Finite Group Databasebeta

← #17997494

Subgroups — #17997494

Order 4736.

776 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D37C211yesmaximal, characteristic
2C2×#11924496C211yesmaximal, characteristic
3C2×#11924496C211yesmaximal, characteristic
4C22×#10596936C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×D37C211yesmaximal, characteristic, complemented
6#14557430C211yesmaximal, characteristic, complemented
7#14557428C211yesmaximal, characteristic, complemented
8#14557408C211yesmaximal, characteristic, complemented
9#14557407C211yesmaximal, characteristic, complemented
10#14557404C211yesmaximal, characteristic, complemented
11#14557402C211yesmaximal, characteristic, complemented
12#14557392C211yesmaximal, characteristic, complemented
13#14557391C211yesmaximal, characteristic, complemented
14#14557384C211yesmaximal, characteristic, complemented
15C37×#385C211yesmaximal, characteristic, complemented
16C22×C22⋊D37C2211yescharacteristic
17C23×Dic37C2211yescharacteristic
18C23×Dic37C2211yescharacteristic
19C22×C4×D37C2211yescharacteristic
20C22×C4×D37C2211yescharacteristic
21C22×C4×D37C2211yescharacteristic
22C4×C22⋊D37—24no—
23#11924496—24no—
24#11924496C418yescomplemented
25C2×C4⋊Dic37C2211yescharacteristic
26C2×C4⋊Dic37C2211yescharacteristic
27C2×#10596936—24no—
28C2×#10596936C2211yescharacteristic
29C2×#10596936C2211yescharacteristic
30C2×#10596936C2211yescharacteristic
31C2×#10596936C2211yescharacteristic
32C2×#10596936C2211yescharacteristic
33C2×#10596936C2211yescharacteristic
34C2×#10596936C2211yescharacteristic
35C2×#10596936C2211yescharacteristic
36C2×#10596936C2211yescharacteristic
37C4⋊C4×D37—24no—
38C2×C22⋊Dic37C2211yescharacteristic
39C2×#10596938C2211yescharacteristic
40C2×#10596938C2211yescharacteristic
41C2×#10596938C2211yescharacteristic
42C2×C4×Dic37C2211yescharacteristic
43C2×C4×Dic37C2211yescharacteristic
44C2×C4×Dic37C2211yescharacteristic
45#11924443C2211yescharacteristic
46#11924443C2211yescharacteristic
47#11924443C2211yescharacteristic
48#11924443C2211yescharacteristic
49C23×C4×C37C2211yescharacteristic
50C2×C4⋊C4×C37C2211yescharacteristic
51C2×C4⋊C4×C37C2211yescharacteristic
52C2×C22⋊C4×C37C2211yescharacteristic
53C2×C22⋊C4×C37C2211yescharacteristic
54#95×C37C2211yescharacteristic
55#95×C37C2211yescharacteristic
56C24×C37C2311yescharacteristic
57C23×D37C2311yescharacteristic
58C22×C4×C37—22no—
59C22×C4×C37—22no—
60C22×C4×C37—41no—
61C22×C4×C37C2311yescharacteristic
62C22×C4×C37C2311yescharacteristic
63C22×C4×C37C2311yescharacteristic
64C22×C4×C37C2311yescharacteristic
65C22×C4×C37C2311yescharacteristic
66C22×C4×C37C2311yescharacteristic
67C2×C22⋊D37C2×C414yes—
68C2×C22⋊D37D414yes—
69C2×C22⋊D37Q814yes—
70C22×Dic37—22no—
