Finite Group Databasebeta

← #26110985

Subgroups — #26110985

Order 12032.

516 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252513C211yesmaximal, characteristic, complemented
2#20244217C211yesmaximal, characteristic, complemented
3C4×#13093951C211yesmaximal, characteristic, complemented
4#20241805C211yesmaximal, characteristic, complemented
5#20241279C211yesmaximal, characteristic, complemented
6#20241220C211yesmaximal, characteristic, complemented
7C47×#3106C211yesmaximal, characteristic
8#15689254—21no—
9#15689195—22no—
10D4×C47⋊C8—21no—
11#15689180—21no—
12#15689176C2211yescharacteristic
13#15689147C2211yescharacteristic
14C2×C4⋊(C47⋊C8)—21no—
15C2×#13093951—22no—
16C2×#13093951—21no—
17C4×#10625329C2211yescharacteristic
18C42×Dic47C2211yescharacteristic
19#15688882—21no—
20D4⋊(C47⋊C8)—21no—
21D4⋊(C47⋊C8)—21no—
22C47×#532C2211yescharacteristic
23C4×#41×C47C2211yescharacteristic
24C47×#482—21no—
25C47×#477C411yescharacteristic, complemented
26C47×#476C411yescharacteristic, complemented
27C47×#460C411yescharacteristic, complemented
28C47×#459C411yescharacteristic, complemented
29C47×#449—21no—
30C4×SD16×C47—21no—
31C4×D8×C47—21no—
32C47×#431C2211yescharacteristic
33C2×#10625329—21no—
34C2×#10625329D412yes—
35C22×C47⋊C8—22no—
36C2×C4×Dic47—21no—
37C2×C4×Dic47—21no—
38C2×C4×Dic47—21no—
39C4⋊(C47⋊C8)—22no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)D411yescharacteristic
43C4⋊(C47⋊C8)D411yescharacteristic
44#13093951—24no—
45#13093951—44no—
46C22⋊(C47⋊C8)—22no—
47C22⋊(C47⋊C8)—21no—
48#13093935—22no—
49#13093935—21no—
50C4×C47⋊C8—21no—
51C4×C47⋊C8—21no—
52C2×#41×C47—21no—
53C2×#41×C47D411yescharacteristic
54C2×SD16×C47—21no—
55C2×D8×C47—21no—
56C4⋊Q8×C47C2×C411yescharacteristic
57#127×C47C2×C411yescharacteristic
58#124×C47—21no—
59#121×C47—21no—
60#121×C47—21no—
61C4×Q8×C47C2×C411yescharacteristic
62C4×Q8×C47D411yescharacteristic
63C4×D4×C47—21no—
64C4×D4×C47—21no—
65C4×D4×C47—21no—
66C4×D4×C47—21no—
67C4×D4×C47C2×C411yescharacteristic
68C4×D4×C47D411yescharacteristic
69#117×C47—21no—
70#117×C47D411yescharacteristic
71C2×C42×C47—21no—
72C2×C42×C47C2311yescharacteristic
73#107×C47—21no—
74#106×C47—21no—
75C4⋊C8×C47C2×C411yescharacteristic
76C4⋊C8×C47C2×C411yescharacteristic
77#103×C47—21no—
78#102×C47—21no—
79#102×C47—21no—
80#102×C47—21no—
81C22⋊C8×C47—21no—
82C4×C8×C47—21no—
83#41×C47—22no—
84#41×C47—41no—
85#41×C47—42no—
86#41×C47—42no—
87C2×Q8×C47—21no—
88C2×Q8×C47C22⋊C411yescharacteristic
89C2×D4×C47—21no—
90C2×D4×C47—21no—
91C2×D4×C47—21no—
92C2×D4×C47—21no—
93C2×D4×C47—41no—
94C2×D4×C47C22⋊C411yescharacteristic
95C22×C4×C47—21no—
96C22×C4×C47—21no—
97C22×C4×C47—21no—
98C22×C4×C47—41no—
99C22×C4×C47C2×D411yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101C22×C4×C47#4111yescharacteristic
102C22×Dic47—41no—
103SD16×C47—42no—
104D8×C47—42no—
105C2×C8×C47—21no—
106C2×C8×C47—21no—
107C4⋊C4×C47—21no—
108C4⋊C4×C47—21no—
109C4⋊C4×C47—21no—
110C4⋊C4×C47—21no—
111C4⋊C4×C47C22⋊C411yescharacteristic
112C4⋊C4×C47C22⋊C411yescharacteristic
113C22⋊C4×C47—21no—
114C22⋊C4×C47—21no—
115C22⋊C4×C47—21no—
116C22⋊C4×C47—41no—
117C22⋊C4×C47—41no—
118C42×C47—21no—
119C42×C47—21no—
120C42×C47—21no—
121C42×C47C22×C411yescharacteristic
122C42×C47C2×D411yescharacteristic
123C42×C47C2×D411yescharacteristic
124C42×C47#4111yescharacteristic
125C4×Dic47—22no—
