Finite Group Databasebeta

← C2×#20241988 #26184183

Subgroups — C2×#20241988 #26184183

Order 12032.

1050 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D47C211yesmaximal, characteristic
2C2×#15689178C211yesmaximal, characteristic
3C2×#15689075C211yesmaximal, characteristic
4#20241988C218yesmaximal, direct product factor
5C2×#15688865C211yesmaximal, characteristic, complemented
6C2×#15688864C211yesmaximal, characteristic, complemented
7C2×#15688864C211yesmaximal, characteristic, complemented
8C2×C47×#330C211yesmaximal, characteristic, complemented
9C22×#10625324—21no—
10C2×#13094016C2211yescharacteristic
11C2×#13094015C411yescharacteristic
12C2×#13094015C411yescharacteristic
13C2×#13094014—21no—
14C2×#13094014—21no—
15#125×D47—22no—
16#125×D47—22no—
17#125×D47C414yes—
18#125×D47C2214yes—
19C2×C4⋊C4×D47—21no—
20C2×C4⋊C4×D47—21no—
21C2×C4⋊C4×D47C411yescharacteristic
22C2×C4⋊C4×D47C411yescharacteristic
23C2×C42×D47C2211yescharacteristic
24#15689178—22no—
25#15689178C2214yes—
26C2×Dic47⋊C8—21no—
27C2×(C2×D47)⋊C8—21no—
28#15689075—22no—
29#15689075C2214yes—
30C2×#13093935C2211yescharacteristic
31C2×#13093935C2211yescharacteristic
32C2×C8×Dic47—21no—
33#15688865C2214yescomplemented
34#15688864C2214yescomplemented
35#15688864C2214yescomplemented
36C2×#125×C47C2211yescharacteristic
37C2×#97×C47C2211yescharacteristic
38C2×#97×C47C2211yescharacteristic
39C47×#330C2214yescomplemented
40C22×C4×D47—21no—
41C22×C4×D47—21no—
42C22×C4×D47C2×C411yescharacteristic
43C22×C4×D47D411yescharacteristic
44C22×C4×D47D411yescharacteristic
45C2×#10625324—28no—
46C2×#10625324—24no—
47C22×C47⋊C8—21no—
48C22×C47⋊C8—21no—
49#13094016—21no—
50#13094016—21no—
51#13094016C2×C412yes—
52#13094016C2312yes—
53#13094015—22no—
54#13094015—22no—
55#13094015C2×C414yes—
56#13094015C2×C414yes—
57#13094014—24no—
58#13094014—24no—
59#13094014—24no—
60#13094014—24no—
61C2×C4⋊Dic47—21no—
62C2×C4⋊Dic47—21no—
63C2×C4⋊Dic47C2×C411yescharacteristic
64C2×C4⋊Dic47C2×C411yescharacteristic
65C2×Dic47⋊C4—21no—
66C2×Dic47⋊C4—21no—
67C2×Dic47⋊C4—21no—
68C2×Dic47⋊C4—21no—
69C2×Dic47⋊C4—21no—
70C2×Dic47⋊C4—21no—
71C4⋊C4×D47—24no—
72C4⋊C4×D47—24no—
73C4⋊C4×D47—22no—
74C4⋊C4×D47—22no—
75C4⋊C4×D47—24no—
76C4⋊C4×D47—24no—
77C4⋊C4×D47C2×C414yes—
78C4⋊C4×D47C2×C414yes—
79C2×C4×Dic47C2×C411yescharacteristic
80C2×C4×Dic47D411yescharacteristic
81C2×C4×Dic47D411yescharacteristic
82C42×D47C2×C412yes—
83C42×D47D412yes—
84C42×D47D412yes—
85C42×D47C2312yes—
86Dic47⋊C8—24no—
87(C2×D47)⋊C8—24no—
88#13093935—21no—
89#13093935—21no—
90#13093935C2312yes—
91#13093935C2312yes—
92C8×Dic47—24no—
93C22×C8×C47—21no—
94C22×C8×C47—21no—
95#125×C47—21no—
96#125×C47—21no—
97#125×C47C2×C412yes—
98#125×C47C2312yes—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47C2×C411yescharacteristic
