Finite Group Databasebeta

← #18003957

Subgroups — #18003957

Order 4736.

698 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 133 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
12−1+4×D37C211yesmaximal, characteristic, complemented
2#14558329C212yesmaximal, complemented
3#14558103C211yesmaximal, characteristic, complemented
4#14557718C211yesmaximal, characteristic, complemented
5#14557717C212yesmaximal, complemented
6#14557716C211yesmaximal, characteristic, complemented
7#14557705C211yesmaximal, characteristic, complemented
8#14557704C212yesmaximal, complemented
9#14557548C212yesmaximal, complemented
10#101×D37C211yesmaximal, characteristic, complemented
11C37×#454C211yesmaximal, characteristic, complemented
12#11924584—22no—
13#11924584C2211yescharacteristic
14#11924583—22no—
15#11924583—22no—
16#11924583C2212yes—
17C2×#10596964C2211yescharacteristic
18#41×D37—22no—
19#41×D37—22no—
20#41×D37C2212yes—
21C2×Q8×D37—22no—
22C2×Q8×D37C2211yescharacteristic
23#11924569C2212yescomplemented
24#11924566C2212yescomplemented
25#11924565—22no—
26#11924562C2212yescomplemented
27#11924560—22no—
28#11924557—22no—
29#11924555—22no—
30M16×D37C2212yes—
31#11924536C2211yescharacteristic, complemented
32#11924534C2211yescharacteristic, complemented
33#11924523C2211yescharacteristic, complemented
34#11924518—22no—
35#11924513—22no—
36#11924493C2211yescharacteristic
37#11924464C2212yescomplemented
38#11924463C2212yescomplemented
39#11924462C2212yescomplemented
40#11924455C2211yescharacteristic, complemented
41#11924454C2212yescomplemented
422−1+4×C37C2211yescharacteristic
43AGL(1,ℤ/8)×C37C2212yescomplemented
44#124×C37C2211yescharacteristic, complemented
45#104×C37C2212yescomplemented
46#101×C37C2211yescharacteristic, complemented
47#41×C37—22no—
48#41×C37—22no—
49#41×C37C2312yes—
50C2×Q8×C37—22no—
51C2×Q8×C37C2311yescharacteristic
52C2×D4×C37C2311yescharacteristic
53C2×C22⋊D37—21no—
54C22×Dic37—21no—
55#10596966—22no—
56#10596966—22no—
57#10596966D412yes—
58Q8×D37—22no—
59Q8×D37—24no—
60Q8×D37—22no—
61Q8×D37—22no—
62Q8×D37—22no—
63Q8×D37—22no—
64Q8×D37D412yes—
65#10596964—22no—
66#10596964—24no—
67#10596964—22no—
68#10596964—24no—
69#10596964—22no—
70#10596964—22no—
71#10596964—22no—
72#10596964D412yes—
73D4×D37—22no—
74D4×D37—22no—
75D4×D37D412yes—
76#10596962—24no—
77#10596962—24no—
78#10596962—22no—
79#10596962—22no—
80#10596962—22no—
81#10596962C2312yes—
82C2×C4×D37—24no—
83C2×C4×D37—22no—
84C2×C4×D37D412yes—
85C2×C4×D37C2311yescharacteristic
86C2×Dic74—24no—
87C2×Dic74—22no—
88C2×Dic74D412yes—
89C2×Dic74C2311yescharacteristic
90C2×Dic74C2311yescharacteristic
91SD16×C37—22no—
92D8×C37—22no—
93M16×C37C2312yes—
94C22⋊C4×C37—22no—
95C42×C37C2311yescharacteristic
96C22⋊Dic37—22no—
97#10596942—22no—
98#10596940—22no—
99#10596940—22no—
100#10596939—22no—
101#10596938—21no—
102C4⋊Dic37—22no—
103#10596936—22no—
104#10596936—21no—
105C4×Dic37C2311yescharacteristic
106#10596934C2312yes—
107Dic148—22no—
108#10596930—22no—
109#10596929—22no—
110C8×D37—22no—
111C23×C37—21no—
112C22×D37—22no—
113C22×D37C2×D411yescharacteristic
114Q8×C37—22no—
115Q8×C37—22no—
116Q8×C37C2×D412yes—
117D4×C37—22no—
118D4×C37—22no—
119D4×C37—22no—
120D4×C37C2×D412yes—
121C2×C4×C37—24no—
122C2×C4×C37—22no—
123C2×C4×C37—21no—
124C2×C4×C37C2×D412yes—
125C2×C4×C37C2411yescharacteristic
126C22⋊D37—24no—
127C22⋊D37—22no—
128C22⋊D37—22no—
129C22⋊D37—22no—
130C22⋊D37—41no—
131C22⋊D37—41no—
132C2×Dic37—24no—
133C2×Dic37—22no—
134C2×Dic37—21no—
135C2×Dic37—21no—
136C2×Dic37—42no—
137C2×Dic37C2×D412yes—
138C2×Dic37C2×D411yescharacteristic
139D148—22no—
140D148—22no—
141D148C2×D412yes—
142C4×D37—24no—
143C4×D37—24no—
144C4×D37—22no—
145C4×D37—22no—
146C4×D37—22no—
147C4×D37—22no—
148C4×D37—22no—
149C4×D37C2×D412yes—
150C4×D37C2×D412yes—
151Dic74—24no—
152Dic74—22no—
153Dic74—22no—
154Dic74—22no—
155Dic74—24no—
156Dic74—22no—
