Finite Group Databasebeta

← C2×#21446033 #29680821

Subgroups — C2×#21446033 #29680821

Order 15616.

1402 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840240C211yesmaximal, characteristic
2C2×#16839802C212yesmaximal
3C22×#14519696C211yesmaximal, characteristic
4#21446033C218yesmaximal, direct product factor
5C2×#16839522C212yesmaximal
6C2×C61×#391C211yesmaximal, characteristic
7C22×#11758194C2212yes—
8#16840240—24no—
9#16840240—22no—
10#16840240C2214yes—
11C2×Q8×Dic61—22no—
12C2×Q8×Dic61—22no—
13C2×#14519736—22no—
14C2×#14519736C2212yes—
15#16839802—24no—
16#16839802C2218yes—
17C2×#14519710—22no—
18C2×#14519708—22no—
19C2×#14519696C418yescomplemented
20C2×#14519696C2214yes—
21#16839522C2218yes—
22C23×Q8×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic
24C22×C42×C61C2211yescharacteristic
25C61×#391—22no—
26C61×#391C2214yes—
27C2×#95×C61—22no—
28C2×#11758194—22no—
29C2×#11758194—24no—
30C2×#11758194C2×C418yes—
31C2×#11758194C2314yes—
32C22×#92418—22no—
33Q8×Dic61—28no—
34Q8×Dic61—28no—
35Q8×Dic61—28no—
36Q8×Dic61—28no—
37#14519736—28no—
38#14519736—28no—
39#14519736—22no—
40#14519736—22no—
41#14519736D414yes—
42#14519736C2314yes—
43C2×C4⋊Dic61—22no—
44C2×C4⋊Dic61—22no—
45C2×C4⋊Dic61D412yes—
46C2×C4⋊Dic61D412yes—
47C2×C22⋊Dic61—22no—
48C2×C4×Dic61—24no—
49C2×C4×Dic61—22no—
50#14519710—28no—
51#14519708—28no—
52#14519696C2×C4116yescomplemented
53C22×Q8×C61—22no—
54C22×Q8×C61—22no—
55C22×Q8×C61—24no—
56C22×Q8×C61C2×C414yes—
57C22×Q8×C61D412yes—
58C22×Q8×C61Q814yes—
59C22×Q8×C61C2312yes—
60C23×C4×C61—21no—
61C23×C4×C61—21no—
62C23×C4×C61D412yes—
63C23×C4×C61C2311yescharacteristic
64C2×C4⋊C4×C61—22no—
65C2×C4⋊C4×C61—22no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61C2312yes—
68C2×C42×C61—24no—
69C2×C42×C61—21no—
70C2×C42×C61C2312yes—
71#95×C61—28no—
72C24×C61C2×D411yescharacteristic
73C2×Q8×C61—28no—
74C2×Q8×C61—28no—
75C2×Q8×C61—24no—
76C2×Q8×C61—28no—
77C2×Q8×C61—28no—
78C2×Q8×C61—24no—
79C2×Q8×C61—24no—
80C2×Q8×C61—24no—
81C2×Q8×C61C4⋊C418yes—
82C2×Q8×C61C22×C414yes—
83C2×Q8×C61C2×Q814yes—
84C22×C4×C61—22no—
85C22×C4×C61—22no—
86C22×C4×C61—24no—
87C22×C4×C61—24no—
88C22×C4×C61—22no—
89C22×C4×C61—22no—
90C22×C4×C61—42no—
91C22×C4×C61—42no—
92C22×C4×C61—44no—
93C22×C4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61C4⋊C418yes—
96C22×C4×C61C22×C412yes—
97C22×C4×C61C2×D414yes—
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D412yes—
100C22×C4×C61C2×D412yes—
101C22×C4×C61C2×Q812yes—
102C22×C4×C61#4114yes—
103C22×C4×C61C2411yescharacteristic
104C22×Dic61—22no—
105C22×Dic61—22no—
106C4⋊C4×C61—24no—
107C4⋊C4×C61—42no—
108C42×C61—24no—
109C42×C61—42no—
110C22⋊Dic61—24no—
111C22⋊Dic61—24no—
112C4⋊Dic61—28no—
113C4⋊Dic61—28no—
114C4⋊Dic61—22no—
115C4⋊Dic61—22no—
116C4⋊Dic61C2×D414yes—
117C4⋊Dic61C2×D414yes—
118C4×Dic61—216no—
119C4×Dic61—24no—
120C4×Dic61—24no—
121#11758194—28no—
122#11758194—24no—
123#11758194C22×C418yes—
