Finite Group Databasebeta

← #18004328

Subgroups — #18004328

Order 4736.

446 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558329C211yesmaximal, characteristic
2C2×#11924565C211yesmaximal, characteristic, complemented
3#137×D37C211yesmaximal, characteristic, complemented
4#14558298C211yesmaximal, characteristic, complemented
5#14557809C211yesmaximal, characteristic, complemented
6#14557808C211yesmaximal, characteristic, complemented
7#14557807C211yesmaximal, characteristic, complemented
8#14557806C211yesmaximal, characteristic, complemented
9#14557795C211yesmaximal, characteristic, complemented
10#14557794C211yesmaximal, characteristic, complemented
11#14557793C211yesmaximal, characteristic, complemented
12#14557580C211yesmaximal, characteristic, complemented
13#14557514C211yesmaximal, characteristic, complemented
14#101×D37C211yesmaximal, characteristic, complemented
15C37×#471C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17#41×D37C2211yescharacteristic
18C2×Q8×D37C2211yescharacteristic
19#11924569C2211yescharacteristic
20#11924569C2211yescharacteristic
21#11924568—21no—
22#11924567C2211yescharacteristic
23#11924566C2211yescharacteristic
24#11924566C2211yescharacteristic
25#11924565—21no—
26#11924565—21no—
27#11924565—21no—
28#11924565—21no—
29#11924565—21no—
30#11924565—21no—
31#11924562C2211yescharacteristic
32#11924560—21no—
33#11924557—21no—
34#11924555—21no—
35C2×Dic148C2211yescharacteristic, complemented
36C2×#10596942C2211yescharacteristic, complemented
37Q16×D37—21no—
38C2×#10596940C2211yescharacteristic, complemented
39SD16×D37—21no—
40#11924544—21no—
41#11924544C2211yescharacteristic
42#11924543C2211yescharacteristic
43#11924542—21no—
44#11924542C2211yescharacteristic
45C2×#10596929—21no—
46C2×#10596929C2211yescharacteristic
47M16×D37—21no—
48M16×D37C2211yescharacteristic
49M16×D37C2211yescharacteristic
50M16×D37C2211yescharacteristic
51#11924472C2211yescharacteristic, complemented
52#11924471C2211yescharacteristic, complemented
53#11924471C2211yescharacteristic, complemented
54#11924455C2211yescharacteristic, complemented
55#11924454C2211yescharacteristic, complemented
56#11924454C2211yescharacteristic, complemented
57#11924454C2211yescharacteristic, complemented
58#11924454C2211yescharacteristic, complemented
59#11924453C2211yescharacteristic, complemented
60#137×C37C2211yescharacteristic
61AGL(1,ℤ/8)×C37C2211yescharacteristic
62C2×SD16×C37C2211yescharacteristic, complemented
63#131×C37C2211yescharacteristic
64#108×C37C2211yescharacteristic, complemented
65#101×C37C2211yescharacteristic, complemented
66#100×C37C2211yescharacteristic, complemented
67#41×C37C2311yescharacteristic
68C2×Q8×C37C2311yescharacteristic
69C2×D4×C37C2311yescharacteristic
70C2×C22⋊D37—21no—
71C22×Dic37—21no—
72#10596966D411yescharacteristic
73Q8×D37—21no—
74Q8×D37—21no—
75Q8×D37—21no—
76Q8×D37—21no—
77Q8×D37D411yescharacteristic
78#10596964—21no—
79#10596964—21no—
80#10596964—21no—
81#10596964—21no—
82#10596964—21no—
83#10596964D411yescharacteristic
84D4×D37—21no—
85D4×D37D411yescharacteristic
86#10596962—21no—
87#10596962C2311yescharacteristic
88C2×C4×D37—21no—
89C2×C4×D37—21no—
90C2×C4×D37C2311yescharacteristic
91C2×Dic74—21no—
92C2×Dic74C2311yescharacteristic
93C2×Dic74C2311yescharacteristic
94Q16×C37—21no—
95SD16×C37—21no—
96SD16×C37—21no—
97SD16×C37—21no—
98SD16×C37—21no—
99D8×C37—21no—
100M16×C37—21no—
101M16×C37C2311yescharacteristic
102M16×C37C2311yescharacteristic
103M16×C37C2311yescharacteristic
104C2×C8×C37—21no—
105C2×C8×C37C2311yescharacteristic
106#10596942—21no—
107#10596942—21no—
108#10596942—21no—
109#10596942—21no—
110#10596942—21no—
111#10596941—21no—
112#10596940—21no—
113#10596940—21no—
114#10596940—21no—
115#10596940—21no—
116#10596940—21no—
117#10596939—21no—
