Finite Group Databasebeta

← #18006106

Subgroups — #18006106

Order 4736.

494 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×#11924565C211yesmaximal, characteristic, complemented
2Q8×C22⋊D37C211yesmaximal, characteristic, complemented
3#14558177C211yesmaximal, characteristic
4#14557924C211yesmaximal, characteristic, complemented
5#14557776C211yesmaximal, characteristic, complemented
6#14557774C211yesmaximal, characteristic, complemented
7#14557753C211yesmaximal, characteristic, complemented
8#14557736C211yesmaximal, characteristic, complemented
9#14557692C211yesmaximal, characteristic, complemented
10#14557689C211yesmaximal, characteristic, complemented
11#14557684C211yesmaximal, characteristic, complemented
12#14557670C211yesmaximal, characteristic, complemented
13#14557634C211yesmaximal, characteristic, complemented
14#14557604C211yesmaximal, characteristic, complemented
15C22×SD16×C37C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×Q8×D37C2211yescharacteristic, complemented
18#11924565—24no—
19C2×Dic148C2211yescharacteristic, complemented
20C2×#10596942C2211yescharacteristic, complemented
21C2×#10596942C2211yescharacteristic, complemented
22C2×#10596940C2211yescharacteristic
23C2×#10596940C2211yescharacteristic
24C2×#10596929C2211yescharacteristic, complemented
25#11924534—21no—
26#11924534C2211yescharacteristic, complemented
27#11924523C2211yescharacteristic
28#11924517—21no—
29#11924515—21no—
30#11924515C2211yescharacteristic
31#11924515C2211yescharacteristic
32#11924512—21no—
33#11924512C2211yescharacteristic, complemented
34#11924508—21no—
35#11924507C2211yescharacteristic
36#11924505—21no—
37Q8×Dic37C2211yescharacteristic, complemented
38D4×Dic37C2211yescharacteristic
39C4×C22⋊D37—21no—
40C4×C22⋊D37C2211yescharacteristic
41C2×C22⋊Dic37—21no—
42#11924470C2211yescharacteristic, complemented
43#11924465C2211yescharacteristic, complemented
44#11924461C2211yescharacteristic, complemented
45#11924461C2211yescharacteristic, complemented
46#11924460C2211yescharacteristic, complemented
47#11924460C2211yescharacteristic, complemented
48#11924457C2211yescharacteristic
49#11924457C2211yescharacteristic
50C22⋊#64436C2211yescharacteristic
51#11924448C2211yescharacteristic, complemented
52#11924446C2211yescharacteristic, complemented
53C22×Q8×C37C2211yescharacteristic
54C22×D4×C37C2211yescharacteristic
55C2×SD16×C37—24no—
56C2×SD16×C37C2211yescharacteristic
57C2×SD16×C37C2211yescharacteristic
58C2×SD16×C37C2211yescharacteristic
59C2×SD16×C37C2211yescharacteristic
60C22×C8×C37C2211yescharacteristic
61C24×C37—21no—
62C2×Q8×C37—21no—
63C2×Q8×C37—22no—
64C2×Q8×C37—41no—
65C2×Q8×C37C2311yescharacteristic
66C2×Q8×C37C2311yescharacteristic
67C2×D4×C37—22no—
68C2×D4×C37—21no—
69C2×D4×C37—41no—
70C2×D4×C37C2311yescharacteristic
71C2×D4×C37C2311yescharacteristic
72C22×C4×C37—21no—
73C22×C4×C37C2311yescharacteristic
74C2×C22⋊D37—21no—
75C2×C22⋊D37—21no—
76C2×C22⋊D37D411yescharacteristic
77C22×Dic37—21no—
78C22×Dic37—21no—
79Q8×D37—22no—
80Q8×D37—41no—
81#10596964—22no—
82#10596964—41no—
83C2×C4×D37—21no—
84C2×C4×D37C2311yescharacteristic
85C2×Dic74—21no—
86C2×Dic74C2311yescharacteristic
87C2×Dic74C2311yescharacteristic
88SD16×C37—22no—
89SD16×C37—22no—
90SD16×C37—22no—
91SD16×C37D414yescomplemented
92C2×C8×C37—22no—
93C2×C8×C37C2311yescharacteristic
94C2×C8×C37C2311yescharacteristic
95C22⋊Dic37—21no—
96C22⋊Dic37—21no—
97C22⋊Dic37—21no—
98C22⋊Dic37—21no—
99C22⋊Dic37—21no—
100C22⋊Dic37—21no—
101C22⋊Dic37D411yescharacteristic
102#10596942—22no—
103#10596942—41no—
