Finite Group Databasebeta

← #26134447

Subgroups — #26134447

Order 12032.

446 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252098C211yesmaximal, characteristic
2C2×Dic47⋊C16C211yesmaximal, characteristic, complemented
3C2×#15688908C211yesmaximal, characteristic, complemented
4C2×#15688907C211yesmaximal, characteristic, complemented
5C2×#15688906C211yesmaximal, characteristic, complemented
6M32×Dic47C211yesmaximal, characteristic, complemented
7C2×C47×#350C211yesmaximal, characteristic, complemented
8C2×#13094030C2211yescharacteristic
9#15689669C411yescharacteristic
10C2×#13093964C2211yescharacteristic
11C22×C47⋊C16C2211yescharacteristic
12#15689199—21no—
13#15689199—21no—
14C8×C22⋊D47—21no—
15C8×C22⋊D47—21no—
16#15689146C411yescharacteristic
17#15689091C411yescharacteristic
18#15689090C411yescharacteristic
19C2×C8×Dic47C2211yescharacteristic
20Dic47⋊C16—21no—
21Dic47⋊C16—21no—
22#15688908—22no—
23#15688907—22no—
24#15688906—22no—
25#15688898—21no—
26C16×Dic47—21no—
27C2×#131×C47C2211yescharacteristic
28C2×M32×C47C2211yescharacteristic
29C22×C16×C47C2211yescharacteristic
30C47×#350—22no—
31C2×#10625350C2×C411yescharacteristic
32#13094030—21no—
33#13094030—21no—
34#13094030—21no—
35#13094030—21no—
36C2×#10625329C2×C411yescharacteristic
37C2×#10625324—21no—
38C22×C47⋊C8C2×C411yescharacteristic
39C2×C8×D47—21no—
40#13094022C811yescharacteristic
41#13094020C811yescharacteristic
42#13094013C811yescharacteristic
43#13094011C811yescharacteristic
44#13093996—21no—
45#13093996—21no—
46C4×C22⋊D47—21no—
47C4×C22⋊D47—21no—
48C2×C4×Dic47C2×C411yescharacteristic
49#13093964—21no—
50#13093964D412yescomplemented
51C2×C47⋊C16—21no—
52C2×C47⋊C16—21no—
53C2×C47⋊C16—21no—
54C2×C47⋊C16—21no—
55Dic47⋊C8—21no—
56Dic47⋊C8—21no—
57C22⋊(C47⋊C8)—21no—
58C22⋊(C47⋊C8)—21no—
59(C2×D47)⋊C8—21no—
60(C2×D47)⋊C8—21no—
61C8×Dic47D411yescharacteristic
62C8×Dic47D411yescharacteristic
63C8×Dic47D411yescharacteristic
64C8×Dic47D411yescharacteristic
65C2×#41×C47C2×C411yescharacteristic
66#131×C47—21no—
67#131×C47—21no—
68#131×C47—21no—
69#131×C47—21no—
70C2×M16×C47—21no—
71C2×M16×C47C2×C411yescharacteristic
72C22×C8×C47—21no—
73C22×C8×C47C2311yescharacteristic
74M32×C47—21no—
75M32×C47D412yescomplemented
76C2×C16×C47—21no—
77C2×C16×C47—21no—
78C2×C16×C47—21no—
79C2×C16×C47—21no—
80#41×C47—21no—
81#41×C47—21no—
82#41×C47—21no—
83#41×C47—21no—
84C2×Q8×C47C2×C811yescharacteristic
85C2×D4×C47—21no—
86C2×D4×C47C2×C811yescharacteristic
87C22×C4×C47—21no—
88C22×C4×C47C22×C411yescharacteristic
89C2×C22⋊D47—21no—
90C2×C22⋊D47—21no—
91C2×C22⋊D47—21no—
92C22×Dic47M1611yescharacteristic
93C22×Dic47M1611yescharacteristic
94#10625350—21no—
95#10625350—21no—
96#10625350—21no—
97#10625350—21no—
98C2×D188C2×C811yescharacteristic
99C2×C4×D47—21no—
100C2×Dic94C2×C811yescharacteristic
101M16×C47—21no—
102M16×C47—21no—
103M16×C47—41no—
104M16×C47—41no—
105C2×C8×C47—21no—
106C2×C8×C47—41no—
107C2×C8×C47—41no—
108C2×C8×C47C2×D411yescharacteristic
109C2×C8×C47C2×D411yescharacteristic
110C2×C8×C47C2×D411yescharacteristic
111C2×C8×C47C2×D411yescharacteristic
112C2×C8×C47#4111yescharacteristic
113C2×C8×C47#4111yescharacteristic
114C22⋊Dic47—21no—
115C22⋊Dic47—21no—
116(C2×D47)⋊C4—21no—
117(C2×D47)⋊C4—21no—
118Dic47⋊C4—21no—
119Dic47⋊C4—21no—
120C4×Dic47C22⋊C411yescharacteristic
121C4×Dic47C22⋊C411yescharacteristic
122C4×Dic47C2×C811yescharacteristic
