Finite Group Databasebeta

← #26109448

Subgroups — #26109448

Order 12032.

454 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#10625350C211yesmaximal, characteristic
2#20243409C212yesmaximal
3#20242147C211yesmaximal, characteristic, complemented
4#20241291C212yesmaximal, complemented
5C4×#107×C47C211yesmaximal, characteristic, complemented
6C4×#10625350C2211yescharacteristic
7C8×Dic94C411yescharacteristic, complemented
8C8×Dic94C411yescharacteristic, complemented
9C8×D188C411yescharacteristic, complemented
10C8×D188C411yescharacteristic, complemented
11C8×C22⋊D47—21no—
12C8×C22⋊D47—21no—
13#15689176C2211yescharacteristic
14#15689174—21no—
15#15689147C2212yes—
16C2×#13093952—22no—
17C4×C8×D47—21no—
18#15688883—22no—
19#15688876—21no—
20#15688876—21no—
21C2×#107×C47—21no—
22C2×C4×C8×C47C2211yescharacteristic
23C4×C4⋊C4×C47C2212yes—
24C47×#340—21no—
25C2×#10625350D411yescharacteristic
26C2×#10625329—22no—
27C2×C8×D47—21no—
28C2×C8×D47—21no—
29C4×Dic94C2×C411yescharacteristic
30C4×Dic94Q811yescharacteristic
31C4×D188C2×C411yescharacteristic
32C4×D188Q811yescharacteristic
33C4×C22⋊D47—21no—
34C4×C22⋊D47—21no—
35#13093983D411yescharacteristic
36#13093981—21no—
37C42×D47—21no—
38C4⋊(C47⋊C8)—22no—
39C4⋊(C47⋊C8)—22no—
40C4⋊(C47⋊C8)C2×C411yescharacteristic
41C4⋊(C47⋊C8)C2×C411yescharacteristic
42Dic47⋊C8—21no—
43Dic47⋊C8—21no—
44#13093952—44no—
45C22⋊(C47⋊C8)—21no—
46(C2×D47)⋊C8—21no—
47(C2×D47)⋊C8—21no—
48C4×C47⋊C8—21no—
49C8×Dic47—21no—
50C8×Dic47—21no—
51C22×C8×C47D411yescharacteristic
52C22×C8×C47D411yescharacteristic
53C2×C4⋊C4×C47—22no—
54C2×C42×C47—22no—
55C2×C42×C47C2311yescharacteristic
56#107×C47—24no—
57C4×C8×C47C2×C411yescharacteristic
58C4×C8×C47C2×C411yescharacteristic
59C4×C8×C47D411yescharacteristic
60C4×C8×C47D411yescharacteristic
61#95×C47—22no—
62C22×C4×C47—42no—
63C22×C4×C47C2×D411yescharacteristic
64C22×C4×C47C2×D411yescharacteristic
65C22×C4×C47#4111yescharacteristic
66C2×C22⋊D47—21no—
67#10625350—21no—
68#10625350—21no—
69#10625350D812yes—
70#10625350Q1612yes—
71C2×D188C4⋊C411yescharacteristic
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×Dic94C4⋊C411yescharacteristic
76C2×C8×C47—22no—
77C2×C8×C47—41no—
78C2×C8×C47C22⋊C411yescharacteristic
79C2×C8×C47C22⋊C411yescharacteristic
80C2×C8×C47C22⋊C411yescharacteristic
81C2×C8×C47C22⋊C411yescharacteristic
82C4⋊C4×C47—24no—
83C4⋊C4×C47—42no—
84C42×C47—42no—
85C42×C47—42no—
86C42×C47C22×C411yescharacteristic
87C42×C47C2×D411yescharacteristic
88C42×C47C2×Q811yescharacteristic
89C42×C47#4111yescharacteristic
90C22⋊Dic47—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93C4⋊Dic47C4⋊C411yescharacteristic
94C4⋊Dic47C4⋊C411yescharacteristic
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100#10625329—42no—
101#10625329—42no—
102C2×C47⋊C8—21no—
103C2×C47⋊C8—21no—
104C2×C47⋊C8—42no—
105C8×D47—42no—
106C8×D47—42no—
107C23×C47#12111yescharacteristic
108C22×D47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—41no—
