Finite Group Databasebeta

← #20250178

Subgroups — #20250178

Order 6016.

598 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094019C211yesmaximal, characteristic, complemented
2#15689048C211yesmaximal, characteristic, complemented
3#15689039C211yesmaximal, characteristic, complemented
4#15689037C211yesmaximal, characteristic, complemented
5#15689031C211yesmaximal, characteristic, complemented
6#15689031C211yesmaximal, characteristic, complemented
7#15689031C211yesmaximal, characteristic, complemented
8#15689026C211yesmaximal, characteristic, complemented
9#15689026C211yesmaximal, characteristic, complemented
10#15689023C211yesmaximal, characteristic, complemented
11#15689011C211yesmaximal, characteristic, complemented
12#15689009C211yesmaximal, characteristic, complemented
13#15689002C211yesmaximal, characteristic, complemented
14#15688996C211yesmaximal, characteristic, complemented
15C2×#121×C47C211yesmaximal, characteristic, complemented
16C22×C22⋊D47C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19#13094019—24no—
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×C22⋊Dic47C2211yescharacteristic
25C2×C22⋊Dic47C2211yescharacteristic
26C2×C22⋊Dic47C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic
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
45C22×D4×C47C2211yescharacteristic
46C22×D4×C47C2211yescharacteristic
47C22×D4×C47C2211yescharacteristic
48C23×C4×C47C2211yescharacteristic
49#121×C47—24no—
50C2×C4⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53C24×C47C2311yescharacteristic
54C24×C47C2311yescharacteristic
55C24×C47C2311yescharacteristic
56C23×D47C2311yescharacteristic
57C2×D4×C47—22no—
58C2×D4×C47—22no—
59C2×D4×C47—22no—
60C2×D4×C47—22no—
61C2×D4×C47—22no—
62C2×D4×C47—41no—
63C2×D4×C47—41no—
64C2×D4×C47—41no—
65C2×D4×C47—41no—
66C22×C4×C47—22no—
67C22×C4×C47—41no—
68C22×C4×C47—41no—
69C22×C4×C47C2311yescharacteristic
70C22×C4×C47C2311yescharacteristic
71C22×C4×C47C2311yescharacteristic
72C22×C4×C47C2311yescharacteristic
73C2×C22⋊D47—22no—
74C2×C22⋊D47—22no—
75C2×C22⋊D47—41no—
76C2×C22⋊D47—41no—
77C2×C22⋊D47—41no—
78C2×C22⋊D47—41no—
79C2×C22⋊D47—41no—
80C2×C22⋊D47—41no—
81C2×C22⋊D47—41no—
82C22×Dic47C2311yescharacteristic
83C22×Dic47C2311yescharacteristic
84C22×Dic47C2311yescharacteristic
85C22×Dic47C2311yescharacteristic
86C22×Dic47C2311yescharacteristic
87C22×Dic47C2311yescharacteristic
88C22×Dic47C2311yescharacteristic
89C4⋊C4×C47D414yescomplemented
90C22⋊C4×C47—22no—
91C22⋊C4×C47—22no—
92C22⋊Dic47—22no—
93C22⋊Dic47—22no—
94C22⋊Dic47—41no—
95C22⋊Dic47—41no—
96C22⋊Dic47—41no—
97C22⋊Dic47—41no—
98C22⋊Dic47—41no—
99C22⋊Dic47—41no—
100C22⋊Dic47—41no—
101(C2×D47)⋊C4—22no—
102(C2×D47)⋊C4—22no—
103(C2×D47)⋊C4—22no—
104(C2×D47)⋊C4—41no—
105C4⋊Dic47—22no—
106C4⋊Dic47—41no—
107Dic47⋊C4—22no—
108Dic47⋊C4—41no—
109C4×Dic47—22no—
110C4×Dic47—41no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—21no—
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×C47—21no—
128C23×C47—21no—
129C23×C47—21no—
