Finite Group Databasebeta

← #17997857

Subgroups — #17997857

Order 4736.

560 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D37C211yesmaximal, characteristic
2C2×#11924493C211yesmaximal, characteristic, complemented
3#14557474C211yesmaximal, characteristic, complemented
4#14557469C211yesmaximal, characteristic, complemented
5#14557467C211yesmaximal, characteristic, complemented
6#14557462C211yesmaximal, characteristic, complemented
7#14557461C211yesmaximal, characteristic, complemented
8#14557460C211yesmaximal, characteristic, complemented
9#14557449C211yesmaximal, characteristic
10#14557448C211yesmaximal, characteristic
11C4×#10596936C211yesmaximal, characteristic, complemented
12C4×C4⋊Dic37C211yesmaximal, characteristic, complemented
13C4×#10596938C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic37C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C37C211yesmaximal, characteristic, complemented
16C22×C22⋊D37C2211yescharacteristic
17C22×C4×D37C2211yescharacteristic
18C4×C22⋊D37—24no—
19#11924493—24no—
20C2×C4⋊Dic37C2211yescharacteristic
21C2×C4⋊Dic37C2211yescharacteristic
22C2×#10596936C2211yescharacteristic
23C2×#10596936C2211yescharacteristic
24C2×#10596936C2211yescharacteristic
25C2×#10596936C2211yescharacteristic
26C2×#10596936C2211yescharacteristic
27C2×C22⋊Dic37C2211yescharacteristic
28C2×C22⋊Dic37C2211yescharacteristic
29C2×C22⋊Dic37C2211yescharacteristic
30C2×#10596938C2211yescharacteristic
31C2×#10596938C2211yescharacteristic
32C2×#10596938C2211yescharacteristic
33C2×#10596938C2211yescharacteristic
34C2×#10596938C2211yescharacteristic
35C2×C4×Dic37C2211yescharacteristic
36C2×C4×Dic37C2211yescharacteristic
37C2×C4×Dic37C2211yescharacteristic
38#11924443C2211yescharacteristic
39#11924443C2211yescharacteristic
40#11924443C2211yescharacteristic
41#11924443C2211yescharacteristic
42#11924443C2211yescharacteristic
43#11924443C2211yescharacteristic
44#11924443C2211yescharacteristic
45#11924443C2211yescharacteristic
46C23×C4×C37C2211yescharacteristic
47C2×C22⋊C4×C37C2211yescharacteristic
48C2×C22⋊C4×C37C2211yescharacteristic
49C2×C42×C37C2211yescharacteristic
50C2×C42×C37C2211yescharacteristic
51#95×C37C2211yescharacteristic
52#95×C37C2211yescharacteristic
53C24×C37C2311yescharacteristic
54C23×D37C2311yescharacteristic
55C22×C4×C37—22no—
56C22×C4×C37—22no—
57C22×C4×C37—22no—
58C22×C4×C37C2311yescharacteristic
59C22×C4×C37C2311yescharacteristic
60C22×C4×C37C2311yescharacteristic
61C22×C4×C37C2311yescharacteristic
62C22×C4×C37C2311yescharacteristic
63C22×C4×C37C2311yescharacteristic
64C2×C22⋊D37—22no—
65C2×C22⋊D37—22no—
66C2×C22⋊D37—22no—
67C22×Dic37C2311yescharacteristic
68C22×Dic37C2311yescharacteristic
69C22×Dic37C2311yescharacteristic
70C22×Dic37C2311yescharacteristic
71C22×Dic37C2311yescharacteristic
72C22×Dic37C2311yescharacteristic
73C22×Dic37C2311yescharacteristic
74C2×C4×D37—22no—
75C2×C4×D37—22no—
76C2×C4×D37D414yes—
77C22⋊C4×C37—22no—
78C22⋊C4×C37—22no—
79C42×C37—22no—
80C42×C37—22no—
81C22⋊Dic37—22no—
82C22⋊Dic37—22no—
83C22⋊Dic37—22no—
84#10596938—22no—
85#10596938—22no—
86#10596938—22no—
87#10596938—22no—
88#10596938—22no—
89C4⋊Dic37—22no—
90C4⋊Dic37—22no—
91#10596936—22no—
