Finite Group Databasebeta

← #18005276

Subgroups — #18005276

Order 4736.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558152C211yesmaximal, characteristic, complemented
2#14558137C211yesmaximal, characteristic, complemented
3#14557942C211yesmaximal, characteristic, complemented
4#14557887C211yesmaximal, characteristic, complemented
5#14557879C211yesmaximal, characteristic, complemented
6#14557783C211yesmaximal, characteristic, complemented
7#14557776C211yesmaximal, characteristic, complemented
8#14557766C211yesmaximal, characteristic, complemented
9#14557759C211yesmaximal, characteristic, complemented
10#14557645C211yesmaximal, characteristic, complemented
11#14557634C211yesmaximal, characteristic, complemented
12SD16×Dic37C211yesmaximal, characteristic, complemented
13D8×Dic37C211yesmaximal, characteristic, complemented
14#14557490C211yesmaximal, characteristic, complemented
15C37×#496C211yesmaximal, characteristic, complemented
16C2×#10596929C2211yescharacteristic
17C2×C8×D37C2211yescharacteristic
18#11924536C2211yescharacteristic
19#11924529—21no—
20#11924528C2211yescharacteristic
21#11924522—21no—
22#11924520—21no—
23#11924517—21no—
24#11924517—21no—
25#11924513—21no—
26#11924512C2211yescharacteristic
27#11924508—21no—
28#11924508—21no—
29#11924507C2211yescharacteristic
30#11924507C2211yescharacteristic
31#11924507C2211yescharacteristic
32Q8×Dic37C2211yescharacteristic
33D4×Dic37C2211yescharacteristic
34D4×Dic37C2211yescharacteristic
35D4×Dic37C2211yescharacteristic
36#11924493C2211yescharacteristic
37#11924470C2211yescharacteristic
38#11924470C2211yescharacteristic
39#11924468C2211yescharacteristic
40#11924468C2211yescharacteristic
41#11924460C2211yescharacteristic
42#11924460C2211yescharacteristic
43#11924457C2211yescharacteristic
44#11924457C2211yescharacteristic
45#11924457C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924457C2211yescharacteristic
49#11924446C2211yescharacteristic
50C4×#64436C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×SD16×C37C2211yescharacteristic
53C2×SD16×C37C2211yescharacteristic
54C2×D8×C37C2211yescharacteristic
55C2×D8×C37C2211yescharacteristic
56#127×C37C2211yescharacteristic
57#124×C37C2211yescharacteristic
58#97×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×D4×C37—21no—
61C2×D4×C37—21no—
62C2×D4×C37C2311yescharacteristic
63C2×D4×C37C2311yescharacteristic
64C2×D4×C37C2311yescharacteristic
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68C22×Dic37—21no—
69C22×Dic37—21no—
70C22×Dic37—21no—
71C2×C4×D37C2311yescharacteristic
72C2×Dic74—21no—
73SD16×C37—22no—
74SD16×C37—22no—
75D8×C37—22no—
76D8×C37—22no—
77C2×C8×C37C2311yescharacteristic
78C2×C8×C37C2311yescharacteristic
79C22⋊C4×C37—21no—
80C22⋊C4×C37—21no—
81C42×C37C2311yescharacteristic
82C22⋊Dic37—21no—
83C22⋊Dic37—21no—
84C22⋊Dic37—21no—
85C22⋊Dic37—21no—
86C22⋊Dic37—21no—
87C22⋊Dic37—21no—
88#10596938—21no—
89#10596938D411yescharacteristic
90#10596938D411yescharacteristic
91C4⋊Dic37—21no—
92C4⋊Dic37—21no—
93C4⋊Dic37C2311yescharacteristic
94C4⋊Dic37C2311yescharacteristic
95C4⋊Dic37C2311yescharacteristic
96C4⋊Dic37C2311yescharacteristic
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100#10596936D411yescharacteristic
101#10596936D411yescharacteristic
102C4×Dic37—21no—
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106#10596929—22no—
107C8×D37—22no—
108C23×C37—21no—
109C23×C37—21no—
110C23×C37—21no—
111C22×D37C2×D411yescharacteristic
112Q8×C37—21no—
113Q8×C37—21no—
114D4×C37—21no—
115D4×C37—21no—
116D4×C37—21no—
117D4×C37—21no—
118D4×C37—21no—
119D4×C37—21no—
120D4×C37—81no—
121D4×C37—81no—
122C2×C4×C37—21no—
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2×D411yescharacteristic
125C2×C4×C37C2411yescharacteristic
126C22⋊D37—81no—
127C22⋊D37—81no—
128C22⋊D37—81no—
129C2×Dic37—21no—
130C2×Dic37—21no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133C2×Dic37—81no—
134C2×Dic37—81no—
135C2×Dic37—81no—
136C2×Dic37C2×D411yescharacteristic
137C2×Dic37C2×D411yescharacteristic
138C2×Dic37C2×D411yescharacteristic
139C4×D37—21no—
140C4×D37—21no—
141Dic74—81no—
142C8×C37#4112yes—
143C8×C37#4112yes—
144#64436—21no—
145#64436—21no—
146C22×C37—41no—
147C22×C37—41no—
148C22×C37—41no—
149C22×C37—41no—
150C22×C37—41no—
151C22×C37—41no—
152C22×C37—41no—
153C22×C37—41no—
154C22×C37—41no—
155C22×C37C22×D411yescharacteristic
156C2×D37—21no—
