Finite Group Databasebeta

← C2×#21444841 #29652136

Subgroups — C2×#21444841 #29652136

Order 15616.

1524 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1524 conjugacy classes of subgroups — too many to draw. Only its 203 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840324C211yesmaximal, characteristic
2C2×#16840081C212yesmaximal, complemented
3C2×#16839698C211yesmaximal, characteristic, complemented
4#21444841C218yesmaximal, direct product factor
5C2×#16839497C212yesmaximal, complemented
6C2×C61×#323C211yesmaximal, characteristic, complemented
7C23×C22⋊D61—21no—
8#16840324—24no—
9#16840324—22no—
10#16840324C2214yes—
11C2×#14519761—22no—
12C2×#14519751—21no—
13C2×#14519751C2212yes—
14C2×#14519747—22no—
15C22×C4⋊Dic61C2211yescharacteristic, complemented
16C22×#11758196—21no—
17C22×C22⋊Dic61—21no—
18#16840081—24no—
19#16840081C2218yescomplemented
20C2×#14519709—22no—
21C2×#14519699—22no—
22#16839698—22no—
23#16839698C2214yescomplemented
24C2×#14519684C2211yescharacteristic, complemented
25#16839497C2218yescomplemented
26C22×C22⋊C4×C61C2211yescharacteristic
27C2×C22⋊C8×C61C2212yescomplemented
28C61×#323C2214yescomplemented
29C24×D61—21no—
30C22×D244—21no—
31C22×D244D412yes—
32C22×C22⋊D61—22no—
33C22×C22⋊D61—24no—
34C22×C22⋊D61—22no—
35C22×C22⋊D61—24no—
36C22×C22⋊D61—44no—
37C22×C22⋊D61—44no—
38C23×Dic61—21no—
39C23×Dic61—21no—
40C23×Dic61—21no—
41#14519761—28no—
42#14519761—28no—
43#14519751—24no—
44#14519751—24no—
45#14519751—22no—
46#14519751—22no—
47#14519751D414yes—
48#14519751C2314yes—
49#14519747—28no—
50#14519747—28no—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61—22no—
53C2×C4⋊Dic61—22no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61D412yes—
56C2×C4⋊Dic61C2312yescomplemented
57C2×#11758196—24no—
58C2×#11758196—44no—
59C2×C22⋊Dic61—24no—
60C2×C22⋊Dic61—44no—
61C2×#11758198—22no—
62C2×#11758198—22no—
63#14519709—28no—
64#14519699—28no—
65#14519684—21no—
66#14519684C2312yescomplemented
67C25×C61D411yescharacteristic
68C23×C4×C61D411yescharacteristic
69C23×C4×C61C2311yescharacteristic
70C22×C8×C61—22no—
71C2×C22⋊C4×C61—22no—
72C2×C22⋊C4×C61—22no—
73C2×C22⋊C4×C61D412yes—
74C2×C22⋊C4×C61C2312yes—
75C22⋊C8×C61—22no—
76C22⋊C8×C61C2314yescomplemented
77C24×C61—21no—
78C24×C61—21no—
79C24×C61—22no—
80C24×C61—42no—
81C24×C61—42no—
82C24×C61SD1614yes—
83C24×C61C2×D411yescharacteristic
84C24×C61C2×D412yes—
85C23×D61—22no—
86C23×D61—24no—
87C23×D61—44no—
88C23×D61—82no—
89C23×D61—82no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—42no—
93C22×C4×C61—42no—
94C22×C4×C61C2×D412yes—
95C22×C4×C61C2×D412yes—
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D412yes—
