Finite Group Databasebeta

← #26110490

Subgroups — #26110490

Order 12032.

546 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246335C211yesmaximal, characteristic
2#20244146C211yesmaximal, characteristic, complemented
3#20243545C211yesmaximal, characteristic, complemented
4#20243389C211yesmaximal, characteristic
5C2×#15688852C211yesmaximal, characteristic
6#20241272C211yesmaximal, characteristic, complemented
7C47×#1279C211yesmaximal, characteristic, complemented
8C2×C4×D188C2211yescharacteristic
9C2×#13093982—21no—
10C2×#13093957—21no—
11C2×#13093956—22no—
12C2×C4⋊(C47⋊C8)C2211yescharacteristic
13C2×#13093946—21no—
14#15689025—21no—
15#15689015—22no—
16#15688993C2211yescharacteristic
17#15688993C2211yescharacteristic
18#15688980—21no—
19C4×C4⋊Dic47—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×C47⋊C8—21no—
29C4×D188—21no—
30C4×D188—21no—
31C4×D188C2×C412yes—
32C4×D188Q812yes—
33#13093982—42no—
34#13093982—42no—
35C2×C4⋊Dic47—21no—
36C2×C4⋊Dic47—21no—
37C2×C4⋊Dic47—21no—
38C2×C4⋊Dic47—21no—
39C2×C4⋊Dic47—21no—
40C2×C4⋊Dic47D411yescharacteristic
41C2×C4⋊Dic47D412yes—
42C2×(C2×D47)⋊C4—21no—
43C2×(C2×D47)⋊C4—22no—
44C2×(C2×D47)⋊C4—22no—
45C2×C4×Dic47—22no—
46#13093957—42no—
47#13093956—44no—
48C4⋊(C47⋊C8)—21no—
49C4⋊(C47⋊C8)C2×C412yes—
50#13093946—42no—
51C47⋊#95—22no—
52C22×C8×C47—21no—
53C22×C8×C47—21no—
54C2×C4⋊C4×C47D411yescharacteristic
55C2×C4⋊C4×C47D411yescharacteristic
56C2×C42×C47—21no—
57C2×C42×C47C2311yescharacteristic
58C4⋊C8×C47—21no—
59C4⋊C8×C47—21no—
60C4×C8×C47—21no—
61C4×C8×C47C2×C412yes—
62#95×C47—21no—
63C23×D47—21no—
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47C2×D411yescharacteristic
67C22×C4×C47C2×D411yescharacteristic
68C22×C4×C47C2×D411yescharacteristic
69C22×Dic47—21no—
70C22×Dic47—22no—
71C22×Dic47—41no—
72C2×D188—21no—
73C2×D188—21no—
74C2×D188—21no—
75C2×D188—21no—
76C2×D188—21no—
77C2×D188C4⋊C412yes—
78C2×C4×D47—22no—
79C2×C4×D47—22no—
80C2×C4×D47—41no—
81C2×C4×D47—41no—
82C2×C4×D47—41no—
83C2×C4×D47—41no—
84C2×C8×C47—22no—
85C2×C8×C47—22no—
86C2×C8×C47—22no—
87C2×C8×C47—41no—
88C2×C8×C47—41no—
89C2×C8×C47—41no—
90C4⋊C4×C47—21no—
91C4⋊C4×C47—21no—
92C4⋊C4×C47—21no—
93C4⋊C4×C47SD1612yes—
94C42×C47—41no—
95C42×C47—41no—
96C42×C47C22×C411yescharacteristic
97C42×C47C2×Q811yescharacteristic
98C42×C47#4111yescharacteristic
99C42×C47#4111yescharacteristic
100(C2×D47)⋊C4—22no—
101(C2×D47)⋊C4—22no—
102(C2×D47)⋊C4—44no—
103(C2×D47)⋊C4—82no—
104C4⋊Dic47—21no—
105C4⋊Dic47—41no—
106C4⋊Dic47—41no—
107C4⋊Dic47—41no—
108C4⋊Dic47—41no—
109C4⋊Dic47—42no—
110C4⋊Dic47—42no—
111C4⋊Dic47—41no—
112C4⋊Dic47—41no—
113C4⋊Dic47—41no—
114C4⋊Dic47—41no—
115C4⋊Dic47C4⋊C412yes—
116C4×Dic47—44no—
117C2×C47⋊C8—22no—
118C2×C47⋊C8—41no—
119C2×C47⋊C8—41no—
120C23×C47#12011yescharacteristic
121C22×D47—22no—
122C22×D47—41no—
123C22×D47—41no—
124C22×D47—41no—
125C22×D47—41no—
126C22×D47—41no—
127C22×D47—41no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—22no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47—41no—
136C2×C4×C47C2×C4⋊C411yescharacteristic
137C2×C4×C47C4×D411yescharacteristic
138C2×C4×C47C4×D411yescharacteristic
139C2×C4×C47C22⋊Q811yescharacteristic
140C2×C4×C47C22⋊Q811yescharacteristic
141C2×C4×C47#12311yescharacteristic
