Finite Group Databasebeta

← #20249698

Subgroups — #20249698

Order 6016.

544 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094022C211yesmaximal, characteristic, complemented
2C2×#13094002C211yesmaximal, characteristic
3C2×#13094000C211yesmaximal, characteristic
4#15689058C211yesmaximal, characteristic
5#15689056C211yesmaximal, characteristic, complemented
6#15689054C211yesmaximal, characteristic, complemented
7#15689043C211yesmaximal, characteristic, complemented
8#15689042C211yesmaximal, characteristic, complemented
9#15689034C211yesmaximal, characteristic
10#15689014C211yesmaximal, characteristic
11#15689013C211yesmaximal, characteristic
12#15689009C211yesmaximal, characteristic, complemented
13#15689007C211yesmaximal, characteristic, complemented
14#15688994C211yesmaximal, characteristic
15C2×C4⋊Q8×C47C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18#13094022—24no—
19#13094002—24no—
20#13094000—24no—
21C2×C4⋊Dic47C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
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×C4×Dic47C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C22×Q8×C47C2211yescharacteristic
48C22×Q8×C47C2211yescharacteristic
49C4⋊Q8×C47—24no—
50C2×C4⋊C4×C47C2211yescharacteristic
51C2×C4⋊C4×C47C2211yescharacteristic
52C2×C4⋊C4×C47C2211yescharacteristic
53C2×C4⋊C4×C47C2211yescharacteristic
54C2×C42×C47C2211yescharacteristic
55C23×D47C2311yescharacteristic
56C2×Q8×C47—22no—
57C2×Q8×C47—22no—
58C2×Q8×C47—22no—
59C2×Q8×C47—22no—
60C2×Q8×C47—41no—
61C2×Q8×C47—41no—
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C22×Dic47C2311yescharacteristic
74C22×Dic47C2311yescharacteristic
75C22×Dic47C2311yescharacteristic
76C2×C4×D47—22no—
77C2×C4×D47—22no—
78C2×C4×D47—41no—
79C2×Dic94—22no—
80C2×Dic94—22no—
81C2×Dic94—41no—
82C4⋊C4×C47—22no—
83C4⋊C4×C47—22no—
84C4⋊C4×C47—22no—
85C4⋊C4×C47D414yes—
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—41no—
92(C2×D47)⋊C4Q814yescomplemented
93C4⋊Dic47—22no—
94Dic47⋊C4—22no—
95Dic47⋊C4—22no—
96Dic47⋊C4—22no—
97Dic47⋊C4—22no—
98Dic47⋊C4—22no—
99Dic47⋊C4—22no—
100Dic47⋊C4—41no—
101Dic47⋊C4D414yes—
102C4×Dic47—22no—
103C23×C47C2411yescharacteristic
104C22×D47—21no—
105C22×D47—21no—
106C22×D47—21no—
107C22×D47—21no—
108C22×D47—21no—
109C22×D47—21no—
110C22×D47C2×Q812yes—
111Q8×C47—44no—
112Q8×C47—44no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
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×C47C2×D412yes—
130C2×C4×C47C2×D412yes—
131C2×C4×C47C2×D412yes—
132C2×C4×C47C2×D412yes—
133C2×C4×C47C2×Q812yes—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—21no—
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×Dic47C2×D412yes—
153C2×Dic47C2×D412yes—
154C2×Dic47C2×Q812yes—
155C4×D47—44no—
156Dic94—44no—
157C22×C47C22×D411yescharacteristic
158C22×C47C22×D411yescharacteristic
159C22×C47C22×Q811yescharacteristic
160C22×C47H(5,𝔽2)11yescharacteristic
161C22×C472−1+411yescharacteristic
162C22×C472−1+411yescharacteristic
163C22×C472−1+411yescharacteristic
164C2×D47—22no—
165C2×D47—22no—
166C2×D47—22no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C4×C47—22no—
172C4×C47—22no—
173C4×C47—22no—
174C4×C47—22no—
175C4×C47—22no—
176C4×C47—41no—
177C4×C47—41no—
178Dic47—22no—
179Dic47—22no—
180Dic47—22no—
181Dic47—41no—
182Dic47—41no—
183Dic47—41no—
184Dic47—41no—
185#2677—471nomaximal, Sylow
186C2×C47#53611yescharacteristic
187C2×C47#53611yescharacteristic
188C2×C47#54411yescharacteristic
189C2×C47D4211yescharacteristic
190C2×C47D4×Q811yescharacteristic
191C2×C47D4×Q811yescharacteristic
192C2×C47#56311yescharacteristic
193D47—42no—
194C2×C4⋊Q8—471no—
195C2×C4⋊Q8D4711yescharacteristic, complemented
196C2×C22⋊Q8—471no—
197C2×C22⋊Q8—471no—
198#399—471no—
199#398—471no—