71C22×Dic37—22no—
72C22×Dic37—22no—
73C22×Dic37—22no—
74C22×Dic37—41no—
75C22×Dic37C2×C414yescomplemented
76C22×Dic37C2311yescharacteristic
77C22×Dic37C2311yescharacteristic
78C22×Dic37C2311yescharacteristic
79C22×Dic37C2311yescharacteristic
80C22×Dic37C2311yescharacteristic
81C22×Dic37C2311yescharacteristic
82C22×Dic37C2311yescharacteristic
83C2×C4×D37—22no—
84C2×C4×D37—22no—
85C2×C4×D37—22no—
86C2×C4×D37—22no—
87C2×C4×D37—22no—
88C2×C4×D37—22no—
89C2×C4×D37—41no—
90C2×C4×D37—41no—
91C2×C4×D37C2×C414yescomplemented
92C4⋊C4×C37—22no—
93C4⋊C4×C37—41no—
94C22⋊C4×C37—22no—
95C22⋊C4×C37C2×C414yescomplemented
96C22⋊Dic37—22no—
97#10596938—22no—
98#10596938—22no—
99#10596938C2×C414yescomplemented
100C4⋊Dic37—22no—
101C4⋊Dic37—41no—
102#10596936—22no—
103#10596936—22no—
104#10596936—22no—
105#10596936—22no—
106#10596936—22no—
107#10596936—22no—
108#10596936—22no—
109#10596936C2×C414yescomplemented
110#10596936D414yescomplemented
111C4×Dic37—22no—
112C4×Dic37—22no—
113C4×Dic37C2×C414yescomplemented
114C23×C37—21no—
115C23×C37—21no—
116C23×C37—21no—
117C23×C37—21no—
118C23×C37C22×C412yes—
119C23×C37C2×D412yes—
120C23×C37C2×Q812yes—
121C23×C37C2411yescharacteristic
122C22×D37—21no—
123C22×D37—21no—
124C22×D37—21no—
125C22×D37—21no—
126C22×D37C22×C412yes—
127C22×D37C2×D412yes—
128C22×D37C2×Q812yes—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—21no—
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—44no—
145C2×C4×C37C22×C412yes—
146C2×C4×C37C22×C412yes—
147C2×C4×C37C2×D412yes—
148C22⋊D37C4⋊C4116yescomplemented
149C2×Dic37—21no—
150C2×Dic37—21no—
151C2×Dic37—21no—
152C2×Dic37—21no—
153C2×Dic37—28no—
154C2×Dic37—21no—
155C2×Dic37—21no—
156C2×Dic37—21no—
157C2×Dic37—21no—
158C2×Dic37—21no—
159C2×Dic37—21no—
160C2×Dic37—21no—
161C2×Dic37—21no—
162C2×Dic37—21no—
163C2×Dic37—44no—
164C2×Dic37C22×C412yes—
165C2×Dic37C22×C412yes—
166C2×Dic37C22×C412yes—
167C2×Dic37C2×D412yes—
168C2×Dic37C2×D412yes—
169C2×Dic37C2×D412yes—
170C2×Dic37C2×Q812yes—
171C2×Dic37#4112yes—
172C4×D37—28no—
173C4×D37—44no—
174C4×D37—44no—
175C22×C37—22no—
176C22×C37—22no—
177C22×C37—22no—
178C22×C37—22no—
179C22×C37—22no—
180C22×C37—22no—
181C22×C37C2×C4⋊C414yescomplemented
182C22×C37C23×C411yescharacteristic
183C22×C37C22×D411yescharacteristic
184C22×C37C22×D411yescharacteristic
185C22×C37C22×Q811yescharacteristic
186C22×C37C2×#4111yescharacteristic
187C22×C37H(5,𝔽2)11yescharacteristic
188C22×C372−1+411yescharacteristic
189C2×D37—22no—
190C2×D37—22no—
191C2×D37—22no—
192C2×D37—22no—
193C2×D37—22no—
194C2×D37—22no—
195C2×D37C2×C4⋊C414yescomplemented
196C4×C37—22no—
197C4×C37—22no—
198C4×C37—22no—
199C4×C37—41no—
200C4×C37—41no—
201C4×C37—41no—
202Dic37—22no—
203Dic37—22no—
204Dic37—41no—
