Finite Group Databasebeta

← #26214929

Subgroups — #26214929

Order 12032.

938 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689251C212yesmaximal
2C42×Dic94C211yesmaximal, characteristic
3#20243262C212yesmaximal
4#20243260C212yesmaximal
5C8×Dic47⋊C4C212yesmaximal
6#20243242C211yesmaximal, characteristic
7#20243242C211yesmaximal, characteristic
8#20243241C211yesmaximal, characteristic
9#97×Dic47C211yesmaximal, characteristic
10#97×Dic47C211yesmaximal, characteristic
11C4×#97×C47C211yesmaximal, characteristic
12C2×C4×Dic94C412yes—
13C2×C4×Dic94C2211yescharacteristic
14#15689251C4116yescomplemented
15C2×C4⋊(C47⋊C8)C2212yes—
16C2×Dic47⋊C8C2212yes—
17C2×Dic47⋊C8C2212yes—
18C2×#13093935C2211yescharacteristic
19C2×#13093935C2211yescharacteristic
20C2×#13093934C2212yes—
21C2×#13093934C2212yes—
22C2×C8×Dic47C2212yes—
23C2×C8×Dic47C2212yes—
24C4×Dic47⋊C4C412yes—
25C4×Dic47⋊C4C412yes—
26C4×Dic47⋊C4C2211yescharacteristic
27C4×Dic47⋊C4C2211yescharacteristic
28C4×C4⋊Dic47C412yes—
29C4×C4⋊Dic47C2211yescharacteristic
30C42×Dic47C2211yescharacteristic
31C42×Dic47C2211yescharacteristic
32#15688878C2212yes—
33#15688877C2212yes—
34#15688877C2212yes—
35C2×#97×C47C2211yescharacteristic
36C2×#97×C47C2212yes—
37C2×#97×C47C2211yescharacteristic
38C2×C4×C8×C47C2212yes—
39C43×C47C2211yescharacteristic
40C22×Dic94C2×C411yescharacteristic
41C22×C47⋊C8C2312yes—
42C22×C47⋊C8C2312yes—
43C4×Dic94—28no—
44C4×Dic94C2×C418yes—
45C2×C4⋊Dic47C2×C412yes—
46C2×C4⋊Dic47C2×C411yescharacteristic
47C2×Dic47⋊C4C2×C412yes—
48C2×Dic47⋊C4C2×C411yescharacteristic
49C2×Dic47⋊C4C2×C411yescharacteristic
50C2×Dic47⋊C4C2×C412yes—
51C2×C4×Dic47C2×C412yes—
52C2×C4×Dic47C2×C412yes—
53C2×C4×Dic47C2×C412yes—
54C2×C4×Dic47C2×C412yes—
55C2×C4×Dic47C2311yescharacteristic
56C2×C4×Dic47C2311yescharacteristic
57C2×C4×Dic47C2311yescharacteristic
58C2×C4×Dic47C2311yescharacteristic
59C4⋊(C47⋊C8)C2×C418yes—
60Dic47⋊C8C2×C418yes—
61Dic47⋊C8C2×C418yes—
62#13093935—22no—
63#13093935—22no—
64#13093934—24no—
65#13093934C2×C418yes—
66C8×Dic47—24no—
67C8×Dic47C2×C418yes—
68C47⋊#95C2×C412yes—
69C47⋊#95C2×C412yes—
70C47⋊#95C2×C412yes—
71C22×C8×C47C2312yes—
72C22×C8×C47C2312yes—
73C2×C42×C47C2×C412yes—
74C2×C42×C47C2×C412yes—
75C2×C42×C47C2311yescharacteristic
76C2×C42×C47C2311yescharacteristic
77C2×C42×C47C2311yescharacteristic
78#97×C47—22no—
79#97×C47C2×C418yes—
80#97×C47Q814yescomplemented
81C4×C8×C47—24no—
82C22×C4×C47C22×C411yescharacteristic
83C22×C4×C47C22×C411yescharacteristic
84C22×C4×C47C22×C412yes—
85C22×C4×C47C22×C412yes—
86C22×C4×C47C2411yescharacteristic
87C22×Dic47C22×C412yes—
88C22×Dic47C22×C411yescharacteristic
89C22×Dic47C22×C411yescharacteristic
90C22×Dic47C22×C411yescharacteristic
91C22×Dic47C22×C412yes—
92C22×Dic47C22×C411yescharacteristic
93C2×Dic94—24no—
94C2×Dic94C4214yes—
95C2×C8×C47—22no—
96C2×C8×C47—22no—
97C2×C8×C47C22×C414yes—
98C2×C8×C47C22×C414yes—
99C2×C8×C47C2×Q814yes—
100C2×C8×C47#4114yes—
101C42×C47—24no—
102C42×C47—22no—
103C42×C47—42no—
