Finite Group Databasebeta

← C2×#21446617 #29683597

Subgroups — C2×#21446617 #29683597

Order 15616.

2094 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×C4×D244C211yesmaximal, characteristic
2C22×C4⋊#92418C211yesmaximal, characteristic, complemented
3C22×#14519689C214yesmaximal, complemented
4#21446617C218yesmaximal, direct product factor
5C22×#97×C61C211yesmaximal, characteristic, complemented
6C23×D244C411yescharacteristic
7C23×C4×D61C2212yes—
8C23×#92418C2212yes—
9C2×C4×D244—24no—
10C2×C4×D244—24no—
11C2×C4×D244C414yes—
12C2×C4×D244C2214yes—
13C22×C4⋊Dic61C411yescharacteristic
14C22×#11758198C412yes—
15C2×C4⋊#92418—24no—
16C2×C4⋊#92418C2214yescomplemented
17C2×#14519689—216no—
18C2×#14519689C22116yescomplemented
19C23×C8×C61C2212yes—
20C22×C42×C61C2211yescharacteristic
21C2×#97×C61—24no—
22C2×#97×C61C2214yescomplemented
23C24×D61C2×C412yes—
24C22×D244—28no—
25C22×D244—24no—
26C22×D244C2×C414yes—
27C23×Dic61C2×C412yes—
28C22×C4×D61—24no—
29C22×C4×D61—24no—
30C22×C4×D61—28no—
31C22×C4×D61—28no—
32C22×C4×D61C2×C414yes—
33C22×C4×D61C2314yes—
34C22×#92418—28no—
35C22×#92418—24no—
36C22×#92418C2314yes—
37C4×D244—216no—
38C4×D244—28no—
39C4×D244—28no—
40C2×C4⋊Dic61—24no—
41C2×C4⋊Dic61C2×C414yes—
42C2×#11758198—28no—
43C2×#11758198C2×C418yes—
44C4⋊#92418—28no—
45#14519689—232no—
46C23×C4×C61C2×C411yescharacteristic
47C23×C4×C61C2×C411yescharacteristic
48C23×C4×C61C2311yescharacteristic
49C22×C8×C61—24no—
50C22×C8×C61—24no—
51C22×C8×C61D418yescomplemented
52C22×C8×C61C2314yes—
53C2×C42×C61C2×C412yes—
54C2×C42×C61D414yes—
55C2×C42×C61D414yes—
56C2×C42×C61C2312yes—
57#97×C61—28no—
58C24×C61C22×C411yescharacteristic
59C23×D61—24no—
60C23×D61—28no—
61C23×D61—24no—
62C23×D61—28no—
63C23×D61M1618yes—
64C23×D61C22×C414yes—
65C22×C4×C61—24no—
66C22×C4×C61—24no—
67C22×C4×C61C22⋊C414yes—
68C22×C4×C61C22⋊C414yes—
69C22×C4×C61C22×C412yes—
70C22×C4×C61C22×C412yes—
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D412yes—
73C22×C4×C61C2×D412yes—
74C22×C4×C61C2×D414yes—
75C22×C4×C61#4114yes—
76C22×C4×C61C2411yescharacteristic
77C22×Dic61—24no—
78C22×Dic61—28no—
79C22×Dic61C22×C414yes—
80C2×D244—232no—
81C2×D244—216no—
82C2×D244—28no—
83C2×C4×D61—28no—
84C2×C4×D61—216no—
85C2×C4×D61—28no—
86C2×C4×D61—24no—
87C2×C4×D61—24no—
88C2×C4×D61—28no—
89C2×C4×D61—416no—
90C2×C4×D61—48no—
91C2×C4×D61—48no—
92C2×C8×C61—216no—
93C2×C8×C61—24no—
94C2×C8×C61—24no—
95C2×C8×C61C2×D418yescomplemented
96C42×C61C22⋊C418yes—
97C42×C61C2×D414yes—
98C42×C61C2×D414yes—
99#11758198—216no—
100C4⋊Dic61—28no—
101C2×#92418—28no—
102C2×#92418—24no—
103C2×#92418—48no—
104C23×C61C2×C22⋊C412yes—
105C23×C61C4×D414yes—
106C23×C61C2×M1614yes—
107C23×C61#13114yes—
108C23×C61C23×C411yescharacteristic
109C22×D61—24no—
110C22×D61—28no—
111C22×D61—24no—
112C22×D61—28no—
113C22×D61—216no—
114C22×D61—232no—
115C22×D61—48no—
116C22×D61—48no—
117C22×D61—416no—