118#10596934—21no—
119#10596934C2311yescharacteristic
120#10596934C2311yescharacteristic
121#10596934C2311yescharacteristic
122C2×#64436—21no—
123C2×#64436C2311yescharacteristic
124Dic148—21no—
125Dic148—21no—
126Dic148—21no—
127Dic148—21no—
128#10596930—21no—
129#10596930—21no—
130#10596929—21no—
131#10596929—21no—
132#10596929—21no—
133#10596929—21no—
134#10596929—21no—
135#10596929D411yescharacteristic
136#10596929D411yescharacteristic
137#10596929D411yescharacteristic
138#10596929D411yescharacteristic
139C8×D37—21no—
140C8×D37—21no—
141C8×D37—21no—
142C8×D37—21no—
143C8×D37—21no—
144C23×C37—21no—
145C22×D37—21no—
146C22×D37#4111yescharacteristic
147Q8×C37—21no—
148Q8×C37—21no—
149Q8×C37C2×D411yescharacteristic
150D4×C37—21no—
151D4×C37—21no—
152D4×C37—21no—
153D4×C37C2×D411yescharacteristic
154C2×C4×C37—21no—
155C2×C4×C37—21no—
156C2×C4×C37C2411yescharacteristic
157C22⋊D37—21no—
158C22⋊D37—21no—
159C22⋊D37—21no—
160C22⋊D37—41no—
161C22⋊D37—41no—
162C2×Dic37—21no—
163C2×Dic37—21no—
164C2×Dic37—21no—
165C2×Dic37—41no—
166C2×Dic37—41no—
167C2×Dic37#4111yescharacteristic
168D148—21no—
169D148C2×D411yescharacteristic
170C4×D37—21no—
171C4×D37—21no—
172C4×D37—21no—
173C4×D37—41no—
174C4×D37—41no—
175C4×D37C2×D411yescharacteristic
176C4×D37C2×D411yescharacteristic
177C4×D37C2×D411yescharacteristic
178C4×D37C2×D411yescharacteristic
179Dic74—21no—
180Dic74—21no—
181Dic74—21no—
182Dic74—21no—
183Dic74—21no—
184Dic74—41no—
185Dic74—41no—
186Dic74C2×D411yescharacteristic
187C8×C37—21no—
188C8×C37—21no—
189C8×C37—21no—
190C8×C37C2×D411yescharacteristic
191C8×C37C2×D411yescharacteristic
192#64436—21no—
193#64436—21no—
194#64436—21no—
195#64436C2×D411yescharacteristic
196#64436C2×D411yescharacteristic
197C22×C37—21no—
198C22×C37—41no—
199C22×C37—81no—
200C22×C37C2×#4111yescharacteristic
201C2×D37—21no—
202C2×D37—41no—
203C2×D37—81no—
204C2×D37#12111yescharacteristic
205C2×D37#12111yescharacteristic
206C4×C37—21no—
207C4×C37—41no—
208C4×C37C22×D411yescharacteristic
209C4×C37C22×D411yescharacteristic
210Dic37—21no—
211Dic37—41no—
212Dic37—41no—
213Dic37#12111yescharacteristic
214Dic37#12111yescharacteristic
215#3069—371nomaximal, Sylow
216C2×C37—21no—
217C2×C37—41no—
218C2×C37—81no—
219C2×C37C2×#12111yescharacteristic
220D37—21no—
221D37—21no—
222D37—41no—
223#575—371no—
224C2×#137—371no—
225C2×#137—371no—
226#568—371no—
227#473—371no—
228#473—371no—
229#473—371no—
230#473—371no—
231#471—371no—
232#471—371no—
233#471—371no—
234#471D3711yescharacteristic, complemented
235#430—371no—
236#413—371no—
237C2×#101—371no—
238C37#306911yescharacteristic, complemented, Sylow
239C2×#41—371no—
240C2×#41—371no—
241C22×Q8—371no—
242#137—371no—
243#137—371no—
244#137—371no—
245#137—371no—
246#137—371no—
247#137—741no—
248#137—741no—
249#137—741no—
250#137—741no—
251#137—741no—
252#137—741no—
253#137—741no—
254#137C2×D3711yescharacteristic
255AGL(1,ℤ/8)—371no—
256AGL(1,ℤ/8)—741no—
257AGL(1,ℤ/8)C2×D3711yescharacteristic
258#135—741no—
259#135—741no—
260C2×Q16—371no—
261C2×Q16—371no—
262C2×Q16—741no—
263C2×SD16—371no—
264C2×SD16—741no—
265C2×SD16C2×D3711yescharacteristic, complemented
266#131—371no—
267#131—371no—
268#131—371no—
269#131—741no—
270#131—741no—
271#131C2×D3711yescharacteristic
272C2×M16—371no—
273C2×M16—371no—
274C2×M16—371no—
275C2×M16—371no—
276C2×M16—741no—
277C2×M16—741no—
278#108—371no—
279#108—371no—
280#108—371no—
281#108C2×D3711yescharacteristic, complemented
282#101—371no—
283#101—371no—
284#101—371no—
285#101—371no—
286#101—371no—
287#101C2×D3711yescharacteristic, complemented
288#100—371no—
289#100C2×D3711yescharacteristic, complemented
290#41—371no—
291#41—371no—
292#41—371no—
293#41—741no—
294#41—741no—
295#41—741no—
296#41—741no—
297#41—741no—
298#41—741no—
299#41C22×D3711yescharacteristic