205Dic37—41no—
206Dic37—41no—
207Dic37C2×C4⋊C414yescomplemented
208Dic37C4×D414yescomplemented
209D4×C4⋊C4—371nomaximal, Sylow
210C2×C37—24no—
211C2×C37C22×C4⋊C411yescharacteristic
212C2×C37C2×C4×D411yescharacteristic
213C2×C37#52011yescharacteristic
214C2×C37D4211yescharacteristic
215C2×C37#54711yescharacteristic
216C2×C37D4×Q811yescharacteristic
217C2×C37#55411yescharacteristic
218D37—24no—
219C2×C4×D4—371no—
220C2×C4×D4—371no—
221C2×C4×D4—371no—
222C22×C4⋊C4—371no—
223C22×C4⋊C4—371no—
224#389—371no—
225#389—371no—
226#385—371no—
227#385—371no—
228#385—371no—
229#385D3711yescharacteristic, complemented
230#384—371no—
231#380—371no—
232#380—371no—
233C4×C4⋊C4—371no—
234C37D4×C4⋊C411yescharacteristic, complemented, Sylow
235C22×D4—371no—
236C23×C4—371no—
237C23×C4—371no—
238C23×C4—371no—
239C23×C4—371no—
240C23×C4—371no—
241C23×C4C2×D3711yescharacteristic
242C4×D4—378no—
243C4×D4—744no—
244C4×D4—744no—
245C2×C4⋊C4—371no—
246C2×C4⋊C4—371no—
247C2×C4⋊C4—371no—
248C2×C4⋊C4—371no—
249C2×C4⋊C4—371no—
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—744no—
257C2×C4⋊C4—744no—
258C2×C4⋊C4C2×D3711yescharacteristic
259C2×C4⋊C4C2×D3711yescharacteristic
260C2×C22⋊C4—371no—
261C2×C22⋊C4—371no—
262C2×C22⋊C4—371no—
263C2×C22⋊C4—371no—
264C2×C22⋊C4C2×D3711yescharacteristic
265C2×C22⋊C4C2×D3711yescharacteristic
266C2×C42—371no—
267C2×C42—371no—
268C2×C42—371no—
269#95—371no—
270#95—371no—
271#95—371no—
272#95—371no—
273#95C2×D3711yescharacteristic
274#95C2×D3711yescharacteristic
275C24—371no—
276C24C22×D3711yescharacteristic
277C2×D4—374no—
278C2×D4—374no—
279C2×D4—374no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—41no—
283C22×C4—371no—
284C22×C4—371no—
285C22×C4—374no—
286C22×C4—371no—
287C22×C4—371no—
288C22×C4—374no—
289C22×C4—371no—
290C22×C4—371no—
291C22×C4—371no—
292C22×C4—742no—
293C22×C4—742no—
294C22×C4—742no—
295C22×C4—742no—
296C22×C4—742no—
297C22×C4—742no—
298C22×C4—742no—
299C22×C4—742no—
300C22×C4—742no—
301C22×C4—742no—
302C22×C4—1481no—
303C22×C4—1481no—
304C22×C4—1481no—
305C22×C4C22×D3711yescharacteristic
306C22×C4C22×D3711yescharacteristic
307C22×C4C22×D3711yescharacteristic
308C22×C4C22×D3711yescharacteristic
309C22×C4C22×D3711yescharacteristic
310C22×C4C22×D3711yescharacteristic
311C4⋊C4—22no—
312C4⋊C4—41no—
313C4⋊C4—374no—
314C4⋊C4—374no—
315C4⋊C4—742no—
316C4⋊C4—742no—
317C4⋊C4—742no—
318C4⋊C4—742no—
319C4⋊C4—742no—
320C4⋊C4—742no—
321C4⋊C4—742no—
322C4⋊C4—742no—
323C4⋊C4—1481no—
324C22⋊C4—22no—
325C22⋊C4—374no—
326C22⋊C4—742no—
327C22⋊C4—742no—
328C22⋊C4—742no—
329C22⋊C4C4×D3714yescomplemented
330C42—374no—
331C42—742no—
332C42—742no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—372no—
338C23—372no—
339C23—372no—
340C23—741no—
