Finite Group Databasebeta

← #18006323

Subgroups — #18006323

Order 4736.

494 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×#11924558C211yesmaximal, characteristic, complemented
2C2×#11924557C211yesmaximal, characteristic, complemented
3#14558201C211yesmaximal, characteristic, complemented
4#14558185C211yesmaximal, characteristic, complemented
5#14557904C211yesmaximal, characteristic, complemented
6#14557763C211yesmaximal, characteristic, complemented
7#14557742C211yesmaximal, characteristic, complemented
8#14557727C211yesmaximal, characteristic, complemented
9#14557696C211yesmaximal, characteristic, complemented
10#14557693C211yesmaximal, characteristic, complemented
11#14557681C211yesmaximal, characteristic, complemented
12#14557676C211yesmaximal, characteristic, complemented
13#14557620C211yesmaximal, characteristic, complemented
14C8×C22⋊D37C211yesmaximal, characteristic, complemented
15C37×#465C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596962C2211yescharacteristic
18C2×#10596962C2211yescharacteristic
19C2×#10596964C2211yescharacteristic
20#11924558—24no—
21#11924557—24no—
22C2×Dic148C2211yescharacteristic
23C2×#10596942C2211yescharacteristic
24C2×#10596930C2211yescharacteristic
25C2×#10596930C2211yescharacteristic
26C2×#10596940C2211yescharacteristic
27C2×#10596941C2211yescharacteristic
28C2×D296C2211yescharacteristic
29C2×#10596939C2211yescharacteristic
30C2×C8×D37C2211yescharacteristic
31#11924534C2211yescharacteristic
32#11924532—21no—
33#11924532C2211yescharacteristic
34#11924521—21no—
35#11924518—21no—
36#11924516C2211yescharacteristic
37#11924511C2211yescharacteristic
38#11924509—21no—
39#11924509—21no—
40#11924508—21no—
41#11924501C2211yescharacteristic
42#11924498C2211yescharacteristic
43C4×C22⋊D37C2211yescharacteristic
44#11924496—21no—
45C4⋊C4×D37—21no—
46#11924465C2211yescharacteristic
47#11924459C2211yescharacteristic
48#11924459C2211yescharacteristic
49#11924456C2211yescharacteristic
50#11924456C2211yescharacteristic
51C22⋊#64436C2211yescharacteristic
52#11924448C2211yescharacteristic
53C8×Dic37C2211yescharacteristic
54C2×SD16×C37C2211yescharacteristic
55C22×C8×C37C2211yescharacteristic
56C22⋊Q8×C37C2211yescharacteristic
57#121×C37C2211yescharacteristic
58#106×C37C2211yescharacteristic
59#103×C37C2211yescharacteristic
60#102×C37C2211yescharacteristic
61C2×Q8×C37C2311yescharacteristic
62C2×D4×C37—21no—
63C2×D4×C37C2311yescharacteristic
64C22×C4×C37C2311yescharacteristic
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37D411yescharacteristic
71C22×Dic37—21no—
72#10596966—22no—
73#10596966—41no—
74#10596964—22no—
75#10596964—41no—
76#10596962—22no—
77#10596962—22no—
78#10596962—41no—
79#10596962—41no—
80C2×D148—21no—
81C2×D148—21no—
82C2×D148C2311yescharacteristic
83C2×D148C2311yescharacteristic
84C2×C4×D37—21no—
85C2×C4×D37—21no—
86C2×C4×D37—21no—
87C2×C4×D37—21no—
88C2×C4×D37C2311yescharacteristic
89C2×Dic74C2311yescharacteristic
90C2×Dic74C2311yescharacteristic
91SD16×C37—22no—
92C2×C8×C37—22no—
93C2×C8×C37C2311yescharacteristic
94C2×C8×C37C2311yescharacteristic
95C4⋊C4×C37—21no—
96C4⋊C4×C37C2311yescharacteristic
97C4⋊C4×C37C2311yescharacteristic
98C22⋊C4×C37—21no—
99C22⋊C4×C37—21no—
100C22⋊Dic37D411yescharacteristic
101#10596942—22no—
