Finite Group Databasebeta

← #26110441

Subgroups — #26110441

Order 12032.

618 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊C4×D188C211yesmaximal, characteristic
2#20244146C211yesmaximal, characteristic, complemented
3#20243548C211yesmaximal, characteristic, complemented
4#20243389C211yesmaximal, characteristic
5C2×#15688852C211yesmaximal, characteristic
6#20241272C211yesmaximal, characteristic, complemented
7C47×#1279C211yesmaximal, characteristic, complemented
8C2×C4×D188—21no—
9C2×C4×D188C2211yescharacteristic
10C2×C4⋊C4×D47—21no—
11C2×#13093958—22no—
12C2×#13093957—21no—
13C2×C4⋊(C47⋊C8)C2211yescharacteristic
14C2×#13093946—21no—
15#15689021—21no—
16#15688997—22no—
17#15688993C2211yescharacteristic
18#15688993C2211yescharacteristic
19#15688980—21no—
20#15688886—21no—
21#15688885—21no—
22#15688852C414yescomplemented
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×C4×C8×C47C2211yescharacteristic
25C4×C4⋊C4×C47C2211yescharacteristic
26C22×D188D411yescharacteristic
27C22×C4×D47—21no—
28C22×C4×D47—22no—
29C22×C47⋊C8—21no—
30C4×D188—21no—
31C4×D188—21no—
32C4×D188—42no—
33C4×D188—42no—
34C4×D188C2×C412yes—
35C4×D188Q812yes—
36C2×C4⋊Dic47—21no—
37C2×C4⋊Dic47—21no—
38C2×C4⋊Dic47—21no—
39C2×C4⋊Dic47—21no—
40C2×C4⋊Dic47—21no—
41C2×C4⋊Dic47D411yescharacteristic
42C2×C4⋊Dic47D412yes—
43C2×Dic47⋊C4—22no—
44C4⋊C4×D47—42no—
45C4⋊C4×D47—42no—
46C2×(C2×D47)⋊C4—21no—
47C2×(C2×D47)⋊C4—22no—
48#13093958—44no—
49#13093957—42no—
50C4⋊(C47⋊C8)—21no—
51C4⋊(C47⋊C8)C2×C412yescomplemented
52#13093946—42no—
53C47⋊#95—22no—
54C22×C8×C47—21no—
55C22×C8×C47—21no—
56C2×C4⋊C4×C47D411yescharacteristic
57C2×C4⋊C4×C47D411yescharacteristic
58C2×C42×C47—21no—
59C2×C42×C47C2311yescharacteristic
60C4⋊C8×C47—21no—
61C4⋊C8×C47—21no—
62C4×C8×C47—21no—
63C4×C8×C47C2×C412yescomplemented
64#95×C47—21no—
65C23×D47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47C2×D411yescharacteristic
69C22×C4×C47C2×D411yescharacteristic
70C22×C4×C47C2×D411yescharacteristic
71C22×Dic47—21no—
72C22×Dic47—22no—
73C22×Dic47—41no—
74C2×D188—21no—
75C2×D188—21no—
76C2×D188—21no—
77C2×D188C4⋊C412yes—
78C2×D188D812yes—
79C2×D188Q1612yes—
80C2×C4×D47—22no—
81C2×C4×D47—22no—
82C2×C4×D47—41no—
83C2×C4×D47—41no—
84C2×C4×D47—41no—
85C2×C4×D47—41no—
86C2×C4×D47—44no—
87C2×C4×D47—44no—
88C2×C4×D47—82no—
89C2×C8×C47—22no—
90C2×C8×C47—22no—
91C2×C8×C47—22no—
92C2×C8×C47—41no—
93C2×C8×C47—41no—
94C2×C8×C47—41no—
95C4⋊C4×C47—21no—
96C4⋊C4×C47—21no—
97C4⋊C4×C47—21no—
98C4⋊C4×C47D812yes—
99C42×C47—41no—
100C42×C47—41no—
101C42×C47C22×C411yescharacteristic
102C42×C47C2×Q811yescharacteristic
103C42×C47#4111yescharacteristic
104C42×C47#4111yescharacteristic
105(C2×D47)⋊C4—22no—
106(C2×D47)⋊C4—22no—
107(C2×D47)⋊C4—44no—
108C4⋊Dic47—21no—
109C4⋊Dic47—41no—
110C4⋊Dic47—41no—
111C4⋊Dic47—41no—
112C4⋊Dic47—41no—
113C4⋊Dic47—42no—
114C4⋊Dic47—42no—
115C4⋊Dic47—41no—
116C4⋊Dic47—41no—
117C4⋊Dic47—41no—
118C4⋊Dic47—41no—
119C4⋊Dic47C4⋊C412yes—
120Dic47⋊C4—44no—
121C2×C47⋊C8—22no—
122C2×C47⋊C8—41no—
123C2×C47⋊C8—41no—
124C23×C47#12011yescharacteristic
125C22×D47—22no—
126C22×D47—22no—
127C22×D47—22no—
128C22×D47—41no—
129C22×D47—41no—
130C22×D47—41no—
131C22×D47—41no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—22no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47C2×C4⋊C411yescharacteristic
141C2×C4×C47C4×D411yescharacteristic
142C2×C4×C47C4×D411yescharacteristic