142C2×C4×C47C2×SD1611yescharacteristic
143C2×C4×C47#13511yescharacteristic
144C2×C4×C47#13511yescharacteristic
145C2×C4×C47#13511yescharacteristic
146C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C47#13711yescharacteristic
150C2×Dic47—22no—
151C2×Dic47—41no—
152C2×Dic47—41no—
153C2×Dic47—42no—
154C2×Dic47—42no—
155C2×Dic47—42no—
156C2×Dic47—81no—
157C2×Dic47—81no—
158C2×Dic47—81no—
159D188—22no—
160D188—22no—
161D188—41no—
162D188—41no—
163C4×D47—42no—
164C4×D47—42no—
165C4×D47—42no—
166C4×D47—42no—
167C8×C47—24no—
168C8×C47—81no—
169C47⋊C8—42no—
170#8889—471nomaximal, Sylow
171C22×C47#38511yescharacteristic
172C22×C47#44911yescharacteristic
173C22×C47#44911yescharacteristic
174C22×C47#45011yescharacteristic
175C22×C47#45211yescharacteristic
176C22×C47#45311yescharacteristic
177C22×C47#45611yescharacteristic
178C2×D47—42no—
179C2×D47—42no—
180C2×D47—42no—
181C2×D47—81no—
182C2×D47—81no—
183C2×D47—81no—
184C2×D47—81no—
185C4×C47—21no—
186C4×C47—21no—
187C4×C47—42no—
188C4×C47—81no—
189C4×C47#42711yescharacteristic
190C4×C47#42811yescharacteristic
191C4×C47C4×SD1611yescharacteristic
192C4×C47#44211yescharacteristic
193C4×C47#47611yescharacteristic
194C4×C47#47811yescharacteristic
195C4×C47#48211yescharacteristic
196C4×C47#48511yescharacteristic
197Dic47—42no—
198Dic47—82no—
199Dic47—161no—
200#2354—471no—
201#1947—471no—
202#1844—471no—
203#1802—471no—
204C2×D4⋊C8—471no—
205#1296—471no—
206#1279D4711yescharacteristic, complemented
207C2×C47#162411yescharacteristic
208C2×C47#163111yescharacteristic
209C2×C47#165211yescharacteristic
210C2×C47#165411yescharacteristic
211C2×C47#185411yescharacteristic
212C2×C47#185911yescharacteristic
213C2×C47#186411yescharacteristic
214D47—82no—
215C2×C4×D4—471no—
216C2×#117—941no—
217C2×#107—941no—
218C2×#106—942no—
219C2×C4⋊C8—471no—
220C2×C4⋊C8C2×D4711yescharacteristic
221C2×#102—941no—
222C2×C4×C8C2×D4711yescharacteristic
223#390—941no—
224#388—942no—
225#384—471no—
226#384—471no—
227#380—941no—
228C4×C4⋊C4—941no—
229C4×C4⋊C4C2×D4711yescharacteristic
230#340—941no—
231#340—941no—
232D4⋊C8—474no—
233C47#888911yescharacteristic, complemented, Sylow
234C22×D4—471no—
235C23×C4—941no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—941no—
239C4×D4—472no—
240C4×D4—472no—
241C4×D4—941no—
242C4×D4—941no—
243#117—1882no—
244#117—1882no—
245C2×C4⋊C4—471no—
246C2×C4⋊C4—472no—
247C2×C4⋊C4—941no—
248C2×C4⋊C4—941no—
249C2×C4⋊C4—941no—
250C2×C4⋊C4—941no—
251C2×C4⋊C4—941no—
252C2×C4⋊C4D18811yescharacteristic
253C2×C4⋊C4D18811yescharacteristic
254C2×C22⋊C4—941no—
255C2×C22⋊C4—942no—
256C2×C22⋊C4—942no—
257C2×C42—21no—
258C2×C42—942no—
259C2×C42C22×D4711yescharacteristic
260#107—1882no—
261#106—1884no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—472no—
265C4⋊C8—941no—
266#102—1882no—
267C4×C8—21no—
268C4×C8C4×D4712yes—
269#95—21no—
270#95—942no—
271C24—941no—
272C2×D4—472no—
273C2×D4—941no—
274C2×D4—941no—
275C2×D4—941no—
276C2×D4—941no—
277C2×D4—941no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—941no—
281C22×C4—942no—
282C22×C4—942no—
283C22×C4—942no—
284C22×C4—1881no—
285C22×C4—1881no—
286C22×C4—1881no—
287C22×C4—1881no—
288C22×C4—1881no—
289C22×C4C2×D18811yescharacteristic
290C22×C4D4×D4711yescharacteristic
