Finite Group Databasebeta

← #18004147

Subgroups — #18004147

Order 4736.

472 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924565C211yesmaximal, characteristic, complemented
2C2×#11924555C211yesmaximal, characteristic
3#14558103C211yesmaximal, characteristic, complemented
4#14558012C211yesmaximal, characteristic, complemented
5#14557754C211yesmaximal, characteristic, complemented
6#14557752C211yesmaximal, characteristic, complemented
7#14557746C211yesmaximal, characteristic, complemented
8#14557744C211yesmaximal, characteristic, complemented
9#14557742C211yesmaximal, characteristic, complemented
10#14557738C211yesmaximal, characteristic, complemented
11#14557736C211yesmaximal, characteristic, complemented
12#14557558C211yesmaximal, characteristic, complemented
13#14557531C211yesmaximal, characteristic, complemented
14#103×D37C211yesmaximal, characteristic, complemented
15C37×#463C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×#10596964C2211yescharacteristic
18C2×Q8×D37C2211yescharacteristic
19#11924565—24no—
20#11924555—24no—
21C2×Dic148C2211yescharacteristic
22C2×Dic148C2211yescharacteristic
23C2×#10596942C2211yescharacteristic
24C2×#10596940C2211yescharacteristic
25C2×#10596940C2211yescharacteristic
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—
36C4×Dic74C2211yescharacteristic
37#11924501C2211yescharacteristic
38D4×Dic37C2211yescharacteristic
39C4×C22⋊D37—21no—
40#11924496—21no—
41#11924493C2211yescharacteristic
42#11924492—21no—
43C2×#10596936—21no—
44C4⋊C4×D37C2211yescharacteristic
45C4⋊#64436C2211yescharacteristic
46#11924465C2211yescharacteristic
47#11924465C2211yescharacteristic
48#11924461C2211yescharacteristic
49#11924461C2211yescharacteristic
50#11924460C2211yescharacteristic
51#11924459C2211yescharacteristic
52#11924459C2211yescharacteristic
53#11924457C2211yescharacteristic
54C2×SD16×C37C2211yescharacteristic
55C2×D8×C37C2211yescharacteristic
56#124×C37C2211yescharacteristic
57C4×D4×C37C2211yescharacteristic
58C4⋊C8×C37C2211yescharacteristic
59#103×C37C2211yescharacteristic
60#102×C37C2211yescharacteristic
61C2×Q8×C37C2311yescharacteristic
62C2×D4×C37C2311yescharacteristic
63C2×D4×C37C2311yescharacteristic
64C22×C4×C37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C22×Dic37—21no—
68C22×Dic37—21no—
69C22×Dic37—21no—
70Q8×D37—22no—
71Q8×D37—22no—
72#10596964—22no—
73#10596964—22no—
74#10596964—22no—
75#10596964D414yes—
76C2×C4×D37—21no—
77C2×C4×D37—21no—
78C2×C4×D37C2311yescharacteristic
79C2×Dic74—21no—
80C2×Dic74C2311yescharacteristic
81C2×Dic74C2311yescharacteristic
82C2×Dic74C2311yescharacteristic
83SD16×C37—22no—
84D8×C37—22no—
85C2×C8×C37C2311yescharacteristic
86C2×C8×C37C2311yescharacteristic
87C4⋊C4×C37C2311yescharacteristic
88C22⋊C4×C37—21no—
89C22⋊C4×C37—21no—
90C22⋊C4×C37—21no—
91C42×C37C2311yescharacteristic
92C22⋊Dic37—21no—
93C22⋊Dic37—21no—
94C22⋊Dic37—21no—
95#10596942—22no—
96#10596940—22no—
97#10596940—22no—
98#10596940—22no—
99#10596938D411yescharacteristic
