Finite Group Databasebeta

← C2×D37⋊#99 #18011189

Subgroups — C2×D37⋊#99 #18011189

Order 4736.

1112 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 210 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×C22⋊#3866C212yesmaximal, complemented
2C2×#11924595C212yesmaximal, complemented
3D37⋊#99C218yesmaximal, direct product factor
4C2×#11924594C212yesmaximal, complemented
5C22×D4×D37C211yesmaximal, characteristic
6C23×#3866—22no—
7C2×C22⋊#3866—24no—
8C2×C22⋊#3866—22no—
9C2×C22⋊#3866C2214yescomplemented
10C2×C22⋊#3866C2218yescomplemented
11#11924595C2218yescomplemented
12#11924594C2218yescomplemented
13C24×D37C411yescharacteristic, complemented
14C24×D37C2211yescharacteristic
15C22×D148C2211yescharacteristic
16C22×C22⋊D37C411yescharacteristic, complemented
17C22×C22⋊D37C2211yescharacteristic
18C2×D4×D37—22no—
19C2×D4×D37—22no—
20C2×D4×D37—24no—
21C2×D4×D37C414yescomplemented
22C2×D4×D37C2214yes—
23C22×C4×D37C411yescharacteristic, complemented
24C22×D4×C37C411yescharacteristic, complemented
25C24×C37C2×C411yescharacteristic
26C24×C37C2×C411yescharacteristic, complemented
27C23×D37—22no—
28C23×D37—21no—
29C23×D37—21no—
30C23×D37—44no—
31C23×D37—44no—
32C23×D37C2×C411yescharacteristic
33C23×D37C2×C412yes—
34C23×D37C2×C414yescomplemented
35C23×D37C2×C411yescharacteristic, complemented
36C23×D37D412yes—
37C23×D37D414yes—
38C23×D37D412yes—
39C23×D37C2312yes—
40C23×D37C2311yescharacteristic
41C22×#3866—24no—
42C22×#3866—28no—
43C22×#3866—48no—
44C2×D4×C37—22no—
45C2×D4×C37—22no—
46C2×D4×C37C2×C414yescomplemented
47C22×C4×C37C2×C411yescharacteristic, complemented
48C2×C22⋊D37—22no—
49C2×C22⋊D37—22no—
50C2×C22⋊D37—22no—
51C2×C22⋊D37—22no—
52C2×C22⋊D37C2×C412yescomplemented
53C2×C22⋊D37C2×C414yescomplemented
54C2×C22⋊D37C2312yes—
55C22×Dic37C2×C411yescharacteristic, complemented
56D4×D37—28no—
57D4×D37—28no—
58D4×D37—28no—
59D4×D37—28no—
60C2×D148—22no—
61C2×D148—22no—
62C2×D148C2×C412yescomplemented
63C2×D148C2312yes—
64C2×C4×D37—22no—
65C2×C4×D37—21no—
66C2×C4×D37—21no—
67C2×C4×D37C2×C414yescomplemented
68C22⋊#3866—24no—
69C22⋊#3866—28no—
70C22⋊#3866C2318yescomplemented
71C23×C37—21no—
72C23×C37—21no—
73C23×C37—42no—
74C23×C37—42no—
75C23×C37C22⋊C412yes—
76C23×C37C22⋊C412yes—
77C23×C37C22×C411yescharacteristic
78C23×C37C22×C412yes—
79C23×C37C22×C412yescomplemented
80C22×D37—28no—
81C22×D37—24no—
82C22×D37—21no—
83C22×D37—21no—
84C22×D37—24no—
85C22×D37—24no—
86C22×D37—44no—
87C22×D37—48no—
88C22×D37—44no—
89C22×D37—44no—
90C22×D37—42no—
91C22×D37—44no—
92C22×D37—48no—
93C22×D37—48no—
94C22×D37—44no—
95C22×D37—42no—
96C22×D37C22⋊C412yes—
97C22×D37C22⋊C411yescharacteristic
98C22×D37C22⋊C414yes—
99C22×D37C22⋊C414yes—
100C22×D37C22⋊C411yescharacteristic
101C22×D37C22×C412yes—
102C22×D37C22×C411yescharacteristic
103C22×D37C22×C412yescomplemented
104C22×D37C2×D412yes—
105C22×D37C2×D414yes—
106C22×D37C2×D412yes—
107C22×D37C2×D414yes—
108C22×D37C2411yescharacteristic
