Finite Group Databasebeta

← #18004149

Subgroups — #18004149

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×#11924568C211yesmaximal, characteristic, complemented
2C2×#11924557C211yesmaximal, characteristic
3#14558103C211yesmaximal, characteristic, complemented
4#14558015C211yesmaximal, characteristic, complemented
5#14557753C211yesmaximal, characteristic, complemented
6#14557747C211yesmaximal, characteristic, complemented
7#14557745C211yesmaximal, characteristic, complemented
8#14557743C211yesmaximal, characteristic, complemented
9#14557741C211yesmaximal, characteristic, complemented
10#14557739C211yesmaximal, characteristic, complemented
11#14557737C211yesmaximal, characteristic, complemented
12#14557558C211yesmaximal, characteristic, complemented
13#14557531C211yesmaximal, characteristic, complemented
14#103×D37C211yesmaximal, characteristic, complemented
15C37×#464C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596964C2211yescharacteristic
18C2×Q8×D37C2211yescharacteristic
19#11924568—24no—
20#11924557—24no—
21C2×#10596942C2211yescharacteristic
22C2×#10596942C2211yescharacteristic
23C2×#10596930C2211yescharacteristic
24C2×#10596930C2211yescharacteristic
25C2×#10596941C2211yescharacteristic
26C2×#10596939C2211yescharacteristic
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×D148—21no—
38C4×D148C2211yescharacteristic
39#11924498—21no—
40#11924498C2211yescharacteristic
41#11924493—21no—
42#11924493C2211yescharacteristic
43C4⋊C4×D37—21no—
44C4⋊C4×D37C2211yescharacteristic
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—
66#10596966—22no—
67#10596966D414yes—
68Q8×D37—22no—
69Q8×D37—22no—
70#10596964—22no—
71#10596964—22no—
72C2×D148—21no—
73C2×D148C2311yescharacteristic
74C2×C4×D37—21no—
75C2×C4×D37—21no—
76C2×C4×D37—21no—
77C2×C4×D37—21no—
78C2×C4×D37—21no—
79C2×C4×D37C2311yescharacteristic
80C2×Dic74—21no—
81C2×Dic74C2311yescharacteristic
82C2×Dic74C2311yescharacteristic
83Q16×C37—22no—
84SD16×C37—22no—
85C2×C8×C37C2311yescharacteristic
86C2×C8×C37C2311yescharacteristic
87C4⋊C4×C37—21no—
88C4⋊C4×C37C2311yescharacteristic
89C22⋊C4×C37—21no—
90C22⋊C4×C37—21no—
91C42×C37—21no—
92C42×C37C2311yescharacteristic
93C22⋊Dic37—21no—
94C22⋊Dic37—21no—
95#10596942—22no—
96#10596942—22no—
97#10596941—22no—
98#10596939—22no—
99#10596938—21no—
100#10596938—21no—
101#10596938D411yescharacteristic
102#10596938D411yescharacteristic
103C4⋊Dic37—21no—
104C4⋊Dic37—21no—
105C4⋊Dic37—21no—
106C4⋊Dic37C2311yescharacteristic
107#10596936—21no—
108#10596936—21no—
109#10596936—21no—
110#10596936D411yescharacteristic
111#10596936D411yescharacteristic
112C4×Dic37—21no—
113C4×Dic37C2311yescharacteristic
114C2×#64436C2311yescharacteristic
115C2×#64436C2311yescharacteristic
116#10596930—22no—
117#10596930—22no—
118#10596929—22no—
119C8×D37—22no—
120C23×C37—21no—
121C22×D37—21no—
122C22×D37C2×D411yescharacteristic
123Q8×C37—21no—
124Q8×C37—21no—
125Q8×C37—21no—
126Q8×C37C2×D412yes—
127D4×C37—21no—
128D4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37C2×D411yescharacteristic
133C2×C4×C37C2×D411yescharacteristic
134C2×C4×C37C2411yescharacteristic
135C22⋊D37—42no—
136C2×Dic37—21no—
137C2×Dic37—21no—
138C2×Dic37—21no—
139C2×Dic37—42no—
140C2×Dic37C2×D411yescharacteristic
141C2×Dic37C2×D411yescharacteristic
142C2×Dic37C2×D411yescharacteristic
143D148—24no—
144D148—21no—
145D148C2×D412yes—
146C4×D37—24no—
147C4×D37—42no—
148C4×D37—81no—
149C4×D37—81no—
150C4×D37—81no—
151C4×D37C2×D412yes—
152C4×D37#4112yes—
153Dic74—21no—
154Dic74—21no—
155Dic74—21no—
156Dic74—21no—
157Dic74—42no—
158C8×C37—21no—
159C8×C37—21no—
160#64436—21no—
161#64436—21no—
162C22×C37—41no—
163C22×C37—41no—
164C22×C37—41no—
165C22×C37C22×D411yescharacteristic
166C2×D37—21no—
167C2×D37—21no—
