Finite Group Databasebeta

← #18004138

Subgroups — #18004138

Order 4736.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924563C211yesmaximal, characteristic, complemented
2C2×#11924559C211yesmaximal, characteristic, complemented
3#14558101C211yesmaximal, characteristic, complemented
4#14558015C211yesmaximal, characteristic, complemented
5#14557757C211yesmaximal, characteristic, complemented
6#14557751C211yesmaximal, characteristic, complemented
7#14557745C211yesmaximal, characteristic, complemented
8#14557733C211yesmaximal, characteristic, complemented
9#14557731C211yesmaximal, characteristic, complemented
10#14557729C211yesmaximal, characteristic, complemented
11#14557727C211yesmaximal, characteristic, complemented
12#14557558C211yesmaximal, characteristic, complemented
13#14557533C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic, complemented
15C37×#464C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596966C2211yescharacteristic
18C2×D4×D37C2211yescharacteristic
19#11924563—24no—
20#11924559—24no—
21C2×#10596941C2211yescharacteristic
22C2×#10596941C2211yescharacteristic, complemented
23C2×#10596941C2211yescharacteristic, complemented
24C2×D296C2211yescharacteristic
25C2×D296C2211yescharacteristic, complemented
26C2×#10596939C2211yescharacteristic
27C2×#10596929C2211yescharacteristic
28C2×C8×D37C2211yescharacteristic
29#11924533C2211yescharacteristic
30#11924532C2211yescharacteristic
31#11924525C2211yescharacteristic
32#11924509—21no—
33#11924509—21no—
34#11924506—21no—
35#11924506—21no—
36Q8×Dic37C2211yescharacteristic, complemented
37C4×D148—21no—
38C4×D148C2211yescharacteristic, complemented
39#11924498—21no—
40#11924498C2211yescharacteristic, complemented
41#11924493—21no—
42#11924493C2211yescharacteristic
43C4⋊C4×D37—21no—
44C4⋊C4×D37C2211yescharacteristic
45C4⋊#64436C2211yescharacteristic, complemented
46#11924465C2211yescharacteristic, complemented
47#11924465C2211yescharacteristic, complemented
48#11924460C2211yescharacteristic, complemented
49#11924458C2211yescharacteristic
50#11924458C2211yescharacteristic, complemented
51#11924457C2211yescharacteristic
52#11924456C2211yescharacteristic
53#11924456C2211yescharacteristic, complemented
54C2×Q16×C37C2211yescharacteristic, complemented
55C2×SD16×C37C2211yescharacteristic
56#124×C37C2211yescharacteristic
57C4×Q8×C37C2211yescharacteristic, complemented
58C4⋊C8×C37C2211yescharacteristic, complemented
59#103×C37C2211yescharacteristic, complemented
60#102×C37C2211yescharacteristic
61C23×D37—21no—
62C2×Q8×C37C2311yescharacteristic
63C2×Q8×C37C2311yescharacteristic
64C2×D4×C37C2311yescharacteristic
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68#10596966—22no—
69#10596966—22no—
70#10596966—22no—
71#10596966D414yescomplemented
72D4×D37—22no—
73D4×D37—22no—
74C2×D148—21no—
75C2×D148—21no—
76C2×D148—21no—
77C2×D148—21no—
78C2×D148C2311yescharacteristic
79C2×D148C2311yescharacteristic
80C2×D148C2311yescharacteristic
81C2×C4×D37—21no—
82C2×C4×D37—21no—
83C2×C4×D37—21no—
84C2×C4×D37—21no—
85C2×C4×D37—21no—
86C2×C4×D37C2311yescharacteristic
87Q16×C37—22no—
88SD16×C37—22no—
89C2×C8×C37C2311yescharacteristic
90C2×C8×C37C2311yescharacteristic
91C4⋊C4×C37—21no—
92C4⋊C4×C37C2311yescharacteristic
93C22⋊C4×C37—21no—
94C22⋊C4×C37—21no—
95C42×C37—21no—
96C42×C37C2311yescharacteristic
97#10596941—22no—
98#10596941—22no—
99#10596941—22no—
100#10596939—22no—
101#10596938—21no—
102#10596938—21no—
103#10596938—21no—
104#10596938—21no—
105#10596938D411yescharacteristic
