Finite Group Databasebeta

← #17997286

Subgroups — #17997286

Order 4736.

668 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924508C211yesmaximal, characteristic
2C2×C4×C22⋊D37C211yesmaximal, characteristic, complemented
3C2×#11924492C211yesmaximal, characteristic, complemented
4#14557436C211yesmaximal, characteristic, complemented
5#14557433C211yesmaximal, characteristic, complemented
6#14557433C211yesmaximal, characteristic, complemented
7#14557430C211yesmaximal, characteristic, complemented
8#14557422C211yesmaximal, characteristic, complemented
9#14557421C211yesmaximal, characteristic, complemented
10#14557409C211yesmaximal, characteristic, complemented
11#14557407C211yesmaximal, characteristic, complemented
12#14557406C211yesmaximal, characteristic, complemented
13#14557391C211yesmaximal, characteristic, complemented
14#14557384C211yesmaximal, characteristic, complemented
15C37×#386C211yesmaximal, characteristic, complemented
16C22×C22⋊D37C2211yescharacteristic
17C22×C22⋊D37C2211yescharacteristic
18C23×Dic37C2211yescharacteristic
19C22×C4×D37C2211yescharacteristic
20#11924508C418yescomplemented
21C4×C22⋊D37—24no—
22#11924492—24no—
23C2×C4⋊Dic37C2211yescharacteristic
24C2×#10596936C2211yescharacteristic
25C2×#10596936C2211yescharacteristic
26C2×#10596936C2211yescharacteristic
27C2×#10596936C2211yescharacteristic
28C2×#10596936C2211yescharacteristic
29C2×#10596936C2211yescharacteristic
30C2×C22⋊Dic37C2211yescharacteristic
31C2×C22⋊Dic37C2211yescharacteristic
32C2×C22⋊Dic37C2211yescharacteristic
33C2×C22⋊Dic37C2211yescharacteristic
34C2×C22⋊Dic37C2211yescharacteristic
35C2×#10596938C2211yescharacteristic
36C2×#10596938C2211yescharacteristic
37C2×#10596938C2211yescharacteristic
38C2×#10596938C2211yescharacteristic
39C2×C4×Dic37C2211yescharacteristic
40C2×C4×Dic37C2211yescharacteristic
41C2×C4×Dic37C2211yescharacteristic
42C2×C4×Dic37C2211yescharacteristic
43#11924443C2211yescharacteristic
44#11924443C2211yescharacteristic
45#11924443C2211yescharacteristic
46#11924443C2211yescharacteristic
47C22×D4×C37C2211yescharacteristic
48C23×C4×C37C2211yescharacteristic
49C2×C22⋊C4×C37C2211yescharacteristic
50C2×C22⋊C4×C37C2211yescharacteristic
51C2×C22⋊C4×C37C2211yescharacteristic
52#95×C37C2211yescharacteristic
53#95×C37C2211yescharacteristic
54C24×C37C2311yescharacteristic
55C24×C37C2311yescharacteristic
56C23×D37C2311yescharacteristic
57C2×D4×C37—41no—
58C2×D4×C37—41no—
59C2×D4×C37C2×C414yescomplemented
60C22×C4×C37—22no—
61C22×C4×C37—41no—
62C22×C4×C37—41no—
63C22×C4×C37C2311yescharacteristic
64C22×C4×C37C2311yescharacteristic
65C22×C4×C37C2311yescharacteristic
66C22×C4×C37C2311yescharacteristic
67C22×C4×C37C2311yescharacteristic
68C2×C22⋊D37—22no—
