Finite Group Databasebeta

← #20247190

Subgroups — #20247190

Order 6016.

648 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094000C211yesmaximal, characteristic, complemented
2C2×#13094000C211yesmaximal, characteristic, complemented
3C2×#13093986C211yesmaximal, characteristic
4C2×C4⋊C4×D47C211yesmaximal, characteristic, complemented
5#15689058C211yesmaximal, characteristic, complemented
6#15689056C211yesmaximal, characteristic, complemented
7#15689045C211yesmaximal, characteristic, complemented
8#15689020C211yesmaximal, characteristic, complemented
9#15689010C211yesmaximal, characteristic, complemented
10#15689001C211yesmaximal, characteristic
11#15689001C211yesmaximal, characteristic
12#15688997C211yesmaximal, characteristic, complemented
13#15688997C211yesmaximal, characteristic, complemented
14#15688994C211yesmaximal, characteristic, complemented
15C47×#395C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21#13094000—24no—
22#13094000—24no—
23#13093986—24no—
24C2×C4⋊Dic47C2211yescharacteristic
25C2×C4⋊Dic47C2211yescharacteristic
26C2×C4⋊Dic47C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C2×Dic47⋊C4C2211yescharacteristic
31C2×Dic47⋊C4C2211yescharacteristic
32C2×Dic47⋊C4C2211yescharacteristic
33C4⋊C4×D47—24no—
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic
39C2×(C2×D47)⋊C4C2211yescharacteristic
40C2×(C2×D47)⋊C4C2211yescharacteristic
41C2×(C2×D47)⋊C4C2211yescharacteristic
42C2×C4×Dic47C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C47⋊#95C2211yescharacteristic
48C22×Q8×C47C2211yescharacteristic
49C2×C4⋊C4×C47C2211yescharacteristic
50C2×C4⋊C4×C47C2211yescharacteristic
51C2×C4⋊C4×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53#95×C47C2211yescharacteristic
54#95×C47C2211yescharacteristic
55C23×D47C2311yescharacteristic
56C23×D47C2311yescharacteristic
57C2×Q8×C47—22no—
58C2×Q8×C47—22no—
59C2×Q8×C47—41no—
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C2×D188—22no—
74C2×D188—22no—
75C2×D188Q814yescomplemented
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×D47—22no—
83C2×C4×D47—22no—
84C2×C4×D47—22no—
85C2×C4×D47—41no—
86C2×C4×D47—41no—
87C2×C4×D47—41no—
88C4⋊C4×C47—22no—
89C4⋊C4×C47—22no—
90C4⋊C4×C47—41no—
91(C2×D47)⋊C4—22no—
92(C2×D47)⋊C4—22no—
93(C2×D47)⋊C4—22no—
94(C2×D47)⋊C4—22no—
95(C2×D47)⋊C4—22no—
96(C2×D47)⋊C4—22no—
97(C2×D47)⋊C4—41no—
98(C2×D47)⋊C4D414yes—
99C4⋊Dic47—22no—
100C4⋊Dic47—22no—
101C4⋊Dic47—22no—
102Dic47⋊C4—22no—
103Dic47⋊C4—22no—
104Dic47⋊C4—22no—
105Dic47⋊C4—22no—
106Dic47⋊C4—22no—
107Dic47⋊C4D414yescomplemented
108C4×Dic47—22no—
109C23×C47C2411yescharacteristic
110C22×D47—21no—
111C22×D47—21no—
112C22×D47—21no—
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—21no—
117C22×D47—21no—
118C22×D47—21no—
119C22×D47—21no—
120C22×D47C2×D412yes—
121C22×D47C2×Q812yes—
122C22×D47C2×Q812yes—
123C22×D47#4112yes—
124Q8×C47—44no—