130C23×C47—21no—
131C23×C47#4112yes—
132C23×C47C2411yescharacteristic
133C22×D47—21no—
134C22×D47—21no—
135C22×D47—21no—
136C22×D47—21no—
137C22×D47—21no—
138C22×D47—21no—
139C22×D47—21no—
140D4×C47—44no—
141D4×C47—44no—
142D4×C47—44no—
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—44no—
153C2×C4×C47C2×D412yes—
154C2×C4×C47C2×D412yes—
155C2×C4×C47C2×D412yes—
156C22⋊D47—44no—
157C22⋊D47—44no—
158C22⋊D47—44no—
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×Dic47—21no—
172C2×Dic47—21no—
173C2×Dic47—21no—
174C2×Dic47—21no—
175C2×Dic47—21no—
176C2×Dic47—21no—
177C2×Dic47—21no—
178C2×Dic47—21no—
179C2×Dic47#4112yes—
180C22×C47—22no—
181C22×C47—22no—
182C22×C47—22no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47—41no—
187C22×C47—41no—
188C22×C47—41no—
189C22×C47—41no—
190C22×C47—41no—
191C22×C47—41no—
192C22×C47—41no—
193C22×C47—41no—
194C22×C47—41no—
195C22×C47—41no—
196C22×C47—41no—
197C22×C47—41no—
198C22×C47—41no—
199C22×C47—41no—
200C22×C47—41no—
201C22×C47C22×D411yescharacteristic
202C22×C47C2×#4111yescharacteristic
203C22×C47C2×#4111yescharacteristic
204C22×C47H(5,𝔽2)11yescharacteristic
205C22×C47H(5,𝔽2)11yescharacteristic
206C22×C47H(5,𝔽2)11yescharacteristic
207C22×C47H(5,𝔽2)11yescharacteristic
208C2×D47—41no—
209C2×D47—41no—
210C2×D47—41no—
211C2×D47—41no—
212C2×D47—41no—
213C2×D47—41no—
214C2×D47—41no—
215C4×C47—22no—
216C4×C47—22no—
217C4×C47—22no—
218C4×C47—41no—
219Dic47—22no—
220Dic47—41no—
221Dic47—41no—
222Dic47—41no—
223Dic47—41no—
224Dic47—41no—
225Dic47—41no—
226#2714—471nomaximal, Sylow
227C2×C47—42no—
228C2×C47—81no—
229C2×C47—81no—
230C2×C47#53511yescharacteristic
231C2×C47#53811yescharacteristic
232C2×C47#53811yescharacteristic
233C2×C47#54611yescharacteristic
234C2×C47#55011yescharacteristic
235C2×C47#55311yescharacteristic
236C2×C47#56011yescharacteristic
237D47—81no—
238C2×#126—471no—
239C2×#121D4711yescharacteristic, complemented
240#397—471no—
241#394—471no—
242#394—471no—
243#392—471no—
244#392—471no—
245#392—471no—
246#390—471no—
247#390—471no—
248#390—471no—
249#388—471no—
250#387—471no—
251#386—471no—
252#385—471no—
253C47#271411yescharacteristic, complemented, Sylow
254C22×D4—471no—
255C22×D4—471no—
256C22×D4—471no—
257C22×D4C2×D4711yescharacteristic
258C22×D4C2×D4711yescharacteristic
259C22×D4C2×D4711yescharacteristic
260C23×C4C2×D4711yescharacteristic
261#126—944no—
262#121—24no—
263C2×C4⋊C4—471no—
264C2×C4⋊C4—471no—
265C2×C4⋊C4—471no—
266C2×C4⋊C4—471no—
267C2×C4⋊C4C2×D4711yescharacteristic
268C2×C22⋊C4—471no—
269C2×C22⋊C4—471no—
270C2×C22⋊C4—471no—
271C2×C22⋊C4—471no—
272C2×C22⋊C4—471no—
273C2×C22⋊C4—471no—
274C2×C22⋊C4—471no—
275C2×C22⋊C4—471no—
276C2×C22⋊C4—471no—
277C2×C22⋊C4—471no—
278C2×C22⋊C4—471no—
279C2×C22⋊C4—471no—
280C2×C22⋊C4—471no—
281C2×C22⋊C4C2×D4711yescharacteristic
282C2×C22⋊C4C2×D4711yescharacteristic
283C2×C42—471no—
284C2×C42—471no—
285#95—471no—
286#95—471no—
287#95—471no—
288#95—471no—
289#95—471no—
290#95—471no—
291C24—471no—
292C24C22×D4711yescharacteristic
