Finite Group Databasebeta

← #18006186

Subgroups — #18006186

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×#11924569C211yesmaximal, characteristic, complemented
2C2×#11924558C211yesmaximal, characteristic, complemented
3#14558204C211yesmaximal, characteristic, complemented
4#14558192C211yesmaximal, characteristic, complemented
5#14557922C211yesmaximal, characteristic, complemented
6#14557786C211yesmaximal, characteristic, complemented
7#14557762C211yesmaximal, characteristic, complemented
8#14557756C211yesmaximal, characteristic, complemented
9#14557734C211yesmaximal, characteristic, complemented
10#14557697C211yesmaximal, characteristic, complemented
11#14557680C211yesmaximal, characteristic, complemented
12#14557680C211yesmaximal, characteristic, complemented
13#14557674C211yesmaximal, characteristic, complemented
14#14557641C211yesmaximal, characteristic, complemented
15C37×#435C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×#10596962C2211yescharacteristic
18C2×#10596962C2211yescharacteristic
19C22×Dic74C2211yescharacteristic
20#11924569—24no—
21#11924558—24no—
22C2×Dic148C2211yescharacteristic
23C2×Dic148C2211yescharacteristic
24C2×#10596930C2211yescharacteristic
25C2×#10596930C2211yescharacteristic
26C2×#10596930C2211yescharacteristic
27C2×#10596930C2211yescharacteristic
28C2×#10596930C2211yescharacteristic
29C2×D296C2211yescharacteristic
30C2×D296C2211yescharacteristic
31#11924533C2211yescharacteristic
32#11924532—21no—
33#11924524C2211yescharacteristic
34#11924522—21no—
35#11924515C2211yescharacteristic
36#11924514—21no—
37#11924510C2211yescharacteristic
38#11924510C2211yescharacteristic
39#11924510C2211yescharacteristic
40#11924509—21no—
41#11924509—21no—
42#11924508—21no—
43C4×Dic74C2211yescharacteristic
44C4×Dic74C2211yescharacteristic
45#11924498—21no—
46#11924496—21no—
47#11924468C2211yescharacteristic
48#11924461C2211yescharacteristic
49#11924461C2211yescharacteristic
50#11924461C2211yescharacteristic
51#11924458C2211yescharacteristic
52#11924458C2211yescharacteristic
53#11924458C2211yescharacteristic
54C2×M16×C37C2211yescharacteristic
55C22×C8×C37C2211yescharacteristic
56C4×D4×C37C2211yescharacteristic
57C4⋊C8×C37C2211yescharacteristic
58C22⋊C8×C37C2211yescharacteristic
59C22⋊C8×C37C2211yescharacteristic
60#97×C37C2211yescharacteristic
61C2×D4×C37D411yescharacteristic
62C22×C4×C37C2311yescharacteristic
63C22×C4×C37C2311yescharacteristic
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C22×Dic37—21no—
71#10596962—22no—
72#10596962—22no—
73#10596962—22no—
74#10596962—41no—
75#10596962—41no—
76#10596962—41no—
77C2×D148—21no—
78C2×D148—21no—
79C2×D148C2311yescharacteristic
80C2×D148C2311yescharacteristic
81C2×D148C2311yescharacteristic
82C2×C4×D37—21no—
83C2×C4×D37—21no—
84C2×C4×D37—21no—
85C2×Dic74—22no—
86C2×Dic74—21no—
87C2×Dic74—41no—
88C2×Dic74C2311yescharacteristic
89C2×Dic74C2311yescharacteristic
90C2×Dic74C2311yescharacteristic
91M16×C37—22no—
92C2×C8×C37—22no—
93C2×C8×C37C2311yescharacteristic
94C2×C8×C37C2311yescharacteristic