102#10596941—41no—
103#10596940—41no—
104#10596939—22no—
105#10596938—21no—
106#10596938—21no—
107#10596938—21no—
108#10596938D411yescharacteristic
109C4⋊Dic37—21no—
110#10596936—21no—
111#10596936—21no—
112#10596936—21no—
113#10596936D411yescharacteristic
114C4×Dic37—21no—
115C4×Dic37C2311yescharacteristic
116C2×#64436C2311yescharacteristic
117C2×#64436C2311yescharacteristic
118Dic148—22no—
119D296—22no—
120#10596930—22no—
121#10596930D414yescomplemented
122C8×D37—22no—
123C23×C37—21no—
124C23×C37C2×D411yescharacteristic
125C22×D37—21no—
126C22×D37—21no—
127C22×D37C2×D411yescharacteristic
128Q8×C37—21no—
129Q8×C37—21no—
130D4×C37—21no—
131D4×C37—21no—
132D4×C37—81no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—21no—
136C2×C4×C37—21no—
137C2×C4×C37—21no—
138C2×C4×C37C2×D411yescharacteristic
139C2×C4×C37C2411yescharacteristic
140C22⋊D37—22no—
141C22⋊D37—42no—
142C22⋊D37—42no—
143C22⋊D37—42no—
144C22⋊D37—42no—
145C22⋊D37—81no—
146C2×Dic37—21no—
147C2×Dic37—21no—
148C2×Dic37—42no—
149C2×Dic37C2×D411yescharacteristic
150C2×Dic37C2×D411yescharacteristic
151C2×Dic37C2×D411yescharacteristic
152D148—21no—
153D148—21no—
154D148—21no—
155D148—42no—
156D148—81no—
157D148C2×D412yes—
158C4×D37—21no—
159C4×D37—21no—
160C4×D37—42no—
161C4×D37—42no—
162C4×D37—42no—
163C4×D37—42no—
164Dic74—21no—
165Dic74—21no—
166Dic74—21no—
167Dic74C2×D412yes—
168C8×C37—21no—
169C8×C37C2×D412yes—
170#64436—21no—
171#64436—21no—
172C22×C37—21no—
173C22×C37—21no—
174C22×C37—21no—
175C22×C37—41no—
176C22×C37—41no—
177C22×C37—41no—
178C22×C37C22×D411yescharacteristic
179C2×D37—21no—
180C2×D37—22no—
181C2×D37—21no—
182C2×D37—21no—
183C2×D37—41no—
184C2×D37—41no—
185C2×D37—41no—
186C2×D37—41no—
187C2×D37—41no—
188C4×C37—21no—
189C4×C37—41no—
190C4×C37—41no—
191C4×C37—41no—
192C4×C37C22×D411yescharacteristic
193C4×C37H(5,𝔽2)11yescharacteristic
194Dic37—22no—
195Dic37—21no—
196Dic37—21no—
197Dic37—41no—
198Dic37#13512yescomplemented
199#3284—371nomaximal, Sylow
200C2×C37—41no—
201C2×C37—81no—
202C2×C37D4211yescharacteristic
203C2×C37C2×#13511yescharacteristic
204C2×C37#57711yescharacteristic
205D37—41no—
206D37—42no—
207D37—81no—
208C2×#135—371no—
209C2×#135—371no—
210#550—371no—
211#547—371no—
212#492—371no—
213#465—371no—
214#465D3711yescharacteristic, complemented
215#462—371no—
216#459—371no—
217#452—371no—
218#452—371no—
219#449—371no—
220#449—371no—
221C4×SD16—371no—
222C8×D4—371no—
223C37#328411yescharacteristic, complemented, Sylow
224C2×#41—371no—
225C2×#41—371no—
226C2×#41—371no—
227C2×#41—371no—
228#135—744no—
229#135—744no—
230C2×Q16—371no—
231C2×Q16—371no—
232C2×SD16—371no—
233C2×SD16—371no—
234C2×SD16—371no—
235C2×SD16—371no—
236C2×SD16C2×D3711yescharacteristic
237C2×D8—371no—
238C2×D8—371no—
239C22×C8—371no—
240C22×C8C2×D3711yescharacteristic
241C4⋊Q8—371no—
242#127—371no—
243#127—741no—
244#123—741no—
245#123—741no—
246C22⋊Q8—371no—
247C22⋊Q8C2×D3711yescharacteristic
248#121—371no—
249#121—741no—
250#121—741no—
251#121—741no—
252#121C2×D3711yescharacteristic
253C4×Q8—371no—
254C4×D4—371no—
255C4×D4—371no—
256C4×D4—741no—
257C2×C4⋊C4—741no—
258#106C2×D3711yescharacteristic
259C4⋊C8—371no—
260#103—371no—
261#103—371no—
262#103C2×D3711yescharacteristic
263#102—371no—
264#102—371no—
265#102C2×D3711yescharacteristic