102C2×C4⋊C4×C47C2×C411yescharacteristic
103C2×C42×C47C2311yescharacteristic
104#97×C47—21no—
105#97×C47—21no—
106#97×C47C2312yes—
107#97×C47C2312yes—
108C23×D47C22⋊C411yescharacteristic
109C22×C4×C47—21no—
110C22×C4×C47—21no—
111C22×C4×C47C22×C411yescharacteristic
112C22×C4×C47C2×D411yescharacteristic
113C22×C4×C47C2×D411yescharacteristic
114C22×Dic47—21no—
115C22×Dic47—21no—
116C22×Dic47C22⋊C411yescharacteristic
117C22×Dic47C22⋊C411yescharacteristic
118C22×Dic47C22⋊C411yescharacteristic
119C2×C4×D47—24no—
120C2×C4×D47—24no—
121C2×C4×D47—24no—
122C2×C4×D47—24no—
123C2×C4×D47—42no—
124C2×C4×D47—44no—
125C2×C4×D47—44no—
126C2×C4×D47C22⋊C412yes—
127C2×C4×D47C22⋊C412yes—
128C2×C4×D47C22⋊C412yes—
129C2×C4×D47C22×C412yes—
130C2×C4×D47C2×D412yes—
131C2×C4×D47C2×D412yes—
132C2×C8×C47—24no—
133C2×C8×C47—22no—
134C2×C8×C47—22no—
135C2×C8×C47—42no—
136C4⋊C4×C47—22no—
137C4⋊C4×C47—22no—
138C4⋊C4×C47—21no—
139C4⋊C4×C47—21no—
140C4⋊C4×C47—22no—
141C4⋊C4×C47—22no—
142C4⋊C4×C47C22×C412yes—
143C4⋊C4×C47C22×C412yes—
144C42×C47C22×C411yescharacteristic
145C42×C47C2×D411yescharacteristic
146C42×C47C2×D411yescharacteristic
147C42×C47C2411yescharacteristic
148C4⋊Dic47—21no—
149C4⋊Dic47—21no—
150C4⋊Dic47—24no—
151C4⋊Dic47—24no—
152C4⋊Dic47C22×C412yes—
153C4⋊Dic47C22×C412yes—
154Dic47⋊C4—22no—
155Dic47⋊C4—22no—
156Dic47⋊C4—22no—
157Dic47⋊C4—22no—
158Dic47⋊C4—24no—
159Dic47⋊C4—24no—
160Dic47⋊C4—24no—
161Dic47⋊C4—24no—
162C4×Dic47C22⋊C412yes—
163C4×Dic47C22⋊C412yes—
164C4×Dic47C22⋊C412yes—
165C4×Dic47C22×C412yes—
166C4×Dic47C2×D412yes—
167C4×Dic47C2×D412yes—
168C2×C47⋊C8—24no—
169C2×C47⋊C8—22no—
170C2×C47⋊C8—22no—
171C2×C47⋊C8—42no—
172#10625324—216no—
173C23×C47C2×C22⋊C411yescharacteristic
174C22×D47—22no—
175C22×D47—22no—
176C22×D47#10414yes—
177C22×D47C2×C22⋊C412yes—
178C2×C4×C47—22no—
179C2×C4×C47—22no—
180C2×C4×C47—22no—
181C2×C4×C47—22no—
182C2×C4×C47—22no—
183C2×C4×C47—42no—
184C2×C4×C47—42no—
185C2×C4×C47C2×C22⋊C411yescharacteristic
186C2×C4×C47C2×C22⋊C411yescharacteristic
187C2×C4×C47C2×C22⋊C411yescharacteristic
188C2×C4×C47C23×C411yescharacteristic
189C2×C4×C47C22×D411yescharacteristic
190C2×C4×C47C22×D411yescharacteristic
191C2×Dic47—22no—
192C2×Dic47—22no—
193C2×Dic47—22no—
194C2×Dic47—22no—
195C2×Dic47—42no—
196C2×Dic47—42no—
197C2×Dic47#10114yes—
198C2×Dic47C2×C22⋊C412yes—
199C2×Dic47C2×C22⋊C412yes—
200C2×Dic47C2×C22⋊C412yes—
201C4×D47—24no—
202C4×D47—24no—
203C4×D47—24no—
204C4×D47—24no—
205C4×D47—42no—
206C4×D47—42no—
207C4×D47—48no—
208C4×D47—48no—
209C8×C47—24no—
210C8×C47—42no—
211C47⋊C8—24no—
212C47⋊C8—42no—
213C2×#1528—471nomaximal, Sylow
214C22×C47C2×#10112yes—
215C22×C47C2×#10412yes—
216C22×C47#42112yes—
217C22×C47C22×C22⋊C411yescharacteristic
218C2×D47—22no—
219C2×D47—22no—
220C2×D47—28no—
