Finite Group Databasebeta

← C2×#21454538 #30543895

Subgroups — C2×#21454538 #30543895

Order 15616.

2806 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519783C212yesmaximal, complemented
2C2×#16840312C211yesmaximal, characteristic
3#21454538C2116yesmaximal, direct product factor
4C2×#16839835C218yesmaximal, complemented
5C2×#16839786C211yesmaximal, characteristic, complemented
6C2×#16839728C212yesmaximal, complemented
7C22×#97×C61C211yesmaximal, characteristic, complemented
8C22×#11758222C2212yes—
9C2×#14519783—216no—
10C2×#14519783C22116yescomplemented
11C22×#11758194C2212yes—
12C22×#11758189C2214yes—
13C22×C8×D61C2214yes—
14#16840312C418yes—
15#16840312C2218yes—
16C2×#14519777C411yescharacteristic
17C2×#14519774C411yescharacteristic
18C2×#14519765C412yes—
19C2×#14519751C414yes—
20C2×C4×D244C2214yes—
21#16839835C22164yescomplemented
22#16839786C2218yescomplemented
23C2×C4⋊#92418C2214yes—
24#16839728C22116yescomplemented
25C2×#14519689C2218yes—
26C23×C8×C61C2211yescharacteristic
27C23×C8×C61C2211yescharacteristic
28C22×C42×C61C2211yescharacteristic
29C2×#97×C61C2214yes—
30C2×#97×C61C2218yescomplemented
31C2×#11758222—28no—
32C2×#11758222—28no—
33C2×#11758222C2×C418yes—
34C2×#11758222C2318yes—
35C22×Dic122C2×C412yes—
36C22×D244C2×C412yes—
37C22×D244C2×C414yes—
38C22×C22⋊D61C2×C414yes—
39C22×C4×D61C2314yes—
40#14519783—264no—
41C2×#11758194—28no—
42C2×#11758194C2318yes—
43C2×#11758189—216no—
44C2×#11758189C23116yes—
45C22×#92418C2314yes—
46C2×C8×D61—216no—
47C2×C8×D61C23116yes—
48#14519777C2×C418yes—
49#14519774C2×C418yes—
50#14519765C2×C4116yes—
51#14519751C2×C4132yes—
52C4×D244C2×C4116yes—
53C4×D244C23116yes—
54C2×C4⋊Dic61C2×C414yes—
55C2×#11758198C2×C418yes—
56C4⋊#92418C23116yes—
57#14519689C23132yes—
58C23×C4×C61C2×C412yes—
59C23×C4×C61C2311yescharacteristic
60C22×C8×C61—24no—
61C22×C8×C61D418yescomplemented
62C22×C8×C61C2312yes—
63C22×C8×C61C2314yes—
64C22×C8×C61C2312yes—
65C22×C8×C61C2314yes—
66C2×C42×C61C2×C411yescharacteristic
67C2×C42×C61C2×C411yescharacteristic
68C2×C42×C61C2×C414yes—
69C2×C42×C61C2312yes—
70C2×C42×C61C2314yes—
71#97×C61C23116yes—
72C24×C61C22×C411yescharacteristic
73C23×D61C22×C414yes—
74C22×C4×C61—44no—
75C22×C4×C61C22×C412yes—
76C22×C4×C61C22×C412yes—
77C22×C4×C61C22×C418yes—
78C22×C4×C61C22×C411yescharacteristic
79C22×C4×C61C22×C412yes—
80C22×C4×C61C2×D414yes—
81C22×C4×C61#4114yes—
82C22×C4×C61C2412yes—
83C22×C4×C61C2411yescharacteristic
84C2×C22⋊D61—216no—
85C2×C22⋊D61C22×C4116yes—
86C22×Dic61C22×C414yes—
87#11758222—232no—
88#11758222—216no—
89#11758222—216no—
90C2×D244—28no—
91C2×D244—48no—
92C2×D244C22×C418yes—
93C2×D244C22×C4116yes—
94C2×C4×D61—28no—
95C2×C4×D61—28no—
96C2×C4×D61C22×C418yes—
97C2×C4×D61C2418yes—
98C2×Dic122—28no—
99C2×Dic122C22×C418yes—
100C2×C8×C61—24no—
101C2×C8×C61—28no—
102C2×C8×C61C2×D418yes—
103C2×C8×C61C2×D4116yescomplemented
104C2×C8×C61C2414yes—
105C2×C8×C61C2414yes—
106C42×C61C22×C414yes—
107C42×C61C22×C414yes—
108C42×C61C22×C414yes—
109C42×C61C2414yes—
