Finite Group Databasebeta

← #20250082

Subgroups — #20250082

Order 6016.

554 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094009C211yesmaximal, characteristic, complemented
2C2×#13094006C211yesmaximal, characteristic, complemented
3#15689058C211yesmaximal, characteristic, complemented
4#15689053C211yesmaximal, characteristic, complemented
5#15689051C211yesmaximal, characteristic, complemented
6#15689038C211yesmaximal, characteristic, complemented
7#15689032C211yesmaximal, characteristic
8#15689023C211yesmaximal, characteristic, complemented
9#15689013C211yesmaximal, characteristic, complemented
10#15689001C211yesmaximal, characteristic, complemented
11#15688999C211yesmaximal, characteristic, complemented
12#15688994C211yesmaximal, characteristic, complemented
13#15688987C211yesmaximal, characteristic, complemented
14#15688980C211yesmaximal, characteristic, complemented
15C47×#396C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21#13094009—24no—
22#13094006—24no—
23C2×C4⋊Dic47C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic
30C2×(C2×D47)⋊C4C2211yescharacteristic
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×C4×Dic47C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C24×C47C2311yescharacteristic
54C23×D47C2311yescharacteristic
55C23×D47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—22no—
63C2×C22⋊D47—22no—
64C2×C22⋊D47—22no—
65C2×C22⋊D47—41no—
66C2×C22⋊D47—41no—
67C2×C22⋊D47—41no—
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C22×Dic47C2311yescharacteristic
74C2×D188—22no—
75C2×D188—22no—
76C2×D188—41no—
77C2×C4×D47—22no—
78C2×C4×D47—22no—
79C2×C4×D47—22no—
80C2×C4×D47—41no—
81C2×C4×D47—41no—
82C2×C4×D47—41no—
83C4⋊C4×C47—22no—
84C4⋊C4×C47—41no—
85C4⋊C4×C47—41no—
86C22⋊C4×C47—22no—
87C22⋊C4×C47—41no—
88C22⋊C4×C47—41no—
89C22⋊Dic47—22no—
90C22⋊Dic47—41no—
91(C2×D47)⋊C4—22no—
92(C2×D47)⋊C4—22no—
93(C2×D47)⋊C4—22no—
94(C2×D47)⋊C4—41no—
95(C2×D47)⋊C4—41no—
96(C2×D47)⋊C4—41no—
97(C2×D47)⋊C4—41no—
98(C2×D47)⋊C4D414yescomplemented
99C4⋊Dic47—22no—
100Dic47⋊C4—22no—
101Dic47⋊C4—22no—
102Dic47⋊C4—41no—
103Dic47⋊C4—41no—
104C4×Dic47—22no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47C2411yescharacteristic
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×D47C2×D412yes—
126C22×D47#4112yes—
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×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47C2×D412yes—
145C22⋊D47—44no—
146C22⋊D47—44no—
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×Dic47C2×D412yes—
164C2×Dic47#4112yes—
165D188—44no—
166C4×D47—44no—
167C4×D47—44no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47C22×D411yescharacteristic
176C22×C47C2×#4111yescharacteristic
177C22×C47C2×#4111yescharacteristic
178C22×C47H(5,𝔽2)11yescharacteristic
179C22×C47H(5,𝔽2)11yescharacteristic
180C22×C47H(5,𝔽2)11yescharacteristic
181C22×C472−1+411yescharacteristic
182C2×D47—22no—
183C2×D47—22no—
184C2×D47—22no—
185C2×D47—22no—
186C2×D47—22no—
187C2×D47—22no—
188C2×D47—41no—
189C2×D47—41no—
190C2×D47—41no—
191C2×D47—41no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—41no—
195C2×D47—41no—
196C4×C47—22no—
197C4×C47—41no—
198C4×C47—41no—
199C4×C47—41no—
200C4×C47—41no—
201C4×C47—41no—
202Dic47—22no—
203Dic47—22no—
204Dic47—41no—
205Dic47—41no—
206Dic47—41no—
207Dic47—41no—
208#2706—471nomaximal, Sylow
209C2×C47—81no—
210C2×C47#53511yescharacteristic
211C2×C47#53911yescharacteristic
212C2×C47#54011yescharacteristic
213C2×C47#54611yescharacteristic
214C2×C47#54711yescharacteristic
215C2×C47#55111yescharacteristic
216C2×C47#56211yescharacteristic
217D47—42no—
218D47—42no—
219C2×#123—471no—
220C2×#123—471no—
221#399—471no—
222#398—471no—
223#397—471no—
224#396D4711yescharacteristic, complemented
225#394—471no—
226#392—471no—
227#390—471no—
228#388—471no—
229#386—471no—
230#386—471no—