104#10596940—22no—
105#10596940—41no—
106#10596938—21no—
107#10596938D411yescharacteristic
108C4⋊Dic37—21no—
109C4⋊Dic37C2311yescharacteristic
110C4⋊Dic37C2311yescharacteristic
111#10596936—21no—
112#10596936—21no—
113#10596936—21no—
114#10596936—21no—
115#10596936—21no—
116#10596936D411yescharacteristic
117C4×Dic37—21no—
118C4×Dic37C2311yescharacteristic
119C2×#64436C2311yescharacteristic
120C2×#64436C2311yescharacteristic
121Dic148—22no—
122#10596929—22no—
123C23×C37—21no—
124C23×C37—21no—
125C23×C37—42no—
126C23×C37—42no—
127C23×C37—81no—
128C23×C37C2×D411yescharacteristic
129C22×D37C2×D411yescharacteristic
130Q8×C37—21no—
131Q8×C37—21no—
132Q8×C37—21no—
133Q8×C37—42no—
134Q8×C37C2×D412yes—
135D4×C37—21no—
136D4×C37—21no—
137D4×C37—21no—
138D4×C37—42no—
139D4×C37C2×D412yes—
140C2×C4×C37—21no—
141C2×C4×C37—21no—
142C2×C4×C37—21no—
143C2×C4×C37—21no—
144C2×C4×C37—42no—
145C2×C4×C37C2×D411yescharacteristic
146C2×C4×C37C2411yescharacteristic
147C22⋊D37—22no—
148C22⋊D37—42no—
149C22⋊D37—81no—
150C2×Dic37—21no—
151C2×Dic37—21no—
152C2×Dic37—21no—
153C2×Dic37—21no—
154C2×Dic37—42no—
155C2×Dic37—81no—
156C2×Dic37C2×D411yescharacteristic
157C2×Dic37C2×D411yescharacteristic
158C2×Dic37C2×D411yescharacteristic
159C4×D37—21no—
160C4×D37—21no—
161C4×D37—42no—
162Dic74—21no—
163Dic74—21no—
164Dic74—21no—
165Dic74—21no—
166Dic74—42no—
167C8×C37—21no—
168C8×C37C2×D412yes—
169#64436—21no—
170#64436—21no—
171C22×C37—21no—
172C22×C37—21no—
173C22×C37—22no—
174C22×C37—41no—
175C22×C37—41no—
176C22×C37—41no—
177C22×C37—41no—
178C22×C37—41no—
179C22×C37—84no—
180C22×C37#13712yescomplemented
181C22×C37C22×D411yescharacteristic
182C2×D37—21no—
183C2×D37—21no—
184C2×D37—21no—
185C4×C37—22no—
186C4×C37—21no—
187C4×C37—41no—
188C4×C37C22×D411yescharacteristic
189C4×C37H(5,𝔽2)11yescharacteristic
190Dic37—21no—
191Dic37—21no—
192Dic37—21no—
193Dic37—41no—
194Dic37—41no—
195Dic37—41no—
196Dic37—41no—
197#3266—371nomaximal, Sylow
198C2×C37—22no—
199C2×C37—42no—
200C2×C37—81no—
201C2×C37D4211yescharacteristic
202C2×C37C2×#13711yescharacteristic
203C2×C37#57711yescharacteristic
204D37—41no—
205C2×#137—371no—
206C22×SD16D3711yescharacteristic, complemented
207D4×Q8—371no—
208#546—371no—
209#497—371no—
210#468—371no—
211#467—371no—
212#464—371no—
213#461—371no—
214#452—371no—
215#451—371no—
216#450—371no—
217#448—371no—
218#440—371no—
219#435—371no—
220C37#326611yescharacteristic, complemented, Sylow
221C2×#41—371no—
222C22×Q8—371no—
223C22×Q8C2×D3711yescharacteristic
224C22×D4C2×D3711yescharacteristic
225#137—744no—
226C2×Q16—371no—
227C2×Q16—371no—
228C2×Q16—371no—
229C2×SD16—24no—
230C2×SD16—371no—
231C2×SD16—371no—
232C2×SD16C2×D3711yescharacteristic
233C2×SD16C2×D3711yescharacteristic
234C2×SD16C2×D3711yescharacteristic
235C2×SD16C2×D3711yescharacteristic
236C2×M16—371no—
237C22×C8C2×D3711yescharacteristic
238C4⋊Q8—371no—
239C4⋊Q8—741no—
240#124—371no—
241#123—741no—
242C22⋊Q8—371no—
243C22⋊Q8—371no—
244C22⋊Q8—371no—
245C22⋊Q8—741no—
246C22⋊Q8—741no—
247#121—371no—
248#121—741no—
249#120—741no—
250C4×Q8—371no—
251C4×D4—371no—
252C4×D4—371no—
253C4×D4—741no—
254C2×C22⋊C4—741no—
255#107—371no—
256C4⋊C8—371no—
257#103—371no—
258#103—371no—
259#103—371no—
260#103—371no—
261#102—371no—
262#102—371no—
263C22⋊C8—371no—
264C22⋊C8—371no—
265#97—371no—
266C24—21no—
267#41—742no—
268#41—1481no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—371no—
273C2×Q8—371no—
274C2×Q8—741no—
275C2×Q8—742no—
276C2×Q8—1481no—
277C2×Q8C22×D3711yescharacteristic
