Finite Group Databasebeta

← #20254939

Subgroups — #20254939

Order 6016.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094054C211yesmaximal, characteristic, complemented
2C2×#13094044C211yesmaximal, characteristic, complemented
3#15689782C211yesmaximal, characteristic, complemented
4#15689515C211yesmaximal, characteristic, complemented
5#15689371C211yesmaximal, characteristic, complemented
6#15689362C211yesmaximal, characteristic, complemented
7#15689338C211yesmaximal, characteristic, complemented
8#15689330C211yesmaximal, characteristic, complemented
9#15689285C211yesmaximal, characteristic, complemented
10#15689283C211yesmaximal, characteristic, complemented
11#15689278C211yesmaximal, characteristic, complemented
12#15689268C211yesmaximal, characteristic, complemented
13#15689223C211yesmaximal, characteristic, complemented
14#15689195C211yesmaximal, characteristic, complemented
15C47×#547C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18#13094054—24no—
19#13094044—24no—
20C2×#10625337C2211yescharacteristic
21C2×#10625337C2211yescharacteristic
22C2×#10625337C2211yescharacteristic
23C2×#10625337C2211yescharacteristic
24C2×#10625335C2211yescharacteristic
25C2×#10625335C2211yescharacteristic
26C2×#10625336C2211yescharacteristic
27C2×#10625336C2211yescharacteristic
28C2×#10625334C2211yescharacteristic
29C2×#10625329C2211yescharacteristic
30C22×C47⋊C8C2211yescharacteristic
31#13094012C2211yescharacteristic
32#13094010—21no—
33#13094003C2211yescharacteristic
34#13094002—21no—
35#13093998C2211yescharacteristic
36#13093996—21no—
37C4×Dic94C2211yescharacteristic
38(C22⋊D47)⋊C4—21no—
39#13093957C2211yescharacteristic
40C4⋊(C47⋊C8)C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093948C2211yescharacteristic
43#13093947C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093944C2211yescharacteristic
47C22⋊(C47⋊C8)C2211yescharacteristic
48C22⋊(C47⋊C8)C2211yescharacteristic
49#13093935C2211yescharacteristic
50C2×#41×C47C2211yescharacteristic
51C2×#41×C47C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53#123×C47—21no—
54#123×C47—21no—
55C22⋊Q8×C47C2211yescharacteristic
56C22⋊Q8×C47C2211yescharacteristic
57#121×C47—21no—
58C4×D4×C47C2211yescharacteristic
59C4×D4×C47C2211yescharacteristic
60C2×C4⋊C4×C47—21no—
61#41×C47—22no—
62#41×C47—22no—
63#41×C47—41no—
64#41×C47—41no—
65C2×Q8×C47C2311yescharacteristic
66C2×Q8×C47C2311yescharacteristic
67C2×D4×C47—21no—
68C2×D4×C47—21no—
69C2×D4×C47D411yescharacteristic
70C2×D4×C47C2311yescharacteristic
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47—21no—
74C22×C4×C47C2311yescharacteristic
75C22×C4×C47C2311yescharacteristic
76C2×C22⋊D47—21no—
77C2×C22⋊D47—21no—
78C22×Dic47—21no—
79#10625350—22no—
80#10625350—41no—
81C2×D188C2311yescharacteristic
82C2×C4×D47—21no—
83C2×Dic94—22no—
84C2×Dic94—21no—
85C2×Dic94—41no—
86C2×Dic94C2311yescharacteristic
87C2×Dic94C2311yescharacteristic
88C4⋊C4×C47—21no—
89C4⋊C4×C47—21no—
90C4⋊C4×C47—21no—
91C4⋊C4×C47—21no—
92C4⋊C4×C47D411yescharacteristic
93C4⋊C4×C47C2311yescharacteristic
94C22⋊C4×C47—21no—
95C22⋊C4×C47—21no—
96C22⋊C4×C47—21no—
