Finite Group Databasebeta

← C4×#15688858 #26107155

Subgroups — C4×#15688858 #26107155

Order 12032.

816 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13093998C211yesmaximal, characteristic
2C2×#15688858C212yesmaximal
3C4×C47⋊#95C211yesmaximal, characteristic, complemented
4#20241268C212yesmaximal, complemented
5C4×C22⋊C8×C47C211yesmaximal, characteristic, complemented
6C2×#13093998C2211yescharacteristic
7C2×C4×D188C411yescharacteristic, complemented
8C2×C4×C22⋊D47—21no—
9C22×C4×Dic47—21no—
10#15689025C411yescharacteristic, complemented
11#15689021C411yescharacteristic, complemented
12#15689014—21no—
13#15689002—21no—
14#15688983C2211yescharacteristic
15C4×C4⋊Dic47C411yescharacteristic, complemented
16C4×(C2×D47)⋊C4—21no—
17C2×C47⋊#95—21no—
18C2×C47⋊#95C2212yes—
19#15688858C418yesdirect product factor
20C22×C42×C47C2211yescharacteristic
21C2×C22⋊C8×C47C2212yes—
22C2×C4×C8×C47—21no—
23C47×#336—21no—
24C22×D188C2×C411yescharacteristic
25C22×C22⋊D47—21no—
26C23×Dic47—22no—
27C22×C4×D47—21no—
28#13093998—22no—
29#13093998C2×C414yes—
30C4×D188—42no—
31C4×C22⋊D47—42no—
32C4×C22⋊D47—42no—
33C2×C4⋊Dic47C2×C411yescharacteristic
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×C4×Dic47—24no—
43C2×C4×Dic47—21no—
44C2×C4×Dic47—42no—
45C2×C4×Dic47—42no—
46C47⋊#95—24no—
47C47⋊#95—21no—
48C47⋊#95—21no—
49C47⋊#95—21no—
50C47⋊#95—22no—
51C47⋊#95C2×C414yescomplemented
52C23×C4×C47D411yescharacteristic
53C23×C4×C47D411yescharacteristic
54C23×C4×C47C2311yescharacteristic
55C22×C8×C47—22no—
56C2×C42×C47—42no—
57C2×C42×C47C2×C411yescharacteristic
58C2×C42×C47C2×C411yescharacteristic
59C2×C42×C47D411yescharacteristic
60C2×C42×C47D411yescharacteristic
61C22⋊C8×C47—22no—
62C22⋊C8×C47C2×C414yescomplemented
63C4×C8×C47—42no—
64C24×C47C2×D411yescharacteristic
65C23×D47—21no—
66C22×C4×C47—22no—
67C22×C4×C47—22no—
68C22×C4×C47—22no—
69C22×C4×C47—22no—
70C22×C4×C47—41no—
71C22×C4×C47—41no—
72C22×C4×C47—41no—
73C22×C4×C47C22⋊C411yescharacteristic
74C22×C4×C47C22⋊C411yescharacteristic
75C22×C4×C47C22⋊C411yescharacteristic
76C22×C4×C47C22⋊C411yescharacteristic
77C22×C4×C47D812yes—
78C22×C4×C47SD1612yes—
79C22×C4×C47C22×C411yescharacteristic
80C22×C4×C47C22×C412yes—
81C22×C4×C47C2×D411yescharacteristic
82C22×C4×C47#4112yes—
83C2×C22⋊D47—24no—
84C2×C22⋊D47—41no—
85C2×C22⋊D47—41no—
86C2×C22⋊D47—42no—
87C22×Dic47—24no—
88C22×Dic47—24no—
89C22×Dic47—21no—
90C22×Dic47—24no—
91C22×Dic47—21no—
92C22×Dic47—21no—
93C22×Dic47—42no—
94C22×Dic47—42no—
95C22×Dic47—42no—
96C22×Dic47—42no—
97C2×D188—21no—
98C2×D188—41no—
99C2×D188—41no—
100C2×D188C4212yescomplemented
101C2×C4×D47—42no—
102C2×C4×D47—42no—