126C4×Dic47—22no—
127C4×Dic47—22no—
128C4×Dic47—41no—
129C4×Dic47—41no—
130C4×Dic47—41no—
131#10625329—22no—
132#10625329—41no—
133#10625329—42no—
134C2×C47⋊C8—21no—
135C2×C47⋊C8—21no—
136C2×C47⋊C8—22no—
137C2×C47⋊C8—41no—
138C2×C47⋊C8—82no—
139C23×C47—21no—
140C23×C47—41no—
141C23×C47#12111yescharacteristic
142Q8×C47—21no—
143Q8×C47—21no—
144Q8×C47—42no—
145D4×C47—21no—
146D4×C47—42no—
147D4×C47—42no—
148D4×C47—41no—
149D4×C47—41no—
150D4×C47—41no—
151D4×C47—41no—
152D4×C47—82no—
153D4×C47#10412yescomplemented
154C2×C4×C47—21no—
155C2×C4×C47—21no—
156C2×C4×C47—21no—
157C2×C4×C47—21no—
158C2×C4×C47—21no—
159C2×C4×C47—21no—
160C2×C4×C47—21no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—42no—
164C2×C4×C47—41no—
165C2×C4×C47—41no—
166C2×C4×C47—41no—
167C2×C4×C47—41no—
168C2×C4×C47—41no—
169C2×C4×C47—81no—
170C2×C4×C47—81no—
171C2×C4×C47C2×C22⋊C411yescharacteristic
172C2×C4×C47C4×D411yescharacteristic
173C2×C4×C47C4×D411yescharacteristic
174C2×C4×C47#12011yescharacteristic
175C2×C4×C47#12111yescharacteristic
176C2×C4×C47#12311yescharacteristic
177C2×Dic47—42no—
178C2×Dic47—42no—
179C2×Dic47—42no—
180C8×C47—41no—
181C8×C47—41no—
182C47⋊C8—42no—
183C47⋊C8—41no—
184C47⋊C8—42no—
185C47⋊C8—41no—
186#8969—471nomaximal, Sylow
187C22×C47—21no—
188C22×C47—22no—
189C22×C47—21no—
190C22×C47—21no—
191C22×C47—41no—
192C22×C47—41no—
193C22×C47—81no—
194C22×C47—81no—
195C22×C47—81no—
196C22×C47#38611yescharacteristic
197C4×C47—21no—
198C4×C47—21no—
199C4×C47—21no—
200C4×C47—41no—
201C4×C47—41no—
202C4×C47—41no—
203C4×C47—81no—
204C4×C47C2×#10411yescharacteristic
205C4×C47#42111yescharacteristic
206C4×C47#44311yescharacteristic
207C4×C47#44411yescharacteristic
208C4×C47#45311yescharacteristic
209C4×C47#45411yescharacteristic
210Dic47—44no—
211#3106D4711yescharacteristic
212#2990—471no—
213#1962—471no—
214C4×#104—471no—
215#1484—471no—
216#1299—471no—
217#1276—471no—
218C2×C47—41no—
219C2×C47—42no—
220C2×C47—161no—
221C2×C47#187111yescharacteristic
222C2×C47#187611yescharacteristic
223C2×C47#188311yescharacteristic
224#532C2×D4711yescharacteristic
225C4×#41C2×D4711yescharacteristic
226#482—21no—
227#477Dic4711yescharacteristic, complemented
228#476Dic4711yescharacteristic, complemented
229#460Dic4711yescharacteristic, complemented
230#459Dic4711yescharacteristic, complemented
231#449—21no—
232#446—941no—
233C4×SD16—21no—
234C4×D8—21no—
235#435—942no—
236C8×D4—941no—
237#432—941no—
238#431—471no—
239#431C2×D4711yescharacteristic
240#423—471no—
241C2×C4⋊C8—941no—
242C2×#104—941no—
243C2×#104—942no—
244C4×M16—471no—
245C43—471no—
246#339—941no—
247D4⋊C8—941no—
248D4⋊C8—941no—
249C47#896911yescharacteristic, complemented, Sylow
250C2×#41—21no—
251C2×#41C22⋊D4711yescharacteristic
252C2×SD16—21no—
253C2×D8—21no—
254C2×M16—472no—
255C2×M16—941no—
256C22×C8—942no—
257C4⋊Q8C2×Dic4711yescharacteristic
258#127C2×Dic4711yescharacteristic
259#124—21no—
260#121—21no—
261#121—21no—
262C4×Q8C2×Dic4711yescharacteristic
263C4×Q8C22⋊D4711yescharacteristic
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4C2×Dic4711yescharacteristic
269C4×D4C22⋊D4711yescharacteristic
270#117—21no—
271#117C22⋊D4711yescharacteristic
272C2×C42—21no—
273C2×C42—941no—
274C2×C42—941no—
275C2×C42—941no—
276C2×C42C22×D4711yescharacteristic
277#107—21no—
278#106—21no—
279C4⋊C8—471no—
280C4⋊C8—471no—