97C22⋊C4×C47D411yescharacteristic
98C22⋊C4×C47D411yescharacteristic
99C42×C47C2311yescharacteristic
100C22⋊Dic47—21no—
101#10625337—22no—
102#10625337—22no—
103#10625337—22no—
104#10625337—41no—
105#10625336—22no—
106#10625336—41no—
107#10625335—22no—
108#10625335D414yescomplemented
109#10625334—22no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4—21no—
112(C2×D47)⋊C4—21no—
113C4⋊Dic47C2311yescharacteristic
114Dic47⋊C4—21no—
115Dic47⋊C4—21no—
116C4×Dic47—21no—
117#10625329—22no—
118C2×C47⋊C8—22no—
119C2×C47⋊C8C2311yescharacteristic
120C2×C47⋊C8C2311yescharacteristic
121C2×C47⋊C8C2311yescharacteristic
122C2×C47⋊C8C2311yescharacteristic
123C23×C47—21no—
124C23×C47C2×D411yescharacteristic
125C23×C47C2×D411yescharacteristic
126C22×D47—21no—
127Q8×C47—21no—
128Q8×C47—21no—
129Q8×C47—21no—
130Q8×C47—21no—
131D4×C47—21no—
132D4×C47—41no—
133D4×C47—42no—
134D4×C47—42no—
135D4×C47C2×D412yes—
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—42no—
144C2×C4×C47—42no—
145C2×C4×C47—42no—
146C2×C4×C47C2×D411yescharacteristic
147C2×C4×C47C2×D411yescharacteristic
148C2×C4×C47C2×D411yescharacteristic
149C2×C4×C47C2×D411yescharacteristic
150C2×C4×C47C2411yescharacteristic
151C22⋊D47—42no—
152C22⋊D47—42no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—42no—
157D188—21no—
158D188—21no—
159C4×D47—42no—
160Dic94—21no—
161Dic94—21no—
162Dic94—21no—
163Dic94—42no—
164Dic94C2×D412yes—
165C47⋊C8—21no—
166C47⋊C8—21no—
167C47⋊C8—21no—
168C47⋊C8C2×D412yes—
169C22×C47—21no—
170C22×C47—21no—
171C22×C47—22no—
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—21no—
175C22×C47—21no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47C22×D411yescharacteristic
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—41no—
182C4×C47—21no—
183C4×C47—21no—
184C4×C47—21no—
185C4×C47—21no—
186C4×C47—41no—
187C4×C47—41no—
188C4×C47—41no—
189C4×C47C22×D411yescharacteristic
190C4×C47H(5,𝔽2)11yescharacteristic
191Dic47—22no—
192Dic47—41no—
193Dic47—41no—
194#3269—471nomaximal, Sylow
195C2×C47—41no—
196C2×C47—41no—
197C2×C47—42no—
198C2×C47D4211yescharacteristic
199C2×C47#57511yescharacteristic
200C2×C47#57811yescharacteristic
201D47—81no—
202C2×#137—471no—
203C2×#135—471no—
204#548—471no—
205#547D4711yescharacteristic, complemented
206#497—471no—
207#468—471no—
208#467—471no—
209#463—471no—
210#462—471no—
211#452—471no—
212#452—471no—
213#451—471no—
214#449—471no—
215#440—471no—
216#435—471no—
217C47#326911yescharacteristic, complemented, Sylow
218C2×#41—471no—
219C2×#41C2×D4711yescharacteristic
220C2×#41C2×D4711yescharacteristic
221C22×Q8—471no—
222#137—944no—
223#135—944no—
224C2×Q16—471no—
225C2×Q16—471no—
226C2×Q16—471no—
227C2×Q16—471no—
228C2×SD16—471no—
229C2×SD16—471no—
230C2×SD16—471no—
231C2×SD16—471no—
232C2×D8—471no—
233C2×M16—471no—
234C22×C8—471no—
235C4⋊Q8C2×D4711yescharacteristic
236#124—471no—
237#124—941no—
238#123—21no—
239#123—21no—
240C22⋊Q8—471no—
241C22⋊Q8—941no—
242C22⋊Q8C2×D4711yescharacteristic
243C22⋊Q8C2×D4711yescharacteristic
244#121—21no—
245#121—471no—
246#121—941no—
247C4×Q8—471no—
248C4×D4—941no—
249C4×D4C2×D4711yescharacteristic
