Finite Group Databasebeta

← #18010438

Subgroups — #18010438

Order 4736.

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

normal subgroups only

This group has 618 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
1C2×#11924601C212yesmaximal, complemented
2C2×#11924600C212yesmaximal, complemented
3#14558504C211yesmaximal, characteristic, complemented
4C4×C22⋊#3866C211yesmaximal, characteristic, complemented
5C2×#41×D37C211yesmaximal, characteristic
6C2×#10596953C2212yescomplemented
7C2×C22⋊#3866—21no—
8C2×C4×#3866C2212yescomplemented
9#11924601—24no—
10#11924600—24no—
11#11924593—21no—
12C22⋊#64438—21no—
13(C2×#3866)⋊C4—21no—
14C2×#10596966C2211yescharacteristic
15C2×#10596962—21no—
16C2×#10596962C411yescharacteristic, complemented
17C2×#10596964—21no—
18C2×#10596964C2211yescharacteristic
19#41×D37—24no—
20#41×D37—24no—
21C2×Q8×D37C411yescharacteristic, complemented
22C2×D4×D37—21no—
23C2×D4×D37C411yescharacteristic, complemented
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#10596966D414yes—
44Q8×D37—22no—
45Q8×D37—22no—
46#10596964—28no—
47#10596964—22no—
48#10596964D414yes—
49D4×D37—28no—
50D4×D37—22no—
51D4×D37—22no—
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—24no—
70C2×#64438—22no—
71C4×#3866—22no—
72C4×#3866—22no—
73#10596953—22no—
74#10596953—22no—
75C23×C37—21no—
76C23×C37C22⋊C411yescharacteristic
77C22×D37—24no—
78C22×D37—21no—
79C22×D37—22no—
80C22×D37—22no—
81C22×D37—41no—
82C22×D37—42no—
83C22×D37—42no—
84C22×D37C22⋊C411yescharacteristic
85C22×D37C2×D411yescharacteristic
86C2×#3866—24no—
87C2×#3866—42no—
88C2×#3866—42no—
89Q8×C37—21no—
90Q8×C37C22⋊C412yescomplemented
91D4×C37—24no—
92D4×C37—21no—
93D4×C37C22⋊C412yescomplemented
94C2×C4×C37—24no—
95C2×C4×C37—21no—
96C2×C4×C37—21no—
97C2×C4×C37—21no—
98C2×C4×C37C22⋊C411yescharacteristic
99C2×C4×C37C22×C411yescharacteristic
100C22⋊D37—24no—
101C22⋊D37—24no—
102C22⋊D37—24no—
103C2×Dic37—21no—
104C2×Dic37—22no—
105C2×Dic37—24no—
106C2×Dic37C22⋊C411yescharacteristic
107C2×Dic37C2×D411yescharacteristic
108D148—24no—
109D148—21no—
110D148C22⋊C412yescomplemented
111C4×D37—24no—
112C4×D37—24no—
113C4×D37—22no—
114C4×D37—21no—
115C4×D37—21no—
116C4×D37—22no—
117C4×D37—24no—
118C4×D37C2×D412yes—
119C4×D37C2×D412yes—
120Dic74—24no—
121Dic74—21no—
122Dic74C22⋊C412yescomplemented
123#64438—42no—
124C22×C37—21no—
125C22×C37—22no—
126C22×C37—21no—
127C22×C37—21no—
128C22×C37—41no—
129C22×C37—41no—
130C22×C37C2×C22⋊C411yescharacteristic
131C2×D37—21no—
132C2×D37—21no—
133C2×D37—21no—
134C2×D37—21no—
135C2×D37—22no—
136C2×D37—44no—
137C2×D37—48no—
138C2×D37—41no—
139C2×D37—41no—
140C2×D37#10412yescomplemented
141C2×D37#12012yes—
142#3866—44no—
143C4×C37—22no—
144C4×C37—21no—
145C4×C37C2×C22⋊C411yescharacteristic
146C4×C37C2×C22⋊C411yescharacteristic
147Dic37—21no—
148Dic37—22no—
149Dic37#12012yes—
150#1789—371nomaximal, Sylow
151C2×C37—41no—
152C2×C37—42no—
153C2×C37#37911yescharacteristic
154C2×C37C2×#10411yescharacteristic
155C2×C37#42111yescharacteristic
156D37—22no—
157D37—22no—
158D37—42no—
159C22×#41—371no—
160C2×#104—372no—
161C2×#104—372no—
162#407—371no—
163C4×C22⋊C4—371no—
164C37#178911yescharacteristic, complemented, Sylow
165C2×#41—371no—
166C2×#41—371no—
167C2×#41—371no—
168C2×#41—741no—