124C2×#92418—28no—
125C2×#92418—24no—
126C23×C61—22no—
127C23×C61—22no—
128C23×C61C2×C4⋊C412yes—
129C23×C61#12011yescharacteristic
130C23×C61#12011yescharacteristic
131C23×C61#12312yes—
132C23×C61C22×D411yescharacteristic
133Q8×C61—28no—
134Q8×C61—28no—
135Q8×C61—216no—
136C2×C4×C61—24no—
137C2×C4×C61—24no—
138C2×C4×C61—28no—
139C2×C4×C61—28no—
140C2×C4×C61—24no—
141C2×C4×C61—48no—
142C2×C4×C61—42no—
143C2×C4×C61—42no—
144C2×C4×C61—44no—
145C2×C4×C61—42no—
146C2×C4×C61—82no—
147C2×C4×C61—82no—
148C2×C4×C61C2×C4⋊C418yes—
149C2×C4×C61C2×C4⋊C412yes—
150C2×C4×C61C4×D414yes—
151C2×C4×C61C4×D414yes—
152C2×C4×C61#12012yes—
153C2×C4×C61C22⋊Q814yes—
154C2×C4×C61C22⋊Q814yes—
155C2×C4×C61#12312yes—
156C2×C4×C61C23×C411yescharacteristic
157C2×C4×C61C22×D412yes—
158C2×C4×C61C22×Q811yescharacteristic
159C2×C4×C61C2×#4112yes—
160C2×Dic61—24no—
161C2×Dic61—24no—
162C2×Dic61—44no—
163C2×Dic61—44no—
164#92418—28no—
165C2×#1857—611nomaximal, Sylow
166C22×C61—24no—
167C22×C61—24no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61#38512yes—
173C22×C61#38512yes—
174C22×C61#45412yes—
175C22×C61#45612yes—
176C22×C61C22×C4⋊C411yescharacteristic
177C22×C61C2×#12011yescharacteristic
178C22×C61C2×#12311yescharacteristic
179C4×C61—28no—
180C4×C61—44no—
181C4×C61—82no—
182C4×C61#38514yes—
183C4×C61C2×C4×D412yes—
184C4×C61C2×C22⋊Q812yes—
185Dic61—44no—
186Dic61—44no—
187C2×#519—611no—
188C2×#428—612no—
189C22×#101—611no—
190C2×#391D6111yescharacteristic
191#1857—618no—
192C2×#339—612no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61—22no—
196C2×C61#185714yescomplemented
197C2×C61C2×#38511yescharacteristic
198C2×C61C2×#45411yescharacteristic
199C2×C61C2×#45611yescharacteristic
200C23×Q8C2×D6111yescharacteristic
201C22×M16—612no—
202#519—614no—
203#519—1224no—
204#519—1222no—
205C2×C4×Q8—1222no—
206C2×C4×Q8—1222no—
207C2×#117—612no—
208C2×#117—1222no—
209C22×C4⋊C4C2×D6111yescharacteristic
210C22×C42C2×D6111yescharacteristic
211#428—618no—
212#428—1224no—
213C2×#107—1222no—
214C2×#106—1222no—
215C2×#101—618no—
216C2×#101—614no—
217#391—22no—
218#391C2×D6114yes—
219C2×#95—22no—
220#339—618no—
221C61C2×#185711yescharacteristic, complemented, Sylow
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—24no—
225C22×Q8Dic12214yes—
226C22×Q8C4×D6114yes—
227C22×Q8C22⋊D6112yes—
228C22×Q8C22×D6112yes—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4C22⋊D6112yes—
232C23×C4C22×D6111yescharacteristic
233C2×M16—618no—
234C2×M16—614no—
235C2×M16—1222no—
236C2×M16—1224no—
237C22×C8—1222no—
238C4×Q8—1228no—
239C4×Q8—1228no—
240C4×Q8—1228no—
241C4×Q8—1228no—
242#117—614no—
243#117—614no—
244#117—1228no—
245#117—1222no—
246#117—1222no—
247#117—1228no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—612no—
252C2×C4⋊C4—612no—
253C2×C4⋊C4—1222no—
254C2×C4⋊C4—1222no—
255C2×C4⋊C4C22×D6112yes—
256C2×C22⋊C4—1222no—
257C2×C42—24no—
258C2×C42—21no—
259C2×C42—1224no—
260C2×C42—1222no—
261C2×C42C22×D6112yes—
