Finite Group Databasebeta

← C2×#21444805 #29652128

Subgroups — C2×#21444805 #29652128

Order 15616.

1480 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840073C212yesmaximal, complemented
2C2×#16839687C211yesmaximal, characteristic, complemented
3#21444805C218yesmaximal, direct product factor
4C2×#16839496C212yesmaximal, complemented
5C2×#16839486C211yesmaximal, characteristic, complemented
6C2×C61×#534C211yesmaximal, characteristic
7C22×C4⋊Dic61C2211yescharacteristic, complemented
8C22×C22⋊Dic61—21no—
9#16840073—24no—
10#16840073C2218yescomplemented
11C2×#14519710—22no—
12C2×#14519698—22no—
13C2×C22⋊#92418C2212yescomplemented
14#16839687—22no—
15#16839687C2214yescomplemented
16C2×#14519684—21no—
17C2×#14519684C2211yescharacteristic, complemented
18#16839496C2218yescomplemented
19#16839486C2214yescomplemented
20C23×D4×C61—21no—
21C61×#534—24no—
22C61×#534—22no—
23C61×#534C2214yes—
24C2×#123×C61—22no—
25C2×#121×C61—21no—
26C2×#121×C61C2212yes—
27C2×#120×C61—22no—
28C22×C22⋊C4×C61C2211yescharacteristic
29C23×Dic61—21no—
30C23×Dic61—21no—
31C22×#92418—22no—
32C2×C4⋊Dic61—22no—
33C2×C4⋊Dic61—22no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2312yescomplemented
36C2×C22⋊Dic61—24no—
37C2×C22⋊Dic61—44no—
38#14519710—28no—
39#14519698—28no—
40C22⋊#92418—22no—
41C22⋊#92418C2314yescomplemented
42#14519684—21no—
43#14519684—24no—
44#14519684C2312yescomplemented
45C25×C61—21no—
46C25×C61D411yescharacteristic
47C22×D4×C61—24no—
48C22×D4×C61—22no—
49C22×D4×C61—24no—
50C22×D4×C61—22no—
51C22×D4×C61—21no—
52C22×D4×C61—44no—
53C22×D4×C61—44no—
54C22×D4×C61D412yes—
55C23×C4×C61—21no—
56C23×C4×C61D411yescharacteristic
57C23×C4×C61C2311yescharacteristic
58#123×C61—28no—
59#123×C61—28no—
60#121×C61—24no—
61#121×C61—22no—
62#121×C61—22no—
63#121×C61—24no—
64#121×C61D414yes—
65#121×C61C2314yes—
66#120×C61—28no—
67#120×C61—28no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61D412yes—
70C2×C22⋊C4×C61—22no—
71C2×C22⋊C4×C61—22no—
72C2×C22⋊C4×C61—22no—
73C2×C22⋊C4×C61—22no—
74C2×C22⋊C4×C61D412yes—
75C2×C22⋊C4×C61C2312yes—
76C24×C61—21no—
77C24×C61—21no—
78C24×C61—22no—
79C24×C61—24no—
80C24×C61—22no—
81C24×C61—42no—
82C24×C61—42no—
83C24×C61—44no—
84C24×C61—82no—
85C24×C61—82no—
86C24×C61D814yes—
87C24×C61C2×D411yescharacteristic
88C24×C61C2×D412yes—
89C2×D4×C61—28no—
90C2×D4×C61—24no—
91C2×D4×C61—24no—
92C2×D4×C61—24no—
93C2×D4×C61—22no—
94C2×D4×C61—44no—
95C2×D4×C61—48no—
96C2×D4×C61—416no—
97C2×D4×C61—48no—
98C2×D4×C61—48no—
99C2×D4×C61—44no—
100C2×D4×C61—44no—
101C2×D4×C61—82no—
102C2×D4×C61C2×D414yes—
103C22×C4×C61—24no—
104C22×C4×C61—21no—
105C22×C4×C61—22no—
106C22×C4×C61—21no—
107C22×C4×C61—42no—
108C22×C4×C61—44no—
109C22×C4×C61—42no—
110C22×C4×C61C2×D412yes—
111C22×C4×C61C2×D412yes—
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D412yes—
114C22×C4×C61C2411yescharacteristic
115C22×Dic61—22no—
116C22×Dic61—22no—
117C22×Dic61—42no—
118C22×Dic61—42no—
119C22×Dic61—41no—
120C22×Dic61—41no—
121C22×Dic61—42no—
122C22×Dic61—42no—
123C22×Dic61—42no—
124C4⋊C4×C61—24no—
125C4⋊C4×C61—22no—
126C4⋊C4×C61C2×D414yes—
127C22⋊C4×C61—28no—
128C22⋊C4×C61—24no—
129C22⋊C4×C61—24no—
130C22⋊C4×C61—24no—
131C22⋊C4×C61—24no—
132C22⋊Dic61—48no—
133C4⋊Dic61—24no—
134C4⋊Dic61—42no—
135C2×#92418—24no—
136C2×#92418—44no—
137C23×C61—22no—
138C23×C61—22no—
139C23×C61—22no—
140C23×C61—24no—
141C23×C61—22no—
142C23×C61—24no—
143C23×C61—24no—
