Finite Group Databasebeta

← #20245909

Subgroups — #20245909

Order 6016.

688 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094009C211yesmaximal, characteristic
2C2×#13093986C211yesmaximal, characteristic
3C2×C42×D47C211yesmaximal, characteristic, complemented
4#15689015C211yesmaximal, characteristic, complemented
5#15689014C211yesmaximal, characteristic, complemented
6#15689004C211yesmaximal, characteristic, complemented
7#15689001C211yesmaximal, characteristic
8#15688997C211yesmaximal, characteristic, complemented
9#15688985C211yesmaximal, characteristic, complemented
10C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
11#15688974C211yesmaximal, characteristic, complemented
12#15688970C211yesmaximal, characteristic, complemented
13#15688970C211yesmaximal, characteristic, complemented
14#15688970C211yesmaximal, characteristic, complemented
15C47×#387C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21#13094009C418yescomplemented
22#13093986—24no—
23C2×C4⋊Dic47C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2211yescharacteristic
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×(C2×D47)⋊C4C2211yescharacteristic
30C2×(C2×D47)⋊C4C2211yescharacteristic
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×C4×Dic47C2211yescharacteristic
35C2×C4×Dic47C2211yescharacteristic
36C2×C4×Dic47C2211yescharacteristic
37C2×C4×Dic47C2211yescharacteristic
38C2×C4×Dic47C2211yescharacteristic
39C2×C4×Dic47C2211yescharacteristic
40C42×D47—24no—
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C42×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53#95×C47C2211yescharacteristic
54C23×D47C2311yescharacteristic
55C23×D47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C2×D188—22no—
70C2×D188—22no—
71C2×D188C2×C414yes—
72C2×C4×D47—22no—
73C2×C4×D47—22no—
74C2×C4×D47—22no—
75C2×C4×D47—22no—
76C2×C4×D47—22no—
77C2×C4×D47—22no—
78C2×C4×D47—22no—
79C2×C4×D47—22no—
80C2×C4×D47—22no—
81C2×C4×D47—22no—
82C2×C4×D47C2×C414yescomplemented
83C2×C4×D47D414yes—
84C4⋊C4×C47—22no—
85C4⋊C4×C47C2×C414yescomplemented
86C42×C47—22no—
87(C2×D47)⋊C4—22no—
88(C2×D47)⋊C4—22no—
89(C2×D47)⋊C4—22no—
90(C2×D47)⋊C4—22no—
91(C2×D47)⋊C4—22no—
92(C2×D47)⋊C4C2×C414yescomplemented
93(C2×D47)⋊C4C2×C414yescomplemented
94(C2×D47)⋊C4C2×C414yescomplemented
95C4⋊Dic47—22no—
96Dic47⋊C4—22no—
97Dic47⋊C4C2×C414yescomplemented
98C4×Dic47—22no—
99C4×Dic47—22no—
100C4×Dic47—22no—
101C4×Dic47—22no—
102C4×Dic47—22no—
103C4×Dic47—22no—
104C23×C47C2411yescharacteristic
105C22×D47—21no—
106C22×D47—21no—
107C22×D47—21no—
108C22×D47—21no—
109C22×D47—21no—
110C22×D47—21no—
111C22×D47—21no—
112C22×D47—21no—
113C22×D47—21no—
114C22×D47—21no—
115C22×D47C22×C412yes—
116C22×D47C22×C412yes—
117C22×D47C2×D412yes—
118C22×D47#4112yes—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
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—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47C22×C412yes—