123C4×Dic47C2×C811yescharacteristic
124#10625329—21no—
125#10625329—21no—
126C2×C47⋊C8—21no—
127C2×C47⋊C8—21no—
128C2×C47⋊C8—21no—
129C2×C47⋊C8C22⋊C411yescharacteristic
130C2×C47⋊C8C22⋊C411yescharacteristic
131#10625324—41no—
132#10625324—41no—
133C8×D47—41no—
134C8×D47—41no—
135C16×C47—22no—
136C16×C47—41no—
137C47⋊C16—22no—
138C47⋊C16—41no—
139C23×C47—21no—
140C23×C47C2×M1611yescharacteristic
141C22×D47—21no—
142Q8×C47—21no—
143Q8×C47—21no—
144D4×C47—21no—
145D4×C47—21no—
146D4×C47—41no—
147D4×C47—41no—
148C2×C4×C47—21no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47C2×C22⋊C411yescharacteristic
152C2×C4×C47C4×D411yescharacteristic
153C2×C4×C47C4×D411yescharacteristic
154C2×C4×C47C22×C811yescharacteristic
155C2×C4×C47#13111yescharacteristic
156C2×C4×C47#13111yescharacteristic
157C22⋊D47—42no—
158C22⋊D47—41no—
159C22⋊D47—41no—
160C22⋊D47—42no—
161C2×Dic47—22no—
162C2×Dic47—21no—
163C2×Dic47—41no—
164C2×Dic47C22⋊C811yescharacteristic
165C2×Dic47C22⋊C811yescharacteristic
166C2×Dic47C22⋊C811yescharacteristic
167C2×Dic47C22⋊C811yescharacteristic
168D188—21no—
169D188—21no—
170C4×D47—41no—
171C4×D47—41no—
172Dic94—21no—
173Dic94—21no—
174C8×C47—41no—
175C8×C47#12111yescharacteristic
176C8×C47#12111yescharacteristic
177C8×C47#12411yescharacteristic
178C8×C47#12711yescharacteristic
179C47⋊C8—21no—
180C47⋊C8—21no—
181C47⋊C8—41no—
182#13193—471nomaximal, Sylow
183C22×C47—21no—
184C22×C47—21no—
185C22×C47—41no—
186C22×C47—41no—
187C22×C47—41no—
188C22×C47C2×C22⋊C811yescharacteristic
189C22×C47#43611yescharacteristic
190C22×C47#43611yescharacteristic
191C2×D47—41no—
192C2×D47—41no—
193C2×D47—41no—
194C4×C47—41no—
195C4×C47#39011yescharacteristic
196C4×C47#40811yescharacteristic
197C4×C47C8×D411yescharacteristic
198C4×C47C8×D411yescharacteristic
199Dic47—21no—
200Dic47—21no—
201Dic47—21no—
202Dic47—41no—
203Dic47#35012yescomplemented
204#2931—471no—
205C2×C4⋊C16—471no—
206C2×#350—471no—
207C2×#350—471no—
208C2×#350—471no—
209C2×#350D4711yescharacteristic, complemented
210C4×M32—471no—
211C2×C47—21no—
212C2×C47—21no—
213C2×C47—81no—
214C2×C47#195411yescharacteristic
215C2×C47C2×#35011yescharacteristic
216C2×C47#211711yescharacteristic
217D47—81no—
218C2×#131—471no—
219C2×#131C2×D4711yescharacteristic
220#532—471no—
221C2×M32—471no—
222C2×M32C2×D4711yescharacteristic
223C22×C16—471no—
224C22×C16C2×D4711yescharacteristic
225#436—941no—
226#436—941no—
227C8×D4—941no—
228C8×D4—941no—
229#423—471no—
230#408—471no—
231#408—471no—
232C2×C4×C8—471no—
233C4⋊C16—941no—
234C4⋊C16—941no—
235#350—22no—
236#350—942no—
237#350—942no—
238#350—942no—
239#346—941no—
240C4×C16—941no—
241C47#1319311yescharacteristic, complemented, Sylow
242C2×#41—471no—
243C2×#41C4×D4711yescharacteristic
244#131—21no—
245#131—21no—
246#131—21no—
247#131—21no—
248#131—941no—
249#131—941no—
250#131—941no—
251#131—941no—
252C2×M16—21no—
253C2×M16—471no—
254C2×M16—941no—
255C2×M16C4×D4711yescharacteristic
256C22×C8—21no—
257C22×C8—471no—
258C22×C8—941no—
259C22×C8C22×D4711yescharacteristic
260C4⋊Q8—471no—
261#127—471no—
262#124—471no—
263#124—471no—
264#121—941no—
265#121—941no—
266C4×D4—941no—
267C4×D4—941no—
268C2×C42—471no—
269M32—21no—
270M32—472no—
271M32—941no—
272M32C22⋊D4712yescomplemented
273C2×C16—21no—
274C2×C16—21no—
275C2×C16—21no—
276C2×C16—21no—
277C2×C16—941no—
278C2×C16—941no—
279C2×C16—941no—
280C2×C16—941no—
281C4⋊C8—941no—
