Finite Group Databasebeta

← #20247356

Subgroups — #20247356

Order 6016.

646 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×#13094010C211yesmaximal, characteristic, complemented
2C2×#13094006C211yesmaximal, characteristic, complemented
3C2×#13094004C211yesmaximal, characteristic, complemented
4C2×#13093986C211yesmaximal, characteristic, complemented
5#15689043C211yesmaximal, characteristic, complemented
6#15689040C211yesmaximal, characteristic, complemented
7#15689032C211yesmaximal, characteristic
8#15689023C211yesmaximal, characteristic, complemented
9#15689016C211yesmaximal, characteristic, complemented
10#15689013C211yesmaximal, characteristic, complemented
11#15689012C211yesmaximal, characteristic, complemented
12#15688999C211yesmaximal, characteristic, complemented
13#15688997C211yesmaximal, characteristic, complemented
14C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
15C47×#396C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21C22×C4×D47C2211yescharacteristic
22#13094010—24no—
23#13094006—24no—
24#13094004—24no—
25#13093986—24no—
26C2×C4⋊Dic47C2211yescharacteristic
27C2×C4⋊Dic47C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
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
41C2×C4×Dic47C2211yescharacteristic
42C2×C4×Dic47C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C47⋊#95C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C4⋊C4×C47C2211yescharacteristic
50C2×C4⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
54#95×C47C2211yescharacteristic
55C24×C47C2311yescharacteristic
56C23×D47C2311yescharacteristic
57C23×D47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47—22no—
65C2×C22⋊D47—22no—
66C2×C22⋊D47—22no—
67C2×C22⋊D47—22no—
68C2×C22⋊D47—41no—
69C2×C22⋊D47—41no—
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C22×Dic47C2311yescharacteristic
74C22×Dic47C2311yescharacteristic
75C22×Dic47C2311yescharacteristic
76C2×D188—22no—
77C2×D188—22no—
78C2×D188—22no—
79C2×C4×D47—22no—
80C2×C4×D47—22no—
81C2×C4×D47—22no—
82C2×C4×D47—22no—
83C2×C4×D47—41no—
84C2×C4×D47—41no—
85C2×Dic94—22no—
86C2×Dic94—22no—
87C2×Dic94—41no—
88C4⋊C4×C47—22no—
89C4⋊C4×C47—22no—
90C4⋊C4×C47—22no—
91C22⋊C4×C47—22no—
92C22⋊C4×C47—22no—
93C22⋊C4×C47—22no—
94C22⋊Dic47—22no—
95C22⋊Dic47—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—22no—
102(C2×D47)⋊C4—22no—
103(C2×D47)⋊C4D414yescomplemented
104C4⋊Dic47—22no—
105C4⋊Dic47D414yescomplemented
106Dic47⋊C4—22no—
107Dic47⋊C4—41no—
108C4×Dic47—22no—
109C4×Dic47—22no—
110C4×Dic47—22no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47—21no—
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×D47C2×D412yes—
132C22×D47#4112yes—
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—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47C2×D412yes—
149C2×C4×C47C2×D412yes—
150C2×C4×C47#4112yes—
151C22⋊D47—44no—
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×Dic47C2×D412yes—
168C2×Dic47C2×D412yes—
169C2×Dic47C2×D412yes—
170C2×Dic47#4112yes—
171D188—28no—
172C4×D47—44no—
173C4×D47—44no—
174Dic94—44no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47C22×D411yescharacteristic
183C22×C47C22×D411yescharacteristic
184C22×C47C2×#4111yescharacteristic
185C22×C47C2×#4111yescharacteristic
186C22×C47C2×#4111yescharacteristic
187C22×C47H(5,𝔽2)11yescharacteristic
188C22×C472−1+411yescharacteristic
189C2×D47—22no—
190C2×D47—22no—
191C2×D47—22no—
192C2×D47—22no—
193C2×D47—22no—
194C2×D47—22no—
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—22no—
212Dic47—22no—
213Dic47—41no—
214Dic47—41no—
215#2461—471nomaximal, Sylow
216C2×C47—81no—
217C2×C47#52511yescharacteristic
218C2×C47#53211yescharacteristic
219C2×C47#54211yescharacteristic
220C2×C47D4211yescharacteristic
221C2×C47#54711yescharacteristic
222C2×C47#54811yescharacteristic
223C2×C47#55111yescharacteristic
224D47—42no—
225D47—42no—
