Finite Group Databasebeta

← #20254060

Subgroups — #20254060

Order 6016.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689745C211yesmaximal, characteristic
2#15689731C211yesmaximal, characteristic, complemented
3#15689531C211yesmaximal, characteristic, complemented
4#15689516C211yesmaximal, characteristic, complemented
5#15689479C211yesmaximal, characteristic, complemented
6#15689472C211yesmaximal, characteristic, complemented
7#15689378C211yesmaximal, characteristic, complemented
8#15689370C211yesmaximal, characteristic
9#15689363C211yesmaximal, characteristic, complemented
10#15689355C211yesmaximal, characteristic
11#15689228C211yesmaximal, characteristic, complemented
12#15689221C211yesmaximal, characteristic, complemented
13C4×#10625325C211yesmaximal, characteristic, complemented
14#15689077C211yesmaximal, characteristic, complemented
15C4×Q16×C47C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625325C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×#10625324C2211yescharacteristic
20C2×C8×D47C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094022C2211yescharacteristic
23#13094019—21no—
24#13094018—21no—
25#13094018—21no—
26#13094016—21no—
27#13094015C2211yescharacteristic
28#13094014—21no—
29#13094013C2211yescharacteristic
30#13094012—21no—
31#13094009—21no—
32#13094004C2211yescharacteristic
33#13094002—21no—
34#13094000C2211yescharacteristic
35#13094000C2211yescharacteristic
36#13093999C2211yescharacteristic
37C4×Dic94C2211yescharacteristic
38C4×D188C2211yescharacteristic
39#13093981C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093955C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093935C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×Q16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×D188—21no—
62C2×D188C2311yescharacteristic
63C2×C4×D47—21no—
64C2×C4×D47C2311yescharacteristic
65C2×Dic94—21no—
66C2×Dic94C2311yescharacteristic
67Q16×C47—22no—
68C2×C8×C47C2311yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47C2311yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C42×C47—21no—
75C42×C47—21no—
76C42×C47C2311yescharacteristic
77#10625337—22no—
78#10625336—22no—
79(C2×D47)⋊C4—21no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4D411yescharacteristic
87(C2×D47)⋊C4D411yescharacteristic
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4D411yescharacteristic
100Dic47⋊C4D411yescharacteristic
101C4×Dic47—21no—
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105#10625325—22no—
106#10625324—22no—
107C8×D47—22no—
108C22×D47—21no—
109C22×D47C2×D411yescharacteristic
110Q8×C47—21no—
111Q8×C47—21no—
112Q8×C47—21no—
113Q8×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2411yescharacteristic
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47C2×D411yescharacteristic
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127D188—21no—
128D188—21no—
129D188—81no—
130C4×D47—21no—
131C4×D47—21no—
132C4×D47—81no—
133Dic94—21no—
134Dic94—21no—
135Dic94—81no—
136C8×C47—21no—
137C8×C47#4112yes—
138C47⋊C8—21no—
139C47⋊C8#4112yes—
140C22×C47C22×D411yescharacteristic
141C2×D47—21no—
142C2×D47—21no—
143C2×D47—21no—
144C2×D47—41no—
145C2×D47—41no—
146C2×D47—41no—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C47C2×#4111yescharacteristic
154C4×C47C2×#4111yescharacteristic
155Dic47—21no—
156Dic47—21no—
157Dic47—21no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161#3178—471nomaximal, Sylow
