Finite Group Databasebeta

← #18006149

Subgroups — #18006149

Order 4736.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924566C211yesmaximal, characteristic, complemented
2C2×#11924555C211yesmaximal, characteristic, complemented
3#14558189C211yesmaximal, characteristic, complemented
4#14558182C211yesmaximal, characteristic, complemented
5#14557924C211yesmaximal, characteristic, complemented
6#14557777C211yesmaximal, characteristic, complemented
7#14557773C211yesmaximal, characteristic, complemented
8#14557746C211yesmaximal, characteristic, complemented
9#14557742C211yesmaximal, characteristic, complemented
10#14557696C211yesmaximal, characteristic, complemented
11#14557692C211yesmaximal, characteristic, complemented
12#14557691C211yesmaximal, characteristic, complemented
13#14557630C211yesmaximal, characteristic, complemented
14#14557607C211yesmaximal, characteristic, complemented
15C37×#449C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×#10596964C2211yescharacteristic
18C22×Dic74C2211yescharacteristic
19#11924566—24no—
20#11924555—24no—
21C2×Dic148C2211yescharacteristic
22C2×Dic148C2211yescharacteristic
23C2×#10596942C2211yescharacteristic
24C2×#10596942C2211yescharacteristic
25C2×#10596940C2211yescharacteristic
26C2×#10596940C2211yescharacteristic
27C2×#10596940C2211yescharacteristic
28C2×#10596934C2211yescharacteristic
29C2×C8×D37C2211yescharacteristic
30#11924534C2211yescharacteristic
31#11924523C2211yescharacteristic
32#11924522—21no—
33#11924519—21no—
34#11924517—21no—
35#11924516C2211yescharacteristic
36#11924515C2211yescharacteristic
37#11924513—21no—
38#11924512C2211yescharacteristic
39#11924508—21no—
40#11924508—21no—
41#11924501C2211yescharacteristic
42D4×Dic37—21no—
43D4×Dic37C2211yescharacteristic
44C4×C22⋊D37C2211yescharacteristic
45C2×#10596936—21no—
46#11924469C2211yescharacteristic
47#11924465C2211yescharacteristic
48#11924461C2211yescharacteristic
49#11924461C2211yescharacteristic
50#11924459C2211yescharacteristic
51#11924457C2211yescharacteristic
52#11924448C2211yescharacteristic
53#11924446C2211yescharacteristic
54C2×#41×C37C2211yescharacteristic
55C2×SD16×C37C2211yescharacteristic
56C2×D8×C37C2211yescharacteristic
57#121×C37C2211yescharacteristic
58#103×C37C2211yescharacteristic
59#102×C37C2211yescharacteristic
60C22⋊C8×C37C2211yescharacteristic
61#41×C37—22no—
62#41×C37—41no—
63C2×Q8×C37C2311yescharacteristic
64C2×D4×C37—21no—
65C2×D4×C37—21no—
66C2×D4×C37C2311yescharacteristic
67C2×D4×C37C2311yescharacteristic
68C22×C4×C37—21no—
69C22×C4×C37C2311yescharacteristic
70C2×C22⋊D37—21no—
71C2×C22⋊D37—21no—
72C2×C22⋊D37D411yescharacteristic
73C22×Dic37—21no—
74C22×Dic37—21no—
75C22×Dic37—21no—
76C22×Dic37—21no—
77#10596964—22no—
78#10596964—22no—
79#10596964—41no—
80#10596964—41no—
81C2×C4×D37C2311yescharacteristic
82C2×Dic74—22no—
83C2×Dic74—21no—
84C2×Dic74—41no—
85C2×Dic74C2311yescharacteristic
86C2×Dic74C2311yescharacteristic
87C2×Dic74C2311yescharacteristic
88SD16×C37—41no—
89D8×C37—22no—
90C2×C8×C37C2311yescharacteristic
91C2×C8×C37C2311yescharacteristic
92C4⋊C4×C37C2311yescharacteristic
93C22⋊C4×C37—21no—
94C22⋊Dic37—21no—
95C22⋊Dic37—21no—
96C22⋊Dic37—21no—
97C22⋊Dic37—21no—
98C22⋊Dic37D411yescharacteristic