92#10596936—22no—
93#10596936—22no—
94#10596936—22no—
95#10596936—22no—
96C4×Dic37—22no—
97C4×Dic37—22no—
98C4×Dic37—22no—
99C23×C37—21no—
100C23×C37—21no—
101C23×C37—21no—
102C23×C37—21no—
103C23×C37—21no—
104C23×C37—21no—
105C23×C37#4112yes—
106C23×C37C2411yescharacteristic
107C22×D37—21no—
108C22×D37—21no—
109C22×D37—21no—
110C22×D37—21no—
111C22×D37—21no—
112C22×D37—21no—
113C22×D37C2×D412yes—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—21no—
128C2×C4×C37—44no—
129C2×C4×C37C2×D412yes—
130C2×C4×C37#4112yes—
131C2×C4×C37#4112yes—
132C2×C4×C37#4112yes—
133C22⋊D37—28no—
134C2×Dic37—21no—
135C2×Dic37—21no—
136C2×Dic37—21no—
137C2×Dic37—21no—
138C2×Dic37—21no—
139C2×Dic37—21no—
140C2×Dic37—21no—
141C2×Dic37—21no—
142C2×Dic37—21no—
143C2×Dic37—21no—
144C2×Dic37—21no—
145C2×Dic37—21no—
146C2×Dic37—21no—
147C2×Dic37—21no—
148C2×Dic37—21no—
149C2×Dic37—21no—
150C2×Dic37—21no—
151C2×Dic37—21no—
152C2×Dic37C2×D412yes—
153C2×Dic37#4112yes—
154C2×Dic37#4112yes—
155C4×D37—28no—
156C22×C37—22no—
157C22×C37—22no—
158C22×C37—22no—
159C22×C37—41no—
160C22×C37—41no—
161C22×C37—41no—
162C22×C37—41no—
163C22×C37C22×D411yescharacteristic
164C22×C37C2×#4111yescharacteristic
165C22×C37C2×#4111yescharacteristic
166C22×C37C2×#4111yescharacteristic
167C22×C37C2×#4111yescharacteristic
168C22×C37C2×#4111yescharacteristic
169C22×C37C2×#4111yescharacteristic
170C2×D37—22no—
171C2×D37—22no—
172C2×D37—22no—
173C2×D37—41no—
174C2×D37—41no—
175C2×D37—41no—
176C2×D37—41no—
177C4×C37—22no—
178C4×C37—41no—
179C4×C37—41no—
180C4×C37—41no—
181C4×C37—41no—
182C4×C37#12314yes—
183Dic37—22no—
184Dic37—22no—
185Dic37—22no—
186Dic37—41no—
187Dic37—41no—
188Dic37—41no—
189Dic37—41no—
190#2395—371nomaximal, Sylow
191C2×C37—42no—
192C2×C37C2×#12311yescharacteristic
193C2×C37#52511yescharacteristic
194C2×C37#52911yescharacteristic
195C2×C37#52911yescharacteristic
196C2×C37#52911yescharacteristic
197C2×C37#52911yescharacteristic
198C2×C37#53211yescharacteristic
199D37—42no—
200C2×C4×D4—371no—
201C2×#117—371no—
202#400—371no—
203#399—371no—
204#398—371no—
205#397—371no—
206#397—371no—
207#397—371no—
208#394—371no—
209#394—371no—
210C4×C4⋊C4—371no—
211C4×C4⋊C4—371no—
212C4×C22⋊C4—371no—
213C4×C22⋊C4—371no—
214C4×C22⋊C4D3711yescharacteristic, complemented
215C37#239511yescharacteristic, complemented, Sylow
216C22×D4—371no—
217C23×C4—371no—
218C23×C4C2×D3711yescharacteristic
219C4×D4—744no—
220#117—744no—
221C2×C4⋊C4—371no—
222C2×C4⋊C4—371no—
223C2×C4⋊C4—371no—
224C2×C4⋊C4—371no—
225C2×C4⋊C4—371no—
226C2×C4⋊C4—371no—
227C2×C4⋊C4—371no—
228C2×C22⋊C4—371no—
229C2×C22⋊C4—371no—
230C2×C22⋊C4—371no—
231C2×C22⋊C4—371no—
232C2×C22⋊C4—371no—
233C2×C22⋊C4—371no—
234C2×C22⋊C4—371no—
235C2×C22⋊C4—371no—
236C2×C22⋊C4C2×D3711yescharacteristic
237C2×C22⋊C4C2×D3711yescharacteristic
238C2×C42—371no—
239C2×C42—371no—
240C2×C42—371no—
241C2×C42C2×D3711yescharacteristic
242C2×C42C2×D3711yescharacteristic
243#95—371no—
244#95—371no—
245#95—371no—
246#95—371no—
247#95—371no—
248#95—371no—
249#95—371no—
250#95—371no—
251#95C2×D3711yescharacteristic
252#95C2×D3711yescharacteristic
253C24—371no—
254C24C22×D3711yescharacteristic
255C2×D4—742no—
256C2×D4—742no—