162C2×C47#53211yescharacteristic
163C2×C47#57711yescharacteristic
164C2×C47#57811yescharacteristic
165D47—41no—
166D47—81no—
167#542—471no—
168#541—471no—
169#501—471no—
170#497—471no—
171#488—471no—
172#487—471no—
173#470—471no—
174#468—471no—
175#467—471no—
176#465—471no—
177#441—471no—
178#440—471no—
179C4×Q16D4711yescharacteristic, complemented
180C4×SD16—471no—
181#405—471no—
182C47#317811yescharacteristic, complemented, Sylow
183C2×Q16—471no—
184C2×Q16C2×D4711yescharacteristic
185C2×SD16—471no—
186C2×SD16—471no—
187C2×M16—471no—
188C22×C8—471no—
189C4⋊Q8—471no—
190C4⋊Q8—471no—
191#126—941no—
192#126—941no—
193#126—941no—
194#125—471no—
195#125—941no—
196#125—941no—
197#124—471no—
198#124—941no—
199#123—941no—
200C22⋊Q8—471no—
201C22⋊Q8—471no—
202C22⋊Q8—471no—
203C22⋊Q8—941no—
204#121—471no—
205C4×Q8—471no—
206C4×Q8C2×D4711yescharacteristic
207C4×Q8C2×D4711yescharacteristic
208C4×D4—471no—
209#117—471no—
210#107—471no—
211#107C2×D4711yescharacteristic
212#106—471no—
213#106—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218#103C2×D4711yescharacteristic
219#103C2×D4711yescharacteristic
220#102—471no—
221#102—471no—
222#97—471no—
223#97—471no—
224C4×C8—471no—
225C4×C8C2×D4711yescharacteristic
226C2×Q8—471no—
227C2×Q8—941no—
228C2×Q8C22×D4711yescharacteristic
229C2×Q8C22×D4711yescharacteristic
230C2×D4—471no—
231C2×D4—941no—
232C22×C4—471no—
233C22×C4—941no—
234Q16—22no—
235Q16—942no—
236SD16—942no—
237SD16—942no—
238M16—942no—
239C2×C8—471no—
240C2×C8—471no—
241C2×C8—942no—
242C2×C8C22×D4711yescharacteristic
243C2×C8C22×D4711yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—471no—
247C4⋊C4—471no—
248C4⋊C4—471no—
249C4⋊C4—471no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4C22×D4711yescharacteristic
260C4⋊C4C22×D4711yescharacteristic
261C22⋊C4—471no—
262C22⋊C4—471no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C42—21no—
271C42—21no—
272C42—471no—
273C42—941no—
274C42C22×D4711yescharacteristic
275C23—471no—
276C23—941no—
277Q8—21no—
278Q8—21no—
279Q8—21no—
280Q8—21no—
281Q8—941no—
282Q8—941no—
283Q8—3761no—
284D4—941no—
285D4—941no—
286D4—3761no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—471no—
292C2×C4—471no—
293C2×C4—471no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—3761no—
300C2×C4D4×D4711yescharacteristic
301C2×C4D4×D4711yescharacteristic
302C2×C4C23×D4711yescharacteristic
303C8—21no—
304C8—472no—
305C8—941no—
306C8#1062535012yes—
307C22—941no—
308C22—941no—
309C22—941no—
310C22—1881no—
311C22—1881no—
312C22—1881no—
313C22C2×D4×D4711yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—941no—
321C4—941no—
322C4—941no—
323C4—1881no—
324C4—1881no—
325C4—1881no—
326C4#41×D4711yescharacteristic
327C4C2×#1062535011yescharacteristic
328C2—3761no—
329C2—1881no—
330C2#1568967011yescharacteristic
331C2#1568993011yescharacteristic
332C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×Q16×C47C2
socleC22×C47C22×D4
hypercenterC4×Q16D47
hypocenterC47#3178
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
2. #15689731C2semidirect
3. #15689531C2semidirect
4. #15689516C2semidirect
5. #15689479C2semidirect
6. #15689472C2semidirect
7. #15689378C2semidirect
9. #15689363C2semidirect
11. #15689228C2semidirect
12. #15689221C2semidirect
13. C4×#10625325C2semidirect
14. #15689077C2semidirect
15. C4×Q16×C47C2semidirect
179. C4×Q16D47semidirect
182. C47#3178semidirect