Finite Group Databasebeta

← #20246214

Subgroups — #20246214

Order 6016.

928 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10625352C211yesmaximal, characteristic
2C2×C4×C22⋊D47C211yesmaximal, characteristic, complemented
3C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
4#15689027C211yesmaximal, characteristic, complemented
5#15689027C211yesmaximal, characteristic, complemented
6#15689003C211yesmaximal, characteristic, complemented
7#15688999C211yesmaximal, characteristic, complemented
8#15688999C211yesmaximal, characteristic, complemented
9#15688985C211yesmaximal, characteristic, complemented
10#15688984C211yesmaximal, characteristic, complemented
11#15688981C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
13C2×C47⋊#95C211yesmaximal, characteristic, complemented
14#95×D47C211yesmaximal, characteristic, complemented
15C47×#386C211yesmaximal, characteristic, complemented
16C2×#10625352—24no—
17C2×#10625352—24no—
18C2×#10625352C418yescomplemented
19C22×Dic94C2211yescharacteristic
20C22×C22⋊D47C2211yescharacteristic
21C22×C22⋊D47C2211yescharacteristic
22C23×Dic47C2211yescharacteristic
23C23×Dic47C2211yescharacteristic
24C23×Dic47C2211yescharacteristic
25C22×C4×D47C2211yescharacteristic
26C22×C4×D47C2211yescharacteristic
27C22×C4×D47C2211yescharacteristic
28C4×C22⋊D47—24no—
29(C22⋊D47)⋊C4—24no—
30C2×Dic47⋊C4C2211yescharacteristic
31C2×Dic47⋊C4C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×C22⋊Dic47C2211yescharacteristic
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
47C47⋊#95C2211yescharacteristic
48C47⋊#95C2211yescharacteristic
49C22×D4×C47C2211yescharacteristic
50C23×C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
54#95×C47C2211yescharacteristic
55#95×C47C2211yescharacteristic
56C24×C47C2311yescharacteristic
57C24×C47C2311yescharacteristic
58C23×D47C2311yescharacteristic
59C2×D4×C47—22no—
60C2×D4×C47—22no—
61C2×D4×C47C2×C414yescomplemented
62C22×C4×C47—22no—
63C22×C4×C47—22no—
64C22×C4×C47—41no—
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C2×C22⋊D47—22no—
71C2×C22⋊D47—22no—
72C2×C22⋊D47C2×C414yes—
73C2×C22⋊D47C2×C414yescomplemented
74C2×C22⋊D47D414yes—
75C2×C22⋊D47D414yes—
76C22×Dic47—22no—
77C22×Dic47—22no—
78C22×Dic47—22no—
79C22×Dic47—22no—
80C22×Dic47—22no—
81C22×Dic47—22no—
82C22×Dic47—41no—
83C22×Dic47C2×C414yescomplemented
84C22×Dic47C2×C414yescomplemented
85C22×Dic47C2311yescharacteristic
86C22×Dic47C2311yescharacteristic
87C22×Dic47C2311yescharacteristic
88C22×Dic47C2311yescharacteristic
89C22×Dic47C2311yescharacteristic
90C22×Dic47C2311yescharacteristic
91C22×Dic47C2311yescharacteristic
92#10625352—232no—
93C2×C4×D47—22no—
94C2×C4×D47—22no—
95C2×C4×D47—22no—
96C2×C4×D47—22no—
97C2×C4×D47—22no—
98C2×C4×D47—22no—
99C2×C4×D47—41no—
100C2×C4×D47—41no—
101C2×C4×D47C2×C414yescomplemented
102C2×Dic94—22no—
103C2×Dic94—22no—
104C2×Dic94C2×C414yescomplemented
105C22⋊C4×C47—22no—
106C22⋊C4×C47—22no—
107C22⋊C4×C47—41no—
108C22⋊Dic47—22no—
109C22⋊Dic47—22no—
110C22⋊Dic47—41no—
111(C2×D47)⋊C4—22no—
112(C2×D47)⋊C4—22no—
113Dic47⋊C4—22no—
114Dic47⋊C4—22no—
115C4×Dic47—22no—
116C4×Dic47—22no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—21no—
121C23×C47—21no—
122C23×C47—21no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47C22×C412yes—
128C23×C47C22×C412yes—
129C23×C47C2×D412yes—
130C23×C47C2×D412yes—
131C23×C47C2411yescharacteristic
132C22×D47—21no—
133C22×D47—21no—
134C22×D47—21no—
135C22×D47—21no—