143C2×C4×C47C22⋊Q811yescharacteristic
144C2×C4×C47C22⋊Q811yescharacteristic
145C2×C4×C47#12311yescharacteristic
146C2×C4×C47C2×D811yescharacteristic
147C2×C4×C47C2×D811yescharacteristic
148C2×C4×C47C2×Q1611yescharacteristic
149C2×C4×C47#13511yescharacteristic
150C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C47#13711yescharacteristic
153C2×C4×C47#13711yescharacteristic
154C2×Dic47—22no—
155C2×Dic47—41no—
156C2×Dic47—41no—
157C2×Dic47—42no—
158C2×Dic47—42no—
159C2×Dic47—42no—
160C2×Dic47—81no—
161C2×Dic47—81no—
162C2×Dic47—81no—
163D188—22no—
164D188—22no—
165D188—22no—
166D188#10714yescomplemented
167C4×D47—42no—
168C4×D47—42no—
169C4×D47—42no—
170C4×D47—42no—
171C4×D47—88no—
172C8×C47—24no—
173C8×C47—81no—
174C47⋊C8—42no—
175#8882—471nomaximal, Sylow
176C22×C47#38511yescharacteristic
177C22×C47#44711yescharacteristic
178C22×C47#44711yescharacteristic
179C22×C47#45111yescharacteristic
180C22×C47#45211yescharacteristic
181C22×C47#45311yescharacteristic
182C22×C47#45611yescharacteristic
183C2×D47—24no—
184C2×D47—42no—
185C2×D47—42no—
186C2×D47—42no—
187C2×D47—42no—
188C2×D47—42no—
189C2×D47—42no—
190C4×C47—21no—
191C4×C47—21no—
192C4×C47—42no—
193C4×C47—81no—
194C4×C47C2×#10711yescharacteristic
195C4×C47#42811yescharacteristic
196C4×C47C4×D811yescharacteristic
197C4×C47#44011yescharacteristic
198C4×C47#47411yescharacteristic
199C4×C47#47811yescharacteristic
200C4×C47#48011yescharacteristic
201C4×C47#48411yescharacteristic
202Dic47—42no—
203Dic47—82no—
204Dic47—161no—
205D4×C4⋊C4—471no—
206#1947—471no—
207#1845—471no—
208#1802—471no—
209C2×D4⋊C8—471no—
210#1296—471no—
211#1279D4711yescharacteristic, complemented
212C2×C47#161911yescharacteristic
213C2×C47#163211yescharacteristic
214C2×C47#164711yescharacteristic
215C2×C47#164911yescharacteristic
216C2×C47#185211yescharacteristic
217C2×C47#185911yescharacteristic
218C2×C47#186211yescharacteristic
219D47—44no—
220C2×C4×D4—471no—
221C2×C4×D4—941no—
222C22×C4⋊C4—941no—
223C2×#107—942no—
224C2×#107—941no—
225C2×C4⋊C8—471no—
226C2×C4⋊C8C2×D4711yescharacteristic
227C2×#102—941no—
228C2×C4×C8C2×D4711yescharacteristic
229#389—941no—
230#385—942no—
231#384—471no—
232#384—471no—
233#380—941no—
234C4×C4⋊C4C2×D4711yescharacteristic
235#340—941no—
236#340—941no—
237D4⋊C8—474no—
238C47#888211yescharacteristic, complemented, Sylow
239C22×D4—471no—
240C23×C4—942no—
241C23×C4—941no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—941no—
245C4×D4—472no—
246C4×D4—472no—
247C4×D4—941no—
248C4×D4—941no—
249C4×D4—1882no—
250C4×D4—1882no—
251C2×C4⋊C4—471no—
252C2×C4⋊C4—472no—
253C2×C4⋊C4—942no—
254C2×C4⋊C4—941no—
255C2×C4⋊C4—941no—
256C2×C4⋊C4—941no—
257C2×C4⋊C4—941no—
258C2×C4⋊C4—941no—
259C2×C4⋊C4—1882no—
260C2×C4⋊C4—1882no—
261C2×C4⋊C4D18811yescharacteristic
262C2×C4⋊C4D18811yescharacteristic
263C2×C22⋊C4—941no—
264C2×C22⋊C4—942no—
265C2×C42—21no—
266C2×C42C22×D4711yescharacteristic
267#107—1884no—
268#107—1882no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—472no—
272C4⋊C8—941no—
273#102—1882no—
274C4×C8—21no—
275C4×C8C4×D4712yescomplemented
276#95—21no—
277#95—942no—
278C24—941no—
279C2×D4—472no—
280C2×D4—472no—
281C2×D4—472no—
282C2×D4—941no—
283C2×D4—941no—
284C2×D4—941no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—941no—
288C22×C4—942no—
289C22×C4—942no—
290C22×C4—942no—
291C22×C4—3762no—
292C22×C4—1884no—
293C22×C4—1884no—
294C22×C4—1881no—
295C22×C4—1881no—
