Finite Group Databasebeta

← #18004124

Subgroups — #18004124

Order 4736.

458 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924565C211yesmaximal, characteristic
2C2×Q16×D37C211yesmaximal, characteristic, complemented
3#14558103C211yesmaximal, characteristic
4#14558009C211yesmaximal, characteristic, complemented
5#14557754C211yesmaximal, characteristic, complemented
6#14557753C211yesmaximal, characteristic, complemented
7#14557752C211yesmaximal, characteristic, complemented
8#14557744C211yesmaximal, characteristic, complemented
9#14557743C211yesmaximal, characteristic, complemented
10#14557742C211yesmaximal, characteristic, complemented
11#14557741C211yesmaximal, characteristic, complemented
12#14557558C211yesmaximal, characteristic, complemented
13#14557540C211yesmaximal, characteristic, complemented
14#14557526C211yesmaximal, characteristic
15C37×#464C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×Q8×D37C2211yescharacteristic
18C2×Q8×D37C2211yescharacteristic
19#11924565—24no—
20C2×Dic148C2211yescharacteristic
21C2×Dic148C2211yescharacteristic
22C2×#10596942C2211yescharacteristic
23C2×#10596942C2211yescharacteristic
24C2×#10596942C2211yescharacteristic
25Q16×D37—24no—
26C2×#10596940C2211yescharacteristic
27C2×#10596929C2211yescharacteristic
28C2×C8×D37C2211yescharacteristic
29#11924536C2211yescharacteristic
30#11924534C2211yescharacteristic
31#11924523C2211yescharacteristic
32#11924518—21no—
33#11924518—21no—
34#11924513—21no—
35#11924513—21no—
36Q8×Dic37C2211yescharacteristic
37C4×Dic74—21no—
38C4×Dic74C2211yescharacteristic
39#11924501—21no—
40#11924501C2211yescharacteristic
41#11924494—21no—
42#11924494C2211yescharacteristic
43#11924493—21no—
44#11924493C2211yescharacteristic
45C4⋊#64436C2211yescharacteristic
46#11924465C2211yescharacteristic
47#11924465C2211yescharacteristic
48#11924461C2211yescharacteristic
49#11924461C2211yescharacteristic
50#11924460C2211yescharacteristic
51#11924459C2211yescharacteristic
52#11924459C2211yescharacteristic
53#11924457C2211yescharacteristic
54C2×Q16×C37C2211yescharacteristic
55C2×SD16×C37C2211yescharacteristic
56#124×C37C2211yescharacteristic
57C4×Q8×C37C2211yescharacteristic
58C4⋊C8×C37C2211yescharacteristic
59#103×C37C2211yescharacteristic
60#102×C37C2211yescharacteristic
61C2×Q8×C37C2311yescharacteristic
62C2×Q8×C37C2311yescharacteristic
63C2×D4×C37C2311yescharacteristic
64C2×C22⋊D37—21no—
65C22×Dic37—21no—
66Q8×D37—22no—
67Q8×D37—22no—
68Q8×D37—22no—
69Q8×D37D414yes—
70#10596964—22no—
71#10596964—22no—
72C2×C4×D37—21no—
73C2×C4×D37—21no—
74C2×C4×D37C2311yescharacteristic
75C2×Dic74—21no—
76C2×Dic74—21no—
77C2×Dic74C2311yescharacteristic
78C2×Dic74C2311yescharacteristic
79C2×Dic74C2311yescharacteristic
80Q16×C37—22no—
81SD16×C37—22no—
82C2×C8×C37C2311yescharacteristic
83C2×C8×C37C2311yescharacteristic
84C4⋊C4×C37—21no—
85C4⋊C4×C37C2311yescharacteristic
86C22⋊C4×C37—21no—
87C22⋊C4×C37—21no—
88C42×C37—21no—
89C42×C37C2311yescharacteristic
90C22⋊Dic37—21no—
91C22⋊Dic37—21no—
92#10596942—22no—
93#10596942—22no—