136C22×D47C22×C412yes—
137C22×D47C2×D412yes—
138C22×D47C2×D412yes—
139D4×C47—28no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—44no—
154C2×C4×C47C22×C412yes—
155C2×C4×C47#4112yescomplemented
156C22⋊D47—28no—
157C22⋊D47C22⋊C4116yescomplemented
158C2×Dic47—28no—
159C2×Dic47—21no—
160C2×Dic47—21no—
161C2×Dic47—21no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—21no—
165C2×Dic47—28no—
166C2×Dic47—21no—
167C2×Dic47—21no—
168C2×Dic47—21no—
169C2×Dic47—21no—
170C2×Dic47—21no—
171C2×Dic47—21no—
172C2×Dic47—21no—
173C2×Dic47—21no—
174C2×Dic47—21no—
175C2×Dic47—44no—
176C2×Dic47C22×C412yes—
177C2×Dic47C22×C412yes—
178C2×Dic47C22×C412yes—
179C2×Dic47C2×D412yes—
180C2×Dic47C2×D412yes—
181C2×Dic47#4112yescomplemented
182C4×D47—28no—
183C4×D47—44no—
184C4×D47—44no—
185Dic94—28no—
186C22×C47—22no—
187C22×C47—22no—
188C22×C47—22no—
189C22×C47—22no—
190C22×C47—22no—
191C22×C47—22no—
192C22×C47—22no—
193C22×C47—22no—
194C22×C47—22no—
195C22×C47—41no—
196C22×C47—41no—
197C22×C47—41no—
198C22×C47—41no—
199C22×C47C2×C22⋊C414yes—
200C22×C47C23×C411yescharacteristic
201C22×C47C22×D411yescharacteristic
202C22×C47C22×D411yescharacteristic
203C22×C47C2×#4111yescharacteristic
204C22×C47C2×#4111yescharacteristic
205C22×C47H(5,𝔽2)11yescharacteristic
206C22×C472−1+411yescharacteristic
207C2×D47—22no—
208C2×D47—22no—
209C2×D47—22no—
210C2×D47—22no—
211C2×D47—22no—
212C2×D47—22no—
213C2×D47C2×C22⋊C414yes—
214C4×C47—22no—
215C4×C47—22no—
216C4×C47—41no—
217C4×C47—41no—
218C4×C47—41no—
219Dic47—22no—
220Dic47—22no—
221Dic47—22no—
222Dic47—41no—
223Dic47—41no—
224Dic47—41no—
225Dic47C2×C22⋊C414yes—
226#2339—471nomaximal, Sylow
227C2×C47—24no—
228C2×C47—42no—
229C2×C47C22×C22⋊C411yescharacteristic
230C2×C47C4×#4111yescharacteristic
231C2×C47#52011yescharacteristic
232C2×C47#54611yescharacteristic
233C2×C47#54611yescharacteristic
234C2×C47#54711yescharacteristic
235C2×C47#54711yescharacteristic
236D47—24no—
237C22×#41—471no—
238C2×C4×D4—471no—
239C2×C4×D4—471no—
240#391—471no—
241#391—471no—
242#386—471no—
243#386—471no—
244#386—471no—
245#386D4711yescharacteristic, complemented
246#381—471no—
247#381—471no—
248#380—471no—
249C4×C22⋊C4—471no—
250C2×#95—471no—
251C2×#95—471no—
252C47#233911yescharacteristic, complemented, Sylow
253C2×#41—478no—
254C2×#41—944no—
255C2×#41—944no—
256C22×Q8—471no—
257C22×D4—471no—
258C22×D4—471no—
259C22×D4C2×D4711yescharacteristic
260C23×C4—471no—
261C23×C4—471no—
262C23×C4—471no—
263C23×C4—471no—
264C23×C4—471no—
265C23×C4—471no—
266C23×C4C2×D4711yescharacteristic
267C4×D4—944no—
268C4×D4—944no—
269C2×C4⋊C4—471no—
270C2×C4⋊C4—471no—
271C2×C22⋊C4—471no—
272C2×C22⋊C4—471no—
273C2×C22⋊C4—471no—
274C2×C22⋊C4—471no—
275C2×C22⋊C4—471no—
276C2×C22⋊C4C2×D4711yescharacteristic
277C2×C22⋊C4C2×D4711yescharacteristic
278C2×C22⋊C4C2×D4711yescharacteristic
279C2×C42—471no—
280C2×C42—471no—
281#95—471no—
282#95—471no—
283#95—471no—
284#95—471no—
285#95—471no—
286#95—471no—
287#95—471no—
288#95—471no—
289#95—471no—
290#95—471no—
291#95C2×D4711yescharacteristic
292#95C2×D4711yescharacteristic
293C24—471no—
294C24C22×D4711yescharacteristic
295C24C22×D4711yescharacteristic
296#41—9432no—
297C2×Q8—474no—
298C2×Q8—942no—
299C2×Q8—942no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—474no—
303C2×D4—474no—
304C2×D4—474no—
305C2×D4—474no—
306C2×D4—942no—
307C2×D4—942no—
308C2×D4C4×D4714yescomplemented
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—41no—
312C22×C4—471no—
