Finite Group Databasebeta

← #26110458

Subgroups — #26110458

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#20243547C211yesmaximal, characteristic, complemented
3#20243385C211yesmaximal, characteristic
4C2×#15688850C211yesmaximal, characteristic
5#20241272C211yesmaximal, characteristic, complemented
6#20241229C211yesmaximal, characteristic, complemented
7C47×#1948C211yesmaximal, characteristic, complemented
8C2×C4×D188C2211yescharacteristic
9C2×#13093982—21no—
10C2×#13093957—22no—
11C2×C4⋊(C47⋊C8)C2211yescharacteristic
12C2×#13093944—21no—
13C2×C4×C47⋊C8C2211yescharacteristic
14#15689025—21no—
15#15689015—22no—
16#15688993C2211yescharacteristic
17#15688980—21no—
18C4×C4⋊Dic47—21no—
19#15688885—21no—
20#15688850C414yescomplemented
21C2×#106×C47—21no—
22C2×C4⋊C8×C47C2211yescharacteristic
23C47×#384C2211yescharacteristic
24C4×C4⋊C4×C47C2211yescharacteristic
25C47×#340—21no—
26C22×D188D411yescharacteristic
27C22×C4×D47—21no—
28C22×C47⋊C8—21no—
29C22×C47⋊C8—21no—
30C4×D188—21no—
31C4×D188—21no—
32C4×D188C2×C412yes—
33C4×D188Q812yes—
34#13093982—42no—
35#13093982—42no—
36C2×C4⋊Dic47—21no—
37C2×C4⋊Dic47—21no—
38C2×C4⋊Dic47D411yescharacteristic
39C2×C4⋊Dic47D412yes—
40C2×(C2×D47)⋊C4—21no—
41C2×(C2×D47)⋊C4—22no—
42C2×(C2×D47)⋊C4—22no—
43C2×C4×Dic47—22no—
44#13093957—44no—
45C4⋊(C47⋊C8)—21no—
46C4⋊(C47⋊C8)—21no—
47#13093944—42no—
48C4×C47⋊C8—21no—
49C4×C47⋊C8C2×C412yes—
50C47⋊#95—22no—
51C22×C8×C47—21no—
52C2×C4⋊C4×C47—21no—
53C2×C4⋊C4×C47—21no—
54C2×C4⋊C4×C47—21no—
55C2×C4⋊C4×C47D411yescharacteristic
56C2×C4⋊C4×C47D411yescharacteristic
57C2×C42×C47—21no—
58C2×C42×C47C2311yescharacteristic
59#106×C47—42no—
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×C47—41no—
67C22×C4×C47C2×D411yescharacteristic
68C22×C4×C47C2×D411yescharacteristic
69C22×C4×C47C2×D411yescharacteristic
70C22×Dic47—21no—
71C22×Dic47—22no—
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—41no—
86C2×C8×C47—41no—
87C4⋊C4×C47—21no—
88C4⋊C4×C47—21no—
89C4⋊C4×C47—21no—
90C4⋊C4×C47—42no—
91C4⋊C4×C47—41no—
92C4⋊C4×C47—41no—
93C4⋊C4×C47—41no—
94C4⋊C4×C47—41no—
95C4⋊C4×C47D812yes—
96C42×C47—41no—
97C42×C47—41no—
98C42×C47C22×C411yescharacteristic
99C42×C47C2×Q811yescharacteristic
100C42×C47#4111yescharacteristic
101C42×C47#4111yescharacteristic
102(C2×D47)⋊C4—22no—
103(C2×D47)⋊C4—22no—
104(C2×D47)⋊C4—44no—
105(C2×D47)⋊C4—82no—
106C4⋊Dic47—21no—
107C4⋊Dic47—41no—
108C4⋊Dic47—41no—
109C4⋊Dic47—41no—
110C4⋊Dic47—41no—
111C4⋊Dic47—42no—
112C4⋊Dic47C4⋊C412yes—
113C4×Dic47—44no—
114C2×C47⋊C8—22no—
115C2×C47⋊C8—22no—
116C2×C47⋊C8—22no—
117C2×C47⋊C8—41no—
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×C47—81no—
137C2×C4×C47—81no—
138C2×C4×C47—81no—
139C2×C4×C47C2×C4⋊C411yescharacteristic
140C2×C4×C47C4×D411yescharacteristic
141C2×C4×C47C4×D411yescharacteristic
142C2×C4×C47C22⋊Q811yescharacteristic
143C2×C4×C47C22⋊Q811yescharacteristic
144C2×C4×C47#12311yescharacteristic
145C2×C4×C47C2×D811yescharacteristic
