Finite Group Databasebeta

← #26133454

Subgroups — #26133454

Order 12032.

512 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689558C211yesmaximal, characteristic
2C2×#15688935C211yesmaximal, characteristic, complemented
3#20245100C211yesmaximal, characteristic, complemented
4#20244254C211yesmaximal, characteristic, complemented
5#20241498C211yesmaximal, characteristic, complemented
6#20241470C211yesmaximal, characteristic, complemented
7C2×C47×#443C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9#15689558—22no—
10#15689558C414yescomplemented
11C2×#13093967—21no—
12C2×#13093965—21no—
13C2×#13093964C2211yescharacteristic
14C2×#13093964C2211yescharacteristic
15C2×#13093958C2211yescharacteristic
16C2×#13093946—21no—
17#15689025—21no—
18#15688935—22no—
19#15688927—21no—
20#15688924—21no—
21C2×#135×C47C2211yescharacteristic
22C2×#131×C47—21no—
23C47×#443—22no—
24C47×#443—22no—
25C2×#108×C47C2211yescharacteristic
26C2×#104×C47—21no—
27C2×C4×C8×C47C2211yescharacteristic
28C22×D188—21no—
29C2×D376—21no—
30C2×D376—21no—
31C2×D376—21no—
32C2×D376—21no—
33C2×D376—21no—
34C2×D376C2×C412yes—
35C2×C4⋊Dic47—21no—
36C2×(C2×D47)⋊C4—42no—
37#13093967—24no—
38#13093965—24no—
39#13093964—21no—
40#13093964—21no—
41#13093964—21no—
42#13093964C2×C412yes—
43C2×C47⋊C16—21no—
44C2×C47⋊C16—21no—
45#13093958—21no—
46#13093958—21no—
47#13093946—41no—
48#13093946—41no—
49C2×#41×C47—21no—
50#135×C47—21no—
51#135×C47—21no—
52#135×C47C2×C412yes—
53#135×C47D412yes—
54C2×Q16×C47D411yescharacteristic
55C2×SD16×C47—21no—
56C2×D8×C47D411yescharacteristic
57#131×C47—24no—
58#131×C47—42no—
59C2×M16×C47—21no—
60C2×M16×C47—41no—
61C22×C8×C47—41no—
62C22×C8×C47D411yescharacteristic
63C22×C8×C47C2311yescharacteristic
64C2×C42×C47D411yescharacteristic
65#108×C47—21no—
66#108×C47D412yes—
67#104×C47—24no—
68C4×C8×C47—21no—
69C4×C8×C47—21no—
70C23×D47—41no—
71#41×C47—22no—
72#41×C47—22no—
73#41×C47—41no—
74#41×C47—41no—
75C2×Q8×C47—21no—
76C2×D4×C47—21no—
77C2×D4×C47—41no—
78C22×C4×C47—21no—
79C22×C4×C47—41no—
80C22×C4×C47C2×D411yescharacteristic
81C22×Dic47—41no—
82C2×D188—22no—
83C2×D188—41no—
84C2×D188—41no—
85C2×D188—41no—
86C2×D188—41no—
87C2×D188—41no—
88Q16×C47—21no—
89Q16×C47C22⋊C412yescomplemented
90SD16×C47—22no—
91SD16×C47—22no—
92D8×C47—21no—
93D8×C47C22⋊C412yescomplemented
94M16×C47—22no—
95M16×C47—44no—
96M16×C47—41no—
97C2×C8×C47—21no—
98C2×C8×C47—21no—
99C2×C8×C47—44no—
100C2×C8×C47—41no—
101C2×C8×C47D811yescharacteristic
102C2×C8×C47D811yescharacteristic
103C2×C8×C47C22×C411yescharacteristic
104C2×C8×C47C2×D411yescharacteristic
105C2×C8×C47C2×D411yescharacteristic
106C2×C8×C47C2×D411yescharacteristic
107C2×C8×C47#4111yescharacteristic
108C2×C8×C47#4111yescharacteristic
109C42×C47—21no—
110C42×C47—21no—
111(C2×D47)⋊C4—84no—
112C4⋊Dic47—41no—
113C4⋊Dic47—41no—
114D376—22no—
115D376—22no—
116D376—41no—
117D376—41no—
118C47⋊C16—22no—
119C47⋊C16—41no—
120C23×C47—41no—
121C23×C47AGL(1,ℤ/8)11yescharacteristic