104C42×C47C22×C414yes—
105C42×C47C2×Q812yes—
106C42×C47#4112yes—
107C4⋊Dic47—24no—
108C4⋊Dic47C4214yes—
109Dic47⋊C4—24no—
110Dic47⋊C4C4214yes—
111Dic47⋊C4C4214yes—
112Dic47⋊C4M1618yes—
113C4×Dic47—22no—
114C4×Dic47—22no—
115C4×Dic47—24no—
116C4×Dic47—24no—
117C4×Dic47—42no—
118C4×Dic47—42no—
119C4×Dic47C22×C414yes—
120C4×Dic47C22×C414yes—
121C2×C47⋊C8—22no—
122C2×C47⋊C8—22no—
123C2×C47⋊C8—22no—
124C2×C47⋊C8—22no—
125C2×C47⋊C8C22×C414yes—
126C2×C47⋊C8C22×C414yes—
127C23×C47C23×C411yescharacteristic
128C2×C4×C47—22no—
129C2×C4×C47—22no—
130C2×C4×C47—22no—
131C2×C4×C47—22no—
132C2×C4×C47—22no—
133C2×C4×C47—22no—
134C2×C4×C47C2×C4212yes—
135C2×C4×C47C2×C4212yes—
136C2×C4×C47C4×Q814yes—
137C2×C4×C47C2×M1614yes—
138C2×C4×C47C23×C412yes—
139C2×C4×C47C22×Q811yescharacteristic
140C2×C4×C47C2×#4112yes—
141C2×C4×C47C2×#4111yescharacteristic
142C2×Dic47—22no—
143C2×Dic47—22no—
144C2×Dic47—22no—
145C2×Dic47—22no—
146C2×Dic47—22no—
147C2×Dic47—22no—
148C2×Dic47—22no—
149C2×Dic47—22no—
150C2×Dic47C2×C4212yes—
151C2×Dic47C2×C4212yes—
152C2×Dic47C2×C4212yes—
153C2×Dic47C2×C4212yes—
154C2×Dic47C2×M1614yes—
155C2×Dic47C2×M1614yes—
156Dic94—28no—
157C8×C47—24no—
158C8×C47C4×Q818yescomplemented
159C47⋊C8—24no—
160C47⋊C8—24no—
161#20520—471nomaximal, Sylow
162C22×C47C22×C4211yescharacteristic
163C22×C47C2×C4×Q811yescharacteristic
164C22×C47C4×#4111yescharacteristic
165C22×C47C22×M1612yes—
166C22×C47#56812yes—
167C4×C47—22no—
168C4×C47—22no—
169C4×C47—24no—
170C4×C47—24no—
171C4×C47C2×C4×Q812yes—
172C4×C47C4×#4112yes—
173Dic47—22no—
174Dic47—22no—
175Dic47—22no—
176Dic47—24no—
177Dic47—42no—
178Dic47C4×M1614yes—
179C2×#446—472no—
180C42×Q8—471no—
181#1771—472no—
182#1771—472no—
183C8×C4⋊C4—472no—
184#1767—471no—
185#1767—471no—
186#1767—471no—
187C4×#97—471no—
188C4×#97—471no—
189C4×#97D4711yescharacteristic
190C2×C47C42×Q811yescharacteristic
191C2×C47C2×C4×M1611yescharacteristic
192C2×C47#287511yescharacteristic
193C2×C47Q8×M1612yes—
194C2×C47#297012yes—
195C2×C4×Q8—472no—
196C2×C4×Q8—471no—
197#446—4716no—
198C2×C4⋊C8—472no—
199C2×C4⋊C8—472no—
200C2×C4⋊C8—472no—
201C2×#97—472no—
202C2×#97—472no—
203C2×#97—471no—
204C2×#97—471no—
205C2×#97C2×D4711yescharacteristic
206C2×#97C2×D4711yescharacteristic
207C2×#97C2×D4712yes—
208C2×C4×C8—472no—
209C2×C4×C8—472no—
210C2×C4×C8C2×D4712yes—
211C4×C4⋊C4—472no—
212C4×C4⋊C4—472no—
213C4×C4⋊C4—472no—
214C4×C4⋊C4—471no—
215C4×C4⋊C4—471no—
216C4×C4⋊C4—471no—
217C43—471no—
218C43—471no—
219C43C2×D4711yescharacteristic
220#336—472no—
221#336—472no—
222#336—472no—
223C47#2052011yescharacteristic, complemented, Sylow
224C22×Q8—471no—
225C22×C8—472no—
226C22×C8—472no—
227C22×C8C22×D4712yes—
228C22×C8C22×D4712yes—
229C4×Q8—478no—
230C4×Q8—948no—
231C2×C4⋊C4—471no—
232C2×C4⋊C4—471no—
233C2×C4⋊C4—472no—
234C2×C4⋊C4—471no—
235C2×C4⋊C4—472no—
236C2×C4⋊C4—472no—
237C2×C42—471no—
238C2×C42—471no—
239C2×C42—472no—
240C2×C42—472no—
241C2×C42—471no—
242C2×C42—471no—
243C2×C42—472no—
244C2×C42—472no—
