Finite Group Databasebeta

← #26115409

Subgroups — #26115409

Order 12032.

742 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251689C211yesmaximal, characteristic
2#20243368C211yesmaximal, characteristic, complemented
3C2×#15688859C212yesmaximal, complemented
4C2×#15688856C212yesmaximal
5C4×#95×C47C211yesmaximal, characteristic, complemented
6C2×#13094012C411yescharacteristic, complemented
7C2×#13094003C2211yescharacteristic
8C2×#13093998C2211yescharacteristic
9C2×C4⋊(C47⋊C8)—21no—
10C2×C22⋊(C47⋊C8)C2212yes—
11#15689029C411yescharacteristic, complemented
12#15689025C411yescharacteristic, complemented
13#15689014—21no—
14#15689014—21no—
15#15689002—21no—
16#15689002—21no—
17#15688989C411yescharacteristic, complemented
18#15688878—21no—
19#15688859—24no—
20#15688856—24no—
21C22×C42×C47—21no—
22C22×C42×C47C2211yescharacteristic
23C2×#95×C47—21no—
24C2×#95×C47C2212yes—
25C22×Dic94C2×C411yescharacteristic
26C22×D188C2×C411yescharacteristic
27C22×C22⋊D47—21no—
28C22×C47⋊C8—22no—
29#13094012—42no—
30#13094003—22no—
31#13094003—22no—
32#13093998—22no—
33#13093998—22no—
34C2×C4⋊Dic47C2×C411yescharacteristic
35C2×C4⋊Dic47C2×C411yescharacteristic
36C2×Dic47⋊C4—21no—
37C2×C22⋊Dic47—21no—
38C2×(C2×D47)⋊C4—21no—
39C2×(C2×D47)⋊C4—21no—
40C2×(C2×D47)⋊C4—21no—
41C2×(C2×D47)⋊C4—21no—
42C2×(C2×D47)⋊C4—21no—
43C4⋊(C47⋊C8)—42no—
44C22⋊(C47⋊C8)—22no—
45C22⋊(C47⋊C8)—22no—
46C47⋊#95—21no—
47C47⋊#95—21no—
48C47⋊#95—21no—
49C47⋊#95—21no—
50C23×C4×C47—22no—
51C23×C4×C47D411yescharacteristic
52C23×C4×C47D411yescharacteristic
53C23×C4×C47C2311yescharacteristic
54C2×C42×C47—24no—
55C2×C42×C47—42no—
56C2×C42×C47—42no—
57C2×C42×C47—42no—
58C2×C42×C47C2×C411yescharacteristic
59C2×C42×C47C2×C411yescharacteristic
60C2×C42×C47D411yescharacteristic
61C2×C42×C47D411yescharacteristic
62#95×C47—24no—
63#95×C47—22no—
64#95×C47D414yes—
65C24×C47C2×D411yescharacteristic
66C23×D47—21no—
67C22×C4×C47—21no—
68C22×C4×C47—21no—
69C22×C4×C47—22no—
70C22×C4×C47—22no—
71C22×C4×C47—24no—
72C22×C4×C47—24no—
73C22×C4×C47—24no—
74C22×C4×C47—22no—
75C22×C4×C47—22no—
76C22×C4×C47—41no—
77C22×C4×C47—41no—
78C22×C4×C47—41no—
79C22×C4×C47—42no—
80C22×C4×C47—42no—
81C22×C4×C47—42no—
82C22×C4×C47—42no—
83C22×C4×C47C22⋊C411yescharacteristic
84C22×C4×C47C22⋊C411yescharacteristic
85C22×C4×C47C22⋊C411yescharacteristic
86C22×C4×C47C22⋊C411yescharacteristic
87C22×C4×C47C22×C411yescharacteristic
88C22×C4×C47C2×D411yescharacteristic
89C22×C4×C47C2×D412yes—
90C22×C4×C47#4112yes—
91C2×C22⋊D47—42no—
92C2×C22⋊D47—42no—
93C2×C22⋊D47—41no—
94C2×C22⋊D47—41no—
95C22×Dic47—21no—
96C22×Dic47—21no—
97C22×Dic47—21no—
98C2×D188—22no—
99C2×D188—41no—
100C2×D188—41no—
101C2×Dic94—22no—
102C2×Dic94—41no—
103C2×Dic94—41no—
104C42×C47—22no—
105C42×C47—22no—
106C42×C47—41no—
107C42×C47—41no—
108C42×C47—48no—
109C22⋊Dic47—42no—
110(C2×D47)⋊C4—42no—
111(C2×D47)⋊C4—42no—
112(C2×D47)⋊C4—42no—
113(C2×D47)⋊C4—42no—
114(C2×D47)⋊C4—41no—
115(C2×D47)⋊C4—41no—
116C4⋊Dic47—22no—
117C4⋊Dic47—22no—
118Dic47⋊C4—41no—
119Dic47⋊C4—41no—
120C2×C47⋊C8—42no—
121C2×C47⋊C8—42no—
122C2×C47⋊C8—42no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47C2×C22⋊C411yescharacteristic
128C23×C47#12112yes—
129C23×C47#13512yes—
130C23×C47AGL(1,ℤ/8)11yescharacteristic
