Finite Group Databasebeta

← C2×#21451690 #29846807

Subgroups — C2×#21451690 #29846807

Order 15616.

2894 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519769C211yesmaximal, characteristic, complemented
2C22×C4×D244C211yesmaximal, characteristic
3#21451690C2116yesmaximal, direct product factor
4C2×#16839699C212yesmaximal, complemented
5C2×#16839694C212yesmaximal, complemented
6C2×#16839689C212yesmaximal, complemented
7C2×#16839680C212yesmaximal
8C2×#16839636C214yesmaximal, complemented
9C2×C61×#383C211yesmaximal, characteristic, complemented
10C23×D244C2211yescharacteristic
11C23×C4×D61C2212yes—
12C2×#14519769—28no—
13C2×#14519769C2218yescomplemented
14C2×C4×D244—28no—
15C2×C4×D244C2218yes—
16C22×C4⋊Dic61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2214yes—
20C22×#11758196C2212yes—
21C22×#11758196C2212yes—
22C22×#11758198C2214yes—
23C22×#11758198C2212yes—
24C22×#11758198C2214yes—
25#16839699C22116yescomplemented
26#16839694C22116yescomplemented
27#16839689C22116yescomplemented
28#16839680C22116yes—
29#16839636C22132yescomplemented
30C2×#14519684C2214yes—
31C22×C42×C61C2211yescharacteristic
32C61×#383C2218yescomplemented
33C2×#95×C61C2212yes—
34C2×#95×C61C2212yes—
35C2×#95×C61C2212yes—
36C24×D61C2312yes—
37C22×D244—28no—
38C22×D244—24no—
39C22×D244C2314yes—
40C23×Dic61C2312yes—
41C23×Dic61C2312yes—
42C23×Dic61C2312yes—
43C22×C4×D61—28no—
44C22×C4×D61—48no—
45C22×C4×D61C2318yes—
46#14519769—232no—
47C4×D244—232no—
48C2×C4⋊Dic61—24no—
49C2×C4⋊Dic61—24no—
50C2×C4⋊Dic61—24no—
51C2×C4⋊Dic61—48no—
52C2×C4⋊Dic61C2314yes—
53C2×C4⋊Dic61C2314yes—
54C2×C4⋊Dic61C2314yes—
55C2×C4⋊Dic61C23116yes—
56C2×#11758196—28no—
57C2×#11758196—28no—
58C2×#11758196C2318yes—
59C2×#11758196C2318yes—
60C2×#11758198—216no—
61C2×#11758198—28no—
62C2×#11758198—48no—
63C2×#11758198C23116yes—
64C2×#11758198C2318yes—
65C2×#11758198C23116yes—
66#14519684C23116yes—
67C23×C4×C61C2314yes—
68C23×C4×C61C2311yescharacteristic
69C23×C4×C61C2311yescharacteristic
70C23×C4×C61C2311yescharacteristic
71C2×C42×C61D418yes—
72C2×C42×C61C2314yes—
73#95×C61C2318yes—
74#95×C61C2318yes—
75#95×C61C2318yes—
76C24×C61C2411yescharacteristic
77C23×D61—24no—
78C23×D61—24no—
79C23×D61—28no—
80C23×D61—28no—
81C23×D61#4118yes—
82C23×D61C2414yes—
83C22×C4×C61—24no—
84C22×C4×C61—24no—
85C22×C4×C61—24no—
86C22×C4×C61—28no—
87C22×C4×C61—28no—
88C22×C4×C61—28no—
89C22×C4×C61C2×D414yes—
90C22×C4×C61C2×D414yes—
91C22×C4×C61C2×D414yes—
92C22×C4×C61C2418yes—
93C22×C4×C61C2412yes—
94C22×C4×C61C2412yes—
95C22×C4×C61C2412yes—
96C22×Dic61—24no—
97C22×Dic61—24no—
98C22×Dic61—24no—
99C22×Dic61—28no—
100C22×Dic61—28no—
101C22×Dic61—24no—
102C22×Dic61—24no—