157Dic74C2×D412yes—
158C8×C37—22no—
159#64436—22no—
160C22×C37—22no—
161C22×C37—42no—
162C22×C37—41no—
163C22×C37C22×D411yescharacteristic
164C2×D37—22no—
165C2×D37—41no—
166C2×D37—44no—
167C2×D37#12011yescharacteristic
168C2×D37#12011yescharacteristic
169C4×C37—22no—
170C4×C37—22no—
171C4×C37—41no—
172C4×C37C22×D412yes—
173Dic37—22no—
174Dic37—22no—
175Dic37—41no—
176Dic37—41no—
177Dic37#12012yes—
178#3020—371nomaximal, Sylow
179C2×C37—21no—
180C2×C37—42no—
181C2×C37—81no—
182C2×C37C2×#12011yescharacteristic
183D37—21no—
184D37—21no—
185D37—42no—
186C2×2−1+4—371no—
187#575—372no—
188#536—371no—
189#456—371no—
190#456—372no—
191#456—371no—
192#454—372no—
193#454—371no—
194#454D3711yescharacteristic, complemented
195#421—372no—
196C2×#101—371no—
197C37#302011yescharacteristic, complemented, Sylow
1982−1+4—372no—
1992−1+4—371no—
2002−1+4—742no—
2012−1+4—742no—
2022−1+4—742no—
2032−1+4C2×D3711yescharacteristic
204C2×#41—372no—
205C2×#41—371no—
206C2×#41—742no—
207C2×#41—742no—
208C22×Q8—371no—
209C22×Q8—742no—
210#137—372no—
211#137—372no—
212#137—742no—
213AGL(1,ℤ/8)—372no—
214AGL(1,ℤ/8)—742no—
215AGL(1,ℤ/8)C2×D3712yescomplemented
216#135—742no—
217#135—742no—
218C2×M16—372no—
219C4⋊Q8—371no—
220C4⋊Q8—371no—
221#124—371no—
222#124C2×D3711yescharacteristic, complemented
223#123—742no—
224C22⋊Q8—742no—
225#117—371no—
226#104—372no—
227#104—372no—
228#104—372no—
229#104C2×D3712yescomplemented
230#101—371no—
231#101—372no—
232#101C2×D3711yescharacteristic, complemented
233#41—22no—
234#41—22no—
235#41—372no—
236#41—372no—
237#41—372no—
238#41—742no—
239#41—742no—
240#41—744no—
241#41—744no—
242#41—742no—
243#41—744no—
244#41—742no—
245#41—742no—
246#41—742no—
247#41—744no—
248#41—742no—
249#41—742no—
250#41—742no—
251#41—742no—
252#41C22×D3712yes—
253C2×Q8—22no—
254C2×Q8—372no—
255C2×Q8—371no—
256C2×Q8—372no—
257C2×Q8—371no—
258C2×Q8—742no—
259C2×Q8—744no—
260C2×Q8—742no—
261C2×Q8—742no—
262C2×Q8—742no—
263C2×Q8—742no—
264C2×Q8—744no—
265C2×Q8—742no—
266C2×Q8C22×D3711yescharacteristic
267C2×D4—372no—
268C2×D4—742no—
269C2×D4—742no—
270C2×D4—741no—
271C2×D4C22×D3711yescharacteristic
272C22×C4—371no—
273C22×C4—372no—
274C22×C4—742no—
275C22×C4—744no—
276C22×C4—741no—
277Q16—742no—
278Q16—742no—
279SD16—22no—
280SD16—742no—
281SD16—742no—
282SD16—742no—
283D8—22no—
284D8—742no—
285M16—372no—
286M16—742no—
287M16C22×D3712yes—
288C2×C8—742no—
289C4⋊C4—741no—
290C4⋊C4—742no—
291C4⋊C4—742no—
292C22⋊C4—22no—
293C22⋊C4—741no—
294C22⋊C4—742no—
295C42—371no—
296C42C22×D3711yescharacteristic
297C23—21no—
298C23—371no—
299C23—742no—
300Q8—22no—
301Q8—22no—
302Q8—372no—
303Q8—742no—
304Q8—744no—
305Q8—744no—
306Q8—742no—
307Q8—742no—
308Q8—742no—
309Q8D4×D3712yes—
310D4—22no—
311D4—22no—
312D4—22no—
313D4—372no—
314D4—742no—
315D4—742no—
316D4—742no—
317D4—742no—
318D4—744no—
319D4—742no—
320D4—1481no—
321D4—1481no—
322D4D4×D3712yes—
323C2×C4—24no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—371no—
327C2×C4—372no—
328C2×C4—372no—
329C2×C4—372no—
330C2×C4—742no—
331C2×C4—742no—
332C2×C4—742no—
333C2×C4—742no—
334C2×C4—744no—
335C2×C4—744no—
336C2×C4—742no—
337C2×C4—744no—
338C2×C4—742no—
339C2×C4—741no—
340C2×C4—741no—
341C2×C4—1482no—
342C2×C4D4×D3712yes—
343C2×C4C23×D3711yescharacteristic
344C8—22no—
345C8—742no—
346C22—22no—
347C22—42no—
348C22—41no—
349C22—371no—
350C22—371no—
351C22—742no—
352C22—1481no—
353C22—1484no—
354C22C2×D4×D3711yescharacteristic
355C4—22no—
356C4—22no—
357C4—41no—
358C4—372no—
359C4—742no—
360C4—742no—
361C4—1481no—
362C4—1481no—
363C4C2×D4×D3712yes—
364C2—21no—
365C2—42no—
366C2—81no—
367C2—741no—
368C2—741no—
369C2—1482no—
370C2#120×D3711yescharacteristic
subgroupG/H
centerC2#120×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#454C2
socleC2×C37C2×#120
hypercenter#454D37
hypocenterC37#3020
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #454