112C2×C4×C47—44no—
113C2×C4×C47—82no—
114C2×C4×C47—82no—
115C2×C4×C47C2×C22⋊C411yescharacteristic
116C2×C4×C47C2×C4⋊C411yescharacteristic
117C2×C4×C47#11711yescharacteristic
118C2×C4×C47#12111yescharacteristic
119C2×C4×C47C22⋊Q811yescharacteristic
120C2×C4×C47C22⋊Q811yescharacteristic
121C2×C4×C47C2×D811yescharacteristic
122C2×C4×C47C2×Q1611yescharacteristic
123C2×C4×C47#13511yescharacteristic
124C2×C4×C47#13511yescharacteristic
125C22⋊D47—22no—
126C22⋊D47—22no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130D188—21no—
131D188#10712yescomplemented
132C4×D47—22no—
133C4×D47—22no—
134C4×D47—42no—
135C4×D47—41no—
136C4×D47—41no—
137Dic94—21no—
138Dic94#10712yescomplemented
139C8×C47—21no—
140C8×C47—21no—
141C8×C47—21no—
142C8×C47#10412yescomplemented
143C47⋊C8—41no—
144C47⋊C8—41no—
145C47⋊C8—82no—
146#8667—471nomaximal, Sylow
147C22×C47—21no—
148C22×C47—21no—
149C22×C47#38011yescharacteristic
150C22×C47#46611yescharacteristic
151C22×C47#46711yescharacteristic
152C2×D47—22no—
153C2×D47—41no—
154C2×D47—41no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—84no—
159C4×C47C2×#10411yescharacteristic
160C4×C47#42111yescharacteristic
161C4×C47C2×#10711yescharacteristic
162C4×C47#42711yescharacteristic
163C4×C47#46611yescharacteristic
164C4×C47#46711yescharacteristic
165Dic47—22no—
166Dic47—41no—
167Dic47—41no—
168C8×#41—471no—
169#1806—472no—
170C4×#107D4711yescharacteristic, complemented
171#1567—471no—
172#1303—472no—
173C2×C47—21no—
174C2×C47—21no—
175C2×C47#180611yescharacteristic
176C2×C47#180811yescharacteristic
177C2×C47#181411yescharacteristic
178D47—42no—
179C4×#41—471no—
180C8×Q8—471no—
181C8×Q8—471no—
182C8×D4—471no—
183C8×D4—471no—
184C8×D4—941no—
185C8×D4—941no—
186#431—471no—
187#431—941no—
188C2×#107—21no—
189#423—472no—
190C2×#104—942no—
191C2×C4×C8—941no—
192C2×C4×C8C2×D4711yescharacteristic
193C4×C4⋊C4C2×D4712yes—
194#340—21no—
195#339—942no—
196#335—941no—
197#335—941no—
198C47#866711yescharacteristic, complemented, Sylow
199C2×#41—471no—
200C2×M16—942no—
201C22×C8—941no—
202C22×C8—941no—
203C22×C8C22⋊D4711yescharacteristic
204C22×C8C22⋊D4711yescharacteristic
205C4×Q8—471no—
206C4×Q8—471no—
207C4×D4—471no—
208C4×D4—471no—
209C4×D4—941no—
210C4×D4—941no—
211#117—471no—
212#117—941no—
213C2×C4⋊C4—22no—
214C2×C42—22no—
215C2×C42—941no—
216C2×C42C22×D4711yescharacteristic
217#107—24no—
218C4⋊C8—471no—
219C4⋊C8—471no—
220C4⋊C8—941no—
221C4⋊C8—941no—
222C4⋊C8—942no—
223C4⋊C8—942no—
224#104—1884no—
225C22⋊C8—941no—
226C22⋊C8—941no—
227C22⋊C8—941no—
228C4×C8—941no—
229C4×C8—941no—
230C4×C8—941no—
231C4×C8C4×D4711yescharacteristic
232C4×C8C4×D4711yescharacteristic
233C4×C8D18811yescharacteristic
234C4×C8D18811yescharacteristic
235#95—22no—
236#41—472no—
237#41—472no—
238#41—941no—
239#41—941no—
240C2×Q8—471no—
241C2×D4—471no—
242C2×D4—941no—
243C22×C4—42no—
244C22×C4—941no—
245C22×C4—941no—
246C22×C4—941no—
