Finite Group Databasebeta

← #26112732

Subgroups — #26112732

Order 12032.

594 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689436C211yesmaximal, characteristic
2#20244224C211yesmaximal, characteristic
3#20243474C211yesmaximal, characteristic, complemented
4#20241955C211yesmaximal, characteristic
5#20241255C211yesmaximal, characteristic, complemented
6#20241236C211yesmaximal, characteristic, complemented
7C47×#2344C211yesmaximal, characteristic, complemented
8C2×#13093998C2211yescharacteristic
9#15689436—22no—
10#15689436—21no—
11#15689436—21no—
12C2×#13093957C412yescomplemented
13C2×#13093944C412yescomplemented
14C2×#13093938—21no—
15C2×#13093938—21no—
16C2×C22⋊(C47⋊C8)C2211yescharacteristic
17C2×C22⋊(C47⋊C8)C2211yescharacteristic
18#15688983C2211yescharacteristic
19#15688885—22no—
20#15688856—22no—
21C2×#117×C47—21no—
22C22×C4⋊C4×C47C2211yescharacteristic
23C47×#389—21no—
24C47×#387—22no—
25C47×#381—21no—
26C47×#380C2211yescharacteristic
27C4×C4⋊C4×C47—21no—
28C4×C22⋊C4×C47C2211yescharacteristic
29C22×D188C2×C411yescharacteristic
30C22×C22⋊D47—21no—
31C22×C47⋊C8—21no—
32C22×C47⋊C8C2×C412yes—
33#13093998—21no—
34#13093998—21no—
35#13093998—21no—
36#13093998—21no—
37C2×C4⋊Dic47—21no—
38C2×C4⋊Dic47C2×C411yescharacteristic
39C2×C22⋊Dic47—21no—
40C2×(C2×D47)⋊C4—21no—
41#13093957—22no—
42#13093957—22no—
43#13093944—22no—
44#13093944—22no—
45#13093938—42no—
46#13093938—42no—
47C22⋊(C47⋊C8)—21no—
48C22⋊(C47⋊C8)—21no—
49C22⋊(C47⋊C8)—21no—
50C22⋊(C47⋊C8)—21no—
51C47⋊#95—21no—
52C23×C4×C47—21no—
53C23×C4×C47C2311yescharacteristic
54#117×C47—42no—
55#117×C47—42no—
56C2×C4⋊C4×C47—21no—
57C2×C4⋊C4×C47—21no—
58C2×C4⋊C4×C47—21no—
59C2×C4⋊C4×C47—22no—
60C2×C4⋊C4×C47—21no—
61C2×C4⋊C4×C47C2×C412yes—
62C2×C4⋊C4×C47D412yes—
63C2×C4⋊C4×C47D411yescharacteristic
64C2×C4⋊C4×C47D411yescharacteristic
65C2×C22⋊C4×C47—21no—
66C2×C22⋊C4×C47D411yescharacteristic
67C2×C22⋊C4×C47D411yescharacteristic
68C2×C42×C47—22no—
69C2×C42×C47—21no—
70#95×C47—22no—
71#95×C47—22no—
72#95×C47—21no—
73#95×C47D412yes—
74C24×C47C2×D411yescharacteristic
75C23×D47—21no—
76C22×C4×C47—22no—
77C22×C4×C47—21no—
78C22×C4×C47—21no—
79C22×C4×C47—21no—
80C22×C4×C47—22no—
81C22×C4×C47—22no—
82C22×C4×C47—21no—
83C22×C4×C47—42no—
84C22×C4×C47—41no—
85C22×C4×C47—41no—
86C22×C4×C47—41no—
87C22×C4×C47—41no—
88C22×C4×C47C22×C411yescharacteristic
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47C2×D411yescharacteristic
91C22×C4×C47C2×D411yescharacteristic
92C22×C4×C47#4111yescharacteristic
93C22×C4×C47#4111yescharacteristic
94C2×C22⋊D47—41no—
95C2×C22⋊D47—41no—
96C2×C22⋊D47—41no—
97C2×C22⋊D47—41no—
98C2×C22⋊D47—41no—
99C2×C22⋊D47—41no—
100C22×Dic47—21no—
101C22×Dic47—41no—
102C2×D188—21no—
103C2×D188—21no—
104C2×D188—42no—
105C4⋊C4×C47—22no—
106C4⋊C4×C47—22no—
107C4⋊C4×C47—21no—
108C4⋊C4×C47—21no—
109C4⋊C4×C47—42no—
110C4⋊C4×C47—44no—
111C4⋊C4×C47C22⋊C412yes—
112C4⋊C4×C47C22⋊C412yes—
113C22⋊C4×C47—21no—
114C22⋊C4×C47—21no—
115C22⋊C4×C47—21no—
116C22⋊C4×C47—41no—
117C22⋊C4×C47—41no—
118C22⋊C4×C47D812yes—
119C42×C47—42no—
120C42×C47—44no—
121C22⋊Dic47—41no—
122C22⋊Dic47—41no—
123(C2×D47)⋊C4—41no—
124(C2×D47)⋊C4—41no—
125C4⋊Dic47—21no—
126C4⋊Dic47—21no—
127C4⋊Dic47—42no—
128C2×C47⋊C8—22no—
129C2×C47⋊C8—42no—
130C2×C47⋊C8—42no—
131C2×C47⋊C8—41no—
132C23×C47—41no—
133C23×C47—41no—
