Finite Group Databasebeta

← #18006398

Subgroups — #18006398

Order 4736.

444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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#14558348C212yesmaximal, complemented
2#14558347C211yesmaximal, characteristic, complemented
3#14557911C211yesmaximal, characteristic, complemented
4#14557808C211yesmaximal, characteristic, complemented
5#14557806C212yesmaximal, complemented
6#14557805C211yesmaximal, characteristic, complemented
7#14557716C212yesmaximal, complemented
8#14557714C212yesmaximal, complemented
9#14557650C211yesmaximal, characteristic, complemented
10#14557648C211yesmaximal, characteristic, complemented
11C37×#578C211yesmaximal, characteristic, complemented
12#11924583C2212yes—
13#11924567—22no—
14#11924567C2212yes—
15#11924566—22no—
16#11924566C2212yes—
17#11924566C2212yes—
18#11924565—22no—
19#11924556—22no—
20#11924556C2211yescharacteristic
21#11924555—21no—
22C2×Dic148C2211yescharacteristic
23C2×#10596942—22no—
24C2×#10596942C2212yes—
25Q16×D37—21no—
26#11924543C2212yes—
27#11924542C2211yescharacteristic
28#11924534C2212yes—
29#11924472C2211yescharacteristic
30#11924471C2211yescharacteristic
31#11924463C2212yes—
32#11924463C2211yescharacteristic
33#11924462C2211yescharacteristic
34#11924455C2212yes—
35#11924454C2212yes—
36C8×Dic37C2211yescharacteristic
372−1+4×C37C2212yes—
38#137×C37—22no—
39#137×C37C2212yes—
40#135×C37—21no—
41#135×C37C2211yescharacteristic
42C2×Q16×C37—21no—
43C2×Q16×C37C2211yescharacteristic
44#131×C37C2211yescharacteristic
45#41×C37—22no—
46#41×C37—22no—
47#41×C37—42no—
48#41×C37C2312yes—
49#41×C37C2311yescharacteristic
50C2×Q8×C37—22no—
51C2×Q8×C37—22no—
52C2×Q8×C37C2312yes—
53Q8×D37—22no—
54#10596964—22no—
55#10596964—42no—
56#10596962—22no—
57#10596962C2311yescharacteristic
58C2×Dic74—22no—
59C2×Dic74C2312yes—
60Q16×C37—22no—
61Q16×C37—21no—
62Q16×C37—21no—
63Q16×C37D411yescharacteristic
64SD16×C37—22no—
65SD16×C37D412yes—
66D8×C37D411yescharacteristic
67M16×C37—21no—
68M16×C37C2311yescharacteristic
69C2×C8×C37—21no—
70C2×C8×C37C2311yescharacteristic
71#10596942—22no—
72#10596942—22no—
73#10596942—22no—
74#10596942—22no—
75#10596942—22no—
76#10596942D411yescharacteristic
77#10596941—22no—
78#10596941D411yescharacteristic
79#10596940—22no—
80#10596940—22no—
81#10596940D411yescharacteristic
82#10596939D411yescharacteristic
83#10596936—42no—
84C4×Dic37C2311yescharacteristic
85#10596934—22no—
86#10596934C2311yescharacteristic
87#10596934C2312yes—
88C2×#64436—22no—
89C2×#64436C2311yescharacteristic
90Dic148—21no—
91Dic148—21no—
92#10596929—21no—
93C8×D37—21no—
94Q8×C37—22no—
95Q8×C37—22no—
96Q8×C37—42no—
97Q8×C37C2×D411yescharacteristic
98Q8×C37C2×D412yes—
99D4×C37—22no—
100D4×C37—21no—
101D4×C37—42no—
102D4×C37C2×D411yescharacteristic
103D4×C37C2×D412yes—
104C2×C4×C37—22no—
105C2×C4×C37—21no—
106C2×C4×C37—22no—
107C2×C4×C37—42no—
108C2×C4×C37—42no—
109C2×C4×C37C2411yescharacteristic
110C22⋊D37—21no—
111C22⋊D37—42no—
112C2×Dic37—21no—
113C2×Dic37—22no—
114C2×Dic37—42no—
115D148C2×D411yescharacteristic
116C4×D37—21no—
117C4×D37—42no—
118Dic74—22no—
119Dic74—22no—
120Dic74—42no—
121Dic74C2×D411yescharacteristic
122C8×C37—21no—
123C8×C37C2×D411yescharacteristic
124C8×C37C2×D411yescharacteristic
125#64436—21no—
126#64436—22no—
127#64436C2×D411yescharacteristic
128#64436C2×D411yescharacteristic
129C22×C37—22no—
130C22×C37—21no—
131C22×C37H(5,𝔽2)11yescharacteristic
132C2×D37—21no—
133C4×C37—22no—
134C4×C37—21no—
135C4×C37—42no—
136C4×C37C22×D411yescharacteristic