266C22⋊C8—371no—
267C22⋊C8—371no—
268C4×C8—371no—
269#41—742no—
270#41—742no—
271#41—742no—
272#41—742no—
273#41—1481no—
274#41—1481no—
275#41—1481no—
276#41—1481no—
277C2×Q8—371no—
278C2×Q8—371no—
279C2×Q8C22×D3711yescharacteristic
280C2×D4—21no—
281C2×D4—371no—
282C2×D4—371no—
283C2×D4—371no—
284C2×D4—741no—
285C2×D4—741no—
286C2×D4—741no—
287C2×D4—741no—
288C2×D4—741no—
289C2×D4—741no—
290C2×D4—741no—
291C2×D4C22×D3711yescharacteristic
292C22×C4—371no—
293C22×C4—741no—
294C22×C4—741no—
295C22×C4—741no—
296C22×C4—741no—
297C22×C4—741no—
298C22×C4C22×D3711yescharacteristic
299Q16—742no—
300Q16—742no—
301SD16—22no—
302SD16—374no—
303SD16—742no—
304SD16—1481no—
305SD16—1481no—
306D8—742no—
307D8—742no—
308C2×C8—22no—
309C2×C8—371no—
310C2×C8—371no—
311C2×C8—742no—
312C2×C8C22×D3711yescharacteristic
313C2×C8C22×D3711yescharacteristic
314C4⋊C4—21no—
315C4⋊C4—371no—
316C4⋊C4—741no—
317C4⋊C4—741no—
318C4⋊C4—741no—
319C4⋊C4—741no—
320C4⋊C4C22×D3711yescharacteristic
321C4⋊C4C22×D3711yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—371no—
325C22⋊C4—371no—
326C22⋊C4—741no—
327C22⋊C4—741no—
328C22⋊C4—741no—
329C42—371no—
330C42—741no—
331C23—21no—
332C23—371no—
333C23—741no—
334C23—741no—
335C23D4×D3711yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—372no—
339Q8—741no—
340Q8—741no—
341Q8—741no—
342D4—21no—
343D4—21no—
344D4—81no—
345D4—372no—
346D4—2961no—
347D4—2961no—
348D4—742no—
349D4—741no—
350D4—741no—
351D4—741no—
352D4—1482no—
353D4—1482no—
354D4—1482no—
355D4—1482no—
356D4—1482no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—371no—
363C2×C4—371no—
364C2×C4—371no—
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×C4—1482no—
374C2×C4D4×D3711yescharacteristic
375C2×C4C23×D3711yescharacteristic
376C8—21no—
377C8—741no—
378C8—741no—
379C8D4×D3712yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—741no—
387C22—741no—
388C22—741no—
389C22—742no—
390C22—1481no—
391C22—1481no—
392C22—1481no—
393C22—1481no—
394C22—1481no—
395C22C2×D4×D3711yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—372no—
401C4—741no—
402C4—741no—
403C4—742no—
404C4—1481no—
405C4C2×D4×D3711yescharacteristic
406C4#1192458211yescharacteristic
407C2—41no—
408C2—81no—
409C2—2961no—
410C2—1481no—
411C2—1482no—
412C2#1455816711yescharacteristic
413C2#135×D3711yescharacteristic
414C2#1455833911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#465C2
socleC22×C37C22×D4
hypercenter#465D37
hypocenterC37#3284
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#11924558C2semidirect
2. C2×#11924557C2semidirect
3. #14558201C2semidirect
4. #14558185C2semidirect
5. #14557904C2semidirect
6. #14557763C2semidirect
7. #14557742C2semidirect
8. #14557727C2semidirect
9. #14557696C2semidirect
10. #14557693C2semidirect
11. #14557681C2semidirect
12. #14557676C2semidirect
13. #14557620C2semidirect
14. C8×C22⋊D37C2semidirect
15. C37×#465C2semidirect
121. #10596930D4semidirect
198. Dic37#135semidirect
214. #465D37semidirect
223. C37#3284semidirect

Maximal subgroups

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

subgroupindex
C2×#119245582
C2×#119245572
#145582012
#145581852
#145579042
#145577632
#145577422
#145577272
#145576962
#145576932
#145576812
#145576762
#145576202
C8×C22⋊D372
C37×#4652
#328437