Finite Group Databasebeta

← #18010436

Subgroups — #18010436

Order 4736.

612 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 94 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×#11924599C212yesmaximal, complemented
2C2×#11924598C212yesmaximal, complemented
3D37⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
4#14558475C211yesmaximal, characteristic, complemented
5C2×#41×D37C211yesmaximal, characteristic
6C2×D37⋊C8C2212yes—
7C2×C4⋊#3866C2212yes—
8C2×C22⋊#3866—21no—
9#11924599—24no—
10#11924598—24no—
11#11924593—21no—
12C22⋊#64438—21no—
13(C2×#3866)⋊C4—21no—
14C2×#10596966C411yescharacteristic, complemented
15C2×#10596962—21no—
16C2×#10596962C411yescharacteristic, complemented
17C2×#10596964—21no—
18C2×#10596964C411yescharacteristic, complemented
19#41×D37—24no—
20#41×D37—24no—
21C2×Q8×D37C2211yescharacteristic
22C2×D4×D37—21no—
23C2×D4×D37C2211yescharacteristic
24C22×C4×D37—21no—
25C22×C4×D37C2211yescharacteristic
26C2×#41×C37C411yescharacteristic, complemented
27C23×D37—21no—
28C23×D37D411yescharacteristic
29C22×#3866—22no—
30#41×C37—22no—
31#41×C37—22no—
32C2×Q8×C37C2×C411yescharacteristic
33C2×D4×C37—21no—
34C2×D4×C37C2×C411yescharacteristic
35C22×C4×C37—21no—
36C22×C4×C37C2×C411yescharacteristic
37C2×C22⋊D37—21no—
38C2×C22⋊D37—21no—
39C2×C22⋊D37—21no—
40C22×Dic37—21no—
41C22×Dic37D411yescharacteristic
42#10596966—22no—
43#10596966—22no—
44Q8×D37—22no—
45Q8×D37D414yes—
46#10596964—28no—
47#10596964—22no—
48#10596964—22no—
49D4×D37—28no—
50D4×D37—22no—
51D4×D37D414yes—
52#10596962—28no—
53#10596962—22no—
54#10596962—22no—
55C2×D148—21no—
56C2×D148C2×C411yescharacteristic
57C2×C4×D37—28no—
58C2×C4×D37—21no—
59C2×C4×D37—21no—
60C2×C4×D37—21no—
61C2×C4×D37—22no—
62C2×C4×D37—22no—
63C2×C4×D37C2×C411yescharacteristic
64C2×C4×D37D411yescharacteristic
65C2×C4×D37D411yescharacteristic
66C2×C4×D37C2311yescharacteristic
67C2×Dic74—21no—
68C2×Dic74C2×C411yescharacteristic
69C22⋊#3866—42no—
70C2×#64438—22no—
71C4⋊#3866—22no—
72C4⋊#3866—22no—
73D37⋊C8—22no—
74D37⋊C8—22no—
75C23×C37—21no—
76C23×C37C22⋊C411yescharacteristic
77C22×D37—21no—
78C22×D37—22no—
79C22×D37—24no—
80C22×D37—22no—
81C22×D37—21no—
82C22×D37—21no—
83C22×D37—42no—
84C22×D37—41no—
85C22×D37—41no—
86C22×D37C22⋊C411yescharacteristic
87C22×D37C2×D411yescharacteristic
88C2×#3866—42no—
89C2×#3866—42no—
90C2×#3866—42no—
91Q8×C37—21no—
92Q8×C37C22⋊C412yescomplemented
93D4×C37—24no—
94D4×C37—21no—
95D4×C37C22⋊C412yescomplemented
96C2×C4×C37—24no—
97C2×C4×C37—21no—
98C2×C4×C37—21no—
99C2×C4×C37—21no—
100C2×C4×C37C22⋊C411yescharacteristic
101C2×C4×C37C22×C411yescharacteristic
102C22⋊D37—24no—
103C22⋊D37—24no—
104C22⋊D37—24no—
105C2×Dic37—24no—
106C2×Dic37—21no—
107C2×Dic37—22no—
108C2×Dic37C22⋊C411yescharacteristic
109C2×Dic37C2×D411yescharacteristic
110D148—24no—
111D148—21no—
112D148C22⋊C412yescomplemented
113C4×D37—24no—
114C4×D37—24no—
115C4×D37—22no—
116C4×D37—24no—
117C4×D37—21no—
118C4×D37—21no—
119C4×D37—22no—
120C4×D37C2×D412yes—
121C4×D37C2×D412yes—
122Dic74—21no—
123Dic74—24no—
124Dic74C22⋊C412yescomplemented
125#64438—42no—
126C22×C37—21no—
127C22×C37—22no—
128C22×C37—21no—
129C22×C37—21no—
130C22×C37—41no—
131C22×C37—41no—
132C22×C37C2×C22⋊C411yescharacteristic
133C2×D37—21no—
134C2×D37—22no—
135C2×D37—21no—
136C2×D37—21no—
137C2×D37—41no—
138C2×D37—41no—
139C2×D37—42no—
140C2×D37—44no—
141C2×D37—42no—
142C2×D37—44no—
143C2×D37#12012yes—
144C2×D37#13512yes—
145C2×D37AGL(1,ℤ/8)11yescharacteristic
146C2×D37#13711yescharacteristic
147#3866—82no—
148C4×C37—22no—
149C4×C37—21no—
150C4×C37C2×C22⋊C411yescharacteristic
151C4×C37C2×C22⋊C411yescharacteristic
152Dic37—22no—
153Dic37—21no—
154Dic37#12012yes—
155#1788—371nomaximal, Sylow
156C2×C37—41no—
157C2×C37—42no—
158C2×C37#37911yescharacteristic
