Finite Group Databasebeta

← #26115201

Subgroups — #26115201

Order 12032.

510 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10625334C211yesmaximal, characteristic
2#20242134C211yesmaximal, characteristic, complemented
3#20241780C211yesmaximal, characteristic, complemented
4#20241779C211yesmaximal, characteristic, complemented
5#20241708C211yesmaximal, characteristic, complemented
6#20241672C211yesmaximal, characteristic, complemented
7C47×#1460C211yesmaximal, characteristic, complemented
8C22×#10625334C411yescharacteristic
9C2×C4×D188C2211yescharacteristic
10C4×#10625334—21no—
11C4×#10625334—21no—
12C4×#10625334—21no—
13C4×#10625334—21no—
14#15689176C2211yescharacteristic
15#15689176C2211yescharacteristic
16C2×#13093957C411yescharacteristic
17C2×#13093945C411yescharacteristic
18C2×#13093944C411yescharacteristic
19C2×C4×C47⋊C8C2211yescharacteristic
20#15688875—21no—
21#15688873—21no—
22#15688852—22no—
23D4⋊(C47⋊C8)—22no—
24#15688846—22no—
25#15688845—21no—
26C8×C47⋊C8—21no—
27C2×C4×D4×C47C2211yescharacteristic
28C47×#431C2211yescharacteristic
29C47×#431C2211yescharacteristic
30C47×#323—22no—
31C22×D188C2×C411yescharacteristic
32C22×C4×D47—21no—
33C2×#10625334—21no—
34C2×#10625334—21no—
35C2×#10625334—22no—
36C2×#10625334C814yescomplemented
37C22×C47⋊C8C2×C411yescharacteristic
38C22×C47⋊C8C2×C411yescharacteristic
39C4×D188—21no—
40C4×D188—21no—
41C4×D188—21no—
42C4×D188—21no—
43C2×C4⋊Dic47C2×C411yescharacteristic
44C2×(C2×D47)⋊C4—21no—
45#13093957—21no—
46#13093957—21no—
47C4⋊(C47⋊C8)—21no—
48C4⋊(C47⋊C8)D412yes—
49#13093945—21no—
50#13093945—21no—
51#13093944—21no—
52#13093944—21no—
53C22⋊(C47⋊C8)—21no—
54C22⋊(C47⋊C8)—21no—
55C4×C47⋊C8—21no—
56C4×C47⋊C8—21no—
57C4×C47⋊C8D411yescharacteristic
58C4×C47⋊C8D411yescharacteristic
59C4×C47⋊C8D411yescharacteristic
60C4×C47⋊C8D411yescharacteristic
61C22×D4×C47C2×C411yescharacteristic
62C23×C4×C47—21no—
63C4×D4×C47—21no—
64C4×D4×C47—21no—
65C4×D4×C47—21no—
66C4×D4×C47—21no—
67C2×C4⋊C4×C47C2×C411yescharacteristic
68C2×C22⋊C4×C47—21no—
69C2×C42×C47C2311yescharacteristic
70C4⋊C8×C47—21no—
71C4⋊C8×C47—21no—
72C22⋊C8×C47—21no—
73C22⋊C8×C47D412yes—
74C4×C8×C47—21no—
75C4×C8×C47—21no—
76C24×C47—21no—
77C23×D47—21no—
78C2×D4×C47—21no—
79C2×D4×C47—21no—
80C2×D4×C47—21no—
81C2×D4×C47—21no—
82C2×D4×C47—21no—
83C2×D4×C47C2×C812yes—
84C22×C4×C47—21no—
85C22×C4×C47—41no—
86C22×C4×C47—41no—
87C22×C4×C47—82no—
88C22×C4×C47C22×C411yescharacteristic
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47#4111yescharacteristic
91C22×Dic47—21no—
92C2×D188—21no—
93C2×D188—21no—
94C2×D188—21no—
95C2×D188—21no—
96C2×D188—21no—
97C2×D188C2×C812yes—
98C2×C4×D47—41no—
99C2×C4×D47—41no—
100C2×C4×D47—82no—
101C2×C8×C47—22no—
102C2×C8×C47—41no—
103C4⋊C4×C47—21no—
104C4⋊C4×C47—21no—
105C22⋊C4×C47—41no—
106C22⋊C4×C47—41no—
107C42×C47C2×D411yescharacteristic
108C42×C47C2×D411yescharacteristic
109C42×C47C2×D411yescharacteristic
110C42×C47#4111yescharacteristic
111#10625334—24no—
112#10625334—24no—
113(C2×D47)⋊C4—41no—
114(C2×D47)⋊C4—41no—
115C4⋊Dic47—21no—
116C4⋊Dic47—21no—
117C2×C47⋊C8—21no—
118C2×C47⋊C8—21no—
119C2×C47⋊C8—22no—
120C2×C47⋊C8—41no—
121C2×C47⋊C8C22⋊C411yescharacteristic
122C2×C47⋊C8C22⋊C411yescharacteristic
