Finite Group Databasebeta

← #20255439

Subgroups — #20255439

Order 6016.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689813C211yesmaximal, characteristic
2#15689491C211yesmaximal, characteristic, complemented
3#15689461C211yesmaximal, characteristic, complemented
4#15689451C211yesmaximal, characteristic, complemented
5#15689430C211yesmaximal, characteristic, complemented
6#15689379C211yesmaximal, characteristic, complemented
7#15689362C211yesmaximal, characteristic, complemented
8#15689330C211yesmaximal, characteristic, complemented
9#15689279C211yesmaximal, characteristic, complemented
10#15689279C211yesmaximal, characteristic, complemented
11#15689228C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic
13#15689132C211yesmaximal, characteristic, complemented
14C2×#13093948C211yesmaximal, characteristic, complemented
15D4×Q8×C47C211yesmaximal, characteristic
16C2×#10625337C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625329C2211yescharacteristic
20C22×C47⋊C8C2211yescharacteristic
21#13094017—21no—
22#13094016C2211yescharacteristic
23#13094014—21no—
24#13094005—21no—
25#13094003C2211yescharacteristic
26#13094003C2211yescharacteristic
27C4×Dic94C2211yescharacteristic
28#13093983C2211yescharacteristic
29#13093980—21no—
30C2×C4⋊Dic47C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35#13093948C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093948C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093948C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093948C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093947C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48C22×Q8×C47C2211yescharacteristic
49C22×Q8×C47C2211yescharacteristic
50C4⋊Q8×C47—21no—
51C4⋊Q8×C47C2211yescharacteristic
52C22⋊Q8×C47—21no—
53C22⋊Q8×C47—21no—
54C22⋊Q8×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic
57C4×D4×C47—21no—
58C4×D4×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47—21no—
61C2×Q8×C47—22no—
62C2×Q8×C47—22no—
63C2×Q8×C47—41no—
64C2×Q8×C47—41no—
65C2×Q8×C47C2311yescharacteristic
66C2×Q8×C47C2311yescharacteristic
67C2×Q8×C47C2311yescharacteristic
68C2×D4×C47D411yescharacteristic
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47C2311yescharacteristic
72C22×C4×C47C2311yescharacteristic
73C22×Dic47—21no—
74C2×Dic94C2311yescharacteristic
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47D411yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C22⋊C4×C47—21no—
83C22⋊C4×C47—21no—
84C22⋊C4×C47D411yescharacteristic
85C22⋊C4×C47D411yescharacteristic
86C42×C47—21no—
87C42×C47C2311yescharacteristic
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47—21no—
91#10625337—22no—
92#10625337—41no—
93#10625337—41no—
94C4⋊Dic47—21no—
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105#10625329—41no—
106C2×C47⋊C8—41no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C23×C47C2×D411yescharacteristic
112C23×C47C2×D411yescharacteristic
113Q8×C47—21no—
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—21no—
118Q8×C47—42no—
119Q8×C47—42no—
120Q8×C47#4112yes—
121D4×C47—22no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—42no—
131C2×C4×C47—42no—
132C2×C4×C47C2×D411yescharacteristic
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2411yescharacteristic
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—42no—
142Dic94—21no—
143Dic94—21no—
144C47⋊C8—21no—
145C47⋊C8—21no—
146C47⋊C8—21no—
147C47⋊C8—21no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47#13712yes—
154C22×C47C22×D411yescharacteristic
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—22no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47C2×#4111yescharacteristic
