Finite Group Databasebeta

← C2×#21444810 #29652140

Subgroups — C2×#21444810 #29652140

Order 15616.

1136 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840090C212yesmaximal, complemented
2C2×#16839687C211yesmaximal, characteristic
3#21444810C218yesmaximal, direct product factor
4C2×#16839499C212yesmaximal, complemented
5C2×#16839486C211yesmaximal, characteristic
6C2×C61×#543C211yesmaximal, characteristic
7C22×C4⋊Dic61C2211yescharacteristic
8C22×C22⋊Dic61—21no—
9#16840090—24no—
10#16840090C2218yescomplemented
11C2×#14519708—22no—
12C2×#14519701—22no—
13C2×C22⋊#92418C2212yes—
14#16839687—22no—
15#16839687C2214yes—
16C2×#14519684—21no—
17C2×#14519684C2211yescharacteristic
18#16839499C2218yescomplemented
19#16839486C2214yes—
20C61×#543—24no—
21C61×#543—22no—
22C61×#543C2214yes—
23C2×C22⋊Q8×C61—22no—
24C2×C22⋊Q8×C61—21no—
25C2×C22⋊Q8×C61—22no—
26C2×C22⋊Q8×C61C2212yes—
27C22×C22⋊C4×C61—21no—
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⋊Dic61C2312yes—
36C2×C22⋊Dic61—24no—
37C2×C22⋊Dic61—44no—
38#14519708—28no—
39#14519701—28no—
40C22⋊#92418—22no—
41C22⋊#92418C2314yes—
42#14519684—21no—
43#14519684—24no—
44#14519684C2312yes—
45C25×C61D411yescharacteristic
46C22×Q8×C61—21no—
47C22×Q8×C61D412yes—
48C23×C4×C61—21no—
49C23×C4×C61—21no—
50C23×C4×C61D411yescharacteristic
51C23×C4×C61C2311yescharacteristic
52C22⋊Q8×C61—28no—
53C22⋊Q8×C61—28no—
54C22⋊Q8×C61—24no—
55C22⋊Q8×C61—28no—
56C22⋊Q8×C61—22no—
57C22⋊Q8×C61—22no—
58C22⋊Q8×C61—24no—
59C22⋊Q8×C61—28no—
60C22⋊Q8×C61D414yes—
61C22⋊Q8×C61C2314yes—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—22no—
64C2×C4⋊C4×C61—22no—
65C2×C4⋊C4×C61D412yes—
66C2×C22⋊C4×C61—24no—
67C2×C22⋊C4×C61—22no—
68C2×C22⋊C4×C61—24no—
69C2×C22⋊C4×C61—22no—
70C2×C22⋊C4×C61—22no—
71C2×C22⋊C4×C61—22no—
72C2×C22⋊C4×C61D412yes—
73C2×C22⋊C4×C61C2312yes—
74C24×C61—21no—
75C24×C61—21no—
76C24×C61—22no—
77C24×C61—42no—
78C24×C61—42no—
79C24×C61SD1614yes—
80C24×C61C2×D411yescharacteristic
81C24×C61C2×D412yes—
82C2×Q8×C61—24no—
83C2×Q8×C61—22no—
84C2×Q8×C61—44no—
85C2×Q8×C61—82no—
86C2×Q8×C61C2×D414yes—
87C22×C4×C61—22no—
88C22×C4×C61—21no—
89C22×C4×C61—22no—
90C22×C4×C61—24no—
91C22×C4×C61—24no—
92C22×C4×C61—21no—
93C22×C4×C61—42no—
94C22×C4×C61—42no—
95C22×C4×C61—82no—
96C22×C4×C61—82no—
97C22×C4×C61C2×D412yes—
98C22×C4×C61C2×D412yes—
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D412yes—
101C22×C4×C61C2411yescharacteristic
102C22×Dic61—22no—
103C22×Dic61—22no—
104C22×Dic61—42no—
105C22×Dic61—42no—
106C22×Dic61—41no—
107C22×Dic61—41no—
108C22×Dic61—42no—
109C22×Dic61—42no—
110C22×Dic61—42no—
111C4⋊C4×C61—24no—
112C4⋊C4×C61—28no—
113C4⋊C4×C61—24no—
114C4⋊C4×C61—22no—
115C4⋊C4×C61—24no—
116C4⋊C4×C61C2×D414yes—
117C22⋊C4×C61—28no—
118C22⋊C4×C61—24no—
119C22⋊C4×C61—24no—
120C22⋊C4×C61—24no—
121C22⋊C4×C61—24no—
122C22⋊Dic61—48no—
123C4⋊Dic61—24no—
124C4⋊Dic61—42no—
125C2×#92418—24no—
126C2×#92418—44no—
127C23×C61—22no—
128C23×C61—22no—
129C23×C61—22no—
130C23×C61—24no—
131C23×C61—22no—
132C23×C61—24no—
133C23×C61—48no—
