Finite Group Databasebeta

← #26105396

Subgroups — #26105396

Order 12032.

516 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20244916C211yesmaximal, characteristic, complemented
2#20244864C211yesmaximal, characteristic, complemented
3#20244791C211yesmaximal, characteristic, complemented
4#20241211C211yesmaximal, characteristic, complemented
5#20241209C211yesmaximal, characteristic, complemented
6#20241209C211yesmaximal, characteristic, complemented
7C47×#2682C211yesmaximal, characteristic
8C2×#13093957—21no—
9C2×#13093955—21no—
10C2×#13093945—21no—
11C2×#13093945—21no—
12#15688993C2211yescharacteristic
13#15688885—21no—
14#15688885—21no—
15#15688878C2211yescharacteristic
16#15688878C2211yescharacteristic
17#15688878C2211yescharacteristic
18C2×#123×C47—21no—
19C2×#121×C47—21no—
20C47×#396—21no—
21C47×#394—21no—
22C47×#392—21no—
23C47×#390C2211yescharacteristic
24C47×#390C2211yescharacteristic
25C47×#389C2211yescharacteristic
26C47×#385—21no—
27C22×C47⋊C8—21no—
28C22×C47⋊C8—21no—
29C22×C47⋊C8—21no—
30C2×C4⋊Dic47—21no—
31C2×C4⋊Dic47—21no—
32C2×C4⋊Dic47—21no—
33#13093957—42no—
34#13093955—42no—
35#13093945—42no—
36#13093945—42no—
37C22×D4×C47—21no—
38C22×D4×C47—21no—
39C22×D4×C47D411yescharacteristic
40C22×D4×C47D411yescharacteristic
41C23×C4×C47—21no—
42#123×C47—42no—
43#123×C47—42no—
44#121×C47—42no—
45#121×C47—42no—
46C2×C4⋊C4×C47—21no—
47C2×C4⋊C4×C47—21no—
48C2×C4⋊C4×C47D411yescharacteristic
49C2×C4⋊C4×C47D411yescharacteristic
50C2×C4⋊C4×C47D411yescharacteristic
51C2×C4⋊C4×C47D411yescharacteristic
52C2×C22⋊C4×C47—21no—
53C2×C22⋊C4×C47—21no—
54C2×C22⋊C4×C47—21no—
55C2×C22⋊C4×C47—21no—
56C2×C22⋊C4×C47—21no—
57C2×C22⋊C4×C47—21no—
58C2×C22⋊C4×C47—21no—
59C2×C42×C47C2311yescharacteristic
60#95×C47—21no—
61#95×C47—21no—
62C24×C47—21no—
63C24×C47—21no—
64C2×D4×C47—21no—
65C2×D4×C47—21no—
66C2×D4×C47—21no—
67C2×D4×C47—41no—
68C2×D4×C47—41no—
69C2×D4×C47—41no—
70C2×D4×C47—41no—
71C2×D4×C47—42no—
72C2×D4×C47—42no—
73C2×D4×C47—42no—
74C2×D4×C47—81no—
75C2×D4×C47—81no—
76C2×D4×C47—81no—
77C2×D4×C47SD1612yes—
78C22×C4×C47—21no—
79C22×C4×C47—21no—
80C22×C4×C47—21no—
81C22×C4×C47—21no—
82C22×C4×C47—42no—
83C22×C4×C47—42no—
84C22×C4×C47—81no—
85C22×C4×C47C2×D411yescharacteristic
86C22×C4×C47C2×D411yescharacteristic
87C22×C4×C47C2×D411yescharacteristic
88C22×Dic47—41no—
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×C47—41no—
96C4⋊C4×C47D812yes—
97C22⋊C4×C47—42no—
98C22⋊C4×C47—42no—
99C22⋊C4×C47—41no—
100C22⋊C4×C47—41no—
101C22⋊C4×C47—41no—
102C22⋊C4×C47—41no—
103C22⋊C4×C47—41no—
104C22⋊C4×C47—41no—
105C22⋊C4×C47—41no—
106C22⋊C4×C47—41no—
107C22⋊C4×C47—81no—
108C42×C47—41no—
109C4⋊Dic47—41no—
110C4⋊Dic47—41no—
111C4⋊Dic47—41no—
112C4⋊Dic47—41no—
113C4⋊Dic47—41no—
114C4⋊Dic47—41no—
115C2×C47⋊C8—22no—
116C2×C47⋊C8—22no—
117C2×C47⋊C8—41no—
118C2×C47⋊C8—41no—
119C2×C47⋊C8—41no—
120C2×C47⋊C8—41no—
121C2×C47⋊C8—41no—
