Finite Group Databasebeta

← #20249937

Subgroups — #20249937

Order 6016.

562 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094005C211yesmaximal, characteristic, complemented
2C2×#13094001C211yesmaximal, characteristic, complemented
3#15689063C211yesmaximal, characteristic, complemented
4#15689051C211yesmaximal, characteristic, complemented
5#15689037C211yesmaximal, characteristic, complemented
6#15689035C211yesmaximal, characteristic, complemented
7#15689035C211yesmaximal, characteristic, complemented
8#15689026C211yesmaximal, characteristic, complemented
9#15689017C211yesmaximal, characteristic, complemented
10#15689005C211yesmaximal, characteristic, complemented
11#15689003C211yesmaximal, characteristic, complemented
12#15689003C211yesmaximal, characteristic, complemented
13#15689003C211yesmaximal, characteristic, complemented
14#15688981C211yesmaximal, characteristic, complemented
15C47×#392C211yesmaximal, characteristic
16C22×Dic94C2211yescharacteristic
17C23×Dic47C2211yescharacteristic
18C23×Dic47C2211yescharacteristic
19#13094005—24no—
20#13094001—24no—
21C2×C4⋊Dic47C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×C22⋊Dic47C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×C22⋊Dic47C2211yescharacteristic
35C2×C22⋊Dic47C2211yescharacteristic
36C2×C4×Dic47C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C22×D4×C47C2211yescharacteristic
47C22×D4×C47C2211yescharacteristic
48C22×D4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C24×C47C2311yescharacteristic
54C24×C47C2311yescharacteristic
55C24×C47C2311yescharacteristic
56C2×D4×C47—22no—
57C2×D4×C47—22no—
58C2×D4×C47—22no—
59C2×D4×C47—22no—
60C2×D4×C47—22no—
61C2×D4×C47—41no—
62C2×D4×C47—41no—
63C2×D4×C47—41no—
64C2×D4×C47—41no—
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C22×Dic47—22no—
70C22×Dic47—22no—
71C22×Dic47—22no—
72C22×Dic47—41no—
73C22×Dic47—41no—
74C22×Dic47—41no—
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C22×Dic47C2311yescharacteristic
81C22×Dic47C2311yescharacteristic
82C22×Dic47C2311yescharacteristic
83C2×Dic94—22no—
84C2×Dic94—41no—
85C2×Dic94—41no—
86C22⋊C4×C47—22no—
87C22⋊C4×C47—41no—
88C22⋊C4×C47—41no—
89C22⋊Dic47—22no—
90C22⋊Dic47—22no—
91C22⋊Dic47—22no—
92C22⋊Dic47—22no—
93C22⋊Dic47—22no—
94C22⋊Dic47—41no—
95C22⋊Dic47—41no—
96C22⋊Dic47—41no—
97C22⋊Dic47—41no—
98C22⋊Dic47—41no—
99C4⋊Dic47—22no—
100Dic47⋊C4—22no—
101Dic47⋊C4—22no—
102Dic47⋊C4—41no—
103Dic47⋊C4D414yescomplemented
104C4×Dic47—41no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—21no—
121C23×C47—21no—
122C23×C47—21no—
123C23×C47—21no—
124C23×C47#4112yes—
125C23×C47#4112yes—
126C23×C47C2411yescharacteristic
127D4×C47—44no—
128D4×C47—44no—
129D4×C47—44no—
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×C47C2×D412yes—
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×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×Dic47—21no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—44no—
165C2×Dic47—44no—
166C2×Dic47C2×D412yes—
167C2×Dic47C2×D412yes—
168Dic94—44no—
169C22×C47—22no—
170C22×C47—22no—
171C22×C47—22no—
172C22×C47—22no—
173C22×C47—22no—
174C22×C47—22no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47—41no—
187C22×C47—41no—
188C22×C47—41no—
189C22×C47—41no—
190C22×C47C22×D411yescharacteristic
191C22×C47C2×#4111yescharacteristic
192C22×C47C2×#4111yescharacteristic
193C22×C47H(5,𝔽2)11yescharacteristic
194C22×C47H(5,𝔽2)11yescharacteristic
195C22×C47H(5,𝔽2)11yescharacteristic
196C22×C472−1+411yescharacteristic
197C4×C47—22no—
198C4×C47—41no—
199C4×C47—41no—
200C4×C47—41no—
201Dic47—22no—
202Dic47—22no—
203Dic47—41no—
204Dic47—41no—
205Dic47—41no—
206Dic47—41no—
207Dic47—41no—
208Dic47—41no—
209#2696—471nomaximal, Sylow
210C2×C47—42no—
211C2×C47—42no—
212C2×C47—81no—
213C2×C47#53511yescharacteristic
214C2×C47#53811yescharacteristic
215C2×C47#53911yescharacteristic
216C2×C47#54611yescharacteristic
