Finite Group Databasebeta

← #16835479

Subgroups — #16835479

Order 3712.

456 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C22×C4⋊#1181C211yesmaximal, characteristic, complemented
2C2×#11745223C212yesmaximal, complemented
3D29⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
4#14272036C212yesmaximal, complemented
5#121×D29C211yesmaximal, characteristic
6C23×#1181—21no—
7C2×D4×D29—21no—
8C2×D4×D29C2211yescharacteristic
9C22×C4×D29C2211yescharacteristic
10C2×C4⋊#1181—21no—
11C2×C4⋊#1181—24no—
12C2×C4⋊#1181C2212yes—
13C2×D29⋊C8C2212yes—
14C29×#121C411yescharacteristic, complemented
15#11745301—21no—
16#11745300C411yescharacteristic, complemented
17#11745292C411yescharacteristic, complemented
18#11745257C411yescharacteristic, complemented
19C4⋊C4×D29C2211yescharacteristic
20#11745246—21no—
21C22⋊C4×D29—21no—
22C22⋊#6599—21no—
23#11745223—24no—
24#11745219—21no—
25C23×D29—21no—
26C23×D29D411yescharacteristic
27C22×#1181—24no—
28C22×#1181—22no—
29C22×#1181—42no—
30C22×#1181—42no—
31C2×D4×C29—21no—
32C2×D4×C29C2×C411yescharacteristic, complemented
33C22×C4×C29C2×C411yescharacteristic
34C2×C22⋊D29—21no—
35C2×C22⋊D29—21no—
36C2×C22⋊D29—21no—
37C22×Dic29D411yescharacteristic
38D4×D29—22no—
39D4×D29—22no—
40D4×D29—42no—
41D4×D29—42no—
42C2×D116—21no—
43C2×D116C2×C411yescharacteristic, complemented
44C2×C4×D29—22no—
45C2×C4×D29—22no—
46C2×C4×D29—21no—
47C2×C4×D29C2×C411yescharacteristic
48C2×C4×D29D411yescharacteristic
49C2×C4×D29D411yescharacteristic
50C2×C4×D29C2311yescharacteristic
51C2×#6599—22no—
52C4⋊#1181—24no—
53C4⋊#1181—22no—
54C4⋊#1181D414yescomplemented
55D29⋊C8—22no—
56D29⋊C8—22no—
57C4⋊C4×C29C2×C411yescharacteristic, complemented
58C22⋊C4×C29—21no—
59C22⋊Dic29—21no—
60#90781—21no—
61#90781—21no—
62C4⋊Dic29C2×C411yescharacteristic, complemented
63#90779—21no—
64C23×C29—21no—
65C23×C29C22⋊C411yescharacteristic
66C22×D29—21no—
67C22×D29—21no—
68C22×D29—21no—
69C22×D29—21no—
70C22×D29—21no—
71C22×D29—41no—
72C22×D29—41no—
73C22×D29—41no—
74C22×D29—41no—
75C22×D29—41no—
76C22×D29—41no—
77C22×D29C22⋊C411yescharacteristic
78C22×D29D812yes—
79C22×D29SD1612yes—
80C22×D29C2×D411yescharacteristic
81C2×#1181—24no—
82C2×#1181—48no—
83C2×#1181—42no—
84C2×#1181—42no—
85D4×C29—22no—
86D4×C29—42no—
87C2×C4×C29—22no—
88C2×C4×C29—21no—
89C2×C4×C29C22⋊C411yescharacteristic
90C2×C4×C29C22×C411yescharacteristic
91C22⋊D29—42no—
92C22⋊D29—42no—
93C22⋊D29—42no—
94C2×Dic29—22no—
95C2×Dic29—21no—
96C2×Dic29C22⋊C411yescharacteristic
97C2×Dic29C2×D411yescharacteristic
98D116—22no—
99D116—42no—
100C4×D29—21no—
101C4×D29—21no—
102C4×D29—22no—
103C4×D29—22no—
104C4×D29—41no—
105C4×D29—41no—
106C4×D29C2×D412yes—
107C4×D29#4112yes—
108#6599—42no—
109#1874—291nomaximal, Sylow
110C22×C29—21no—
111C22×C29—21no—
112C22×C29—41no—
113C22×C29—41no—
114C22×C29—41no—
115C22×C29#10212yescomplemented
116C22×C29C2×C22⋊C411yescharacteristic
117C2×D29—21no—
118C2×D29—21no—
119C2×D29—22no—
120C2×D29—22no—
121C2×D29—22no—
122C2×D29—22no—
123C2×D29—41no—
124C2×D29—41no—
125C2×D29—41no—
126C2×D29—81no—
127C2×D29—81no—
128C2×D29—81no—
129C2×D29—81no—
130C2×D29#10212yescomplemented
131C2×D29#12011yescharacteristic
132C2×D29#12311yescharacteristic
133C2×D29C2×D811yescharacteristic
134C2×D29C2×SD1611yescharacteristic
135C2×D29AGL(1,ℤ/8)11yescharacteristic
136C2×D29#13711yescharacteristic
137#1181—44no—
138C4×C29—21no—
139C4×C29—41no—
140C4×C29C4×D412yes—
141Dic29—21no—
142Dic29—41no—
143Dic29#12112yes—
144C2×#121—291no—
145C22×C4⋊C4—291no—
146C2×#102—292no—
147C2×C22⋊C8—291no—
148#340—292no—
149C2×C29—22no—
150C2×C29—81no—
151C2×C29#38611yescharacteristic
152C2×C29C2×#10211yescharacteristic