99#10596942—22no—
100#10596942—22no—
101#10596940—22no—
102#10596940—22no—
103#10596940D414yescomplemented
104#10596938—21no—
105#10596938—21no—
106#10596938D411yescharacteristic
107C4⋊Dic37—21no—
108C4⋊Dic37C2311yescharacteristic
109#10596936—21no—
110#10596936—21no—
111#10596936—21no—
112#10596936—21no—
113#10596936—21no—
114#10596936D411yescharacteristic
115C4×Dic37—21no—
116C4×Dic37C2311yescharacteristic
117#10596934—22no—
118C2×#64436C2311yescharacteristic
119C2×#64436C2311yescharacteristic
120Dic148—22no—
121Dic148—41no—
122C8×D37—22no—
123C23×C37—21no—
124C23×C37—21no—
125C23×C37C2×D411yescharacteristic
126C22×D37C2×D411yescharacteristic
127Q8×C37—21no—
128Q8×C37—21no—
129D4×C37—21no—
130D4×C37—21no—
131D4×C37—21no—
132D4×C37—42no—
133D4×C37—42no—
134D4×C37C2×D412yes—
135C2×C4×C37—21no—
136C2×C4×C37—21no—
137C2×C4×C37—21no—
138C2×C4×C37—21no—
139C2×C4×C37—42no—
140C2×C4×C37C2×D411yescharacteristic
141C2×C4×C37C2411yescharacteristic
142C22⋊D37—41no—
143C22⋊D37—42no—
144C22⋊D37—42no—
145C2×Dic37—21no—
146C2×Dic37—21no—
147C2×Dic37—21no—
148C2×Dic37—21no—
149C2×Dic37—42no—
150C2×Dic37—42no—
151C2×Dic37—42no—
152C2×Dic37—42no—
153C2×Dic37C2×D411yescharacteristic
154C2×Dic37C2×D411yescharacteristic
155C2×Dic37C2×D411yescharacteristic
156C4×D37—21no—
157C4×D37—21no—
158Dic74—21no—
159Dic74—21no—
160Dic74—21no—
161Dic74—21no—
162Dic74—21no—
163Dic74—42no—
164Dic74C2×D412yes—
165C8×C37—21no—
166C8×C37—21no—
167#64436—21no—
168#64436C2×D412yes—
169C22×C37—21no—
170C22×C37—22no—
171C22×C37—21no—
172C22×C37—21no—
173C22×C37—41no—
174C22×C37—41no—
175C22×C37—41no—
176C22×C37—41no—
177C22×C37—41no—
178C22×C37C22×D411yescharacteristic
179C2×D37—21no—
180C2×D37—21no—
181C2×D37—21no—
182C4×C37—21no—
183C4×C37—41no—
184C4×C37—41no—
185C4×C37C22×D411yescharacteristic
186C4×C37H(5,𝔽2)11yescharacteristic
187Dic37—22no—
188Dic37—21no—
189Dic37—21no—
190Dic37—21no—
191Dic37—41no—
192Dic37—41no—
193Dic37—41no—
194#3269—371nomaximal, Sylow
195C2×C37—41no—
196C2×C37—42no—
197C2×C37—81no—
198C2×C37D4211yescharacteristic
199C2×C37#57511yescharacteristic
200C2×C37#57811yescharacteristic
201D37—41no—
202C2×#137—371no—
203C2×#135—371no—
204#548—371no—
205#547—371no—
206#497—371no—
207#468—371no—
208#467—371no—
209#463—371no—
210#462—371no—
211#452—371no—
212#452—371no—
213#451—371no—
214#449D3711yescharacteristic, complemented
215#440—371no—
216#435—371no—
217C37#326911yescharacteristic, complemented, Sylow
218C2×#41—371no—
219C2×#41—371no—
220C2×#41C2×D3711yescharacteristic
221C22×Q8—371no—
222#137—744no—
223#135—744no—
224C2×Q16—371no—
225C2×Q16—371no—
226C2×Q16—371no—
227C2×Q16—371no—
228C2×SD16—371no—
229C2×SD16—371no—
230C2×SD16—371no—
231C2×SD16C2×D3711yescharacteristic
232C2×D8C2×D3711yescharacteristic
233C2×M16—371no—
234C22×C8—371no—
235C4⋊Q8—371no—
236#124—371no—
237#124—741no—
238#123—741no—
239#123—741no—
240C22⋊Q8—371no—
241C22⋊Q8—371no—
242C22⋊Q8—371no—
243C22⋊Q8—741no—
244#121—741no—
245#121—741no—
246#121C2×D3711yescharacteristic
247C4×Q8—371no—
248C4×D4—371no—
249C4×D4—371no—
250C4×D4—741no—
251C2×C4⋊C4—741no—
252#107—371no—
253C4⋊C8—371no—
254#103—371no—
255#103—371no—
256#103—371no—
257#103C2×D3711yescharacteristic
258#102—371no—
259#102C2×D3711yescharacteristic
