Finite Group Databasebeta

← C4×#15688856 #26107153

Subgroups — C4×#15688856 #26107153

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
2C4×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
3C2×#15688856C212yesmaximal
4#20241267C212yesmaximal, complemented
5C4×#95×C47C211yesmaximal, characteristic, complemented
6C2×#13093998C2211yescharacteristic
7C2×C4×D188C411yescharacteristic, complemented
8C2×C4×C22⋊D47—21no—
9C2×C22⋊(C47⋊C8)C2212yes—
10C2×C4×C47⋊C8—21no—
11#15689025C411yescharacteristic, complemented
12#15689021C411yescharacteristic, complemented
13#15689014—21no—
14#15689002—21no—
15#15688983C2211yescharacteristic
16C4×C4⋊Dic47C411yescharacteristic, complemented
17C4×(C2×D47)⋊C4—21no—
18#15688878—21no—
19#15688856C418yesdirect product factor
20C22×C42×C47—21no—
21C22×C42×C47C2211yescharacteristic
22C2×#95×C47—21no—
23C2×#95×C47C2212yes—
24C22×D188C2×C411yescharacteristic
25C22×C22⋊D47—21no—
26C22×C4×D47—21no—
27C22×C47⋊C8—22no—
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—21no—
43C22⋊(C47⋊C8)—22no—
44C22⋊(C47⋊C8)C2×C414yescomplemented
45C4×C47⋊C8—42no—
46C47⋊#95—21no—
47C47⋊#95—21no—
48C47⋊#95—21no—
49C23×C4×C47—22no—
50C23×C4×C47D411yescharacteristic
51C23×C4×C47D411yescharacteristic
52C23×C4×C47C2311yescharacteristic
53C2×C42×C47—24no—
54C2×C42×C47—42no—
55C2×C42×C47—42no—
56C2×C42×C47—42no—
57C2×C42×C47C2×C411yescharacteristic
58C2×C42×C47C2×C411yescharacteristic
59C2×C42×C47D411yescharacteristic
60C2×C42×C47D411yescharacteristic
61#95×C47—24no—
62#95×C47—22no—
63#95×C47C2×C414yescomplemented
64C24×C47C2×D411yescharacteristic
65C23×D47—21no—
66C22×C4×C47—22no—
67C22×C4×C47—22no—
68C22×C4×C47—24no—
69C22×C4×C47—24no—
70C22×C4×C47—24no—
71C22×C4×C47—22no—
72C22×C4×C47—22no—
73C22×C4×C47—41no—
74C22×C4×C47—41no—
75C22×C4×C47—41no—
76C22×C4×C47—42no—
77C22×C4×C47—42no—
78C22×C4×C47—42no—
79C22×C4×C47—42no—
80C22×C4×C47C22⋊C411yescharacteristic
81C22×C4×C47C22⋊C411yescharacteristic
82C22×C4×C47C22⋊C411yescharacteristic
83C22×C4×C47C22⋊C411yescharacteristic
84C22×C4×C47D812yes—
85C22×C4×C47SD1612yes—
86C22×C4×C47C22×C411yescharacteristic
87C22×C4×C47C22×C412yes—
88C22×C4×C47C2×D411yescharacteristic
89C22×C4×C47#4112yes—
90C2×C22⋊D47—24no—
91C2×C22⋊D47—41no—
92C2×C22⋊D47—41no—
93C2×C22⋊D47—42no—
94C22×Dic47—21no—
95C22×Dic47—21no—
96C22×Dic47—21no—
97C2×D188—21no—
98C2×D188—41no—
99C2×D188—41no—
100C2×D188C4212yescomplemented
101C2×C4×D47—42no—
102C2×C4×D47—42no—
103C2×C4×D47—42no—
104C42×C47—22no—
105C42×C47—22no—
106C42×C47—41no—
107C42×C47—41no—
108C42×C47—48no—
109C22⋊Dic47—41no—
110C22⋊Dic47—41no—
111(C2×D47)⋊C4—24no—
112(C2×D47)⋊C4—42no—
113(C2×D47)⋊C4—42no—
114(C2×D47)⋊C4—42no—
115C4⋊Dic47—21no—
116C4⋊Dic47—41no—
117C4⋊Dic47—41no—
118C4⋊Dic47C4212yescomplemented
119Dic47⋊C4—42no—
120C4×Dic47—42no—
121C2×C47⋊C8—24no—
122C2×C47⋊C8—42no—
123C2×C47⋊C8—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—28no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—42no—
155C2×C4×C47—42no—
156C2×C4×C47—44no—
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#9912yes—
164C2×C4×C47#10212yes—
165C2×C4×C47#10212yes—
166C2×C4×C47#10412yes—
167C2×C4×C47#10412yes—
168C2×C4×C47C2×C4211yescharacteristic
169C2×C4×C47#11711yescharacteristic
170C2×C4×C47C4×D412yes—
171C22⋊D47—44no—
172C22⋊D47—44no—
173C2×Dic47—22no—
174C2×Dic47—41no—
175C2×Dic47—41no—
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—
185C47⋊C8—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—48no—
217C4×C47—41no—
218C4×C47#32714yescomplemented
219Dic47—42no—
220Dic47—81no—
221Dic47—81no—
222C4×#121—471no—
223C4×C22⋊C8—471no—
224C2×#327—472no—
225C4×#95D4711yescharacteristic, complemented
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—21no—
241C22×C42C2×D4711yescharacteristic
242C2×C22⋊C8—472no—