164C4×C47H(5,𝔽2)11yescharacteristic
165Dic47—41no—
166Dic47—41no—
167Dic47—41no—
168Dic47—41no—
169#3312—471nomaximal, Sylow
170C2×C47—22no—
171C2×C47—41no—
172C2×C47#54611yescharacteristic
173C2×C47C2×#13711yescharacteristic
174C2×C47#57811yescharacteristic
175#552—471no—
176D4×Q8D4711yescharacteristic
177#491—471no—
178#485—471no—
179#483—471no—
180#479—471no—
181#470—471no—
182#467—471no—
183#462—471no—
184#451—471no—
185#451—471no—
186#441—471no—
187#435—471no—
188#419—471no—
189C2×#103—471no—
190C47#331211yescharacteristic, complemented, Sylow
191C22×Q8C2×D4711yescharacteristic
192C22×Q8C2×D4711yescharacteristic
193C2×Q16—471no—
194C2×Q16—471no—
195C2×Q16—471no—
196C2×M16—471no—
197C22×C8—471no—
198C4⋊Q8—21no—
199C4⋊Q8C2×D4711yescharacteristic
200#126—941no—
201#125—471no—
202#125—941no—
203#123—941no—
204C22⋊Q8—21no—
205C22⋊Q8—21no—
206C22⋊Q8—471no—
207C22⋊Q8—471no—
208C22⋊Q8C2×D4711yescharacteristic
209C22⋊Q8C2×D4711yescharacteristic
210C4×Q8—471no—
211C4×Q8C2×D4711yescharacteristic
212C4×D4—21no—
213C4×D4C2×D4711yescharacteristic
214#117—471no—
215#117—941no—
216C2×C4⋊C4—471no—
217#107—471no—
218#106—471no—
219#106—471no—
220C4⋊C8—471no—
221#103—471no—
222#103—471no—
223#103—471no—
224#103—471no—
225#103—471no—
226#103—471no—
227#103—471no—
228#103—471no—
229#103—471no—
230#103—471no—
231C22⋊C8—471no—
232C22⋊C8—471no—
233#97—471no—
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—471no—
241C2×Q8C22×D4711yescharacteristic
242C2×Q8C22×D4711yescharacteristic
243C2×Q8C22×D4711yescharacteristic
244C2×D4C22⋊D4711yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—941no—
248C22×C4C22×D4711yescharacteristic
249C22×C4C22×D4711yescharacteristic
250Q16—942no—
251Q16—1881no—
252Q16—1881no—
253M16—1881no—
254C2×C8—471no—
255C2×C8—471no—
256C2×C8—471no—
257C2×C8—471no—
258C2×C8—1881no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—471no—
265C4⋊C4—471no—
266C4⋊C4—471no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4C22⋊D4711yescharacteristic
274C4⋊C4C22×D4711yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4C22⋊D4711yescharacteristic
281C22⋊C4C22⋊D4711yescharacteristic
282C42—21no—
283C42—941no—
284C42—941no—
285C42C22×D4711yescharacteristic
286C23C2×C22⋊D4711yescharacteristic
287C23C2×C22⋊D4711yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—42no—
294Q8—42no—
295Q8—941no—
296Q8—941no—
297Q8#1062535212yes—
298D4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4—1882no—
314C2×C4C2×C22⋊D4711yescharacteristic
315C2×C4C2×C22⋊D4711yescharacteristic
316C2×C4C2×C22⋊D4711yescharacteristic
317C2×C4C2×C22⋊D4711yescharacteristic
318C2×C4C23×D4711yescharacteristic
319C8—941no—
320C8—941no—
321C8—941no—
322C8—941no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22#1309405512yes—
329C22C22×C22⋊D4711yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—1881no—
339C4—1881no—
340C4—1881no—
341C4—1881no—
342C4C2×#1062535211yescharacteristic
343C4#1309406911yescharacteristic
344C2—22no—
345C2—41no—
346C2#1568976711yescharacteristic
347C2C2×#1309405511yescharacteristic
348C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingD4×Q8×C47C2
socleC22×C47C22×D4
hypercenterD4×Q8D47
hypocenterC47#3312
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
2. #15689491C2semidirect
3. #15689461C2semidirect
4. #15689451C2semidirect
5. #15689430C2semidirect
6. #15689379C2semidirect
7. #15689362C2semidirect
8. #15689330C2semidirect
9. #15689279C2semidirect
10. #15689279C2semidirect
11. #15689228C2semidirect
13. #15689132C2semidirect
14. C2×#13093948C2semidirect
190. C47#3312semidirect