Finite Group Databasebeta

← #16835485

Subgroups — #16835485

Order 3712.

402 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 80 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×D4×#1181C211yesmaximal, characteristic
2C2×#11745225C211yesmaximal, characteristic, complemented
3C2×#11745223C211yesmaximal, characteristic
4(C2×#1181)⋊Q8C211yesmaximal, characteristic, complemented
5#14272037C211yesmaximal, characteristic, complemented
6(C2×#1181)⋊C8C211yesmaximal, characteristic, complemented
7C2×SD16×D29C211yesmaximal, characteristic
8C23×#1181—21no—
9C2×Q8×D29C2211yescharacteristic
10C2×D4×D29C2211yescharacteristic
11C2×C22⋊#1181—21no—
12D4×#1181—22no—
13D4×#1181—22no—
14C2×C4⋊#1181C2211yescharacteristic
15C2×C4⋊#1181C2211yescharacteristic
16C2×C4×#1181C2211yescharacteristic
17C2×D29⋊C8C2211yescharacteristic
18C2×SD16×C29C411yescharacteristic, complemented
19C2×#90784C411yescharacteristic, complemented
20C2×#90783C411yescharacteristic, complemented
21SD16×D29—22no—
22SD16×D29—22no—
23C2×#90773C411yescharacteristic, complemented
24C2×C8×D29C2211yescharacteristic
25#11745225—22no—
26#11745223—22no—
27(C2×#1181)⋊C4—21no—
28(C2×#1181)⋊C4—21no—
29C23×D29—21no—
30C22×#1181—24no—
31C22×#1181—21no—
32C22×#1181—21no—
33C22×#1181—42no—
34C22×#1181—42no—
35C22×#1181D411yescharacteristic
36C22×#1181D411yescharacteristic
37C2×Q8×C29C2×C411yescharacteristic, complemented
38C2×D4×C29C2×C411yescharacteristic
39C2×C22⋊D29—21no—
40Q8×D29—21no—
41Q8×D29—21no—
42Q8×D29—21no—
43Q8×D29—21no—
44D4×D29—21no—
45D4×D29—21no—
46D4×D29D412yes—
47D4×D29D412yes—
48C2×D116C2×C411yescharacteristic
49C2×C4×D29—21no—
50C2×C4×D29C2311yescharacteristic
51C2×Dic58—21no—
52C2×Dic58C2×C411yescharacteristic, complemented
53C22⋊#1181—24no—
54C2×#6599—21no—
55C4⋊#1181—21no—
56C4⋊#1181—21no—
57C4⋊#1181—21no—
58C4⋊#1181D412yes—
59C4×#1181—21no—
60C4×#1181—21no—
61D29⋊C8—21no—
62D29⋊C8—21no—
63SD16×C29—22no—
64C2×C8×C29C2×C411yescharacteristic, complemented
65#90784—22no—
66#90783—22no—
67C2×#6597C2×C411yescharacteristic, complemented
68#90773—22no—
69C8×D29—21no—
70C8×D29—21no—
71C23×C29—21no—
72C22×D29—21no—
73C22×D29—22no—
74C22×D29—22no—
75C22×D29—41no—
76C22×D29—41no—
77C22×D29—41no—
78C22×D29—41no—
79C22×D29C2×D411yescharacteristic
80C2×#1181—21no—
81C2×#1181—21no—
82C2×#1181—21no—
83C2×#1181—22no—
84C2×#1181—21no—
85C2×#1181—21no—
86C2×#1181—48no—
87C2×#1181—41no—
88C2×#1181—41no—
89C2×#1181—41no—
90C2×#1181—41no—
91C2×#1181—41no—
92C2×#1181SD1612yescomplemented
93Q8×C29—21no—
94Q8×C29—21no—
95D4×C29—21no—
96D4×C29C22⋊C412yes—
97C2×C4×C29—21no—
98C2×C4×C29C22×C411yescharacteristic
99C22⋊D29—22no—
100C22⋊D29—22no—
101C2×Dic29—21no—
102C2×Dic29#4111yescharacteristic
103D116—21no—
104D116C22⋊C412yes—
105C4×D29—41no—
106C4×D29—41no—
107C4×D29C2×D411yescharacteristic
108C4×D29C2×D411yescharacteristic
109C4×D29C2×D411yescharacteristic
110C4×D29#4111yescharacteristic
111Dic58—21no—
112Dic58—21no—
113Dic58—41no—
114Dic58—41no—
115#6599—41no—
116C8×C29—21no—
117#6597—21no—
118#1877—291nomaximal, Sylow
119C22×C29—22no—
120C22×C29—41no—
121C22×C29—41no—
122C22×C29C4×D411yescharacteristic
123C2×D29—22no—
124C2×D29—41no—
125C2×D29—41no—
126C2×D29—42no—
127C2×D29—42no—
128C2×D29—42no—
129C2×D29—42no—
130C2×D29#12011yescharacteristic
131C2×D29#12111yescharacteristic
132C2×D29C2×SD1611yescharacteristic
133C2×D29#13511yescharacteristic
134C2×D29AGL(1,ℤ/8)11yescharacteristic
135C2×D29#13711yescharacteristic
136#1181—22no—
137#1181—42no—
138#1181—41no—
139#1181—81no—
140C4×C29—41no—
141C4×C29C2×C22⋊C411yescharacteristic
142C4×C29C4×D411yescharacteristic
143Dic29—41no—
144Dic29#12111yescharacteristic
145Dic29#12311yescharacteristic
146C22×SD16—291no—
147C2×C4×D4—291no—
148C2×#103—291no—