94#10596942—22no—
95#10596940—22no—
96#10596938—21no—
97#10596938D411yescharacteristic
98#10596938D411yescharacteristic
99C4⋊Dic37—21no—
100C4⋊Dic37—21no—
101C4⋊Dic37—21no—
102C4⋊Dic37C2311yescharacteristic
103#10596936—21no—
104#10596936—21no—
105#10596936—21no—
106#10596936—21no—
107#10596936D411yescharacteristic
108#10596936D411yescharacteristic
109C4×Dic37—21no—
110C4×Dic37—21no—
111C4×Dic37—21no—
112C4×Dic37—21no—
113C4×Dic37C2311yescharacteristic
114C2×#64436C2311yescharacteristic
115C2×#64436C2311yescharacteristic
116Dic148—22no—
117Dic148—22no—
118#10596929—22no—
119C8×D37—22no—
120C23×C37—21no—
121C22×D37C2×D411yescharacteristic
122Q8×C37—21no—
123Q8×C37—21no—
124Q8×C37—21no—
125Q8×C37C2×D412yes—
126D4×C37—21no—
127D4×C37—21no—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37C2×D411yescharacteristic
132C2×C4×C37C2×D411yescharacteristic
133C2×C4×C37C2411yescharacteristic
134C22⋊D37—42no—
135C2×Dic37—21no—
136C2×Dic37—21no—
137C2×Dic37—21no—
138C2×Dic37—21no—
139C2×Dic37—42no—
140C2×Dic37C2×D411yescharacteristic
141C2×Dic37C2×D411yescharacteristic
142C2×Dic37C2×D411yescharacteristic
143C4×D37—24no—
144C4×D37—42no—
145C4×D37C2×D412yes—
146C4×D37#4112yes—
147Dic74—21no—
148Dic74—24no—
149Dic74—21no—
150Dic74—21no—
151Dic74—21no—
152Dic74—21no—
153Dic74—42no—
154Dic74C2×D412yes—
155C8×C37—21no—
156C8×C37—21no—
157#64436—21no—
158#64436—21no—
159C22×C37—41no—
160C22×C37—41no—
161C22×C37—41no—
162C22×C37C22×D411yescharacteristic
163C2×D37—21no—
164C2×D37—21no—
165C2×D37#12112yes—
166C4×C37—22no—
167C4×C37—21no—
168C4×C37—21no—
169C4×C37—41no—
170C4×C37—41no—
171C4×C37C22×D411yescharacteristic
172C4×C37C2×#4111yescharacteristic
173Dic37—22no—
174Dic37—21no—
175Dic37—21no—
176Dic37—41no—
177Dic37—41no—
178Dic37—41no—
179Dic37#12112yes—
180#3044—371nomaximal, Sylow
181C2×C37—81no—
182C2×C37C2×#12111yescharacteristic
183C2×C37#57811yescharacteristic
184C2×C37#57811yescharacteristic
185D37—22no—
186C2×#137—371no—
187C22×Q16—371no—
188#536—371no—
189#519—371no—
190#464—371no—
191#464—371no—
192#464—371no—
193#464D3711yescharacteristic, complemented
194#462—371no—
195#462—371no—
196#462—371no—
197#462—371no—
198#424—371no—
199#419—371no—
200#416—371no—
201C37#304411yescharacteristic, complemented, Sylow
202C2×#41—371no—
203C22×Q8—371no—
204C22×Q8—371no—
205#137—744no—
206C2×Q16—371no—
207C2×Q16—371no—
208C2×Q16—371no—
209C2×Q16—371no—
210C2×Q16—371no—
211C2×Q16—744no—
212C2×Q16C2×D3711yescharacteristic
213C2×SD16—371no—
214C2×SD16C2×D3711yescharacteristic
215C2×M16—371no—
216C22×C8—371no—
217C4⋊Q8—371no—
218C4⋊Q8—371no—
219#124—371no—
220#124C2×D3711yescharacteristic
221#123—741no—
222#123—741no—
223C22⋊Q8—741no—
224C22⋊Q8—741no—
225C4×Q8—371no—
226C4×Q8—371no—
227C4×Q8—371no—
228C4×Q8—741no—
229C4×Q8—741no—
230C4×Q8C2×D3711yescharacteristic
231#117—371no—
232#117—371no—
233#117—741no—
234#117—741no—
235C4⋊C8—371no—
236C4⋊C8—371no—
237C4⋊C8—371no—
238C4⋊C8C2×D3711yescharacteristic
239#103—371no—
240#103—371no—
241#103—371no—
242#103—371no—
243#103—371no—