123C2×C47⋊C8C22⋊C411yescharacteristic
124C2×C47⋊C8C22⋊C411yescharacteristic
125C2×C47⋊C8C2×C812yes—
126C2×C47⋊C8M1612yes—
127C23×C47—22no—
128C23×C47—41no—
129C23×C47—41no—
130C23×C47—81no—
131C23×C47—81no—
132C23×C47C4×D411yescharacteristic
133C22×D47—22no—
134C22×D47—41no—
135C22×D47—41no—
136C22×D47—81no—
137C22×D47—81no—
138D4×C47—22no—
139D4×C47—22no—
140D4×C47—41no—
141D4×C47—41no—
142C2×C4×C47—22no—
143C2×C4×C47—41no—
144C2×C4×C47—41no—
145C2×C4×C47—82no—
146C2×C4×C47—82no—
147C2×C4×C47—81no—
148C2×C4×C47C2×C22⋊C411yescharacteristic
149C2×C4×C47C4×D411yescharacteristic
150C2×C4×C47#12111yescharacteristic
151C2×C4×C47#12111yescharacteristic
152C2×C4×C47#12411yescharacteristic
153C2×C4×C47#12711yescharacteristic
154C2×C4×C47C22×C811yescharacteristic
155C2×C4×C47C2×M1611yescharacteristic
156C2×C4×C47#13111yescharacteristic
157C2×C4×C47#13111yescharacteristic
158C2×Dic47—41no—
159C2×Dic47—81no—
160D188—22no—
161D188—22no—
162D188—41no—
163D188—41no—
164C4×D47—82no—
165C4×D47—82no—
166C8×C47—42no—
167C8×C47—81no—
168C47⋊C8—21no—
169C47⋊C8—21no—
170C47⋊C8—42no—
171C47⋊C8—81no—
172C47⋊C8C22⋊C812yes—
173C47⋊C8C22⋊C812yes—
174#9668—471nomaximal, Sylow
175C22×C47—21no—
176C22×C47—21no—
177C22×C47—42no—
178C22×C47—82no—
179C22×C47—82no—
180C22×C47—81no—
181C22×C47—81no—
182C22×C47#39011yescharacteristic
183C22×C47C8×D411yescharacteristic
184C22×C47#43611yescharacteristic
185C2×D47—42no—
186C2×D47—82no—
187C2×D47—81no—
188C2×D47—81no—
189C2×D47—82no—
190C4×C47—21no—
191C4×C47—21no—
192C4×C47—21no—
193C4×C47—81no—
194C4×C47C2×C22⋊C811yescharacteristic
195C4×C47#40811yescharacteristic
196C4×C47C8×D411yescharacteristic
197C4×C47#43611yescharacteristic
198C4×C47#47212yes—
199Dic47—81no—
200C2×C4×D8—471no—
201#1564—471no—
202#1478—471no—
203#1478—471no—
204#1460—471no—
205#1460D4711yescharacteristic, complemented
206#1450—471no—
207C2×C47—21no—
208C2×C47—21no—
209C2×C47—82no—
210C2×C47#195411yescharacteristic
211C2×C47#197611yescharacteristic
212C2×C47#197811yescharacteristic
213D47—82no—
214C22×D8—471no—
215C2×C4×D4—471no—
216C2×C4×D4C2×D4711yescharacteristic
217C4×D8—941no—
218C4×D8—941no—
219C4×D8—941no—
220C4×D8—941no—
221#431—471no—
222#431—471no—
223#431C2×D4711yescharacteristic
224#431C2×D4711yescharacteristic
225C2×#107—471no—
226C2×#102—471no—
227C2×#102—471no—
228C2×C4×C8—471no—
229#335—941no—
230#334—941no—
231D4⋊C8—942no—
232D4⋊C8—942no—
233#323—22no—
234#323—942no—
235#322—941no—
236C82—941no—
237C47#966811yescharacteristic, complemented, Sylow
238C22×D4—471no—
239C22×D4C4×D4711yescharacteristic
240C23×C4—21no—
241C23×C4—941no—
242C2×D8—474no—
243C2×D8—942no—
244C2×D8—941no—
245C2×D8—941no—
246C22×C8—471no—
247C22×C8—471no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—941no—
253C4×D4—941no—
254C4×D4—941no—
255C4×D4—941no—
256C2×C4⋊C4—471no—
257C2×C4⋊C4C4×D4711yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—941no—
260C2×C42C22×D4711yescharacteristic
261#107—941no—
262#107—941no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—472no—
266C4⋊C8—941no—
267#102—941no—
268#102—941no—
269#102—941no—
270#102—941no—
271C22⋊C8—21no—
272C22⋊C8—941no—
273C22⋊C8—941no—
274C22⋊C8C22⋊D4712yes—
275C4×C8—21no—
