Finite Group Databasebeta

← #20246439

Subgroups — #20246439

Order 6016.

716 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093997C211yesmaximal, characteristic
2C2×C4×D188C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D47C211yesmaximal, characteristic, complemented
4#15689016C211yesmaximal, characteristic, complemented
5#15689014C211yesmaximal, characteristic, complemented
6#15689010C211yesmaximal, characteristic, complemented
7#15689007C211yesmaximal, characteristic, complemented
8#15689002C211yesmaximal, characteristic, complemented
9#15689001C211yesmaximal, characteristic, complemented
10#15688999C211yesmaximal, characteristic, complemented
11#15688999C211yesmaximal, characteristic, complemented
12C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
13#15688970C211yesmaximal, characteristic, complemented
14#95×D47C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21C22×C4×D47C2211yescharacteristic
22C22×C4×D47C2211yescharacteristic
23#13093997C418yescomplemented
24C4×D188—24no—
25C4×C22⋊D47—24no—
26C2×C4⋊Dic47C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×C4×Dic47C2211yescharacteristic
38C2×C4×Dic47C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C23×C4×C47C2211yescharacteristic
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C42×C47C2211yescharacteristic
51C2×C42×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53#95×C47C2211yescharacteristic
54C24×C47C2311yescharacteristic
55C23×D47C2311yescharacteristic
56C23×D47C2311yescharacteristic
57C22×C4×C47—22no—
58C22×C4×C47—22no—
59C22×C4×C47—41no—
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47—22no—
67C2×C22⋊D47—22no—
68C2×C22⋊D47—41no—
69C2×C22⋊D47—41no—
70C2×C22⋊D47C2×C414yescomplemented
71C2×C22⋊D47C2×C414yescomplemented
72C22×Dic47C2311yescharacteristic
73C22×Dic47C2311yescharacteristic
74C22×Dic47C2311yescharacteristic
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2311yescharacteristic
78C2×D188—22no—
79C2×D188—22no—
80C2×D188C2×C414yescomplemented
81C2×C4×D47—22no—
82C2×C4×D47—22no—
83C2×C4×D47—22no—
84C2×C4×D47—22no—
85C2×C4×D47—22no—
86C2×C4×D47—22no—
87C2×C4×D47—41no—
88C2×C4×D47—41no—
89C2×C4×D47—41no—
90C2×C4×D47—41no—
91C2×C4×D47—41no—
92C2×C4×D47C2×C414yescomplemented
93C22⋊C4×C47—22no—
94C22⋊C4×C47C2×C414yescomplemented
95C42×C47—22no—
96C42×C47—41no—
97C22⋊Dic47—22no—
98C22⋊Dic47—41no—
99(C2×D47)⋊C4—22no—
100(C2×D47)⋊C4—22no—
101(C2×D47)⋊C4—22no—
102(C2×D47)⋊C4—41no—
103(C2×D47)⋊C4C2×C414yescomplemented
104(C2×D47)⋊C4D414yescomplemented
105C4⋊Dic47—22no—
106Dic47⋊C4—22no—
107Dic47⋊C4C2×C414yescomplemented
108C4×Dic47—22no—
109C4×Dic47—41no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47C22×C412yes—
117C23×C47C2411yescharacteristic
118C22×D47—21no—
119C22×D47—21no—
120C22×D47—21no—
121C22×D47—21no—
122C22×D47—21no—
123C22×D47—21no—
124C22×D47—21no—
125C22×D47—21no—
126C22×D47—21no—
127C22×D47—21no—
128C22×D47C22×C412yes—
129C22×D47C22×C412yes—
130C22×D47C2×D412yes—
131C22×D47#4112yes—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—44no—
146C2×C4×C47C22×C412yes—
147C2×C4×C47C22×C412yes—
148C2×C4×C47C2×D412yes—
149C2×C4×C47#4112yes—
150C2×C4×C47#4112yes—
151C22⋊D47—28no—