293C24C22×D4711yescharacteristic
294C24C22×D4711yescharacteristic
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—942no—
305C2×D4—942no—
306C2×D4—1881no—
307C2×D4—1881no—
308C2×D4—1881no—
309C2×D4—1881no—
310C2×D4—1881no—
311C2×D4—1881no—
312C2×D4—1881no—
313C22×C4—22no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—471no—
317C22×C4—471no—
318C22×C4—471no—
319C22×C4—471no—
320C22×C4—471no—
321C22×C4—471no—
322C22×C4—471no—
323C22×C4C22×D4711yescharacteristic
324C22×C4C22×D4711yescharacteristic
325C22×C4C22×D4711yescharacteristic
326C22×C4C22×D4711yescharacteristic
327C4⋊C4—942no—
328C4⋊C4—942no—
329C4⋊C4—1881no—
330C4⋊C4—1881no—
331C4⋊C4C22⋊D4714yescomplemented
332C22⋊C4—22no—
333C22⋊C4—22no—
334C22⋊C4—942no—
335C22⋊C4—942no—
336C22⋊C4—942no—
337C22⋊C4—942no—
338C22⋊C4—942no—
339C22⋊C4—1881no—
340C22⋊C4—1881no—
341C22⋊C4—1881no—
342C22⋊C4—1881no—
343C22⋊C4—1881no—
344C22⋊C4—1881no—
345C22⋊C4—1881no—
346C22⋊C4—1881no—
347C42—942no—
348C42—1881no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—941no—
370C23—941no—
371C23—941no—
372C23—941no—
373C23—941no—
374C23—941no—
375C23—941no—
376C23#1062535212yes—
377C23C23×D4711yescharacteristic
378D4—44no—
379D4—44no—
380D4—44no—
381D4—1884no—
382D4—1884no—
383D4—1884no—
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—941no—
396C2×C4—941no—
397C2×C4—941no—
398C2×C4—941no—
399C2×C4—941no—
400C2×C4—941no—
401C2×C4—941no—
402C2×C4—941no—
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×C4C2×C22⋊D4712yes—
416C2×C4C2×C22⋊D4712yes—
417C2×C4C2×C22⋊D4712yes—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—1881no—
440C22—1881no—
441C22—1881no—
442C22—1881no—
443C22—1881no—
444C22—1881no—
445C22—1881no—
446C22C22×C22⋊D4711yescharacteristic
447C22#41×D4711yescharacteristic
448C22C2×#1062535211yescharacteristic
449C22#1309406911yescharacteristic
450C22#1309406911yescharacteristic
451C22#1309406911yescharacteristic
452C22#1309407011yescharacteristic
453C4—22no—
454C4—22no—
455C4—22no—
456C4—41no—
457C4—942no—
458C4—1881no—
459C4—1881no—
460C4—1881no—
461C4—1881no—
462C4—1881no—
463C4—1881no—
464C2—42no—
465C2—81no—
466C2—81no—
467C2—3761no—
468C2#1568969011yescharacteristic
469C2#1568970511yescharacteristic
470C2#1568971011yescharacteristic
471C2#1568976711yescharacteristic
472C2#1568979211yescharacteristic
473C2#1568981611yescharacteristic
474C2#1568986111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#121×C47C2
hypercenterC2×#121D47
hypocenterC47#2714
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#13094019C2semidirect
2. #15689048C2semidirect
3. #15689039C2semidirect
4. #15689037C2semidirect
5. #15689031C2semidirect
6. #15689031C2semidirect
7. #15689031C2semidirect
8. #15689026C2semidirect
9. #15689026C2semidirect
10. #15689023C2semidirect
11. #15689011C2semidirect
12. #15689009C2semidirect
13. #15689002C2semidirect
14. #15688996C2semidirect
15. C2×#121×C47C2semidirect
89. C4⋊C4×C47D4semidirect
239. C2×#121D47semidirect
253. C47#2714semidirect
331. C4⋊C4C22⋊D47semidirect