Finite Group Databasebeta

← #18006572

Subgroups — #18006572

Order 4736.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558229C211yesmaximal, characteristic, complemented
2#14557901C211yesmaximal, characteristic, complemented
3#14557871C211yesmaximal, characteristic, complemented
4#14557861C211yesmaximal, characteristic, complemented
5#14557833C211yesmaximal, characteristic, complemented
6#14557781C211yesmaximal, characteristic, complemented
7#14557764C211yesmaximal, characteristic, complemented
8#14557735C211yesmaximal, characteristic, complemented
9#14557678C211yesmaximal, characteristic, complemented
10#14557678C211yesmaximal, characteristic, complemented
11#14557643C211yesmaximal, characteristic, complemented
12#14557605C211yesmaximal, characteristic, complemented
13#14557534C211yesmaximal, characteristic, complemented
14#14557529C211yesmaximal, characteristic, complemented
15C37×#547C211yesmaximal, characteristic, complemented
16C2×#10596941C2211yescharacteristic
17C2×#10596941C2211yescharacteristic
18C2×#10596939C2211yescharacteristic
19C2×#10596934C2211yescharacteristic
20C22×#64436C2211yescharacteristic
21#11924531—21no—
22#11924528C2211yescharacteristic
23#11924518—21no—
24#11924510C2211yescharacteristic
25#11924510C2211yescharacteristic
26#11924508—21no—
27C4×D148C2211yescharacteristic
28#11924496—21no—
29#11924495C2211yescharacteristic
30C2×C4⋊Dic37C2211yescharacteristic
31#11924469C2211yescharacteristic
32#11924467C2211yescharacteristic
33#11924467C2211yescharacteristic
34C4⋊#64436C2211yescharacteristic
35#11924460C2211yescharacteristic
36#11924460C2211yescharacteristic
37#11924460C2211yescharacteristic
38#11924460C2211yescharacteristic
39#11924460C2211yescharacteristic
40#11924460C2211yescharacteristic
41#11924457C2211yescharacteristic
42#11924457C2211yescharacteristic
43#11924457C2211yescharacteristic
44#11924456C2211yescharacteristic
45C22⋊#64436C2211yescharacteristic
46C22⋊#64436C2211yescharacteristic
47#11924447C2211yescharacteristic
48C2×#41×C37C2211yescharacteristic
49C2×#41×C37C2211yescharacteristic
50C4⋊Q8×C37C2211yescharacteristic
51#123×C37—21no—
52#123×C37—21no—
53C22⋊Q8×C37C2211yescharacteristic
54C22⋊Q8×C37C2211yescharacteristic
55#121×C37—21no—
56C4×D4×C37C2211yescharacteristic
57C4×D4×C37C2211yescharacteristic
58C2×C4⋊C4×C37—21no—
59#41×C37—22no—
60#41×C37—22no—
61#41×C37—41no—
62#41×C37—41no—
63C2×Q8×C37C2311yescharacteristic
64C2×Q8×C37C2311yescharacteristic
65C2×D4×C37—21no—
66C2×D4×C37—21no—
67C2×D4×C37D411yescharacteristic
68C2×D4×C37C2311yescharacteristic
69C22×C4×C37—21no—
70C22×C4×C37—21no—
71C22×C4×C37—21no—
72C22×C4×C37C2311yescharacteristic
73C22×C4×C37C2311yescharacteristic
74C2×C22⋊D37—21no—
75C2×C22⋊D37—21no—
76C22×Dic37—21no—
77C2×D148C2311yescharacteristic
78C2×C4×D37—21no—
79C4⋊C4×C37—21no—
80C4⋊C4×C37—21no—
81C4⋊C4×C37—21no—
82C4⋊C4×C37—21no—
83C4⋊C4×C37D411yescharacteristic
84C4⋊C4×C37C2311yescharacteristic
85C22⋊C4×C37—21no—
86C22⋊C4×C37—21no—
87C22⋊C4×C37—21no—
88C22⋊C4×C37D411yescharacteristic