153C2×C29#41711yescharacteristic
154D29—22no—
155D29—81no—
156D29#44711yescharacteristic
157D29#44811yescharacteristic
158D29#48011yescharacteristic
159D29#48111yescharacteristic
160C22×D4—291no—
161C22×D4—581no—
162C23×C4—291no—
163C23×C4—581no—
164C22×C8—292no—
165#121—291no—
166#121—291no—
167#121—291no—
168#121—581no—
169#121—581no—
170#121#118111yescharacteristic, complemented
171C2×C4⋊C4—292no—
172C2×C4⋊C4—291no—
173C2×C4⋊C4—584no—
174C2×C4⋊C4—581no—
175C2×C22⋊C4—581no—
176#102—584no—
177C22⋊C8—581no—
178C22⋊C8—581no—
179C29#187411yescharacteristic, complemented, Sylow
180C24—291no—
181C24—581no—
182C2×D4—21no—
183C2×D4—291no—
184C2×D4—581no—
185C2×D4—582no—
186C2×D4—582no—
187C2×D4—581no—
188C2×D4—581no—
189C2×D4—581no—
190C2×D4—1162no—
191C2×D4—1162no—
192C2×D4C2×#118111yescharacteristic, complemented
193C22×C4—291no—
194C22×C4—291no—
195C22×C4—291no—
196C22×C4—291no—
197C22×C4—291no—
198C22×C4—582no—
199C22×C4—582no—
200C22×C4—581no—
201C22×C4—582no—
202C22×C4—584no—
203C22×C4—1162no—
204C22×C4—1162no—
205C22×C4C2×#118111yescharacteristic
206C2×C8—582no—
207C2×C8—582no—
208C2×C8—582no—
209C4⋊C4—294no—
210C4⋊C4—291no—
211C4⋊C4—581no—
212C4⋊C4—582no—
213C4⋊C4—584no—
214C4⋊C4C2×#118111yescharacteristic, complemented
215C22⋊C4—21no—
216C22⋊C4—581no—
217C22⋊C4—581no—
218C22⋊C4—581no—
219C23—21no—
220C23—291no—
221C23—291no—
222C23—292no—
223C23—292no—
224C23—581no—
225C23—581no—
226C23—581no—
227C23—581no—
228C23—581no—
229C23—1161no—
230C23—1161no—
231C23—1161no—
232C23—1161no—
233C23—1161no—
234C23—1161no—
235C23C22⋊#118111yescharacteristic
236D4—22no—
237D4—42no—
238D4—582no—
239D4—1162no—
240D4—1162no—
241D4—1162no—
242D4—1162no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—291no—
246C2×C4—292no—
247C2×C4—292no—
248C2×C4—291no—
249C2×C4—582no—
250C2×C4—581no—
251C2×C4—581no—
252C2×C4—582no—
253C2×C4—582no—
254C2×C4—584no—
255C2×C4—581no—
256C2×C4—1161no—
257C2×C4—1161no—
258C2×C4—1162no—
259C2×C4—1162no—
260C2×C4—1168no—
261C2×C4C22⋊#118111yescharacteristic
262C2×C4C22×#118111yescharacteristic
263C8—1162no—
264C22—21no—
265C22—21no—
266C22—41no—
267C22—41no—
268C22—41no—
269C22—291no—
270C22—291no—
271C22—291no—
272C22—291no—
273C22—291no—
274C22—291no—
275C22—292no—
276C22—582no—
277C22—582no—
278C22—582no—
279C22—582no—
280C22—581no—
281C22—581no—
282C22—1161no—
283C22—1161no—
284C22—1161no—
285C22—2321no—
286C22—2321no—
287C22—2321no—
288C22—2321no—
289C22#1174522312yescomplemented
290C22C2×C22⋊#118111yescharacteristic
291C4—21no—
292C4—41no—
293C4—292no—
294C4—581no—
295C4—1164no—
296C4—1161no—
297C4D4×#118112yes—
298C2—22no—
299C2—81no—
300C2—291no—
301C2—291no—
302C2—291no—
303C2—291no—
304C2—582no—
305C2—2321no—
306C2#1427211111yescharacteristic
307C2C2×#1174522311yescharacteristic
308C2#1427215411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#121C4
socleC22×C29C2×C22⋊C4
prime radical#121×D29C2
cosocleC2×C4×D29C23
hypercenter#121#1181
hypocenterC29#1874
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊#1181C2semidirect
2. C2×#11745223C2semidirect
3. D29⋊(C22⋊C8)C2semidirect
4. #14272036C2semidirect
14. C29×#121C4semidirect
16. #11745300C4semidirect
17. #11745292C4semidirect
18. #11745257C4semidirect
32. C2×D4×C29C2×C4semidirect
43. C2×D116C2×C4semidirect
54. C4⋊#1181D4semidirect
57. C4⋊C4×C29C2×C4semidirect
62. C4⋊Dic29C2×C4semidirect
115. C22×C29#102semidirect
130. C2×D29#102semidirect
170. #121#1181semidirect
179. C29#1874semidirect
192. C2×D4C2×#1181semidirect
214. C4⋊C4C2×#1181semidirect
289. C22#11745223semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#11812
C2×#117452232
D29⋊(C22⋊C8)2
#142720362
#121×D292
#187429