Finite Group Databasebeta

← C2×#21445268 #29662312

Subgroups — C2×#21445268 #29662312

Order 15616.

726 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840112C211yesmaximal, characteristic, complemented
2C2×#16840052C211yesmaximal, characteristic
3C2×D4×#92418C211yesmaximal, characteristic
4#21445268C218yesmaximal, direct product factor
5C2×#16839514C211yesmaximal, characteristic, complemented
6C2×#16839510C211yesmaximal, characteristic, complemented
7C2×#16839508C211yesmaximal, characteristic, complemented
8C2×C61×#474C211yesmaximal, characteristic
9C23×#92418—21no—
10C2×#14519777C2211yescharacteristic
11#16840112—22no—
12#16840112C2214yescomplemented
13#16840052—22no—
14#16840052C2214yes—
15D4×#92418—22no—
16D4×#92418C2214yes—
17C2×#14519708—21no—
18C2×C4⋊#92418C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519701—21no—
21C2×#14519701—21no—
22C2×#14519698—21no—
23C2×C22⋊#92418—21no—
24C2×C4×#92418C2211yescharacteristic
25#16839514C2214yescomplemented
26#16839510C2214yescomplemented
27#16839508C2214yescomplemented
28C2×C4⋊Q8×C61C2211yescharacteristic
29C2×C4×D4×C61C2211yescharacteristic
30C61×#474—22no—
31C61×#474C2214yes—
32C2×#107×C61—21no—
33C2×C4⋊C8×C61C2211yescharacteristic
34C2×#102×C61—21no—
35C22×Dic122—21no—
36C22×#92418—21no—
37C22×#92418—21no—
38C22×#92418—24no—
39C22×#92418—44no—
40C22×#92418D411yescharacteristic
41C22×#92418D411yescharacteristic
42#14519777—21no—
43#14519777—21no—
44#14519777—21no—
45#14519777C2312yes—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61—21no—
48#14519708—24no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418C2312yes—
52C4⋊#92418C2312yes—
53#14519701—24no—
54#14519701—24no—
55#14519698—24no—
56C22⋊#92418—24no—
57C4×#92418D412yes—
58C4×#92418C2312yes—
59C22×Q8×C61—21no—
60C22×D4×C61D411yescharacteristic
61C23×C4×C61—21no—
62C22×C8×C61—21no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66C4⋊Q8×C61C2312yes—
67C4×D4×C61—21no—
68C4×D4×C61—21no—
69C4×D4×C61D412yes—
70C4×D4×C61C2312yes—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C22⋊C4×C61—21no—
75C2×C42×C61C2311yescharacteristic
76#107×C61—24no—
77C4⋊C8×C61—21no—
78C4⋊C8×C61C2312yes—
79#102×C61—24no—
80C24×C61—21no—
81C2×Q8×C61—22no—
82C2×Q8×C61—41no—
83C2×Q8×C61—42no—
84C2×Q8×C61—42no—
85C2×D4×C61—21no—
86C2×D4×C61—22no—
87C2×D4×C61Q1614yes—
88C2×D4×C61C2×D412yes—
89C22×C4×C61—21no—
90C22×C4×C61—22no—
91C22×C4×C61—22no—
92C22×C4×C61—42no—
93C22×C4×C61—42no—
94C22×C4×C61—41no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C22×Dic61—41no—
99C2×Dic122—22no—
100C2×Dic122—41no—
101C2×Dic122—82no—
102C2×C8×C61—22no—
103C2×C8×C61—42no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—22no—
106C4⋊C4×C61—22no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61C2×D412yes—
110C22⋊C4×C61—22no—
111C22⋊C4×C61—22no—
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61#4111yescharacteristic
115C42×C61C2411yescharacteristic
116C4⋊Dic61—22no—
117C4⋊Dic61—22no—
118C4⋊Dic61—41no—
119C4⋊Dic61—41no—
120C2×#92418—22no—