69C2×C22⋊D37—22no—
70C2×C22⋊D37—41no—
71C2×C22⋊D37—41no—
72C2×C22⋊D37C2×C414yes—
73C2×C22⋊D37C2×C414yescomplemented
74C22×Dic37—22no—
75C22×Dic37—22no—
76C22×Dic37C2×C414yescomplemented
77C22×Dic37C2311yescharacteristic
78C22×Dic37C2311yescharacteristic
79C22×Dic37C2311yescharacteristic
80C22×Dic37C2311yescharacteristic
81C22×Dic37C2311yescharacteristic
82C22×Dic37C2311yescharacteristic
83C22×Dic37C2311yescharacteristic
84C2×C4×D37—22no—
85C2×C4×D37—41no—
86C2×C4×D37—41no—
87C22⋊C4×C37—22no—
88C22⋊C4×C37—41no—
89C22⋊C4×C37—41no—
90C22⋊Dic37—22no—
91C22⋊Dic37—22no—
92C22⋊Dic37—41no—
93C22⋊Dic37—41no—
94C22⋊Dic37C2×C414yescomplemented
95#10596938—22no—
96#10596938—41no—
97#10596938—41no—
98#10596938C2×C414yescomplemented
99C4⋊Dic37—41no—
100#10596936—22no—
101#10596936—22no—
102#10596936—22no—
103#10596936—22no—
104#10596936—41no—
105#10596936C2×C414yescomplemented
106C4×Dic37—22no—
107C4×Dic37—41no—
108C4×Dic37—41no—
109C4×Dic37D414yescomplemented
110C23×C37—21no—
111C23×C37—21no—
112C23×C37—21no—
113C23×C37—21no—
114C23×C37—21no—
115C23×C37—21no—
116C23×C37—21no—
117C23×C37—21no—
118C23×C37—21no—
119C23×C37—21no—
120C23×C37—21no—
121C23×C37—21no—
122C23×C37C22×C412yes—
123C23×C37C22×C412yes—
124C23×C37C2411yescharacteristic
125C22×D37—21no—
126C22×D37—21no—
127C22×D37—21no—
128C22×D37—21no—
129C22×D37—21no—
130C22×D37—21no—
131C22×D37C22×C412yes—
132D4×C37—44no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—21no—
136C2×C4×C37—21no—
137C2×C4×C37—21no—
138C2×C4×C37—21no—
139C2×C4×C37—21no—
140C2×C4×C37—21no—
141C2×C4×C37—21no—
142C2×C4×C37—21no—
143C2×C4×C37—21no—
144C2×C4×C37—21no—
145C2×C4×C37—21no—
146C2×C4×C37—44no—
147C2×C4×C37C22×C412yes—
148C2×C4×C37C2×D412yes—
149C22⋊D37—28no—
150C22⋊D37—44no—
151C2×Dic37—21no—
152C2×Dic37—21no—
153C2×Dic37—21no—
154C2×Dic37—21no—
155C2×Dic37—21no—
156C2×Dic37—21no—
157C2×Dic37—28no—
158C2×Dic37—21no—
159C2×Dic37—21no—
160C2×Dic37—21no—
161C2×Dic37—21no—
162C2×Dic37—21no—
163C2×Dic37—21no—
164C2×Dic37—21no—
165C2×Dic37—21no—
166C2×Dic37—21no—
167C2×Dic37C22×C412yes—
168C2×Dic37C22×C412yes—
169C2×Dic37C22×C412yes—
170C2×Dic37C2×D412yes—
171C2×Dic37C2×D412yes—
172C2×Dic37#4112yes—
173C4×D37—44no—
174C22×C37—22no—
175C22×C37—22no—
176C22×C37—22no—
177C22×C37—22no—
178C22×C37—22no—
179C22×C37—22no—
180C22×C37—41no—
181C22×C37—41no—
182C22×C37—41no—
183C22×C37—41no—
184C22×C37—41no—
185C22×C37—41no—
186C22×C37—41no—
187C22×C37—41no—
188C22×C37C23×C411yescharacteristic
189C22×C37C22×D411yescharacteristic
190C22×C37C2×#4111yescharacteristic
191C22×C37H(5,𝔽2)11yescharacteristic
192C22×C37H(5,𝔽2)11yescharacteristic
193C22×C37H(5,𝔽2)11yescharacteristic
194C22×C372−1+411yescharacteristic
195C2×D37—22no—
196C2×D37—22no—