95C2×C8×C37C2311yescharacteristic
96C2×C8×C37C2311yescharacteristic
97C4⋊C4×C37D411yescharacteristic
98C22⋊C4×C37D411yescharacteristic
99C22⋊C4×C37D411yescharacteristic
100C42×C37C2311yescharacteristic
101C22⋊Dic37—21no—
102#10596938—21no—
103#10596938—21no—
104#10596938—21no—
105#10596938—21no—
106#10596938—21no—
107C4⋊Dic37C2311yescharacteristic
108C4⋊Dic37C2311yescharacteristic
109#10596936—21no—
110#10596936—21no—
111#10596936—21no—
112C4×Dic37—21no—
113C4×Dic37—21no—
114Dic148—22no—
115Dic148D414yescomplemented
116D296—22no—
117D296—41no—
118#10596930—22no—
119#10596930—22no—
120#10596930—22no—
121#10596930—22no—
122#10596930—41no—
123C23×C37C2×D411yescharacteristic
124C23×C37C2×D411yescharacteristic
125C22×D37—21no—
126C22×D37—21no—
127C22×D37—21no—
128D4×C37—41no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—21no—
133C2×C4×C37C2×D411yescharacteristic
134C2×C4×C37C2×D411yescharacteristic
135C2×C4×C37C2×D411yescharacteristic
136C2×C4×C37C2×D411yescharacteristic
137C2×C4×C37C2411yescharacteristic
138C22⋊D37—42no—
139C22⋊D37—42no—
140C22⋊D37—42no—
141C22⋊D37—42no—
142C22⋊D37—81no—
143C22⋊D37—81no—
144C2×Dic37—21no—
145C2×Dic37—21no—
146C2×Dic37—21no—
147C2×Dic37—21no—
148C2×Dic37—21no—
149C2×Dic37—42no—
150D148—21no—
151D148—21no—
152D148—21no—
153D148—21no—
154D148—21no—
155D148—21no—
156D148—42no—
157D148—81no—
158C4×D37—42no—
159C4×D37—42no—
160C4×D37—42no—
161Dic74—21no—
162Dic74—21no—
163Dic74—21no—
164Dic74—21no—
165Dic74—42no—
166Dic74C2×D412yes—
167Dic74C2×D412yes—
168C8×C37—21no—
169C8×C37—21no—
170C8×C37—21no—
171C8×C37C2×D412yes—
172C22×C37—21no—
173C22×C37—21no—
174C22×C37—21no—
175C22×C37—21no—
176C22×C37—21no—
177C22×C37—21no—
178C22×C37C22×D411yescharacteristic
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—21no—
189C4×C37—21no—
190C4×C37—21no—
191C4×C37—21no—
192C4×C37C22×D411yescharacteristic
193C4×C37H(5,𝔽2)11yescharacteristic
194Dic37—22no—
195Dic37—22no—
196Dic37—41no—
197Dic37—41no—
198Dic37—41no—
199#3271—371nomaximal, Sylow
200C2×C37—41no—
201C2×C37—41no—
202C2×C37D4211yescharacteristic
203C2×C37#57511yescharacteristic
204C2×C37#57711yescharacteristic
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#441—371no—
222#435D3711yescharacteristic, complemented
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×Q16—371no—
232C2×SD16—371no—
233C2×SD16—371no—
234C2×SD16—371no—
235C2×SD16—371no—
236C2×SD16—371no—
237C2×D8—371no—
238C2×D8—371no—
239C2×M16C2×D3711yescharacteristic
240C22×C8C2×D3711yescharacteristic
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×Q8—371no—
254C4×Q8—371no—
255C4×D4—741no—
256C4×D4—741no—
257C4×D4C2×D3711yescharacteristic
258#106—371no—
259C4⋊C8C2×D3711yescharacteristic
260#103—371no—
261#103—371no—
262#103—371no—
263#102—371no—
264#102—371no—
265#102—371no—
266C22⋊C8C2×D3711yescharacteristic
267C22⋊C8C2×D3711yescharacteristic
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—371no—
277C2×Q8—371no—
278C2×Q8—742no—
279C2×Q8—741no—
280C2×Q8—1481no—
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×D4—741no—
