Finite Group Databasebeta

← #18006183

Subgroups — #18006183

Order 4736.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924568C211yesmaximal, characteristic, complemented
2C2×#11924559C211yesmaximal, characteristic, complemented
3#14558205C211yesmaximal, characteristic, complemented
4#14558195C211yesmaximal, characteristic, complemented
5#14557922C211yesmaximal, characteristic, complemented
6#14557787C211yesmaximal, characteristic, complemented
7#14557763C211yesmaximal, characteristic, complemented
8#14557755C211yesmaximal, characteristic, complemented
9#14557733C211yesmaximal, characteristic, complemented
10#14557698C211yesmaximal, characteristic, complemented
11#14557681C211yesmaximal, characteristic, complemented
12#14557681C211yesmaximal, characteristic, complemented
13#14557673C211yesmaximal, characteristic, complemented
14#14557606C211yesmaximal, characteristic, complemented
15C37×#441C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596966C2211yescharacteristic
18C2×#10596966C2211yescharacteristic
19C2×Q8×D37C2211yescharacteristic
20#11924568—24no—
21#11924559—24no—
22C2×#10596942C2211yescharacteristic
23C2×#10596930C2211yescharacteristic
24C2×#10596930C2211yescharacteristic
25C2×#10596941C2211yescharacteristic
26C2×#10596941C2211yescharacteristic
27C2×#10596941C2211yescharacteristic
28C2×D296C2211yescharacteristic
29C2×D296C2211yescharacteristic
30C2×#10596929C2211yescharacteristic
31C2×C8×D37C2211yescharacteristic
32#11924533—21no—
33#11924533C2211yescharacteristic
34#11924524—21no—
35#11924524C2211yescharacteristic
36#11924516—21no—
37#11924516C2211yescharacteristic
38#11924511—21no—
39#11924511—21no—
40#11924511—21no—
41#11924511C2211yescharacteristic
42#11924511C2211yescharacteristic
43#11924511C2211yescharacteristic
44C4×D148—21no—
45C4×D148—21no—
46C4×D148C2211yescharacteristic
47C4⋊#64436C2211yescharacteristic
48#11924459C2211yescharacteristic
49#11924456C2211yescharacteristic
50#11924456C2211yescharacteristic
51#11924456C2211yescharacteristic
52#11924448C2211yescharacteristic
53#11924448C2211yescharacteristic
54C2×Q16×C37C2211yescharacteristic
55C4×Q8×C37C2211yescharacteristic
56C4×Q8×C37C2211yescharacteristic
57#106×C37C2211yescharacteristic
58#103×C37C2211yescharacteristic
59#103×C37C2211yescharacteristic
60#97×C37C2211yescharacteristic
61C2×Q8×C37C2311yescharacteristic
62C2×Q8×C37C2311yescharacteristic
63#10596966—22no—
64#10596966—22no—
65#10596966—22no—
66#10596966—41no—
67#10596966—41no—
68#10596966—41no—
69Q8×D37—22no—
70Q8×D37—41no—
71C2×D148—21no—
72C2×D148—21no—
73C2×D148—21no—
74C2×D148—21no—
75C2×D148—21no—
76C2×D148—21no—
77C2×D148—21no—
78C2×D148—21no—
79C2×D148D411yescharacteristic
80C2×D148C2311yescharacteristic
81C2×D148C2311yescharacteristic
82C2×D148C2311yescharacteristic
83C2×C4×D37—21no—
84C2×C4×D37—21no—
85C2×C4×D37—21no—
86C2×C4×D37—21no—
87C2×C4×D37C2311yescharacteristic
88C2×C4×D37C2311yescharacteristic
89C2×Dic74—21no—
90C2×Dic74C2311yescharacteristic
91Q16×C37D414yescomplemented
92C2×C8×C37C2311yescharacteristic
93C2×C8×C37C2311yescharacteristic
94C4⋊C4×C37—21no—
95C4⋊C4×C37—21no—
96C4⋊C4×C37C2311yescharacteristic
97C4⋊C4×C37C2311yescharacteristic
98C42×C37—21no—
99C42×C37—21no—
100C42×C37C2311yescharacteristic
101#10596942—22no—
102#10596941—22no—
103#10596941—22no—