136C2×C4×C47C22×C412yes—
137C2×C4×C47C22×C412yes—
138C2×C4×C47C2×D412yes—
139C2×C4×C47#4112yes—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47C22×C412yes—
153C2×Dic47C22×C412yes—
154C2×Dic47C2×D412yes—
155C2×Dic47#4112yes—
156C2×Dic47#4112yes—
157C2×Dic47#4112yes—
158D188—28no—
159C4×D47—28no—
160C4×D47—28no—
161C4×D47—28no—
162C4×D47—44no—
163C22×C47C23×C411yescharacteristic
164C22×C47C22×D411yescharacteristic
165C22×C47C2×#4111yescharacteristic
166C22×C47C2×#4111yescharacteristic
167C22×C47C2×#4111yescharacteristic
168C22×C47C2×#4111yescharacteristic
169C22×C47C2×#4111yescharacteristic
170C2×D47—22no—
171C2×D47—22no—
172C2×D47—22no—
173C2×D47—22no—
174C2×D47—22no—
175C2×D47—22no—
176C2×D47—22no—
177C2×D47—22no—
178C2×D47—22no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47C4×D414yes—
184C4×C47—22no—
185C4×C47—22no—
186C4×C47—22no—
187C4×C47—22no—
188C4×C47—22no—
189C4×C47—41no—
190C4×C47—41no—
191Dic47—22no—
192Dic47—22no—
193Dic47—22no—
194Dic47—41no—
195Dic47—41no—
196Dic47#12314yescomplemented
197C4×#123—471nomaximal, Sylow
198C2×C47C2×C4×D411yescharacteristic
199C2×C47C4×#4111yescharacteristic
200C2×C47C4×#4111yescharacteristic
201C2×C47C2×#12311yescharacteristic
202C2×C47#52511yescharacteristic
203C2×C47#52911yescharacteristic
204C2×C47#52911yescharacteristic
205D47—24no—
206D47—42no—
207C2×#123—471no—
208C2×C4×D4—471no—
209C22×C42—471no—
210#388—471no—
211#388—471no—
212#387—471no—
213#387D4711yescharacteristic, complemented
214#386—471no—
215#385—471no—
216#381—471no—
217C4×C4⋊C4—471no—
218C4×C4⋊C4—471no—
219C4×C22⋊C4—471no—
220C4×C22⋊C4—471no—
221C4×C22⋊C4—471no—
222C47C4×#12311yescharacteristic, complemented, Sylow
223C22×D4—471no—
224C23×C4—471no—
225C23×C4—471no—
226C23×C4—471no—
227C23×C4—471no—
228#123—478no—
229C4×D4—944no—
230C2×C4⋊C4—471no—
231C2×C4⋊C4—471no—
232C2×C4⋊C4—471no—
233C2×C4⋊C4C2×D4711yescharacteristic
234C2×C4⋊C4C2×D4711yescharacteristic
235C2×C22⋊C4—471no—
236C2×C22⋊C4—471no—
237C2×C22⋊C4—471no—
238C2×C22⋊C4—471no—
239C2×C22⋊C4—471no—
240C2×C22⋊C4—471no—
241C2×C22⋊C4—471no—
242C2×C22⋊C4—471no—
243C2×C42—471no—
244C2×C42—471no—
245C2×C42—471no—
246C2×C42—471no—
247C2×C42—471no—
248C2×C42—471no—
249C2×C42—944no—
250C2×C42C2×D4711yescharacteristic
251#95—471no—
252#95—471no—
253#95—471no—
254#95—471no—
255#95—471no—
256#95—471no—
257#95C2×D4711yescharacteristic
258#95C2×D4711yescharacteristic
259#95C2×D4711yescharacteristic
260#95C2×D4711yescharacteristic
261C24—471no—
262C24—471no—
263C2×D4—474no—
264C2×D4—942no—
265C2×D4—942no—
266C22×C4—471no—
267C22×C4—471no—
268C22×C4—471no—
269C22×C4—471no—
270C22×C4—474no—
271C22×C4—474no—
272C22×C4—471no—
273C22×C4—471no—
274C22×C4—942no—
275C22×C4—942no—
276C22×C4—942no—
277C22×C4—942no—
278C22×C4—942no—
279C22×C4—942no—
280C22×C4—942no—
281C22×C4—942no—
282C22×C4—942no—
283C22×C4—942no—
284C22×C4C22×D4711yescharacteristic
285C22×C4C22×D4711yescharacteristic