122C22×D47—42no—
123C22×D47—82no—
124C22×D47—82no—
125C22×D47—81no—
126C22×D47—81no—
127Q8×C47—22no—
128Q8×C47—41no—
129D4×C47—22no—
130D4×C47—42no—
131D4×C47—42no—
132D4×C47—41no—
133C2×C4×C47—22no—
134C2×C4×C47—41no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—42no—
138C2×C4×C47—42no—
139C2×C4×C47C4×D411yescharacteristic
140C2×C4×C47#12011yescharacteristic
141C2×C4×C47#12111yescharacteristic
142C2×C4×C47C2×D811yescharacteristic
143C2×C4×C47#13511yescharacteristic
144C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
145C2×Dic47—82no—
146C2×Dic47—81no—
147D188—42no—
148D188—42no—
149D188—81no—
150D188—81no—
151C8×C47—21no—
152C8×C47—21no—
153C8×C47—42no—
154C8×C47C2×C22⋊C411yescharacteristic
155C8×C47C4×D411yescharacteristic
156C8×C47#12111yescharacteristic
157C8×C47#12311yescharacteristic
158#13029—471nomaximal, Sylow
159C22×C47—21no—
160C22×C47—21no—
161C22×C47—42no—
162C22×C47—81no—
163C22×C47—81no—
164C22×C47#44211yescharacteristic
165C22×C47#44911yescharacteristic
166C22×C47#45911yescharacteristic
167C2×D47—84no—
168C2×D47—82no—
169C2×D47—162no—
170C2×D47—161no—
171C2×D47—161no—
172C4×C47—42no—
173C4×C47—42no—
174C4×C47#38611yescharacteristic
175C4×C47C4×D811yescharacteristic
176C4×C47#44711yescharacteristic
177C4×C47#46311yescharacteristic
178Dic47—161no—
179C2×#509—471no—
180C2×#443D4711yescharacteristic, complemented
181C2×#361—471no—
182#2139—471no—
183#1970—471no—
184#1387—471no—
185#1376—471no—
186C2×C47—21no—
187C2×C47—21no—
188C2×C47—82no—
189C2×C47#187911yescharacteristic
190C2×C47#221211yescharacteristic
191C2×C47#221311yescharacteristic
192D47—162no—
193C2×#135C2×D4711yescharacteristic
194C22×D8—471no—
195C2×#131—21no—
196#509—474no—
197#509—942no—
198C2×SD32—941no—
199C2×D16—941no—
200C2×M32—471no—
201C2×M32—471no—
202#443—22no—
203#443—22no—
204C2×#108C2×D4711yescharacteristic
205C2×#107—471no—
206C2×#104—21no—
207C2×#102—941no—
208C2×C4×C8C2×D4711yescharacteristic
209#390—941no—
210#361—942no—
211#358—941no—
212#357—941no—
213C47#1302911yescharacteristic, complemented, Sylow
214C2×#41—21no—
215C22×D4—941no—
216#135—21no—
217#135—21no—
218#135C4×D4712yes—
219#135C22⋊D4712yes—
220C2×Q16D18811yescharacteristic
221C2×SD16—21no—
222C2×D8—472no—
223C2×D8—941no—
224C2×D8—941no—
225C2×D8—941no—
226C2×D8—941no—
227C2×D8—941no—
228C2×D8D18811yescharacteristic
229#131—24no—
230#131—42no—
231C2×M16—21no—
232C2×M16—41no—
233C22×C8—41no—
234C22×C8C22⋊D4711yescharacteristic
235C22×C8C22×D4711yescharacteristic
236C2×C4⋊C4—941no—
237C2×C22⋊C4—1882no—
238C2×C42C22⋊D4711yescharacteristic
239SD32—944no—
240D16—944no—
241M32—472no—
242M32—941no—
243M32—941no—
244M32—941no—
245C2×C16—941no—
246C2×C16—941no—
247#108—21no—
248#108C22⋊D4712yes—
249#107—941no—
250#107—941no—
251#104—24no—
252#102—1881no—
253#102—1881no—
254C4×C8—21no—
255C4×C8—21no—
256C24—1881no—
257#41—22no—
258#41—22no—
259#41—41no—
260#41—41no—
261C2×Q8—21no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—942no—
