Finite Group Databasebeta

← #26133365

Subgroups — #26133365

Order 12032.

462 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252305C211yesmaximal, characteristic, complemented
2#20245124C211yesmaximal, characteristic, complemented
3#20245116C211yesmaximal, characteristic, complemented
4#20244287C211yesmaximal, characteristic, complemented
5#20241484C211yesmaximal, characteristic, complemented
6#20241476C211yesmaximal, characteristic, complemented
7C2×C47×#508C211yesmaximal, characteristic
8#15689890—21no—
9C2×#13093964C2211yescharacteristic
10#15689245—22no—
11#15689240—22no—
12C2×#13093960C2211yescharacteristic
13#15689161C2211yescharacteristic
14#15689140—21no—
15#15689140—21no—
16#15689097—21no—
17#15689078C2211yescharacteristic
18#15688933—22no—
19#15688930—22no—
20C2×#135×C47C2211yescharacteristic
21C2×#135×C47C2211yescharacteristic
22C47×#508—22no—
23C47×#508—22no—
24C2×Q32×C47C411yescharacteristic, complemented
25C2×SD32×C47C411yescharacteristic, complemented
26C2×SD32×C47C411yescharacteristic, complemented
27C2×D16×C47C411yescharacteristic, complemented
28C22×C16×C47C2211yescharacteristic
29#13094031—24no—
30#13094031—42no—
31C2×#10625329—21no—
32C2×#10625329—42no—
33C2×#10625329D411yescharacteristic
34#13093983—21no—
35#13093983D411yescharacteristic
36#13093964—21no—
37#13093964—21no—
38C2×C47⋊C16—21no—
39#13093960—21no—
40#13093960D412yes—
41#13093958—21no—
42#13093956—21no—
43#13093951—24no—
44#13093951—42no—
45#13093939—42no—
46#13093934—21no—
47C8×Dic47—21no—
48C2×#41×C47—21no—
49C2×#41×C47—21no—
50#135×C47—21no—
51#135×C47—21no—
52#135×C47—21no—
53#135×C47—21no—
54#135×C47—21no—
55#135×C47—21no—
56#135×C47D412yes—
57#135×C47D412yes—
58C2×Q16×C47C2×C411yescharacteristic
59C2×Q16×C47C2×C411yescharacteristic
60C2×SD16×C47—21no—
61C2×SD16×C47—21no—
62C2×D8×C47C2×C411yescharacteristic
63C2×D8×C47C2×C411yescharacteristic
64C22×C8×C47C2311yescharacteristic
65Q32×C47—22no—
66SD32×C47—22no—
67SD32×C47—22no—
68D16×C47—22no—
69C2×C16×C47—21no—
70C2×C16×C47—21no—
71C2×C16×C47C2×C411yescharacteristic
72C2×C16×C47C2×C411yescharacteristic
73#41×C47—22no—
74#41×C47—22no—
75#41×C47—41no—
76#41×C47—41no—
77#41×C47—41no—
78#41×C47—41no—
79#41×C47—41no—
80#41×C47—41no—
81C2×Q8×C47—21no—
82C2×Q8×C47—21no—
83C2×D4×C47—21no—
84C2×D4×C47—21no—
85C2×D4×C47—41no—
86C2×D4×C47—41no—
87C22×C4×C47—41no—
88C22×C4×C47—41no—
89C22×C4×C47C2×D411yescharacteristic
90Q16×C47—21no—
91Q16×C47—21no—
92Q16×C47—21no—
93Q16×C47C22⋊C412yes—
94SD16×C47—22no—
95SD16×C47—22no—
96SD16×C47—41no—
97SD16×C47—41no—
98D8×C47—21no—
99D8×C47—21no—
100D8×C47—21no—
101D8×C47C22⋊C412yes—
102C2×C8×C47C22×C411yescharacteristic
103C2×C8×C47C2×D411yescharacteristic
104C2×C8×C47C2×D411yescharacteristic
105C2×C8×C47C2×D411yescharacteristic
106C2×C8×C47#4111yescharacteristic
107C2×C8×C47#4111yescharacteristic
108C22⋊Dic47—21no—
109C22⋊Dic47—41no—
110C4⋊Dic47—21no—
111C4⋊Dic47—41no—
112C4×Dic47—21no—
113C4×Dic47—41no—
114#10625329—21no—
115#10625329—22no—
