Finite Group Databasebeta

← #17995726

Subgroups — #17995726

Order 4736.

430 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 73 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
1#14558092C211yesmaximal, characteristic
2C2×#11924520C211yesmaximal, characteristic, complemented
3C2×#11924517C211yesmaximal, characteristic, complemented
4C2×#11924450C211yesmaximal, characteristic, complemented
5#14557394C211yesmaximal, characteristic, complemented
6#14557299C211yesmaximal, characteristic, complemented
7C2×#99×C37C211yesmaximal, characteristic, complemented
8C22×C22⋊D37C2211yescharacteristic
9C23×Dic37C2211yescharacteristic
10#11924520—22no—
11#11924520—22no—
12#11924519—21no—
13#11924517—21no—
14#11924517—22no—
15#11924517—22no—
16#11924508—22no—
17#11924505—21no—
18#11924504—21no—
19C2×C4⋊Dic37—21no—
20C2×#10596936—21no—
21C2×C22⋊Dic37—21no—
22C2×C22⋊Dic37C2211yescharacteristic
23C2×C22⋊Dic37C2211yescharacteristic
24C2×#10596938—21no—
25#11924450—22no—
26#11924443—22no—
27C22×D4×C37C2211yescharacteristic
28C2×C22⋊C4×C37C2211yescharacteristic
29C2×C22⋊C4×C37C2211yescharacteristic
30#99×C37—22no—
31C24×C37D411yescharacteristic
32C24×C37C2311yescharacteristic
33C23×D37D411yescharacteristic
34C2×D4×C37—21no—
35C2×D4×C37—21no—
36C2×D4×C37—21no—
37C2×D4×C37—21no—
38C2×D4×C37—21no—
39C2×D4×C37—21no—
40C22×C4×C37—21no—
41C22×C4×C37—21no—
42C22×C4×C37D411yescharacteristic
43C2×C22⋊D37—21no—
44C2×C22⋊D37—21no—
45C2×C22⋊D37—21no—
46C2×C22⋊D37—21no—
47C2×C22⋊D37—21no—
48C2×C22⋊D37—21no—
49C2×C22⋊D37—22no—
50C22×Dic37—21no—
51C22×Dic37—21no—
52C22×Dic37—21no—
53C22×Dic37—21no—
54C22×Dic37—21no—
55C22×Dic37—21no—
56C22×Dic37—21no—
57C22×Dic37D411yescharacteristic
58C22×Dic37D412yes—
59C22×Dic37D412yescomplemented
60C22⋊C4×C37—21no—
61C22⋊C4×C37—21no—
62C22⋊C4×C37—21no—
63C22⋊C4×C37D412yescomplemented
64C22⋊Dic37—24no—
65C22⋊Dic37—22no—
66C22⋊Dic37—21no—
67C22⋊Dic37—21no—
68C22⋊Dic37—21no—
69C22⋊Dic37D412yescomplemented
70#10596938—24no—
71#10596938—22no—
72C4⋊Dic37—24no—
73#10596936—24no—
74#10596936—22no—
75C23×C37—21no—
76C23×C37—21no—
77C23×C37—21no—
78C23×C37—42no—
79C23×C37—42no—
80C23×C37C2×D411yescharacteristic
81C23×C37C2×D411yescharacteristic
82C23×C37C2×D411yescharacteristic
83C23×C37C2×D411yescharacteristic
84C23×C37C2×D411yescharacteristic
85C23×C37C2×D411yescharacteristic
86C23×C37#4111yescharacteristic
87C22×D37—21no—
88C22×D37—21no—
89C22×D37—21no—
90C22×D37—42no—
91D4×C37—41no—
92D4×C37—41no—
93D4×C37—41no—
94D4×C37—41no—
95C2×C4×C37—21no—
96C2×C4×C37—21no—
97C2×C4×C37—22no—
98C2×C4×C37—21no—
99C2×C4×C37—42no—
100C2×C4×C37—42no—
101C2×C4×C37—41no—
102C22⋊D37—41no—
103C22⋊D37—41no—
104C22⋊D37—41no—
105C22⋊D37—41no—
106C22⋊D37—82no—
107C2×Dic37—22no—
108C2×Dic37—22no—
109C2×Dic37—21no—
110C2×Dic37—22no—
111C2×Dic37—21no—
112C2×Dic37—22no—
113C2×Dic37—22no—
114C2×Dic37—21no—
115C2×Dic37—42no—
116C2×Dic37—41no—
117C2×Dic37—41no—
118C2×Dic37—41no—
119C2×Dic37—41no—
120C2×Dic37—42no—
121C22×C37—22no—
122C22×C37—22no—
123C22×C37—22no—
124C22×C37—41no—
125C22×C37—41no—
126C22×C37—41no—
127C22×C37—41no—
128C22×C37—42no—
129C22×C37—41no—
130C22×C37—42no—
131C22×C37—81no—
132C22×C37#12011yescharacteristic
133C22×C37#12011yescharacteristic
134C22×C37#12011yescharacteristic
135C22×C37#12111yescharacteristic
136C22×C37#12111yescharacteristic
137C22×C37#12111yescharacteristic
138C22×C37#12711yescharacteristic
139C2×D37—42no—
140C2×D37—41no—
141C2×D37—42no—
142C2×D37—81no—
143C4×C37—42no—
144C4×C37—41no—
145C4×C37—81no—
146Dic37—42no—
147Dic37—42no—
148Dic37—41no—
149Dic37—42no—
150#2022—371nomaximal, Sylow
151C2×C37—21no—
152C2×C37—21no—