104#10596941—22no—
105#10596938—21no—
106#10596938—21no—
107#10596938—21no—
108#10596938—21no—
109#10596938—21no—
110#10596938—21no—
111#10596938D411yescharacteristic
112#10596938D411yescharacteristic
113C4⋊Dic37—21no—
114C4⋊Dic37D411yescharacteristic
115C2×#64436C2311yescharacteristic
116C2×#64436C2311yescharacteristic
117D296—22no—
118D296—41no—
119#10596930—22no—
120#10596930—41no—
121#10596929—22no—
122C8×D37—22no—
123C22×D37—21no—
124C22×D37—21no—
125C22×D37—21no—
126C22×D37C2×D411yescharacteristic
127C22×D37C2×D411yescharacteristic
128Q8×C37—21no—
129Q8×C37—21no—
130Q8×C37C2×D412yes—
131Q8×C37C2×D412yes—
132C2×C4×C37—21no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—21no—
136C2×C4×C37C2×D411yescharacteristic
137C2×C4×C37C2×D411yescharacteristic
138C2×C4×C37C2411yescharacteristic
139C2×Dic37—21no—
140C2×Dic37C2×D411yescharacteristic
141C2×Dic37C2×D411yescharacteristic
142D148—21no—
143D148—21no—
144D148—21no—
145D148—21no—
146D148—21no—
147D148—21no—
148D148—41no—
149D148—42no—
150D148—42no—
151D148—42no—
152D148—42no—
153D148—42no—
154D148—81no—
155D148—81no—
156D148—81no—
157C4×D37—21no—
158C4×D37—21no—
159C4×D37—21no—
160C4×D37—21no—
161C4×D37—42no—
162C4×D37—42no—
163C4×D37—42no—
164C4×D37—42no—
165Dic74—21no—
166Dic74—21no—
167Dic74—42no—
168C8×C37—21no—
169C8×C37C2×D412yes—
170#64436—21no—
171#64436—21no—
172C22×C37C22×D411yescharacteristic
173C2×D37—21no—
174C2×D37—21no—
175C2×D37—21no—
176C2×D37—21no—
177C2×D37—21no—
178C2×D37—21no—
179C2×D37—41no—
180C2×D37—41no—
181C2×D37—41no—
182C2×D37—41no—
183C2×D37—41no—
184C2×D37—41no—
185C2×D37—41no—
186C2×D37—41no—
187C2×D37—41no—
188C4×C37—22no—
189C4×C37—22no—
190C4×C37—21no—
191C4×C37—21no—
192C4×C37—41no—
193C4×C37—41no—
194C4×C37C22×D411yescharacteristic
195C4×C37H(5,𝔽2)11yescharacteristic
196Dic37—21no—
197Dic37—21no—
198Dic37—41no—
199#3271—371nomaximal, Sylow
200C2×C37D4211yescharacteristic
201C2×C37#57511yescharacteristic
202C2×C37#57711yescharacteristic
203D37—41no—
204D37—41no—
205D37—81no—
206D37—81no—
207D37—81no—
208C2×#137—371no—
209C2×#135—371no—
210#550—371no—
211#548—371no—
212#496—371no—
213#469—371no—
214#465—371no—
215#464—371no—
216#460—371no—
217#452—371no—
218#449—371no—
219#449—371no—
220#448—371no—
221#441D3711yescharacteristic, complemented
222#435—371no—
223C37#327111yescharacteristic, complemented, Sylow
224C2×#41—371no—
225C2×#41—371no—
226C2×#41—371no—
227C22×Q8—371no—
228#137—744no—
229#135—744no—
230C2×Q16—371no—
231C2×Q16C2×D3711yescharacteristic
232C2×SD16—371no—
233C2×SD16—371no—
234C2×SD16—371no—
235C2×SD16—371no—
236C2×SD16—371no—
237C2×D8—371no—
238C2×D8—371no—
239C2×M16—371no—
240C22×C8—371no—
241#127—371no—
242#127—741no—
243#124—371no—
244#124—741no—
245C22⋊Q8—371no—
246C22⋊Q8—741no—
247#121—371no—
248#121—371no—
249#121—371no—
250#121—741no—
251#121—741no—
252#121—741no—
253C4×Q8C2×D3711yescharacteristic
254C4×Q8C2×D3711yescharacteristic
255C4×D4—371no—
256C4×D4—741no—
257C4×D4—741no—
258#106C2×D3711yescharacteristic
259C4⋊C8—371no—
260#103—371no—
261#103C2×D3711yescharacteristic
262#103C2×D3711yescharacteristic
263#102—371no—
264#102—371no—
265#102—371no—
266C22⋊C8—371no—
267C22⋊C8—371no—
268#97C2×D3711yescharacteristic
269#41—742no—
270#41—742no—
271#41—742no—
272#41—1481no—
273#41—1481no—
274#41—1481no—
275C2×Q8—371no—