250C4×D4C2×D4711yescharacteristic
251C2×C4⋊C4—21no—
252#107—471no—
253C4⋊C8—471no—
254#103—471no—
255#103—471no—
256#103—471no—
257#103—471no—
258#102—471no—
259#102—471no—
260C22⋊C8—471no—
261C22⋊C8—471no—
262#97—471no—
263#41—22no—
264#41—22no—
265#41—41no—
266#41—41no—
267#41—942no—
268#41—1881no—
269C2×Q8—471no—
270C2×Q8—471no—
271C2×Q8—942no—
272C2×Q8—941no—
273C2×Q8—1881no—
274C2×Q8C22×D4711yescharacteristic
275C2×Q8C22×D4711yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—471no—
279C2×D4—941no—
280C2×D4—941no—
281C2×D4C22⋊D4711yescharacteristic
282C2×D4C22×D4711yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—941no—
287C22×C4—941no—
288C22×C4C22×D4711yescharacteristic
289C22×C4C22×D4711yescharacteristic
290Q16—942no—
291Q16—942no—
292Q16—942no—
293Q16—1881no—
294SD16—474no—
295SD16—942no—
296SD16—942no—
297SD16—1881no—
298D8—942no—
299M16—942no—
300C2×C8—471no—
301C2×C8—471no—
302C2×C8—471no—
303C2×C8—471no—
304C2×C8—942no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—471no—
310C4⋊C4—941no—
311C4⋊C4—941no—
312C4⋊C4C22⋊D4711yescharacteristic
313C4⋊C4C22×D4711yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—941no—
318C22⋊C4—941no—
319C22⋊C4—941no—
320C22⋊C4—941no—
321C22⋊C4C22⋊D4711yescharacteristic
322C22⋊C4C22⋊D4711yescharacteristic
323C42—941no—
324C42C22×D4711yescharacteristic
325C23—21no—
326C23—941no—
327C23C2×C22⋊D4711yescharacteristic
328C23C2×C22⋊D4711yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—472no—
334Q8—941no—
335Q8—941no—
336Q8—941no—
337Q8—1882no—
338D4—21no—
339D4—41no—
340D4—42no—
341D4—42no—
342D4—941no—
343D4—941no—
344D4—1882no—
345D4—1882no—
346D4D4×D4712yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—941no—
358C2×C4—941no—
359C2×C4—941no—
360C2×C4—1882no—
361C2×C4—1882no—
362C2×C4C2×C22⋊D4711yescharacteristic
363C2×C4C2×C22⋊D4711yescharacteristic
364C2×C4C2×C22⋊D4711yescharacteristic
365C2×C4C2×C22⋊D4711yescharacteristic
366C2×C4C23×D4711yescharacteristic
367C8—472no—
368C8—941no—
369C8—941no—
370C8—941no—
371C22—21no—
372C22—21no—
373C22—22no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—1881no—
381C22—1881no—
382C22—1881no—
383C22C22×C22⋊D4711yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—942no—
392C4—1881no—
393C4—1881no—
394C4C2×D4×D4711yescharacteristic
395C4#1309406911yescharacteristic
396C2—41no—
397C2—41no—
398C2—42no—
399C2—3761no—
400C2D4×C22⋊D4711yescharacteristic
401C2#1568992111yescharacteristic
402C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#547C2
socleC22×C47C22×D4
hypercenter#547D47
hypocenterC47#3269
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C2×#13094054C2semidirect
2. C2×#13094044C2semidirect
3. #15689782C2semidirect
4. #15689515C2semidirect
5. #15689371C2semidirect
6. #15689362C2semidirect
7. #15689338C2semidirect
8. #15689330C2semidirect
9. #15689285C2semidirect
10. #15689283C2semidirect
11. #15689278C2semidirect
12. #15689268C2semidirect
13. #15689223C2semidirect
14. #15689195C2semidirect
15. C47×#547C2semidirect
108. #10625335D4semidirect
205. #547D47semidirect
217. C47#3269semidirect