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×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47C2×D412yes—
143C2×C4×C47C2×D412yes—
144C2×C4×C47C2×Q812yes—
145C2×C4×C47#4112yes—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—21no—
160C2×Dic47—21no—
161C2×Dic47C2×D412yes—
162C2×Dic47C2×D412yes—
163C2×Dic47C2×D412yes—
164D188—28no—
165C4×D47—28no—
166C4×D47—44no—
167C4×D47—44no—
168C4×D47—44no—
169C22×C47C22×D411yescharacteristic
170C22×C47C22×D411yescharacteristic
171C22×C47C22×Q811yescharacteristic
172C22×C47C2×#4111yescharacteristic
173C22×C47C2×#4111yescharacteristic
174C22×C47H(5,𝔽2)11yescharacteristic
175C22×C472−1+411yescharacteristic
176C2×D47—22no—
177C2×D47—22no—
178C2×D47—22no—
179C2×D47—22no—
180C2×D47—22no—
181C2×D47—22no—
182C2×D47—22no—
183C2×D47—22no—
184C2×D47—22no—
185C2×D47—41no—
186C2×D47—41no—
187C2×D47—41no—
188C2×D47—41no—
189C2×D47C22⋊Q814yescomplemented
190C4×C47—22no—
191C4×C47—22no—
192C4×C47—22no—
193C4×C47—22no—
194C4×C47—41no—
195C4×C47—41no—
196C4×C47—41no—
197Dic47—22no—
198Dic47—22no—
199Dic47—22no—
200Dic47—41no—
201Dic47—41no—
202Dic47—41no—
203#2449—471nomaximal, Sylow
204C2×C47C2×C22⋊Q811yescharacteristic
205C2×C47#52511yescharacteristic
206C2×C47#53911yescharacteristic
207C2×C47D4211yescharacteristic
208C2×C47#54711yescharacteristic
209C2×C47D4×Q811yescharacteristic
210C2×C47#55411yescharacteristic
211D47—24no—
212D47—42no—
213C2×C22⋊Q8—471no—
214C2×C22⋊Q8—471no—
215C2×C4×D4—471no—
216C22×C4⋊C4—471no—
217#399—471no—
218#398—471no—
219#396—471no—
220#395D4711yescharacteristic, complemented
221#389—471no—
222#387—471no—
223#386—471no—
224#386—471no—
225#385—471no—
226#385—471no—
227#385—471no—
228C47#244911yescharacteristic, complemented, Sylow
229C22×Q8C2×D4711yescharacteristic
230C22×D4—471no—
231C23×C4—471no—
232C23×C4—471no—
233C23×C4—471no—
234C23×C4—471no—
235C22⋊Q8—944no—
236C22⋊Q8—944no—
237C4×D4—944no—
238C2×C4⋊C4—471no—
239C2×C4⋊C4—471no—
240C2×C4⋊C4—471no—
241C2×C4⋊C4—471no—
242C2×C4⋊C4—471no—
243C2×C4⋊C4—471no—
244C2×C4⋊C4—471no—
245C2×C4⋊C4—471no—
246C2×C4⋊C4—471no—
247C2×C4⋊C4—944no—
248C2×C4⋊C4C2×D4711yescharacteristic
249C2×C4⋊C4C2×D4711yescharacteristic
250C2×C4⋊C4C2×D4711yescharacteristic
251C2×C22⋊C4—471no—
252C2×C22⋊C4—471no—
253C2×C22⋊C4—471no—
254C2×C22⋊C4—471no—
255C2×C22⋊C4—471no—
256C2×C22⋊C4—471no—
257C2×C22⋊C4—471no—
258C2×C22⋊C4—471no—
259C2×C42—471no—
260#95—471no—
261#95—471no—
262#95—471no—
263#95—471no—
264#95—471no—
265#95C2×D4711yescharacteristic
266#95C2×D4711yescharacteristic
267#95C2×D4711yescharacteristic
268C24—471no—
269C24—471no—
270C2×Q8—22no—
271C2×Q8—22no—
272C2×Q8—41no—
273C2×D4—474no—
274C2×D4—942no—
275C2×D4—942no—
276C22×C4—471no—
277C22×C4—471no—
278C22×C4—471no—
279C22×C4—471no—
280C22×C4—471no—
281C22×C4—471no—
282C22×C4—942no—
283C22×C4—942no—
284C22×C4—942no—
285C22×C4—942no—
286C22×C4—942no—
287C22×C4—942no—