276C2×Q8—741no—
277C2×Q8—742no—
278C2×Q8—1481no—
279C2×Q8C22×D3711yescharacteristic
280C2×Q8C22×D3711yescharacteristic
281C2×D4—371no—
282C2×D4—371no—
283C2×D4—371no—
284C2×D4—371no—
285C2×D4—741no—
286C2×D4—741no—
287C2×D4—741no—
288C2×D4—741no—
289C2×D4—741no—
290C2×D4—741no—
291C2×D4—741no—
292C2×D4—741no—
293C22×C4—371no—
294C22×C4—371no—
295C22×C4—741no—
296C22×C4—741no—
297C22×C4—741no—
298C22×C4—741no—
299Q16—742no—
300Q16D14814yescomplemented
301SD16—742no—
302SD16—742no—
303SD16—742no—
304SD16—742no—
305SD16—1481no—
306D8—742no—
307D8—1481no—
308M16—742no—
309C2×C8—371no—
310C2×C8—371no—
311C2×C8—742no—
312C2×C8C22×D3711yescharacteristic
313C2×C8C22×D3711yescharacteristic
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—371no—
317C4⋊C4—741no—
318C4⋊C4C22×D3711yescharacteristic
319C4⋊C4C22×D3711yescharacteristic
320C22⋊C4—371no—
321C22⋊C4—371no—
322C22⋊C4—741no—
323C22⋊C4—741no—
324C22⋊C4—741no—
325C22⋊C4—741no—
326C22⋊C4—741no—
327C22⋊C4—741no—
328C42—21no—
329C42—21no—
330C42C22×D3711yescharacteristic
331C23—371no—
332C23—371no—
333C23—741no—
334C23—741no—
335C23—741no—
336Q8—21no—
337Q8—21no—
338Q8—741no—
339Q8—741no—
340Q8—1482no—
341Q8C2×D14812yes—
342Q8C2×D14812yes—
343D4—2961no—
344D4—2961no—
345D4—2961no—
346D4—741no—
347D4—741no—
348D4—741no—
349D4—741no—
350D4—741no—
351D4—741no—
352D4—1481no—
353D4—1482no—
354D4—1482no—
355D4—1482no—
356D4—1482no—
357D4—1482no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—371no—
363C2×C4—371no—
364C2×C4—741no—
365C2×C4—741no—
366C2×C4—741no—
367C2×C4—741no—
368C2×C4—741no—
369C2×C4—1482no—
370C2×C4—1482no—
371C2×C4—1482no—
372C2×C4—1482no—
373C2×C4D4×D3711yescharacteristic
374C2×C4D4×D3711yescharacteristic
375C2×C4C23×D3711yescharacteristic
376C8—21no—
377C8—741no—
378C8—741no—
379C8C2×D14812yes—
380C22—741no—
381C22—741no—
382C22—741no—
383C22—741no—
384C22—741no—
385C22—741no—
386C22—1481no—
387C22—1481no—
388C22—1481no—
389C22—1481no—
390C22—1481no—
391C22—1481no—
392C22—1481no—
393C22—1481no—
394C22—1481no—
395C22C2×D4×D3711yescharacteristic
396C4—21no—
397C4—21no—
398C4—22no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—741no—
403C4—741no—
404C4—1481no—
405C4C22×D14811yescharacteristic
406C4#1192458211yescharacteristic
407C2—2961no—
408C2—2961no—
409C2—2961no—
410C2—1481no—
411C2—1481no—
412C2D4×D14811yescharacteristic
413C2#1455833211yescharacteristic
414C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#441C2
socleC22×C37C22×D4
hypercenter#441D37
hypocenterC37#3271
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. C2×#11924568C2semidirect
2. C2×#11924559C2semidirect
3. #14558205C2semidirect
4. #14558195C2semidirect
5. #14557922C2semidirect
6. #14557787C2semidirect
7. #14557763C2semidirect
8. #14557755C2semidirect
9. #14557733C2semidirect
10. #14557698C2semidirect
11. #14557681C2semidirect
12. #14557681C2semidirect
13. #14557673C2semidirect
14. #14557606C2semidirect
15. C37×#441C2semidirect
91. Q16×C37D4semidirect
221. #441D37semidirect
223. C37#3271semidirect
300. Q16D148semidirect

Maximal subgroups

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

subgroupindex
C2×#119245682
C2×#119245592
#145582052
#145581952
#145579222
#145577872
#145577632
#145577552
#145577332
#145576982
#145576812
#145576732
#145576062
C37×#4412
#327137