262#107—1228no—
263#106—1228no—
264#101—6116no—
265#95—28no—
266C24C2×C22⋊D6111yescharacteristic
267C2×Q8—24no—
268C2×Q8—24no—
269C2×Q8—28no—
270C2×Q8—28no—
271C2×Q8—24no—
272C2×Q8—28no—
273C2×Q8—28no—
274C2×Q8—24no—
275C2×Q8#1175819618yes—
276C2×Q8C2×Dic12214yes—
277C2×Q8C2×C4×D6114yes—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—44no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—1222no—
290C22×C4—1222no—
291C22×C4#1175819618yes—
292C22×C4C2×Dic12212yes—
293C22×C4C2×C4×D6112yes—
294C22×C4D4×D6112yes—
295C22×C4D4×D6112yes—
296C22×C4#1175822414yes—
297C22×C4C2×C22⋊D6114yes—
298C22×C4C2×C22⋊D6111yescharacteristic
299C22×C4C23×D6111yescharacteristic
300M16—618no—
301M16—1224no—
302M16—1228no—
303C2×C8—1224no—
304C2×C8—1228no—
305C4⋊C4—24no—
306C4⋊C4—42no—
307C4⋊C4—614no—
308C4⋊C4—614no—
309C4⋊C4—1228no—
310C4⋊C4—1228no—
311C4⋊C4—1222no—
312C4⋊C4—1222no—
313C22⋊C4—1224no—
314C22⋊C4—1224no—
315C42—24no—
316C42—42no—
317C42—12216no—
318C42—1224no—
319C42—1224no—
320C23—22no—
321C23—22no—
322C23C2×#1175819612yes—
323C23#1451974511yescharacteristic
324C23#1451974511yescharacteristic
325C23#1451975812yes—
326C23C22×C22⋊D6111yescharacteristic
327Q8—28no—
328Q8—28no—
329Q8—216no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—28no—
333C2×C4—28no—
334C2×C4—24no—
335C2×C4—42no—
336C2×C4—48no—
337C2×C4—42no—
338C2×C4—44no—
339C2×C4—42no—
340C2×C4—82no—
341C2×C4—82no—
342C2×C4—1224no—
343C2×C4—1224no—
344C2×C4—2444no—
345C2×C4—2444no—
346C2×C4C2×#1175819618yes—
347C2×C4C2×#1175819612yes—
348C2×C4#1451973714yes—
349C2×C4#1451973714yes—
350C2×C4#1451974512yes—
351C2×C4#1451975414yes—
352C2×C4#1451975414yes—
353C2×C4#1451975812yes—
354C2×C4C22×C4×D6111yescharacteristic
355C2×C4C2×D4×D6112yes—
356C2×C4C22×Dic12211yescharacteristic
357C2×C4C2×#1175822412yes—
358C8—1228no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—24no—
364C22—24no—
365C22#1683963412yes—
366C22#1683963412yes—
367C22#1683993412yes—
368C22#1683994412yes—
369C22C22×#1175819611yescharacteristic
370C22C2×#1451974511yescharacteristic
371C22C2×#1451975811yescharacteristic
372C4—28no—
373C4—44no—
374C4—82no—
375C4—2444no—
376C4—2444no—
377C4#1683963414yes—
378C4C2×#1451973712yes—
379C4C2×#1451975412yes—
380C2—21no—
381C2—21no—
382C2—22no—
383C2#2144603314yesdirect product factor
384C2C2×#1683963411yescharacteristic
385C2C2×#1683993411yescharacteristic
386C2C2×#1683994411yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#391C2
socleC23×C61#120
prime radicalC24×C61C2×D4
cosocleC22×C4×C61C24
hypercenterC2×#391D61
hypocenterC61C2×#1857
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
4. #21446033C2direct (N × H)
19. C2×#14519696C4semidirect
52. #14519696C2×C4semidirect
196. C2×C61#1857semidirect
221. C61C2×#1857semidirect
383. C2#21446033direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402402
C2×#168398022
C22×#145196962
#214460332
C2×#168395222
C2×C61×#3912
C2×#185761