103C2×C4×D47—42no—
104C2×C8×C47—24no—
105C2×C8×C47—42no—
106C2×C8×C47—42no—
107C42×C47—22no—
108C42×C47—22no—
109C42×C47—41no—
110C42×C47—41no—
111C22⋊Dic47—41no—
112C22⋊Dic47—41no—
113(C2×D47)⋊C4—24no—
114(C2×D47)⋊C4—42no—
115(C2×D47)⋊C4—42no—
116(C2×D47)⋊C4—42no—
117C4⋊Dic47—21no—
118C4⋊Dic47—41no—
119C4⋊Dic47—41no—
120C4⋊Dic47C4212yescomplemented
121Dic47⋊C4—42no—
122C4×Dic47—48no—
123C4×Dic47—42no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—21no—
128C23×C47C2×C22⋊C411yescharacteristic
129C23×C47C4×D412yes—
130C23×C47C2×D811yescharacteristic
131C23×C47C2×SD1611yescharacteristic
132C23×C47#13512yes—
133C22×D47—22no—
134C22×D47—41no—
135C22×D47—41no—
136C22×D47—41no—
137C22×D47—41no—
138C22×D47—41no—
139C22×D47—41no—
140C2×C4×C47—21no—
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—24no—
149C2×C4×C47—24no—
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—42no—
154C2×C4×C47—42no—
155C2×C4×C47—44no—
156C2×C4×C47#9912yes—
157C2×C4×C47#10212yes—
158C2×C4×C47#10212yes—
159C2×C4×C47#10412yes—
160C2×C4×C47#10412yes—
161C2×C4×C47C2×C4211yescharacteristic
162C2×C4×C47#11711yescharacteristic
163C2×C4×C47C4×D412yes—
164C22⋊D47—44no—
165C22⋊D47—44no—
166C2×Dic47—28no—
167C2×Dic47—22no—
168C2×Dic47—44no—
169C2×Dic47—44no—
170C2×Dic47—44no—
171C2×Dic47—44no—
172C2×Dic47—44no—
173C2×Dic47—41no—
174C2×Dic47—41no—
175C2×Dic47—44no—
176C2×Dic47—41no—
177C2×Dic47—41no—
178C2×Dic47—41no—
179C2×Dic47—41no—
180C2×Dic47—41no—
181C2×Dic47—41no—
182D188—42no—
183D188—42no—
184C4×D47—84no—
185C8×C47—44no—
186C4×#327—471nomaximal, Sylow
187C22×C47—21no—
188C22×C47—21no—
189C22×C47—22no—
190C22×C47—22no—
191C22×C47—22no—
192C22×C47—21no—
193C22×C47—21no—
194C22×C47—22no—
195C22×C47C4×C22⋊C411yescharacteristic
196C22×C47C2×#9911yescharacteristic
197C22×C47#41011yescharacteristic
198C22×C47C2×#10211yescharacteristic
199C22×C47#41611yescharacteristic
200C22×C47C2×#10411yescharacteristic
201C22×C47C2×#10411yescharacteristic
202C22×C47C4×D812yes—
203C22×C47C4×SD1612yes—
204C2×D47—42no—
205C2×D47—42no—
206C2×D47—42no—
207C2×D47—81no—
208C2×D47—81no—
209C2×D47—81no—
210C2×D47—81no—
211C4×C47—22no—
212C4×C47—22no—
213C4×C47—21no—
214C4×C47—21no—
215C4×C47—22no—
216C4×C47—41no—
217C4×C47#32714yescomplemented
218Dic47—48no—
219Dic47—42no—
220Dic47—81no—
221Dic47—81no—
222C4×#121—471no—
223C4×C22⋊C8D4711yescharacteristic, complemented
224C2×#327—472no—
225C4×#95—471no—
226#1294—472no—
227C2×C47—22no—
228C2×C47—22no—
229C2×C47C2×#32711yescharacteristic
230C2×C47#150011yescharacteristic
231C2×C47#150111yescharacteristic
232C2×C47#150211yescharacteristic
233C2×C47C4×#9911yescharacteristic