341C23—741no—
342C23—741no—
343C23—741no—
344C23C2×C4×D3712yes—
345C23D4×D3712yes—
346C23Q8×D3712yes—
347C23C23×D3711yescharacteristic
348D4—3716no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—44no—
365C2×C4—372no—
366C2×C4—372no—
367C2×C4—372no—
368C2×C4—372no—
369C2×C4—372no—
370C2×C4—372no—
371C2×C4—372no—
372C2×C4—372no—
373C2×C4—748no—
374C2×C4—748no—
375C2×C4—741no—
376C2×C4—741no—
377C2×C4—741no—
378C2×C4—741no—
379C2×C4—741no—
380C2×C4—741no—
381C2×C4—741no—
382C2×C4—741no—
383C2×C4—741no—
384C2×C4—741no—
385C2×C4—741no—
386C2×C4—741no—
387C2×C4—741no—
388C2×C4—1484no—
389C2×C4—1484no—
390C2×C4—1484no—
391C2×C4C2×C4×D3712yes—
392C2×C4C2×C4×D3712yes—
393C2×C4D4×D3712yes—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—374no—
401C22—742no—
402C22—742no—
403C22—742no—
404C22—742no—
405C22—742no—
406C22—742no—
407C22C4⋊C4×D3714yescomplemented
408C22C22×C4×D3711yescharacteristic
409C22C2×D4×D3711yescharacteristic
410C22C2×D4×D3711yescharacteristic
411C22C2×Q8×D3711yescharacteristic
412C22#41×D3711yescharacteristic
413C22#1192458111yescharacteristic
414C22#1192458311yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—374no—
422C4—374no—
423C4—742no—
424C4—742no—
425C4—1481no—
426C4—1481no—
427C4—1481no—
428C2—24no—
429C2—744no—
430C2C2×C4⋊C4×D3711yescharacteristic
431C2C4×D4×D3711yescharacteristic
432C2#1455801211yescharacteristic
433C2#1455816511yescharacteristic
434C2#1455818111yescharacteristic
435C2#1455819611yescharacteristic
436C2#1455823711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#385C2
socle, cosocleC23×C37C24
prime radicalC22×C22⋊D37C22
hypercenter#385D37
hypocenterC37D4×C4⋊C4
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
4. C22×#10596936C2semidirect
5. C2×C4⋊C4×D37C2semidirect
6. #14557430C2semidirect
7. #14557428C2semidirect
8. #14557408C2semidirect
9. #14557407C2semidirect
10. #14557404C2semidirect
11. #14557402C2semidirect
12. #14557392C2semidirect
13. #14557391C2semidirect
14. #14557384C2semidirect
15. C37×#385C2semidirect
24. #11924496C4semidirect
75. C22×Dic37C2×C4semidirect
91. C2×C4×D37C2×C4semidirect
95. C22⋊C4×C37C2×C4semidirect
99. #10596938C2×C4semidirect
109. #10596936C2×C4semidirect
110. #10596936D4semidirect
113. C4×Dic37C2×C4semidirect
148. C22⋊D37C4⋊C4semidirect
181. C22×C37C2×C4⋊C4semidirect
195. C2×D37C2×C4⋊C4semidirect
207. Dic37C2×C4⋊C4semidirect
208. Dic37C4×D4semidirect
229. #385D37semidirect
234. C37D4×C4⋊C4semidirect
329. C22⋊C4C4×D37semidirect
407. C22C4⋊C4×D37semidirect

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×#119244962
C22×#105969362
C2×C4⋊C4×D372
#145574302
#145574282
#145574082
#145574072
#145574042
#145574022
#145573922
#145573912
#145573842
C37×#3852
D4×C4⋊C437