243C2×C4×C8—941no—
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—21no—
252C2×#95C2×D4712yes—
253#336—941no—
254#327—478no—
255C47C4×#32711yescharacteristic, complemented, Sylow
256C22×D4—471no—
257C22×D4—941no—
258C23×C4—22no—
259C23×C4—941no—
260C23×C4C22⋊D4711yescharacteristic
261C23×C4C22⋊D4711yescharacteristic
262C23×C4C22×D4711yescharacteristic
263C22×C8—942no—
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—24no—
279C2×C42—42no—
280C2×C42—42no—
281C2×C42—42no—
282C2×C42—941no—
283C2×C42C4×D4711yescharacteristic
284C2×C42C4×D4711yescharacteristic
285C2×C42D18811yescharacteristic
286C2×C42D18811yescharacteristic
287C22⋊C8—474no—
288C22⋊C8—942no—
289C4×C8—1882no—
290#95—24no—
291#95—22no—
292#95—941no—
293#95—941no—
294#95—941no—
295#95C4×D4714yescomplemented
296C24—941no—
297C24C2×C22⋊D4711yescharacteristic
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—24no—
309C22×C4—24no—
310C22×C4—24no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—941no—
321C22×C4—941no—
322C22×C4—941no—
323C22×C4—1882no—
324C22×C4—1882no—
325C22×C4—1882no—
326C22×C4(C2×D47)⋊C411yescharacteristic
327C22×C4(C2×D47)⋊C411yescharacteristic
328C22×C4(C2×D47)⋊C411yescharacteristic
329C22×C4(C2×D47)⋊C411yescharacteristic
330C22×C4#1062533412yes—
331C22×C4#1062533612yes—
332C22×C4C2×C4×D4711yescharacteristic
333C22×C4C2×C4×D4712yes—
334C22×C4C2×D18811yescharacteristic
335C22×C4#1062535012yes—
336C2×C8—944no—
337C2×C8—1882no—
338C2×C8—1882no—
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—48no—
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×C22⋊D4712yes—
369C23C2×#1062533411yescharacteristic
370C23C2×#1062533611yescharacteristic
371C23#1309404412yes—
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—28no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—44no—
399C2×C4—942no—
400C2×C4—3764no—
401C2×C4—1881no—
402C2×C4—1881no—
403C2×C4—1881no—
404C2×C4—1881no—
405C2×C4—1881no—
406C2×C4—1881no—
407C2×C4—1881no—
408C2×C4—1881no—
409C2×C4#1309393812yes—
410C2×C4#1309394412yes—
411C2×C4#1309394412yes—
412C2×C4#1309395212yes—
413C2×C4#1309395212yes—
414C2×C4C42×D4711yescharacteristic
415C2×C4#1309398111yescharacteristic
416C2×C4C4×D18812yes—
417C8—1884no—
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×#1309394411yescharacteristic
437C22#1568911711yescharacteristic
438C22C2×#1309395211yescharacteristic
439C22C2×#1309395211yescharacteristic
440C22C4×#1062533412yes—
441C22C4×#1062533612yes—
442C4—22no—
443C4—22no—
444C4—22no—
445C4—21no—
446C4—21no—
447C4—48no—
448C4—41no—
449C4—3761no—
450C4—3761no—
451C4—1882no—
452C4#1568885614yesdirect product factor
453C2—22no—
454C2—22no—
455C2—3762no—
456C2C2×#1568885611yescharacteristic
457C2#2024187211yescharacteristic
458C2#2024187711yescharacteristic
459C2#2024188211yescharacteristic
460C2C4×#1309393811yescharacteristic
461C2C4×#1309395211yescharacteristic
462C2C4×#1309394411yescharacteristic
subgroupG/H
centerC22×C4(C2×D47)⋊C4
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC4×#95×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#13093998C22
cosocleC23×C4×C47C23
hypercenterC4×#95D47
hypocenterC47C4×#327
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊(C47⋊C8)C2semidirect
4. #20241267C2semidirect
5. C4×#95×C47C2semidirect
7. C2×C4×D188C4semidirect
11. #15689025C4semidirect
12. #15689021C4semidirect
16. C4×C4⋊Dic47C4semidirect
19. #15688856C4direct (N × H)
44. C22⋊(C47⋊C8)C2×C4semidirect
63. #95×C47C2×C4semidirect
100. C2×D188C42semidirect
118. C4⋊Dic47C42semidirect
218. C4×C47#327semidirect
225. C4×#95D47semidirect
255. C47C4×#327semidirect
295. #95C4×D47semidirect
452. C4#15688856direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#130939982
C4×C22⋊(C47⋊C8)2
C2×#156888562
#202412672
C4×#95×C472
C4×#32747