260C22⋊C8—371no—
261C22⋊C8C2×D3711yescharacteristic
262#97—371no—
263#41—22no—
264#41—41no—
265#41—742no—
266#41—742no—
267#41—1481no—
268#41—1481no—
269C2×Q8—371no—
270C2×Q8—371no—
271C2×Q8—371no—
272C2×Q8—742no—
273C2×Q8—741no—
274C2×Q8—1481no—
275C2×Q8C22×D3711yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—371no—
279C2×D4—741no—
280C2×D4—741no—
281C2×D4C22×D3711yescharacteristic
282C2×D4C22×D3711yescharacteristic
283C22×C4—21no—
284C22×C4—371no—
285C22×C4—741no—
286C22×C4—741no—
287C22×C4—741no—
288C22×C4—741no—
289C22×C4C22×D3711yescharacteristic
290Q16—742no—
291Q16—742no—
292Q16—742no—
293Q16—1481no—
294SD16—41no—
295SD16—374no—
296SD16—742no—
297SD16—742no—
298D8—22no—
299M16—742no—
300C2×C8—371no—
301C2×C8—371no—
302C2×C8—742no—
303C2×C8C22×D3711yescharacteristic
304C2×C8C22×D3711yescharacteristic
305C4⋊C4—371no—
306C4⋊C4—371no—
307C4⋊C4—741no—
308C4⋊C4—741no—
309C4⋊C4—741no—
310C4⋊C4—741no—
311C4⋊C4—741no—
312C4⋊C4—741no—
313C4⋊C4C22×D3711yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—371no—
316C22⋊C4—371no—
317C22⋊C4—741no—
318C22⋊C4—741no—
319C22⋊C4—741no—
320C22⋊C4—741no—
321C22⋊C4—741no—
322C22⋊C4—741no—
323C42—371no—
324C42—741no—
325C23—21no—
326C23—21no—
327C23—371no—
328C23D4×D3711yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—372no—
332Q8—741no—
333Q8—741no—
334Q8—741no—
335Q8—741no—
336Q8—741no—
337Q8—1482no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—1481no—
344D4—1482no—
345D4—1482no—
346D4D4×D3712yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—371no—
353C2×C4—371no—
354C2×C4—371no—
355C2×C4—741no—
356C2×C4—741no—
357C2×C4—741no—
358C2×C4—741no—
359C2×C4—741no—
360C2×C4—741no—
361C2×C4—1482no—
362C2×C4—1482no—
363C2×C4—1482no—
364C2×C4—1482no—
365C2×C4D4×D3711yescharacteristic
366C2×C4C23×D3711yescharacteristic
367C8—21no—
368C8—21no—
369C8—372no—
370C8—741no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—741no—
381C22—741no—
382C22—741no—
383C22C2×D4×D3711yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—741no—
388C4—741no—
389C4—741no—
390C4—742no—
391C4—1481no—
392C4—1481no—
393C4—1481no—
394C4C2×D4×D3711yescharacteristic
395C4#1192458111yescharacteristic
396C2—41no—
397C2—42no—
398C2—81no—
399C2—1481no—
400C2#1455816511yescharacteristic
401C2#1455832911yescharacteristic
402C2#1455834711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#449C2
socleC22×C37C22×D4
hypercenter#449D37
hypocenterC37#3269
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#11924566C2semidirect
2. C2×#11924555C2semidirect
3. #14558189C2semidirect
4. #14558182C2semidirect
5. #14557924C2semidirect
6. #14557777C2semidirect
7. #14557773C2semidirect
8. #14557746C2semidirect
9. #14557742C2semidirect
10. #14557696C2semidirect
11. #14557692C2semidirect
12. #14557691C2semidirect
13. #14557630C2semidirect
14. #14557607C2semidirect
15. C37×#449C2semidirect
103. #10596940D4semidirect
214. #449D37semidirect
217. C37#3269semidirect

Maximal subgroups

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

subgroupindex
C2×#119245662
C2×#119245552
#145581892
#145581822
#145579242
#145577772
#145577732
#145577462
#145577422
#145576962
#145576922
#145576912
#145576302
#145576072
C37×#4492
#326937