159C2×C37#41611yescharacteristic
160C2×C37#41711yescharacteristic
161D37—41no—
162D37—42no—
163D37#44912yes—
164D37#45212yes—
165C22×#41—371no—
166C2×#103—372no—
167C2×#102—372no—
168C2×C22⋊C8—371no—
169#380—371no—
170C37#178811yescharacteristic, complemented, Sylow
171C2×#41—371no—
172C2×#41—371no—
173C2×#41—371no—
174C2×#41—741no—
175C2×#41—741no—
176C2×#41—744no—
177C2×#41—744no—
178C2×#41#386611yescharacteristic, complemented
179C22×Q8—371no—
180C22×D4—371no—
181C22×D4—741no—
182C23×C4—371no—
183C23×C4—741no—
184C22×C8—372no—
185C2×C4⋊C4—372no—
186C2×C22⋊C4—741no—
187#103—744no—
188#102—744no—
189C22⋊C8—741no—
190C22⋊C8—741no—
191#95—741no—
192C24—371no—
193C24—741no—
194#41—22no—
195#41—22no—
196#41—742no—
197#41—742no—
198#41—748no—
199#41—742no—
200#41—748no—
201#41—742no—
202#41—742no—
203#41—742no—
204C2×Q8—374no—
205C2×Q8—371no—
206C2×Q8—741no—
207C2×Q8—742no—
208C2×Q8C2×#386611yescharacteristic
209C2×D4—21no—
210C2×D4—374no—
211C2×D4—371no—
212C2×D4—741no—
213C2×D4—742no—
214C2×D4—741no—
215C2×D4—748no—
216C2×D4—741no—
217C2×D4—741no—
218C2×D4C2×#386611yescharacteristic
219C22×C4—21no—
220C22×C4—371no—
221C22×C4—371no—
222C22×C4—371no—
223C22×C4—371no—
224C22×C4—371no—
225C22×C4—742no—
226C22×C4—742no—
227C22×C4—741no—
228C22×C4—741no—
229C22×C4—748no—
230C22×C4—741no—
231C22×C4—741no—
232C22×C4—742no—
233C22×C4C2×#386611yescharacteristic
234C2×C8—742no—
235C2×C8—742no—
236C2×C8—742no—
237C4⋊C4—742no—
238C4⋊C4—742no—
239C22⋊C4—1482no—
240C23—21no—
241C23—371no—
242C23—371no—
243C23—741no—
244C23—744no—
245C23—742no—
246C23—742no—
247C23—741no—
248C23—741no—
249C23—1482no—
250C23—1481no—
251C23—1481no—
252C23C22⋊#386611yescharacteristic
253Q8—21no—
254Q8—372no—
255Q8—744no—
256Q8—741no—
257Q8C22⋊#386612yescomplemented
258D4—24no—
259D4—21no—
260D4—372no—
261D4—744no—
262D4—744no—
263D4—744no—
264D4—744no—
265D4—741no—
266D4C22⋊#386612yescomplemented
267C2×C4—24no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—371no—
272C2×C4—372no—
273C2×C4—372no—
274C2×C4—371no—
275C2×C4—742no—
276C2×C4—742no—
277C2×C4—744no—
278C2×C4—744no—
279C2×C4—744no—
280C2×C4—742no—
281C2×C4—744no—
282C2×C4—741no—
283C2×C4—741no—
284C2×C4—741no—
285C2×C4—1482no—
286C2×C4—1482no—
287C2×C4—1482no—
288C2×C4C22⋊#386611yescharacteristic
289C2×C4C22×#386611yescharacteristic
290C8—1482no—
291C22—21no—
292C22—22no—
293C22—21no—
294C22—21no—
295C22—41no—
296C22—41no—
297C22—372no—
298C22—372no—
299C22—371no—
300C22—371no—
301C22—742no—
302C22—741no—
303C22—741no—
304C22—741no—
305C22—1482no—
306C22—1482no—
307C22—1484no—
308C22—1484no—
309C22—1481no—
310C22—1481no—
311C22C2×C22⋊#386611yescharacteristic
312C4—21no—
313C4—22no—
314C4—372no—
315C4—2962no—
316C4—741no—
317C4—742no—
318C4C2×C22⋊#386611yescharacteristic
319C4C2×C22⋊#386611yescharacteristic
320C2—41no—
321C2—42no—
322C2—372no—
323C2—372no—
324C2—1481no—
325C2—1482no—
326C2#1455847411yescharacteristic
327C2#1455852311yescharacteristic
328C2#1455852411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×#41×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC2×#41×D37C2
cosocleC2×C4×D37C23
hypercenterC2×#41#3866
hypocenterC37#1788
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#11924599C2semidirect
2. C2×#11924598C2semidirect
3. D37⋊(C22⋊C8)C2semidirect
4. #14558475C2semidirect
14. C2×#10596966C4semidirect
16. C2×#10596962C4semidirect
18. C2×#10596964C4semidirect
26. C2×#41×C37C4semidirect
92. Q8×C37C22⋊C4semidirect
95. D4×C37C22⋊C4semidirect
112. D148C22⋊C4semidirect
124. Dic74C22⋊C4semidirect
170. C37#1788semidirect
178. C2×#41#3866semidirect
257. Q8C22⋊#3866semidirect
266. D4C22⋊#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119245992
C2×#119245982
D37⋊(C22⋊C8)2
#145584752
C2×#41×D372
#178837