Finite Group Databasebeta

← #20256143

Subgroups — #20256143

Order 6016.

358 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689858C211yesmaximal, characteristic, complemented
2#15689833C211yesmaximal, characteristic, complemented
3#15689488C211yesmaximal, characteristic, complemented
4#15689483C211yesmaximal, characteristic, complemented
5#15689478C211yesmaximal, characteristic, complemented
6#15689431C211yesmaximal, characteristic, complemented
7#15689424C211yesmaximal, characteristic, complemented
8#15689404C211yesmaximal, characteristic, complemented
9#15689339C211yesmaximal, characteristic, complemented
10#15689339C211yesmaximal, characteristic, complemented
11#15689319C211yesmaximal, characteristic
12#15689236C211yesmaximal, characteristic, complemented
13#15689225C211yesmaximal, characteristic, complemented
14C4×D376C211yesmaximal, characteristic, complemented
15C47×#446C211yesmaximal, characteristic, complemented
16C2×#10625325C2211yescharacteristic
17C2×D376C2211yescharacteristic
18C2×D376C2211yescharacteristic
19#13094024C2211yescharacteristic
20#13094021C2211yescharacteristic
21#13094016C2211yescharacteristic
22#13094016C2211yescharacteristic
23#13094013—21no—
24#13094012C2211yescharacteristic
25#13094012C2211yescharacteristic
26#13094009—21no—
27#13094009—21no—
28#13094002—21no—
29#13094002—21no—
30#13094000—21no—
31C4×Dic94C2211yescharacteristic
32C4×D188C2211yescharacteristic
33C4×D188C2211yescharacteristic
34C4×D188C2211yescharacteristic
35C4×D188C2211yescharacteristic
36C4×D188C2211yescharacteristic
37#13093986—21no—
38C4⋊C4×D47—21no—
39#13093958C2211yescharacteristic
40#13093958C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52C4×Q8×C47C2211yescharacteristic
53C4⋊C8×C47C2211yescharacteristic
54C4⋊C8×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic
56#97×C47C2211yescharacteristic
57#97×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C2×Q8×C47D411yescharacteristic
60C2×D188—21no—
61C2×D188—21no—
62C2×D188C2311yescharacteristic
63C2×D188C2311yescharacteristic
64C2×D188C2311yescharacteristic
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×Dic94—21no—
71C2×Dic94C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C4⋊C4×C47D411yescharacteristic
77C4⋊C4×C47D411yescharacteristic
78C4⋊C4×C47D411yescharacteristic
79C42×C47C2311yescharacteristic
80C42×C47C2311yescharacteristic
81C42×C47C2311yescharacteristic
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—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101C4×Dic47—21no—
102D376—22no—
103D376—22no—
104#10625325—22no—
105C22×D47—21no—
106C22×D47—21no—
107C22×D47—21no—
108Q8×C47—41no—
109C2×C4×C47C2×D411yescharacteristic
110C2×C4×C47C2×D411yescharacteristic
111C2×C4×C47C2×D411yescharacteristic
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2×D411yescharacteristic
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2411yescharacteristic
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121D188—21no—
122D188—21no—
123D188—21no—
124D188—21no—
125D188—21no—
126D188—42no—
127D188—81no—
128D188#4112yes—
129C4×D47—42no—
130C4×D47—81no—
131C4×D47—81no—
132C4×D47—81no—
133C4×D47—81no—
134Dic94—21no—
135Dic94—21no—
136Dic94—81no—
137C8×C47—21no—
138C8×C47—21no—
139C8×C47—21no—
140C8×C47—21no—
141C22×C47C22×D411yescharacteristic
142C2×D47—22no—
143C2×D47—41no—
144C2×D47—41no—
145C2×D47—41no—
146C2×D47—41no—
147C2×D47—41no—
148C2×D47—41no—
149C2×D47—41no—
150C2×D47—41no—
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47C2×#4111yescharacteristic
158C4×C472−1+411yescharacteristic
159Dic47—41no—
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164#3370—471nomaximal, Sylow
165C2×C47#54811yescharacteristic