146C2×C4×C47#13511yescharacteristic
147C2×C4×C47#13511yescharacteristic
148C2×C4×C47#13511yescharacteristic
149C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C47#13711yescharacteristic
152C2×C4×C47#13711yescharacteristic
153C2×Dic47—22no—
154C2×Dic47—41no—
155C2×Dic47—41no—
156C2×Dic47—42no—
157C2×Dic47—42no—
158C2×Dic47—42no—
159D188—22no—
160D188—22no—
161D188—41no—
162D188—41no—
163C4×D47—42no—
164C4×D47—42no—
165C4×D47—42no—
166C4×D47—42no—
167C8×C47—42no—
168C47⋊C8—24no—
169C47⋊C8—81no—
170#8885—471nomaximal, Sylow
171C22×C47#38511yescharacteristic
172C22×C47#44711yescharacteristic
173C22×C47#44911yescharacteristic
174C22×C47#45211yescharacteristic
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—161no—
190C4×C47#42711yescharacteristic
191C4×C47#42811yescharacteristic
192C4×C47C4×D811yescharacteristic
193C4×C47#44011yescharacteristic
194C4×C47#47411yescharacteristic
195C4×C47#47811yescharacteristic
196C4×C47#48211yescharacteristic
197C4×C47#48511yescharacteristic
198Dic47—42no—
199Dic47—82no—
200#2354—471no—
201#1948D4711yescharacteristic, complemented
202#1845—471no—
203#1802—471no—
204C2×D4⋊C8—471no—
205#1296—471no—
206#1279—471no—
207C2×C47#162111yescharacteristic
208C2×C47#163411yescharacteristic
209C2×C47#164711yescharacteristic
210C2×C47#165011yescharacteristic
211C2×C47#185411yescharacteristic
212C2×C47#185911yescharacteristic
213C2×C47#186211yescharacteristic
214D47—82no—
215C2×C4×D4—471no—
216C2×#117—941no—
217C2×#107—942no—
218C2×#106—21no—
219C2×C4⋊C8—471no—
220C2×C4⋊C8C2×D4711yescharacteristic
221C2×#102—941no—
222C2×C4×C8—471no—
223#390—941no—
224#388—942no—
225#384—471no—
226#384C2×D4711yescharacteristic
227#380—941no—
228C4×C4⋊C4—941no—
229C4×C4⋊C4C2×D4711yescharacteristic
230#340—21no—
231#340—941no—
232D4⋊C8—474no—
233C47#888511yescharacteristic, complemented, Sylow
234C22×D4—471no—
235C23×C4—941no—
236C22×C8—21no—
237C22×C8—941no—
238C22×C8—941no—
239C4×D4—472no—
240C4×D4—472no—
241C4×D4—941no—
242C4×D4—941no—
243#117—1882no—
244#117—1882no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—471no—
249C2×C4⋊C4—472no—
250C2×C4⋊C4—941no—
251C2×C4⋊C4—941no—
252C2×C4⋊C4C22⋊D4711yescharacteristic
253C2×C4⋊C4C22⋊D4711yescharacteristic
254C2×C22⋊C4—941no—
255C2×C22⋊C4—942no—
256C2×C22⋊C4—942no—
257C2×C42—21no—
258C2×C42—942no—
259C2×C42C22×D4711yescharacteristic
260#107—1884no—
261#106—42no—
262C4⋊C8—21no—
263C4⋊C8—941no—
264C4⋊C8—941no—
265C4⋊C8C4×D4712yes—
266#102—1882no—
267C4×C8—472no—
268C4×C8—941no—
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—41no—
281C22×C4—941no—
282C22×C4—942no—
283C22×C4—942no—
284C22×C4—942no—
285C22×C4—1881no—
286C22×C4—1881no—
287C22×C4—1881no—
288C22×C4—1881no—
289C22×C4D4×D4711yescharacteristic
290C22×C4D4×D4711yescharacteristic
291C22×C4C2×C22⋊D4711yescharacteristic
292C2×C8—22no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—942no—
296C2×C8—942no—
297C2×C8—942no—
298C2×C8—1881no—