106#10596938D411yescharacteristic
107C4⋊Dic37—21no—
108C4⋊Dic37C2311yescharacteristic
109#10596936—21no—
110#10596936D411yescharacteristic
111#10596936D411yescharacteristic
112C4×Dic37—21no—
113C4×Dic37C2311yescharacteristic
114C2×#64436C2311yescharacteristic
115C2×#64436C2311yescharacteristic
116D296—22no—
117D296—22no—
118#10596929—22no—
119C8×D37—22no—
120C23×C37—21no—
121C22×D37—21no—
122C22×D37—21no—
123C22×D37—21no—
124C22×D37—42no—
125C22×D37—81no—
126C22×D37—81no—
127C22×D37C2×D411yescharacteristic
128Q8×C37—21no—
129Q8×C37—21no—
130Q8×C37—21no—
131Q8×C37C2×D412yes—
132D4×C37—21no—
133D4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—21no—
136C2×C4×C37—21no—
137C2×C4×C37C2×D411yescharacteristic
138C2×C4×C37C2×D411yescharacteristic
139C2×C4×C37C2411yescharacteristic
140C22⋊D37—42no—
141C22⋊D37—81no—
142C22⋊D37—81no—
143C2×Dic37—21no—
144C2×Dic37C2×D411yescharacteristic
145C2×Dic37C2×D411yescharacteristic
146C2×Dic37C2×D411yescharacteristic
147D148—24no—
148D148—21no—
149D148—21no—
150D148—21no—
151D148—21no—
152D148—21no—
153D148—42no—
154D148—81no—
155D148—81no—
156D148C2×D412yes—
157C4×D37—24no—
158C4×D37—42no—
159C4×D37—81no—
160C4×D37—81no—
161C4×D37—81no—
162C4×D37C2×D412yes—
163C4×D37#4112yes—
164C8×C37—21no—
165C8×C37—21no—
166#64436—21no—
167#64436—21no—
168C22×C37—41no—
169C22×C37—41no—
170C22×C37—41no—
171C22×C37C22×D411yescharacteristic
172C2×D37—21no—
173C2×D37—21no—
174C2×D37—22no—
175C2×D37—41no—
176C2×D37—41no—
177C2×D37—41no—
178C2×D37—41no—
179C2×D37—41no—
180C2×D37—41no—
181C2×D37—41no—
182C2×D37—41no—
183C2×D37—84no—
184C2×D37#12112yes—
185C4×C37—22no—
186C4×C37—21no—
187C4×C37—21no—
188C4×C37—41no—
189C4×C37—41no—
190C4×C37C22×D411yescharacteristic
191C4×C37C2×#4111yescharacteristic
192Dic37—21no—
193Dic37—21no—
194Dic37—41no—
195Dic37#12112yes—
196#3045—371nomaximal, Sylow
197C2×C37—81no—
198C2×C37C2×#12111yescharacteristic
199C2×C37#57611yescharacteristic
200C2×C37#57711yescharacteristic
201D37—22no—
202D37—42no—
203D37—81no—
204D37—81no—
205C2×AGL(1,ℤ/8)—371no—
206C2×#135—371no—
207#535—371no—
208#520—371no—
209#464—371no—
210#464D3711yescharacteristic, complemented
211#463—371no—
212#463—371no—
213#460—371no—
214#460—371no—
215#459—371no—
216#459—371no—
217#424—371no—
218#417—371no—
219C2×#102—371no—
220C37#304511yescharacteristic, complemented, Sylow
221C2×#41—371no—
222C2×#41—371no—
223C22×D4—371no—
224AGL(1,ℤ/8)—744no—
225#135—744no—
226C2×Q16C2×D3711yescharacteristic, complemented
227C2×SD16—371no—
228C2×SD16—371no—
229C2×SD16—371no—
230C2×SD16C2×D3711yescharacteristic
231C2×D8—371no—
232C2×D8—371no—
233C2×D8—371no—
234C2×M16—371no—
235C22×C8—371no—
236#127—371no—
237#127—371no—
238#124—371no—
239#124C2×D3711yescharacteristic
240#121—741no—
241#121—741no—
242#120—741no—
243#120—741no—
244C4×Q8—371no—
245C4×Q8C2×D3711yescharacteristic, complemented
246C4×D4—371no—
247C4×D4—371no—
248C4×D4—741no—
249C4×D4—741no—
250#117—371no—
251#117—741no—
252C2×C4⋊C4—371no—
253C2×C4⋊C4—741no—
254C4⋊C8—371no—
255C4⋊C8—371no—
256C4⋊C8—371no—
257C4⋊C8C2×D3711yescharacteristic, complemented
258#103—371no—
259#103C2×D3711yescharacteristic, complemented
260#102—371no—
261#102—371no—
262#102—371no—
263#102—371no—
264#102—371no—
265#102C2×D3711yescharacteristic
266C24—741no—
267#41—374no—
268#41—742no—
269#41—742no—
270#41—742no—
271C2×Q8C22×D3711yescharacteristic
272C2×Q8C22×D3711yescharacteristic
273C2×D4—371no—
274C2×D4—371no—
275C2×D4—371no—
276C2×D4—741no—
277C2×D4—741no—
278C2×D4—742no—
279C2×D4—742no—
280C2×D4—741no—