100#10596938D411yescharacteristic
101C4⋊Dic37—21no—
102C4⋊Dic37—21no—
103C4⋊Dic37C2311yescharacteristic
104#10596936—21no—
105#10596936—21no—
106#10596936—21no—
107#10596936—21no—
108#10596936—21no—
109#10596936D411yescharacteristic
110#10596936D411yescharacteristic
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—
121C23×C37—21no—
122C22×D37C2×D411yescharacteristic
123Q8×C37—21no—
124Q8×C37—21no—
125D4×C37—21no—
126D4×C37—21no—
127D4×C37—21no—
128D4×C37C2×D412yes—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—81no—
132C2×C4×C37C2×D411yescharacteristic
133C2×C4×C37C2×D411yescharacteristic
134C2×C4×C37C2411yescharacteristic
135C22⋊D37—24no—
136C22⋊D37—42no—
137C2×Dic37—21no—
138C2×Dic37—24no—
139C2×Dic37—21no—
140C2×Dic37—21no—
141C2×Dic37—21no—
142C2×Dic37—42no—
143C2×Dic37—81no—
144C2×Dic37C2×D411yescharacteristic
145C2×Dic37C2×D411yescharacteristic
146C2×Dic37C2×D411yescharacteristic
147C4×D37—42no—
148C4×D37—81no—
149C4×D37C2×D412yes—
150C4×D37#4112yes—
151Dic74—21no—
152Dic74—21no—
153Dic74—21no—
154Dic74—21no—
155Dic74—21no—
156Dic74—42no—
157Dic74C2×D412yes—
158C8×C37—21no—
159C8×C37—21no—
160#64436—21no—
161#64436—21no—
162C22×C37—22no—
163C22×C37—41no—
164C22×C37—41no—
165C22×C37—41no—
166C22×C37—41no—
167C22×C37—41no—
168C22×C37C22×D411yescharacteristic
169C2×D37—21no—
170C2×D37—21no—
171C2×D37#12112yes—
172C4×C37—21no—
173C4×C37—21no—
174C4×C37—41no—
175C4×C37—41no—
176C4×C37C22×D411yescharacteristic
177C4×C37C2×#4111yescharacteristic
178Dic37—22no—
179Dic37—21no—
180Dic37—21no—
181Dic37—41no—
182Dic37—41no—
183Dic37—41no—
184Dic37#12112yes—
185#3046—371nomaximal, Sylow
186C2×C37—42no—
187C2×C37—81no—
188C2×C37C2×#12111yescharacteristic
189C2×C37#57711yescharacteristic
190C2×C37#57811yescharacteristic
191D37—22no—
192C2×#137—371no—
193C2×#135—371no—
194#536—371no—
195#520—371no—
196#464—371no—
197#464—371no—
198#463—371no—
199#463D3711yescharacteristic, complemented
200#462—371no—
201#462—371no—
202#461—371no—
203#461—371no—
204#424—371no—
205#417—371no—
206C2×#103—371no—
207C37#304611yescharacteristic, complemented, Sylow
208C2×#41—371no—
209C2×#41—371no—
210C22×Q8—371no—
211#137—744no—
212#135—744no—
213C2×Q16—371no—
214C2×Q16—371no—
215C2×Q16—371no—
216C2×SD16—371no—
217C2×SD16—371no—
218C2×SD16—371no—
219C2×SD16C2×D3711yescharacteristic
220C2×D8C2×D3711yescharacteristic
221C2×M16—371no—
222C22×C8—371no—
223C4⋊Q8—371no—
224C4⋊Q8—371no—
225#124—371no—
226#124C2×D3711yescharacteristic
227#123—741no—
228#123—741no—
229C22⋊Q8—741no—
230C22⋊Q8—741no—
231C4×Q8—371no—
232C4×Q8—371no—
233C4×D4—371no—
234C4×D4—741no—
235C4×D4—741no—
236C4×D4C2×D3711yescharacteristic
237#117—371no—
238#117—741no—
239C2×C4⋊C4—371no—
240C2×C4⋊C4—741no—
241C4⋊C8—371no—
242C4⋊C8—371no—
243C4⋊C8—371no—
244C4⋊C8C2×D3711yescharacteristic
245#103—371no—
246#103—371no—
247#103—371no—
248#103—371no—
249#103—371no—
250#103C2×D3711yescharacteristic
251#102—371no—
252#102C2×D3711yescharacteristic
253#41—374no—
254#41—742no—