281C4⋊C8—942no—
282C4⋊C8—941no—
283C4⋊C8—941no—
284C4⋊C8C2×Dic4711yescharacteristic
285C4⋊C8C2×Dic4711yescharacteristic
286#104—944no—
287#104—1884no—
288#103—21no—
289#102—21no—
290#102—21no—
291#102—21no—
292C22⋊C8—21no—
293C22⋊C8—942no—
294C22⋊C8—941no—
295#97—942no—
296#97—941no—
297C4×C8—21no—
298C4×C8—941no—
299C4×C8—941no—
300#41—22no—
301#41—41no—
302#41—42no—
303#41—42no—
304C2×Q8—21no—
305C2×Q8C22⋊Dic4711yescharacteristic
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—41no—
311C2×D4C22⋊Dic4711yescharacteristic
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—41no—
316C22×C4—1881no—
317C22×C4D4×D4711yescharacteristic
318C22×C4#1062535211yescharacteristic
319C22×C4C2×C22⋊D4711yescharacteristic
320SD16—42no—
321D8—42no—
322M16—942no—
323M16—1881no—
324M16—1882no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—941no—
328C2×C8—941no—
329C2×C8—942no—
330C2×C8—3762no—
331C2×C8—1881no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4C22⋊Dic4711yescharacteristic
337C4⋊C4C22⋊Dic4711yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C42—21no—
344C42—21no—
345C42—21no—
346C42—942no—
347C42—942no—
348C42—942no—
349C42—1881no—
350C42—1881no—
351C42—1881no—
352C42D4×D4711yescharacteristic
353C42#1062535211yescharacteristic
354C42C22×Dic4711yescharacteristic
355C42C2×C22⋊D4711yescharacteristic
356C23—21no—
357C23—41no—
358C23#1309399611yescharacteristic
359Q8—21no—
360Q8—21no—
361Q8—42no—
362D4—21no—
363D4—42no—
364D4—42no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—82no—
370D4#1309395112yescomplemented
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—1882no—
389C2×C4—1882no—
390C2×C4—1882no—
391C2×C4C2×C22⋊Dic4711yescharacteristic
392C2×C4D4×Dic4711yescharacteristic
393C2×C4D4×Dic4711yescharacteristic
394C2×C4#1309399211yescharacteristic
395C2×C4#1309399611yescharacteristic
396C2×C4#1309400511yescharacteristic
397C8—41no—
398C8—41no—
399C8—1882no—
400C8—1881no—
401C8—1882no—
402C8—1881no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—22no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22#1568900311yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—81no—
420C4—1884no—
421C4C2×#1309395111yescharacteristic
422C4#1568914011yescharacteristic
423C4#1568924011yescharacteristic
424C4#1568924511yescharacteristic
425C4#1568928911yescharacteristic
426C4#1568929411yescharacteristic
427C2—41no—
428C2—42no—
429C2—161no—
430C2#2024369111yescharacteristic
431C2#2024371711yescharacteristic
432C2#2024376611yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
Fitting, prime radicalC47×#3106C2
socleC22×C47#386
cosocleC2×C42×C47C23
hypercenter#3106D47
hypocenterC47#8969
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #20252513C2semidirect
2. #20244217C2semidirect
3. C4×#13093951C2semidirect
4. #20241805C2semidirect
5. #20241279C2semidirect
6. #20241220C2semidirect
25. C47×#477C4semidirect
26. C47×#476C4semidirect
27. C47×#460C4semidirect
28. C47×#459C4semidirect
153. D4×C47#104semidirect
227. #477Dic47semidirect
228. #476Dic47semidirect
229. #460Dic47semidirect
230. #459Dic47semidirect
249. C47#8969semidirect
370. D4#13093951semidirect

Maximal subgroups

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

subgroupindex
#202525132
#202442172
C4×#130939512
#202418052
#202412792
#202412202
C47×#31062
#896947