149C2×#102—291no—
150#391—291no—
151#340—291no—
152#336—291no—
153C2×C29—42no—
154C2×C29#38611yescharacteristic
155C2×C29C4×SD1611yescharacteristic
156C2×C29#44011yescharacteristic
157D29—42no—
158D29#45011yescharacteristic
159D29#45211yescharacteristic
160D29#46111yescharacteristic
161D29#46311yescharacteristic
162C22×Q8—291no—
163C22×D4—291no—
164C23×C4—581no—
165C2×SD16—291no—
166C2×SD16—291no—
167C2×SD16—291no—
168C2×SD16—582no—
169C2×SD16—582no—
170C2×SD16#118111yescharacteristic, complemented
171C22×C8—291no—
172C22×C8—291no—
173C4×D4—582no—
174C4×D4—582no—
175C2×C4⋊C4—291no—
176C2×C4⋊C4—291no—
177C2×C22⋊C4—581no—
178C2×C42—291no—
179#103—582no—
180#102—582no—
181#95—581no—
182#95—581no—
183C29#187711yescharacteristic, complemented, Sylow
184C24—581no—
185C2×Q8—291no—
186C2×Q8—581no—
187C2×Q8—581no—
188C2×Q8—581no—
189C2×Q8—581no—
190C2×Q8—581no—
191C2×Q8C2×#118111yescharacteristic, complemented
192C2×D4—292no—
193C2×D4—292no—
194C2×D4—291no—
195C2×D4—581no—
196C2×D4—581no—
197C2×D4—581no—
198C2×D4C2×#118111yescharacteristic
199C22×C4—291no—
200C22×C4—291no—
201C22×C4—291no—
202C22×C4—581no—
203C22×C4—581no—
204C22×C4—584no—
205C22×C4—581no—
206C22×C4—1162no—
207C22×C4—1162no—
208SD16—22no—
209SD16—582no—
210SD16—582no—
211SD16—582no—
212C2×C8—291no—
213C2×C8—581no—
214C2×C8—581no—
215C2×C8—581no—
216C2×C8—581no—
217C2×C8—581no—
218C2×C8C2×#118111yescharacteristic, complemented
219C4⋊C4—292no—
220C4⋊C4—581no—
221C4⋊C4—581no—
222C4⋊C4—581no—
223C22⋊C4—584no—
224C42—581no—
225C42—581no—
226C23—21no—
227C23—291no—
228C23—582no—
229C23—582no—
230C23—581no—
231C23—1161no—
232C23—1161no—
233C23—1161no—
234C23—1161no—
235Q8—21no—
236Q8—21no—
237Q8—581no—
238Q8—581no—
239Q8—1161no—
240Q8—1161no—
241D4—21no—
242D4—292no—
243D4—582no—
244D4—582no—
245D4—581no—
246D4C22⋊#118112yes—
247C2×C4—21no—
248C2×C4—291no—
249C2×C4—291no—
250C2×C4—291no—
251C2×C4—291no—
252C2×C4—291no—
253C2×C4—292no—
254C2×C4—581no—
255C2×C4—581no—
256C2×C4—581no—
257C2×C4—582no—
258C2×C4—581no—
259C2×C4—581no—
260C2×C4—581no—
261C2×C4—1161no—
262C2×C4—1161no—
263C2×C4—1168no—
264C2×C4—1161no—
265C2×C4—1161no—
266C2×C4—1161no—
267C2×C4—1161no—
268C2×C4—1161no—
269C2×C4C22×#118111yescharacteristic
270C8—21no—
271C8—581no—
272C8—1161no—
273C22—22no—
274C22—41no—
275C22—41no—
276C22—291no—
277C22—291no—
278C22—291no—
279C22—291no—
280C22—291no—
281C22—291no—
282C22—582no—
283C22—1162no—
284C22—1162no—
285C22—1162no—
286C22—1162no—
287C22—1161no—
288C22—1161no—
289C22D4×#118111yescharacteristic
290C4—41no—
291C4—291no—
292C4—291no—
293C4—582no—
294C4—1161no—
295C4—1162no—
296C4—1161no—
297C4—2321no—
298C4D4×#118111yescharacteristic
299C4C2×C22⋊#118111yescharacteristic
300C2—42no—
301C2—291no—
302C2—291no—
303C2—291no—
304C2—291no—
305C2—1162no—
306C2#1427211111yescharacteristic
307C2SD16×#118111yescharacteristic
308C2#1427220211yescharacteristic
subgroupG/H
centerC22D4×#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC2×SD16×C29C4
socleC22×C29C4×D4
prime radicalC2×D4×D29C22
cosocleC2×C4×D29C23
hypercenterC2×SD16#1181
hypocenterC29#1877
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#11745225C2semidirect
4. (C2×#1181)⋊Q8C2semidirect
5. #14272037C2semidirect
6. (C2×#1181)⋊C8C2semidirect
18. C2×SD16×C29C4semidirect
19. C2×#90784C4semidirect
20. C2×#90783C4semidirect
23. C2×#90773C4semidirect
37. C2×Q8×C29C2×C4semidirect
52. C2×Dic58C2×C4semidirect
64. C2×C8×C29C2×C4semidirect
67. C2×#6597C2×C4semidirect
92. C2×#1181SD16semidirect
170. C2×SD16#1181semidirect
183. C29#1877semidirect
191. C2×Q8C2×#1181semidirect
218. C2×C8C2×#1181semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#11812
C2×#117452252
C2×#117452232
(C2×#1181)⋊Q82
#142720372
(C2×#1181)⋊C82
C2×SD16×D292
#187729