276C4×C8—21no—
277C4×C8—471no—
278C4×C8—471no—
279C4×C8—471no—
280C4×C8—471no—
281C4×C8—941no—
282C4×C8—941no—
283C24—21no—
284C24—941no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—472no—
291C2×D4—941no—
292C2×D4—941no—
293C2×D4—941no—
294C2×D4—941no—
295C2×D4—941no—
296C2×D4C8×D4712yes—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—82no—
301C22×C4—941no—
302C22×C4—3762no—
303C22×C4—1881no—
304C22×C4—1881no—
305C22×C4C2×C4×D4711yescharacteristic
306C22×C4#1062535011yescharacteristic
307C22×C4C2×C22⋊D4711yescharacteristic
308D8—944no—
309D8—944no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—471no—
313C2×C8—471no—
314C2×C8—472no—
315C2×C8—472no—
316C2×C8—471no—
317C2×C8—471no—
318C2×C8—941no—
319C2×C8—941no—
320C2×C8—942no—
321C2×C8—1881no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—941no—
325C4⋊C4—941no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—1881no—
329C22⋊C4—1881no—
330C42D4×D4711yescharacteristic
331C42D4×D4711yescharacteristic
332C42D4×D4711yescharacteristic
333C42#1062535211yescharacteristic
334C23—22no—
335C23—41no—
336C23—41no—
337C23—81no—
338C23—81no—
339C23—942no—
340C23—3761no—
341C23—3761no—
342C23—1881no—
343C23—1881no—
344C23C4×C22⋊D4711yescharacteristic
345D4—22no—
346D4—22no—
347D4—41no—
348D4—41no—
349D4—942no—
350D4—942no—
351D4—1881no—
352D4—1881no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—81no—
359C2×C4—3762no—
360C2×C4—3762no—
361C2×C4—3761no—
362C2×C4—1881no—
363C2×C4C22⋊C4×D4711yescharacteristic
364C2×C4(C22⋊D47)⋊C411yescharacteristic
365C2×C4#1309399611yescharacteristic
366C2×C4#1309399711yescharacteristic
367C2×C4#1309401011yescharacteristic
368C2×C4#1309402011yescharacteristic
369C2×C4C2×C8×D4711yescharacteristic
370C2×C4M16×D4711yescharacteristic
371C2×C4#1309403011yescharacteristic
372C2×C4#1309403211yescharacteristic
373C8—42no—
374C8—81no—
375C8—472no—
376C8—472no—
377C8—941no—
378C8—941no—
379C8—3761no—
380C8—1882no—
381C22—21no—
382C22—21no—
383C22—42no—
384C22—82no—
385C22—82no—
386C22—81no—
387C22—81no—
388C22—3762no—
389C22—3762no—
390C22—3761no—
391C22—3761no—
392C22—1882no—
393C22#1568902311yescharacteristic
394C22C8×C22⋊D4711yescharacteristic
395C22#1568919911yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—81no—
400C4—3761no—
401C4C22⋊C8×D4711yescharacteristic
402C4#1568908811yescharacteristic
403C4(C22⋊D47)⋊C811yescharacteristic
404C4#1568919811yescharacteristic
405C4#1568939212yes—
406C2—21no—
407C2—21no—
408C2—82no—
409C2—3762no—
410C2#2024418011yescharacteristic
411C2#2024428311yescharacteristic
412C2#2024429511yescharacteristic
subgroupG/H
centerC2×C4#13093997
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC47×#1460C2
socleC22×C47#390
prime radicalC22×#10625334C4
cosocleC2×C42×C47C23
hypercenter#1460D47
hypocenterC47#9668
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. #20242134C2semidirect
3. #20241780C2semidirect
4. #20241779C2semidirect
5. #20241708C2semidirect
6. #20241672C2semidirect
7. C47×#1460C2semidirect
36. C2×#10625334C8semidirect
205. #1460D47semidirect
237. C47#9668semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106253342
#202421342
#202417802
#202417792
#202417082
#202416722
C47×#14602
#966847