226C2×#124—471no—
227C2×#123—471no—
228C2×C22⋊Q8—471no—
229C2×C4×D4—471no—
230#396D4711yescharacteristic, complemented
231#395—471no—
232#394—471no—
233#392—471no—
234#390—471no—
235#388—471no—
236#388—471no—
237#388—471no—
238#386—471no—
239#385—471no—
240C4×C4⋊C4—471no—
241C47#246111yescharacteristic, complemented, Sylow
242C22×Q8—471no—
243C22×D4—471no—
244C22×D4—471no—
245C22×D4—471no—
246C23×C4—471no—
247C23×C4—471no—
248#124—944no—
249#123—944no—
250C22⋊Q8—944no—
251C4×D4—944no—
252C2×C4⋊C4—471no—
253C2×C4⋊C4—471no—
254C2×C4⋊C4—471no—
255C2×C4⋊C4—471no—
256C2×C4⋊C4C2×D4711yescharacteristic
257C2×C4⋊C4C2×D4711yescharacteristic
258C2×C4⋊C4C2×D4711yescharacteristic
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⋊C4—471no—
266C2×C22⋊C4—471no—
267C2×C22⋊C4—471no—
268C2×C22⋊C4—471no—
269C2×C22⋊C4C2×D4711yescharacteristic
270C2×C22⋊C4C2×D4711yescharacteristic
271C2×C22⋊C4C2×D4711yescharacteristic
272C2×C42—471no—
273C2×C42—471no—
274C2×C42—471no—
275#95—471no—
276#95—471no—
277#95—471no—
278#95—471no—
279#95—471no—
280#95C2×D4711yescharacteristic
281C24—471no—
282C24—471no—
283C24C22×D4711yescharacteristic
284C2×Q8—942no—
285C2×Q8—942no—
286C2×Q8—1881no—
287C2×D4—942no—
288C2×D4—942no—
289C2×D4—942no—
290C2×D4—942no—
291C2×D4—942no—
292C2×D4—942no—
293C2×D4—942no—
294C2×D4—1881no—
295C2×D4—1881no—
296C22×C4—471no—
297C22×C4—471no—
298C22×C4—471no—
299C22×C4—471no—
300C22×C4—471no—
301C22×C4—471no—
302C22×C4—942no—
303C22×C4—942no—
304C22×C4—942no—
305C22×C4—942no—
306C22×C4—1881no—
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—1881no—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—22no—
324C22⋊C4—474no—
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—
334C42—942no—
335C42—942no—
336C42—942no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—472no—
345C23—472no—
346C23—941no—
347C23—941no—
348C23—941no—
349C23—941no—
350C23—941no—
351C23—941no—
352C23—941no—
353C23—941no—
354C23—941no—
355C23—941no—
356C23—941no—
357C23—941no—
358C23C23×D4711yescharacteristic
359Q8—1884no—
360D4—948no—
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—472no—
379C2×C4—472no—
380C2×C4—472no—
381C2×C4—472no—
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—1884no—
397C2×C4—1884no—
398C2×C4D4×D4712yes—
399C2×C4D4×D4712yes—
400C2×C4#1062535212yes—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—942no—
409C22—942no—
410C22—942no—
411C22—942no—
412C22—942no—
413C22—942no—
414C22—1881no—
415C22—1881no—
416C22—1881no—
417C22—1881no—
418C22—1881no—
419C22—1881no—
420C22—1881no—
421C22—1881no—
422C22C2×D4×D4711yescharacteristic
423C22C2×D4×D4711yescharacteristic
424C22#41×D4711yescharacteristic
425C22#41×D4711yescharacteristic
426C22C2×#1062535211yescharacteristic
427C22#1309407011yescharacteristic
428C22#1309407211yescharacteristic
429C4—22no—
430C4—22no—
431C4—22no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—942no—
436C4—942no—
437C4—942no—
438C4—942no—
439C4—1881no—
440C4—1881no—
441C2—81no—
442C2—1882no—
443C2—1882no—
444C2#1568963311yescharacteristic
445C2#1568966811yescharacteristic
446C2#1568974611yescharacteristic
447C2#1568975711yescharacteristic
448C2#1568977511yescharacteristic
449C2#1568978311yescharacteristic
450C2#1568979811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#396C2
hypercenter#396D47
hypocenterC47#2461
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#13094010C2semidirect
2. C2×#13094006C2semidirect
3. C2×#13094004C2semidirect
4. C2×#13093986C2semidirect
5. #15689043C2semidirect
6. #15689040C2semidirect
8. #15689023C2semidirect
9. #15689016C2semidirect
10. #15689013C2semidirect
11. #15689012C2semidirect
12. #15688999C2semidirect
13. #15688997C2semidirect
14. C4⋊C4×Dic47C2semidirect
15. C47×#396C2semidirect
103. (C2×D47)⋊C4D4semidirect
105. C4⋊Dic47D4semidirect
230. #396D47semidirect
241. C47#2461semidirect