Finite Group Databasebeta

← #26132216

Subgroups — #26132216

Order 12032.

450 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13094030C211yesmaximal, characteristic
2C2×C4⋊(C47⋊C16)C211yesmaximal, characteristic, complemented
3C2×#15688908C212yesmaximal
4#20241478C212yesmaximal, complemented
5C47×#2150C211yesmaximal, characteristic, complemented
6C2×#13094030C411yescharacteristic
7C2×#13094030C2211yescharacteristic
8C4×#10625350C411yescharacteristic
9C22×C47⋊C16C2212yes—
10#15689078C411yescharacteristic
11#15689078C2211yescharacteristic
12#15689077—21no—
13#15689077—21no—
14C4×#10625329C411yescharacteristic
15C4×#10625324—21no—
16C4×C8×D47—21no—
17C4⋊(C47⋊C16)—21no—
18C4⋊(C47⋊C16)—21no—
19#15688908—24no—
20C2×M32×C47C2212yes—
21C2×C4×C8×C47C2211yescharacteristic
22C47×C4⋊C16—21no—
23C47×C4⋊C16—21no—
24C2×#10625350C2×C411yescharacteristic
25#13094030—22no—
26#13094030—21no—
27#13094030—21no—
28#13094030—22no—
29#13094030D412yes—
30#13094030Q812yes—
31C2×#10625329C2×C411yescharacteristic
32C2×#10625329C2×C411yescharacteristic
33C2×#10625324—21no—
34C2×#10625324—21no—
35C2×C8×D47—21no—
36C2×C8×D47—21no—
37C4×Dic94C811yescharacteristic
38C4×Dic94C811yescharacteristic
39C4×D188C811yescharacteristic
40C4×D188C811yescharacteristic
41C4×C22⋊D47—21no—
42C4×C22⋊D47—21no—
43#13093983C2×C411yescharacteristic
44#13093981—21no—
45C42×D47—21no—
46C2×C47⋊C16—22no—
47C2×C47⋊C16—22no—
48C2×C47⋊C16—22no—
49#13093935—21no—
50#13093934—21no—
51#13093934—21no—
52C4×C47⋊C8—21no—
53C8×Dic47—21no—
54C8×Dic47—21no—
55C22×C8×C47C2×C411yescharacteristic
56C22×C8×C47C2311yescharacteristic
57C2×C42×C47C2×C411yescharacteristic
58M32×C47—22no—
59M32×C47—22no—
60C2×C16×C47—22no—
61C4×C8×C47D411yescharacteristic
62C4×C8×C47D411yescharacteristic
63C4×C8×C47D411yescharacteristic
64C4×C8×C47D411yescharacteristic
65C22×C4×C47M1611yescharacteristic
66C22×C4×C47M1611yescharacteristic
67C22×C4×C47C22×C411yescharacteristic
68C2×C22⋊D47—21no—
69#10625350—21no—
70#10625350—21no—
71#10625350C4⋊C412yes—
72#10625350M1612yes—
73C2×D188C2×C811yescharacteristic
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47—21no—
77C2×Dic94C2×C811yescharacteristic
78C2×C8×C47—21no—
79C2×C8×C47—21no—
80C2×C8×C47C22⋊C411yescharacteristic
81C2×C8×C47C22⋊C411yescharacteristic
82C2×C8×C47C2×D411yescharacteristic
83C2×C8×C47C2×D411yescharacteristic
84C2×C8×C47C2×D411yescharacteristic
85C2×C8×C47C2×Q811yescharacteristic
86C2×C8×C47#4111yescharacteristic
87C2×C8×C47#4111yescharacteristic
88C42×C47C22⋊C411yescharacteristic
89C42×C47C22⋊C411yescharacteristic
90C42×C47C2×C811yescharacteristic
91C42×C47C2×C811yescharacteristic
92C22⋊Dic47—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95C4⋊Dic47C2×C811yescharacteristic
96C4⋊Dic47C2×C811yescharacteristic
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102#10625329—21no—
103#10625329—21no—
104#10625329C4⋊C412yes—
105#10625329M1612yes—
106C2×C47⋊C8—21no—
107C2×C47⋊C8—21no—
108#10625324—24no—
109#10625324—22no—
110#10625324—22no—
111C8×D47—24no—
112C8×D47—22no—