234C2×C47C4×#10411yescharacteristic
235C2×C47C4×#10211yescharacteristic
236D47—82no—
237C2×#121—471no—
238C2×C4×D4—471no—
239C2×C4×D4—941no—
240C22×C42—941no—
241C22×C42C2×D4711yescharacteristic
242C2×C22⋊C8C2×D4712yes—
243C2×C4×C8—21no—
244#390—471no—
245#389—471no—
246#388—941no—
247#386—941no—
248#380—471no—
249C4×C4⋊C4—471no—
250C4×C22⋊C4—941no—
251C2×#95—472no—
252C2×#95—941no—
253#336—21no—
254#327—478no—
255C47C4×#32711yescharacteristic, complemented, Sylow
256C22×D4—471no—
257C22×D4—941no—
258C23×C4—942no—
259C23×C4—941no—
260C23×C4D18811yescharacteristic
261C23×C4D18811yescharacteristic
262C23×C4C22×D4711yescharacteristic
263C22×C8—22no—
264#121—474no—
265#121—942no—
266C4×D4—1882no—
267C4×D4—1882no—
268C4×D4—1882no—
269C2×C4⋊C4—471no—
270C2×C4⋊C4—471no—
271C2×C4⋊C4—471no—
272C2×C4⋊C4—941no—
273C2×C22⋊C4—941no—
274C2×C22⋊C4—941no—
275C2×C22⋊C4—941no—
276C2×C22⋊C4—941no—
277C2×C22⋊C4—941no—
278C2×C42—42no—
279C2×C42—944no—
280C2×C42—941no—
281C2×C42—1882no—
282C2×C42—1882no—
283C2×C42C4×D4711yescharacteristic
284C2×C42C4×D4711yescharacteristic
285C2×C42C22⋊D4711yescharacteristic
286C2×C42C22⋊D4711yescharacteristic
287C22⋊C8—22no—
288C22⋊C8C4×D4714yescomplemented
289C4×C8—42no—
290#95—474no—
291#95—944no—
292#95—941no—
293#95—941no—
294#95—942no—
295#95—941no—
296C24—941no—
297C24C2×D18811yescharacteristic
298C2×D4—472no—
299C2×D4—944no—
300C2×D4—941no—
301C2×D4—1881no—
302C2×D4—1881no—
303C2×D4—1881no—
304C2×D4—1881no—
305C2×D4—1882no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—944no—
314C22×C4—944no—
315C22×C4—941no—
316C22×C4—944no—
317C22×C4—941no—
318C22×C4—941no—
319C22×C4—1882no—
320C22×C4—1882no—
321C22×C4—1882no—
322C22×C4—1882no—
323C22×C4—1882no—
324C22×C4—1882no—
325C22×C4—1882no—
326C22×C4#1062532512yes—
327C22×C4D37612yes—
328C22×C4(C2×D47)⋊C411yescharacteristic
329C22×C4(C2×D47)⋊C411yescharacteristic
330C22×C4(C2×D47)⋊C411yescharacteristic
331C22×C4(C2×D47)⋊C411yescharacteristic
332C22×C4C2×C4×D4711yescharacteristic
333C22×C4C2×C4×D4712yes—
334C22×C4#1062535012yes—
335C22×C4C2×C22⋊D4711yescharacteristic
336C2×C8—24no—
337C2×C8—42no—
338C2×C8—42no—
339C4⋊C4—472no—
340C4⋊C4—941no—
341C4⋊C4—1881no—
342C4⋊C4—1881no—
343C4⋊C4—1882no—
344C22⋊C4—944no—
345C22⋊C4—1882no—
346C22⋊C4—1881no—
347C22⋊C4—1881no—
348C22⋊C4—1882no—
349C22⋊C4—1882no—
350C42—22no—
351C42—22no—
352C42—41no—
353C42—41no—
354C42—1888no—
355C42—1882no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—942no—
361C23—1881no—
362C23—1881no—
363C23—1881no—
364C23—1881no—
365C23—1881no—
366C23—1881no—
367C23C2×(C2×D47)⋊C411yescharacteristic
368C23C4×D18812yes—