110#11758198C22×C4132yes—
111C4⋊Dic61C22×C4116yes—
112#11758194—216no—
113C2×#92418—28no—
114C2×#92418C2418yes—
115#11758189—232no—
116C8×D61—232no—
117C23×C61—24no—
118C23×C61C4×D414yes—
119C23×C61C23×C412yes—
120C23×C61C23×C411yescharacteristic
121C22×D61—28no—
122C22×D61—216no—
123C22×D61C23×C418yes—
124C2×C4×C61—24no—
125C2×C4×C61—24no—
126C2×C4×C61—48no—
127C2×C4×C61C4×D414yes—
128C2×C4×C61C4×D418yes—
129C2×C4×C61C23×C414yes—
130C2×C4×C61C23×C414yes—
131C2×C4×C61C23×C412yes—
132C2×C4×C61C23×C411yescharacteristic
133C2×C4×C61C22×D412yes—
134C2×C4×C61C22×D414yes—
135C2×C4×C61C2×#4112yes—
136C2×C4×C61C2×#4114yes—
137C2×C4×C61C2511yescharacteristic
138C22⋊D61—232no—
139C2×Dic61—28no—
140C2×Dic61C23×C418yes—
141D244—216no—
142D244—416no—
143C4×D61—216no—
144C4×D61—28no—
145C4×D61—28no—
146Dic122—216no—
147C8×C61—24no—
148C8×C61C22×D418yes—
149#92418—28no—
150C2×#2932—611nomaximal, Sylow
151C22×C61—28no—
152C22×C61—24no—
153C22×C61C2×C4×D414yes—
154C22×C61C2×C4×D412yes—
155C22×C61#56814yes—
156C22×C61C24×C411yescharacteristic
157C2×D61—28no—
158C2×D61—216no—
159C2×D61—416no—
160C4×C61—24no—
161C4×C61—24no—
162C4×C61C2×C4×D414yes—
163C4×C61C2×C4×D412yes—
164C4×C61C23×D411yescharacteristic
165C4×C61C22×#4111yescharacteristic
166Dic61—28no—
167C22×#131—612no—
168C2×#532—611no—
169#2932—6116no—
170C2×#435—618no—
171C2×#423—611no—
172C2×#408—612no—
173C22×#97D6111yescharacteristic, complemented
174C2×C61—24no—
175C2×C61#293214yescomplemented
176C2×C61C22×C4×D411yescharacteristic
177C2×C61C2×#56812yes—
178D61—48no—
179C22×#41—612no—
180C2×#131—6116no—
181C2×#131—12216no—
182C22×M16—612no—
183C22×M16—614no—
184C23×C8—614no—
185C23×C8C2×D6111yescharacteristic
186C23×C8C2×D6111yescharacteristic
187#532—618no—
188#532—618no—
189C2×C4⋊Q8—611no—
190C2×#127—611no—
191C2×#124—612no—
192C2×#121—614no—
193C2×C4×D4—614no—
194C22×C42C2×D6111yescharacteristic
195#435—6164no—
196#423—618no—
197C2×C4⋊C8—614no—
198#408—6116no—
199C2×C22⋊C8—618no—
200C2×#97C2×D6114yes—
201C2×#97C2×D6118yescomplemented
202C61C2×#293211yescharacteristic, complemented, Sylow
203C2×#41—618no—
204C2×#41—618no—
205C2×#41—1228no—
206C2×#41—1228no—
207C22×Q8—612no—
208C22×D4—614no—
209C22×D4—612no—
210C22×D4—614no—
211C23×C4—614no—
212C23×C4C4×D6112yes—
213C23×C4C22×D6111yescharacteristic
214#131—12264no—
215C2×M16—618no—
216C2×M16—6116no—
217C2×M16—1228no—
218C2×M16—12216no—
219C22×C8—24no—
220C22×C8—614no—
221C22×C8—6116no—
222C22×C8—12216no—
223C22×C8D24418yescomplemented
224C22×C8C22×D6114yes—
225C22×C8C22×D6112yes—
226C22×C8C22×D6112yes—
227C22×C8C22×D6114yes—
228C4⋊Q8—618no—
229#127—618no—
230#124—6116no—
231#121—6132no—
232C4×D4—6116no—
233C4×D4—6116no—
234C2×C4⋊C4—614no—
235C2×C22⋊C4—618no—
236C2×C42C4×D6111yescharacteristic
237C2×C42C4×D6111yescharacteristic
238C2×C42C4×D6114yes—
239C2×C42C22×D6114yes—
240C2×C42C22×D6112yes—
241C4⋊C8—6116no—
242C22⋊C8—6132no—
243#97C22×D61116yes—
244C24—614no—
245C24C2×C4×D6111yescharacteristic
246#41—12216no—
247#41—12216no—
248#41—12232no—
249C2×Q8—618no—