157C2×D37—21no—
158C2×D37—21no—
159C4×C37—21no—
160C4×C37—21no—
161C4×C37—41no—
162C4×C37C2×#4111yescharacteristic
163C4×C37C2×#4111yescharacteristic
164Dic37—21no—
165Dic37—21no—
166Dic37—21no—
167Dic37—41no—
168Dic37—41no—
169Dic37—41no—
170Dic37—41no—
171#3179—371nomaximal, Sylow
172C2×C37—81no—
173C2×C37—81no—
174C2×C37—81no—
175C2×C37#53211yescharacteristic
176C2×C37#57611yescharacteristic
177C2×C37#57711yescharacteristic
178D37—41no—
179#542—371no—
180#540—371no—
181#501—371no—
182#496D3711yescharacteristic, complemented
183#488—371no—
184#486—371no—
185#469—371no—
186#468—371no—
187#466—371no—
188#465—371no—
189#442—371no—
190#440—371no—
191C4×SD16—371no—
192C4×D8—371no—
193#405—371no—
194C37#317911yescharacteristic, complemented, Sylow
195C2×SD16C2×D3711yescharacteristic
196C2×SD16C2×D3711yescharacteristic
197C2×D8C2×D3711yescharacteristic
198C2×D8C2×D3711yescharacteristic
199C2×M16—371no—
200C22×C8—371no—
201C4⋊Q8—371no—
202#127C2×D3711yescharacteristic
203#126—741no—
204#125—371no—
205#124—741no—
206#124C2×D3711yescharacteristic
207#123—741no—
208#123—741no—
209#123—741no—
210C22⋊Q8—371no—
211C22⋊Q8—741no—
212#121—371no—
213#121—371no—
214#121—371no—
215#121—741no—
216#121—741no—
217C4×Q8—371no—
218C4×D4—371no—
219C4×D4—371no—
220C4×D4—371no—
221#117—371no—
222#107—371no—
223#107—371no—
224#106—371no—
225#106—371no—
226#103—371no—
227#103—371no—
228#102—371no—
229#102—371no—
230#102—371no—
231#102—371no—
232#102—371no—
233#102—371no—
234#97—371no—
235#97C2×D3711yescharacteristic
236C4×C8—371no—
237C4×C8—371no—
238C2×Q8—741no—
239C2×Q8C22×D3711yescharacteristic
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—741no—
243C2×D4—741no—
244C2×D4—741no—
245C2×D4C22×D3711yescharacteristic
246C2×D4C22×D3711yescharacteristic
247C2×D4C22×D3711yescharacteristic
248C22×C4—371no—
249C22×C4—741no—
250C22×C4—741no—
251C22×C4—741no—
252SD16—22no—
253SD16—22no—
254D8—22no—
255D8—22no—
256M16—742no—
257C2×C8—371no—
258C2×C8—371no—
259C2×C8—742no—
260C2×C8C22×D3711yescharacteristic
261C2×C8C22×D3711yescharacteristic
262C4⋊C4—371no—
263C4⋊C4—371no—
264C4⋊C4—371no—
265C4⋊C4—371no—
266C4⋊C4—371no—
267C4⋊C4—371no—
268C4⋊C4—741no—
269C4⋊C4—741no—
270C4⋊C4—741no—
271C4⋊C4—741no—
272C4⋊C4—741no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—371no—
276C22⋊C4—371no—
277C22⋊C4—741no—
278C22⋊C4—741no—
279C22⋊C4—741no—
280C22⋊C4—741no—
281C22⋊C4—741no—
282C22⋊C4—741no—
283C22⋊C4—741no—
284C42—371no—
285C42—741no—
286C42C22×D3711yescharacteristic
287C23—21no—
288C23—21no—
289C23—21no—
290C23—371no—
291Q8—21no—
292Q8—21no—
293Q8—2961no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—2961no—
303D4—2961no—
304D4—2961no—
305C2×C4—21no—
306C2×C4—371no—
307C2×C4—371no—
308C2×C4—371no—
309C2×C4—2961no—
310C2×C4—2961no—
311C2×C4—2961no—
312C2×C4—741no—
313C2×C4—741no—
314C2×C4—741no—
315C2×C4—741no—
316C2×C4—741no—
317C2×C4—741no—
318C2×C4D4×D3711yescharacteristic
319C2×C4D4×D3711yescharacteristic
320C2×C4C23×D3711yescharacteristic
321C8—741no—
322C8—741no—
323C8#1059696412yes—
324C8#1059696412yes—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—741no—
335C22—741no—
336C22—741no—
337C22C2×D4×D3711yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—741no—
342C4—741no—
343C4—741no—
344C4—1481no—
345C4—1481no—
346C4—1481no—
347C4—1481no—
348C4C2×#1059696411yescharacteristic
349C4C2×#1059696411yescharacteristic
350C2—81no—
351C2—81no—
352C2—81no—
353C2—1481no—
354C2#1455808111yescharacteristic
355C2#1455833711yescharacteristic
356C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#496C2
socleC22×C37C22×D4
hypercenter#496D37
hypocenterC37#3179
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #14558152C2semidirect
2. #14558137C2semidirect
3. #14557942C2semidirect
4. #14557887C2semidirect
5. #14557879C2semidirect
6. #14557783C2semidirect
7. #14557776C2semidirect
8. #14557766C2semidirect
9. #14557759C2semidirect
10. #14557645C2semidirect
11. #14557634C2semidirect
12. SD16×Dic37C2semidirect
13. D8×Dic37C2semidirect
14. #14557490C2semidirect
15. C37×#496C2semidirect
182. #496D37semidirect
194. C37#3179semidirect

Maximal subgroups

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

subgroupindex
#145581522
#145581372
#145579422
#145578872
#145578792
#145577832
#145577762
#145577662
#145577592
#145576452
#145576342
SD16×Dic372
D8×Dic372
#145574902
C37×#4962
#317937