113C8×D47—22no—
114C16×C47—42no—
115C47⋊C16—42no—
116C23×C47C2×M1611yescharacteristic
117C22×D47—21no—
118C2×C4×C47—22no—
119C2×C4×C47—41no—
120C2×C4×C47C22⋊C811yescharacteristic
121C2×C4×C47C22⋊C811yescharacteristic
122C2×C4×C47C22⋊C811yescharacteristic
123C2×C4×C47C22⋊C811yescharacteristic
124C2×C4×C47C2×C22⋊C411yescharacteristic
125C2×C4×C47C2×C4⋊C411yescharacteristic
126C2×C4×C47#11711yescharacteristic
127C2×C4×C47C22×C811yescharacteristic
128C2×C4×C47C2×M1611yescharacteristic
129C2×C4×C47C2×M1611yescharacteristic
130C22⋊D47—22no—
131C22⋊D47—22no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135D188—21no—
136D188C4⋊C812yes—
137C4×D47—22no—
138C4×D47—22no—
139C4×D47—42no—
140C4×D47—42no—
141Dic94—21no—
142Dic94C4⋊C812yes—
143C8×C47—21no—
144C8×C47—21no—
145C8×C47#12111yescharacteristic
146C8×C47#12111yescharacteristic
147C8×C47C22⋊Q811yescharacteristic
148C8×C47C22⋊Q811yescharacteristic
149C47⋊C8—22no—
150C47⋊C8—22no—
151#12787—471nomaximal, Sylow
152C22×C47—21no—
153C22×C47—21no—
154C22×C47C2×C22⋊C811yescharacteristic
155C22×C47#42311yescharacteristic
156C22×C47#43211yescharacteristic
157C2×D47—22no—
158C2×D47—41no—
159C2×D47—41no—
160C4×C47—21no—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47#35012yescomplemented
164C4×C47#38011yescharacteristic
165C4×C47#40711yescharacteristic
166C4×C47C2×C4⋊C811yescharacteristic
167C4×C47#43111yescharacteristic
168Dic47—22no—
169Dic47—41no—
170Dic47—41no—
171C4×#131—471no—
172#2150D4711yescharacteristic, complemented
173C2×C4⋊C16—471no—
174C2×#350—472no—
175#1379—472no—
176C2×C47—21no—
177C2×C47—21no—
178C2×C47#179711yescharacteristic
179C2×C47C2×#35011yescharacteristic
180C2×C47#211711yescharacteristic
181D47—42no—
182C2×#131—471no—
183C2×#131—471no—
184C4×#41—471no—
185C2×M32C2×D4712yes—
186C22×C16—472no—
187#405—471no—
188#405—471no—
189#405—941no—
190#405—941no—
191C4×M16—471no—
192C4×M16—941no—
193C2×C4×C8—941no—
194C2×C4×C8C2×D4711yescharacteristic
195C4⋊C16—21no—
196C4⋊C16—21no—
197C4⋊C16—941no—
198C4⋊C16—941no—
199#350—944no—
200C47#1278711yescharacteristic, complemented, Sylow
201C2×#41—471no—
202#131—472no—
203#131—472no—
204#131—942no—
205#131—942no—
206#131—941no—
207#131—941no—
208C2×M16—471no—
209C2×M16—471no—
210C2×M16—941no—
211C2×M16—941no—
212C22×C8—941no—
213C22×C8—941no—
214C22×C8C4×D4711yescharacteristic
215C22×C8C22×D4711yescharacteristic
216C4×Q8—471no—
217C4×Q8—471no—
218C4×D4—471no—
219C4×D4—471no—
220C4×D4—941no—
221C4×D4—941no—
222#117—471no—
223#117—941no—
224C2×C42—941no—
225C2×C42C4×D4711yescharacteristic
226M32—22no—
227M32—22no—
228C2×C16—22no—
229C2×C16—942no—
230C2×C16—942no—
231C2×C16—942no—
232#97—941no—
233#97—941no—
234#97—941no—
235C4×C8—941no—
236C4×C8—941no—
237C4×C8—941no—
238C4×C8D18811yescharacteristic
239C4×C8D18811yescharacteristic
240C4×C8C22⋊D4711yescharacteristic
241C4×C8C22⋊D4711yescharacteristic
242#41—472no—
243#41—472no—
244#41—941no—
245#41—941no—
246C2×Q8—471no—
247C2×D4—471no—
248C2×D4—941no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4—941no—