122C2×C47⋊C8—41no—
123C2×C47⋊C8—41no—
124C23×C47—22no—
125C23×C47—41no—
126C23×C47—41no—
127C23×C47—41no—
128C23×C47—41no—
129C23×C47—41no—
130C23×C47—41no—
131C23×C47—41no—
132C23×C47—41no—
133C23×C47—41no—
134C23×C47—41no—
135C23×C47—41no—
136C23×C47—41no—
137C23×C47—41no—
138C23×C47#12011yescharacteristic
139D4×C47—42no—
140D4×C47—42no—
141D4×C47—81no—
142D4×C47—81no—
143D4×C47—84no—
144D4×C47—84no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—22no—
152C2×C4×C47—41no—
153C2×C4×C47—41no—
154C2×C4×C47—41no—
155C2×C4×C47—41no—
156C2×C4×C47—41no—
157C2×C4×C47—41no—
158C2×C4×C47—41no—
159C2×C4×C47—41no—
160C2×C4×C47—41no—
161C2×C4×C47—41no—
162C2×C4×C47—41no—
163C2×C4×C47—84no—
164C2×C4×C47C2×D811yescharacteristic
165C2×C4×C47C2×SD1611yescharacteristic
166C2×C4×C47#13511yescharacteristic
167C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
170C2×Dic47—81no—
171C2×Dic47—81no—
172C2×Dic47—81no—
173C47⋊C8—42no—
174C47⋊C8—42no—
175C47⋊C8—81no—
176#7800—471nomaximal, Sylow
177C22×C47—42no—
178C22×C47—42no—
179C22×C47—42no—
180C22×C47—81no—
181C22×C47—81no—
182C22×C47—81no—
183C22×C47—81no—
184C22×C47—81no—
185C22×C47—81no—
186C22×C47—81no—
187C22×C47—81no—
188C22×C47—81no—
189C22×C47—81no—
190C22×C47—81no—
191C22×C47#44711yescharacteristic
192C22×C47#44911yescharacteristic
193C22×C47#45011yescharacteristic
194C22×C47#45311yescharacteristic
195C22×C47#45511yescharacteristic
196C22×C47#45611yescharacteristic
197C22×C47#45811yescharacteristic
198C4×C47—21no—
199C4×C47—21no—
200C4×C47—21no—
201C4×C47—21no—
202C4×C47—21no—
203C4×C47—21no—
204C4×C47—42no—
205C4×C47—81no—
206C4×C47—81no—
207C4×C47—81no—
208Dic47—161no—
209#2682D4711yescharacteristic
210#2093—471no—
211#2084—471no—
212#2071—471no—
213#1271—471no—
214#1270—471no—
215#1270—471no—
216C2×C47—82no—
217C2×C47—161no—
218C2×C47#161011yescharacteristic
219C2×C47#161211yescharacteristic
220C2×C47#161311yescharacteristic
221C2×C47#162111yescharacteristic
222C2×C47#163911yescharacteristic
223C2×C47#165411yescharacteristic
224C2×C47#166111yescharacteristic
225C2×#123—21no—
226C2×#121—21no—
227C2×#107—941no—
228C2×#106—941no—
229C2×#102—941no—
230C2×#102—941no—
231#396—21no—
232#394—21no—
233#392—21no—
234#390C2×D4711yescharacteristic
235#390C2×D4711yescharacteristic
236#389C2×D4711yescharacteristic
237#385—21no—
238#384—471no—
239#340—941no—
240#340—941no—
241#336—471no—
242#336—471no—
243#336—471no—
244C47#780011yescharacteristic, complemented, Sylow
245C22×D4—21no—
246C22×D4—21no—
247C22×D4C22⋊D4711yescharacteristic
248C22×D4C22⋊D4711yescharacteristic
249C23×C4—21no—
250C22×C8—941no—
251C22×C8—941no—
252C22×C8—941no—
253#123—42no—
254#123—42no—
255#121—42no—
256#121—42no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—941no—
260C2×C4⋊C4—941no—
261C2×C4⋊C4—941no—
262C2×C4⋊C4C22⋊D4711yescharacteristic
263C2×C4⋊C4C22⋊D4711yescharacteristic
264C2×C4⋊C4C22⋊D4711yescharacteristic