121C2×#92418—22no—
122C2×#92418—22no—
123C2×#92418—22no—
124C2×#92418—48no—
125C2×#92418—42no—
126C2×#92418—42no—
127C2×#92418C2×D412yes—
128C2×#92418C2×D412yes—
129C23×C61—22no—
130C23×C61—24no—
131C23×C61—42no—
132C23×C61—42no—
133C23×C61#12111yescharacteristic
134Q8×C61—42no—
135Q8×C61—42no—
136Q8×C61—82no—
137D4×C61—22no—
138D4×C61—24no—
139D4×C61C2×Q1614yes—
140C2×C4×C61—22no—
141C2×C4×C61—22no—
142C2×C4×C61—42no—
143C2×C4×C61—42no—
144C2×C4×C61—42no—
145C2×C4×C61—44no—
146C2×C4×C61—42no—
147C2×C4×C61—82no—
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61C2×Q1612yes—
152C2×C4×C61#13512yes—
153C2×C4×C61#13512yes—
154C2×C4×C61AGL(1,ℤ/8)12yes—
155C2×C4×C61C22×D411yescharacteristic
156C2×C4×C61C22×D411yescharacteristic
157C2×C4×C61C2×#4111yescharacteristic
158C2×Dic61—42no—
159C2×Dic61—82no—
160Dic122—82no—
161Dic122—82no—
162C8×C61—42no—
163#92418—22no—
164#92418—22no—
165#92418—42no—
166#92418—42no—
167C2×#1683—611nomaximal, Sylow
168C22×C61—24no—
169C22×C61—48no—
170C22×C61—42no—
171C22×C61—42no—
172C22×C61#46312yes—
173C22×C61#46712yes—
174C22×C61#47112yes—
175C22×C61C2×#12111yescharacteristic
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—42no—
179C4×C61—82no—
180C4×C61#46312yes—
181C4×C61#46712yes—
182C4×C61C22×Q1611yescharacteristic
183C4×C61C2×#13511yescharacteristic
184C4×C61C2×#13511yescharacteristic
185C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
186Dic61—82no—
187C2×#487—611no—
188C2×#476—611no—
189C2×#474D6111yescharacteristic
190C2×C8×D4—611no—
191#1683—618no—
192C2×#335—611no—
193C2×#333—611no—
194C2×#332—611no—
195C2×C61—44no—
196C2×C61#168314yescomplemented
197C2×C61C2×#46311yescharacteristic
198C2×C61C2×#46711yescharacteristic
199C2×C61C2×#47111yescharacteristic
200C23×C8—1221no—
201C2×C4⋊Q8—611no—
202C2×C4⋊Q8C2×D6111yescharacteristic
203C2×C4×D4C2×D6111yescharacteristic
204#487—614no—
205#487—1222no—
206#476—614no—
207#476—1222no—
208#474—22no—
209#474C2×D6114yes—
210C8×D4—614no—
211C8×D4—1222no—
212C2×#107—21no—
213C2×#106—1221no—
214C2×C4⋊C8—611no—
215C2×C4⋊C8—611no—
216C2×C4⋊C8C2×D6111yescharacteristic
217C2×#103—1221no—
218C2×#103—1221no—
219C2×#102—21no—
220C2×#102—1221no—
221C2×C22⋊C8—1221no—
222C2×C4×C8—611no—
223#335—614no—
224#333—614no—
225#332—614no—
226C61C2×#168311yescharacteristic, complemented, Sylow
227C22×Q8—21no—
228C22×Q8—1221no—
229C22×D4C22⋊D6111yescharacteristic
230C23×C4—21no—
231C22×C8—21no—
232C22×C8—611no—
233C22×C8—611no—
234C22×C8—1224no—
235C22×C8—1221no—
236C22×C8—1221no—
237C22×C8—2444no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—612no—
242C4⋊Q8—1221no—
243C4⋊Q8—1221no—
244C4⋊Q8—1221no—
245C4⋊Q8C22×D6112yes—
246C4×D4—21no—
247C4×D4—21no—
248C4×D4C22⋊D6112yes—
249C4×D4C22×D6112yes—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4C22⋊D6111yescharacteristic
255C2×C22⋊C4—21no—
256C2×C42C22×D6111yescharacteristic
257#107—24no—
258#106—1224no—
259C4⋊C8—21no—
260C4⋊C8—612no—
261C4⋊C8—612no—
262C4⋊C8—1221no—
263C4⋊C8—1221no—
264C4⋊C8C22×D6112yes—