291C22×C4D4×D4711yescharacteristic
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—942no—
299C2×C8—1881no—
300C2×C8—1881no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—472no—
305C4⋊C4—941no—
306C4⋊C4—1882no—
307C4⋊C4—1882no—
308C4⋊C4—1881no—
309C4⋊C4—1881no—
310C4⋊C4—1881no—
311C4⋊C4—1881no—
312C4⋊C4—1881no—
313C4⋊C4—1881no—
314C4⋊C4—1881no—
315C4⋊C4—1881no—
316C4⋊C4#1062532512yes—
317C22⋊C4—942no—
318C22⋊C4—942no—
319C22⋊C4—3762no—
320C22⋊C4—1884no—
321C42—41no—
322C42—41no—
323C42—1884no—
324C42C2×C4×D4711yescharacteristic
325C42#1062535011yescharacteristic
326C42#1062535211yescharacteristic
327C42Q8×D4711yescharacteristic
328C23—942no—
329C23—1881no—
330C23—1881no—
331C23—1881no—
332C23—1881no—
333C23—1881no—
334C23—1881no—
335C23#1309399411yescharacteristic
336D4—942no—
337D4—942no—
338D4—1881no—
339D4—1881no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—942no—
349C2×C4—3761no—
350C2×C4—3761no—
351C2×C4—3761no—
352C2×C4—1882no—
353C2×C4—1882no—
354C2×C4—1882no—
355C2×C4—1881no—
356C2×C4—1881no—
357C2×C4—1882no—
358C2×C4—1882no—
359C2×C4—1882no—
360C2×C4—1882no—
361C2×C4C4⋊C4×D4711yescharacteristic
362C2×C4(C22⋊D47)⋊C411yescharacteristic
363C2×C4C4×D18811yescharacteristic
364C2×C4#1309400211yescharacteristic
365C2×C4#1309400411yescharacteristic
366C2×C4#1309400611yescharacteristic
367C2×C4C2×#1062532511yescharacteristic
368C2×C4#1309404511yescharacteristic
369C2×C4#1309404511yescharacteristic
370C2×C4#1309404611yescharacteristic
371C2×C4#1309404811yescharacteristic
372C2×C4#1309405211yescharacteristic
373C2×C4#1309405211yescharacteristic
374C2×C4#1309405611yescharacteristic
375C8—24no—
376C8—81no—
377C8—1882no—
378C22—3761no—
379C22—3761no—
380C22—3761no—
381C22—3761no—
382C22—1882no—
383C22—1882no—
384C22—1882no—
385C22#1568899711yescharacteristic
386C22#1568926911yescharacteristic
387C22#1568927011yescharacteristic
388C22#1568927611yescharacteristic
389C22#1568928811yescharacteristic
390C22#1568929211yescharacteristic
391C22#1568930711yescharacteristic
392C4—21no—
393C4—21no—
394C4—42no—
395C4—81no—
396C4—3762no—
397C4—1882no—
398C4—7521no—
399C4#1568915811yescharacteristic
400C4#1568916411yescharacteristic
401C4C4×#1062532511yescharacteristic
402C4#1568923611yescharacteristic
403C4#1568941411yescharacteristic
404C4#1568942411yescharacteristic
405C4#1568944611yescharacteristic
406C4#1568946211yescharacteristic
407C2—3762no—
408C2#2024247311yescharacteristic
409C2#2024251711yescharacteristic
410C2#2024266011yescharacteristic
411C2#2024267511yescharacteristic
412C2#2024358811yescharacteristic
413C2#2024361511yescharacteristic
414C2#2024365211yescharacteristic
subgroupG/H
centerC23#13093994
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1279C2
socleC23×C47#120
prime radicalC22×D188D4
cosocleC2×C42×C47C23
hypercenter#1279D47
hypocenterC47#8889
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. #20243545C2semidirect
6. #20241272C2semidirect
7. C47×#1279C2semidirect
22. #15688852C4semidirect
206. #1279D47semidirect
233. C47#8889semidirect

Maximal subgroups

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

subgroupindex
#202463352
#202441462
#202435452
#202433892
C2×#156888522
#202412722
C47×#12792
#888947