Finite Group Databasebeta

← #26119673

Subgroups — #26119673

Order 12032.

516 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20248557C211yesmaximal, characteristic
2#20244189C211yesmaximal, characteristic, complemented
3#20243385C211yesmaximal, characteristic
4C2×#15688871C211yesmaximal, characteristic, complemented
5C2×#15688850C211yesmaximal, characteristic
6#20241229C211yesmaximal, characteristic, complemented
7C47×#1947C211yesmaximal, characteristic, complemented
8C2×#13094024C2211yescharacteristic
9C2×C4×D188C2211yescharacteristic
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11C2×#13093947—22no—
12C2×#13093944—21no—
13C2×C4×C47⋊C8C2211yescharacteristic
14#15689036—22no—
15#15689025—21no—
16#15688989—21no—
17#15688980—21no—
18#15688980—21no—
19#15688885—21no—
20#15688871—22no—
21#15688850—22no—
22C2×#107×C47—21no—
23C2×C4⋊C8×C47C2211yescharacteristic
24C47×#384C2211yescharacteristic
25C4×C4⋊C4×C47C2211yescharacteristic
26C47×#340—21no—
27C22×Dic94D412yes—
28C22×D188D411yescharacteristic
29C22×C4×D47—21no—
30C22×C47⋊C8—21no—
31C22×C47⋊C8—21no—
32#13094024—21no—
33#13094024—21no—
34#13094024—21no—
35#13094024—21no—
36C4×D188—21no—
37C4×D188—21no—
38C4×D188—21no—
39C4×D188—21no—
40C2×C4⋊Dic47—21no—
41C2×C4⋊Dic47—21no—
42C2×C4⋊Dic47D411yescharacteristic
43C2×(C2×D47)⋊C4—21no—
44C2×(C2×D47)⋊C4—22no—
45C2×(C2×D47)⋊C4—22no—
46C4⋊(C47⋊C8)—21no—
47C4⋊(C47⋊C8)—21no—
48#13093947—44no—
49#13093944—42no—
50C4×C47⋊C8—21no—
51C4×C47⋊C8—21no—
52C47⋊#95—22no—
53C47⋊#95—22no—
54C22×C8×C47—21no—
55C2×C4⋊C4×C47—21no—
56C2×C4⋊C4×C47—21no—
57C2×C4⋊C4×C47—21no—
58C2×C4⋊C4×C47D411yescharacteristic
59C2×C4⋊C4×C47D411yescharacteristic
60C2×C42×C47—21no—
61C2×C42×C47C2311yescharacteristic
62#107×C47—42no—
63C4⋊C8×C47—21no—
64C4⋊C8×C47D412yes—
65#95×C47—21no—
66C23×D47—21no—
67C22×C4×C47—21no—
68C22×C4×C47—21no—
69C22×C4×C47—41no—
70C22×C4×C47C2×D411yescharacteristic
71C22×C4×C47C2×D411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×Dic47—21no—
74C22×Dic47—22no—
75C2×D188—21no—
76C2×D188—21no—
77C2×D188—21no—
78C2×D188—21no—
79C2×D188—21no—
80C2×D188Q1612yes—
81C2×C4×D47—41no—
82C2×C4×D47—41no—
83C2×C4×D47—41no—
84C2×C4×D47—41no—
85C2×C4×D47—41no—
86C2×C4×D47—41no—
87C2×Dic94—22no—
88C2×Dic94—22no—
89C2×Dic94—42no—
90C2×Dic94—42no—
91C2×C8×C47—22no—
92C2×C8×C47—41no—
93C2×C8×C47—41no—
94C4⋊C4×C47—21no—
95C4⋊C4×C47—21no—
96C4⋊C4×C47—21no—
97C4⋊C4×C47—21no—
98C4⋊C4×C47—42no—
99C4⋊C4×C47—41no—
100C4⋊C4×C47—41no—
101C4⋊C4×C47—41no—
102C4⋊C4×C47—41no—
103C42×C47—41no—
104C42×C47—41no—
105C42×C47C2×D411yescharacteristic
106C42×C47#4111yescharacteristic
107C42×C47#4111yescharacteristic
108C42×C47#4111yescharacteristic
109(C2×D47)⋊C4—41no—
110(C2×D47)⋊C4—41no—
111(C2×D47)⋊C4—82no—
112(C2×D47)⋊C4—82no—
113C4⋊Dic47—21no—
114C4⋊Dic47—21no—
115C4⋊Dic47—41no—
116C4⋊Dic47—41no—
117C4⋊Dic47—41no—
118C4⋊Dic47—41no—
119C2×C47⋊C8—22no—
120C2×C47⋊C8—41no—
121C2×C47⋊C8—41no—
122C2×C47⋊C8—41no—
123C2×C47⋊C8—41no—
124C2×C47⋊C8—41no—
125C23×C47#12011yescharacteristic
126C22×D47—22no—
127C22×D47—41no—
128C22×D47—41no—
129C22×D47—41no—
130C22×D47—41no—
131C22×D47—41no—
132C22×D47—41no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—41no—
141C2×C4×C47—81no—
142C2×C4×C47—81no—
143C2×C4×C47—81no—
144C2×C4×C47#12111yescharacteristic