169C2×#41—741no—
170C2×#41—744no—
171C2×#41—744no—
172C2×#41#386611yescharacteristic, complemented
173C22×Q8—371no—
174C22×D4—371no—
175C22×D4—741no—
176C23×C4—371no—
177C23×C4—741no—
178C2×M16—372no—
179C2×C22⋊C4—741no—
180C2×C42—372no—
181#104—744no—
182#104—744no—
183C22⋊C8—741no—
184C22⋊C8—741no—
185#95—741no—
186C24—371no—
187C24—741no—
188#41—22no—
189#41—22no—
190#41—374no—
191#41—374no—
192#41—742no—
193#41—742no—
194#41—748no—
195#41—742no—
196#41—742no—
197#41—748no—
198C2×Q8—371no—
199C2×Q8—741no—
200C2×Q8—742no—
201C2×Q8—742no—
202C2×Q8C2×#386611yescharacteristic
203C2×D4—21no—
204C2×D4—371no—
205C2×D4—741no—
206C2×D4—741no—
207C2×D4—742no—
208C2×D4—748no—
209C2×D4—741no—
210C2×D4—741no—
211C2×D4—742no—
212C2×D4C2×#386611yescharacteristic
213C22×C4—21no—
214C22×C4—371no—
215C22×C4—371no—
216C22×C4—371no—
217C22×C4—371no—
218C22×C4—371no—
219C22×C4—742no—
220C22×C4—742no—
221C22×C4—741no—
222C22×C4—741no—
223C22×C4—748no—
224C22×C4—741no—
225C22×C4—741no—
226C22×C4—742no—
227C22×C4C2×#386611yescharacteristic
228M16—742no—
229M16—742no—
230C2×C8—742no—
231C22⋊C4—744no—
232C42—742no—
233C42—742no—
234C23—21no—
235C23—371no—
236C23—371no—
237C23—742no—
238C23—742no—
239C23—744no—
240C23—741no—
241C23—1481no—
242C23—1482no—
243C23—1482no—
244C23C22⋊#386611yescharacteristic
245Q8—21no—
246Q8—372no—
247Q8—744no—
248Q8—741no—
249Q8C22⋊#386612yescomplemented
250D4—24no—
251D4—21no—
252D4—372no—
253D4—744no—
254D4—744no—
255D4—744no—
256D4—744no—
257D4—741no—
258D4C22⋊#386612yescomplemented
259C2×C4—24no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—371no—
264C2×C4—372no—
265C2×C4—372no—
266C2×C4—371no—
267C2×C4—742no—
268C2×C4—744no—
269C2×C4—742no—
270C2×C4—744no—
271C2×C4—744no—
272C2×C4—742no—
273C2×C4—744no—
274C2×C4—741no—
275C2×C4—741no—
276C2×C4—741no—
277C2×C4—744no—
278C2×C4—1482no—
279C2×C4—1482no—
280C2×C4C22⋊#386611yescharacteristic
281C2×C4C22×#386611yescharacteristic
282C8—1482no—
283C22—21no—
284C22—22no—
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—372no—
290C22—372no—
291C22—741no—
292C22—741no—
293C22—741no—
294C22—741no—
295C22—742no—
296C22—1484no—
297C22—1488no—
298C22—1481no—
299C22—1481no—
300C22C2×C22⋊#386611yescharacteristic
301C4—21no—
302C4—22no—
303C4—372no—
304C4—741no—
305C4—742no—
306C4—1484no—
307C4C2×C22⋊#386611yescharacteristic
308C4C2×C22⋊#386611yescharacteristic
309C2—41no—
310C2—42no—
311C2—742no—
312C2—742no—
313C2—1482no—
314C2#1455847411yescharacteristic
315C2D37⋊#10411yescharacteristic
316C2#1455853011yescharacteristic
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#1789
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×#11924601C2semidirect
2. C2×#11924600C2semidirect
3. #14558504C2semidirect
4. C4×C22⋊#3866C2semidirect
6. C2×#10596953C22semidirect
8. C2×C4×#3866C22semidirect
16. C2×#10596962C4semidirect
21. C2×Q8×D37C4semidirect
23. C2×D4×D37C4semidirect
26. C2×#41×C37C4semidirect
90. Q8×C37C22⋊C4semidirect
93. D4×C37C22⋊C4semidirect
110. D148C22⋊C4semidirect
122. Dic74C22⋊C4semidirect
140. C2×D37#104semidirect
164. C37#1789semidirect
172. C2×#41#3866semidirect
249. Q8C22⋊#3866semidirect
258. D4C22⋊#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119246012
C2×#119246002
#145585042
C4×C22⋊#38662
C2×#41×D372
#178937