Complements

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

NH ≅ G/Ntype
1. 2−1+4×D37C2semidirect
2. #14558329C2semidirect
3. #14558103C2semidirect
4. #14557718C2semidirect
5. #14557717C2semidirect
6. #14557716C2semidirect
7. #14557705C2semidirect
8. #14557704C2semidirect
9. #14557548C2semidirect
10. #101×D37C2semidirect
11. C37×#454C2semidirect
23. #11924569C22semidirect
24. #11924566C22semidirect
26. #11924562C22semidirect
31. #11924536C22semidirect
32. #11924534C22semidirect
33. #11924523C22semidirect
37. #11924464C22semidirect
38. #11924463C22semidirect
39. #11924462C22semidirect
40. #11924455C22semidirect
41. #11924454C22semidirect
43. AGL(1,ℤ/8)×C37C22semidirect
44. #124×C37C22semidirect
45. #104×C37C22semidirect
46. #101×C37C22semidirect
194. #454D37semidirect
197. C37#3020semidirect
215. AGL(1,ℤ/8)C2×D37semidirect
222. #124C2×D37semidirect
229. #104C2×D37semidirect
232. #101C2×D37semidirect

Maximal subgroups

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

subgroupindex
2−1+4×D372
#145583292
#145581032
#145577182
#145577172
#145577162
#145577052
#145577042
#145575482
#101×D372
C37×#4542
#302037