98C22×C4×C61C2411yescharacteristic
99C2×C22⋊D61—28no—
100C2×C22⋊D61—24no—
101C2×C22⋊D61—24no—
102C2×C22⋊D61—48no—
103C2×C22⋊D61—416no—
104C2×C22⋊D61—48no—
105C2×C22⋊D61—48no—
106C2×C22⋊D61—44no—
107C2×C22⋊D61—44no—
108C22×Dic61—24no—
109C22×Dic61—24no—
110C22×Dic61—22no—
111C22×Dic61—22no—
112C22×Dic61—22no—
113C22×Dic61—42no—
114C22×Dic61—44no—
115C22×Dic61—42no—
116C22×Dic61—42no—
117C22×Dic61—42no—
118C22×Dic61—41no—
119C22×Dic61—41no—
120C2×D244—24no—
121C2×D244—22no—
122C2×D244—44no—
123C2×D244—82no—
124C2×D244C2×D414yes—
125C2×C8×C61—24no—
126C2×C8×C61—44no—
127C22⋊C4×C61—24no—
128C22⋊C4×C61—24no—
129C22⋊Dic61—48no—
130#11758198—28no—
131#11758198—24no—
132#11758198—24no—
133C4⋊Dic61—24no—
134C4⋊Dic61—22no—
135C4⋊Dic61—24no—
136C4⋊Dic61—42no—
137C4⋊Dic61C2×D414yes—
138#11758196—48no—
139C23×C61—22no—
140C23×C61—22no—
141C23×C61—22no—
142C23×C61—24no—
143C23×C61—22no—
144C23×C61—24no—
145C23×C61—42no—
146C23×C61—48no—
147C23×C61—42no—
148C23×C61—42no—
149C23×C61—42no—
150C23×C61—84no—
151C23×C61—81no—
152C23×C61—81no—
153C23×C61#12011yescharacteristic
154C23×C61#12011yescharacteristic
155C23×C61C2×SD1612yes—
156C23×C61C2×SD1614yes—
157C23×C61AGL(1,ℤ/8)12yes—
158C23×C61C22×D411yescharacteristic
159C22×D61—24no—
160C22×D61—48no—
161C22×D61—44no—
162C22×D61—44no—
163C22×D61—44no—
164C22×D61—84no—
165C22×D61—84no—
166C22×D61—816no—
167C2×C4×C61—24no—
168C2×C4×C61—22no—
169C2×C4×C61—42no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—42no—
173C2×C4×C61—42no—
174C2×C4×C61—81no—
175C2×C4×C61#12012yes—
176C2×C4×C61C22×D412yes—
177C22⋊D61—416no—
178C22⋊D61—44no—
179C22⋊D61—44no—
180C22⋊D61—48no—
181C2×Dic61—24no—
182C2×Dic61—24no—
183C2×Dic61—48no—
184C2×Dic61—42no—
185C2×Dic61—48no—
186C2×Dic61—42no—
187C2×Dic61—44no—
188C2×Dic61—42no—
189C2×Dic61—42no—
190C2×Dic61—42no—
191C2×Dic61—82no—
192C2×Dic61—82no—
193D244—44no—
194D244—82no—
195D244—84no—
196C8×C61—44no—
197C2×#1613—611nomaximal, Sylow
198C22×C61—24no—
199C22×C61—24no—
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—21no—
204C22×C61—24no—
205C22×C61—44no—
206C22×C61—48no—
207C22×C61—42no—
208C22×C61—42no—
209C22×C61—82no—
210C22×C61—84no—
211C22×C61#45012yes—
212C22×C61#45012yes—
213C22×C61#45312yes—
214C22×C61#45812yes—
215C22×C61C2×#12011yescharacteristic
216C22×C61C22×SD1611yescharacteristic
217C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
218C2×D61—44no—
219C2×D61—44no—
220C2×D61—44no—
221C2×D61—816no—
222C2×D61—88no—
223C4×C61—22no—
224C4×C61—22no—
225C4×C61—42no—
226Dic61—44no—
227Dic61—44no—
228Dic61—82no—
229C2×#534—611no—
230C2×#481—612no—
231C2×#399—611no—
232#1613—618no—
233C2×#327—612no—
234C2×#323D6111yescharacteristic, complemented