221C2×D47C2×#10414yes—
222C4×C47—21no—
223C4×C47—21no—
224C4×C47—21no—
225C4×C47—21no—
226C4×C47—21no—
227C4×C47—21no—
228C4×C47—42no—
229C4×C47—42no—
230Dic47—22no—
231Dic47—22no—
232Dic47—42no—
233Dic47—42no—
234Dic47C2×#10114yes—
235C22×#125—471no—
236C2×#432—471no—
237C2×C4×M16—471no—
238#1528—478no—
239C2×#330—471no—
240C2×#330—471no—
241C2×#330—471no—
242C2×#330D4711yescharacteristic, complemented
243C2×C47#152814yescomplemented
244C2×C47C22×#10111yescharacteristic
245C2×C47C22×#10411yescharacteristic
246C2×C47C2×#42111yescharacteristic
247D47—24no—
248C22×M16—941no—
249C2×#125—474no—
250C2×#125—474no—
251C2×#125—471no—
252C2×#125—471no—
253C2×#125—471no—
254C2×#125—941no—
255C2×#125—941no—
256C2×#125—942no—
257C2×#125—942no—
258C2×#125C2×D4711yescharacteristic
259C22×C4⋊C4—471no—
260C22×C4⋊C4—471no—
261C22×C4⋊C4—941no—
262C22×C4⋊C4—941no—
263C22×C42—471no—
264#432—474no—
265#432—942no—
266C2×C4⋊C8—941no—
267C2×C22⋊C8—941no—
268C4×M16—474no—
269C4×M16—942no—
270C2×#97—471no—
271C2×#97—471no—
272C2×#97C2×D4711yescharacteristic
273C2×#97C2×D4711yescharacteristic
274C2×C4×C8—941no—
275#330—474no—
276#330—474no—
277#330—474no—
278#330C2×D4714yescomplemented
279C47C2×#152811yescharacteristic, complemented, Sylow
280C23×C4—471no—
281C23×C4—471no—
282C23×C4—471no—
283C23×C4—941no—
284C23×C4—941no—
285C2×M16—944no—
286C2×M16—948no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—941no—
290C22×C8—941no—
291#125—21no—
292#125—21no—
293#125—474no—
294#125—474no—
295#125—472no—
296#125—472no—
297#125—944no—
298#125—944no—
299#125—944no—
300#125—944no—
301#125—942no—
302#125—942no—
303#125—941no—
304#125—941no—
305#125C4×D4712yes—
306#125C22×D4712yes—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—471no—
310C2×C4⋊C4—471no—
311C2×C4⋊C4—474no—
312C2×C4⋊C4—474no—
313C2×C4⋊C4—942no—
314C2×C4⋊C4—942no—
315C2×C4⋊C4—944no—
316C2×C4⋊C4—944no—
317C2×C4⋊C4—944no—
318C2×C4⋊C4—944no—
319C2×C4⋊C4—941no—
320C2×C4⋊C4—941no—
321C2×C4⋊C4—941no—
322C2×C4⋊C4—941no—
323C2×C4⋊C4—941no—
324C2×C4⋊C4—941no—
325C2×C4⋊C4—941no—
326C2×C4⋊C4—941no—
327C2×C4⋊C4C4×D4711yescharacteristic
328C2×C4⋊C4C4×D4711yescharacteristic
329C2×C42—471no—
330C2×C42—471no—
331C2×C42—471no—
332C2×C42—472no—
333C2×C42—472no—
334C2×C42—472no—
335C2×C42—472no—
336C2×C42C22×D4711yescharacteristic
337C4⋊C8—944no—
338C22⋊C8—944no—
339#97—21no—
340#97—21no—
341#97—472no—
342#97—472no—
343#97—941no—
344#97—941no—
345#97C22×D4712yes—
346#97C22×D4712yes—
347C4×C8—944no—
348C24—471no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—471no—
352C22×C4—471no—
353C22×C4—471no—
354C22×C4—472no—
355C22×C4—472no—
356C22×C4—472no—
357C22×C4—472no—
358C22×C4—472no—
359C22×C4—472no—
360C22×C4—944no—
361C22×C4—944no—
362C22×C4—944no—
363C22×C4—944no—
364C22×C4—941no—
365C22×C4—941no—