247C22×C4D4×D4711yescharacteristic
248C22×C4#1062535211yescharacteristic
249C22×C4C2×C22⋊D4711yescharacteristic
250M16—1882no—
251M16—1882no—
252C2×C8—22no—
253C2×C8—41no—
254C2×C8—941no—
255C2×C8—941no—
256C2×C8—1882no—
257C2×C8—1882no—
258C2×C8—1882no—
259C2×C8(C2×D47)⋊C411yescharacteristic
260C2×C8(C2×D47)⋊C411yescharacteristic
261C2×C8(C2×D47)⋊C411yescharacteristic
262C2×C8(C2×D47)⋊C411yescharacteristic
263C4⋊C4—24no—
264C4⋊C4—42no—
265C4⋊C4—471no—
266C4⋊C4—471no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C42—42no—
273C42—42no—
274C42—941no—
275C42—941no—
276C42—941no—
277C42C2×C4×D4711yescharacteristic
278C42C2×D18811yescharacteristic
279C42Q8×D4711yescharacteristic
280C42#1062535411yescharacteristic
281C23—941no—
282C23#1309399511yescharacteristic
283Q8—472no—
284Q8—941no—
285D4—472no—
286D4—942no—
287D4—942no—
288D4—941no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—44no—
293C2×C4—82no—
294C2×C4—82no—
295C2×C4—941no—
296C2×C4—942no—
297C2×C4—942no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—1882no—
301C2×C4—1881no—
302C2×C4—1881no—
303C2×C4C2×(C2×D47)⋊C411yescharacteristic
304C2×C4C4⋊C4×D4711yescharacteristic
305C2×C4#1309398211yescharacteristic
306C2×C4#1309399911yescharacteristic
307C2×C4#1309400011yescharacteristic
308C2×C4#1309400411yescharacteristic
309C2×C4D8×D4711yescharacteristic
310C2×C4Q16×D4711yescharacteristic
311C2×C4#1309404311yescharacteristic
312C2×C4#1309404711yescharacteristic
313C8—21no—
314C8—21no—
315C8—21no—
316C8—3762no—
317C8—1881no—
318C8—1881no—
319C8#1309395212yescomplemented
320C22—21no—
321C22—21no—
322C22—942no—
323C22—1881no—
324C22—1881no—
325C22#1568898011yescharacteristic
326C22#1568935611yescharacteristic
327C22#1568936111yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—84no—
332C4—942no—
333C4—1881no—
334C4—1881no—
335C4C2×#1309395211yescharacteristic
336C4#1568914111yescharacteristic
337C4#107×D4711yescharacteristic
338C4#1568916011yescharacteristic
339C4#1568936011yescharacteristic
340C4#1568936511yescharacteristic
341C2—21no—
342C2—21no—
343C2—1882no—
344C2#2024340911yescharacteristic
345C2#2024341411yescharacteristic
346C2#2024343911yescharacteristic
subgroupG/H
centerC2×C4#13093999
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC4×#107×C47C2
socleC22×C47#380
prime radicalC2×#10625350D4
cosocleC2×C42×C47C23
hypercenterC4×#107D47
hypocenterC47#8667
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
3. #20242147C2semidirect
4. #20241291C2semidirect
5. C4×#107×C47C2semidirect
7. C8×Dic94C4semidirect
8. C8×Dic94C4semidirect
9. C8×D188C4semidirect
10. C8×D188C4semidirect
131. D188#107semidirect
138. Dic94#107semidirect
142. C8×C47#104semidirect
170. C4×#107D47semidirect
198. C47#8667semidirect
319. C8#13093952semidirect

Maximal subgroups

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

subgroupindex
C8×#106253502
#202434092
#202421472
#202412912
C4×#107×C472
#866747