300C2×Q8—371no—
301C2×Q8—371no—
302C2×Q8—371no—
303C2×Q8—741no—
304C2×Q8—741no—
305C2×Q8—741no—
306C2×Q8—741no—
307C2×Q8—741no—
308C2×Q8C22×D3711yescharacteristic
309C2×D4—371no—
310C2×D4—741no—
311C2×D4—741no—
312C2×D4C22×D3711yescharacteristic
313C22×C4—371no—
314C22×C4—741no—
315C22×C4—741no—
316C22×C4—741no—
317Q16—21no—
318Q16—741no—
319Q16—741no—
320Q16—741no—
321Q16—741no—
322Q16—741no—
323Q16—741no—
324Q16—741no—
325Q16—741no—
326Q16—741no—
327SD16—21no—
328SD16—21no—
329SD16—21no—
330SD16—21no—
331SD16—741no—
332SD16—741no—
333SD16—741no—
334SD16—741no—
335SD16—741no—
336SD16—741no—
337SD16—741no—
338SD16—741no—
339D8—21no—
340D8—741no—
341M16—21no—
342M16—371no—
343M16—371no—
344M16—371no—
345M16—371no—
346M16—371no—
347M16—371no—
348M16—371no—
349M16—741no—
350M16—741no—
351M16—741no—
352M16—741no—
353M16—741no—
354M16—741no—
355M16C22×D3711yescharacteristic
356M16C22×D3711yescharacteristic
357M16C22×D3711yescharacteristic
358C2×C8—21no—
359C2×C8—371no—
360C2×C8—741no—
361C2×C8—741no—
362C2×C8—741no—
363C2×C8—741no—
364C2×C8—741no—
365C2×C8—741no—
366C2×C8C22×D3711yescharacteristic
367C23—21no—
368C23—371no—
369C23—741no—
370Q8—21no—
371Q8—21no—
372Q8—371no—
373Q8—741no—
374Q8—741no—
375Q8—741no—
376Q8—741no—
377Q8—741no—
378Q8—1481no—
379Q8—1481no—
380Q8D4×D3711yescharacteristic
381D4—21no—
382D4—21no—
383D4—21no—
384D4—371no—
385D4—741no—
386D4—741no—
387D4—741no—
388D4—741no—
389D4—1481no—
390D4—1481no—
391D4D4×D3711yescharacteristic
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—371no—
395C2×C4—371no—
396C2×C4—371no—
397C2×C4—371no—
398C2×C4—371no—
399C2×C4—741no—
400C2×C4—741no—
401C2×C4—741no—
402C2×C4—741no—
403C2×C4—741no—
404C2×C4—741no—
405C2×C4—1481no—
406C2×C4—1481no—
407C2×C4—1481no—
408C2×C4—1481no—
409C2×C4C23×D3711yescharacteristic
410C8—21no—
411C8—21no—
412C8—21no—
413C8—371no—
414C8—371no—
415C8—741no—
416C8—741no—
417C8—741no—
418C8D4×D3711yescharacteristic
419C8D4×D3711yescharacteristic
420C22—21no—
421C22—41no—
422C22—81no—
423C22—371no—
424C22—371no—
425C22—2961no—
426C22—741no—
427C22—1481no—
428C22#41×D3711yescharacteristic
429C4—21no—
430C4—41no—
431C4—371no—
432C4—371no—
433C4—741no—
434C4—1481no—
435C4—1481no—
436C4C2×D4×D3711yescharacteristic
437C4C2×D4×D3711yescharacteristic
438C2—21no—
439C2—41no—
440C2—81no—
441C2—741no—
442C2—741no—
443C2—1481no—
444C2#121×D3711yescharacteristic
subgroupG/H
centerC2#121×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#471C2
socleC2×C37C2×#121
prime radical#14558329C2
hypercenter#471D37
hypocenterC37#3069
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
2. C2×#11924565C2semidirect
3. #137×D37C2semidirect
4. #14558298C2semidirect
5. #14557809C2semidirect
6. #14557808C2semidirect
7. #14557807C2semidirect
8. #14557806C2semidirect
9. #14557795C2semidirect
10. #14557794C2semidirect
11. #14557793C2semidirect
12. #14557580C2semidirect
13. #14557514C2semidirect
14. #101×D37C2semidirect
15. C37×#471C2semidirect
35. C2×Dic148C22semidirect
36. C2×#10596942C22semidirect
38. C2×#10596940C22semidirect
51. #11924472C22semidirect
52. #11924471C22semidirect
53. #11924471C22semidirect
54. #11924455C22semidirect
55. #11924454C22semidirect
56. #11924454C22semidirect
57. #11924454C22semidirect
58. #11924454C22semidirect
59. #11924453C22semidirect
62. C2×SD16×C37C22semidirect
64. #108×C37C22semidirect
65. #101×C37C22semidirect
66. #100×C37C22semidirect
234. #471D37semidirect
238. C37#3069semidirect
265. C2×SD16C2×D37semidirect
281. #108C2×D37semidirect
287. #101C2×D37semidirect
289. #100C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583292
C2×#119245652
#137×D372
#145582982
#145578092
#145578082
#145578072
#145578062
#145577952
#145577942
#145577932
#145575802
#145575142
#101×D372
C37×#4712
#306937