292C2×D4D14811yescharacteristic
293C22×C4—741no—
294C22×C4—741no—
295C22×C4—741no—
296C22×C4—741no—
297C22×C4C22×D3711yescharacteristic
298C22×C4C22×D3711yescharacteristic
299Q16—374no—
300Q16—742no—
301SD16—742no—
302SD16—742no—
303SD16—742no—
304SD16—742no—
305SD16—1481no—
306D8—742no—
307D8—1481no—
308M16—22no—
309C2×C8—22no—
310C2×C8C22×D3711yescharacteristic
311C2×C8C22×D3711yescharacteristic
312C2×C8C22×D3711yescharacteristic
313C2×C8C22×D3711yescharacteristic
314C4⋊C4—371no—
315C4⋊C4—371no—
316C4⋊C4—741no—
317C4⋊C4—741no—
318C4⋊C4—741no—
319C4⋊C4D14811yescharacteristic
320C22⋊C4—741no—
321C22⋊C4—741no—
322C22⋊C4—741no—
323C22⋊C4—741no—
324C22⋊C4—741no—
325C22⋊C4—741no—
326C22⋊C4D14811yescharacteristic
327C22⋊C4D14811yescharacteristic
328C42—741no—
329C42—741no—
330C42C22×D3711yescharacteristic
331C23—741no—
332C23—741no—
333C23—741no—
334C23C2×D14811yescharacteristic
335C23C2×D14811yescharacteristic
336Q8—372no—
337Q8—372no—
338Q8—741no—
339Q8—741no—
340Q8—741no—
341Q8—741no—
342Q8—1482no—
343D4—41no—
344D4—2961no—
345D4—2961no—
346D4—2961no—
347D4—741no—
348D4—741no—
349D4—741no—
350D4—741no—
351D4—741no—
352D4—741no—
353D4—1482no—
354D4—1482no—
355D4—1482no—
356D4—1482no—
357D4—1482no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—741no—
363C2×C4—741no—
364C2×C4—741no—
365C2×C4—741no—
366C2×C4—741no—
367C2×C4—1482no—
368C2×C4—1482no—
369C2×C4—1482no—
370C2×C4—1482no—
371C2×C4C2×D14811yescharacteristic
372C2×C4C2×D14811yescharacteristic
373C2×C4C2×D14811yescharacteristic
374C2×C4C2×D14811yescharacteristic
375C2×C4C23×D3711yescharacteristic
376C8—21no—
377C8—21no—
378C8—21no—
379C8D4×D3712yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—1481no—
387C22—1481no—
388C22—1481no—
389C22—1481no—
390C22—1481no—
391C22—1481no—
392C22—1481no—
393C22—1481no—
394C22—1481no—
395C22C22×D14811yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—742no—
401C4—742no—
402C4—1481no—
403C4—1481no—
404C4—1481no—
405C4C2×D4×D3711yescharacteristic
406C4#1192458211yescharacteristic
407C2—41no—
408C2—41no—
409C2—2961no—
410C2—2961no—
411C2—2961no—
412C2D4×D14811yescharacteristic
413C2#1455833311yescharacteristic
414C2#1455834511yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#435C2
socleC22×C37C22×D4
hypercenter#435D37
hypocenterC37#3271
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#11924569C2semidirect
2. C2×#11924558C2semidirect
3. #14558204C2semidirect
4. #14558192C2semidirect
5. #14557922C2semidirect
6. #14557786C2semidirect
7. #14557762C2semidirect
8. #14557756C2semidirect
9. #14557734C2semidirect
10. #14557697C2semidirect
11. #14557680C2semidirect
12. #14557680C2semidirect
13. #14557674C2semidirect
14. #14557641C2semidirect
15. C37×#435C2semidirect
115. Dic148D4semidirect
222. #435D37semidirect
223. C37#3271semidirect

Maximal subgroups

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

subgroupindex
C2×#119245692
C2×#119245582
#145582042
#145581922
#145579222
#145577862
#145577622
#145577562
#145577342
#145576972
#145576802
#145576742
#145576412
C37×#4352
#327137