Finite Group Databasebeta

← #26115385

Subgroups — #26115385

Order 12032.

486 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251765C211yesmaximal, characteristic
2#20243539C211yesmaximal, characteristic
3#20243243C211yesmaximal, characteristic
4C2×#15688870C211yesmaximal, characteristic
5C2×#15688869C211yesmaximal, characteristic
6C2×#15688868C211yesmaximal, characteristic
7C2×C47×#332C211yesmaximal, characteristic
8C2×#13094024C2211yescharacteristic
9C2×C4⋊(C47⋊C8)C2211yescharacteristic
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11C2×Dic47⋊C8—22no—
12C2×#13093934—21no—
13#15689030—21no—
14#15689030—21no—
15#15689028—22no—
16#15688988C414yes—
17C42×Dic47C2211yescharacteristic
18#15688877—21no—
19#15688870—22no—
20#15688869—22no—
21#15688868—22no—
22C2×C4⋊Q8×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C47×#332—22no—
26C22×Dic94—21no—
27C22×C47⋊C8—21no—
28C22×C47⋊C8—21no—
29#13094024—21no—
30#13094024—21no—
31#13094024—21no—
32#13094024—21no—
33C2×C4⋊Dic47—21no—
34C2×C4⋊Dic47C2×C412yes—
35C2×C4×Dic47C2×C412yes—
36C2×C4×Dic47D412yes—
37C2×C4×Dic47D411yescharacteristic
38C2×C4×Dic47D411yescharacteristic
39C4⋊(C47⋊C8)—21no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)D412yes—
43Dic47⋊C8—44no—
44#13093934—42no—
45C47⋊#95—24no—
46C47⋊#95—24no—
47C22×Q8×C47—21no—
48C22×C8×C47—21no—
49C22×C8×C47—21no—
50C4⋊Q8×C47—21no—
51C4⋊Q8×C47—21no—
52C4⋊Q8×C47—21no—
53C4⋊Q8×C47—21no—
54C2×C4⋊C4×C47—21no—
55C2×C4⋊C4×C47C2×C412yes—
56C2×C42×C47C2311yescharacteristic
57C4⋊C8×C47—21no—
58C4⋊C8×C47—21no—
59C4⋊C8×C47—21no—
60C4⋊C8×C47D412yes—
61C2×Q8×C47—41no—
62C2×Q8×C47—41no—
63C2×Q8×C47—41no—
64C2×Q8×C47—41no—
65C2×Q8×C47—41no—
66C2×Q8×C47—41no—
67C22×C4×C47—22no—
68C22×C4×C47C22×C411yescharacteristic
69C22×C4×C47C2×D411yescharacteristic
70C22×C4×C47C2×D411yescharacteristic
71C22×Dic47—22no—
72C22×Dic47C22⋊C412yes—
73C22×Dic47C22⋊C412yes—
74C2×Dic94—41no—
75C2×Dic94—41no—
76C2×Dic94—42no—
77C2×Dic94—42no—
78C2×C8×C47—22no—
79C2×C8×C47—41no—
80C2×C8×C47—41no—
81C2×C8×C47—41no—
82C2×C8×C47—42no—
83C4⋊C4×C47—22no—
84C4⋊C4×C47—22no—
85C4⋊C4×C47—41no—
86C4⋊C4×C47—41no—
87C42×C47C2×D411yescharacteristic
88C42×C47C2×D411yescharacteristic
89C42×C47#4111yescharacteristic
90C42×C47#4111yescharacteristic
91C4⋊Dic47—22no—
92C4⋊Dic47—22no—
93C4⋊Dic47—41no—
94C4⋊Dic47—41no—
95C4×Dic47—21no—
96C4×Dic47—21no—
97C4×Dic47—21no—
98C4×Dic47—22no—
99C4×Dic47—22no—
100C4×Dic47—21no—
101C4×Dic47—24no—
102C2×C47⋊C8—22no—
103C2×C47⋊C8—41no—
104C2×C47⋊C8—41no—
105C2×C47⋊C8—41no—
106C2×C47⋊C8—42no—
107C23×C47C2×C22⋊C411yescharacteristic
108Q8×C47—81no—
109Q8×C47—81no—
110Q8×C47—81no—
111Q8×C47—81no—
112C2×C4×C47—22no—
113C2×C4×C47—42no—
114C2×C4×C47—42no—
115C2×C4×C47—42no—
116C2×C4×C47C4×D411yescharacteristic
117C2×C4×C47C4×D411yescharacteristic
118C2×C4×C47#12111yescharacteristic
119C2×C4×C47#12111yescharacteristic
120C2×C4×C47#12411yescharacteristic
121C2×C4×C47#12711yescharacteristic
122C2×C4×C47#13511yescharacteristic
123C2×C4×C47#13511yescharacteristic
124C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C47AGL(1,ℤ/8)12yes—
126C2×C4×C47#13711yescharacteristic
127C2×C4×C47#13712yes—
128C2×Dic47—22no—
129C2×Dic47—22no—
130C2×Dic47—22no—
131C2×Dic47—22no—
132C2×Dic47—22no—
133C2×Dic47—42no—
134C2×Dic47—44no—
135C2×Dic47#10114yes—
136Dic94—82no—
137Dic94—81no—
138Dic94—81no—
139C8×C47—42no—
140C8×C47—81no—
141C47⋊C8—42no—
142C47⋊C8—81no—
143#9708—471nomaximal, Sylow
144C22×C47#39011yescharacteristic
145C22×C47C2×#10112yes—
146C22×C47#41611yescharacteristic
147C22×C47#41711yescharacteristic
148C22×C47#41712yes—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—82no—
152C4×C47#46311yescharacteristic
153C4×C47#46311yescharacteristic
154C4×C47#46411yescharacteristic
155C4×C47#46411yescharacteristic
156C4×C47#48912yes—
157C4×C47#49611yescharacteristic
158C4×C47#49711yescharacteristic
159Dic47—24no—