153C2×C37—21no—
154C2×C37—21no—
155C2×C37—21no—
156C2×C37—21no—
157C2×C37—81no—
158C2×C37#39211yescharacteristic
159C2×C37#45812yes—
160D37—81no—
161#534—371no—
162C2×#123—371no—
163C2×#123—371no—
164C2×#99—371no—
165C2×#99D3711yescharacteristic, complemented
166#381—371no—
167#342—371no—
168C37#202211yescharacteristic, complemented, Sylow
169C22×D4—371no—
170C22×D4C2×D3711yescharacteristic
171C23×C4—371no—
172#123—742no—
173#123—742no—
174#123—742no—
175#123—741no—
176#123—741no—
177#123—742no—
178#121—742no—
179#120—741no—
180#120—741no—
181C2×C4⋊C4—741no—
182C2×C4⋊C4—741no—
183C2×C22⋊C4—371no—
184C2×C22⋊C4—371no—
185C2×C22⋊C4—741no—
186C2×C22⋊C4—741no—
187C2×C22⋊C4C2×D3711yescharacteristic
188C2×C22⋊C4C2×D3711yescharacteristic
189#99—22no—
190#99—742no—
191#95—742no—
192C24—371no—
193C24D14811yescharacteristic
194C24C22×D3711yescharacteristic
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—742no—
202C2×D4—741no—
203C2×D4—741no—
204C2×D4—741no—
205C2×D4—741no—
206C2×D4—741no—
207C2×D4—741no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—371no—
211C22×C4—372no—
212C22×C4—372no—
213C22×C4—741no—
214C22×C4—741no—
215C22×C4—741no—
216C22×C4—741no—
217C22×C4—741no—
218C22×C4—741no—
219C22×C4—741no—
220C22×C4D14811yescharacteristic
221C4⋊C4—744no—
222C4⋊C4—742no—
223C4⋊C4—744no—
224C22⋊C4—21no—
225C22⋊C4—21no—
226C22⋊C4—21no—
227C22⋊C4—372no—
228C22⋊C4—744no—
229C22⋊C4—742no—
230C22⋊C4—744no—
231C22⋊C4—742no—
232C22⋊C4—741no—
233C22⋊C4—741no—
234C22⋊C4—741no—
235C22⋊C4C22⋊D3712yescomplemented
236C23—21no—
237C23—21no—
238C23—21no—
239C23—42no—
240C23—42no—
241C23—741no—
242C23—741no—
243C23—741no—
244C23—1482no—
245C23C2×D14811yescharacteristic
246C23#1059696211yescharacteristic
247C23D4×D3711yescharacteristic
248C23D4×D3711yescharacteristic
249C23D4×D3711yescharacteristic
250C23D4×D3711yescharacteristic
251C23C2×C22⋊D3711yescharacteristic
252D4—41no—
253D4—41no—
254D4—41no—
255D4—41no—
256D4—2962no—
257D4—1481no—
258D4—1481no—
259D4—1481no—
260D4—1481no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—742no—
269C2×C4—741no—
270C2×C4—742no—
271C2×C4—742no—
272C2×C4—742no—
273C2×C4—741no—
274C2×C4—742no—
275C2×C4—741no—
276C2×C4—1482no—
277C2×C4—1481no—
278C2×C4—1481no—
279C2×C4—1481no—
280C2×C4—1481no—
281C2×C4—1482no—
282C22—22no—
283C22—22no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—41no—
291C22—42no—
292C22—81no—
293C22—2961no—
294C22—1482no—
295C22—1481no—
296C22—1482no—
297C22#1192450411yescharacteristic
298C22#1192450611yescharacteristic
299C22#1192450611yescharacteristic
300C22#1192450911yescharacteristic
301C22#1192450911yescharacteristic
302C22#1192451011yescharacteristic
303C22#1192453211yescharacteristic
304C4—42no—
305C4—41no—
306C4—81no—
307C4—1482no—
308C4—1482no—
309C4—1481no—
310C4—1482no—
311C2—21no—
312C2—21no—
313C2—21no—
314C2—21no—
315C2—21no—
316C2—21no—
317C2—81no—
318C2—2961no—
319C2#1455744211yescharacteristic
320C2#1455772412yes—
subgroupG/H
centerC22#11924506
commutator, cosocleC24×C37C23
FrattiniC24C22×D37
FittingC2×#99×C37C2
socleC22×C37#120
prime radical#14558092C2
hypercenterC2×#99D37
hypocenterC37#2022
LCSG ▷ C24×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#11924520C2semidirect
3. C2×#11924517C2semidirect
4. C2×#11924450C2semidirect
5. #14557394C2semidirect
6. #14557299C2semidirect
7. C2×#99×C37C2semidirect
59. C22×Dic37D4semidirect
63. C22⋊C4×C37D4semidirect
69. C22⋊Dic37D4semidirect
165. C2×#99D37semidirect
168. C37#2022semidirect
235. C22⋊C4C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145580922
C2×#119245202
C2×#119245172
C2×#119244502
#145573942
#145572992
C2×#99×C372
#202237