217C2×C47#54811yescharacteristic
218C2×C47#55111yescharacteristic
219C2×C47#56211yescharacteristic
220C2×#123—471no—
221C2×C22⋊Q8—471no—
222#400—471no—
223#397—471no—
224#394—471no—
225#393—471no—
226#393—471no—
227#392D4711yescharacteristic
228#390—471no—
229#388—471no—
230#387—471no—
231#386—471no—
232#386—471no—
233#386—471no—
234#380—471no—
235C47#269611yescharacteristic, complemented, Sylow
236C22×Q8—471no—
237C22×D4C2×D4711yescharacteristic
238C22×D4C2×D4711yescharacteristic
239C22×D4C2×D4711yescharacteristic
240C23×C4—471no—
241C23×C4—471no—
242#123—944no—
243C22⋊Q8—944no—
244C2×C4⋊C4—471no—
245C2×C4⋊C4—471no—
246C2×C4⋊C4—471no—
247C2×C4⋊C4—471no—
248C2×C4⋊C4—471no—
249C2×C22⋊C4—471no—
250C2×C22⋊C4—471no—
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×C22⋊C4C2×D4711yescharacteristic
260C2×C22⋊C4C2×D4711yescharacteristic
261C2×C22⋊C4C2×D4711yescharacteristic
262C2×C42—471no—
263#95—471no—
264#95—471no—
265#95—471no—
266#95—471no—
267#95—471no—
268#95—471no—
269#95—471no—
270#95—471no—
271#95—471no—
272#95C2×D4711yescharacteristic
273C24C22×D4711yescharacteristic
274C24C22×D4711yescharacteristic
275C24C22×D4711yescharacteristic
276C2×Q8—942no—
277C2×Q8—1881no—
278C2×Q8—1881no—
279C2×D4—22no—
280C2×D4—22no—
281C2×D4—22no—
282C2×D4—22no—
283C2×D4—22no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C22×C4—471no—
289C22×C4—471no—
290C22×C4—471no—
291C22×C4—471no—
292C22×C4—471no—
293C22×C4—471no—
294C22×C4—471no—
295C22×C4—471no—
296C22×C4—942no—
297C22×C4—942no—
298C22×C4—942no—
299C22×C4—1881no—
300C22×C4—1881no—
301C22×C4—1881no—
302C22×C4C22×D4711yescharacteristic
303C22×C4C22×D4711yescharacteristic
304C22×C4C22×D4711yescharacteristic
305C22×C4C22×D4711yescharacteristic
306C4⋊C4—474no—
307C4⋊C4—942no—
308C4⋊C4—942no—
309C4⋊C4—942no—
310C4⋊C4—1881no—
311C22⋊C4—22no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—942no—
315C22⋊C4—942no—
316C22⋊C4—942no—
317C22⋊C4—942no—
318C22⋊C4—942no—
319C22⋊C4—1881no—
320C22⋊C4—1881no—
321C22⋊C4—1881no—
322C22⋊C4—1881no—
323C22⋊C4—1881no—
324C42—1881no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23#1062535212yes—
345C23#1062535212yes—
346C23C23×D4711yescharacteristic
347Q8—1884no—
348D4—44no—
349D4—44no—
350D4—44no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—472no—
363C2×C4—472no—
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—941no—
376C2×C4—941no—
377C2×C4—941no—
378C2×C4—941no—
379C2×C4—941no—
380C2×C4—941no—
381C2×C4—941no—
382C2×C4—941no—
383C2×C4—941no—
384C2×C4—941no—
385C2×C4—941no—
386C2×C4—1884no—
387C2×C4—1884no—
388C2×C4D4×D4712yes—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22C2×D4×D4711yescharacteristic
411C22C2×#1062535211yescharacteristic
412C22C2×#1062535211yescharacteristic
413C22#1309406911yescharacteristic
414C22#1309406911yescharacteristic
415C22#1309406911yescharacteristic
416C22#1309407111yescharacteristic
417C4—22no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—942no—
422C4—942no—
423C4—1881no—
424C4—1881no—
425C4—1881no—
426C4—1881no—
427C4—1881no—
428C4—1881no—
429C2—42no—
430C2—42no—
431C2—81no—
432C2#1568968611yescharacteristic
433C2#1568970811yescharacteristic
434C2#1568971811yescharacteristic
435C2#1568976011yescharacteristic
436C2#1568977911yescharacteristic
437C2#1568980411yescharacteristic
438C2#1568986811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#392C2
hypercenter#392D47
hypocenterC47#2696
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#13094005C2semidirect
2. C2×#13094001C2semidirect
3. #15689063C2semidirect
4. #15689051C2semidirect
5. #15689037C2semidirect
6. #15689035C2semidirect
7. #15689035C2semidirect
8. #15689026C2semidirect
9. #15689017C2semidirect
10. #15689005C2semidirect
11. #15689003C2semidirect
12. #15689003C2semidirect
13. #15689003C2semidirect
14. #15688981C2semidirect
103. Dic47⋊C4D4semidirect
235. C47#2696semidirect