231#385—471no—
232#382—471no—
233#380—471no—
234C47#270611yescharacteristic, complemented, Sylow
235C22×D4—471no—
236C22×D4—471no—
237C22×D4—471no—
238C23×C4—471no—
239C23×C4—471no—
240#123—944no—
241#123—944no—
242C2×C4⋊C4—471no—
243C2×C4⋊C4—471no—
244C2×C4⋊C4—471no—
245C2×C4⋊C4—471no—
246C2×C4⋊C4—471no—
247C2×C4⋊C4C2×D4711yescharacteristic
248C2×C4⋊C4C2×D4711yescharacteristic
249C2×C4⋊C4C2×D4711yescharacteristic
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⋊C4—471no—
260C2×C22⋊C4C2×D4711yescharacteristic
261C2×C22⋊C4C2×D4711yescharacteristic
262C2×C22⋊C4C2×D4711yescharacteristic
263C2×C42—471no—
264#95—471no—
265#95—471no—
266#95—471no—
267#95—471no—
268#95—471no—
269#95—471no—
270#95—471no—
271#95C2×D4711yescharacteristic
272C24—471no—
273C24—471no—
274C24C22×D4711yescharacteristic
275C2×D4—942no—
276C2×D4—942no—
277C2×D4—942no—
278C2×D4—942no—
279C2×D4—942no—
280C2×D4—1881no—
281C2×D4—1881no—
282C2×D4—1881no—
283C2×D4—1881no—
284C22×C4—471no—
285C22×C4—471no—
286C22×C4—471no—
287C22×C4—471no—
288C22×C4—471no—
289C22×C4—471no—
290C22×C4—942no—
291C22×C4—942no—
292C22×C4—942no—
293C22×C4—1881no—
294C22×C4—1881no—
295C22×C4—1881no—
296C22×C4C22×D4711yescharacteristic
297C22×C4C22×D4711yescharacteristic
298C22×C4C22×D4711yescharacteristic
299C22×C4C22×D4711yescharacteristic
300C22×C4C22×D4711yescharacteristic
301C22×C4C22×D4711yescharacteristic
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—942no—
306C4⋊C4—942no—
307C4⋊C4—942no—
308C4⋊C4—1881no—
309C4⋊C4—1881no—
310C22⋊C4—22no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—474no—
314C22⋊C4—942no—
315C22⋊C4—942no—
316C22⋊C4—942no—
317C22⋊C4—942no—
318C22⋊C4—1881no—
319C22⋊C4—1881no—
320C22⋊C4—1881no—
321C22⋊C4—1881no—
322C22⋊C4—1881no—
323C42—942no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—472no—
332C23—472no—
333C23—941no—
334C23—941no—
335C23—941no—
336C23—941no—
337C23—941no—
338C23—941no—
339C23—941no—
340C23—941no—
341C23—941no—
342C23—941no—
343C23—941no—
344C23—941no—
345C23C23×D4711yescharacteristic
346D4—1884no—
347D4—1884no—
348D4—1884no—
349C2×C4—21no—
350C2×C4—21no—
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—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—472no—
367C2×C4—472no—
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—1884no—
385C2×C4—1884no—
386C2×C4D4×D4712yes—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—942no—
395C22—942no—
396C22—942no—
397C22—942no—
398C22—942no—
399C22—942no—
400C22—1881no—
401C22—1881no—
402C22—1881no—
403C22—1881no—
404C22—1881no—
405C22—1881no—
406C22—1881no—
407C22—1881no—
408C22C2×D4×D4711yescharacteristic
409C22#41×D4711yescharacteristic
410C22#41×D4711yescharacteristic
411C22#1309406911yescharacteristic
412C22#1309406911yescharacteristic
413C22#1309407011yescharacteristic
414C22#1309407211yescharacteristic
415C4—22no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—942no—
422C4—942no—
423C4—1881no—
424C4—1881no—
425C4—1881no—
426C4—1881no—
427C2—81no—
428C2—1882no—
429C2—1882no—
430C2#1568968911yescharacteristic
431C2#1568971911yescharacteristic
432C2#1568972311yescharacteristic
433C2#1568976211yescharacteristic
434C2#1568977511yescharacteristic
435C2#1568979811yescharacteristic
436C2#1568986911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#396C2
hypercenter#396D47
hypocenterC47#2706
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#13094009C2semidirect
2. C2×#13094006C2semidirect
3. #15689058C2semidirect
4. #15689053C2semidirect
5. #15689051C2semidirect
6. #15689038C2semidirect
8. #15689023C2semidirect
9. #15689013C2semidirect
10. #15689001C2semidirect
11. #15688999C2semidirect
12. #15688994C2semidirect
13. #15688987C2semidirect
14. #15688980C2semidirect
15. C47×#396C2semidirect
98. (C2×D47)⋊C4D4semidirect
224. #396D47semidirect
234. C47#2706semidirect