Finite Group Databasebeta

← #20247128

Subgroups — #20247128

Order 6016.

674 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094009C211yesmaximal, characteristic, complemented
2C2×#13093999C211yesmaximal, characteristic
3C2×C4×D188C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×D47C211yesmaximal, characteristic, complemented
5#15689060C211yesmaximal, characteristic, complemented
6#15689053C211yesmaximal, characteristic, complemented
7#15689050C211yesmaximal, characteristic, complemented
8#15689041C211yesmaximal, characteristic, complemented
9#15689014C211yesmaximal, characteristic, complemented
10#15689001C211yesmaximal, characteristic, complemented
11#15689001C211yesmaximal, characteristic, complemented
12#15689001C211yesmaximal, characteristic, complemented
13#15688997C211yesmaximal, characteristic, complemented
14#15688997C211yesmaximal, characteristic, complemented
15C47×#387C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C22×D188C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21C22×C4×D47C2211yescharacteristic
22C22×C4×D47C2211yescharacteristic
23#13094009—24no—
24#13093999—24no—
25C4×D188—24no—
26C2×C4⋊Dic47C2211yescharacteristic
27C2×C4⋊Dic47C2211yescharacteristic
28C2×C4⋊Dic47C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C2×Dic47⋊C4C2211yescharacteristic
31C2×Dic47⋊C4C2211yescharacteristic
32C4⋊C4×D47—24no—
33C2×(C2×D47)⋊C4C2211yescharacteristic
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×(C2×D47)⋊C4C2211yescharacteristic
43C2×(C2×D47)⋊C4C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C47⋊#95C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C4⋊C4×C47C2211yescharacteristic
50C2×C42×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53#95×C47C2211yescharacteristic
54#95×C47C2211yescharacteristic
55C23×D47C2311yescharacteristic
56C23×D47C2311yescharacteristic
57C23×D47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C2×D188—22no—
71C2×D188—22no—
72C2×D188—22no—
73C2×D188—22no—
74C2×D188—22no—
75C2×D188—22no—
76C2×D188—22no—
77C2×D188—41no—
78C2×D188D414yes—
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—22no—
86C2×C4×D47—22no—
87C2×C4×D47—22no—
88C2×C4×D47—41no—
89C2×C4×D47—41no—
90C2×C4×D47—41no—
91C4⋊C4×C47—22no—
92C4⋊C4×C47D414yescomplemented
93C42×C47—22no—
94(C2×D47)⋊C4—22no—
95(C2×D47)⋊C4—22no—
96(C2×D47)⋊C4—22no—
97(C2×D47)⋊C4—22no—
98(C2×D47)⋊C4—22no—
99(C2×D47)⋊C4—22no—
100(C2×D47)⋊C4—22no—
101(C2×D47)⋊C4—22no—
102(C2×D47)⋊C4—22no—
103(C2×D47)⋊C4—22no—
104(C2×D47)⋊C4—41no—
105C4⋊Dic47—22no—
106C4⋊Dic47—22no—
107C4⋊Dic47—41no—
108Dic47⋊C4—22no—
109Dic47⋊C4—22no—
110Dic47⋊C4—22no—
111C23×C47C2411yescharacteristic
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×D47—21no—
121C22×D47—21no—
122C22×D47—21no—
123C22×D47—21no—
124C22×D47—21no—
125C22×D47—21no—
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—21no—
129C22×D47C2×D412yes—
130C22×D47C2×D412yes—
131C22×D47#4112yes—
132C22×D47#4112yes—
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×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47C2×D412yes—