152C22⋊D47—44no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—21no—
160C2×Dic47—21no—
161C2×Dic47—21no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—21no—
165C2×Dic47—21no—
166C2×Dic47—21no—
167C2×Dic47—21no—
168C2×Dic47C22×C412yes—
169C2×Dic47C22×C412yes—
170C2×Dic47C2×D412yes—
171D188—28no—
172C4×D47—44no—
173C4×D47—44no—
174C4×D47—44no—
175C4×D47—44no—
176C22×C47—22no—
177C22×C47—22no—
178C22×C47—22no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47C23×C411yescharacteristic
184C22×C47C22×D411yescharacteristic
185C22×C47C2×#4111yescharacteristic
186C22×C47C2×#4111yescharacteristic
187C22×C47C2×#4111yescharacteristic
188C22×C47H(5,𝔽2)11yescharacteristic
189C22×C47H(5,𝔽2)11yescharacteristic
190C2×D47—22no—
191C2×D47—22no—
192C2×D47—22no—
193C2×D47—22no—
194C2×D47—22no—
195C2×D47—22no—
196C2×D47—22no—
197C2×D47—22no—
198C2×D47—22no—
199C2×D47—41no—
200C2×D47—41no—
201C2×D47—41no—
202C2×D47—41no—
203C2×D47C4×D414yes—
204C4×C47—22no—
205C4×C47—22no—
206C4×C47—22no—
207C4×C47—22no—
208C4×C47—22no—
209C4×C47—41no—
210Dic47—22no—
211Dic47—22no—
212Dic47—22no—
213Dic47—41no—
214Dic47—41no—
215Dic47—41no—
216#2364—471nomaximal, Sylow
217C2×C47—42no—
218C2×C47C2×C4×D411yescharacteristic
219C2×C47C4×#4111yescharacteristic
220C2×C47#51811yescharacteristic
221C2×C47#54611yescharacteristic
222C2×C47#54611yescharacteristic
223C2×C47#55311yescharacteristic
224C2×C47#55311yescharacteristic
225D47—24no—
226D47—42no—
227C2×#121—471no—
228C2×C4×D4—471no—
229C2×C4×D4—471no—
230#388—471no—
231#388—471no—
232#387—471no—
233#387—471no—
234#386—471no—
235#386—471no—
236#386—471no—
237#386—471no—
238C4×C22⋊C4—471no—
239C4×C22⋊C4—471no—
240C4×C22⋊C4D4711yescharacteristic, complemented
241C2×#95—471no—
242C47#236411yescharacteristic, complemented, Sylow
243C22×D4—471no—
244C22×D4—471no—
245C22×D4—471no—
246C23×C4—471no—
247C23×C4—471no—
248C23×C4—471no—
249C23×C4—471no—
250C23×C4C2×D4711yescharacteristic
251#121—478no—
252C4×D4—944no—
253C4×D4—944no—
254C2×C4⋊C4—471no—
255C2×C4⋊C4—471no—
256C2×C4⋊C4—471no—
257C2×C22⋊C4—471no—
258C2×C22⋊C4—471no—
259C2×C22⋊C4—471no—
260C2×C22⋊C4—471no—
261C2×C22⋊C4—471no—
262C2×C22⋊C4—471no—
263C2×C22⋊C4—471no—
264C2×C22⋊C4—471no—
265C2×C22⋊C4C2×D4711yescharacteristic
266C2×C22⋊C4C2×D4711yescharacteristic
267C2×C42—471no—
268C2×C42—471no—
269C2×C42C2×D4711yescharacteristic
270C2×C42C2×D4711yescharacteristic
271#95—471no—
272#95—471no—
273#95—471no—
274#95—471no—
275#95—471no—
276#95—471no—
277#95—471no—
278#95—471no—
279#95C2×D4711yescharacteristic
280#95C2×D4711yescharacteristic
281C24—471no—
282C24—471no—
283C24C22×D4711yescharacteristic
284C2×D4—474no—
285C2×D4—474no—
286C2×D4—474no—
287C2×D4—942no—
288C2×D4—942no—
289C2×D4—942no—
290C2×D4—942no—
291C2×D4—1881no—
292C2×D4—1881no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—41no—
296C22×C4—471no—
297C22×C4—471no—
298C22×C4—471no—
299C22×C4—474no—
300C22×C4—471no—
301C22×C4—471no—
302C22×C4—471no—
303C22×C4—942no—
304C22×C4—942no—
305C22×C4—942no—
306C22×C4—942no—
307C22×C4—942no—
308C22×C4—942no—
309C22×C4—1881no—
310C22×C4—1881no—
311C22×C4—1881no—
312C22×C4—1881no—
313C22×C4—1881no—
314C22×C4C22×D4711yescharacteristic