137C4×C37C22×D411yescharacteristic
138Dic37—22no—
139Dic37—21no—
140Dic37—42no—
141#3293—371nomaximal, Sylow
142C2×C37—21no—
143C2×C37—42no—
144C2×C37—41no—
145C2×C37D4211yescharacteristic
146D37—41no—
147#578—372no—
148#578—371no—
149#578D3711yescharacteristic, complemented
150#494—371no—
151#473—372no—
152#473—371no—
153#473—371no—
154#456—372no—
155#456—372no—
156#443—371no—
157#443—371no—
158C37#329311yescharacteristic, complemented, Sylow
1592−1+4—372no—
1602−1+4C2×D3712yes—
161#137—22no—
162#137—372no—
163#137—372no—
164#137—372no—
165#137—742no—
166#137—742no—
167#137—742no—
168#137C2×D3712yes—
169#135—21no—
170#135—371no—
171#135—742no—
172#135—741no—
173#135C2×D3711yescharacteristic
174C2×Q16—21no—
175C2×Q16—372no—
176C2×Q16—371no—
177C2×Q16—742no—
178C2×Q16—741no—
179C2×Q16C2×D3711yescharacteristic
180#131—372no—
181#131—371no—
182#131C2×D3711yescharacteristic
183C4⋊Q8—372no—
184#108—371no—
185#108—371no—
186#104—371no—
187#104—372no—
188#104—371no—
189#101—372no—
190#101—372no—
191C4×C8—371no—
192#41—22no—
193#41—22no—
194#41—42no—
195#41—371no—
196#41—742no—
197#41—742no—
198#41—1482no—
199#41C22×D3711yescharacteristic
200#41C22×D3712yes—
201C2×Q8—22no—
202C2×Q8—22no—
203C2×Q8—372no—
204C2×Q8—742no—
205C2×Q8—742no—
206C2×Q8C22×D3712yes—
207Q16—22no—
208Q16—21no—
209Q16—21no—
210Q16—371no—
211Q16—742no—
212Q16—742no—
213Q16—742no—
214Q16—742no—
215Q16—742no—
216Q16—741no—
217Q16—741no—
218Q16C22⋊D3711yescharacteristic
219SD16—22no—
220SD16—371no—
221SD16—371no—
222SD16—742no—
223SD16—742no—
224SD16—742no—
225SD16C22⋊D3712yes—
226D8—371no—
227D8C22⋊D3711yescharacteristic
228M16—21no—
229M16—372no—
230M16—371no—
231M16—742no—
232M16—741no—
233M16C22×D3711yescharacteristic
234C2×C8—21no—
235C2×C8—371no—
236C2×C8—742no—
237C2×C8—741no—
238C2×C8C22×D3711yescharacteristic
239C4⋊C4—1482no—
240C42—371no—
241Q8—22no—
242Q8—22no—
243Q8—42no—
244Q8—371no—
245Q8—742no—
246Q8—742no—
247Q8—1482no—
248Q8D4×D3711yescharacteristic
249Q8C2×C22⋊D3712yes—
250D4—21no—
251D4—22no—
252D4—42no—
253D4—371no—
254D4—741no—
255D4—1482no—
256D4D4×D3711yescharacteristic
257D4C2×C22⋊D3712yes—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—741no—
264C2×C4—741no—
265C2×C4—742no—
266C2×C4—1482no—
267C2×C4—1482no—
268C2×C4C23×D3711yescharacteristic
269C8—21no—
270C8—371no—
271C8—371no—
272C8—742no—
273C8—741no—
274C8C2×C22⋊D3711yescharacteristic
275C8C2×C22⋊D3711yescharacteristic
276C22—21no—
277C22—22no—
278C22—741no—
279C22#1192458111yescharacteristic
280C4—21no—
281C4—22no—
282C4—42no—
283C4—742no—
284C4—741no—
285C4—1482no—
286C4C2×D4×D3711yescharacteristic
287C4C22×C22⋊D3711yescharacteristic
288C2—21no—
289C2—41no—
290C2—42no—
291C2—1481no—
292C2D4×C22⋊D3711yescharacteristic
subgroupG/H
centerC2D4×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#578C2
socleC2×C37D42
hypercenter#578D37
hypocenterC37#3293
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #578

Complements

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

NH ≅ G/Ntype
1. #14558348C2semidirect
2. #14558347C2semidirect
3. #14557911C2semidirect
4. #14557808C2semidirect
5. #14557806C2semidirect
6. #14557805C2semidirect
7. #14557716C2semidirect
8. #14557714C2semidirect
9. #14557650C2semidirect
10. #14557648C2semidirect
11. C37×#578C2semidirect
149. #578D37semidirect
158. C37#3293semidirect

Maximal subgroups

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

subgroupindex
#145583482
#145583472
#145579112
#145578082
#145578062
#145578052
#145577162
#145577142
#145576502
#145576482
C37×#5782
#329337