144C23×C61—48no—
145C23×C61—42no—
146C23×C61—42no—
147C23×C61—48no—
148C23×C61—42no—
149C23×C61—42no—
150C23×C61—44no—
151C23×C61—44no—
152C23×C61—44no—
153C23×C61—84no—
154C23×C61—81no—
155C23×C61—81no—
156C23×C61—84no—
157C23×C61—84no—
158C23×C61—816no—
159C23×C61#12011yescharacteristic
160C23×C61#12011yescharacteristic
161C23×C61C2×D812yes—
162C23×C61C2×D814yes—
163C23×C61AGL(1,ℤ/8)12yes—
164C23×C61C22×D411yescharacteristic
165D4×C61—44no—
166D4×C61—416no—
167D4×C61—44no—
168D4×C61—44no—
169D4×C61—48no—
170D4×C61—82no—
171D4×C61—84no—
172C2×C4×C61—24no—
173C2×C4×C61—22no—
174C2×C4×C61—24no—
175C2×C4×C61—42no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—48no—
179C2×C4×C61—44no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61—81no—
183C2×C4×C61#12012yes—
184C2×C4×C61C22×D412yes—
185C2×Dic61—42no—
186C2×Dic61—42no—
187C2×Dic61—42no—
188C2×Dic61—42no—
189C2×Dic61—42no—
190C2×Dic61—42no—
191C2×Dic61—84no—
192C2×Dic61—82no—
193C2×Dic61—82no—
194#92418—44no—
195C2×#1607—611nomaximal, Sylow
196C22×C61—24no—
197C22×C61—24no—
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—24no—
203C22×C61—44no—
204C22×C61—48no—
205C22×C61—42no—
206C22×C61—42no—
207C22×C61—44no—
208C22×C61—44no—
209C22×C61—44no—
210C22×C61—82no—
211C22×C61—84no—
212C22×C61—816no—
213C22×C61—88no—
214C22×C61#44712yes—
215C22×C61#44712yes—
216C22×C61#45512yes—
217C22×C61#45812yes—
218C22×C61C2×#12011yescharacteristic
219C22×C61C22×D811yescharacteristic
220C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
221C4×C61—22no—
222C4×C61—22no—
223C4×C61—44no—
224C4×C61—42no—
225Dic61—82no—
226Dic61—82no—
227C2×#534D6111yescharacteristic
228C2×#480—612no—
229C2×#397—611no—
230#1607—618no—
231C2×#327—612no—
232C2×#323—611no—
233C2×C61—21no—
234C2×C61—21no—
235C2×C61—22no—
236C2×C61—44no—
237C2×C61—84no—
238C2×C61#160714yescomplemented
239C2×C61C2×#44711yescharacteristic
240C2×C61C2×#45511yescharacteristic
241C2×C61C2×#45811yescharacteristic
242C23×D4—21no—
243#534—24no—
244#534—22no—
245#534C2×D6114yes—
246C2×#123—22no—
247C2×#121—21no—
248C2×#121C2×D6112yes—
249C2×#120—22no—
250C22×C4⋊C4—611no—
251C22×C22⋊C4—1221no—
252C22×C22⋊C4C2×D6111yescharacteristic
253#480—618no—
254#480—1224no—
255C2×#107—1222no—
256C2×#102—1222no—
257C2×C22⋊C8—612no—
258#397—614no—
259#397—1222no—
260C2×#95—611no—
261C2×#95—1221no—
262#327—618no—
263#323—614no—
264C61C2×#160711yescharacteristic, complemented, Sylow
265C25—21no—
266C25C22⋊D6111yescharacteristic
267C22×D4—22no—
268C22×D4—24no—
269C22×D4—22no—
270C22×D4—24no—
271C22×D4—21no—
272C22×D4—44no—
273C22×D4—44no—
274C22×D4C22⋊D6112yes—
275C23×C4—21no—
276C23×C4—1221no—
277C23×C4—1221no—
278C23×C4C22⋊D6111yescharacteristic
279C23×C4C22×D6111yescharacteristic
280C22×C8—1222no—
281#123—28no—
282#123—28no—
283#121—24no—
284#121—24no—
285#121—22no—
286#121—22no—
287#121C22⋊D6114yes—
288#121C22×D6114yes—
289#120—28no—
290#120—28no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—612no—
293C2×C4⋊C4—1222no—
294C2×C4⋊C4—1222no—
295C2×C4⋊C4—1221no—
296C2×C4⋊C4C22⋊D6112yes—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—1224no—
302C2×C22⋊C4—2444no—
303C2×C22⋊C4C22⋊D6112yes—
304C2×C22⋊C4C22×D6112yes—
305#107—1228no—
306#102—1228no—
307C22⋊C8—614no—
308C22⋊C8—1222no—
309#95—612no—
310#95—1221no—
311#95—1224no—
312C24—21no—
313C24—21no—
314C24—22no—
315C24—24no—
316C24—22no—
317C24—42no—
318C24—42no—
319C24—44no—