160Dic47—42no—
161Dic47—82no—
162#2862—471no—
163#1842—471no—
164#1767—471no—
165C2×#332—471no—
166C2×#332—471no—
167C2×#332—471no—
168C2×#332D4711yescharacteristic
169C2×C47#155212yes—
170C2×C47#156112yes—
171C2×C47#195911yescharacteristic
172C2×C47#196611yescharacteristic
173C2×C47#198311yescharacteristic
174C2×C4⋊Q8—471no—
175C2×C4⋊Q8C2×D4711yescharacteristic
176C2×C4⋊C8—471no—
177C2×C4⋊C8—471no—
178C2×C4⋊C8—942no—
179C2×C4⋊C8C2×D4711yescharacteristic
180C2×C4⋊C8C2×D4711yescharacteristic
181C2×#97—941no—
182#391—942no—
183#391—941no—
184#391—941no—
185#382—474no—
186C43—471no—
187#336—941no—
188#332—22no—
189#332—942no—
190#332—942no—
191#332—942no—
192C47#970811yescharacteristic, complemented, Sylow
193C22×Q8—21no—
194C22×Q8—941no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—941no—
198C22×C8—941no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—941no—
204C4⋊Q8—941no—
205C4⋊Q8—941no—
206C4⋊Q8—941no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—472no—
209C2×C4⋊C4—941no—
210C2×C4⋊C4C4×D4712yes—
211C2×C42—472no—
212C2×C42—471no—
213C2×C42—471no—
214C2×C42—472no—
215C2×C42C22×D4711yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—472no—
220C4⋊C8—941no—
221C4⋊C8—941no—
222C4⋊C8—941no—
223C4⋊C8—1884no—
224C4⋊C8C22⋊D4712yes—
225#97—1882no—
226#95—944no—
227#95—944no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—1881no—
235C2×Q8—1881no—
236C2×Q8—1882no—
237C2×Q8—1882no—
238C22×C4—22no—
239C22×C4—472no—
240C22×C4—472no—
241C22×C4—942no—
242C22×C4C2×C4×D4711yescharacteristic
243C22×C4D4×D4711yescharacteristic
244C22×C4D4×D4711yescharacteristic
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—42no—
250C2×C8—942no—
251C2×C8—1881no—
252C2×C8—1882no—
253C2×C8—1881no—
254C2×C8—1881no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—942no—
260C4⋊C4—942no—
261C4⋊C4—1881no—
262C4⋊C4—1881no—
263C42—944no—
264C42—941no—
265C42—941no—
266C42—941no—
267C42—942no—
268C42—941no—
269C42—942no—
270C42#1062535011yescharacteristic
271C42D4×D4711yescharacteristic
272C42#1062535211yescharacteristic
273C42C2×C22⋊D4711yescharacteristic
274C23C22⋊C4×D4711yescharacteristic
275Q8—81no—
276Q8—81no—
277Q8—81no—
278Q8—81no—
279Q8—3762no—
280Q8—3761no—
281Q8—3761no—
282C2×C4—22no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—474no—
287C2×C4—942no—
288C2×C4—942no—
289C2×C4—942no—
290C2×C4—942no—
291C2×C4—942no—
292C2×C4—1882no—
293C2×C4—1884no—
294C2×C4(C22⋊D47)⋊C411yescharacteristic
295C2×C4C4×C22⋊D4711yescharacteristic
296C2×C4#1309399611yescharacteristic
297C2×C4#1309399711yescharacteristic
298C2×C4#1309401011yescharacteristic
299C2×C4#1309402011yescharacteristic
300C2×C4#1309404311yescharacteristic
301C2×C4#1309404511yescharacteristic
302C2×C4#1309404811yescharacteristic
303C2×C4#1309405112yes—
304C2×C4#1309405311yescharacteristic
305C2×C4#1309405612yes—
306C8—42no—
307C8—81no—
308C8—3761no—
309C8—1882no—
310C22#1568902311yescharacteristic
311C22#101×D4712yes—
312C22#1568911611yescharacteristic
313C22#1568912111yescharacteristic
314C22#1568912312yes—
315C4—21no—
316C4—21no—
317C4—82no—
318C4—944no—
319C4—3762no—
320C4—1882no—
321C4#1568933611yescharacteristic
322C4#1568933711yescharacteristic
323C4#1568934311yescharacteristic
324C4#1568934411yescharacteristic
325C4#1568948412yes—
326C4#1568950911yescharacteristic
327C4#1568951611yescharacteristic
328C2#2024208512yes—
329C2#2024212412yes—
330C2#2024420111yescharacteristic
331C2#2024423011yescharacteristic
332C2#2024431911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×#332C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×#332D47
hypocenterC47#9708
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
192. C47#9708semidirect

Maximal subgroups

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

subgroupindex
#202517652
#202435392
#202432432
C2×#156888702
C2×#156888692
C2×#156888682
C2×C47×#3322
#970847