197C2×D37—22no—
198C2×D37—41no—
199C2×D37—41no—
200C2×D37—41no—
201C2×D37—41no—
202C4×C37—22no—
203C4×C37—22no—
204C4×C37—41no—
205C4×C37—41no—
206C4×C37—41no—
207Dic37—22no—
208Dic37—22no—
209Dic37—22no—
210Dic37—41no—
211Dic37—41no—
212Dic37—41no—
213Dic37C4×D414yes—
214#2324—371nomaximal, Sylow
215C2×C37—42no—
216C2×C37—42no—
217C2×C37C2×C4×D411yescharacteristic
218C2×C37#51811yescharacteristic
219C2×C37#52011yescharacteristic
220C2×C37#53511yescharacteristic
221C2×C37#53711yescharacteristic
222C2×C37#54011yescharacteristic
223C2×C37#54211yescharacteristic
224D37—42no—
225C2×#121—371no—
226C2×C4×D4—371no—
227C2×#117—371no—
228#390—371no—
229#390—371no—
230#390—371no—
231#389—371no—
232#388—371no—
233#388—371no—
234#386—371no—
235#386D3711yescharacteristic, complemented
236#385—371no—
237#385—371no—
238#380—371no—
239C4×C4⋊C4—371no—
240C37#232411yescharacteristic, complemented, Sylow
241C22×D4—371no—
242C22×D4—371no—
243C22×D4C2×D3711yescharacteristic
244C23×C4—371no—
245C23×C4—371no—
246C23×C4C2×D3711yescharacteristic
247#121—378no—
248C4×D4—744no—
249#117—744no—
250C2×C4⋊C4—371no—
251C2×C4⋊C4—371no—
252C2×C4⋊C4—371no—
253C2×C4⋊C4—371no—
254C2×C4⋊C4—371no—
255C2×C4⋊C4—371no—
256C2×C4⋊C4—371no—
257C2×C22⋊C4—371no—
258C2×C22⋊C4—371no—
259C2×C22⋊C4—371no—
260C2×C22⋊C4—371no—
261C2×C22⋊C4—371no—
262C2×C22⋊C4—371no—
263C2×C22⋊C4—371no—
264C2×C22⋊C4—371no—
265C2×C22⋊C4—371no—
266C2×C22⋊C4C2×D3711yescharacteristic
267C2×C22⋊C4C2×D3711yescharacteristic
268C2×C22⋊C4C2×D3711yescharacteristic
269C2×C42—371no—
270C2×C42—371no—
271C2×C42—371no—
272C2×C42—371no—
273#95—371no—
274#95—371no—
275#95—371no—
276#95—371no—
277#95C2×D3711yescharacteristic
278#95C2×D3711yescharacteristic
279C24—371no—
280C24C22×D3711yescharacteristic
281C24C22×D3711yescharacteristic
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—374no—
285C2×D4—374no—
286C2×D4—742no—
287C2×D4—742no—
288C2×D4—1481no—
289C2×D4—1481no—
290C2×D4C4×D3714yescomplemented
291C22×C4—22no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—371no—
295C22×C4—374no—
296C22×C4—371no—
297C22×C4—371no—
298C22×C4—371no—
299C22×C4—371no—
300C22×C4—371no—
301C22×C4—371no—
302C22×C4—742no—
303C22×C4—742no—
304C22×C4—742no—
305C22×C4—1481no—
306C22×C4—1481no—
307C22×C4C22×D3711yescharacteristic
308C22×C4C22×D3711yescharacteristic
309C22×C4C22×D3711yescharacteristic
310C22×C4C22×D3711yescharacteristic
311C22×C4C22×D3711yescharacteristic
312C4⋊C4—374no—
313C4⋊C4—742no—
314C4⋊C4—742no—
315C4⋊C4—742no—
316C4⋊C4—742no—
317C4⋊C4—1481no—
318C4⋊C4—1481no—
319C22⋊C4—22no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—374no—
323C22⋊C4—374no—
324C22⋊C4—742no—
325C22⋊C4—742no—
326C22⋊C4—742no—
327C22⋊C4—1481no—
