Finite Group Databasebeta

← #26133341

Subgroups — #26133341

Order 12032.

526 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093969C211yesmaximal, characteristic
2C2×C4×Dic188C211yesmaximal, characteristic, complemented
3C2×#15688928C211yesmaximal, characteristic, complemented
4C2×#15688925C211yesmaximal, characteristic
5#20244254C211yesmaximal, characteristic
6#20241480C211yesmaximal, characteristic, complemented
7C47×#1374C211yesmaximal, characteristic, complemented
8C22×Dic188C2211yescharacteristic
9C22×D376C2211yescharacteristic
10C2×C4×Dic94—21no—
11C2×#13093969—22no—
12C2×#13093969—22no—
13C2×#13093969C414yescomplemented
14C4×Dic188—22no—
15C4×Dic188—22no—
16C2×#13093958C2211yescharacteristic
17C2×#13093958C2211yescharacteristic
18C2×#13093949—21no—
19C2×#13093946—21no—
20#15689025—21no—
21#15688928—22no—
22#15688925—22no—
23C22×C16×C47C2211yescharacteristic
24C22×C16×C47C2211yescharacteristic
25C2×C4×C8×C47C2211yescharacteristic
26C22×Dic94—21no—
27C22×D188—21no—
28C2×Dic188—21no—
29C2×Dic188—21no—
30C2×Dic188—21no—
31C2×Dic188C2×C412yes—
32C2×Dic188D412yes—
33C2×Dic188D412yes—
34C2×D376—21no—
35C2×D376—21no—
36C2×D376—21no—
37C2×D376—21no—
38C2×D376—21no—
39C2×D376C2×C412yes—
40C4×Dic94—24no—
41C4×Dic94—42no—
42C2×C4⋊Dic47—21no—
43C2×C4⋊Dic47—21no—
44C2×Dic47⋊C4—41no—
45C2×(C2×D47)⋊C4—41no—
46C2×(C2×D47)⋊C4—41no—
47C2×C4×Dic47—41no—
48#13093969—28no—
49#13093958—21no—
50#13093958—21no—
51#13093958—21no—
52#13093958D412yes—
53#13093949—24no—
54#13093946—42no—
55C22×C8×C47D411yescharacteristic
56C22×C8×C47C2311yescharacteristic
57C2×C42×C47D411yescharacteristic
58C2×C16×C47—21no—
59C2×C16×C47—21no—
60C2×C16×C47—21no—
61C2×C16×C47—21no—
62C2×C16×C47—21no—
63C2×C16×C47C2×C412yes—
64C4×C8×C47—21no—
65C4×C8×C47—21no—
66C23×D47—41no—
67C22×C4×C47D811yescharacteristic
68C22×C4×C47D811yescharacteristic
69C22×C4×C47C2×D411yescharacteristic
70C22×Dic47—41no—
71C22×Dic47—41no—
72C22×Dic47—41no—
73C2×D188—22no—
74C2×D188—41no—
75C2×D188—41no—
76C2×D188—41no—
77C2×D188—41no—
78C2×D188—41no—
79C2×Dic94—22no—
80C2×Dic94—22no—
81C2×Dic94—22no—
82C2×Dic94—41no—
83C2×Dic94—41no—
84C2×Dic94—41no—
85C2×C8×C47—21no—
86C2×C8×C47—21no—
87C2×C8×C47—21no—
88C2×C8×C47C22×C411yescharacteristic
89C2×C8×C47C2×D411yescharacteristic
90C2×C8×C47C2×D411yescharacteristic
91C2×C8×C47C2×D411yescharacteristic
92C2×C8×C47#4111yescharacteristic
93C2×C8×C47#4111yescharacteristic
94C42×C47—21no—
95C42×C47—21no—
96(C2×D47)⋊C4—82no—
97(C2×D47)⋊C4—82no—
98C4⋊Dic47—22no—
99C4⋊Dic47—41no—
100C4⋊Dic47—41no—
101C4⋊Dic47—41no—
102Dic47⋊C4—44no—
103C4×Dic47—44no—
104Dic188—22no—
105Dic188—22no—
106Dic188—22no—
107Dic188C22⋊C414yescomplemented
108D376—22no—
109D376—22no—
110D376—41no—
111D376—41no—
112C16×C47—22no—
113C16×C47—41no—
114C23×C47C2×D811yescharacteristic
115C22×D47—42no—
116C22×D47—81no—
117C22×D47—81no—
118C22×D47—81no—
119C22×D47—81no—
120C22×D47—81no—
121C22×D47—81no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47SD3212yescomplemented
128C2×C4×C47C4×D411yescharacteristic