131C23×C47#13711yescharacteristic
132C22×D47—41no—
133C22×D47—41no—
134C22×D47—41no—
135C22×D47—41no—
136C22×D47—41no—
137C22×D47—41no—
138C22×D47—41no—
139C2×C4×C47—24no—
140C2×C4×C47—24no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
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—28no—
152C2×C4×C47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—42no—
156C2×C4×C47—42no—
157C2×C4×C47—44no—
158C2×C4×C47—44no—
159C2×C4×C47—44no—
160C2×C4×C47—44no—
161C2×C4×C47—44no—
162C2×C4×C47—44no—
163C2×C4×C47—44no—
164C2×C4×C47#9912yes—
165C2×C4×C47#10412yes—
166C2×C4×C47#10412yes—
167C2×C4×C47C4×D412yes—
168C2×C4×C47#12411yescharacteristic
169C2×C4×C47#12711yescharacteristic
170C22⋊D47—82no—
171C22⋊D47—82no—
172C2×Dic47—41no—
173C2×Dic47—41no—
174C2×Dic47—41no—
175C2×Dic47—41no—
176C2×Dic47—41no—
177C2×Dic47—41no—
178C2×Dic47—41no—
179C2×Dic47—41no—
180C2×Dic47—41no—
181D188—82no—
182Dic94—82no—
183C47⋊C8—82no—
184#9713—471nomaximal, Sylow
185C22×C47—22no—
186C22×C47—22no—
187C22×C47—22no—
188C22×C47—22no—
189C22×C47—21no—
190C22×C47—21no—
191C22×C47—21no—
192C22×C47—21no—
193C22×C47#39011yescharacteristic
194C22×C47C2×#9911yescharacteristic
195C22×C47#41011yescharacteristic
196C22×C47#41611yescharacteristic
197C22×C47#41711yescharacteristic
198C22×C47C2×#10411yescharacteristic
199C22×C47C2×#10411yescharacteristic
200C22×C47#46312yes—
201C22×C47#46412yes—
202C2×D47—81no—
203C2×D47—81no—
204C2×D47—81no—
205C2×D47—81no—
206C2×D47—81no—
207C2×D47—81no—
208C2×D47—81no—
209C4×C47—21no—
210C4×C47—22no—
211C4×C47—21no—
212C4×C47—22no—
213C4×C47—22no—
214C4×C47—22no—
215C4×C47—48no—
216C4×C47—41no—
217Dic47—81no—
218Dic47—81no—
219Dic47—81no—
220#2850—471no—
221#1797—471no—
222C2×#328—472no—
223C2×#327—472no—
224C4×#95D4711yescharacteristic, complemented
225C2×C47—22no—
226C2×C47—22no—
227C2×C47#150011yescharacteristic
228C2×C47#150111yescharacteristic
229C2×C47#150411yescharacteristic
230C2×C47#150911yescharacteristic
231C2×C47#196211yescharacteristic
232C2×C47#196411yescharacteristic
233C2×C47#198311yescharacteristic
234D47—161no—
235C2×#124—471no—
236C2×C22⋊Q8—471no—
237C2×#121—471no—
238C22×C42—21no—
239C22×C42C2×D4711yescharacteristic
240C2×C4⋊C8—941no—
241C2×C22⋊C8—472no—
242#391—471no—
243#390—471no—
244#388—941no—
245#388—941no—
246#386—941no—
247#386—941no—
248#382—471no—
249C2×#95—21no—
250C2×#95C2×D4712yes—
251#336—941no—
252#328—944no—
253#327—944no—
254C47#971311yescharacteristic, complemented, Sylow
255C22×Q8—471no—
256C22×D4—471no—
257C22×D4—941no—
258C23×C4—22no—
259C23×C4C22⋊D4711yescharacteristic
260C23×C4C22⋊D4711yescharacteristic
261C23×C4C22×D4711yescharacteristic
262C22×C8—942no—
263#124—1882no—
264C22⋊Q8—942no—
265C22⋊Q8—942no—
266#121—942no—
267#121—942no—
268C2×C4⋊C4—471no—
269C2×C4⋊C4—471no—
270C2×C4⋊C4—941no—
271C2×C22⋊C4—941no—
272C2×C22⋊C4—941no—
273C2×C22⋊C4—941no—
274C2×C22⋊C4—941no—
275C2×C22⋊C4—941no—
276C2×C22⋊C4—941no—
277C2×C42—24no—
278C2×C42—42no—
279C2×C42—42no—
280C2×C42—42no—
281C2×C42C4×D4711yescharacteristic
282C2×C42C4×D4711yescharacteristic
283C2×C42D18811yescharacteristic
284C2×C42D18811yescharacteristic
285C4⋊C8—1882no—
286C22⋊C8—942no—
287C22⋊C8—942no—
288#95—24no—
289#95—22no—
290#95—941no—
291#95—941no—
292#95—941no—
293#95—941no—
294#95D18814yes—