245C2×C42C4×D4712yes—
246C2×C42C4×D4712yes—
247C2×C42C22×D4711yescharacteristic
248C2×C42C22×D4711yescharacteristic
249C2×C42C22×D4711yescharacteristic
250C4⋊C8—478no—
251C4⋊C8—478no—
252C4⋊C8—478no—
253#97—22no—
254#97—478no—
255#97—944no—
256#97—942no—
257#97—942no—
258#97Dic9414yescomplemented
259#97C4×D4718yes—
260C4×C8—24no—
261C4×C8—478no—
262C4×C8—944no—
263#95—472no—
264#95—472no—
265#95—472no—
266C2×Q8—474no—
267C2×Q8—944no—
268C22×C4—471no—
269C22×C4—471no—
270C22×C4—471no—
271C22×C4—472no—
272C22×C4—471no—
273C22×C4—472no—
274C22×C4C2×C4×D4711yescharacteristic
275C22×C4C2×C4×D4711yescharacteristic
276C22×C4C2×C4×D4712yes—
277C22×C4C2×C4×D4712yes—
278C22×C4C23×D4711yescharacteristic
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—474no—
282C2×C8—474no—
283C2×C8—942no—
284C2×C8—942no—
285C2×C8—942no—
286C2×C8—942no—
287C2×C8C2×Dic9414yes—
288C2×C8C2×C4×D4714yes—
289C2×C8C2×C4×D4714yes—
290C2×C8#1062535014yes—
291C4⋊C4—474no—
292C4⋊C4—474no—
293C4⋊C4—474no—
294C4⋊C4—478no—
295C4⋊C4—944no—
296C4⋊C4—944no—
297C42—24no—
298C42—22no—
299C42—42no—
300C42—474no—
301C42—474no—
302C42—944no—
303C42—944no—
304C42—942no—
305C42—942no—
306C42—1882no—
307C42—1882no—
308C42C2×Dic9412yes—
309C42C2×C4×D4714yes—
310C42#1062535012yes—
311C23C22×C4×D4711yescharacteristic
312Q8—948no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—472no—
320C2×C4—474no—
321C2×C4—472no—
322C2×C4—472no—
323C2×C4—472no—
324C2×C4—474no—
325C2×C4—942no—
326C2×C4—942no—
327C2×C4—942no—
328C2×C4—942no—
329C2×C4—942no—
330C2×C4—942no—
331C2×C4—942no—
332C2×C4—942no—
333C2×C4C42×D4712yes—
334C2×C4C42×D4712yes—
335C2×C4C4×Dic9414yes—
336C2×C4M16×D4714yes—
337C2×C4C22×C4×D4712yes—
338C2×C4C22×Dic9411yescharacteristic
339C2×C4C2×#1062535012yes—
340C2×C4C2×#1062535011yescharacteristic
341C8—24no—
342C8—944no—
343C8—944no—
344C8C4×Dic9418yescomplemented
345C22C2×C42×D4711yescharacteristic
346C22C2×C4×Dic9411yescharacteristic
347C22C4×#1062535011yescharacteristic
348C22C2×M16×D4712yes—
349C22#1568988912yes—
350C4—22no—
351C4—22no—
352C4—24no—
353C4—24no—
354C4—474no—
355C4—942no—
356C4—942no—
357C4—942no—
358C4—944no—
359C4—1882no—
360C4C2×C4×Dic9412yes—
361C4C4×#1062535012yes—
362C2C42×Dic9411yescharacteristic
363C2C4×M16×D4711yescharacteristic
364C2#2025181711yescharacteristic
365C2M16×Dic9412yes—
366C2#2025239912yes—
subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC22×C47C22×C42
FittingC4×#97×C47C2
socle, prime radicalC23×C47C23×C4
cosocleC22×C4×C47C24
hypercenterC4×#97D47
hypocenterC47#20520
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C4×#97

Complements

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

NH ≅ G/Ntype
14. #15689251C4semidirect
80. #97×C47Q8semidirect
158. C8×C47C4×Q8semidirect
223. C47#20520semidirect
258. #97Dic94semidirect
344. C8C4×Dic94semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#156892512
C42×Dic942
#202432622
#202432602
C8×Dic47⋊C42
#202432422
#202432412
#97×Dic472
C4×#97×C472
#2052047