151C2×C4×C47C2×D412yes—
152C2×C4×C47C2×D412yes—
153C2×C4×C47C2×D412yes—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—21no—
160C2×Dic47—21no—
161C2×Dic47—21no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—21no—
165C2×Dic47—21no—
166C2×Dic47—21no—
167C2×Dic47—21no—
168C2×Dic47#4112yes—
169D188—28no—
170D188—44no—
171D188—44no—
172C4×D47—28no—
173C4×D47—44no—
174C4×D47—44no—
175C4×D47—44no—
176C22×C47C22×D411yescharacteristic
177C22×C47C22×D411yescharacteristic
178C22×C47C2×#4111yescharacteristic
179C22×C47C2×#4111yescharacteristic
180C22×C47C2×#4111yescharacteristic
181C22×C47H(5,𝔽2)11yescharacteristic
182C22×C472−1+411yescharacteristic
183C2×D47—22no—
184C2×D47—22no—
185C2×D47—22no—
186C2×D47—22no—
187C2×D47—22no—
188C2×D47—22no—
189C2×D47—22no—
190C2×D47—22no—
191C2×D47—22no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—41no—
195C2×D47—41no—
196C2×D47—41no—
197C2×D47—41no—
198C2×D47—41no—
199C2×D47—41no—
200C2×D47—41no—
201C2×D47—41no—
202C2×D47—41no—
203C2×D47#12314yescomplemented
204C4×C47—22no—
205C4×C47—22no—
206C4×C47—22no—
207C4×C47—22no—
208C4×C47—41no—
209C4×C47—41no—
210C4×C47—41no—
211Dic47—22no—
212Dic47—41no—
213Dic47—41no—
214Dic47—41no—
215Dic47—41no—
216#2443—471nomaximal, Sylow
217C2×C47C2×#12311yescharacteristic
218C2×C47#52511yescharacteristic
219C2×C47#53911yescharacteristic
220C2×C47D4211yescharacteristic
221C2×C47#54711yescharacteristic
222C2×C47#54811yescharacteristic
223C2×C47#55311yescharacteristic
224D47—24no—
225D47—42no—
226D47—81no—
227C2×#123—471no—
228C2×#121—471no—
229C2×C4×D4—471no—
230C22×C4⋊C4—471no—
231#399—471no—
232#398—471no—
233#397—471no—
234#394—471no—
235#388—471no—
236#387D4711yescharacteristic, complemented
237#386—471no—
238#386—471no—
239#386—471no—
240#385—471no—
241#385—471no—
242C47#244311yescharacteristic, complemented, Sylow
243C22×D4—471no—
244C22×D4—471no—
245C22×D4—471no—
246C23×C4—471no—
247C23×C4—471no—
248C23×C4—471no—
249C23×C4—471no—
250#123—944no—
251#121—944no—
252C4×D4—944no—
253C2×C4⋊C4—471no—
254C2×C4⋊C4—471no—
255C2×C4⋊C4—471no—
256C2×C4⋊C4—471no—
257C2×C4⋊C4—471no—
258C2×C4⋊C4—471no—
259C2×C4⋊C4—944no—
260C2×C4⋊C4C2×D4711yescharacteristic
261C2×C4⋊C4C2×D4711yescharacteristic
262C2×C22⋊C4—471no—
263C2×C22⋊C4—471no—
264C2×C22⋊C4—471no—
265C2×C22⋊C4—471no—
266C2×C22⋊C4—471no—
267C2×C22⋊C4—471no—
268C2×C22⋊C4—471no—
269C2×C22⋊C4—471no—
270C2×C22⋊C4—471no—
271C2×C22⋊C4—471no—
272C2×C22⋊C4—471no—
273C2×C42C2×D4711yescharacteristic
274#95—471no—
275#95—471no—
276#95—471no—
277#95—471no—
278#95C2×D4711yescharacteristic
279#95C2×D4711yescharacteristic
280#95C2×D4711yescharacteristic
281#95C2×D4711yescharacteristic
282C24—471no—
283C24—471no—
284C24—471no—
285C2×D4—474no—
286C2×D4—942no—
287C2×D4—942no—
288C2×D4—942no—
289C2×D4—942no—
290C2×D4—942no—
291C2×D4—942no—
292C2×D4—942no—
293C2×D4—1881no—
294C22×C4—471no—
295C22×C4—471no—
296C22×C4—471no—
297C22×C4—471no—
298C22×C4—471no—
299C22×C4—942no—
300C22×C4—942no—
301C22×C4—942no—
302C22×C4—942no—
303C22×C4—942no—
304C22×C4—942no—
305C22×C4—942no—
306C22×C4—942no—