278C2×Q8C22×D3711yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—371no—
283C2×D4—741no—
284C2×D4—741no—
285C2×D4C22×D3711yescharacteristic
286C2×D4C22×D3711yescharacteristic
287C22×C4—21no—
288C22×C4—371no—
289C22×C4—741no—
290C22×C4—741no—
291C22×C4—741no—
292C22×C4C22×D3711yescharacteristic
293Q16—742no—
294Q16—742no—
295Q16—1481no—
296SD16—22no—
297SD16—22no—
298SD16—22no—
299SD16—742no—
300SD16—1481no—
301SD16C22⋊D3714yescomplemented
302M16—742no—
303C2×C8—22no—
304C2×C8—371no—
305C2×C8—371no—
306C2×C8C22×D3711yescharacteristic
307C2×C8C22×D3711yescharacteristic
308C4⋊C4—371no—
309C4⋊C4—371no—
310C4⋊C4—371no—
311C4⋊C4—741no—
312C4⋊C4—741no—
313C4⋊C4—741no—
314C4⋊C4—741no—
315C4⋊C4—741no—
316C4⋊C4—741no—
317C22⋊C4—371no—
318C22⋊C4—371no—
319C22⋊C4—741no—
320C22⋊C4—741no—
321C22⋊C4—741no—
322C22⋊C4—741no—
323C22⋊C4—741no—
324C22⋊C4—741no—
325C22⋊C4—741no—
326C42—371no—
327C42—741no—
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23—371no—
334C23D4×D3711yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—42no—
339Q8—741no—
340Q8—741no—
341Q8—741no—
342Q8—741no—
343Q8—1482no—
344Q8C2×C22⋊D3712yes—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—2961no—
350D4—742no—
351D4—1482no—
352D4C2×C22⋊D3712yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—371no—
359C2×C4—371no—
360C2×C4—371no—
361C2×C4—2961no—
362C2×C4—741no—
363C2×C4—741no—
364C2×C4—741no—
365C2×C4—741no—
366C2×C4—741no—
367C2×C4—741no—
368C2×C4—1482no—
369C2×C4—1482no—
370C2×C4D4×D3711yescharacteristic
371C2×C4C23×D3711yescharacteristic
372C8—21no—
373C8—741no—
374C8—741no—
375C8C2×C22⋊D3712yes—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—84no—
385C22—741no—
386C22—741no—
387C22—741no—
388C22#1192456512yescomplemented
389C22C2×D4×D3711yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—741no—
394C4—741no—
395C4—741no—
396C4—1481no—
397C4—1481no—
398C4—1481no—
399C4—1481no—
400C4C22×C22⋊D3711yescharacteristic
401C4#1192458111yescharacteristic
402C2—22no—
403C2—42no—
404C2—81no—
405C2—1481no—
406C2D4×C22⋊D3711yescharacteristic
407C2C2×#1192456511yescharacteristic
408C2#1455833911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC22×SD16×C37C2
socleC22×C37C22×D4
prime radical#14558177C2
hypercenterC22×SD16D37
hypocenterC37#3266
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#11924565C2semidirect
2. Q8×C22⋊D37C2semidirect
4. #14557924C2semidirect
5. #14557776C2semidirect
6. #14557774C2semidirect
7. #14557753C2semidirect
8. #14557736C2semidirect
9. #14557692C2semidirect
10. #14557689C2semidirect
11. #14557684C2semidirect
12. #14557670C2semidirect
13. #14557634C2semidirect
14. #14557604C2semidirect
15. C22×SD16×C37C2semidirect
17. C2×Q8×D37C22semidirect
19. C2×Dic148C22semidirect
20. C2×#10596942C22semidirect
21. C2×#10596942C22semidirect
24. C2×#10596929C22semidirect
26. #11924534C22semidirect
33. #11924512C22semidirect
37. Q8×Dic37C22semidirect
42. #11924470C22semidirect
43. #11924465C22semidirect
44. #11924461C22semidirect
45. #11924461C22semidirect
46. #11924460C22semidirect
47. #11924460C22semidirect
51. #11924448C22semidirect
52. #11924446C22semidirect
91. SD16×C37D4semidirect
180. C22×C37#137semidirect
206. C22×SD16D37semidirect
220. C37#3266semidirect
301. SD16C22⋊D37semidirect
388. C22#11924565semidirect

Maximal subgroups

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

subgroupindex
C2×#119245652
Q8×C22⋊D372
#145581772
#145579242
#145577762
#145577742
#145577532
#145577362
#145576922
#145576892
#145576842
#145576702
#145576342
#145576042
C22×SD16×C372
#326637