134C23×C61—42no—
135C23×C61—42no—
136C23×C61—42no—
137C23×C61—42no—
138C23×C61—84no—
139C23×C61—81no—
140C23×C61—81no—
141C23×C61#12011yescharacteristic
142C23×C61#12011yescharacteristic
143C23×C61C2×SD1612yes—
144C23×C61C2×SD1614yes—
145C23×C61#13712yes—
146C23×C61C22×D411yescharacteristic
147Q8×C61—44no—
148Q8×C61—82no—
149Q8×C61—84no—
150C2×C4×C61—24no—
151C2×C4×C61—24no—
152C2×C4×C61—22no—
153C2×C4×C61—24no—
154C2×C4×C61—42no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—42no—
158C2×C4×C61—44no—
159C2×C4×C61—44no—
160C2×C4×C61—42no—
161C2×C4×C61—81no—
162C2×C4×C61—84no—
163C2×C4×C61—84no—
164C2×C4×C61#12012yes—
165C2×C4×C61C22×D412yes—
166C2×Dic61—42no—
167C2×Dic61—42no—
168C2×Dic61—42no—
169C2×Dic61—42no—
170C2×Dic61—42no—
171C2×Dic61—42no—
172C2×Dic61—84no—
173C2×Dic61—82no—
174C2×Dic61—82no—
175#92418—44no—
176C2×#1608—611nomaximal, Sylow
177C22×C61—24no—
178C22×C61—24no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—24no—
184C22×C61—44no—
185C22×C61—48no—
186C22×C61—42no—
187C22×C61—42no—
188C22×C61—82no—
189C22×C61—84no—
190C22×C61#44812yes—
191C22×C61#44812yes—
192C22×C61#45512yes—
193C22×C61#45812yes—
194C22×C61C2×#12011yescharacteristic
195C22×C61C22×SD1611yescharacteristic
196C22×C61C2×#13711yescharacteristic
197C4×C61—22no—
198C4×C61—22no—
199C4×C61—42no—
200C4×C61—44no—
201C4×C61—44no—
202Dic61—82no—
203Dic61—82no—
204C2×#543D6111yescharacteristic
205C2×#483—612no—
206C2×#397—611no—
207#1608—618no—
208C2×#328—612no—
209C2×#323—611no—
210C2×C61—21no—
211C2×C61—21no—
212C2×C61—22no—
213C2×C61—44no—
214C2×C61#160814yescomplemented
215C2×C61C2×#44811yescharacteristic
216C2×C61C2×#45511yescharacteristic
217C2×C61C2×#45811yescharacteristic
218#543—24no—
219#543—22no—
220#543C2×D6114yes—
221C2×C22⋊Q8—22no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—22no—
224C2×C22⋊Q8C2×D6112yes—
225C22×C4⋊C4—611no—
226C22×C22⋊C4—21no—
227C22×C22⋊C4—1221no—
228C22×C22⋊C4C2×D6111yescharacteristic
229#483—618no—
230#483—1224no—
231C2×#106—1222no—
232C2×#103—1222no—
233C2×C22⋊C8—612no—
234#397—614no—
235#397—1222no—
236C2×#95—611no—
237C2×#95—1221no—
238#328—618no—
239#323—614no—
240C61C2×#160811yescharacteristic, complemented, Sylow
241C25C22⋊D6111yescharacteristic
242C22×Q8—21no—
243C22×Q8C22⋊D6112yes—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—1221no—
247C23×C4—1221no—
248C23×C4C22⋊D6111yescharacteristic
249C23×C4C22×D6111yescharacteristic
250C22×C8—1222no—
251C22⋊Q8—28no—
252C22⋊Q8—28no—
253C22⋊Q8—24no—
254C22⋊Q8—28no—
255C22⋊Q8—24no—
256C22⋊Q8—22no—
257C22⋊Q8—22no—
258C22⋊Q8—28no—
259C22⋊Q8C22⋊D6114yes—
260C22⋊Q8C22×D6114yes—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—612no—
265C2×C4⋊C4—1222no—
266C2×C4⋊C4—1222no—
267C2×C4⋊C4—1221no—
268C2×C4⋊C4C22⋊D6112yes—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—24no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—24no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—1224no—
276C2×C22⋊C4—2444no—
277C2×C22⋊C4C22⋊D6112yes—
278C2×C22⋊C4C22×D6112yes—
279#106—1228no—