134C23×C47C4×D411yescharacteristic
135C23×C47#12011yescharacteristic
136C23×C47#12111yescharacteristic
137C23×C47C2×D811yescharacteristic
138C23×C47#13511yescharacteristic
139C23×C47AGL(1,ℤ/8)11yescharacteristic
140C23×C47AGL(1,ℤ/8)11yescharacteristic
141C22×D47—41no—
142C22×D47—41no—
143C22×D47—41no—
144C22×D47—81no—
145C22×D47—81no—
146C2×C4×C47—22no—
147C2×C4×C47—22no—
148C2×C4×C47—22no—
149C2×C4×C47—22no—
150C2×C4×C47—22no—
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—42no—
158C2×C4×C47—42no—
159C2×C4×C47—41no—
160C2×C4×C47—41no—
161C2×C4×C47—41no—
162C2×C4×C47—41no—
163C2×C4×C47—42no—
164C2×C4×C47—42no—
165C2×C4×C47—41no—
166C2×C4×C47—42no—
167C2×C4×C47—42no—
168C2×C4×C47—41no—
169C2×C4×C47—42no—
170C2×C4×C47—41no—
171C2×C4×C47C2×C22⋊C411yescharacteristic
172C2×C4×C47C4×D411yescharacteristic
173C2×C4×C47#12111yescharacteristic
174C2×C4×C47#12311yescharacteristic
175C22⋊D47—81no—
176C22⋊D47—81no—
177C22⋊D47—81no—
178C22⋊D47—81no—
179C2×Dic47—41no—
180C2×Dic47—41no—
181C2×Dic47—41no—
182C2×Dic47—81no—
183C2×Dic47—81no—
184C2×Dic47—81no—
185D188—42no—
186D188—81no—
187C47⋊C8—42no—
188C47⋊C8—81no—
189#9260—471nomaximal, Sylow
190C22×C47—21no—
191C22×C47—21no—
192C22×C47—21no—
193C22×C47—21no—
194C22×C47—21no—
195C22×C47—21no—
196C22×C47—41no—
197C22×C47—41no—
198C22×C47—41no—
199C22×C47—41no—
200C22×C47#38611yescharacteristic
201C22×C47C4×D811yescharacteristic
202C22×C47#44211yescharacteristic
203C22×C47#44711yescharacteristic
204C22×C47#44911yescharacteristic
205C22×C47#45911yescharacteristic
206C22×C47#46311yescharacteristic
207C2×D47—81no—
208C2×D47—81no—
209C2×D47—81no—
210C2×D47—161no—
211C2×D47—161no—
212C4×C47—21no—
213C4×C47—21no—
214C4×C47—21no—
215C4×C47—42no—
216C4×C47—42no—
217C4×C47—42no—
218C4×C47—82no—
219C4×C47—81no—
220C4×C47#41012yes—
221Dic47—81no—
222Dic47—161no—
223C2×#480—471no—
224#2344D4711yescharacteristic, complemented
225#1964—471no—
226#1823—471no—
227#1519—471no—
228#1289—471no—
229#1282—471no—
230C2×C47—21no—
231C2×C47—21no—
232C2×C47—21no—
233C2×C47—21no—
234C2×C47—21no—
235C2×C47—21no—
236C2×C47#187911yescharacteristic
237C2×C47#189911yescharacteristic
238C2×C47#190511yescharacteristic
239D47—161no—
240C2×#121—471no—
241C2×#117—21no—
242C22×C4⋊C4C2×D4711yescharacteristic
243#480—942no—
244#480—941no—
245#480—941no—
246C2×#107—472no—
247C2×#102—472no—
248C2×#99—941no—
249C2×#99—941no—
250C2×C22⋊C8—471no—
251C2×C22⋊C8—471no—
252#389—21no—
253#387—22no—
254#381—21no—
255#380—471no—
256#380C2×D4711yescharacteristic
257C4×C4⋊C4—21no—
258C4×C22⋊C4C2×D4711yescharacteristic
259#340—942no—
260#327—942no—
261C47#926011yescharacteristic, complemented, Sylow
262C22×D4—471no—
263C22×D4—941no—
264C23×C4—21no—
265C23×C4C22×D4711yescharacteristic
266C22×C8—472no—
267C22×C8—941no—
268#121—941no—
269#121—941no—
270#121—941no—
271#121—941no—
272#117—42no—
273#117—42no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—471no—
280C2×C4⋊C4—941no—
281C2×C4⋊C4C4×D4712yes—
282C2×C4⋊C4D18812yes—
283C2×C4⋊C4C22⋊D4711yescharacteristic
284C2×C4⋊C4C22⋊D4711yescharacteristic
285C2×C22⋊C4—21no—
286C2×C22⋊C4—941no—
287C2×C22⋊C4—941no—
288C2×C22⋊C4C22⋊D4711yescharacteristic
289C2×C22⋊C4C22⋊D4711yescharacteristic
290C2×C42—22no—
291C2×C42—21no—
292#107—942no—
293#107—942no—
294#102—942no—
295#102—942no—
296#99—1882no—
297#99—1882no—