369C23C2×D37611yescharacteristic
370C23C2×#1062532511yescharacteristic
371C23#1309404612yes—
372D4—1882no—
373D4—1882no—
374D4—1884no—
375D4—1884no—
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—24no—
385C2×C4—24no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—44no—
392C2×C4—948no—
393C2×C4—942no—
394C2×C4—3764no—
395C2×C4—1881no—
396C2×C4—1881no—
397C2×C4—1881no—
398C2×C4—1881no—
399C2×C4—1881no—
400C2×C4—1881no—
401C2×C4—1884no—
402C2×C4—1884no—
403C2×C4—1884no—
404C2×C4—1884no—
405C2×C4—1884no—
406C2×C4—1881no—
407C2×C4—1881no—
408C2×C4—1884no—
409C2×C4#1309393812yes—
410C2×C4#1309394612yes—
411C2×C4#1309394612yes—
412C2×C4#1309395012yes—
413C2×C4#1309395012yes—
414C2×C4C42×D4711yescharacteristic
415C2×C4#1309398111yescharacteristic
416C2×C4C4×C22⋊D4712yes—
417C8—44no—
418C22—21no—
419C22—21no—
420C22—22no—
421C22—22no—
422C22—21no—
423C22—21no—
424C22—22no—
425C22—22no—
426C22—3761no—
427C22—3761no—
428C22—3761no—
429C22—3761no—
430C22—1882no—
431C22—1882no—
432C22—1882no—
433C22C4×(C2×D47)⋊C411yescharacteristic
434C22C2×#1309393811yescharacteristic
435C22#1568909611yescharacteristic
436C22C2×#1309394611yescharacteristic
437C22#1568912011yescharacteristic
438C22C2×#1309395011yescharacteristic
439C22C2×#1309395011yescharacteristic
440C22C4×D37612yes—
441C22C4×#1062532512yes—
442C4—22no—
443C4—22no—
444C4—22no—
445C4—21no—
446C4—21no—
447C4—41no—
448C4—3761no—
449C4—3761no—
450C4—1888no—
451C4—1882no—
452C4#1568885814yesdirect product factor
453C2—22no—
454C2—22no—
455C2—3762no—
456C2C2×#1568885811yescharacteristic
457C2#2024187511yescharacteristic
458C2#2024188011yescharacteristic
459C2#2024188411yescharacteristic
460C2C4×#1309393811yescharacteristic
461C2C4×#1309395011yescharacteristic
462C2C4×#1309394611yescharacteristic
subgroupG/H
centerC22×C4(C2×D47)⋊C4
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC4×C22⋊C8×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#13093998C22
cosocleC23×C4×C47C23
hypercenterC4×C22⋊C8D47
hypocenterC47C4×#327
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C4×C47⋊#95C2semidirect
4. #20241268C2semidirect
5. C4×C22⋊C8×C47C2semidirect
7. C2×C4×D188C4semidirect
10. #15689025C4semidirect
11. #15689021C4semidirect
15. C4×C4⋊Dic47C4semidirect
19. #15688858C4direct (N × H)
51. C47⋊#95C2×C4semidirect
62. C22⋊C8×C47C2×C4semidirect
100. C2×D188C42semidirect
120. C4⋊Dic47C42semidirect
217. C4×C47#327semidirect
223. C4×C22⋊C8D47semidirect
255. C47C4×#327semidirect
288. C22⋊C8C4×D47semidirect
452. C4#15688858direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#130939982
C2×#156888582
C4×C47⋊#952
#202412682
C4×C22⋊C8×C472
C4×#32747