313C22×C4—474no—
314C22×C4—474no—
315C22×C4—471no—
316C22×C4—471no—
317C22×C4—471no—
318C22×C4—474no—
319C22×C4—471no—
320C22×C4—471no—
321C22×C4—471no—
322C22×C4—942no—
323C22×C4—942no—
324C22×C4—942no—
325C22×C4—942no—
326C22×C4—942no—
327C22×C4—942no—
328C22×C4—942no—
329C22×C4—942no—
330C22×C4—942no—
331C22×C4—942no—
332C22×C4—942no—
333C22×C4—942no—
334C22×C4—1881no—
335C22×C4—1881no—
336C22×C4—1881no—
337C22×C4C22×D4711yescharacteristic
338C22×C4C22×D4711yescharacteristic
339C22×C4C22×D4711yescharacteristic
340C22×C4C22×D4711yescharacteristic
341C22×C4C22×D4711yescharacteristic
342C4⋊C4—942no—
343C4⋊C4—942no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—41no—
347C22⋊C4—942no—
348C22⋊C4—942no—
349C22⋊C4—942no—
350C22⋊C4—942no—
351C22⋊C4—1881no—
352C42—942no—
353C42—942no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—472no—
365C23—472no—
366C23—472no—
367C23—941no—
368C23—941no—
369C23—941no—
370C23—941no—
371C23C2×C4×D4712yes—
372C23C2×C4×D4712yes—
373C23D4×D4712yes—
374C23D4×D4712yes—
375C23C23×D4711yescharacteristic
376Q8—948no—
377D4—28no—
378D4—4716no—
379D4—948no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—44no—
394C2×C4—472no—
395C2×C4—472no—
396C2×C4—472no—
397C2×C4—472no—
398C2×C4—472no—
399C2×C4—472no—
400C2×C4—948no—
401C2×C4—948no—
402C2×C4—948no—
403C2×C4—941no—
404C2×C4—941no—
405C2×C4—941no—
406C2×C4—941no—
407C2×C4—941no—
408C2×C4—941no—
409C2×C4—941no—
410C2×C4—941no—
411C2×C4—941no—
412C2×C4—941no—
413C2×C4—941no—
414C2×C4—941no—
415C2×C4—941no—
416C2×C4—941no—
417C2×C4—941no—
418C2×C4—1884no—
419C2×C4—1884no—
420C2×C4—1884no—
421C2×C4C2×C4×D4712yes—
422C2×C4#1062535212yescomplemented
423C22—22no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—474no—
437C22—942no—
438C22—942no—
439C22—942no—
440C22—942no—
441C22—942no—
442C22—942no—
443C22C22⋊C4×D4714yes—
444C22C22×C4×D4711yescharacteristic
445C22C2×D4×D4711yescharacteristic
446C22C2×D4×D4711yescharacteristic
447C22#41×D4711yescharacteristic
448C22C2×#1062535211yescharacteristic
449C22#1309406911yescharacteristic
450C22#1309407111yescharacteristic
451C4—22no—
452C4—22no—
453C4—41no—
454C4—41no—
455C4—41no—
456C4—474no—
457C4—942no—
458C4—942no—
459C4—942no—
460C4—1881no—
461C4—1881no—
462C4—1881no—
463C2—24no—
464C2—42no—
465C2—944no—
466C2C2×C22⋊C4×D4711yescharacteristic
467C2C4×#1062535211yescharacteristic
468C2#1568960211yescharacteristic
469C2#1568976011yescharacteristic
470C2#1568976211yescharacteristic
471C2#1568977111yescharacteristic
472C2#1568977311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#386C2
socleC23×C47C24
hypercenter#386D47
hypocenterC47#2339
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D47C2semidirect
3. C2×(C22⋊D47)⋊C4C2semidirect
4. #15689027C2semidirect
5. #15689027C2semidirect
6. #15689003C2semidirect
7. #15688999C2semidirect
8. #15688999C2semidirect
9. #15688985C2semidirect
10. #15688984C2semidirect
11. #15688981C2semidirect
12. C22⋊C4×Dic47C2semidirect
13. C2×C47⋊#95C2semidirect
14. #95×D47C2semidirect
15. C47×#386C2semidirect
18. C2×#10625352C4semidirect
61. C2×D4×C47C2×C4semidirect
73. C2×C22⋊D47C2×C4semidirect
83. C22×Dic47C2×C4semidirect
84. C22×Dic47C2×C4semidirect
101. C2×C4×D47C2×C4semidirect
104. C2×Dic94C2×C4semidirect
155. C2×C4×C47#41semidirect
157. C22⋊D47C22⋊C4semidirect
181. C2×Dic47#41semidirect
245. #386D47semidirect
252. C47#2339semidirect
308. C2×D4C4×D47semidirect
422. C2×C4#10625352semidirect