298C22⋊C8—941no—
299C22⋊C8—941no—
300C22⋊C8—941no—
301C22⋊C8—941no—
302#95—22no—
303#95—22no—
304#95—21no—
305#95—941no—
306#95C22⋊D4712yes—
307C24—941no—
308C24C2×C22⋊D4711yescharacteristic
309C2×D4—941no—
310C2×D4—941no—
311C2×D4—1882no—
312C2×D4—1881no—
313C2×D4—1881no—
314C2×D4—1881no—
315C2×D4—1881no—
316C2×D4—1881no—
317C2×D4—1881no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—42no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—941no—
331C22×C4—1881no—
332C22×C4C2×C4×D4711yescharacteristic
333C22×C4C2×D18811yescharacteristic
334C22×C4#1062535011yescharacteristic
335C22×C4#1062535011yescharacteristic
336C22×C4C2×C22⋊D4711yescharacteristic
337C22×C4C2×C22⋊D4711yescharacteristic
338C2×C8—942no—
339C2×C8—1882no—
340C2×C8—1881no—
341C2×C8—1882no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—42no—
347C4⋊C4—44no—
348C4⋊C4—941no—
349C4⋊C4—941no—
350C4⋊C4—1882no—
351C4⋊C4(C2×D47)⋊C412yes—
352C4⋊C4(C2×D47)⋊C412yes—
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—1881no—
359C22⋊C4—1881no—
360C22⋊C4—1881no—
361C22⋊C4—1881no—
362C22⋊C4#1062533412yes—
363C42—42no—
364C42—44no—
365C23—41no—
366C23—41no—
367C23—3761no—
368C23—3761no—
369C23—1881no—
370C23—1881no—
371C23—1881no—
372C23C4×C22⋊D4711yescharacteristic
373C23#1309399311yescharacteristic
374C23#1309399811yescharacteristic
375C23C2×#1062533411yescharacteristic
376C23#1309404411yescharacteristic
377C23#1309404911yescharacteristic
378C23#1309405011yescharacteristic
379D4—3761no—
380D4—3761no—
381D4—3761no—
382D4—3761no—
383D4—3761no—
384D4—1882no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—3761no—
411C2×C4—3761no—
412C2×C4—3761no—
413C2×C4—1881no—
414C2×C4—1881no—
415C2×C4—1881no—
416C2×C4C2×(C2×D47)⋊C411yescharacteristic
417C2×C4C4×C22⋊D4711yescharacteristic
418C2×C4#1309399811yescharacteristic
419C2×C4#1309400711yescharacteristic
420C8—3761no—
421C8—1882no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—3761no—
433C22—3761no—
434C22—3761no—
435C22—7521no—
436C22—7521no—
437C22#1568900211yescharacteristic
438C22C4×#1062533411yescharacteristic
439C22#1568923311yescharacteristic
440C22#1568925711yescharacteristic
441C22#1568926811yescharacteristic
442C22#1568931811yescharacteristic
443C22#1568933811yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—42no—
448C4—42no—
449C4—42no—
450C4—82no—
451C4—81no—
452C4—3761no—
453C4—7521no—
454C4#1568909612yes—
455C2—21no—
456C2—21no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—7521no—
462C2#2024373611yescharacteristic
463C2#2024384611yescharacteristic
464C2#2024388211yescharacteristic
subgroupG/H
centerC22#15689002
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#2344C2
socleC22×C47#386
prime radicalC2×#13093998C22
cosocleC23×C4×C47C23
hypercenter#2344D47
hypocenterC47#9260
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2344

Complements

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

NH ≅ G/Ntype
3. #20243474C2semidirect
5. #20241255C2semidirect
6. #20241236C2semidirect
7. C47×#2344C2semidirect
12. C2×#13093957C4semidirect
13. C2×#13093944C4semidirect
224. #2344D47semidirect
261. C47#9260semidirect

Maximal subgroups

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

subgroupindex
C2×#156894362
#202442242
#202434742
#202419552
#202412552
#202412362
C47×#23442
#926047