315C22×C4C22×D4711yescharacteristic
316C22×C4C22×D4711yescharacteristic
317C22×C4C22×D4711yescharacteristic
318C22×C4C22×D4711yescharacteristic
319C22×C4C22×D4711yescharacteristic
320C4⋊C4—474no—
321C4⋊C4—942no—
322C4⋊C4—942no—
323C22⋊C4—22no—
324C22⋊C4—474no—
325C22⋊C4—474no—
326C22⋊C4—942no—
327C22⋊C4—942no—
328C22⋊C4—942no—
329C22⋊C4—942no—
330C22⋊C4—1881no—
331C22⋊C4—1881no—
332C22⋊C4C4×D4714yescomplemented
333C42—22no—
334C42—41no—
335C42—942no—
336C42—1881no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—472no—
344C23—472no—
345C23—472no—
346C23—472no—
347C23—941no—
348C23—941no—
349C23—941no—
350C23—941no—
351C23—941no—
352C23—941no—
353C23—941no—
354C23—941no—
355C23—941no—
356C23—941no—
357C23C2×C4×D4712yes—
358C23C23×D4711yescharacteristic
359D4—948no—
360D4—948no—
361D4—1884no—
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—21no—
374C2×C4—21no—
375C2×C4—44no—
376C2×C4—472no—
377C2×C4—472no—
378C2×C4—472no—
379C2×C4—941no—
380C2×C4—941no—
381C2×C4—941no—
382C2×C4—941no—
383C2×C4—941no—
384C2×C4—941no—
385C2×C4—941no—
386C2×C4—941no—
387C2×C4—941no—
388C2×C4—941no—
389C2×C4—941no—
390C2×C4—941no—
391C2×C4—941no—
392C2×C4—941no—
393C2×C4—941no—
394C2×C4—1884no—
395C2×C4—1884no—
396C2×C4—1884no—
397C2×C4—1884no—
398C2×C4C2×C4×D4712yes—
399C2×C4C2×C4×D4712yes—
400C2×C4#1062535012yes—
401C2×C4#1062535012yes—
402C2×C4D4×D4712yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—474no—
411C22—942no—
412C22—942no—
413C22—942no—
414C22—942no—
415C22—942no—
416C22—942no—
417C22—942no—
418C22—942no—
419C22—942no—
420C22—1881no—
421C22—1881no—
422C22—1881no—
423C22—1881no—
424C22C22×C4×D4711yescharacteristic
425C22C2×D4×D4711yescharacteristic
426C22#41×D4711yescharacteristic
427C22C2×#1062535011yescharacteristic
428C22C2×#1062535011yescharacteristic
429C22#1309406911yescharacteristic
430C22#1309407011yescharacteristic
431C4—22no—
432C4—22no—
433C4—22no—
434C4—22no—
435C4—22no—
436C4—41no—
437C4—942no—
438C4—942no—
439C4—942no—
440C4—1881no—
441C4—1881no—
442C4—1881no—
443C2—42no—
444C2—944no—
445C2—1882no—
446C2C4×D4×D4711yescharacteristic
447C2C4×#1062535011yescharacteristic
448C2#1568959511yescharacteristic
449C2#1568976311yescharacteristic
450C2#1568976911yescharacteristic
451C2#1568981711yescharacteristic
452C2#1568982311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC4×C22⋊C4×C47C2
socleC23×C47C24
hypercenterC4×C22⋊C4D47
hypocenterC47#2364
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D188C2semidirect
3. C2×C4×C22⋊D47C2semidirect
4. #15689016C2semidirect
5. #15689014C2semidirect
6. #15689010C2semidirect
7. #15689007C2semidirect
8. #15689002C2semidirect
9. #15689001C2semidirect
10. #15688999C2semidirect
11. #15688999C2semidirect
12. C4×(C2×D47)⋊C4C2semidirect
13. #15688970C2semidirect
14. #95×D47C2semidirect
15. C4×C22⋊C4×C47C2semidirect
23. #13093997C4semidirect
70. C2×C22⋊D47C2×C4semidirect
71. C2×C22⋊D47C2×C4semidirect
80. C2×D188C2×C4semidirect
92. C2×C4×D47C2×C4semidirect
94. C22⋊C4×C47C2×C4semidirect
103. (C2×D47)⋊C4C2×C4semidirect
104. (C2×D47)⋊C4D4semidirect
107. Dic47⋊C4C2×C4semidirect
240. C4×C22⋊C4D47semidirect
242. C47#2364semidirect
332. C22⋊C4C4×D47semidirect