296C22×C4—1881no—
297C22×C4—1881no—
298C22×C4—1881no—
299C22×C4C2×D18811yescharacteristic
300C22×C4D4×D4711yescharacteristic
301C22×C4D4×D4711yescharacteristic
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—942no—
309C2×C8—1881no—
310C2×C8—1881no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—472no—
315C4⋊C4—941no—
316C4⋊C4—1882no—
317C4⋊C4—1882no—
318C4⋊C4—1884no—
319C4⋊C4—1881no—
320C4⋊C4—1881no—
321C4⋊C4—1881no—
322C4⋊C4—1881no—
323C4⋊C4—1881no—
324C4⋊C4—1881no—
325C4⋊C4—1881no—
326C4⋊C4—1881no—
327C4⋊C4D37612yes—
328C22⋊C4—942no—
329C22⋊C4—942no—
330C22⋊C4—1884no—
331C42—41no—
332C42—41no—
333C42C2×C4×D4711yescharacteristic
334C42#1062535011yescharacteristic
335C42#1062535211yescharacteristic
336C42Q8×D4711yescharacteristic
337C23—942no—
338C23—942no—
339C23—942no—
340C23—1881no—
341C23—1881no—
342C23—1881no—
343C23—1881no—
344C23#1309399411yescharacteristic
345D4—474no—
346D4—942no—
347D4—942no—
348D4—942no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—942no—
358C2×C4—3768no—
359C2×C4—3761no—
360C2×C4—3761no—
361C2×C4—3761no—
362C2×C4—1882no—
363C2×C4—1882no—
364C2×C4—1882no—
365C2×C4—1881no—
366C2×C4—1881no—
367C2×C4—1882no—
368C2×C4—1882no—
369C2×C4—1882no—
370C2×C4—1882no—
371C2×C4C4⋊C4×D4711yescharacteristic
372C2×C4(C22⋊D47)⋊C411yescharacteristic
373C2×C4C4×D18811yescharacteristic
374C2×C4#1309400211yescharacteristic
375C2×C4#1309400411yescharacteristic
376C2×C4#1309400611yescharacteristic
377C2×C4D8×D4711yescharacteristic
378C2×C4C2×D37611yescharacteristic
379C2×C4Q16×D4711yescharacteristic
380C2×C4#1309404611yescharacteristic
381C2×C4#1309405111yescharacteristic
382C2×C4#1309405211yescharacteristic
383C2×C4#1309405311yescharacteristic
384C2×C4#1309405711yescharacteristic
385C8—24no—
386C8—81no—
387C8—1882no—
388C22—944no—
389C22—1882no—
390C22—1882no—
391C22—1882no—
392C22—1882no—
393C22—1882no—
394C22—1882no—
395C22#1568899711yescharacteristic
396C22#1568925811yescharacteristic
397C22#1568925911yescharacteristic
398C22#1568928011yescharacteristic
399C22#1568928711yescharacteristic
400C22#1568929211yescharacteristic
401C22#1568930711yescharacteristic
402C4—21no—
403C4—21no—
404C4—42no—
405C4—81no—
406C4—3762no—
407C4—1882no—
408C4—7521no—
409C4#107×D4711yescharacteristic
410C4#1568916211yescharacteristic
411C4C4×D37611yescharacteristic
412C4#1568922511yescharacteristic
413C4#1568940411yescharacteristic
414C4#1568942411yescharacteristic
415C4#1568943511yescharacteristic
416C4#1568945711yescharacteristic
417C2—1884no—
418C2#2024244411yescharacteristic
419C2#2024252511yescharacteristic
420C2#2024262611yescharacteristic
421C2#2024263911yescharacteristic
422C2#2024357711yescharacteristic
423C2#2024361511yescharacteristic
424C2#2024363811yescharacteristic
subgroupG/H
centerC23#13093994
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1279C2
socleC23×C47#120
prime radicalC22×D188D4
cosocleC2×C42×C47C23
hypercenter#1279D47
hypocenterC47#8882
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #20244146C2semidirect
3. #20243548C2semidirect
6. #20241272C2semidirect
7. C47×#1279C2semidirect
22. #15688852C4semidirect
51. C4⋊(C47⋊C8)C2×C4semidirect
63. C4×C8×C47C2×C4semidirect
166. D188#107semidirect
211. #1279D47semidirect
238. C47#8882semidirect
275. C4×C8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×D1882
#202441462
#202435482
#202433892
C2×#156888522
#202412722
C47×#12792
#888247