200#398—471no—
201#395—471no—
202#395—471no—
203#393—471no—
204#388—471no—
205#388—471no—
206#387—471no—
207#387—471no—
208#385—471no—
209C47#267711yescharacteristic, complemented, Sylow
210C22×Q8—471no—
211C22×Q8C2×D4711yescharacteristic
212C22×Q8C2×D4711yescharacteristic
213C23×C4—471no—
214C4⋊Q8—24no—
215C4⋊Q8—944no—
216C22⋊Q8—944no—
217C22⋊Q8—944no—
218C2×C4⋊C4—471no—
219C2×C4⋊C4—471no—
220C2×C4⋊C4—471no—
221C2×C4⋊C4—471no—
222C2×C4⋊C4—471no—
223C2×C4⋊C4—471no—
224C2×C4⋊C4—471no—
225C2×C4⋊C4—471no—
226C2×C4⋊C4—471no—
227C2×C4⋊C4C2×D4711yescharacteristic
228C2×C4⋊C4C2×D4711yescharacteristic
229C2×C4⋊C4C2×D4711yescharacteristic
230C2×C4⋊C4C2×D4711yescharacteristic
231C2×C22⋊C4—471no—
232C2×C22⋊C4—471no—
233C2×C22⋊C4—471no—
234C2×C22⋊C4—471no—
235C2×C22⋊C4—471no—
236C2×C22⋊C4—471no—
237C2×C42—471no—
238C2×C42C2×D4711yescharacteristic
239#95—471no—
240#95—471no—
241#95—471no—
242#95—471no—
243#95—471no—
244#95—471no—
245#95—471no—
246#95—471no—
247#95—471no—
248#95—471no—
249C24—471no—
250C2×Q8—22no—
251C2×Q8—22no—
252C2×Q8—22no—
253C2×Q8—22no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—942no—
257C2×Q8—942no—
258C2×Q8—1881no—
259C22×C4—471no—
260C22×C4—471no—
261C22×C4—471no—
262C22×C4—471no—
263C22×C4—471no—
264C22×C4—471no—
265C22×C4—471no—
266C22×C4—942no—
267C22×C4—942no—
268C22×C4—1881no—
269C22×C4C22×D4711yescharacteristic
270C22×C4C22×D4711yescharacteristic
271C22×C4C22×D4711yescharacteristic
272C22×C4C22×D4711yescharacteristic
273C22×C4C22×D4711yescharacteristic
274C22×C4C22×D4711yescharacteristic
275C22×C4C22×D4711yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—474no—
280C4⋊C4—942no—
281C4⋊C4—942no—
282C4⋊C4—942no—
283C4⋊C4—942no—
284C4⋊C4—942no—
285C4⋊C4—942no—
286C4⋊C4—942no—
287C4⋊C4—1881no—
288C4⋊C4C22⋊D4714yes—
289C22⋊C4—474no—
290C22⋊C4—942no—
291C22⋊C4—942no—
292C22⋊C4—942no—
293C22⋊C4—942no—
294C22⋊C4—1881no—
295C42—22no—
296C42—942no—
297C23—472no—
298C23—941no—
299C23—941no—
300C23—941no—
301C23—941no—
302C23—941no—
303C23—941no—
304C23C23×D4711yescharacteristic
305Q8—44no—
306Q8—44no—
307Q8—1884no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—472no—
325C2×C4—472no—
326C2×C4—472no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4—941no—
333C2×C4—941no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—941no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—941no—
344C2×C4—941no—
345C2×C4—1884no—
346C2×C4D4×D4712yes—
347C2×C4Q8×D4712yes—
348C2×C4C2×C22⋊D4712yes—
349C2×C4C2×C22⋊D4712yes—
350C2×C4C2×C22⋊D4712yes—
351C22—942no—
352C22—942no—
353C22—942no—
354C22—1881no—
355C22—1881no—
356C22—1881no—
357C22—1881no—
358C22C2×D4×D4711yescharacteristic
359C22C22×C22⋊D4711yescharacteristic
360C22C2×Q8×D4711yescharacteristic
361C22#1309406911yescharacteristic
362C22#1309407211yescharacteristic
363C22#1309407211yescharacteristic
364C22#1309407211yescharacteristic
365C4—22no—
366C4—22no—
367C4—22no—
368C4—22no—
369C4—22no—
370C4—41no—
371C4—41no—
372C4—942no—
373C4—942no—
374C4—942no—
375C4—1881no—
376C4—1881no—
377C4—1881no—
378C4—1881no—
379C2—1882no—
380C2#1568969711yescharacteristic
381C2#1568969811yescharacteristic
382C2#1568975011yescharacteristic
383C2D4×C22⋊D4711yescharacteristic
384C2Q8×C22⋊D4711yescharacteristic
385C2#1568978811yescharacteristic
386C2#1568987211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C4⋊Q8×C47C2
hypercenterC2×C4⋊Q8D47
hypocenterC47#2677
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#13094022C2semidirect
5. #15689056C2semidirect
6. #15689054C2semidirect
7. #15689043C2semidirect
8. #15689042C2semidirect
12. #15689009C2semidirect
13. #15689007C2semidirect
15. C2×C4⋊Q8×C47C2semidirect
92. (C2×D47)⋊C4Q8semidirect
195. C2×C4⋊Q8D47semidirect
209. C47#2677semidirect