257C2×D4—742no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—371no—
262C22×C4—371no—
263C22×C4—371no—
264C22×C4—374no—
265C22×C4—371no—
266C22×C4—371no—
267C22×C4—371no—
268C22×C4—371no—
269C22×C4—742no—
270C22×C4—742no—
271C22×C4C22×D3711yescharacteristic
272C22×C4C22×D3711yescharacteristic
273C22×C4C22×D3711yescharacteristic
274C22×C4C22×D3711yescharacteristic
275C22×C4C22×D3711yescharacteristic
276C22×C4C22×D3711yescharacteristic
277C4⋊C4—742no—
278C4⋊C4—742no—
279C4⋊C4—742no—
280C4⋊C4—742no—
281C4⋊C4—742no—
282C4⋊C4—742no—
283C4⋊C4—742no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—742no—
287C22⋊C4—742no—
288C22⋊C4—742no—
289C22⋊C4—742no—
290C22⋊C4—742no—
291C22⋊C4—742no—
292C22⋊C4—742no—
293C22⋊C4—742no—
294C42—22no—
295C42—22no—
296C42—742no—
297C42—742no—
298C42—742no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—372no—
306C23—741no—
307C23—741no—
308C23—741no—
309C23—741no—
310C23—741no—
311C23—741no—
312C23#1059696212yes—
313C23C23×D3711yescharacteristic
314D4—748no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—44no—
330C2×C4—372no—
331C2×C4—372no—
332C2×C4—372no—
333C2×C4—741no—
334C2×C4—741no—
335C2×C4—741no—
336C2×C4—741no—
337C2×C4—741no—
338C2×C4—741no—
339C2×C4—748no—
340C2×C4—741no—
341C2×C4—741no—
342C2×C4—741no—
343C2×C4—741no—
344C2×C4—741no—
345C2×C4—741no—
346C2×C4—741no—
347C2×C4—741no—
348C2×C4—741no—
349C2×C4—741no—
350C2×C4—741no—
351C2×C4—741no—
352C2×C4#1059696212yes—
353C2×C4#1059696212yes—
354C2×C4D4×D3712yes—
355C2×C4#1059696412yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—742no—
364C22—742no—
365C22—742no—
366C22—1481no—
367C22—1481no—
368C22—1481no—
369C22—1481no—
370C22C2×D4×D3711yescharacteristic
371C22#41×D3711yescharacteristic
372C22#41×D3711yescharacteristic
373C22C2×#1059696411yescharacteristic
374C22C2×#1059696211yescharacteristic
375C22C2×#1059696211yescharacteristic
376C22C2×#1059696211yescharacteristic
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—742no—
383C4—742no—
384C4—742no—
385C4—1481no—
386C4—1481no—
387C4—1481no—
388C4—1481no—
389C4#1192451814yes—
390C2—42no—
391C2—1482no—
392C2C2×#1192451811yescharacteristic
393C2#1455804211yescharacteristic
394C2#1455806111yescharacteristic
395C2#1455806311yescharacteristic
396C2#1455806311yescharacteristic
397C2#1455806711yescharacteristic
398C2#1455808011yescharacteristic
subgroupG/H
centerC22×C4C22×D37
commutator, socle, cosocleC23×C37C24
FrattiniC23C23×D37
FittingC4×C22⋊C4×C37C2
prime radicalC22×C22⋊D37C22
hypercenterC4×C22⋊C4D37
hypocenterC37#2395
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11924493C2semidirect
3. #14557474C2semidirect
4. #14557469C2semidirect
5. #14557467C2semidirect
6. #14557462C2semidirect
7. #14557461C2semidirect
8. #14557460C2semidirect
11. C4×#10596936C2semidirect
12. C4×C4⋊Dic37C2semidirect
13. C4×#10596938C2semidirect
14. C4×C22⋊Dic37C2semidirect
15. C4×C22⋊C4×C37C2semidirect
214. C4×C22⋊C4D37semidirect
215. C37#2395semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D372
C2×#119244932
#145574742
#145574692
#145574672
#145574622
#145574612
#145574602
#145574492
#145574482
C4×#105969362
C4×C4⋊Dic372
C4×#105969382
C4×C22⋊Dic372
C4×C22⋊C4×C372
#239537