Finite Group Databasebeta

← #26200144

Subgroups — #26200144

Order 12032.

650 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253506C212yesmaximal, complemented
2C2×C8×Dic94C211yesmaximal, characteristic, complemented
3#20242801C214yesmaximal, complemented
4#20242789C212yesmaximal, complemented
5#20242745C212yesmaximal, complemented
6#20242151C211yesmaximal, characteristic, complemented
7#20242083C212yesmaximal, complemented
8C47×#3169C211yesmaximal, characteristic
9C2×C4×Dic94C2211yescharacteristic
10#15689434—22no—
11#15689415C2214yes—
12#15689320C2214yes—
13#15689261—22no—
14C8×Dic94—21no—
15C8×Dic94—21no—
16C8×Dic94C2212yes—
17C8×Dic94C2212yes—
18#15689223—24no—
19#15689180C2212yes—
20C2×C4⋊(C47⋊C8)C2211yescharacteristic
21C2×Dic47⋊C8—21no—
22C2×C8×Dic47—21no—
23#15688876C2212yes—
24#15688874C2212yes—
25#15688872C2214yes—
26#15688867C2214yes—
27C47×#532C2212yes—
28C47×#500C2211yescharacteristic
29C47×#493C2211yescharacteristic
30C47×#486C2212yes—
31C47×#466—21no—
32C47×#466—21no—
33C4×D8×C47—21no—
34C4×D8×C47—21no—
35C2×C4×C8×C47C2211yescharacteristic
36C22×Dic94D411yescharacteristic
37C2×#10625335—24no—
38C22×C47⋊C8—21no—
39C4×Dic94—21no—
40C4×Dic94—21no—
41C4×Dic94D412yes—
42C4×Dic94C2312yes—
43C2×C4⋊Dic47D411yescharacteristic
44C2×Dic47⋊C4—21no—
45C2×C4×Dic47—21no—
46#13093957—24no—
47C4⋊(C47⋊C8)—21no—
48C4⋊(C47⋊C8)C2312yes—
49C4⋊(C47⋊C8)C2314yes—
50Dic47⋊C8—22no—
51Dic47⋊C8—22no—
52#13093947—24no—
53#13093945—24no—
54C22⋊(C47⋊C8)—22no—
55#13093935—22no—
56C8×Dic47—22no—
57C8×Dic47—22no—
58C2×#41×C47—22no—
59C2×D8×C47—21no—
60C2×D8×C47—21no—
61C22×C8×C47D411yescharacteristic
62C22×C8×C47D411yescharacteristic
63C4⋊Q8×C47C2312yes—
64#127×C47C2312yes—
65#124×C47—22no—
66#121×C47—22no—
67#121×C47—22no—
68C4×D4×C47—22no—
69C4×D4×C47—22no—
70C2×C42×C47C2311yescharacteristic
71#107×C47—21no—
72#107×C47—21no—
73#102×C47—22no—
74#102×C47—22no—
75C4×C8×C47D411yescharacteristic
76C4×C8×C47D411yescharacteristic
77C4×C8×C47C2311yescharacteristic
78C4×C8×C47C2311yescharacteristic
79#41×C47—84no—
80C2×Q8×C47—22no—
81C2×D4×C47—22no—
82C2×D4×C47—22no—
83C2×D4×C47—22no—
84C2×D4×C47—42no—
85C22×C4×C47—42no—
86C22×C4×C47C2×D411yescharacteristic
87C22×C4×C47C2×D411yescharacteristic
88C22×C4×C47#4111yescharacteristic
89C22×Dic47—21no—
90C22×Dic47—21no—
91C2×Dic94—21no—
92C2×Dic94—24no—
93C2×Dic94C2×D412yes—
94D8×C47—42no—
95D8×C47—42no—
96C2×C8×C47—22no—
97C2×C8×C47—41no—
98C2×C8×C47C2×D411yescharacteristic
99C2×C8×C47C2×D411yescharacteristic
100C2×C8×C47C2×D411yescharacteristic
101C2×C8×C47C2×D411yescharacteristic
102C4⋊C4×C47—22no—
103C4⋊C4×C47—22no—
104C22⋊C4×C47—42no—
105C22⋊C4×C47—42no—
106C42×C47C2×D411yescharacteristic
107C42×C47C2×D411yescharacteristic
108C42×C47#4111yescharacteristic