295C24—941no—
296C24C2×C22⋊D4711yescharacteristic
297C2×Q8—942no—
298C2×Q8—1881no—
299C2×Q8—1881no—
300C2×D4—942no—
301C2×D4—1881no—
302C2×D4—1881no—
303C2×D4—1882no—
304C2×D4—1882no—
305C2×D4—1881no—
306C2×D4—1881no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—941no—
324C22×C4—941no—
325C22×C4—941no—
326C22×C4(C2×D47)⋊C411yescharacteristic
327C22×C4(C2×D47)⋊C411yescharacteristic
328C22×C4(C2×D47)⋊C411yescharacteristic
329C22×C4(C2×D47)⋊C411yescharacteristic
330C22×C4C2×C4×D4711yescharacteristic
331C22×C4C2×D18811yescharacteristic
332C22×C4C2×D18812yes—
333C22×C4#1062535012yes—
334C2×C8—1882no—
335C2×C8—1882no—
336C2×C8—1882no—
337C4⋊C4—942no—
338C4⋊C4—942no—
339C4⋊C4—1881no—
340C4⋊C4—1881no—
341C22⋊C4—1882no—
342C22⋊C4—1882no—
343C22⋊C4—1882no—
344C22⋊C4—1882no—
345C22⋊C4—1882no—
346C22⋊C4—1881no—
347C22⋊C4—1881no—
348C42—22no—
349C42—22no—
350C42—41no—
351C42—41no—
352C42—48no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—1881no—
358C23—1881no—
359C23—1881no—
360C23—1881no—
361C23—1881no—
362C23—1881no—
363C23—1881no—
364C23C2×(C2×D47)⋊C411yescharacteristic
365C23#1309399812yes—
366C23#1309404412yes—
367C23#1309405011yescharacteristic
368C23#1309405511yescharacteristic
369Q8—3762no—
370D4—3762no—
371D4—3762no—
372D4—3762no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—28no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—1881no—
399C2×C4—1881no—
400C2×C4—1881no—
401C2×C4—1881no—
402C2×C4—1881no—
403C2×C4—1881no—
404C2×C4—1881no—
405C2×C4—1881no—
406C2×C4—1881no—
407C2×C4#1309393812yes—
408C2×C4#1309395212yes—
409C2×C4#1309395212yes—
410C2×C4C4×D18812yes—
411C2×C4#1309401211yescharacteristic
412C2×C4#1309402111yescharacteristic
413C8—3762no—
414C22—22no—
415C22—22no—
416C22—22no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—22no—
422C22—3761no—
423C22—3761no—
424C22—3761no—
425C22—3761no—
426C22—3761no—
427C22—3761no—
428C22—3761no—
429C22#1568902511yescharacteristic
430C22C2×#1309393811yescharacteristic
431C22#1568909611yescharacteristic
432C22#1568911711yescharacteristic
433C22#1568912211yescharacteristic
434C22C2×#1309395211yescharacteristic
435C22C2×#1309395211yescharacteristic
436C22#1568933812yes—
437C22#1568934512yes—
438C4—21no—
439C4—22no—
440C4—21no—
441C4—22no—
442C4—22no—
443C4—22no—
444C4—48no—
445C4—41no—
446C4—3761no—
447C4—3761no—
448C4—3761no—
449C2—22no—
450C2—22no—
451C2—7521no—
452C2#2024187211yescharacteristic
453C2#2024187711yescharacteristic
454C2#2024189011yescharacteristic
455C2#2024191111yescharacteristic
456C2#2024421611yescharacteristic
457C2#2024422411yescharacteristic
458C2#2024432011yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC4×#95×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#13093998C22
cosocleC23×C4×C47C23
hypercenterC4×#95D47
hypocenterC47#9713
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. #20243368C2semidirect
3. C2×#15688859C2semidirect
5. C4×#95×C47C2semidirect
6. C2×#13094012C4semidirect
11. #15689029C4semidirect
12. #15689025C4semidirect
17. #15688989C4semidirect
224. C4×#95D47semidirect
254. C47#9713semidirect

Maximal subgroups

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

subgroupindex
#202516892
#202433682
C2×#156888592
C2×#156888562
C4×#95×C472
#971347