#6599—24no—
96#1894—291nomaximal, Sylow
97C22×C29—21no—
98C22×C29—21no—
99C22×C29—21no—
100C22×C29C2×C22⋊C411yescharacteristic
101C2×D29—21no—
102C2×D29—21no—
103C2×D29—21no—
104C2×D29—42no—
105C2×D29—42no—
106C2×D29#12112yes—
107C2×D29AGL(1,ℤ/8)11yescharacteristic
108C2×D29#13712yes—
109C2×D29#13711yescharacteristic
110#1181—82no—
111C4×C29—21no—
112C4×C29—41no—
113C4×C29—41no—
114C4×C29C4×D412yes—
115Dic29—21no—
116Dic29—41no—
117Dic29—41no—
118Dic29#12011yescharacteristic
119Dic29#12311yescharacteristic
120C22×M16—291no—
121C2×C22⋊Q8—291no—
122C2×#103—292no—
123#380—291no—
124#340—292no—
125C2×C29—41no—
126C2×C29#38611yescharacteristic
127C2×C29#41711yescharacteristic
128C2×C29#41911yescharacteristic
129D29—41no—
130D29#46812yes—
131D29#47012yes—
132C22×Q8—291no—
133C23×C4—291no—
134C2×M16—584no—
135C2×M16—581no—
136C2×M16—581no—
137C22×C8—292no—
138C22⋊Q8—291no—
139C22⋊Q8—291no—
140C22⋊Q8—291no—
141C22⋊Q8—581no—
142C22⋊Q8—581no—
143C22⋊Q8#118111yescharacteristic, complemented
144C2×C4⋊C4—291no—
145C2×C4⋊C4—292no—
146C2×C4⋊C4—581no—
147C2×C22⋊C4—581no—
148C2×C22⋊C4—581no—
149#103—584no—
150#95—581no—
151C29#189411yescharacteristic, complemented, Sylow
152C24—291no—
153C2×Q8—291no—
154C2×Q8—581no—
155C2×Q8—582no—
156C2×Q8—582no—
157C2×Q8C2×#118111yescharacteristic
158C22×C4—291no—
159C22×C4—291no—
160C22×C4—291no—
161C22×C4—291no—
162C22×C4—291no—
163C22×C4—582no—
164C22×C4—582no—
165C22×C4—581no—
166C22×C4—581no—
167C22×C4—582no—
168C22×C4C2×#118111yescharacteristic
169M16—584no—
170M16—584no—
171C2×C8—294no—
172C2×C8—582no—
173C2×C8—582no—
174C4⋊C4—21no—
175C4⋊C4—291no—
176C4⋊C4—581no—
177C4⋊C4—581no—
178C4⋊C4—581no—
179C4⋊C4—582no—
180C4⋊C4—582no—
181C4⋊C4—581no—
182C4⋊C4C2×#118111yescharacteristic
183C22⋊C4—21no—
184C22⋊C4—581no—
185C22⋊C4—581no—
186C22⋊C4—581no—
187C22⋊C4—1162no—
188C23—291no—
189C23—291no—
190C23—581no—
191C23—582no—
192C23—581no—
193C23—582no—
194C23C22⋊#118111yescharacteristic
195Q8—22no—
196Q8—582no—
197Q8—1161no—
198Q8—1161no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—291no—
203C2×C4—292no—
204C2×C4—292no—
205C2×C4—291no—
206C2×C4—581no—
207C2×C4—581no—
208C2×C4—582no—
209C2×C4—581no—
210C2×C4—581no—
211C2×C4—582no—
212C2×C4—581no—
213C2×C4—581no—
214C2×C4—1162no—
215C2×C4—1161no—
216C2×C4—1161no—
217C2×C4—1162no—
218C2×C4—1162no—
219C2×C4—1162no—
220C2×C4C22⋊#118111yescharacteristic
221C2×C4C22×#118111yescharacteristic
222C8—584no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—292no—
227C22—291no—
228C22—291no—
229C22—292no—
230C22—581no—
231C22—581no—
232C22—581no—
233C22—1162no—
234C22—1162no—
235C22C2×C22⋊#118111yescharacteristic
236C4—21no—
237C4—41no—
238C4—41no—
239C4—291no—
240C4—291no—
241C4—581no—
242C4—1161no—
243C4—1161no—
244C4—2322no—
245C4D4×#118112yes—
246C2—41no—
247C2—292no—
248C2—292no—
249C2—1161no—
250C2#1427211111yescharacteristic
251C2#1427215411yescharacteristic
252C2#1427215611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×C22⋊Q8C4
socleC22×C29C2×C22⋊C4
prime radicalC23×D29D4
cosocleC2×C4×D29C23
hypercenterC22⋊Q8#1181
hypocenterC29#1894
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#11745225C2semidirect
4. #14272036C2semidirect
14. C29×C22⋊Q8C4semidirect
15. #11745308C4semidirect
16. #11745286C4semidirect
17. #11745259C4semidirect
143. C22⋊Q8#1181semidirect
151. C29#1894semidirect

Maximal subgroups

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

subgroupindex
C2×D29⋊M162
C2×#117452252
#142721052
#142720362
C22⋊Q8×D292
#189429