280#103—1228no—
281C22⋊C8—614no—
282C22⋊C8—1222no—
283#95—612no—
284#95—1221no—
285#95—1224no—
286C24—21no—
287C24—22no—
288C24—21no—
289C24—42no—
290C24—42no—
291C24#1175820114yes—
292C24C2×C22⋊D6111yescharacteristic
293C24C2×C22⋊D6112yes—
294C2×Q8—24no—
295C2×Q8—22no—
296C2×Q8—44no—
297C2×Q8—82no—
298C2×Q8C2×C22⋊D6114yes—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—21no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—82no—
308C22×C4—82no—
309C22×C4—1222no—
310C22×C4—1222no—
311C22×C4—2442no—
312C22×C4—2442no—
313C22×C4—2442no—
314C22×C4—2441no—
315C22×C4—2441no—
316C22×C4—2442no—
317C22×C4—2442no—
318C22×C4C2×C22⋊D6112yes—
319C22×C4C2×C22⋊D6112yes—
320C22×C4C2×C22⋊D6112yes—
321C22×C4C2×C22⋊D6111yescharacteristic
322C22×C4C23×D6111yescharacteristic
323C2×C8—1224no—
324C2×C8—2444no—
325C4⋊C4—24no—
326C4⋊C4—28no—
327C4⋊C4—24no—
328C4⋊C4—24no—
329C4⋊C4—22no—
330C4⋊C4—1224no—
331C4⋊C4—2442no—
332C4⋊C4C2×C22⋊D6114yes—
333C22⋊C4—28no—
334C22⋊C4—24no—
335C22⋊C4—24no—
336C22⋊C4—24no—
337C22⋊C4—24no—
338C22⋊C4—2448no—
339C23—22no—
340C23—22no—
341C23—22no—
342C23—24no—
343C23—22no—
344C23—24no—
345C23—48no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—81no—
351C23—81no—
352C23—84no—
353C23#1451974611yescharacteristic
354C23#1451974611yescharacteristic
355C23C2×#1175820112yes—
356C23C2×#1175820114yes—
357C23#1451980812yes—
358C23C22×C22⋊D6111yescharacteristic
359Q8—44no—
360Q8—82no—
361Q8—84no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—24no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—42no—
373C2×C4—81no—
374C2×C4—84no—
375C2×C4—84no—
376C2×C4—4884no—
377C2×C4—4882no—
378C2×C4—4882no—
379C2×C4—2442no—
380C2×C4—2442no—
381C2×C4—2442no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4—2442no—
385C2×C4#1451974612yes—
386C2×C4C22×C22⋊D6112yes—
387C8—2444no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—24no—
393C22—24no—
394C22—24no—
395C22—44no—
396C22—42no—
397C22—42no—
398C22—48no—
399C22—82no—
400C22—84no—
401C22#1683990112yes—
402C22#1683990112yes—
403C22#1683994012yes—
404C22#1683995212yes—
405C22C2×#1451974611yescharacteristic
406C22C22×#1175820111yescharacteristic
407C22C2×#1451980811yescharacteristic
408C4—22no—
409C4—22no—
410C4—42no—
411C4—44no—
412C4—44no—
413C4—4882no—
414C4—4882no—
415C2—21no—
416C2—21no—
417C2—22no—
418C2—44no—
419C2#2144481014yesdirect product factor
420C2C2×#1683990111yescharacteristic
421C2C2×#1683994011yescharacteristic
422C2C2×#1683995211yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#543C2
socleC23×C61#120
prime radicalC25×C61D4
hypercenterC2×#543D61
hypocenterC61C2×#1608
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
1. C2×#16840090C2semidirect
3. #21444810C2direct (N × H)
4. C2×#16839499C2semidirect
10. #16840090C22semidirect
18. #16839499C22semidirect
214. C2×C61#1608semidirect
240. C61C2×#1608semidirect
419. C2#21444810direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168400902
C2×#168396872
#214448102
C2×#168394992
C2×#168394862
C2×C61×#5432
C2×#160861