116#10625329—44no—
117#10625329—41no—
118#10625329D812yes—
119C2×C47⋊C8—21no—
120C2×C47⋊C8—44no—
121C2×C47⋊C8—41no—
122C16×C47—21no—
123C16×C47—21no—
124C47⋊C16—41no—
125C23×C47—41no—
126C23×C47—41no—
127C23×C47AGL(1,ℤ/8)11yescharacteristic
128Q8×C47—22no—
129Q8×C47—41no—
130Q8×C47—41no—
131Q8×C47—41no—
132D4×C47—22no—
133D4×C47—42no—
134D4×C47—42no—
135D4×C47—41no—
136D4×C47—41no—
137D4×C47—41no—
138D4×C47—81no—
139D4×C47—81no—
140C2×C4×C47—41no—
141C2×C4×C47—42no—
142C2×C4×C47—42no—
143C2×C4×C47—41no—
144C2×C4×C47—81no—
145C2×C4×C47—81no—
146C2×C4×C47C4×D411yescharacteristic
147C2×C4×C47#12011yescharacteristic
148C2×C4×C47#12111yescharacteristic
149C2×C4×C47C2×D811yescharacteristic
150C2×C4×C47#13511yescharacteristic
151C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
152C2×Dic47—41no—
153C2×Dic47—81no—
154C8×C47C2×C22⋊C411yescharacteristic
155C8×C47C4×D411yescharacteristic
156C8×C47#12111yescharacteristic
157C8×C47#12311yescharacteristic
158C47⋊C8—22no—
159C47⋊C8—42no—
160#13016—471nomaximal, Sylow
161C22×C47—41no—
162C22×C47—42no—
163C22×C47—81no—
164C22×C47—161no—
165C22×C47—161no—
166C22×C47#44211yescharacteristic
167C22×C47#44911yescharacteristic
168C22×C47#45911yescharacteristic
169C4×C47—42no—
170C4×C47—81no—
171C4×C47#38611yescharacteristic
172C4×C47C4×D811yescharacteristic
173C4×C47#44711yescharacteristic
174C4×C47#46311yescharacteristic
175Dic47—81no—
176Dic47—161no—
177C2×#508D4711yescharacteristic
178#2957—471no—
179#2145—471no—
180#2143—471no—
181#1976—471no—
182#1382—471no—
183#1379—471no—
184C2×C47—21no—
185C2×C47—21no—
186C2×C47—21no—
187C2×C47—82no—
188C2×C47—161no—
189C2×C47#187911yescharacteristic
190C2×#135C2×D4711yescharacteristic
191C2×#135C2×D4711yescharacteristic
192#568—941no—
193#508—22no—
194#508—22no—
195C2×Q32Dic4711yescharacteristic, complemented
196C2×SD32Dic4711yescharacteristic, complemented
197C2×SD32Dic4711yescharacteristic, complemented
198C2×D16Dic4711yescharacteristic, complemented
199C2×M32—471no—
200C22×C16C2×D4711yescharacteristic
201#444—942no—
202#443—942no—
203C2×#108—471no—
204#427—471no—
205#421—941no—
206#421—941no—
207#410—941no—
208#405—471no—
209#360—942no—
210#359—942no—
211C47#1301611yescharacteristic, complemented, Sylow
212C2×#41—21no—
213C2×#41—21no—
214#135—21no—
215#135—21no—
216#135—21no—
217#135—21no—
218#135—21no—
219#135—21no—
220#135C22⋊D4712yes—
221#135C22⋊D4712yes—
222C2×Q16C2×Dic4711yescharacteristic
223C2×Q16C2×Dic4711yescharacteristic
224C2×SD16—21no—
225C2×SD16—21no—
226C2×D8C2×Dic4711yescharacteristic
227C2×D8C2×Dic4711yescharacteristic
228#131—944no—
229#131—1882no—
230C2×M16—471no—
231C2×M16—941no—
232C2×M16—1882no—
233C22×C8C22×D4711yescharacteristic
234#117—471no—
235#117—941no—
236Q32—22no—
237SD32—22no—
238SD32—22no—
239D16—22no—
240M32—941no—
241M32—941no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—941no—
245C2×C16C2×Dic4711yescharacteristic
246C2×C16C2×Dic4711yescharacteristic
247#108—472no—
248#108—941no—
249#107—941no—