320C24—82no—
321C24—82no—
322C24#1175819914yes—
323C24C2×C22⋊D6111yescharacteristic
324C24C2×C22⋊D6112yes—
325C2×D4—28no—
326C2×D4—24no—
327C2×D4—24no—
328C2×D4—24no—
329C2×D4—22no—
330C2×D4—44no—
331C2×D4—48no—
332C2×D4—416no—
333C2×D4—48no—
334C2×D4—48no—
335C2×D4—44no—
336C2×D4—44no—
337C2×D4—82no—
338C2×D4C2×C22⋊D6114yes—
339C22×C4—24no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—42no—
344C22×C4—44no—
345C22×C4—42no—
346C22×C4—1222no—
347C22×C4—1222no—
348C22×C4—2442no—
349C22×C4—2442no—
350C22×C4—2441no—
351C22×C4—2441no—
352C22×C4—2442no—
353C22×C4—2442no—
354C22×C4—2442no—
355C22×C4C2×C22⋊D6112yes—
356C22×C4C2×C22⋊D6112yes—
357C22×C4C2×C22⋊D6112yes—
358C22×C4C2×C22⋊D6111yescharacteristic
359C22×C4C23×D6111yescharacteristic
360C2×C8—1224no—
361C2×C8—2444no—
362C4⋊C4—24no—
363C4⋊C4—22no—
364C4⋊C4—1224no—
365C4⋊C4—2442no—
366C4⋊C4C2×C22⋊D6114yes—
367C22⋊C4—28no—
368C22⋊C4—24no—
369C22⋊C4—24no—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—2448no—
373C23—22no—
374C23—22no—
375C23—22no—
376C23—24no—
377C23—22no—
378C23—24no—
379C23—24no—
380C23—48no—
381C23—42no—
382C23—42no—
383C23—48no—
384C23—42no—
385C23—42no—
386C23—44no—
387C23—44no—
388C23—44no—
389C23—81no—
390C23—81no—
391C23—84no—
392C23—84no—
393C23—84no—
394C23—816no—
395C23#1451974611yescharacteristic
396C23#1451974611yescharacteristic
397C23C2×#1175819912yes—
398C23C2×#1175819914yes—
399C23#1451980312yes—
400C23C22×C22⋊D6111yescharacteristic
401D4—44no—
402D4—416no—
403D4—44no—
404D4—44no—
405D4—48no—
406D4—82no—
407D4—84no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—48no—
415C2×C4—42no—
416C2×C4—44no—
417C2×C4—42no—
418C2×C4—81no—
419C2×C4—4884no—
420C2×C4—4882no—
421C2×C4—4882no—
422C2×C4—2442no—
423C2×C4—2442no—
424C2×C4—2442no—
425C2×C4—2442no—
426C2×C4—2442no—
427C2×C4—2442no—
428C2×C4#1451974612yes—
429C2×C4C22×C22⋊D6112yes—
430C8—2444no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—24no—
436C22—24no—
437C22—24no—
438C22—44no—
439C22—42no—
440C22—42no—
441C22—48no—
442C22—44no—
443C22—44no—
444C22—44no—
445C22—82no—
446C22—84no—
447C22—816no—
448C22—88no—
449C22#1683989612yes—
450C22#1683989612yes—
451C22#1683994012yes—
452C22#1683995212yes—
453C22C2×#1451974611yescharacteristic
454C22C22×#1175819911yescharacteristic
455C22C2×#1451980311yescharacteristic
456C4—22no—
457C4—22no—
458C4—42no—
459C4—44no—
460C4—4882no—
461C4—4882no—
462C2—21no—
463C2—21no—
464C2—22no—
465C2—44no—
466C2—84no—
467C2#2144480514yesdirect product factor
468C2C2×#1683989611yescharacteristic
469C2C2×#1683994011yescharacteristic
470C2C2×#1683995211yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#534C2
socleC23×C61#120
hypercenterC2×#534D61
hypocenterC61C2×#1607
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. C2×#16840073C2semidirect
2. C2×#16839687C2semidirect
3. #21444805C2direct (N × H)
4. C2×#16839496C2semidirect
5. C2×#16839486C2semidirect
7. C22×C4⋊Dic61C22semidirect
10. #16840073C22semidirect
13. C2×C22⋊#92418C22semidirect
15. #16839687C22semidirect
17. C2×#14519684C22semidirect
18. #16839496C22semidirect
19. #16839486C22semidirect
35. C2×C4⋊Dic61C23semidirect
41. C22⋊#92418C23semidirect
44. #14519684C23semidirect
238. C2×C61#1607semidirect
264. C61C2×#1607semidirect
467. C2#21444805direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168400732
C2×#168396872
#214448052
C2×#168394962
C2×#168394862
C2×C61×#5342
C2×#160761