299C2×C8—1881no—
300C2×C8—1881no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—42no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—472no—
310C4⋊C4—941no—
311C4⋊C4—1882no—
312C4⋊C4—1881no—
313C4⋊C4—1881no—
314C4⋊C4—1881no—
315C4⋊C4—1881no—
316C4⋊C4#1062533412yes—
317C22⋊C4—942no—
318C22⋊C4—942no—
319C22⋊C4—3762no—
320C22⋊C4—1884no—
321C42—41no—
322C42—41no—
323C42—1884no—
324C42C2×C4×D4711yescharacteristic
325C42#1062535011yescharacteristic
326C42Q8×D4711yescharacteristic
327C42#1062535411yescharacteristic
328C23—942no—
329C23—1881no—
330C23—1881no—
331C23—1881no—
332C23—1881no—
333C23—1881no—
334C23—1881no—
335C23#1309399211yescharacteristic
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—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—942no—
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×C4C4×C22⋊D4711yescharacteristic
363C2×C4#1309398611yescharacteristic
364C2×C4#1309400011yescharacteristic
365C2×C4#1309400211yescharacteristic
366C2×C4#1309400911yescharacteristic
367C2×C4C2×#1062533411yescharacteristic
368C2×C4#1309404411yescharacteristic
369C2×C4#1309404511yescharacteristic
370C2×C4#1309404511yescharacteristic
371C2×C4#1309404911yescharacteristic
372C2×C4#1309405111yescharacteristic
373C2×C4#1309405311yescharacteristic
374C2×C4#1309405511yescharacteristic
375C8—42no—
376C8—944no—
377C8—3761no—
378C22—3761no—
379C22—3761no—
380C22—3761no—
381C22—3761no—
382C22—1882no—
383C22—1882no—
384C22—1882no—
385C22#1568899411yescharacteristic
386C22#1568925611yescharacteristic
387C22#1568926711yescharacteristic
388C22#1568928211yescharacteristic
389C22#1568928311yescharacteristic
390C22#1568928911yescharacteristic
391C22#1568930411yescharacteristic
392C4—21no—
393C4—21no—
394C4—42no—
395C4—81no—
396C4—161no—
397C4—3762no—
398C4—1882no—
399C4#1568915811yescharacteristic
400C4#1568916211yescharacteristic
401C4C4×#1062533411yescharacteristic
402C4#1568922111yescharacteristic
403C4#1568940011yescharacteristic
404C4#1568942011yescharacteristic
405C4#1568944911yescharacteristic
406C4#1568946711yescharacteristic
407C2—3762no—
408C2#2024245111yescharacteristic
409C2#2024253211yescharacteristic
410C2#2024262111yescharacteristic
411C2#2024264311yescharacteristic
412C2#2024358611yescharacteristic
413C2#2024361111yescharacteristic
414C2#2024363411yescharacteristic
subgroupG/H
centerC23#13093992
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1948C2
socleC23×C47#120
prime radicalC22×D188D4
cosocleC2×C42×C47C23
hypercenter#1948D47
hypocenterC47#8885
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
2. #20243547C2semidirect
5. #20241272C2semidirect
6. #20241229C2semidirect
7. C47×#1948C2semidirect
20. #15688850C4semidirect
201. #1948D47semidirect
233. C47#8885semidirect

Maximal subgroups

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

subgroupindex
#202463352
#202435472
#202433852
C2×#156888502
#202412722
#202412292
C47×#19482
#888547