89C22⋊C4×C37D411yescharacteristic
90C42×C37C2311yescharacteristic
91C22⋊Dic37—21no—
92#10596941—41no—
93#10596941—41no—
94#10596939—22no—
95#10596938—21no—
96#10596938—21no—
97#10596938—21no—
98C4⋊Dic37—21no—
99C4⋊Dic37C2311yescharacteristic
100C4⋊Dic37C2311yescharacteristic
101C4⋊Dic37C2311yescharacteristic
102#10596936—21no—
103#10596936—21no—
104C4×Dic37—21no—
105#10596934—41no—
106C2×#64436—41no—
107C2×#64436C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C2×#64436C2311yescharacteristic
111C23×C37—21no—
112C23×C37C2×D411yescharacteristic
113C23×C37C2×D411yescharacteristic
114C22×D37—21no—
115Q8×C37—21no—
116Q8×C37—21no—
117Q8×C37—21no—
118Q8×C37—21no—
119D4×C37—21no—
120D4×C37—41no—
121D4×C37—42no—
122D4×C37—42no—
123D4×C37#4112yes—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—21no—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—42no—
132C2×C4×C37—42no—
133C2×C4×C37—42no—
134C2×C4×C37C2×D411yescharacteristic
135C2×C4×C37C2×D411yescharacteristic
136C2×C4×C37C2×D411yescharacteristic
137C2×C4×C37C2×D411yescharacteristic
138C2×C4×C37C2411yescharacteristic
139C22⋊D37—42no—
140C22⋊D37—81no—
141C2×Dic37—21no—
142C2×Dic37—21no—
143C2×Dic37—21no—
144C2×Dic37—81no—
145D148—21no—
146D148—21no—
147C4×D37—81no—
148#64436—21no—
149#64436—21no—
150#64436—21no—
151#64436—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37—22no—
155C22×C37—21no—
156C22×C37—21no—
157C22×C37—21no—
158C22×C37—21no—
159C22×C37—41no—
160C22×C37—41no—
161C22×C37C22×D411yescharacteristic
162C2×D37—41no—
163C2×D37—41no—
164C2×D37—41no—
165C4×C37—21no—
166C4×C37—21no—
167C4×C37—21no—
168C4×C37—21no—
169C4×C37—41no—
170C4×C37—41no—
171C4×C37—41no—
172C4×C37C2×#4111yescharacteristic
173C4×C37H(5,𝔽2)11yescharacteristic
174Dic37—41no—
175Dic37—41no—
176Dic37—41no—
177#3307—371nomaximal, Sylow
178C2×C37—41no—
179C2×C37—41no—
180C2×C37—42no—
181C2×C37#54611yescharacteristic
182C2×C37#57511yescharacteristic
183C2×C37#57711yescharacteristic
184D37—81no—
185#553—371no—
186#547D3711yescharacteristic, complemented
187#491—371no—
188#485—371no—
189#483—371no—
190#478—371no—
191#468—371no—
192#465—371no—
193#461—371no—
194#449—371no—
195#449—371no—
196#442—371no—
197#435—371no—
198#417—371no—
199#416—371no—
200C37#330711yescharacteristic, complemented, Sylow
201C2×#41C2×D3711yescharacteristic
202C2×#41C2×D3711yescharacteristic
203C2×SD16—371no—
204C2×SD16—371no—
205C2×D8—371no—
206C2×M16—371no—
207C22×C8—371no—
208C4⋊Q8C2×D3711yescharacteristic
209#126—741no—
210#125—371no—
211#123—21no—
212#123—21no—
213#123—741no—
214C22⋊Q8C2×D3711yescharacteristic
215C22⋊Q8C2×D3711yescharacteristic
216#121—21no—
217#121—371no—
218#121—371no—
219#121—741no—
220C4×D4—371no—
221C4×D4—741no—
222C4×D4C2×D3711yescharacteristic
223C4×D4C2×D3711yescharacteristic
224#117—371no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—371no—
227#107—371no—
228#106—371no—
229#106—371no—
230C4⋊C8—371no—
231#103—371no—
232#103—371no—
233#103—371no—
234#103—371no—
235#103—371no—
236#103—371no—
237#102—371no—