129C2×C4×C47#12011yescharacteristic
130C2×C4×C47#12111yescharacteristic
131C2×C4×C47#13511yescharacteristic
132C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
134C2×Dic47—42no—
135C2×Dic47—42no—
136C2×Dic47—42no—
137C2×Dic47—42no—
138C2×Dic47—81no—
139C2×Dic47—81no—
140C2×Dic47—81no—
141C2×Dic47—81no—
142C2×Dic47—81no—
143D188—42no—
144D188—42no—
145D188—81no—
146D188—81no—
147Dic94—24no—
148Dic94—42no—
149Dic94—42no—
150Dic94—42no—
151C8×C47—41no—
152C8×C47C2×C22⋊C411yescharacteristic
153C8×C47C4×D411yescharacteristic
154C8×C47#12111yescharacteristic
155C8×C47#12311yescharacteristic
156#13013—471nomaximal, Sylow
157C22×C47C4×D811yescharacteristic
158C22×C47#44711yescharacteristic
159C22×C47#45911yescharacteristic
160C22×C47C2×SD3211yescharacteristic
161C22×C47#50811yescharacteristic
162C22×C47#50911yescharacteristic
163C22×C47#51011yescharacteristic
164C2×D47—82no—
165C2×D47—82no—
166C2×D47—82no—
167C2×D47—161no—
168C2×D47—161no—
169C2×D47—161no—
170C2×D47—161no—
171C4×C47—22no—
172C4×C47—41no—
173C4×C47#38611yescharacteristic
174C4×C47#44211yescharacteristic
175C4×C47#44911yescharacteristic
176C4×C47#46311yescharacteristic
177Dic47—44no—
178Dic47—82no—
179Dic47—161no—
180C22×SD32—471no—
181C2×C4×Q16—471no—
182C2×#358—471no—
183C2×#357—471no—
184#1970—471no—
185#1380—471no—
186#1374D4711yescharacteristic, complemented
187C2×C47#187911yescharacteristic
188C2×C47C4×SD3211yescharacteristic
189C2×C47#217511yescharacteristic
190C2×C47#218511yescharacteristic
191C2×C47#218611yescharacteristic
192C2×C47#220711yescharacteristic
193C2×C47#221111yescharacteristic
194D47—162no—
195C22×Q16—471no—
196C22×D8—471no—
197C2×C4×Q8—941no—
198C2×SD32—474no—
199C2×SD32—942no—
200C2×SD32—942no—
201C22×C16C2×D4711yescharacteristic
202C22×C16C2×D4711yescharacteristic
203C4×Q16—942no—
204C4×Q16—942no—
205C2×#107—471no—
206C2×#107—471no—
207C2×#103—941no—
208C2×#102—941no—
209C2×C4×C8C2×D4711yescharacteristic
210#390—941no—
211#358—942no—
212#357—942no—
213C47#1301311yescharacteristic, complemented, Sylow
214C22×Q8—941no—
215C22×D4—941no—
216C2×Q16—472no—
217C2×Q16—472no—
218C2×Q16—472no—
219C2×Q16—941no—
220C2×Q16—941no—
221C2×Q16—941no—
222C2×D8—472no—
223C2×D8—941no—
224C2×D8—941no—
225C2×D8—941no—
226C2×D8—941no—
227C2×D8—941no—
228C22×C8D18811yescharacteristic
229C22×C8C22×D4711yescharacteristic
230C4×Q8—944no—
231C4×Q8—1882no—
232C2×C4⋊C4—941no—
233C2×C4⋊C4—941no—
234C2×C4⋊C4—1881no—
235C2×C22⋊C4—1881no—
236C2×C22⋊C4—1881no—
237C2×C42—1881no—
238C2×C42D18811yescharacteristic
239SD32—948no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—21no—
245C2×C16C4×D4712yes—
246#107—472no—
247#107—941no—
248#107—941no—
249#107—941no—
250#103—944no—
251#102—1882no—
252C4×C8—21no—
253C4×C8—21no—
254C24—1881no—
255C2×Q8—942no—
256C2×Q8—942no—
257C2×Q8—942no—
258C2×Q8—1881no—
259C2×Q8—1881no—
260C2×Q8—1881no—
261C2×D4—942no—
262C2×D4—1881no—
263C2×D4—1881no—
264C2×D4—1881no—
265C2×D4—1881no—
266C2×D4—1881no—
267C22×C4—1881no—
268C22×C4—1881no—
269C22×C4—1881no—