328C22⋊C4—1481no—
329C22⋊C4—1481no—
330C22⋊C4—1481no—
331C42—374no—
332C42—742no—
333C42—1481no—
334C42—1481no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—372no—
348C23—741no—
349C23—741no—
350C23—741no—
351C23—741no—
352C23—741no—
353C23—741no—
354C23C2×C4×D3712yes—
355C23C2×C4×D3712yes—
356C23C23×D3711yescharacteristic
357D4—44no—
358D4—748no—
359D4—1484no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—44no—
374C2×C4—372no—
375C2×C4—372no—
376C2×C4—372no—
377C2×C4—372no—
378C2×C4—372no—
379C2×C4—372no—
380C2×C4—748no—
381C2×C4—741no—
382C2×C4—741no—
383C2×C4—741no—
384C2×C4—741no—
385C2×C4—741no—
386C2×C4—741no—
387C2×C4—741no—
388C2×C4—741no—
389C2×C4—741no—
390C2×C4—741no—
391C2×C4—741no—
392C2×C4—741no—
393C2×C4—741no—
394C2×C4—741no—
395C2×C4—741no—
396C2×C4—1484no—
397C2×C4C2×C4×D3712yes—
398C2×C4D4×D3712yes—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—742no—
414C22—742no—
415C22—742no—
416C22—1481no—
417C22—1481no—
418C22—1481no—
419C22—1481no—
420C22C22×C4×D3711yescharacteristic
421C22C2×D4×D3711yescharacteristic
422C22#41×D3711yescharacteristic
423C22#1192458111yescharacteristic
424C22#1192458111yescharacteristic
425C22#1192458111yescharacteristic
426C22#1192458311yescharacteristic
427C4—22no—
428C4—22no—
429C4—41no—
430C4—41no—
431C4—41no—
432C4—374no—
433C4—742no—
434C4—742no—
435C4—742no—
436C4—1481no—
437C4—1481no—
438C4—1481no—
439C2—42no—
440C2—42no—
441C2—1482no—
442C2C4×D4×D3711yescharacteristic
443C2#1455800611yescharacteristic
444C2#1455801211yescharacteristic
445C2#1455809811yescharacteristic
446C2#1455811211yescharacteristic
447C2#1455813311yescharacteristic
448C2#1455815111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#386C2
socle, cosocleC23×C37C24
prime radicalC2×#11924508C2
hypercenter#386D37
hypocenterC37#2324
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D37C2semidirect
3. C2×#11924492C2semidirect
4. #14557436C2semidirect
5. #14557433C2semidirect
6. #14557433C2semidirect
7. #14557430C2semidirect
8. #14557422C2semidirect
9. #14557421C2semidirect
10. #14557409C2semidirect
11. #14557407C2semidirect
12. #14557406C2semidirect
13. #14557391C2semidirect
14. #14557384C2semidirect
15. C37×#386C2semidirect
20. #11924508C4semidirect
59. C2×D4×C37C2×C4semidirect
73. C2×C22⋊D37C2×C4semidirect
76. C22×Dic37C2×C4semidirect
94. C22⋊Dic37C2×C4semidirect
98. #10596938C2×C4semidirect
105. #10596936C2×C4semidirect
109. C4×Dic37D4semidirect
235. #386D37semidirect
240. C37#2324semidirect
290. C2×D4C4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245082
C2×C4×C22⋊D372
C2×#119244922
#145574362
#145574332
#145574302
#145574222
#145574212
#145574092
#145574072
#145574062
#145573912
#145573842
C37×#3862
#232437