265C2×C4⋊C4C22⋊D4711yescharacteristic
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C42C22×D4711yescharacteristic
274#107—1882no—
275#106—1882no—
276#102—1882no—
277#102—1882no—
278#95—21no—
279#95—21no—
280C24—21no—
281C24—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—81no—
293C2×D4—81no—
294C2×D4—81no—
295C2×D4#1062533512yes—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—81no—
303C22×C4—1881no—
304C22×C4C2×C22⋊D4711yescharacteristic
305C22×C4C2×C22⋊D4711yescharacteristic
306C22×C4C2×C22⋊D4711yescharacteristic
307C2×C8—942no—
308C2×C8—942no—
309C2×C8—1881no—
310C2×C8—1881no—
311C2×C8—1881no—
312C2×C8—1881no—
313C2×C8—1881no—
314C2×C8—1881no—
315C2×C8—1881no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—42no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—1881no—
324C4⋊C4—1881no—
325C4⋊C4—1881no—
326C4⋊C4—1881no—
327C4⋊C4—1881no—
328C4⋊C4—1881no—
329C4⋊C4#1062533412yes—
330C22⋊C4—42no—
331C22⋊C4—42no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—81no—
341C42—41no—
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23#1309399311yescharacteristic
357D4—42no—
358D4—42no—
359D4—81no—
360D4—81no—
361D4—84no—
362D4—84no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—84no—
382C2×C4—3761no—
383C2×C4—3761no—
384C2×C4—3761no—
385C2×C4C2×#1062533411yescharacteristic
386C2×C4C2×#1062533511yescharacteristic
387C2×C4#1309404411yescharacteristic
388C2×C4#1309404911yescharacteristic
389C2×C4#1309405011yescharacteristic
390C2×C4#1309405011yescharacteristic
391C8—3761no—
392C8—1882no—
393C8—1882no—
394C22—42no—
395C22—42no—
396C22—42no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22#1568925711yescharacteristic
409C22#1568926811yescharacteristic
410C22#1568927411yescharacteristic
411C22#1568929111yescharacteristic
412C22#1568930111yescharacteristic
413C22#1568930611yescharacteristic
414C22#1568931311yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4—7521no—
426C2—82no—
427C2—161no—
428C2#2024239111yescharacteristic
429C2#2024240211yescharacteristic
430C2#2024240811yescharacteristic
431C2#2024245311yescharacteristic
432C2#2024256711yescharacteristic
433C2#2024267211yescharacteristic
434C2#2024270511yescharacteristic
subgroupG/H
centerC23#13093993
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
Fitting, prime radicalC47×#2682C2
socleC23×C47#120
hypercenter#2682D47
hypocenterC47#7800
LCSG ▷ C2×C42×C47 ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2682

Complements

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

NH ≅ G/Ntype
1. #20244916C2semidirect
2. #20244864C2semidirect
3. #20244791C2semidirect
4. #20241211C2semidirect
5. #20241209C2semidirect
6. #20241209C2semidirect
244. C47#7800semidirect

Maximal subgroups

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

subgroupindex
#202449162
#202448642
#202447912
#202412112
#202412092
C47×#26822
#780047