265#103—1224no—
266#103—1224no—
267#102—24no—
268#102—1224no—
269C22⋊C8—1224no—
270C4×C8—612no—
271C4×C8—612no—
272C24—21no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—42no—
276C2×Q8—42no—
277C2×Q8—1222no—
278C2×Q8—4882no—
279C2×Q8—2441no—
280C2×D4—21no—
281C2×D4—22no—
282C2×D4#1175820214yes—
283C2×D4C2×C22⋊D6112yes—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—41no—
290C22×C4—2441no—
291C22×C4D4×D6111yescharacteristic
292C22×C4#1175822411yescharacteristic
293C22×C4C2×C22⋊D6111yescharacteristic
294C2×C8—22no—
295C2×C8—42no—
296C2×C8—612no—
297C2×C8—612no—
298C2×C8—1222no—
299C2×C8—1222no—
300C2×C8—1222no—
301C2×C8—1222no—
302C2×C8—2448no—
303C2×C8—2442no—
304C2×C8—2442no—
305C4⋊C4—21no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—1222no—
311C4⋊C4—1222no—
312C4⋊C4—2441no—
313C4⋊C4—2441no—
314C4⋊C4C2×C22⋊D6112yes—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C42D4×D6111yescharacteristic
318C42#1175822411yescharacteristic
319C42C2×C22⋊D6111yescharacteristic
320C42C23×D6111yescharacteristic
321C23—22no—
322C23—24no—
323C23—42no—
324C23—42no—
325C23#1451974911yescharacteristic
326Q8—42no—
327Q8—42no—
328Q8—82no—
329Q8—4882no—
330Q8—4882no—
331D4—24no—
332D4—22no—
333D4C2×#1175820214yes—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—82no—
342C2×C4—4882no—
343C2×C4—2442no—
344C2×C4#1451974911yescharacteristic
345C2×C4#1451974911yescharacteristic
346C2×C4#1451974911yescharacteristic
347C2×C4C2×#1175820212yes—
348C2×C4#1451979612yes—
349C2×C4#1451979712yes—
350C2×C4#1451980112yes—
351C2×C4C2×D4×D6111yescharacteristic
352C2×C4C22×C22⋊D6111yescharacteristic
353C2×C4C2×#1175822411yescharacteristic
354C8—42no—
355C8—1222no—
356C8—1222no—
357C8—2442no—
358C8—2442no—
359C22—24no—
360C22—42no—
361C22—48no—
362C22—42no—
363C22#1683997512yes—
364C22#1684000112yes—
365C22#1684002712yes—
366C22C2×#1451974911yescharacteristic
367C4—21no—
368C4—21no—
369C4—42no—
370C4—82no—
371C4—4882no—
372C4#1683997512yes—
373C4#1684000112yes—
374C4C22×#1175820211yescharacteristic
375C4C2×#1451979611yescharacteristic
376C4C2×#1451979711yescharacteristic
377C4C2×#1451980111yescharacteristic
378C2—44no—
379C2#2144526814yesdirect product factor
380C2C2×#1683997511yescharacteristic
381C2C2×#1684000111yescharacteristic
382C2C2×#1684002711yescharacteristic
subgroupG/H
centerC23#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#474C2
socleC23×C61#121
prime radicalC22×D4×C61D4
hypercenterC2×#474D61
hypocenterC61C2×#1683
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#16840112C2semidirect
4. #21445268C2direct (N × H)
5. C2×#16839514C2semidirect
6. C2×#16839510C2semidirect
7. C2×#16839508C2semidirect
12. #16840112C22semidirect
25. #16839514C22semidirect
26. #16839510C22semidirect
27. #16839508C22semidirect
196. C2×C61#1683semidirect
226. C61C2×#1683semidirect
379. C2#21445268direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401122
C2×#168400522
C2×D4×#924182
#214452682
C2×#168395142
C2×#168395102
C2×#168395082
C2×C61×#4742
C2×#168361