Finite Group Databasebeta

← #26110689

Subgroups — #26110689

Order 12032.

644 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246452C211yesmaximal, characteristic
2#20244193C211yesmaximal, characteristic
3#20244144C211yesmaximal, characteristic, complemented
4C2×#15688866C211yesmaximal, characteristic
5#20241229C211yesmaximal, characteristic, complemented
6#20241227C211yesmaximal, characteristic, complemented
7C47×#1947C211yesmaximal, characteristic, complemented
8C2×#13094021C2211yescharacteristic
9C2×C4×D188—21no—
10C2×#13093986—21no—
11C2×#13093957—21no—
12C2×C4⋊(C47⋊C8)C2211yescharacteristic
13C2×#13093944—22no—
14C2×C4×C47⋊C8C2211yescharacteristic
15#15689025—21no—
16#15689024—21no—
17#15689001—22no—
18C4×C4⋊Dic47C2211yescharacteristic
19#15688885—21no—
20#15688866C414yescomplemented
21C2×#107×C47—21no—
22C2×C4⋊C8×C47C2211yescharacteristic
23C47×#384C2211yescharacteristic
24C4×C4⋊C4×C47C2211yescharacteristic
25C47×#340—21no—
26C22×D188—21no—
27C22×D188—21no—
28C22×D188D412yes—
29C22×C4×D47—22no—
30C22×C47⋊C8—21no—
31C22×C47⋊C8—21no—
32#13094021—21no—
33#13094021—21no—
34#13094021C2×C412yes—
35#13094021Q812yes—
36C4×D188—42no—
37C4×D188—42no—
38#13093986—42no—
39#13093986—42no—
40C2×C4⋊Dic47D411yescharacteristic
41C2×C4⋊Dic47D411yescharacteristic
42C2×(C2×D47)⋊C4—22no—
43C2×(C2×D47)⋊C4—22no—
44C2×(C2×D47)⋊C4—22no—
45C2×C4×Dic47—21no—
46#13093957—42no—
47C4⋊(C47⋊C8)—21no—
48C4⋊(C47⋊C8)C2×C412yescomplemented
49#13093944—44no—
50C4×C47⋊C8—21no—
51C4×C47⋊C8—21no—
52C47⋊#95—21no—
53C22×C8×C47—21no—
54C2×C4⋊C4×C47—21no—
55C2×C4⋊C4×C47—21no—
56C2×C4⋊C4×C47—21no—
57C2×C4⋊C4×C47D411yescharacteristic
58C2×C4⋊C4×C47D411yescharacteristic
59C2×C42×C47—21no—
60C2×C42×C47C2311yescharacteristic
61#107×C47—42no—
62C4⋊C8×C47—21no—
63C4⋊C8×C47C2×C412yescomplemented
64#95×C47—21no—
65C23×D47—22no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47—41no—
69C22×C4×C47C2×D411yescharacteristic
70C22×C4×C47C2×D411yescharacteristic
71C22×C4×C47C2×D411yescharacteristic
72C22×Dic47—21no—
73C22×Dic47—21no—
74C2×D188—22no—
75C2×D188—22no—
76C2×D188—22no—
77C2×D188—22no—
78C2×D188—22no—
79C2×D188—41no—
80C2×D188—41no—
81C2×D188—41no—
82C2×D188—41no—
83C2×D188—41no—
84C2×D188—41no—
85C2×D188—41no—
86C2×D188—41no—
87C2×D188—42no—
88C2×D188—42no—
89C2×D188C4⋊C414yes—
90C2×C4×D47—44no—
91C2×C4×D47—44no—
92C2×C4×D47—82no—
93C2×C8×C47—22no—
94C2×C8×C47—41no—
95C2×C8×C47—41no—
96C4⋊C4×C47—21no—
97C4⋊C4×C47—21no—
98C4⋊C4×C47—21no—
99C4⋊C4×C47—42no—
100C4⋊C4×C47—41no—
101C4⋊C4×C47—41no—
102C4⋊C4×C47—41no—
103C4⋊C4×C47—41no—
104C4⋊C4×C47D812yes—
105C42×C47—41no—
106C42×C47—41no—
107C42×C47C22×C411yescharacteristic
108C42×C47C2×Q811yescharacteristic
109C42×C47#4111yescharacteristic
110C42×C47#4111yescharacteristic
111(C2×D47)⋊C4—44no—
112(C2×D47)⋊C4—44no—
113(C2×D47)⋊C4—82no—
114C4⋊Dic47—21no—
115C4⋊Dic47—21no—
116C4⋊Dic47—21no—
117C4⋊Dic47D812yes—
118C4×Dic47—41no—
119C4×Dic47—41no—
120C2×C47⋊C8—22no—
121C2×C47⋊C8—22no—
122C2×C47⋊C8—41no—
123C2×C47⋊C8—41no—
124C2×C47⋊C8—41no—
125C2×C47⋊C8—41no—
126C23×C47#12011yescharacteristic
127C22×D47—24no—
128C22×D47—42no—
129C22×D47—42no—
130C22×D47—42no—
131C22×D47—42no—
132C22×D47—42no—
133C22×D47—42no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—22no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—41no—
141C2×C4×C47—41no—
142C2×C4×C47—81no—
143C2×C4×C47—81no—
144C2×C4×C47—81no—
145C2×C4×C47C2×C4⋊C411yescharacteristic