238#102—371no—
239#102—371no—
240#102—371no—
241C22⋊C8—371no—
242C22⋊C8—371no—
243#97—371no—
244#41—22no—
245#41—22no—
246#41—41no—
247#41—41no—
248C2×Q8C22×D3711yescharacteristic
249C2×Q8C22×D3711yescharacteristic
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—371no—
253C2×D4—741no—
254C2×D4—741no—
255C2×D4C22⋊D3711yescharacteristic
256C2×D4C22×D3711yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—741no—
261C22×C4—741no—
262C22×C4C22×D3711yescharacteristic
263C22×C4C22×D3711yescharacteristic
264SD16—1481no—
265SD16—1481no—
266D8—742no—
267M16—1481no—
268C2×C8—371no—
269C2×C8—371no—
270C2×C8—371no—
271C2×C8—371no—
272C2×C8—1481no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—371no—
278C4⋊C4—371no—
279C4⋊C4—371no—
280C4⋊C4—741no—
281C4⋊C4—741no—
282C4⋊C4—741no—
283C4⋊C4C22⋊D3711yescharacteristic
284C4⋊C4C22×D3711yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—741no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4—741no—
292C22⋊C4C22⋊D3711yescharacteristic
293C22⋊C4C22⋊D3711yescharacteristic
294C42—741no—
295C42C22×D3711yescharacteristic
296C23—21no—
297C23—741no—
298C23C2×C22⋊D3711yescharacteristic
299C23C2×C22⋊D3711yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—21no—
304D4—21no—
305D4—41no—
306D4—42no—
307D4—42no—
308D4—2961no—
309D4—741no—
310D4—741no—
311D4—1482no—
312D4#1059696412yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—2961no—
324C2×C4—2961no—
325C2×C4—741no—
326C2×C4—741no—
327C2×C4—741no—
328C2×C4C2×C22⋊D3711yescharacteristic
329C2×C4C2×C22⋊D3711yescharacteristic
330C2×C4C2×C22⋊D3711yescharacteristic
331C2×C4C2×C22⋊D3711yescharacteristic
332C2×C4C23×D3711yescharacteristic
333C8—741no—
334C8—741no—
335C8—741no—
336C8—741no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—22no—
344C22—41no—
345C22—41no—
346C22—1481no—
347C22—1481no—
348C22—1481no—
349C22C22×C22⋊D3711yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—1481no—
358C4—1481no—
359C4—1481no—
360C4C2×#1059696411yescharacteristic
361C4#1192458111yescharacteristic
362C2—41no—
363C2—41no—
364C2—42no—
365C2—2961no—
366C2#1455817711yescharacteristic
367C2#1455833111yescharacteristic
368C2#1455834111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#547C2
socleC22×C37C22×D4
hypercenter#547D37
hypocenterC37#3307
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #14558229C2semidirect
2. #14557901C2semidirect
3. #14557871C2semidirect
4. #14557861C2semidirect
5. #14557833C2semidirect
6. #14557781C2semidirect
7. #14557764C2semidirect
8. #14557735C2semidirect
9. #14557678C2semidirect
10. #14557678C2semidirect
11. #14557643C2semidirect
12. #14557605C2semidirect
13. #14557534C2semidirect
14. #14557529C2semidirect
15. C37×#547C2semidirect
186. #547D37semidirect
200. C37#3307semidirect

Maximal subgroups

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

subgroupindex
#145582292
#145579012
#145578712
#145578612
#145578332
#145577812
#145577642
#145577352
#145576782
#145576432
#145576052
#145575342
#145575292
C37×#5472
#330737