244#103C2×D3711yescharacteristic
245#102—371no—
246#102C2×D3711yescharacteristic
247#41—742no—
248#41—742no—
249C2×Q8—374no—
250C2×Q8—371no—
251C2×Q8—371no—
252C2×Q8—371no—
253C2×Q8—741no—
254C2×Q8—741no—
255C2×Q8—742no—
256C2×Q8—742no—
257C2×Q8—742no—
258C2×Q8C22×D3711yescharacteristic
259C2×Q8C22×D3711yescharacteristic
260C2×D4—741no—
261C2×D4C22×D3711yescharacteristic
262C22×C4—371no—
263C22×C4—741no—
264C22×C4—741no—
265C22×C4—741no—
266Q16—22no—
267Q16—742no—
268Q16—742no—
269Q16—742no—
270Q16—742no—
271Q16—742no—
272SD16—22no—
273SD16—742no—
274M16—742no—
275C2×C8—371no—
276C2×C8—371no—
277C2×C8—742no—
278C2×C8C22×D3711yescharacteristic
279C2×C8C22×D3711yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—371no—
282C4⋊C4—371no—
283C4⋊C4—371no—
284C4⋊C4—741no—
285C4⋊C4—741no—
286C4⋊C4—741no—
287C4⋊C4—741no—
288C4⋊C4—741no—
289C4⋊C4—741no—
290C4⋊C4—741no—
291C4⋊C4C22×D3711yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—371no—
295C22⋊C4—371no—
296C22⋊C4—741no—
297C22⋊C4—741no—
298C22⋊C4—741no—
299C42—21no—
300C42—371no—
301C42—741no—
302C42—741no—
303C42—741no—
304C42—741no—
305C42C22×D3711yescharacteristic
306C23—21no—
307C23—371no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—372no—
312Q8—744no—
313Q8—741no—
314Q8—741no—
315Q8—741no—
316Q8—741no—
317Q8—741no—
318Q8—1482no—
319Q8D4×D3712yes—
320D4—21no—
321D4—21no—
322D4—1482no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—371no—
327C2×C4—372no—
328C2×C4—372no—
329C2×C4—371no—
330C2×C4—371no—
331C2×C4—744no—
332C2×C4—741no—
333C2×C4—741no—
334C2×C4—741no—
335C2×C4—741no—
336C2×C4—1482no—
337C2×C4—1482no—
338C2×C4D4×D3711yescharacteristic
339C2×C4D4×D3711yescharacteristic
340C2×C4C23×D3711yescharacteristic
341C8—21no—
342C8—21no—
343C8—741no—
344C8—741no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—372no—
349C22—741no—
350C22—741no—
351C22C2×D4×D3711yescharacteristic
352C4—22no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—372no—
358C4—742no—
359C4—741no—
360C4—741no—
361C4—1481no—
362C4—1481no—
363C4—1481no—
364C4C2×D4×D3711yescharacteristic
365C4#41×D3711yescharacteristic
366C2—81no—
367C2—742no—
368C2#121×D3711yescharacteristic
369C2#1455834711yescharacteristic
370C2#1455834911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#464C2
socleC22×C37C22×D4
prime radicalC2×#10596964C22
hypercenter#464D37
hypocenterC37#3044
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. C2×Q16×D37C2semidirect
4. #14558009C2semidirect
5. #14557754C2semidirect
6. #14557753C2semidirect
7. #14557752C2semidirect
8. #14557744C2semidirect
9. #14557743C2semidirect
10. #14557742C2semidirect
11. #14557741C2semidirect
12. #14557558C2semidirect
13. #14557540C2semidirect
15. C37×#464C2semidirect
193. #464D37semidirect
201. C37#3044semidirect

Maximal subgroups

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

subgroupindex
C2×#119245652
C2×Q16×D372
#145581032
#145580092
#145577542
#145577532
#145577522
#145577442
#145577432
#145577422
#145577412
#145575582
#145575402
#145575262
C37×#4642
#304437