146C2×C4×C47C4×D411yescharacteristic
147C2×C4×C47C4×D411yescharacteristic
148C2×C4×C47C22⋊Q811yescharacteristic
149C2×C4×C47C22⋊Q811yescharacteristic
150C2×C4×C47#12311yescharacteristic
151C2×C4×C47C2×D811yescharacteristic
152C2×C4×C47C2×D811yescharacteristic
153C2×C4×C47#13511yescharacteristic
154C2×C4×C47#13511yescharacteristic
155C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C47#13711yescharacteristic
158C2×C4×C47#13711yescharacteristic
159C2×Dic47—22no—
160C2×Dic47—41no—
161C2×Dic47—41no—
162C2×Dic47—41no—
163C2×Dic47—41no—
164C2×Dic47—41no—
165D188—44no—
166D188—42no—
167D188—42no—
168D188—42no—
169D188—42no—
170D188—42no—
171D188—42no—
172D188—42no—
173D188—42no—
174D188—82no—
175C4×D47—88no—
176C8×C47—42no—
177C47⋊C8—42no—
178C47⋊C8—42no—
179#8920—471nomaximal, Sylow
180C22×C47#38511yescharacteristic
181C22×C47#44711yescharacteristic
182C22×C47#44711yescharacteristic
183C22×C47#45211yescharacteristic
184C22×C47#45211yescharacteristic
185C22×C47#45311yescharacteristic
186C22×C47#45511yescharacteristic
187C2×D47—44no—
188C2×D47—44no—
189C2×D47—44no—
190C2×D47—82no—
191C2×D47—82no—
192C2×D47—82no—
193C2×D47—82no—
194C4×C47—21no—
195C4×C47—21no—
196C4×C47—42no—
197C4×C47—81no—
198C4×C47—161no—
199C4×C47C4×D811yescharacteristic
200C4×C47C4×D811yescharacteristic
201C4×C47#44011yescharacteristic
202C4×C47#44011yescharacteristic
203C4×C47#47411yescharacteristic
204C4×C47#47411yescharacteristic
205C4×C47#47811yescharacteristic
206C4×C47#47811yescharacteristic
207Dic47—42no—
208Dic47—81no—
209#2366—471no—
210#1957—471no—
211#1947—471no—
212#1947D4711yescharacteristic, complemented
213C2×#331—471no—
214#1279—471no—
215#1279—471no—
216C2×C47#161911yescharacteristic
217C2×C47#163011yescharacteristic
218C2×C47#164111yescharacteristic
219C2×C47#164111yescharacteristic
220C2×C47#185611yescharacteristic
221C2×C47#186211yescharacteristic
222C2×C47#186211yescharacteristic
223D47—84no—
224C2×#127—471no—
225C2×C4×D4—941no—
226C2×C4×D4—941no—
227C2×#107—21no—
228C2×#107—941no—
229C2×C4⋊C8—471no—
230C2×C4⋊C8C2×D4711yescharacteristic
231C2×#102—942no—
232C2×C4×C8—471no—
233#390—941no—
234#390—941no—
235#386—942no—
236#384C2×D4711yescharacteristic
237C4×C4⋊C4—471no—
238C4×C4⋊C4C2×D4711yescharacteristic
239#340—21no—
240#340—941no—
241#331—474no—
242C47#892011yescharacteristic, complemented, Sylow
243C22×D4—472no—
244C22×D4—941no—
245C22×D4—941no—
246C23×C4—942no—
247C22×C8—21no—
248C22×C8—941no—
249C22×C8—941no—
250#127—472no—
251#127—472no—
252#127—941no—
253#127—941no—
254C4×D4—1882no—
255C4×D4—1882no—
256C4×D4—1882no—
257C4×D4—1882no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—471no—
262C2×C4⋊C4—471no—
263C2×C4⋊C4C22⋊D4711yescharacteristic
264C2×C4⋊C4C22⋊D4711yescharacteristic
265C2×C22⋊C4—942no—
266C2×C22⋊C4—942no—
267C2×C22⋊C4—942no—
268C2×C42—21no—
269C2×C42—941no—
270C2×C42C22×D4711yescharacteristic
271#107—42no—
272#107—1882no—
273C4⋊C8—21no—
274C4⋊C8—472no—
275C4⋊C8—941no—
276C4⋊C8C4×D4712yescomplemented
277#102—1884no—
278C4×C8—941no—
279C4×C8—941no—
280#95—21no—
281#95—941no—
282C24—942no—
283C2×D4—474no—
284C2×D4—942no—
285C2×D4—942no—
286C2×D4—942no—
287C2×D4—942no—
288C2×D4—942no—
289C2×D4—1882no—
290C2×D4—1882no—
291C2×D4—1881no—
292C2×D4—1881no—
293C2×D4—1881no—
294C2×D4—1881no—
295C2×D4—1881no—
296C2×D4—1881no—
297C2×D4—1881no—
298C2×D4—1881no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—41no—
302C22×C4—941no—