145C2×C4×C47#12111yescharacteristic
146C2×C4×C47#12111yescharacteristic
147C2×C4×C47#12311yescharacteristic
148C2×C4×C47#12311yescharacteristic
149C2×C4×C47#12411yescharacteristic
150C2×C4×C47C2×Q1611yescharacteristic
151C2×C4×C47#13511yescharacteristic
152C2×C4×C47#13511yescharacteristic
153C2×C4×C47#13511yescharacteristic
154C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C47#13711yescharacteristic
157C2×C4×C47#13711yescharacteristic
158C2×Dic47—41no—
159C2×Dic47—42no—
160C2×Dic47—41no—
161C2×Dic47—41no—
162C2×Dic47—42no—
163C2×Dic47—42no—
164D188—22no—
165D188—22no—
166D188—41no—
167D188—41no—
168C4×D47—81no—
169C4×D47—81no—
170C4×D47—81no—
171C4×D47—81no—
172Dic94—44no—
173Dic94—82no—
174C8×C47—42no—
175C47⋊C8—42no—
176C47⋊C8—81no—
177#10413—471nomaximal, Sylow
178C22×C47#39411yescharacteristic
179C22×C47#44911yescharacteristic
180C22×C47#44911yescharacteristic
181C22×C47#45111yescharacteristic
182C22×C47#45211yescharacteristic
183C22×C47#45311yescharacteristic
184C22×C47#45511yescharacteristic
185C2×D47—42no—
186C2×D47—42no—
187C2×D47—42no—
188C2×D47—81no—
189C2×D47—81no—
190C2×D47—81no—
191C2×D47—81no—
192C4×C47—21no—
193C4×C47—21no—
194C4×C47—81no—
195C4×C47—81no—
196C4×C47—161no—
197C4×C47#46311yescharacteristic
198C4×C47#46411yescharacteristic
199C4×C47#46711yescharacteristic
200C4×C47#46811yescharacteristic
201C4×C47#48411yescharacteristic
202C4×C47#48511yescharacteristic
203C4×C47#48811yescharacteristic
204C4×C47#48911yescharacteristic
205Dic47—82no—
206Dic47—81no—
207#2563—471no—
208#1956—471no—
209#1947D4711yescharacteristic, complemented
210#1802—471no—
211C2×#333—471no—
212C2×D4⋊C8—471no—
213#1279—471no—
214C2×C47#162411yescharacteristic
215C2×C47#163211yescharacteristic
216C2×C47#164411yescharacteristic
217C2×C47#164611yescharacteristic
218C2×C47#203611yescharacteristic
219C2×C47#203711yescharacteristic
220C2×C47#204211yescharacteristic
221D47—82no—
222C2×C4⋊Q8—471no—
223C2×C4×D4—471no—
224C2×#107—21no—
225C2×C4⋊C8—471no—
226C2×C4⋊C8C2×D4711yescharacteristic
227C2×#103—942no—
228C2×#102—941no—
229C2×C4×C8—471no—
230#393—942no—
231#390—941no—
232#384C2×D4711yescharacteristic
233#382—941no—
234#380—941no—
235#380—941no—
236C4×C4⋊C4C2×D4711yescharacteristic
237#340—21no—
238#340—941no—
239#333—942no—
240D4⋊C8—942no—
241C47#1041311yescharacteristic, complemented, Sylow
242C22×Q8—472no—
243C22×D4—471no—
244C23×C4—941no—
245C22×C8—21no—
246C22×C8—941no—
247C22×C8—941no—
248C4⋊Q8—941no—
249C4⋊Q8—941no—
250C4⋊Q8—941no—
251C4⋊Q8—941no—
252C4×D4—941no—
253C4×D4—941no—
254C4×D4—941no—
255C4×D4—941no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—471no—
260C2×C4⋊C4—941no—
261C2×C4⋊C4—941no—
262C2×C4⋊C4C22⋊D4711yescharacteristic
263C2×C4⋊C4C22⋊D4711yescharacteristic
264C2×C22⋊C4—942no—
265C2×C22⋊C4—942no—
266C2×C22⋊C4—941no—
267C2×C42—21no—
268C2×C42C22×D4711yescharacteristic
269#107—42no—
270C4⋊C8—21no—
271C4⋊C8—941no—
272C4⋊C8—941no—
273C4⋊C8D18812yes—
274#103—1884no—
275#102—1882no—
276C4×C8—941no—
277C4×C8—941no—
278#95—21no—
279#95—942no—
280#95—942no—
281C24—941no—
282C2×Q8—942no—
283C2×Q8—942no—
284C2×Q8—1882no—
285C2×Q8—1882no—
286C2×D4—472no—
287C2×D4—941no—
288C2×D4—941no—
289C2×D4—941no—
290C2×D4—941no—
291C2×D4—941no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—41no—
295C22×C4—941no—