265C2×D4—1881no—
266C2×D4—1881no—
267C2×D4—1881no—
268C2×D4—1881no—
269C2×D4—1881no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4—1881no—
273C22×C4C2×C22⋊D4711yescharacteristic
274Q16—21no—
275Q16(C2×D47)⋊C412yescomplemented
276SD16—22no—
277SD16—22no—
278D8—21no—
279D8—942no—
280D8—942no—
281D8—1881no—
282D8—1881no—
283D8(C2×D47)⋊C412yescomplemented
284M16—22no—
285M16—44no—
286M16—41no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—44no—
290C2×C8—41no—
291C2×C8#1062533411yescharacteristic
292C2×C8#1062533411yescharacteristic
293C2×C8C2×C4×D4711yescharacteristic
294C2×C8C2×D18811yescharacteristic
295C2×C8#1062535011yescharacteristic
296C2×C8#1062535011yescharacteristic
297C2×C8C2×C22⋊D4711yescharacteristic
298C2×C8C2×C22⋊D4711yescharacteristic
299C4⋊C4—1881no—
300C4⋊C4—1881no—
301C22⋊C4—3764no—
302C42—21no—
303C42—21no—
304C16—942no—
305C16—1881no—
306C23—41no—
307C23—3762no—
308C23—3762no—
309C23—3761no—
310C23—3761no—
311C23—1882no—
312C23#1309404911yescharacteristic
313Q8—22no—
314Q8—41no—
315D4—22no—
316D4—42no—
317D4—42no—
318D4—41no—
319D4—3761no—
320D4—3761no—
321D4—1882no—
322D4—1882no—
323C2×C4—22no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—3762no—
330C2×C4—3761no—
331C2×C4C4×C22⋊D4711yescharacteristic
332C2×C4#1309399311yescharacteristic
333C2×C4#1309399811yescharacteristic
334C2×C4C2×#1062533411yescharacteristic
335C2×C4#1309404411yescharacteristic
336C2×C4#1309405011yescharacteristic
337C8—21no—
338C8—21no—
339C8—42no—
340C8C2×(C2×D47)⋊C411yescharacteristic
341C8C4×C22⋊D4711yescharacteristic
342C8#1309399811yescharacteristic
343C8#1309400711yescharacteristic
344C22—21no—
345C22—21no—
346C22—42no—
347C22—81no—
348C22—81no—
349C22—3764no—
350C22—3762no—
351C22—7522no—
352C22—7521no—
353C22—7521no—
354C22#1568923311yescharacteristic
355C22#1568926811yescharacteristic
356C22#1568931811yescharacteristic
357C4—42no—
358C4—42no—
359C4—7521no—
360C4#1568900211yescharacteristic
361C4C4×#1062533411yescharacteristic
362C4#1568925711yescharacteristic
363C4#1568933811yescharacteristic
364C2—21no—
365C2—21no—
366C2—82no—
367C2—7522no—
368C2#2024373611yescharacteristic
369C2#2024545711yescharacteristic
370C2#2024546411yescharacteristic
subgroupG/H
centerC22#15689318
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC2×C47×#443C2
socleC22×C47#459
prime radicalC2×#15689558C2
cosocleC22×C8×C47C23
hypercenterC2×#443D47
hypocenterC47#13029
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
2. C2×#15688935C2semidirect
3. #20245100C2semidirect
4. #20244254C2semidirect
5. #20241498C2semidirect
6. #20241470C2semidirect
7. C2×C47×#443C2semidirect
10. #15689558C4semidirect
89. Q16×C47C22⋊C4semidirect
93. D8×C47C22⋊C4semidirect
180. C2×#443D47semidirect
213. C47#13029semidirect
275. Q16(C2×D47)⋊C4semidirect
283. D8(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#156895582
C2×#156889352
#202451002
#202442542
#202414982
#202414702
C2×C47×#4432
#1302947