270C22×C4D37611yescharacteristic
271C22×C4D37611yescharacteristic
272C22×C4C2×D18811yescharacteristic
273Q16—474no—
274Q16—942no—
275Q16—942no—
276Q16—942no—
277D8—942no—
278D8—942no—
279D8—1881no—
280D8—1881no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8C2×C4×D4711yescharacteristic
285C2×C8#1062535011yescharacteristic
286C2×C8D4×D4711yescharacteristic
287C2×C8D4×D4711yescharacteristic
288C2×C8D4×D4711yescharacteristic
289C2×C8#1062535411yescharacteristic
290C4⋊C4—942no—
291C4⋊C4—1884no—
292C4⋊C4—1881no—
293C4⋊C4—1881no—
294C4⋊C4—1881no—
295C22⋊C4—3762no—
296C22⋊C4—3762no—
297C42—21no—
298C42—21no—
299C42—1884no—
300C16—22no—
301C16—41no—
302C23—3761no—
303C23—3761no—
304C23—3761no—
305C23—3761no—
306C23—3761no—
307C23—3761no—
308C23—1882no—
309C23C2×D37611yescharacteristic
310Q8—944no—
311Q8—1882no—
312Q8—1882no—
313Q8—1882no—
314D4—3761no—
315D4—3761no—
316D4—1882no—
317D4—1882no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—3761no—
324C2×C4—3761no—
325C2×C4—3761no—
326C2×C4—3761no—
327C2×C4—3761no—
328C2×C4—1882no—
329C2×C4—1882no—
330C2×C4—1882no—
331C2×C4—1882no—
332C2×C4#1309396912yescomplemented
333C2×C4C4×D18811yescharacteristic
334C2×C4#1309399411yescharacteristic
335C2×C4#1309399911yescharacteristic
336C2×C4#1309404611yescharacteristic
337C2×C4#1309405211yescharacteristic
338C2×C4#1309405211yescharacteristic
339C8—41no—
340C8C22⋊C4×D4711yescharacteristic
341C8#1309398611yescharacteristic
342C8#1309399711yescharacteristic
343C8#1309400911yescharacteristic
344C22—3762no—
345C22—3762no—
346C22—3762no—
347C22—7521no—
348C22—7521no—
349C22—7521no—
350C22—7521no—
351C22C4×D37611yescharacteristic
352C22#1568925911yescharacteristic
353C22#1568931911yescharacteristic
354C22C2×#1309396911yescharacteristic
355C22#1568955511yescharacteristic
356C22#1568956111yescharacteristic
357C22#1568956611yescharacteristic
358C4—22no—
359C4—41no—
360C4—3762no—
361C4—1884no—
362C4—7521no—
363C4#1568900111yescharacteristic
364C4#1568923611yescharacteristic
365C4#1568927011yescharacteristic
366C4#1568933911yescharacteristic
367C2—7522no—
368C2#2024373511yescharacteristic
369C2C4×#1309396911yescharacteristic
370C2#2024525411yescharacteristic
371C2#2024530711yescharacteristic
372C2#2024531311yescharacteristic
373C2#2024542911yescharacteristic
374C2#2024545111yescharacteristic
subgroupG/H
centerC23C2×D376
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1374C2
socleC23×C47C2×D8
prime radicalC22×D376C22
cosocleC22×C8×C47C23
hypercenter#1374D47
hypocenterC47#13013
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic188C2semidirect
3. C2×#15688928C2semidirect
6. #20241480C2semidirect
7. C47×#1374C2semidirect
13. C2×#13093969C4semidirect
107. Dic188C22⋊C4semidirect
127. C2×C4×C47SD32semidirect
186. #1374D47semidirect
213. C47#13013semidirect
332. C2×C4#13093969semidirect

Maximal subgroups

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

subgroupindex
C22×#130939692
C2×C4×Dic1882
C2×#156889282
C2×#156889252
#202442542
#202414802
C47×#13742
#1301347