Finite Group Databasebeta

← #18010636

Subgroups — #18010636

Order 4736.

312 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 68 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
1D37⋊#131C211yesmaximal, characteristic
2#14558524C211yesmaximal, characteristic
3C2×#11924599C211yesmaximal, characteristic, complemented
4D37⋊#101C211yesmaximal, characteristic, complemented
5#14558412C211yesmaximal, characteristic, complemented
6#14558408C211yesmaximal, characteristic, complemented
7#137×D37C211yesmaximal, characteristic
8#11924624—21no—
9#11924623—21no—
10#11924623—22no—
11D37⋊M16—21no—
12D37⋊M16C2211yescharacteristic
13D37⋊M16C2211yescharacteristic
14C2×D37⋊C8—21no—
15C2×D37⋊C8C2211yescharacteristic
16C2×C4⋊#3866C2211yescharacteristic
17#11924599—21no—
18#11924599—21no—
19#11924599—21no—
20#11924598—21no—
21#11924597—22no—
22#41×D37C2211yescharacteristic
23C2×Q8×D37C2211yescharacteristic
24#11924569C411yescharacteristic, complemented
25#11924568—21no—
26#11924567C411yescharacteristic, complemented
27#11924566C411yescharacteristic, complemented
28#11924565—21no—
29Q16×D37—21no—
30SD16×D37—21no—
31M16×D37C2211yescharacteristic
32#137×C37C411yescharacteristic, complemented
33C22×#3866—21no—
34#41×C37C2×C411yescharacteristic
35C2×Q8×C37C2×C411yescharacteristic
36#10596966D411yescharacteristic
37Q8×D37—21no—
38Q8×D37—21no—
39Q8×D37—21no—
40Q8×D37—21no—
41Q8×D37D411yescharacteristic
42#10596964—21no—
43#10596964D411yescharacteristic
44D4×D37—21no—
45D4×D37D411yescharacteristic
46#10596962—21no—
47#10596962C2×C411yescharacteristic
48C2×C4×D37—21no—
49C2×C4×D37—21no—
50C2×C4×D37C2311yescharacteristic
51C2×Dic74—21no—
52C2×Dic74C2×C411yescharacteristic
53#10596957—22no—
54#10596957—21no—
55#10596957D412yes—
56C2×#64438—22no—
57C2×#64438—21no—
58C4⋊#3866—21no—
59C4⋊#3866—21no—
60#10596953—22no—
61#10596953—21no—
62#10596953—21no—
63D37⋊C8—22no—
64D37⋊C8—21no—
65D37⋊C8—21no—
66D37⋊C8—21no—
67D37⋊C8D411yescharacteristic
68D37⋊C8D411yescharacteristic
69Q16×C37—21no—
70SD16×C37—21no—
71M16×C37C2×C411yescharacteristic
72#10596942—21no—
73#10596942—21no—
74#10596941—21no—
75#10596940—21no—
76#10596934C2×C411yescharacteristic
77Dic148—21no—
78#10596930—21no—
79#10596929—21no—
80C8×D37—21no—
81C22×D37—21no—
82C22×D37#4111yescharacteristic
83C2×#3866—41no—
84C2×#3866—81no—
85Q8×C37—21no—
86Q8×C37—21no—
87Q8×C37C22⋊C411yescharacteristic
88D4×C37—21no—
89D4×C37C22⋊C411yescharacteristic
90C2×C4×C37—21no—
91C2×C4×C37—21no—
92C2×C4×C37C22×C411yescharacteristic
93C22⋊D37—21no—
94C22⋊D37—21no—
95C22⋊D37—21no—
96C2×Dic37—21no—
97C2×Dic37—21no—
98C2×Dic37C2×D411yescharacteristic
99D148—21no—
100D148C22⋊C411yescharacteristic
101C4×D37—21no—
102C4×D37—21no—
103C4×D37—21no—
104C4×D37—41no—
105C4×D37—41no—
106C4×D37C2×D411yescharacteristic
107C4×D37C2×D411yescharacteristic
108C4×D37C2×D411yescharacteristic
109C4×D37#4111yescharacteristic
110Dic74—21no—
111Dic74—21no—
112Dic74—21no—
113Dic74—41no—
114Dic74—41no—
115Dic74C22⋊C411yescharacteristic
116#64438—21no—
117#64438—22no—
118#64438—21no—
119#64438—41no—
120C8×C37—21no—
121#64436—21no—
122C22×C37—21no—
123C22×C37C4×D411yescharacteristic
124C2×D37—21no—
125C2×D37—21no—
126C2×D37—21no—
127C2×D37—41no—
128C2×D37—41no—
129C2×D37#12111yescharacteristic
130C2×D37#12311yescharacteristic
131#3866—81no—
132C4×C37—21no—
133C4×C37—41no—
134C4×C37C2×C22⋊C411yescharacteristic
135C4×C37C4×D411yescharacteristic