303C22×C4—941no—
304C22×C4—3762no—
305C22×C4—1884no—
306C22×C4—1884no—
307C22×C4D4×D4711yescharacteristic
308C22×C4D4×D4711yescharacteristic
309C22×C4C2×C22⋊D4711yescharacteristic
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—942no—
314C2×C8—942no—
315C2×C8—1881no—
316C2×C8—1881no—
317C2×C8—1881no—
318C2×C8—1881no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—42no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—472no—
328C4⋊C4—941no—
329C4⋊C4—941no—
330C4⋊C4—941no—
331C4⋊C4#1062533412yes—
332C22⋊C4—3762no—
333C22⋊C4—1884no—
334C22⋊C4—1884no—
335C42—41no—
336C42—41no—
337C42—1881no—
338C42—1881no—
339C42C2×C4×D4711yescharacteristic
340C42#1062535011yescharacteristic
341C42Q8×D4711yescharacteristic
342C42#1062535411yescharacteristic
343C23—944no—
344C23—1882no—
345C23—1882no—
346C23—1882no—
347C23—1882no—
348C23—1882no—
349C23—1882no—
350C23#1309399211yescharacteristic
351D4—3762no—
352D4—1884no—
353D4—1882no—
354D4—1882no—
355D4—1882no—
356D4—1882no—
357D4—1882no—
358D4—1882no—
359D4—1882no—
360D4—1882no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—942no—
373C2×C4—3768no—
374C2×C4—1881no—
375C2×C4—1881no—
376C2×C4—1881no—
377C2×C4—1881no—
378C2×C4—1881no—
379C2×C4C4⋊C4×D4711yescharacteristic
380C2×C4C4×C22⋊D4711yescharacteristic
381C2×C4#1309398611yescharacteristic
382C2×C4#1309400011yescharacteristic
383C2×C4#1309400211yescharacteristic
384C2×C4#1309400911yescharacteristic
385C2×C4D8×D4711yescharacteristic
386C2×C4C2×#1062533411yescharacteristic
387C2×C4#1309404411yescharacteristic
388C2×C4#1309404711yescharacteristic
389C2×C4#1309404811yescharacteristic
390C2×C4#1309404911yescharacteristic
391C2×C4#1309405511yescharacteristic
392C2×C4#1309405611yescharacteristic
393C8—42no—
394C8—1882no—
395C8—1882no—
396C22—3762no—
397C22—3762no—
398C22—3762no—
399C22—3762no—
400C22—1884no—
401C22—1884no—
402C22—1884no—
403C22#1568899411yescharacteristic
404C22#1568925511yescharacteristic
405C22#1568925611yescharacteristic
406C22#1568928311yescharacteristic
407C22#1568928411yescharacteristic
408C22#1568928911yescharacteristic
409C22#1568929911yescharacteristic
410C4—21no—
411C4—21no—
412C4—42no—
413C4—81no—
414C4—161no—
415C4—3761no—
416C4—1882no—
417C4C4×#1062533411yescharacteristic
418C4#1568920511yescharacteristic
419C4#1568922111yescharacteristic
420C4#1568922211yescharacteristic
421C4#1568940011yescharacteristic
422C4#1568940211yescharacteristic
423C4#1568942011yescharacteristic
424C4#1568942611yescharacteristic
425C2—3764no—
426C2#2024244111yescharacteristic
427C2#2024250811yescharacteristic
428C2#2024257911yescharacteristic
429C2#2024258011yescharacteristic
430C2#2024359611yescharacteristic
431C2#2024363211yescharacteristic
432C2#2024363411yescharacteristic
subgroupG/H
centerC23#13093992
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1947C2
socleC23×C47#120
prime radicalC2×#13094021C22
cosocleC2×C42×C47C23
hypercenter#1947D47
hypocenterC47#8920
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
3. #20244144C2semidirect
5. #20241229C2semidirect
6. #20241227C2semidirect
7. C47×#1947C2semidirect
20. #15688866C4semidirect
48. C4⋊(C47⋊C8)C2×C4semidirect
63. C4⋊C8×C47C2×C4semidirect
212. #1947D47semidirect
242. C47#8920semidirect
276. C4⋊C8C4×D47semidirect

Maximal subgroups

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

subgroupindex
#202464522
#202441932
#202441442
C2×#156888662
#202412292
#202412272
C47×#19472
#892047