109C2×#3866—28no—
110C2×#3866—48no—
111C2×#3866—416no—
112D4×C37—28no—
113C2×C4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37C22×C412yescomplemented
116C22⋊D37—28no—
117C22⋊D37—24no—
118C22⋊D37—24no—
119C2×Dic37—21no—
120C2×Dic37—21no—
121C2×Dic37C22×C412yescomplemented
122D148—24no—
123D148—24no—
124C4×D37—24no—
125C4×D37—24no—
126C22×C37—22no—
127C22×C37—24no—
128C22×C37—22no—
129C22×C37—42no—
130C22×C37—42no—
131C22×C37—42no—
132C22×C37—42no—
133C22×C37—42no—
134C22×C37C2×C22⋊C411yescharacteristic
135C22×C37C2×C22⋊C414yes—
136C22×C37C2×C22⋊C411yescharacteristic
137C22×C37C23×C411yescharacteristic
138C2×D37—24no—
139C2×D37—22no—
140C2×D37—28no—
141C2×D37—24no—
142C2×D37—24no—
143C2×D37—28no—
144C2×D37—22no—
145C2×D37—44no—
146C2×D37—41no—
147C2×D37—44no—
148C2×D37—42no—
149C2×D37—41no—
150C2×D37—48no—
151C2×D37—42no—
152C2×D37—42no—
153C2×D37—48no—
154C2×D37—42no—
155C2×D37#9914yescomplemented
156C2×D37C2×C22⋊C412yes—
157C2×D37C2×C22⋊C412yes—
158C2×D37C2×C22⋊C412yes—
159C2×D37C22×D412yes—
160#3866—48no—
161C4×C37—22no—
162Dic37—22no—
163C22×#99—371nomaximal, Sylow
164C2×C37—21no—
165C2×C37—21no—
166C2×C37—24no—
167C2×C37—42no—
168C2×C37C2×#9912yescomplemented
169C2×C37C22×C22⋊C411yescharacteristic
170D37—22no—
171D37—22no—
172D37—22no—
173D37—42no—
174D37C2×#9914yescomplemented
175C23×D4—371no—
176C22×C22⋊C4—372no—
177C2×#99—372no—
178C2×#99—378no—
179C2×#99—372no—
180C37C22×#9911yescharacteristic, complemented, Sylow
181C25—371no—
182C25—371no—
183C22×D4—371no—
184C22×D4—371no—
185C22×D4—374no—
186C22×D4—374no—
187C22×D4—371no—
188C22×D4—742no—
189C22×D4—744no—
190C22×D4—742no—
191C22×D4#386611yescharacteristic, complemented
192C23×C4—371no—
193C23×C4—742no—
194C2×C22⋊C4—374no—
195C2×C22⋊C4—378no—
196C2×C22⋊C4—744no—
197C2×C22⋊C4—742no—
198#99—378no—
199#99—378no—
200C24—372no—
201C24—371no—
202C24—374no—
203C24—372no—
204C24—372no—
205C24—372no—
206C24—371no—
207C24—371no—
208C24—374no—
209C24—742no—
210C24—741no—
211C24—741no—
212C24—1484no—
213C24—1484no—
214C24C2×#386611yescharacteristic
215C24C2×#386611yescharacteristic, complemented
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—374no—
219C2×D4—372no—
220C2×D4—372no—
221C2×D4—372no—
222C2×D4—372no—
223C2×D4—742no—
224C2×D4—742no—
225C2×D4—748no—
226C2×D4—748no—
227C2×D4—748no—
228C2×D4—748no—
229C2×D4—742no—
230C2×D4—742no—
231C2×D4—742no—
232C2×D4—742no—
233C2×D4C2×#386614yescomplemented
234C22×C4—371no—
235C22×C4—374no—
236C22×C4—742no—
237C22×C4—741no—
238C22×C4—741no—
239C22×C4—748no—
240C22×C4—744no—
241C22×C4—1488no—
242C22×C4C2×#386611yescharacteristic, complemented
243C22⋊C4—378no—
244C22⋊C4—748no—
245C22⋊C4—744no—
246C23—21no—
247C23—21no—
248C23—42no—
249C23—42no—
250C23—371no—
251C23—374no—
252C23—372no—
253C23—374no—
254C23—372no—
255C23—371no—
256C23—372no—
257C23—374no—
258C23—372no—
259C23—374no—
260C23—371no—
261C23—371no—
262C23—372no—