250#106—941no—
251#104—944no—
252#104—1882no—
253#99—1882no—
254#97—941no—
255C4×C8—941no—
256#41—22no—
257#41—22no—
258#41—41no—
259#41—41no—
260#41—41no—
261#41—41no—
262#41—41no—
263#41—41no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4D4×D4711yescharacteristic
273Q16—21no—
274Q16—21no—
275Q16—21no—
276Q16C22⋊Dic4712yes—
277SD16—22no—
278SD16—22no—
279SD16—41no—
280SD16—41no—
281D8—21no—
282D8—21no—
283D8—21no—
284D8C22⋊Dic4712yes—
285M16—472no—
286M16—941no—
287M16—942no—
288M16—1884no—
289M16—1881no—
290C2×C8—941no—
291C2×C8—1884no—
292C2×C8—1881no—
293C2×C8D4×D4711yescharacteristic
294C2×C8#1062535211yescharacteristic
295C2×C8#1062535211yescharacteristic
296C2×C8C22×Dic4711yescharacteristic
297C2×C8C2×C22⋊D4711yescharacteristic
298C2×C8C2×C22⋊D4711yescharacteristic
299C4⋊C4—941no—
300C4⋊C4—1881no—
301C22⋊C4—941no—
302C22⋊C4—1881no—
303C42—941no—
304C42—1881no—
305C16—21no—
306C16—21no—
307C16—1881no—
308C23—41no—
309C23—41no—
310C23#1309404811yescharacteristic
311Q8—22no—
312Q8—41no—
313Q8—41no—
314Q8—41no—
315D4—22no—
316D4—42no—
317D4—42no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—81no—
322D4—81no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—3761no—
330C2×C4—1881no—
331C2×C4D4×Dic4711yescharacteristic
332C2×C4#1309399211yescharacteristic
333C2×C4#1309399611yescharacteristic
334C2×C4D8×D4711yescharacteristic
335C2×C4#1309404311yescharacteristic
336C2×C4#1309404811yescharacteristic
337C8—942no—
338C8—1882no—
339C8C2×C22⋊Dic4711yescharacteristic
340C8D4×Dic4711yescharacteristic
341C8#1309399611yescharacteristic
342C8#1309400511yescharacteristic
343C22—41no—
344C22—42no—
345C22—81no—
346C22—161no—
347C22—161no—
348C22#1568923511yescharacteristic
349C22#1568926511yescharacteristic
350C22#1568931611yescharacteristic
351C4—42no—
352C4—81no—
353C4—3761no—
354C4—7521no—
355C4#1568900311yescharacteristic
356C4D8×Dic4711yescharacteristic
357C4#1568925511yescharacteristic
358C4#1568933611yescharacteristic
359C2—21no—
360C2—21no—
361C2—21no—
362C2—82no—
363C2—161no—
364C2#2024373811yescharacteristic
subgroupG/H
centerC4#15689255
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
Fitting, prime radicalC2×C47×#508C2
socleC2×C47#1879
cosocleC22×C8×C47C23
hypercenterC2×#508D47
hypocenterC47#13016
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#508

Complements

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

NH ≅ G/Ntype
1. #20252305C2semidirect
2. #20245124C2semidirect
3. #20245116C2semidirect
4. #20244287C2semidirect
5. #20241484C2semidirect
6. #20241476C2semidirect
24. C2×Q32×C47C4semidirect
25. C2×SD32×C47C4semidirect
26. C2×SD32×C47C4semidirect
27. C2×D16×C47C4semidirect
195. C2×Q32Dic47semidirect
196. C2×SD32Dic47semidirect
197. C2×SD32Dic47semidirect
198. C2×D16Dic47semidirect
211. C47#13016semidirect

Maximal subgroups

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

subgroupindex
#202523052
#202451242
#202451162
#202442872
#202414842
#202414762
C2×C47×#5082
#1301647