288C22×C4—942no—
289C22×C4—942no—
290C22×C4—942no—
291C22×C4—1881no—
292C22×C4—1881no—
293C22×C4—1881no—
294C22×C4C22×D4711yescharacteristic
295C22×C4C22×D4711yescharacteristic
296C22×C4C22×D4711yescharacteristic
297C22×C4C22×D4711yescharacteristic
298C22×C4C22×D4711yescharacteristic
299C22×C4C22×D4711yescharacteristic
300C22×C4C22×D4711yescharacteristic
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—474no—
305C4⋊C4—942no—
306C4⋊C4—942no—
307C4⋊C4—942no—
308C4⋊C4—942no—
309C4⋊C4—942no—
310C4⋊C4—942no—
311C4⋊C4—942no—
312C4⋊C4—942no—
313C22⋊C4—474no—
314C22⋊C4—942no—
315C22⋊C4—942no—
316C22⋊C4—942no—
317C22⋊C4—942no—
318C22⋊C4—942no—
319C22⋊C4—942no—
320C22⋊C4—1881no—
321C42—942no—
322C23—472no—
323C23—472no—
324C23—472no—
325C23—472no—
326C23—941no—
327C23—941no—
328C23—941no—
329C23—941no—
330C23—941no—
331C23—941no—
332C23—941no—
333C23—941no—
334C23—941no—
335C23—941no—
336C23C23×D4711yescharacteristic
337Q8—44no—
338D4—948no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—472no—
357C2×C4—472no—
358C2×C4—472no—
359C2×C4—948no—
360C2×C4—941no—
361C2×C4—941no—
362C2×C4—941no—
363C2×C4—941no—
364C2×C4—941no—
365C2×C4—941no—
366C2×C4—941no—
367C2×C4—941no—
368C2×C4—941no—
369C2×C4—941no—
370C2×C4—941no—
371C2×C4—941no—
372C2×C4—941no—
373C2×C4—941no—
374C2×C4—941no—
375C2×C4—1884no—
376C2×C4—1884no—
377C2×C4—1884no—
378C2×C4D4×D4712yes—
379C2×C4D4×D4712yes—
380C2×C4Q8×D4712yes—
381C2×C4#1062535412yes—
382C22—474no—
383C22—942no—
384C22—942no—
385C22—942no—
386C22—942no—
387C22—942no—
388C22—942no—
389C22—942no—
390C22—942no—
391C22—942no—
392C22—1881no—
393C22—1881no—
394C22—1881no—
395C22—1881no—
396C22C2×D4×D4711yescharacteristic
397C22C2×D4×D4711yescharacteristic
398C22C2×Q8×D4711yescharacteristic
399C22#41×D4711yescharacteristic
400C22C2×#1062535411yescharacteristic
401C22#1309406911yescharacteristic
402C22#1309407211yescharacteristic
403C4—22no—
404C4—22no—
405C4—22no—
406C4—22no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—942no—
411C4—942no—
412C4—942no—
413C4—1881no—
414C4—1881no—
415C4—1881no—
416C2—944no—
417C2—1882no—
418C2C22⋊Q8×D4711yescharacteristic
419C2#1568963611yescharacteristic
420C2#1568971911yescharacteristic
421C2#1568975511yescharacteristic
422C2#1568977611yescharacteristic
423C2#1568978811yescharacteristic
424C2#1568983411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2449
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#13094000C2semidirect
2. C2×#13094000C2semidirect
4. C2×C4⋊C4×D47C2semidirect
5. #15689058C2semidirect
6. #15689056C2semidirect
7. #15689045C2semidirect
8. #15689020C2semidirect
9. #15689010C2semidirect
12. #15688997C2semidirect
13. #15688997C2semidirect
14. #15688994C2semidirect
15. C47×#395C2semidirect
75. C2×D188Q8semidirect
107. Dic47⋊C4D4semidirect
189. C2×D47C22⋊Q8semidirect
220. #395D47semidirect
228. C47#2449semidirect