136Dic37—21no—
137Dic37—41no—
138Dic37#12011yescharacteristic
139Dic37#12111yescharacteristic
140#1908—371nomaximal, Sylow
141C2×C37—21no—
142C2×C37—41no—
143C2×C37#38611yescharacteristic
144D37—21no—
145D37—41no—
146D37#47111yescharacteristic
147D37#47311yescharacteristic
148C2×#137—371no—
149C2×#131—371no—
150#417—371no—
151C2×#103—371no—
152C2×#101—371no—
153#343—371no—
154#341—371no—
155C37#190811yescharacteristic, complemented, Sylow
156C2×#41—371no—
157C22×Q8—371no—
158#137—371no—
159#137—371no—
160#137—371no—
161#137—741no—
162#137—741no—
163#137#386611yescharacteristic, complemented
164C2×Q16—741no—
165C2×SD16—741no—
166#131—742no—
167#131—741no—
168#131—741no—
169C2×M16—371no—
170C2×M16—371no—
171C2×M16—371no—
172C2×M16—741no—
173C22×C8—371no—
174C22×C8—741no—
175C2×C4⋊C4—371no—
176#103—741no—
177#103—741no—
178#103—741no—
179#102—741no—
180#101—742no—
181#41—371no—
182#41—371no—
183#41—371no—
184#41—741no—
185#41—741no—
186#41C2×#386611yescharacteristic
187C2×Q8—371no—
188C2×Q8—371no—
189C2×Q8—741no—
190C2×Q8—741no—
191C2×Q8—741no—
192C2×Q8—741no—
193C2×Q8—741no—
194C2×Q8C2×#386611yescharacteristic
195C2×D4—371no—
196C2×D4—741no—
197C22×C4—371no—
198C22×C4—741no—
199C22×C4—741no—
200C22×C4—741no—
201Q16—21no—
202Q16—741no—
203Q16—741no—
204Q16—741no—
205SD16—21no—
206SD16—741no—
207SD16—741no—
208SD16—741no—
209M16—372no—
210M16—371no—
211M16—741no—
212M16—741no—
213M16—742no—
214M16—742no—
215M16—741no—
216M16—741no—
217M16C2×#386611yescharacteristic
218C2×C8—371no—
219C2×C8—371no—
220C2×C8—741no—
221C2×C8—741no—
222C2×C8—741no—
223C2×C8—741no—
224C2×C8—742no—
225C2×C8—742no—
226C2×C8—741no—
227C4⋊C4—741no—
228C4⋊C4—741no—
229C23—371no—
230C23—741no—
231Q8—21no—
232Q8—21no—
233Q8—371no—
234Q8—741no—
235Q8—741no—
236Q8—741no—
237Q8—1481no—
238Q8—1481no—
239Q8C22⋊#386611yescharacteristic
240D4—21no—
241D4—371no—
242D4—741no—
243D4—741no—
244D4—741no—
245D4—741no—
246D4C22⋊#386611yescharacteristic
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—371no—
250C2×C4—371no—
251C2×C4—371no—
252C2×C4—371no—
253C2×C4—371no—
254C2×C4—2961no—
255C2×C4—741no—
256C2×C4—741no—
257C2×C4—741no—
258C2×C4—741no—
259C2×C4—741no—
260C2×C4—1481no—
261C2×C4—1481no—
262C2×C4—1481no—
263C2×C4C22×#386611yescharacteristic
264C8—21no—
265C8—741no—
266C8—741no—
267C8—742no—
268C8—741no—
269C8—1481no—
270C22—21no—
271C22—371no—
272C22—371no—
273C22—741no—
274C22—741no—
275C22—741no—
276C22—1481no—
277C22—1481no—
278C22D4×#386611yescharacteristic
279C4—21no—
280C4—41no—
281C4—371no—
282C4—371no—
283C4—2961no—
284C4—741no—
285C4—1481no—
286C4C2×C22⋊#386611yescharacteristic
287C4D4×#386611yescharacteristic
288C2—21no—
289C2—41no—
290C2—371no—
291C2—371no—
292C2—741no—
293C2—1481no—
294C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#137×C37C4
socleC2×C37#386
prime radical#41×D37C22
cosocleC2×C4×D37C23
hypercenter#137#3866
hypocenterC37#1908
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
3. C2×#11924599C2semidirect
4. D37⋊#101C2semidirect
5. #14558412C2semidirect
6. #14558408C2semidirect
24. #11924569C4semidirect
26. #11924567C4semidirect
27. #11924566C4semidirect
32. #137×C37C4semidirect
155. C37#1908semidirect
163. #137#3866semidirect

Maximal subgroups

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

subgroupindex
D37⋊#1312
#145585242
C2×#119245992
D37⋊#1012
#145584122
#145584082
#137×D372
#190837