296C22×C4—942no—
297C22×C4—1881no—
298C22×C4—1881no—
299C22×C4—1881no—
300C22×C4—1881no—
301C22×C4—1881no—
302C22×C4—1881no—
303C22×C4D4×D4711yescharacteristic
304C22×C4D4×D4711yescharacteristic
305C22×C4C2×C22⋊D4711yescharacteristic
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—942no—
310C2×C8—1881no—
311C2×C8—1881no—
312C2×C8—1881no—
313C2×C8—1881no—
314C2×C8—1881no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—42no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—941no—
325C4⋊C4—941no—
326C4⋊C4—1881no—
327C4⋊C4—1881no—
328C4⋊C4—1881no—
329C4⋊C4—1881no—
330C22⋊C4—3762no—
331C22⋊C4—3762no—
332C22⋊C4—1881no—
333C22⋊C4—1881no—
334C42—41no—
335C42—41no—
336C42C2×D18811yescharacteristic
337C42#1062535011yescharacteristic
338C42#1062535411yescharacteristic
339C42#1062535411yescharacteristic
340C23—942no—
341C23—1881no—
342C23—1881no—
343C23—1881no—
344C23—1881no—
345C23—1881no—
346C23—1881no—
347C23#1309399211yescharacteristic
348Q8—3762no—
349Q8—1884no—
350D4—942no—
351D4—942no—
352D4—1881no—
353D4—1881no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—3761no—
366C2×C4—3761no—
367C2×C4—3761no—
368C2×C4—3761no—
369C2×C4—1881no—
370C2×C4—1881no—
371C2×C4—1882no—
372C2×C4—1881no—
373C2×C4—1882no—
374C2×C4—1882no—
375C2×C4#1309399811yescharacteristic
376C2×C4#1309399911yescharacteristic
377C2×C4#1309399911yescharacteristic
378C2×C4#1309400911yescharacteristic
379C2×C4#1309400911yescharacteristic
380C2×C4#1309401311yescharacteristic
381C2×C4Q16×D4711yescharacteristic
382C2×C4#1309404311yescharacteristic
383C2×C4#1309404411yescharacteristic
384C2×C4#1309404411yescharacteristic
385C2×C4#1309404811yescharacteristic
386C2×C4#1309405011yescharacteristic
387C2×C4#1309405511yescharacteristic
388C2×C4#1309405611yescharacteristic
389C8—42no—
390C8—3761no—
391C8—1882no—
392C22—3761no—
393C22—3761no—
394C22—3761no—
395C22—3761no—
396C22—1882no—
397C22—1882no—
398C22—1882no—
399C22#1568904011yescharacteristic
400C22#1568926511yescharacteristic
401C22#1568926611yescharacteristic
402C22#1568927711yescharacteristic
403C22#1568928311yescharacteristic
404C22#1568928911yescharacteristic
405C22#1568929911yescharacteristic
406C4—21no—
407C4—21no—
408C4—81no—
409C4—81no—
410C4—161no—
411C4—3762no—
412C4—3761no—
413C4#1568933811yescharacteristic
414C4#1568934511yescharacteristic
415C4#1568936511yescharacteristic
416C4#1568937011yescharacteristic
417C4#1568946011yescharacteristic
418C4#1568946611yescharacteristic
419C4#1568948011yescharacteristic
420C4#1568948511yescharacteristic
421C2—3762no—
422C2#2024247011yescharacteristic
423C2#2024252111yescharacteristic
424C2#2024260011yescharacteristic
425C2#2024261511yescharacteristic
426C2#2024459311yescharacteristic
427C2#2024460011yescharacteristic
428C2#2024462911yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1947C2
socleC23×C47#120
prime radicalC22×D188D4
hypercenter#1947D47
hypocenterC47#10413
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
2. #20244189C2semidirect
4. C2×#15688871C2semidirect
6. #20241229C2semidirect
7. C47×#1947C2semidirect
209. #1947D47semidirect
241. C47#10413semidirect

Maximal subgroups

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

subgroupindex
#202485572
#202441892
#202433852
C2×#156888712
C2×#156888502
#202412292
C47×#19472
#1041347