118C22×D61C2×M1618yes—
119C2×C4×C61—24no—
120C2×C4×C61—24no—
121C2×C4×C61—28no—
122C2×C4×C61—28no—
123C2×C4×C61C2×C22⋊C414yes—
124C2×C4×C61C2×C22⋊C414yes—
125C2×C4×C61C2×C22⋊C412yes—
126C2×C4×C61C4×D414yes—
127C2×C4×C61#12118yes—
128C2×C4×C61#12414yes—
129C2×C4×C61#12714yes—
130C2×C4×C61C22×D411yescharacteristic
131C2×C4×C61C22×D412yes—
132C2×C4×C61C22×D411yescharacteristic
133C2×C4×C61C2×#4112yes—
134C2×Dic61—24no—
135C2×Dic61—28no—
136C2×Dic61—48no—
137D244—232no—
138C4×D61—48no—
139C4×D61—44no—
140C4×D61—44no—
141C4×D61—416no—
142C8×C61—28no—
143#92418—44no—
144C2×#1955—611nomaximal, Sylow
145C22×C61#39014yes—
146C22×C61#40714yes—
147C22×C61#40814yes—
148C22×C61#435116yes—
149C22×C61C22×C22⋊C411yescharacteristic
150C22×C61C2×C4×D412yes—
151C22×C61C22×M1612yes—
152C22×C61C2×#13112yes—
153C2×D61—28no—
154C2×D61—216no—
155C2×D61—44no—
156C2×D61—48no—
157C2×D61—432no—
158C2×D61—44no—
159C4×C61—24no—
160C4×C61—24no—
161C4×C61#39014yes—
162C4×C61C2×#12112yes—
163C4×C61C2×#12411yescharacteristic
164C4×C61C2×#12711yescharacteristic
165Dic61—44no—
166C22×C4×D4—611no—
167C22×C4⋊C8—611no—
168C22×C22⋊C8—614no—
169C22×#97D6111yescharacteristic, complemented
170#1955—618no—
171C2×C61#195518yescomplemented
172C2×C61C2×#39011yescharacteristic
173C2×C61C2×#40711yescharacteristic
174C2×C61C2×#40811yescharacteristic
175C2×C61C2×#43514yes—
176D61—48no—
177C23×D4—611no—
178C24×C4—612no—
179C23×C8—612no—
180C23×C8C2×D6112yes—
181C2×C4×D4—614no—
182C2×C4×D4—614no—
183C2×C4×D4—1224no—
184C2×C4×D4—1224no—
185C22×C4⋊C4—611no—
186C22×C22⋊C4—612no—
187C22×C42C2×D6111yescharacteristic
188C2×C4⋊C8—614no—
189C2×C4⋊C8—1224no—
190C2×C22⋊C8—6116no—
191C2×C22⋊C8—12216no—
192C2×#97—24no—
193C2×#97C2×D6114yescomplemented
194C61C2×#195511yescharacteristic, complemented, Sylow
195C25—612no—
196C22×D4—614no—
197C22×D4—1228no—
198C22×D4—1224no—
199C23×C4—612no—
200C23×C4—614no—
201C23×C4—614no—
202C23×C4—1224no—
203C23×C4—1228no—
204C23×C4—1228no—
205C23×C4—1224no—
206C23×C4C4×D6111yescharacteristic
207C23×C4C4×D6111yescharacteristic
208C23×C4C22×D6111yescharacteristic
209C22×C8—24no—
210C22×C8—24no—
211C22×C8—614no—
212C22×C8—1228no—
213C22×C8—1224no—
214C22×C8D24418yescomplemented
215C22×C8C22×D6114yes—
216C4×D4—12216no—
217C4×D4—1228no—
218C4×D4—1228no—
219C2×C4⋊C4—614no—
220C2×C4⋊C4—1224no—
221C2×C22⋊C4—618no—
222C2×C22⋊C4—1228no—
223C2×C42C4×D6112yes—
224C2×C42D24414yes—
225C2×C42C22⋊D6114yes—
226C2×C42C22×D6112yes—
227C4⋊C8—1228no—
228C22⋊C8—12232no—
229#97—28no—
230C24—614no—
231C24—618no—
232C24—1224no—
233C24—1228no—
234C24—1224no—
235C24—1228no—
236C24C2×C4×D6111yescharacteristic
237C2×D4—12216no—
238C2×D4—12232no—
239C2×D4—1228no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—614no—
243C22×C4—1224no—
244C22×C4—1228no—
245C22×C4—1224no—
246C22×C4—1228no—
247C22×C4—1224no—
248C22×C4—1228no—
249C22×C4—1228no—
250C22×C4—12216no—
251C22×C4—24416no—