109C42×C47C2411yescharacteristic
110#10625335—48no—
111C4⋊Dic47—21no—
112C4⋊Dic47C2×D412yes—
113Dic47⋊C4—22no—
114Dic47⋊C4—22no—
115C4×Dic47—22no—
116C4×Dic47—22no—
117C2×C47⋊C8—22no—
118C2×C47⋊C8—24no—
119C2×C47⋊C8—42no—
120C23×C47—42no—
121C23×C47#12111yescharacteristic
122Q8×C47—82no—
123D4×C47—44no—
124D4×C47—42no—
125D4×C47—42no—
126D4×C47—82no—
127D4×C47—84no—
128C2×C4×C47—22no—
129C2×C4×C47—22no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—42no—
133C2×C4×C47—84no—
134C2×C4×C47#12111yescharacteristic
135C2×C4×C47#12111yescharacteristic
136C2×C4×C47#12111yescharacteristic
137C2×C4×C47C22×D411yescharacteristic
138C2×C4×C47C22×D411yescharacteristic
139C2×C4×C47C2×#4111yescharacteristic
140C2×Dic47—24no—
141C2×Dic47—22no—
142C2×Dic47—22no—
143C2×Dic47—42no—
144Dic94—24no—
145Dic94—22no—
146Dic94#13514yes—
147C8×C47—21no—
148C8×C47—21no—
149C8×C47—21no—
150C8×C47#13712yes—
151C47⋊C8—44no—
152C47⋊C8—42no—
153#19264—471nomaximal, Sylow
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—82no—
157C22×C47—82no—
158C22×C47—82no—
159C22×C47#47212yes—
160C22×C47C2×#12111yescharacteristic
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—21no—
165C4×C47—82no—
166C4×C47C2×#13512yes—
167C4×C47C2×#13711yescharacteristic
168C4×C47#57511yescharacteristic
169Dic47—24no—
170Dic47—42no—
171#3169D4711yescharacteristic
172#3112—472no—
173C2×C8×Q8—471no—
174#1678—474no—
175#1676—472no—
176#1668—472no—
177#1568—471no—
178#1551—472no—
179C2×C47—22no—
180C2×C47—162no—
181C2×C47#303711yescharacteristic
182C2×C47#305011yescharacteristic
183C2×C47C2×#47211yescharacteristic
184#532C2×D4712yes—
185C2×C4×Q8—471no—
186#500C2×D4711yescharacteristic
187#493C2×D4711yescharacteristic
188#486C2×D4712yes—
189#480—942no—
190#477—474no—
191#466—21no—
192#466—21no—
193#460—474no—
194#448—942no—
195C8×Q8—472no—
196C8×Q8—472no—
197C8×Q8—941no—
198C8×Q8—941no—
199#440—944no—
200C4×D8—21no—
201C4×D8—21no—
202#432—472no—
203C2×C4⋊C8—471no—
204C2×C4⋊C8—941no—
205C2×C4×C8—941no—
206C2×C4×C8C2×D4711yescharacteristic
207#335—472no—
208#334—472no—
209#333—474no—
210#331—474no—
211C47#1926411yescharacteristic, complemented, Sylow
212C2×#41—22no—
213C22×Q8—471no—
214C2×SD16—944no—
215C2×D8—21no—
216C2×D8—21no—
217C22×C8—941no—
218C22×C8C22⋊D4711yescharacteristic
219C22×C8C22⋊D4711yescharacteristic
220C4⋊Q8C22×D4712yes—
221#127C22×D4712yes—
222#124—22no—
223#121—22no—
224#121—22no—
225C4×Q8—472no—
226C4×Q8—472no—
227C4×Q8—941no—
228C4×Q8—941no—
229C4×D4—22no—
230C4×D4—22no—
231C2×C4⋊C4—471no—
232C2×C4⋊C4—941no—
233C2×C42—941no—
234C2×C42C22×D4711yescharacteristic
235#107—21no—
236#107—21no—
237#107—944no—
238C4⋊C8—472no—
239C4⋊C8—474no—
240C4⋊C8—942no—
241C4⋊C8—942no—
242C4⋊C8—941no—
243#103—944no—
244#102—22no—
245#102—22no—