366C22×C4—1882no—
367C22×C4—1884no—
368C22×C4—1884no—
369C22×C4C2×C4×D4711yescharacteristic
370C22×C4D4×D4711yescharacteristic
371C22×C4D4×D4711yescharacteristic
372M16—9416no—
373C2×C8—24no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—42no—
377C2×C8—944no—
378C2×C8—942no—
379C2×C8—942no—
380C2×C8—1882no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—472no—
388C4⋊C4—472no—
389C4⋊C4—944no—
390C4⋊C4—944no—
391C4⋊C4—944no—
392C4⋊C4—944no—
393C4⋊C4—944no—
394C4⋊C4—944no—
395C4⋊C4—942no—
396C4⋊C4—942no—
397C4⋊C4—941no—
398C4⋊C4—941no—
399C4⋊C4—942no—
400C4⋊C4—942no—
401C4⋊C4C2×C4×D4712yes—
402C4⋊C4C2×C4×D4712yes—
403C42—472no—
404C42—472no—
405C42—472no—
406C42—472no—
407C42—472no—
408C42—472no—
409C42C2×C4×D4711yescharacteristic
410C42D4×D4711yescharacteristic
411C42D4×D4711yescharacteristic
412C42C23×D4711yescharacteristic
413C23—472no—
414C23—474no—
415C23—942no—
416C23—942no—
417C23C22⋊C4×D4711yescharacteristic
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—472no—
426C2×C4—474no—
427C2×C4—472no—
428C2×C4—472no—
429C2×C4—944no—
430C2×C4—944no—
431C2×C4—944no—
432C2×C4—944no—
433C2×C4—942no—
434C2×C4—942no—
435C2×C4—942no—
436C2×C4—942no—
437C2×C4—1882no—
438C2×C4—1882no—
439C2×C4—1888no—
440C2×C4—1888no—
441C2×C4—1882no—
442C2×C4—1882no—
443C2×C4C22⋊C4×D4711yescharacteristic
444C2×C4C22⋊C4×D4711yescharacteristic
445C2×C4C22⋊C4×D4711yescharacteristic
446C2×C4C22×C4×D4711yescharacteristic
447C2×C4C2×D4×D4711yescharacteristic
448C2×C4C2×D4×D4711yescharacteristic
449C8—24no—
450C8—42no—
451C8—944no—
452C8—1882no—
453C22—474no—
454C22—942no—
455C22—948no—
456C22—942no—
457C22#101×D4712yes—
458C22#104×D4712yes—
459C22#1568913812yes—
460C22C2×C22⋊C4×D4711yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—21no—
467C4—42no—
468C4—42no—
469C4—474no—
470C4—942no—
471C4—942no—
472C4—1882no—
473C4—1882no—
474C2—944no—
475C2#2024198814yesdirect product factor
476C2C2×#101×D4711yescharacteristic
477C2C2×#104×D4711yescharacteristic
478C2C2×#1568913811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC2×C47×#330C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC42×C47C24
hypercenterC2×#330D47
hypocenterC47C2×#1528
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
4. #20241988C2direct (N × H)
5. C2×#15688865C2semidirect
6. C2×#15688864C2semidirect
7. C2×#15688864C2semidirect
8. C2×C47×#330C2semidirect
33. #15688865C22semidirect
34. #15688864C22semidirect
35. #15688864C22semidirect
39. C47×#330C22semidirect
242. C2×#330D47semidirect
243. C2×C47#1528semidirect
278. #330C2×D47semidirect
279. C47C2×#1528semidirect
475. C2#20241988direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#125×D472
C2×#156891782
C2×#156890752
#202419882
C2×#156888652
C2×#156888642
C2×C47×#3302
C2×#152847