252C22×C4—2448no—
253C22×C4—2448no—
254C22×C4#1175819814yes—
255C22×C4#1175819814yes—
256C22×C4C2×C4×D6112yes—
257C22×C4C2×C4×D6112yes—
258C22×C4C2×C4×D6111yescharacteristic
259C22×C4C2×D24412yes—
260C22×C4C2×D24414yes—
261C22×C4#1175822214yes—
262C22×C4C2×C22⋊D6112yes—
263C22×C4C23×D6111yescharacteristic
264C2×C8—24no—
265C2×C8—24no—
266C2×C8—216no—
267C2×C8—1228no—
268C2×C8—1224no—
269C2×C8—2448no—
270C2×C8C2×D24418yescomplemented
271C4⋊C4—1228no—
272C22⋊C4—12216no—
273C42#1175819818yes—
274C42C2×D24414yes—
275C42C2×C22⋊D6114yes—
276C23—618no—
277C23—1224no—
278C23—1228no—
279C23—12216no—
280C23—1224no—
281C23—1228no—
282C23—12232no—
283C23—2448no—
284C23—24416no—
285C23—2448no—
286C23C2×#1175819812yes—
287C23C4×D24414yes—
288C23M16×D6114yes—
289C23#1451978514yes—
290C23C22×C4×D6111yescharacteristic
291D4—12232no—
292C2×C4—28no—
293C2×C4—28no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4—1224no—
297C2×C4—1228no—
298C2×C4—2448no—
299C2×C4—2448no—
300C2×C4—2444no—
301C2×C4—2444no—
302C2×C4—24416no—
303C2×C4C2×#1175819814yes—
304C2×C4C2×#1175819814yes—
305C2×C4C2×#1175819812yes—
306C2×C4C4×D24414yes—
307C2×C4#1451975118yes—
308C2×C4#1451976514yes—
309C2×C4#1451977414yes—
310C2×C4C22×C22⋊D6111yescharacteristic
311C2×C4C22×D24412yes—
312C2×C4C22×D24411yescharacteristic
313C2×C4C2×#1175822212yes—
314C8—28no—
315C8—2444no—
316C22—12216no—
317C22—1228no—
318C22—2444no—
319C22—2448no—
320C22—2444no—
321C22—24432no—
322C22#1683966414yes—
323C22#1683972514yes—
324C22#1683973014yes—
325C22#16839835116yes—
326C22C22×#1175819811yescharacteristic
327C22C2×C4×D24412yes—
328C22C2×M16×D6112yes—
329C22C2×#1451978512yes—
330C4—24no—
331C4—24no—
332C4—2444no—
333C4#1683966414yes—
334C4C2×#1451975112yes—
335C4C2×#1451976511yescharacteristic
336C4C2×#1451977411yescharacteristic
337C2—2448no—
338C2#2144661718yesdirect product factor
339C2C2×#1683966411yescharacteristic
340C2C2×#1683972511yescharacteristic
341C2C2×#1683973011yescharacteristic
342C2C2×#1683983514yes—
subgroupG/H
centerC23×C4C22×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×#97×C61C2
socleC24×C61C22×C4
prime radicalC23×D244C4
cosocleC22×C4×C61C24
hypercenterC22×#97D61
hypocenterC61C2×#1955
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C22×#97

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊#92418C2semidirect
3. C22×#14519689C2semidirect
4. #21446617C2direct (N × H)
5. C22×#97×C61C2semidirect
16. C2×C4⋊#92418C22semidirect
18. C2×#14519689C22semidirect
22. C2×#97×C61C22semidirect
51. C22×C8×C61D4semidirect
95. C2×C8×C61C2×D4semidirect
169. C22×#97D61semidirect
171. C2×C61#1955semidirect
193. C2×#97C2×D61semidirect
194. C61C2×#1955semidirect
214. C22×C8D244semidirect
270. C2×C8C2×D244semidirect
338. C2#21446617direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D2442
C22×C4⋊#924182
C22×#145196892
#214466172
C22×#97×C612
C2×#195561