307C22×C4—942no—
308C22×C4—1881no—
309C22×C4—1881no—
310C22×C4—1881no—
311C22×C4C22×D4711yescharacteristic
312C22×C4C22×D4711yescharacteristic
313C22×C4C22×D4711yescharacteristic
314C22×C4C22×D4711yescharacteristic
315C22×C4C22×D4711yescharacteristic
316C22×C4C22×D4711yescharacteristic
317C22×C4C22×D4711yescharacteristic
318C4⋊C4—22no—
319C4⋊C4—942no—
320C4⋊C4—942no—
321C4⋊C4—942no—
322C4⋊C4—942no—
323C4⋊C4—942no—
324C4⋊C4—1881no—
325C4⋊C4D18814yescomplemented
326C22⋊C4—942no—
327C22⋊C4—942no—
328C22⋊C4—942no—
329C22⋊C4—942no—
330C22⋊C4—942no—
331C22⋊C4—942no—
332C22⋊C4—942no—
333C22⋊C4—942no—
334C22⋊C4—942no—
335C22⋊C4—942no—
336C22⋊C4—1881no—
337C42—22no—
338C23—472no—
339C23—472no—
340C23—472no—
341C23—472no—
342C23—941no—
343C23—941no—
344C23—941no—
345C23—941no—
346C23—941no—
347C23—941no—
348C23—941no—
349C23—941no—
350C23—941no—
351C23—941no—
352C23—941no—
353C23—941no—
354C23—941no—
355C23—941no—
356C23—941no—
357C23—941no—
358C23—941no—
359C23C23×D4711yescharacteristic
360D4—948no—
361D4—1884no—
362D4—1884no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—472no—
381C2×C4—948no—
382C2×C4—941no—
383C2×C4—941no—
384C2×C4—941no—
385C2×C4—941no—
386C2×C4—941no—
387C2×C4—941no—
388C2×C4—941no—
389C2×C4—941no—
390C2×C4—941no—
391C2×C4—941no—
392C2×C4—941no—
393C2×C4—941no—
394C2×C4—941no—
395C2×C4—941no—
396C2×C4—1884no—
397C2×C4—1884no—
398C2×C4—1884no—
399C2×C4C2×D18812yes—
400C2×C4C2×D18812yes—
401C2×C4C2×D18812yes—
402C2×C4D4×D4712yes—
403C22—474no—
404C22—942no—
405C22—942no—
406C22—942no—
407C22—942no—
408C22—942no—
409C22—942no—
410C22—942no—
411C22—942no—
412C22—942no—
413C22—1881no—
414C22—1881no—
415C22—1881no—
416C22—1881no—
417C22—1881no—
418C22—1881no—
419C22—1881no—
420C22—1881no—
421C22—1881no—
422C22—1881no—
423C22—1881no—
424C22C2×D4×D4711yescharacteristic
425C22C22×D18811yescharacteristic
426C22#41×D4711yescharacteristic
427C22#41×D4711yescharacteristic
428C22#41×D4711yescharacteristic
429C22#1309407011yescharacteristic
430C22#1309407211yescharacteristic
431C4—22no—
432C4—22no—
433C4—22no—
434C4—22no—
435C4—41no—
436C4—41no—
437C4—41no—
438C4—942no—
439C4—1881no—
440C4—1881no—
441C4—1881no—
442C4—1881no—
443C2—944no—
444C2—3761no—
445C2—1882no—
446C2#123×D4711yescharacteristic
447C2#1568963511yescharacteristic
448C2#1568972111yescharacteristic
449C2D4×D18811yescharacteristic
450C2#1568977511yescharacteristic
451C2#1568978511yescharacteristic
452C2#1568982411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#387C2
hypercenter#387D47
hypocenterC47#2443
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#13094009C2semidirect
3. C2×C4×D188C2semidirect
4. C2×C4⋊C4×D47C2semidirect
5. #15689060C2semidirect
6. #15689053C2semidirect
7. #15689050C2semidirect
8. #15689041C2semidirect
9. #15689014C2semidirect
10. #15689001C2semidirect
11. #15689001C2semidirect
12. #15689001C2semidirect
13. #15688997C2semidirect
14. #15688997C2semidirect
15. C47×#387C2semidirect
92. C4⋊C4×C47D4semidirect
203. C2×D47#123semidirect
236. #387D47semidirect
242. C47#2443semidirect
325. C4⋊C4D188semidirect