Finite Group Databasebeta

← #20254095

Subgroups — #20254095

Order 6016.

366 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689677C211yesmaximal, characteristic, complemented
2#15689660C211yesmaximal, characteristic
3#15689530C211yesmaximal, characteristic, complemented
4#15689516C211yesmaximal, characteristic, complemented
5#15689490C211yesmaximal, characteristic, complemented
6#15689484C211yesmaximal, characteristic, complemented
7#15689363C211yesmaximal, characteristic, complemented
8#15689361C211yesmaximal, characteristic, complemented
9#15689355C211yesmaximal, characteristic
10#15689353C211yesmaximal, characteristic
11#15689228C211yesmaximal, characteristic, complemented
12#15689225C211yesmaximal, characteristic, complemented
13#15689221C211yesmaximal, characteristic, complemented
14#97×D47C211yesmaximal, characteristic, complemented
15C47×#441C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625325C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20C2×C8×D47C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094022C2211yescharacteristic
23#13094019—21no—
24#13094015C2211yescharacteristic
25#13094014—21no—
26#13094013C2211yescharacteristic
27#13094009—21no—
28#13094004C2211yescharacteristic
29#13094002—21no—
30#13094000C2211yescharacteristic
31#13094000C2211yescharacteristic
32#13093999C2211yescharacteristic
33C4×Dic94—21no—
34C4×Dic94C2211yescharacteristic
35C4×D188—21no—
36C4×D188C2211yescharacteristic
37#13093981—21no—
38#13093981—21no—
39C42×D47C2211yescharacteristic
40#13093958C2211yescharacteristic
41#13093957C2211yescharacteristic
42#13093955C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093935C2211yescharacteristic
50#13093934C2211yescharacteristic
51#13093934C2211yescharacteristic
52C2×Q16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×D188—21no—
62C2×D188C2311yescharacteristic
63C2×C4×D47—21no—
64C2×C4×D47D411yescharacteristic
65C2×C4×D47D411yescharacteristic
66C2×C4×D47C2311yescharacteristic
67C2×Dic94—21no—
68C2×Dic94C2311yescharacteristic
69Q16×C47—22no—
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C42×C47—21no—
77C42×C47—21no—
78C42×C47C2311yescharacteristic
79#10625337—22no—
80#10625336—22no—
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)⋊C4—21no—
87(C2×D47)⋊C4—21no—
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—
99C4×Dic47—21no—
100C4×Dic47D411yescharacteristic
101C4×Dic47D411yescharacteristic
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105#10625325—22no—
106C8×D47—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—42no—
130C4×D47—22no—
131C4×D47—21no—
132C4×D47—21no—
133C4×D47—41no—
134C4×D47—42no—
135Dic94—21no—
136Dic94—21no—
137Dic94—42no—
138C8×C47—21no—
139C8×C47#4112yes—
140C47⋊C8—21no—
141C47⋊C8#4112yes—
142C22×C47C22×D411yescharacteristic
143C2×D47—21no—
144C2×D47—21no—
145C2×D47—41no—
146C2×D47—41no—
147C2×D47—41no—
148C2×D47#13712yes—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C47—41no—
154C4×C47—41no—
155C4×C47C2×#4111yescharacteristic
156C4×C47C2×#4111yescharacteristic
157Dic47—21no—
158Dic47—21no—
159Dic47—21no—
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163#3181—471nomaximal, Sylow
164C2×C47#53211yescharacteristic
165C2×C47C2×#13711yescharacteristic
166C2×C47#57511yescharacteristic
167D47—22no—
168D47—81no—
169#533—471no—
170#529—471no—
171#501—471no—
172#497—471no—
173#491—471no—
174#489—471no—
175#467—471no—
176#467—471no—
177#465—471no—
178#465—471no—
179#441—471no—
180#441D4711yescharacteristic, complemented
181#440—471no—
182#440—471no—
183C2×#97—471no—
184C47#318111yescharacteristic, complemented, Sylow
185C2×Q16—471no—
186C2×Q16C2×D4711yescharacteristic
187C2×SD16—471no—
188C2×SD16—471no—
189C22×C8—471no—
190C22×C8—471no—
191C4⋊Q8—471no—
192C4⋊Q8—471no—
193#126—941no—
194#125—471no—
195#125—941no—
196#124—471no—
197#123—941no—
198C22⋊Q8—471no—
199C22⋊Q8—471no—
200C22⋊Q8—471no—
201C22⋊Q8—941no—
202#121—471no—
203C4×Q8—471no—
204C4×Q8—941no—
205C4×Q8C2×D4711yescharacteristic
206C4×Q8C2×D4711yescharacteristic
207C4×D4—471no—
208C4×D4—941no—
209#117—941no—
210#117—941no—
211C2×C42—471no—
212#107—471no—
213#107—471no—
214#106—471no—
215#106C2×D4711yescharacteristic
216#103—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220#103C2×D4711yescharacteristic
221#103C2×D4711yescharacteristic
222#102—471no—
223#102—471no—
224#97—471no—
225#97—471no—
226#97—471no—
227#97C2×D4711yescharacteristic
228C2×Q8—471no—
229C2×Q8—941no—
230C2×Q8C22×D4711yescharacteristic
231C2×Q8C22×D4711yescharacteristic
232C2×D4—471no—
233C2×D4—941no—
234C22×C4—471no—
235C22×C4—471no—
236C22×C4—471no—
237C22×C4—941no—
238Q16—22no—
239Q16—942no—
240SD16—942no—
241SD16—942no—
242C2×C8—471no—
243C2×C8—471no—
244C2×C8—942no—
245C2×C8—942no—
246C2×C8C22×D4711yescharacteristic
247C2×C8C22×D4711yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—471no—
251C4⋊C4—471no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4C22×D4711yescharacteristic
262C4⋊C4C22×D4711yescharacteristic
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—471no—
274C42—471no—
275C42—941no—
276C42C22×D4711yescharacteristic
277C23—471no—
278C23—941no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—941no—
284Q8—941no—
285Q8—1882no—
286D4—941no—
287D4—941no—
288D4—1882no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—471no—
294C2×C4—471no—
295C2×C4—471no—
296C2×C4—942no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—1881no—
303C2×C4—1882no—
304C2×C4D4×D4711yescharacteristic
305C2×C4D4×D4711yescharacteristic
306C2×C4C23×D4711yescharacteristic
307C8—21no—
308C8—472no—
309C8—941no—
310C8#1062535012yes—
311C22—472no—
312C22—941no—
313C22—941no—
314C22—1881no—
315C22—1881no—
316C22—1881no—
317C22C2×D4×D4711yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—941no—
325C4—941no—
326C4—941no—
327C4—1881no—
328C4—1881no—
329C4—1881no—
330C4#41×D4711yescharacteristic
331C4C2×#1062535011yescharacteristic
332C2—942no—
333C2—3761no—
334C2#1568967011yescharacteristic
335C2#137×D4711yescharacteristic
336C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#441C2
socleC22×C47C22×D4
hypercenter#441D47
hypocenterC47#3181
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #15689677C2semidirect
3. #15689530C2semidirect
4. #15689516C2semidirect
5. #15689490C2semidirect
6. #15689484C2semidirect
7. #15689363C2semidirect
8. #15689361C2semidirect
11. #15689228C2semidirect
12. #15689225C2semidirect
13. #15689221C2semidirect
14. #97×D47C2semidirect
15. C47×#441C2semidirect
180. #441D47semidirect
184. C47#3181semidirect