282C4⋊C8—941no—
283C22⋊C8—941no—
284C22⋊C8—941no—
285C22⋊C8—941no—
286C22⋊C8—941no—
287C4×C8—471no—
288C4×C8—471no—
289C4×C8—471no—
290C4×C8—471no—
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
295#41—941no—
296#41—941no—
297#41—941no—
298#41—941no—
299C2×Q8—471no—
300C2×Q8C8×D4711yescharacteristic
301C2×D4—21no—
302C2×D4—471no—
303C2×D4—941no—
304C2×D4—941no—
305C2×D4—941no—
306C2×D4C8×D4711yescharacteristic
307C22×C4—21no—
308C22×C4—471no—
309C22×C4—471no—
310C22×C4—941no—
311C22×C4C2×C4×D4711yescharacteristic
312M16—21no—
313M16—21no—
314M16—41no—
315M16—41no—
316M16—941no—
317M16—941no—
318M16—1881no—
319M16—1881no—
320C2×C8—21no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—471no—
324C2×C8—471no—
325C2×C8—941no—
326C2×C8—941no—
327C2×C8—941no—
328C2×C8—1881no—
329C2×C8—1881no—
330C2×C8#1062535011yescharacteristic
331C2×C8D4×D4711yescharacteristic
332C2×C8D4×D4711yescharacteristic
333C2×C8D4×D4711yescharacteristic
334C2×C8#1062535211yescharacteristic
335C2×C8C2×C22⋊D4711yescharacteristic
336C4⋊C4—941no—
337C4⋊C4—941no—
338C22⋊C4—941no—
339C22⋊C4—941no—
340C22⋊C4—941no—
341C22⋊C4—941no—
342C42—471no—
343C42—471no—
344C42—471no—
345C42—471no—
346C16—22no—
347C16—41no—
348C16—942no—
349C16—1881no—
350C23—21no—
351C23—941no—
352C23M16×D4711yescharacteristic
353Q8—21no—
354Q8—21no—
355Q8—941no—
356Q8—941no—
357D4—21no—
358D4—21no—
359D4—41no—
360D4—41no—
361D4—941no—
362D4—941no—
363D4—1882no—
364D4—1882no—
365D4—1881no—
366D4—1881no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—471no—
371C2×C4—471no—
372C2×C4—471no—
373C2×C4—471no—
374C2×C4—942no—
375C2×C4—941no—
376C2×C4—1881no—
377C2×C4—1881no—
378C2×C4—1881no—
379C2×C4C22⋊C4×D4711yescharacteristic
380C2×C4(C22⋊D47)⋊C411yescharacteristic
381C2×C4C4×C22⋊D4711yescharacteristic
382C2×C4C2×C8×D4711yescharacteristic
383C2×C4#1309403011yescharacteristic
384C2×C4#1309403211yescharacteristic
385C8—41no—
386C8—941no—
387C8—941no—
388C8—1881no—
389C8#1309399611yescharacteristic
390C8#1309399711yescharacteristic
391C8#1309401011yescharacteristic
392C8#1309402011yescharacteristic
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—1881no—
399C22—1881no—
400C22—1881no—
401C22C22⋊C8×D4711yescharacteristic
402C22#1568919811yescharacteristic
403C22#1568919911yescharacteristic
404C4—41no—
405C4—472no—
406C4—941no—
407C4—941no—
408C4—941no—
409C4—1881no—
410C4#1568902311yescharacteristic
411C4#1568908811yescharacteristic
412C4(C22⋊D47)⋊C811yescharacteristic
413C4C8×C22⋊D4711yescharacteristic
414C2—21no—
415C2—21no—
416C2—81no—
417C2—3761no—
418C2#2024418011yescharacteristic
419C2#350×D4711yescharacteristic
420C2#2024501411yescharacteristic
subgroupG/H
centerC2×C8D4×D47
commutatorC2×C4×C47C22×C8
FrattiniC22×C8C22×D47
FittingC2×C47×#350C2
socleC22×C47C2×C22⋊C8
prime radical#15689669C4
cosocleC22×C8×C47C23
hypercenterC2×#350D47
hypocenterC47#13193
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
2. C2×Dic47⋊C16C2semidirect
3. C2×#15688908C2semidirect
4. C2×#15688907C2semidirect
5. C2×#15688906C2semidirect
6. M32×Dic47C2semidirect
7. C2×C47×#350C2semidirect
50. #13093964D4semidirect
75. M32×C47D4semidirect
203. Dic47#350semidirect
209. C2×#350D47semidirect
241. C47#13193semidirect
272. M32C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
#202520982
C2×Dic47⋊C162
C2×#156889082
C2×#156889072
C2×#156889062
M32×Dic472
C2×C47×#3502
#1319347