235C2×C61—21no—
236C2×C61—21no—
237C2×C61—22no—
238C2×C61—44no—
239C2×C61#161314yescomplemented
240C2×C61C2×#45011yescharacteristic
241C2×C61C2×#45311yescharacteristic
242C2×C61C2×#45811yescharacteristic
243D61—84no—
244C23×D4—1221no—
245#534—614no—
246#534—1224no—
247#534—1222no—
248C2×#123—1222no—
249C2×#121—612no—
250C2×#121—1221no—
251C2×#120—1222no—
252C22×C4⋊C4—611no—
253C22×C4⋊C4—1221no—
254C22×C22⋊C4—1221no—
255C22×C22⋊C4C2×D6111yescharacteristic
256#481—618no—
257#481—1224no—
258C2×#106—1222no—
259C2×#102—1222no—
260C2×C22⋊C8C2×D6112yescomplemented
261#399—614no—
262#399—1222no—
263C2×#95—611no—
264#327—618no—
265#323C2×D6114yescomplemented
266C61C2×#161311yescharacteristic, complemented, Sylow
267C25—1221no—
268C25D24411yescharacteristic
269C22×D4—612no—
270C22×D4—1221no—
271C22×D4—1222no—
272C22×D4—1224no—
273C22×D4—1222no—
274C22×D4—1224no—
275C22×D4—2444no—
276C22×D4—2444no—
277C23×C4—1221no—
278C23×C4—1221no—
279C23×C4—1221no—
280C23×C4D24411yescharacteristic
281C23×C4C22×D6111yescharacteristic
282C22×C8—22no—
283#123—1228no—
284#123—1228no—
285#121—614no—
286#121—614no—
287#121—1224no—
288#121—1222no—
289#121—1224no—
290#121—1222no—
291#120—1228no—
292#120—1228no—
293C2×C4⋊C4—612no—
294C2×C4⋊C4—612no—
295C2×C4⋊C4—1221no—
296C2×C4⋊C4—1222no—
297C2×C4⋊C4—1222no—
298C2×C4⋊C4—1221no—
299C2×C4⋊C4—1224no—
300C2×C4⋊C4—2444no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—1222no—
304C2×C22⋊C4—1222no—
305C2×C22⋊C4—1224no—
306C2×C22⋊C4—2444no—
307C2×C22⋊C4D24412yes—
308C2×C22⋊C4C22×D6112yes—
309#106—1228no—
310#102—1228no—
311C22⋊C8—22no—
312C22⋊C8C22×D6114yescomplemented
313#95—612no—
314#95—1221no—
315C24—21no—
316C24—21no—
317C24—22no—
318C24—42no—
319C24—42no—
320C24—1224no—
321C24—1222no—
322C24—4882no—
323C24—4882no—
324C24—2444no—
325C24#1175819014yes—
326C24C2×D24411yescharacteristic
327C24C2×D24412yes—
328C2×D4—614no—
329C2×D4—1224no—
330C2×D4—1228no—
331C2×D4—1224no—
332C2×D4—1224no—
333C2×D4—1222no—
334C2×D4—4882no—
335C2×D4—2444no—
336C2×D4—2448no—
337C2×D4—24416no—
338C2×D4—2448no—
339C2×D4—2448no—
340C2×D4—2444no—
341C2×D4—2444no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—1224no—
347C22×C4—1224no—
348C22×C4—1222no—
349C22×C4—1222no—
350C22×C4—1222no—
351C22×C4—2442no—
352C22×C4—2442no—
353C22×C4—2441no—
354C22×C4—2441no—
355C22×C4—2444no—
356C22×C4—2442no—
357C22×C4—2442no—
358C22×C4C2×D24412yes—
359C22×C4C2×D24411yescharacteristic
360C22×C4D4×D6112yes—
361C22×C4D4×D6112yes—
362C22×C4C23×D6111yescharacteristic
363C2×C8—24no—
364C2×C8—44no—
365C4⋊C4—614no—
366C4⋊C4—1224no—
367C4⋊C4—1222no—
368C4⋊C4—1224no—
369C4⋊C4—2448no—
370C4⋊C4—2442no—
371C22⋊C4—24no—
372C22⋊C4—24no—
