Finite Group Databasebeta

← #20249736

Subgroups — #20249736

Order 6016.

618 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094007C211yesmaximal, characteristic, complemented
2C2×#13094000C211yesmaximal, characteristic, complemented
3C2×#13093997C211yesmaximal, characteristic
4#15689054C211yesmaximal, characteristic, complemented
5#15689045C211yesmaximal, characteristic, complemented
6#15689040C211yesmaximal, characteristic, complemented
7#15689038C211yesmaximal, characteristic, complemented
8#15689038C211yesmaximal, characteristic, complemented
9#15689034C211yesmaximal, characteristic, complemented
10#15689024C211yesmaximal, characteristic, complemented
11#15689018C211yesmaximal, characteristic, complemented
12#15689016C211yesmaximal, characteristic, complemented
13#15689002C211yesmaximal, characteristic, complemented
14#15688994C211yesmaximal, characteristic, complemented
15C2×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20#13094007—24no—
21#13094000—24no—
22#13093997—24no—
23C2×C4⋊Dic47C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
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×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic
39C2×(C2×D47)⋊C4C2211yescharacteristic
40C2×C4×Dic47C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C22×Q8×C47C2211yescharacteristic
48C23×C4×C47C2211yescharacteristic
49C22⋊Q8×C47—24no—
50C2×C4⋊C4×C47C2211yescharacteristic
51C2×C4⋊C4×C47C2211yescharacteristic
52C2×C4⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
54C2×C22⋊C4×C47C2211yescharacteristic
55C24×C47C2311yescharacteristic
56C23×D47C2311yescharacteristic
57C23×D47C2311yescharacteristic
58C2×Q8×C47—22no—
59C2×Q8×C47—22no—
60C2×Q8×C47—41no—
61C22×C4×C47—22no—
62C22×C4×C47—22no—
63C22×C4×C47—41no—
64C22×C4×C47C2311yescharacteristic
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⋊D47—22no—
73C2×C22⋊D47—22no—
74C2×C22⋊D47—41no—
75C2×C22⋊D47—41no—
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C22×Dic47C2311yescharacteristic
81C22×Dic47C2311yescharacteristic
82C2×D188—22no—
83C2×D188—22no—
84C2×D188—41no—
85C2×C4×D47—22no—
86C2×C4×D47—22no—
87C2×C4×D47—41no—
88C4⋊C4×C47—22no—
89C4⋊C4×C47—22no—
90C4⋊C4×C47—22no—
91C22⋊C4×C47—22no—
92C22⋊C4×C47D414yes—
93C22⋊Dic47—22no—
94C22⋊Dic47—41no—
95(C2×D47)⋊C4—22no—
96(C2×D47)⋊C4—22no—
97(C2×D47)⋊C4—22no—
98(C2×D47)⋊C4—22no—
99(C2×D47)⋊C4—22no—
100(C2×D47)⋊C4—22no—
101(C2×D47)⋊C4—41no—
102(C2×D47)⋊C4—41no—
103(C2×D47)⋊C4—41no—
104C4⋊Dic47—22no—
105Dic47⋊C4—22no—
106Dic47⋊C4—22no—
107Dic47⋊C4—22no—
108Dic47⋊C4—41no—
109Dic47⋊C4D414yescomplemented
110C4×Dic47—41no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47C2×D412yes—
118C23×C47C2411yescharacteristic
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×D47—21no—
129C22×D47—21no—
130C22×D47—21no—
131C22×D47—21no—
132C22×D47#4112yes—
133Q8×C47—44no—
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—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—44no—
150C2×C4×C47C2×D412yes—
151C2×C4×C47C2×D412yes—
152C2×C4×C47C2×D412yes—
153C22⋊D47—44no—
154C22⋊D47—44no—
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×Dic47—21no—
169C2×Dic47—21no—
170C2×Dic47—21no—
171C2×Dic47C2×D412yes—
172C2×Dic47C2×D412yes—
173D188—44no—
174C4×D47—44no—
175C22×C47—22no—
176C22×C47—22no—
177C22×C47—22no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47C22×D411yescharacteristic
183C22×C47C22×D411yescharacteristic
184C22×C47C2×#4111yescharacteristic
185C22×C47H(5,𝔽2)11yescharacteristic
186C22×C47H(5,𝔽2)11yescharacteristic
187C22×C472−1+411yescharacteristic
188C22×C472−1+411yescharacteristic
189C2×D47—22no—
190C2×D47—22no—
191C2×D47—22no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—41no—
195C2×D47—41no—
196C2×D47—41no—
197C2×D47—41no—
198C2×D47—41no—
199C2×D47—41no—
200C2×D47—41no—
201C2×D47—41no—
202C2×D47—41no—
203C4×C47—22no—
204C4×C47—22no—
205C4×C47—22no—
206C4×C47—41no—
207C4×C47—41no—
208C4×C47—41no—
209Dic47—22no—
210Dic47—22no—
211Dic47—41no—
212Dic47—41no—
213Dic47—41no—
214Dic47—41no—
215#2681—471nomaximal, Sylow
216C2×C47—42no—
217C2×C47#53611yescharacteristic
218C2×C47#53711yescharacteristic
219C2×C47#53911yescharacteristic
220C2×C47D4211yescharacteristic
221C2×C47#54611yescharacteristic
222C2×C47#54811yescharacteristic
223C2×C47#56211yescharacteristic
224D47—42no—
225D47—81no—
226C2×#123—471no—
227C2×C22⋊Q8—471no—