252C22×C4#1062532411yescharacteristic
253C22×C4#1062532411yescharacteristic
254C22×C4C2×C4×D4711yescharacteristic
255M16—472no—
256M16—472no—
257M16—944no—
258M16—941no—
259M16—941no—
260M16—942no—
261M16—942no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—944no—
265C2×C8—941no—
266C2×C8—941no—
267C2×C8—942no—
268C2×C8—942no—
269C2×C8(C2×D47)⋊C411yescharacteristic
270C2×C8(C2×D47)⋊C411yescharacteristic
271C2×C8C2×D18811yescharacteristic
272C2×C8D4×D4711yescharacteristic
273C2×C8#1062535211yescharacteristic
274C2×C8Q8×D4711yescharacteristic
275C2×C8#1062535411yescharacteristic
276C2×C8C2×C22⋊D4711yescharacteristic
277C4⋊C4—471no—
278C4⋊C4—471no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C42—941no—
285C42—941no—
286C42—941no—
287C42C8×D4711yescharacteristic
288C42C8×D4711yescharacteristic
289C42(C2×D47)⋊C411yescharacteristic
290C42(C2×D47)⋊C411yescharacteristic
291C16—42no—
292C16—1882no—
293C23—941no—
294C23C2×#1062532411yescharacteristic
295Q8—472no—
296Q8—941no—
297D4—472no—
298D4—942no—
299D4—942no—
300D4—941no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—941no—
304C2×C4—942no—
305C2×C4—942no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—1882no—
309C2×C4—1882no—
310C2×C4(C2×D47)⋊C811yescharacteristic
311C2×C4(C2×D47)⋊C811yescharacteristic
312C2×C4(C2×D47)⋊C811yescharacteristic
313C2×C4(C2×D47)⋊C811yescharacteristic
314C2×C4C2×(C2×D47)⋊C411yescharacteristic
315C2×C4C4⋊C4×D4711yescharacteristic
316C2×C4#1309398211yescharacteristic
317C2×C4C2×C8×D4711yescharacteristic
318C2×C4M16×D4711yescharacteristic
319C2×C4M16×D4711yescharacteristic
320C8—21no—
321C8—21no—
322C8—942no—
323C8—942no—
324C8#1309399511yescharacteristic
325C8#1309399911yescharacteristic
326C8#1309400011yescharacteristic
327C8#1309400411yescharacteristic
328C22—21no—
329C22—21no—
330C22—942no—
331C22—1881no—
332C22—1881no—
333C22C2×(C2×D47)⋊C811yescharacteristic
334C22#1568914511yescharacteristic
335C22#1568917911yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—942no—
340C4—1881no—
341C4—1881no—
342C4#1568890812yescomplemented
343C4#1568898011yescharacteristic
344C4#1568908611yescharacteristic
345C4C4⋊C8×D4711yescharacteristic
346C4#1568917511yescharacteristic
347C2—21no—
348C2—21no—
349C2—1882no—
350C2#2024336511yescharacteristic
351C2C2×#1568890811yescharacteristic
352C2#2024501711yescharacteristic
subgroupG/H
centerC2×C8C2×C22⋊D47
commutatorC2×C4×C47C22×C8
FrattiniC22×C8C22×D47
FittingC47×#2150C2
socleC22×C47C2×C22⋊C8
prime radicalC2×#10625350C2×C4
cosocleC22×C8×C47C23
hypercenter#2150D47
hypocenterC47#12787
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ #2150

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊(C47⋊C16)C2semidirect
4. #20241478C2semidirect
5. C47×#2150C2semidirect
163. C4×C47#350semidirect
172. #2150D47semidirect
200. C47#12787semidirect
342. C4#15688908semidirect

Maximal subgroups

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

subgroupindex
C4×#130940302
C2×C4⋊(C47⋊C16)2
C2×#156889082
#202414782
C47×#21502
#1278747