168C2×D37—22no—
169C2×D37—41no—
170C2×D37—41no—
171C2×D37#12112yes—
172C4×C37—22no—
173C4×C37—21no—
174C4×C37—21no—
175C4×C37—41no—
176C4×C37—41no—
177C4×C37C22×D411yescharacteristic
178C4×C37C2×#4111yescharacteristic
179Dic37—21no—
180Dic37—21no—
181Dic37—41no—
182Dic37—41no—
183Dic37—41no—
184Dic37#12112yes—
185#3046—371nomaximal, Sylow
186C2×C37—81no—
187C2×C37C2×#12111yescharacteristic
188C2×C37#57711yescharacteristic
189C2×C37#57811yescharacteristic
190D37—22no—
191D37—42no—
192C2×#137—371no—
193C2×#135—371no—
194#536—371no—
195#520—371no—
196#464—371no—
197#464D3711yescharacteristic, complemented
198#463—371no—
199#463—371no—
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×Q16C2×D3711yescharacteristic
216C2×SD16—371no—
217C2×SD16—371no—
218C2×SD16—371no—
219C2×SD16C2×D3711yescharacteristic
220C2×D8—371no—
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×Q8C2×D3711yescharacteristic
233C4×D4—371no—
234C4×D4—371no—
235C4×D4—741no—
236C4×D4—741no—
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—741no—
260C2×Q8—742no—
261C2×Q8—742no—
262C2×Q8C22×D3711yescharacteristic
263C2×Q8C22×D3711yescharacteristic
264C2×D4—371no—
265C2×D4—741no—
266C2×D4—741no—
267C2×D4C22×D3711yescharacteristic
268C22×C4—371no—
269C22×C4—741no—
270C22×C4—741no—
271C22×C4—741no—
272C22×C4—741no—
273C22×C4—741no—
274C22×C4—741no—
275Q16—22no—
276Q16—742no—
277Q16—742no—
278SD16—22no—
279SD16—742no—
280SD16—742no—
281SD16—742no—
282D8—742no—
283M16—742no—
284C2×C8—371no—
285C2×C8—371no—
286C2×C8—742no—
287C2×C8C22×D3711yescharacteristic
288C2×C8C22×D3711yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—371no—
291C4⋊C4—371no—
292C4⋊C4—371no—
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—371no—
303C22⋊C4—371no—
304C22⋊C4—741no—
305C22⋊C4—741no—
306C22⋊C4—741no—
307C22⋊C4—741no—
308C42—21no—
309C42—371no—
310C42—741no—
311C42C22×D3711yescharacteristic
312C23—21no—
313C23—371no—
314C23—741no—
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—741no—
319Q8—741no—
320Q8—741no—
321Q8—741no—
322Q8—1482no—
323Q8D4×D3712yes—
324D4—21no—
325D4—21no—
326D4—372no—
327D4—744no—
328D4—741no—
329D4—1482no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—371no—
334C2×C4—372no—
335C2×C4—372no—
336C2×C4—371no—
337C2×C4—371no—
338C2×C4—2961no—
339C2×C4—2961no—
340C2×C4—2961no—
341C2×C4—744no—
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—41no—
355C22—41no—
356C22—41no—
357C22—372no—
358C22—741no—
359C22—741no—
360C22—742no—
361C22—1481no—
362C22—1481no—
363C22C2×D4×D3711yescharacteristic
364C4—22no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—372no—
370C4—741no—
371C4—741no—
372C4—1481no—
373C4—1481no—
374C4—1481no—
375C4C2×D4×D3711yescharacteristic
376C4#41×D3711yescharacteristic
377C2—81no—
378C2—742no—
379C2—1482no—
380C2#121×D3711yescharacteristic
381C2#1455834011yescharacteristic
382C2#1455834911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#464C2
socleC22×C37C22×D4
prime radicalC2×#11924557C2
hypercenter#464D37
hypocenterC37#3046
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
1. C2×#11924568C2semidirect
3. #14558103C2semidirect
4. #14558015C2semidirect
5. #14557753C2semidirect
6. #14557747C2semidirect
7. #14557745C2semidirect
8. #14557743C2semidirect
9. #14557741C2semidirect
10. #14557739C2semidirect
11. #14557737C2semidirect
12. #14557558C2semidirect
13. #14557531C2semidirect
14. #103×D37C2semidirect
15. C37×#464C2semidirect
197. #464D37semidirect
207. C37#3046semidirect

Maximal subgroups

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

subgroupindex
C2×#119245682
C2×#119245572
#145581032
#145580152
#145577532
#145577472
#145577452
#145577432
#145577412
#145577392
#145577372
#145575582
#145575312
#103×D372
C37×#4642
#304637