263C23—748no—
264C23—744no—
265C23—744no—
266C23—744no—
267C23—741no—
268C23—741no—
269C23—1482no—
270C23—1484no—
271C23—1482no—
272C23—1484no—
273C23—1488no—
274C23—1484no—
275C23—1484no—
276C23—1488no—
277C23—1488no—
278C23—1484no—
279C23C22⋊#386612yes—
280C23C22⋊#386612yes—
281C23C22×#386611yescharacteristic
282C23C22×#386612yes—
283C23C22×#386612yescomplemented
284D4—28no—
285D4—744no—
286D4—744no—
287D4—744no—
288D4—744no—
289D4—748no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—372no—
293C2×C4—744no—
294C2×C4—744no—
295C2×C4—741no—
296C2×C4—741no—
297C2×C4—748no—
298C2×C4—14816no—
299C2×C4—1488no—
300C2×C4C22×#386612yescomplemented
301C22—22no—
302C22—24no—
303C22—22no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—42no—
308C22—42no—
309C22—374no—
310C22—372no—
311C22—372no—
312C22—372no—
313C22—372no—
314C22—748no—
315C22—744no—
316C22—744no—
317C22—748no—
318C22—744no—
319C22—742no—
320C22—742no—
321C22—1482no—
322C22—1481no—
323C22—1481no—
324C22—1484no—
325C22—1484no—
326C22—1482no—
327C22—1482no—
328C22—1488no—
329C22—1488no—
330C22—1482no—
331C22C2×C22⋊#386611yescharacteristic
332C22C2×C22⋊#386614yes—
333C22C2×C22⋊#386611yescharacteristic
334C22C23×#386611yescharacteristic
335C4—22no—
336C4—742no—
337C4—1488no—
338C2—21no—
339C2—21no—
340C2—24no—
341C2—42no—
342C2—374no—
343C2—742no—
344C2—742no—
345C2—742no—
346C2—1482no—
347C2D37⋊#9912yesdirect product factor
348C2C22×C22⋊#386611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC22×C37C23×C4
FrattiniC22C23×#3866
FittingC22×D4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D4×D37C2
cosocleC22×D37C24
hypercenterC22×D4#3866
hypocenterC37C22×#99
LCSG ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊#3866C2semidirect
2. C2×#11924595C2semidirect
3. D37⋊#99C2direct (N × H)
4. C2×#11924594C2semidirect
9. C2×C22⋊#3866C22semidirect
10. C2×C22⋊#3866C22semidirect
11. #11924595C22semidirect
12. #11924594C22semidirect
13. C24×D37C4semidirect
16. C22×C22⋊D37C4semidirect
21. C2×D4×D37C4semidirect
23. C22×C4×D37C4semidirect
24. C22×D4×C37C4semidirect
26. C24×C37C2×C4semidirect
34. C23×D37C2×C4semidirect
35. C23×D37C2×C4semidirect
46. C2×D4×C37C2×C4semidirect
47. C22×C4×C37C2×C4semidirect
52. C2×C22⋊D37C2×C4semidirect
53. C2×C22⋊D37C2×C4semidirect
55. C22×Dic37C2×C4semidirect
62. C2×D148C2×C4semidirect
67. C2×C4×D37C2×C4semidirect
70. C22⋊#3866C23semidirect
79. C23×C37C22×C4semidirect
103. C22×D37C22×C4semidirect
115. C2×C4×C37C22×C4semidirect
121. C2×Dic37C22×C4semidirect
155. C2×D37#99semidirect
168. C2×C37C2×#99semidirect
174. D37C2×#99semidirect
180. C37C22×#99semidirect
191. C22×D4#3866semidirect
215. C24C2×#3866semidirect
233. C2×D4C2×#3866semidirect
242. C22×C4C2×#3866semidirect
283. C23C22×#3866semidirect
300. C2×C4C22×#3866semidirect
347. C2D37⋊#99direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊#38662
C2×#119245952
D37⋊#992
C2×#119245942
C22×D4×D372
C22×#9937