373C22⋊C4—1228no—
374C22⋊C4—1224no—
375C22⋊C4—1224no—
376C22⋊C4—2448no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—24no—
381C23—22no—
382C23—24no—
383C23—42no—
384C23—48no—
385C23—42no—
386C23—42no—
387C23—42no—
388C23—81no—
389C23—81no—
390C23—84no—
391C23—1224no—
392C23—48816no—
393C23—4884no—
394C23—4884no—
395C23—2448no—
396C23—2444no—
397C23—2444no—
398C23—2444no—
399C23#1451974711yescharacteristic
400C23#1451974711yescharacteristic
401C23C2×#1175819012yes—
402C23C2×#1175819014yes—
403C23#1451980512yes—
404C23C22×D24411yescharacteristic
405D4—4882no—
406D4—4884no—
407D4—2444no—
408D4—24416no—
409D4—2444no—
410D4—2444no—
411D4—2448no—
412C2×C4—24no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—81no—
420C2×C4—1224no—
421C2×C4—1224no—
422C2×C4—4882no—
423C2×C4—4882no—
424C2×C4—2442no—
425C2×C4—2442no—
426C2×C4—2442no—
427C2×C4—2442no—
428C2×C4—2448no—
429C2×C4—2448no—
430C2×C4—2442no—
431C2×C4—2444no—
432C2×C4#1451974712yes—
433C2×C4C2×D4×D6112yes—
434C8—44no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—24no—
440C22—24no—
441C22—24no—
442C22—44no—
443C22—42no—
444C22—42no—
445C22—48no—
446C22—82no—
447C22—84no—
448C22—48816no—
449C22—4888no—
450C22—2444no—
451C22—2444no—
452C22—2444no—
453C22#1683991512yes—
454C22#1683991512yes—
455C22#1683993212yes—
456C22#1683995312yes—
457C22C2×#1451974711yescharacteristic
458C22C22×#1175819011yescharacteristic
459C22C2×#1451980511yescharacteristic
460C4—22no—
461C4—22no—
462C4—42no—
463C4—4882no—
464C4—2444no—
465C4—2444no—
466C2—21no—
467C2—21no—
468C2—22no—
469C2—44no—
470C2—4884no—
471C2#2144484114yesdirect product factor
472C2C2×#1683991511yescharacteristic
473C2C2×#1683993211yescharacteristic
474C2C2×#1683995311yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#323C2
socleC23×C61#120
prime radicalC2×#16840324C2
hypercenterC2×#323D61
hypocenterC61C2×#1613
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. C2×#16840081C2semidirect
3. C2×#16839698C2semidirect
4. #21444841C2direct (N × H)
5. C2×#16839497C2semidirect
6. C2×C61×#323C2semidirect
15. C22×C4⋊Dic61C22semidirect
19. #16840081C22semidirect
23. #16839698C22semidirect
24. C2×#14519684C22semidirect
25. #16839497C22semidirect
27. C2×C22⋊C8×C61C22semidirect
28. C61×#323C22semidirect
56. C2×C4⋊Dic61C23semidirect
66. #14519684C23semidirect
76. C22⋊C8×C61C23semidirect
234. C2×#323D61semidirect
239. C2×C61#1613semidirect
260. C2×C22⋊C8C2×D61semidirect
265. #323C2×D61semidirect
266. C61C2×#1613semidirect
312. C22⋊C8C22×D61semidirect
471. C2#21444841direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403242
C2×#168400812
C2×#168396982
#214448412
C2×#168394972
C2×C61×#3232
C2×#161361