250C2×Q8—1228no—
251C2×D4—6116no—
252C2×D4—618no—
253C2×D4—6116no—
254C2×D4—12216no—
255C2×D4—1228no—
256C2×D4—2448no—
257C22×C4—44no—
258C22×C4—614no—
259C22×C4—618no—
260C22×C4—618no—
261C22×C4—1228no—
262C22×C4—1228no—
263C22×C4C2×C4×D6112yes—
264C22×C4C2×C4×D6112yes—
265C22×C4C2×C4×D6118yes—
266C22×C4C2×C4×D6111yescharacteristic
267C22×C4C2×C4×D6112yes—
268C22×C4C2×D24414yes—
269C22×C4#1175822214yes—
270C22×C4C23×D6112yes—
271C22×C4C23×D6111yescharacteristic
272M16—12216no—
273M16—12232no—
274C2×C8—24no—
275C2×C8—28no—
276C2×C8—618no—
277C2×C8—1228no—
278C2×C8—12232no—
279C2×C8C2×D24418yes—
280C2×C8C2×D244116yescomplemented
281C2×C8C23×D6114yes—
282C2×C8C23×D6114yes—
283C4⋊C4—6116no—
284C22⋊C4—6132no—
285C42C2×C4×D6114yes—
286C42C2×C4×D6114yes—
287C42C2×C4×D6114yes—
288C42C23×D6114yes—
289C23—24no—
290C23—618no—
291C23—1228no—
292C23—12216no—
293C23C4×D24414yes—
294C23C22×C4×D6112yes—
295C23C22×C4×D6111yescharacteristic
296Q8—12216no—
297D4—12232no—
298D4—12216no—
299D4—24416no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—48no—
303C2×C4—618no—
304C2×C4—1228no—
305C2×C4—12216no—
306C2×C4—1228no—
307C2×C4—1228no—
308C2×C4C4×D24414yes—
309C2×C4C4×D24418yes—
310C2×C4C22×C4×D6114yes—
311C2×C4C22×C4×D6114yes—
312C2×C4C22×C4×D6111yescharacteristic
313C2×C4C22×C4×D6112yes—
314C2×C4C22×D24412yes—
315C2×C4C22×D24414yes—
316C2×C4C2×#1175822212yes—
317C2×C4C2×#1175822214yes—
318C2×C4C24×D6111yescharacteristic
319C8—24no—
320C8—1228no—
321C8C22×D24418yes—
322C22—24no—
323C22—28no—
324C22—1228no—
325C22—12216no—
326C22—24416no—
327C22C2×C4×D24414yes—
328C22C2×C4×D24412yes—
329C22#1684052814yes—
330C22C23×C4×D6111yescharacteristic
331C4—24no—
332C4—24no—
333C4—1228no—
334C4C2×C4×D24412yes—
335C4C2×C4×D24414yes—
336C4C23×D24411yescharacteristic
337C4C22×#1175822211yescharacteristic
338C2—24no—
339C2—2448no—
340C2#2145453814yesdirect product factor
341C2C22×C4×D24411yescharacteristic
342C2C2×#1684052812yes—
subgroupG/H
centerC22×C4C23×D61
commutatorC22×C61C24×C4
FrattiniC2×C4C24×D61
FittingC22×#97×C61C2
socleC23×C61C23×C4
prime radicalC2×#16840312C2
cosocleC2×C4×C61C25
hypercenterC22×#97D61
hypocenterC61C2×#2932
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×#97

Complements

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

NH ≅ G/Ntype
1. C22×#14519783C2semidirect
3. #21454538C2direct (N × H)
4. C2×#16839835C2semidirect
5. C2×#16839786C2semidirect
6. C2×#16839728C2semidirect
7. C22×#97×C61C2semidirect
10. C2×#14519783C22semidirect
21. #16839835C22semidirect
22. #16839786C22semidirect
24. #16839728C22semidirect
30. C2×#97×C61C22semidirect
61. C22×C8×C61D4semidirect
103. C2×C8×C61C2×D4semidirect
173. C22×#97D61semidirect
175. C2×C61#2932semidirect
201. C2×#97C2×D61semidirect
202. C61C2×#2932semidirect
223. C22×C8D244semidirect
280. C2×C8C2×D244semidirect
340. C2#21454538direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197832
C2×#168403122
#214545382
C2×#168398352
C2×#168397862
C2×#168397282
C22×#97×C612
C2×#293261