228C2×C22⋊Q8D4711yescharacteristic, complemented
229C2×#121—471no—
230#398—471no—
231#396—471no—
232#394—471no—
233#394—471no—
234#394—471no—
235#393—471no—
236#390—471no—
237#389—471no—
238#388—471no—
239#386—471no—
240#385—471no—
241C47#268111yescharacteristic, complemented, Sylow
242C22×Q8C2×D4711yescharacteristic
243C22×D4—471no—
244C22×D4—471no—
245C22×D4—471no—
246C23×C4—471no—
247C23×C4C2×D4711yescharacteristic
248#123—944no—
249C22⋊Q8—24no—
250C22⋊Q8—944no—
251#121—944no—
252C2×C4⋊C4—471no—
253C2×C4⋊C4—471no—
254C2×C4⋊C4—471no—
255C2×C4⋊C4—471no—
256C2×C4⋊C4—471no—
257C2×C4⋊C4—471no—
258C2×C4⋊C4C2×D4711yescharacteristic
259C2×C4⋊C4C2×D4711yescharacteristic
260C2×C4⋊C4C2×D4711yescharacteristic
261C2×C22⋊C4—471no—
262C2×C22⋊C4—471no—
263C2×C22⋊C4—471no—
264C2×C22⋊C4—471no—
265C2×C22⋊C4—471no—
266C2×C22⋊C4—471no—
267C2×C22⋊C4—471no—
268C2×C22⋊C4—471no—
269C2×C22⋊C4—471no—
270C2×C22⋊C4—471no—
271C2×C22⋊C4—471no—
272C2×C22⋊C4C2×D4711yescharacteristic
273C2×C22⋊C4C2×D4711yescharacteristic
274C2×C42—471no—
275#95—471no—
276#95—471no—
277#95—471no—
278#95—471no—
279#95—471no—
280#95—471no—
281C24—471no—
282C24—471no—
283C24C22×D4711yescharacteristic
284C2×Q8—22no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×D4—942no—
288C2×D4—942no—
289C2×D4—942no—
290C2×D4—942no—
291C2×D4—942no—
292C2×D4—942no—
293C2×D4—1881no—
294C2×D4—1881no—
295C2×D4—1881no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—41no—
299C22×C4—471no—
300C22×C4—471no—
301C22×C4—471no—
302C22×C4—471no—
303C22×C4—471no—
304C22×C4—471no—
305C22×C4—942no—
306C22×C4—942no—
307C22×C4—1881no—
308C22×C4C22×D4711yescharacteristic
309C22×C4C22×D4711yescharacteristic
310C22×C4C22×D4711yescharacteristic
311C22×C4C22×D4711yescharacteristic
312C22×C4C22×D4711yescharacteristic
313C22×C4C22×D4711yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—474no—
318C4⋊C4—942no—
319C4⋊C4—942no—
320C4⋊C4—942no—
321C4⋊C4—942no—
322C4⋊C4—1881no—
323C22⋊C4—22no—
324C22⋊C4—942no—
325C22⋊C4—942no—
326C22⋊C4—942no—
327C22⋊C4—942no—
328C22⋊C4—942no—
329C22⋊C4—942no—
330C22⋊C4—942no—
331C22⋊C4—1881no—
332C22⋊C4—1881no—
333C22⋊C4—1881no—
334C22⋊C4—1881no—
335C22⋊C4C22⋊D4714yes—
336C42—1881no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—472no—
344C23—941no—
345C23—941no—
346C23—941no—
347C23—941no—
348C23—941no—
349C23—941no—
350C23—941no—
351C23—941no—
352C23—941no—
353C23—941no—
354C23—941no—
355C23—941no—
356C23—941no—
357C23C2×C22⋊D4712yes—
358C23C23×D4711yescharacteristic
359Q8—44no—
360D4—1884no—
361D4—1884no—
362D4—1884no—
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—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—44no—
379C2×C4—472no—
380C2×C4—472no—
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—941no—
395C2×C4—941no—
396C2×C4—941no—
397C2×C4—1884no—
398C2×C4D4×D4712yes—
399C2×C4C2×C22⋊D4712yes—
400C2×C4C2×C22⋊D4712yes—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—942no—
409C22—942no—
410C22—942no—
411C22—1881no—
412C22—1881no—
413C22—1881no—
414C22—1881no—
415C22—1881no—
416C22—1881no—
417C22—1881no—
418C22—1881no—
419C22—1881no—
420C22—1881no—
421C22—1881no—
422C22C2×D4×D4711yescharacteristic
423C22C22×C22⋊D4711yescharacteristic
424C22#41×D4711yescharacteristic
425C22#1309406911yescharacteristic
426C22#1309407011yescharacteristic
427C22#1309407211yescharacteristic
428C22#1309407211yescharacteristic
429C4—22no—
430C4—22no—
431C4—22no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—942no—
436C4—942no—
437C4—1881no—
438C4—1881no—
439C4—1881no—
440C4—1881no—
441C2—42no—
442C2—3761no—
443C2—1882no—
444C2#1568969711yescharacteristic
445C2#1568970311yescharacteristic
446C2#1568971911yescharacteristic
447C2D4×C22⋊D4711yescharacteristic
448C2#1568976111yescharacteristic
449C2#1568978311yescharacteristic
450C2#1568986911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C22⋊Q8×C47C2
hypercenterC2×C22⋊Q8D47
hypocenterC47#2681
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#13094007C2semidirect
2. C2×#13094000C2semidirect
4. #15689054C2semidirect
5. #15689045C2semidirect
6. #15689040C2semidirect
7. #15689038C2semidirect
8. #15689038C2semidirect
9. #15689034C2semidirect
10. #15689024C2semidirect
11. #15689018C2semidirect
12. #15689016C2semidirect
13. #15689002C2semidirect
14. #15688994C2semidirect
15. C2×C22⋊Q8×C47C2semidirect
109. Dic47⋊C4D4semidirect
228. C2×C22⋊Q8D47semidirect
241. C47#2681semidirect