246#102—944no—
247C22⋊C8—942no—
248#97—942no—
249C4×C8—942no—
250C4×C8—942no—
251C4×C8C22⋊D4711yescharacteristic
252C4×C8C22⋊D4711yescharacteristic
253C4×C8C22×D4711yescharacteristic
254C4×C8C22×D4711yescharacteristic
255#41—84no—
256C2×Q8—22no—
257C2×Q8—472no—
258C2×Q8—944no—
259C2×Q8—941no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—42no—
264C22×C4—42no—
265C22×C4—941no—
266C22×C4—941no—
267C22×C4D4×D4711yescharacteristic
268C22×C4#1062535211yescharacteristic
269C22×C4C2×C22⋊D4711yescharacteristic
270SD16—1888no—
271D8—42no—
272D8—42no—
273C2×C8—22no—
274C2×C8—41no—
275C2×C8—944no—
276C2×C8—942no—
277C2×C8—1882no—
278C2×C8C2×C22⋊D4711yescharacteristic
279C2×C8C2×C22⋊D4711yescharacteristic
280C2×C8C2×C22⋊D4711yescharacteristic
281C2×C8C2×C22⋊D4711yescharacteristic
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—472no—
285C4⋊C4—942no—
286C4⋊C4—941no—
287C4⋊C4—942no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C42—942no—
291C42—942no—
292C42D4×D4711yescharacteristic
293C42#1062535211yescharacteristic
294C42C2×C22⋊D4711yescharacteristic
295C42C23×D4711yescharacteristic
296C23—42no—
297C23#1309399511yescharacteristic
298Q8—82no—
299Q8—474no—
300Q8—944no—
301Q8—942no—
302D4—44no—
303D4—42no—
304D4—42no—
305D4—82no—
306D4—84no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—84no—
313C2×C4—944no—
314C2×C4—942no—
315C2×C4—942no—
316C2×C4—1882no—
317C2×C4#1309399511yescharacteristic
318C2×C4#1309399511yescharacteristic
319C2×C4#1309399511yescharacteristic
320C2×C4C2×D4×D4711yescharacteristic
321C2×C4C22×C22⋊D4711yescharacteristic
322C2×C4C2×#1062535211yescharacteristic
323C8—21no—
324C8—21no—
325C8—21no—
326C8—1884no—
327C8—1882no—
328C8#1309405412yes—
329C22—21no—
330C22—21no—
331C22—82no—
332C22—82no—
333C22—82no—
334C22#1568939012yes—
335C22C2×#1309399511yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—82no—
341C4—944no—
342C4—1882no—
343C4#135×D4712yes—
344C4C2×#1309405411yescharacteristic
345C4#1568992111yescharacteristic
346C2—22no—
347C2—162no—
348C2#2025285611yescharacteristic
349C2#2025296511yescharacteristic
350C2C2×#1568939011yescharacteristic
subgroupG/H
centerC22C2×#13093995
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
Fitting, prime radicalC47×#3169C2
socleC22×C47C2×#121
hypercenter#3169D47
hypocenterC47#19264
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #20253506C2semidirect
2. C2×C8×Dic94C2semidirect
3. #20242801C2semidirect
4. #20242789C2semidirect
5. #20242745C2semidirect
6. #20242151C2semidirect
7. #20242083C2semidirect
211. C47#19264semidirect

Maximal subgroups

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

subgroupindex
#202535062
C2×C8×Dic942
#202428012
#202427892
#202427452
#202421512
#202420832
C47×#31692
#1926447