166C2×C47#57511yescharacteristic
167C2×C47#57611yescharacteristic
168D47—42no—
169D47—81no—
170D47—81no—
171#559—471no—
172#554—471no—
173#490—471no—
174#489—471no—
175#488—471no—
176#479—471no—
177#478—471no—
178#474—471no—
179#463—471no—
180#463—471no—
181#459—471no—
182#446D4711yescharacteristic, complemented
183#442—471no—
184#440—471no—
185C4×D8—471no—
186C47#337011yescharacteristic, complemented, Sylow
187C2×SD16—471no—
188C2×D8—471no—
189C2×D8—471no—
190C4⋊Q8—471no—
191#127—471no—
192#125—471no—
193#125—471no—
194#124—471no—
195#124—471no—
196#124—941no—
197#123—941no—
198#123—941no—
199C22⋊Q8—941no—
200C22⋊Q8—941no—
201C22⋊Q8—941no—
202C4×Q8—471no—
203C4×Q8C2×D4711yescharacteristic
204C4×D4—471no—
205C4×D4—471no—
206C4×D4—471no—
207C4×D4—471no—
208C4×D4—471no—
209C4×D4—941no—
210C2×C4⋊C4—941no—
211#107—471no—
212#107—471no—
213#106—471no—
214C4⋊C8C2×D4711yescharacteristic
215C4⋊C8C2×D4711yescharacteristic
216C4⋊C8C2×D4711yescharacteristic
217#103—471no—
218#103—471no—
219#103—471no—
220#102—471no—
221#102—471no—
222#102—471no—
223#102—471no—
224#102—471no—
225#102—471no—
226#102—471no—
227#97C2×D4711yescharacteristic
228#97C2×D4711yescharacteristic
229C4×C8C2×D4711yescharacteristic
230C2×Q8—471no—
231C2×Q8—941no—
232C2×Q8D18811yescharacteristic
233C2×D4—471no—
234C2×D4—471no—
235C2×D4—471no—
236C2×D4—941no—
237C2×D4—941no—
238C22×C4—941no—
239C22×C4—941no—
240C22×C4—941no—
241C22×C4—941no—
242C22×C4—941no—
243SD16—942no—
244D8—942no—
245D8—942no—
246C2×C8C22×D4711yescharacteristic
247C2×C8C22×D4711yescharacteristic
248C2×C8C22×D4711yescharacteristic
249C2×C8C22×D4711yescharacteristic
250C4⋊C4—471no—
251C4⋊C4—471no—
252C4⋊C4—471no—
253C4⋊C4—471no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4D18811yescharacteristic
261C4⋊C4D18811yescharacteristic
262C4⋊C4D18811yescharacteristic
263C22⋊C4—941no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C42—941no—
273C42C22×D4711yescharacteristic
274C42C22×D4711yescharacteristic
275C42C22×D4711yescharacteristic
276C23—941no—
277C23—941no—
278C23—941no—
279Q8—41no—
280Q8—941no—
281Q8—941no—
282Q8—3761no—
283D4—472no—
284D4—941no—
285D4—941no—
286D4—941no—
287D4—941no—
288D4—941no—
289D4—3761no—
290D4—1882no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—3761no—
297C2×C4—3761no—
298C2×C4—3761no—
299C2×C4—3761no—
300C2×C4—1882no—
301C2×C4C2×D18811yescharacteristic
302C2×C4C2×D18811yescharacteristic
303C2×C4C2×D18811yescharacteristic
304C2×C4C2×D18811yescharacteristic
305C2×C4C2×D18811yescharacteristic
306C2×C4C2×D18811yescharacteristic
307C2×C4C23×D4711yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—21no—
312C22—942no—
313C22—1881no—
314C22—1881no—
315C22—1881no—
316C22—1881no—
317C22—1881no—
318C22—1881no—
319C22—1881no—
320C22—1881no—
321C22C22×D18811yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—1881no—
329C4—1881no—
330C4—1881no—
331C4—1881no—
332C4—1881no—
333C4#41×D4711yescharacteristic
334C4#1309407211yescharacteristic
335C2—3761no—
336C2—3761no—
337C2—1882no—
338C2#1568978511yescharacteristic
339C2#1568992311yescharacteristic
340C2#1568992811yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#446C2
socleC22×C47C22×D4
hypercenter#446D47
hypocenterC47#3370
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #15689858C2semidirect
2. #15689833C2semidirect
3. #15689488C2semidirect
4. #15689483C2semidirect
5. #15689478C2semidirect
6. #15689431C2semidirect
7. #15689424C2semidirect
8. #15689404C2semidirect
9. #15689339C2semidirect
10. #15689339C2semidirect
12. #15689236C2semidirect
13. #15689225C2semidirect
14. C4×D376C2semidirect
15. C47×#446C2semidirect
182. #446D47semidirect
186. C47#3370semidirect