281C2×D4—741no—
282C2×D4—741no—
283C2×D4—741no—
284C2×D4—741no—
285C2×D4C22×D3711yescharacteristic
286C22×C4—371no—
287C22×C4—741no—
288C22×C4—741no—
289C22×C4—741no—
290C22×C4—741no—
291C22×C4—741no—
292Q16—22no—
293SD16—22no—
294SD16—742no—
295SD16—742no—
296SD16—742no—
297D8—742no—
298D8—742no—
299D8—742no—
300M16—742no—
301C2×C8—371no—
302C2×C8—371no—
303C2×C8—742no—
304C2×C8C22×D3711yescharacteristic
305C2×C8C22×D3711yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—371no—
308C4⋊C4—371no—
309C4⋊C4—371no—
310C4⋊C4—741no—
311C4⋊C4—741no—
312C4⋊C4C22×D3711yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—371no—
316C22⋊C4—371no—
317C22⋊C4—741no—
318C22⋊C4—741no—
319C22⋊C4—741no—
320C22⋊C4—741no—
321C42—21no—
322C42—371no—
323C42—741no—
324C42C22×D3711yescharacteristic
325C23—21no—
326C23—371no—
327C23—2961no—
328C23—2961no—
329C23—741no—
330C23—741no—
331C23—741no—
332C23—1482no—
333Q8—21no—
334Q8—21no—
335Q8—21no—
336Q8D4×D3712yes—
337D4—21no—
338D4—21no—
339D4—372no—
340D4—2961no—
341D4—2961no—
342D4—2961no—
343D4—2961no—
344D4—744no—
345D4—741no—
346D4—741no—
347D4—741no—
348D4—741no—
349D4—741no—
350D4—1482no—
351D4—1482no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—371no—
356C2×C4—372no—
357C2×C4—372no—
358C2×C4—371no—
359C2×C4—371no—
360C2×C4—2961no—
361C2×C4—2961no—
362C2×C4—2961no—
363C2×C4—744no—
364C2×C4—741no—
365C2×C4—1482no—
366C2×C4D4×D3711yescharacteristic
367C2×C4D4×D3711yescharacteristic
368C2×C4C23×D3711yescharacteristic
369C8—21no—
370C8—21no—
371C8—741no—
372C8—741no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—372no—
377C22—2964no—
378C22—741no—
379C22—741no—
380C22—742no—
381C22—1481no—
382C22—1481no—
383C22—1481no—
384C22—1481no—
385C22—1481no—
386C22—1481no—
387C22—1481no—
388C22—1481no—
389C22C2×D4×D3711yescharacteristic
390C4—22no—
391C4—21no—
392C4—21no—
393C4—41no—
394C4—41no—
395C4—372no—
396C4—741no—
397C4—741no—
398C4—1481no—
399C4C2×D4×D3711yescharacteristic
400C4#41×D3711yescharacteristic
401C2—81no—
402C2—2961no—
403C2—2961no—
404C2—742no—
405C2—1482no—
406C2#121×D3711yescharacteristic
407C2#1455833511yescharacteristic
408C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#464C2
socleC22×C37C22×D4
hypercenter#464D37
hypocenterC37#3045
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×#11924563C2semidirect
2. C2×#11924559C2semidirect
3. #14558101C2semidirect
4. #14558015C2semidirect
5. #14557757C2semidirect
6. #14557751C2semidirect
7. #14557745C2semidirect
8. #14557733C2semidirect
9. #14557731C2semidirect
10. #14557729C2semidirect
11. #14557727C2semidirect
12. #14557558C2semidirect
13. #14557533C2semidirect
14. #102×D37C2semidirect
15. C37×#464C2semidirect
22. C2×#10596941C22semidirect
23. C2×#10596941C22semidirect
25. C2×D296C22semidirect
36. Q8×Dic37C22semidirect
38. C4×D148C22semidirect
40. #11924498C22semidirect
45. C4⋊#64436C22semidirect
46. #11924465C22semidirect
47. #11924465C22semidirect
48. #11924460C22semidirect
50. #11924458C22semidirect
53. #11924456C22semidirect
54. C2×Q16×C37C22semidirect
57. C4×Q8×C37C22semidirect
58. C4⋊C8×C37C22semidirect
59. #103×C37C22semidirect
71. #10596966D4semidirect
210. #464D37semidirect
220. C37#3045semidirect
226. C2×Q16C2×D37semidirect
245. C4×Q8C2×D37semidirect
257. C4⋊C8C2×D37semidirect
259. #103C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245632
C2×#119245592
#145581012
#145580152
#145577572
#145577512
#145577452
#145577332
#145577312
#145577292
#145577272
#145575582
#145575332
#102×D372
C37×#4642
#304537