286C22×C4C22×D4711yescharacteristic
287C22×C4C22×D4711yescharacteristic
288C22×C4C22×D4711yescharacteristic
289C22×C4C22×D4711yescharacteristic
290C22×C4C22×D4711yescharacteristic
291C4⋊C4—22no—
292C4⋊C4—474no—
293C4⋊C4—942no—
294C4⋊C4—942no—
295C4⋊C4C4×D4714yescomplemented
296C22⋊C4—474no—
297C22⋊C4—474no—
298C22⋊C4—474no—
299C22⋊C4—942no—
300C22⋊C4—942no—
301C22⋊C4—942no—
302C22⋊C4—942no—
303C22⋊C4—942no—
304C42—22no—
305C42—942no—
306C42—942no—
307C42—942no—
308C42—942no—
309C42—942no—
310C42—942no—
311C23—472no—
312C23—472no—
313C23—472no—
314C23—472no—
315C23—941no—
316C23—941no—
317C23—941no—
318C23—941no—
319C23—941no—
320C23—941no—
321C23—941no—
322C23—941no—
323C23—941no—
324C23—941no—
325C23C23×D4711yescharacteristic
326D4—948no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—472no—
344C2×C4—472no—
345C2×C4—472no—
346C2×C4—472no—
347C2×C4—472no—
348C2×C4—472no—
349C2×C4—948no—
350C2×C4—948no—
351C2×C4—948no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4—941no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—941no—
358C2×C4—941no—
359C2×C4—941no—
360C2×C4—941no—
361C2×C4—941no—
362C2×C4—941no—
363C2×C4—941no—
364C2×C4—1884no—
365C2×C4C2×C4×D4712yes—
366C2×C4C2×C4×D4712yes—
367C2×C4C2×C4×D4712yes—
368C2×C4D4×D4712yes—
369C2×C4#1062535412yes—
370C22—474no—
371C22—942no—
372C22—942no—
373C22—942no—
374C22—942no—
375C22—942no—
376C22—942no—
377C22—942no—
378C22—942no—
379C22—942no—
380C22—1881no—
381C22—1881no—
382C22—1881no—
383C22—1881no—
384C22C22×C4×D4711yescharacteristic
385C22C2×D4×D4711yescharacteristic
386C22#41×D4711yescharacteristic
387C22#41×D4711yescharacteristic
388C22#41×D4711yescharacteristic
389C22#41×D4711yescharacteristic
390C22C2×#1062535411yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—22no—
396C4—41no—
397C4—41no—
398C4—474no—
399C4—942no—
400C4—942no—
401C4—942no—
402C4—1881no—
403C4—1881no—
404C2—944no—
405C2—1882no—
406C2C4×D4×D4711yescharacteristic
407C2#1568959111yescharacteristic
408C2C4×#1062535411yescharacteristic
409C2#123×D4711yescharacteristic
410C2#1568963611yescharacteristic
411C2#1568965611yescharacteristic
412C2#1568965811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#387C2
socleC23×C47C24
hypercenter#387D47
hypocenterC47C4×#123
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
3. C2×C42×D47C2semidirect
4. #15689015C2semidirect
5. #15689014C2semidirect
6. #15689004C2semidirect
8. #15688997C2semidirect
9. #15688985C2semidirect
10. C4⋊C4×Dic47C2semidirect
11. #15688974C2semidirect
12. #15688970C2semidirect
13. #15688970C2semidirect
14. #15688970C2semidirect
15. C47×#387C2semidirect
21. #13094009C4semidirect
82. C2×C4×D47C2×C4semidirect
85. C4⋊C4×C47C2×C4semidirect
92. (C2×D47)⋊C4C2×C4semidirect
93. (C2×D47)⋊C4C2×C4semidirect
94. (C2×D47)⋊C4C2×C4semidirect
97. Dic47⋊C4C2×C4semidirect
196. Dic47#123semidirect
213. #387D47semidirect
222. C47C4×#123semidirect
295. C4⋊C4C4×D47semidirect