255#41—742no—
256#41—742no—
257C2×Q8—371no—
258C2×Q8—371no—
259C2×Q8—371no—
260C2×Q8—741no—
261C2×Q8—742no—
262C2×Q8—742no—
263C2×Q8C22×D3711yescharacteristic
264C2×D4—741no—
265C2×D4—741no—
266C2×D4C22×D3711yescharacteristic
267C2×D4C22×D3711yescharacteristic
268C22×C4—21no—
269C22×C4—371no—
270C22×C4—741no—
271C22×C4—741no—
272C22×C4—741no—
273C22×C4—741no—
274C22×C4—741no—
275Q16—742no—
276Q16—742no—
277Q16—742no—
278SD16—22no—
279SD16—742no—
280SD16—742no—
281SD16—742no—
282D8—22no—
283M16—742no—
284C2×C8—371no—
285C2×C8—371no—
286C2×C8—742no—
287C2×C8C22×D3711yescharacteristic
288C2×C8C22×D3711yescharacteristic
289C4⋊C4—371no—
290C4⋊C4—371no—
291C4⋊C4—371no—
292C4⋊C4—741no—
293C4⋊C4—741no—
294C4⋊C4—741no—
295C4⋊C4—741no—
296C4⋊C4—741no—
297C4⋊C4—741no—
298C4⋊C4—741no—
299C4⋊C4C22×D3711yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—371no—
304C22⋊C4—371no—
305C22⋊C4—741no—
306C22⋊C4—741no—
307C22⋊C4—741no—
308C42—371no—
309C42—741no—
310C42—741no—
311C42C22×D3711yescharacteristic
312C23—21no—
313C23—21no—
314C23—371no—
315Q8—21no—
316Q8—21no—
317Q8—372no—
318Q8—741no—
319Q8—741no—
320Q8—741no—
321Q8—741no—
322Q8—741no—
323Q8—1482no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—744no—
328D4—1482no—
329D4D4×D3712yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—371no—
334C2×C4—372no—
335C2×C4—372no—
336C2×C4—371no—
337C2×C4—371no—
338C2×C4—2961no—
339C2×C4—2961no—
340C2×C4—744no—
341C2×C4—741no—
342C2×C4—741no—
343C2×C4—741no—
344C2×C4—741no—
345C2×C4—1482no—
346C2×C4—1482no—
347C2×C4D4×D3711yescharacteristic
348C2×C4D4×D3711yescharacteristic
349C2×C4C23×D3711yescharacteristic
350C8—21no—
351C8—21no—
352C8—741no—
353C8—741no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—372no—
361C22—741no—
362C22—741no—
363C22C2×D4×D3711yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—372no—
369C4—742no—
370C4—741no—
371C4—741no—
372C4—1481no—
373C4—1481no—
374C4—1481no—
375C4C2×D4×D3711yescharacteristic
376C4#41×D3711yescharacteristic
377C2—42no—
378C2—81no—
379C2—742no—
380C2#121×D3711yescharacteristic
381C2#1455834311yescharacteristic
382C2#1455834711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#463C2
socleC22×C37C22×D4
prime radicalC2×#11924555C2
hypercenter#463D37
hypocenterC37#3046
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#11924565C2semidirect
3. #14558103C2semidirect
4. #14558012C2semidirect
5. #14557754C2semidirect
6. #14557752C2semidirect
7. #14557746C2semidirect
8. #14557744C2semidirect
9. #14557742C2semidirect
10. #14557738C2semidirect
11. #14557736C2semidirect
12. #14557558C2semidirect
13. #14557531C2semidirect
14. #103×D37C2semidirect
15. C37×#463C2semidirect
199. #463D37semidirect
207. C37#3046semidirect

Maximal subgroups

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

subgroupindex
C2×#119245652
C2×#119245552
#145581032
#145580122
#145577542
#145577522
#145577462
#145577442
#145577422
#145577382
#145577362
#145575582
#145575312
#103×D372
C37×#4632
#304637