103C22×Dic61C2414yes—
104C22×Dic61C2414yes—
105C22×Dic61C2414yes—
106C2×D244—232no—
107C2×D244—216no—
108C2×D244—28no—
109C2×C4×D61—216no—
110C2×C4×D61—416no—
111C2×C4×D61—432no—
112C42×C61C2×D4116yes—
113#11758198—232no—
114#11758198—216no—
115#11758198—416no—
116C4⋊Dic61—28no—
117C4⋊Dic61—28no—
118C4⋊Dic61—28no—
119C4⋊Dic61—416no—
120#11758196—216no—
121#11758196—216no—
122C23×C61C22×D412yes—
123C23×C61C2×#4114yes—
124C23×C61H(5,𝔽2)14yes—
125C23×C612−1+414yes—
126C23×C61C2511yescharacteristic
127C22×D61—216no—
128C22×D61—232no—
129C22×D61—24no—
130C22×D61—24no—
131C22×D61—28no—
132C22×D61—28no—
133C22×D61—48no—
134C22×D61—48no—
135C22×D61—416no—
136C22×D61C2×#4118yes—
137C2×C4×C61—28no—
138C2×C4×C61—28no—
139C2×C4×C61—28no—
140C2×C4×C61—24no—
141C2×C4×C61—24no—
142C2×C4×C61—24no—
143C2×C4×C61—28no—
144C2×C4×C61—28no—
145C2×C4×C61—28no—
146C2×C4×C61—416no—
147C2×C4×C61C22×D414yes—
148C2×C4×C61C22×D414yes—
149C2×C4×C61C22×D414yes—
150C2×Dic61—24no—
151C2×Dic61—24no—
152C2×Dic61—24no—
153C2×Dic61—28no—
154C2×Dic61—24no—
155C2×Dic61—28no—
156C2×Dic61—24no—
157C2×Dic61—48no—
158C2×Dic61—48no—
159C2×Dic61—48no—
160D244—232no—
161C4×D61—432no—
162C2×#2633—611nomaximal, Sylow
163C22×C61#52514yes—
164C22×C61#53514yes—
165C22×C61#53614yes—
166C22×C61#539116yes—
167C22×C61C23×D411yescharacteristic
168C22×C61C22×#4112yes—
169C22×C61C2×H(5,𝔽2)12yes—
170C22×C61C2×2−1+412yes—
171C2×D61—28no—
172C2×D61—216no—
173C2×D61—432no—
174C2×D61—44no—
175C2×D61—44no—
176C2×D61—48no—
177C4×C61—24no—
178C4×C61—24no—
179C4×C61—24no—
180C4×C61—48no—
181Dic61—44no—
182Dic61—44no—
183Dic61—44no—
184C22×#125—611no—
185C22×C4×D4—611no—
186#2633—6116no—
187C2×#399—612no—
188C2×#398—612no—
189C2×#397—612no—
190C2×#394—612no—
191C2×#385—614no—
192C2×#383D6111yescharacteristic, complemented
193C2×C61#263318yescomplemented
194C2×C61C2×#52511yescharacteristic
195C2×C61C2×#53511yescharacteristic
196C2×C61C2×#53611yescharacteristic
197C2×C61C2×#53914yes—
198D61—48no—
199C23×D4—611no—
200C24×C4—612no—
201C2×#125—618no—
202C2×#125—1228no—
203C2×C4×D4—618no—
204C2×C4×D4—1228no—
205C22×C4⋊C4—612no—
206C22×C4⋊C4—612no—
207C22×C4⋊C4—611no—
208C22×C4⋊C4—611no—
209C22×C4⋊C4—611no—
210C22×C4⋊C4—614no—
211C22×C22⋊C4—614no—
212C22×C22⋊C4—612no—
213C22×C22⋊C4—614no—
214C22×C42C2×D6111yescharacteristic
215#399—6116no—
216#398—6116no—
217#397—6116no—
218#394—6116no—
219#385—6132no—
220#383C2×D6118yescomplemented
221C2×#95—614no—
222C2×#95C2×D6112yes—
223C2×#95C2×D6112yes—
224C2×#95C2×D6112yes—
225C61C2×#263311yescharacteristic, complemented, Sylow
226C25—612no—
227C22×D4—614no—
228C22×D4—1228no—
229C22×D4—1224no—
230C23×C4—612no—
231C23×C4—612no—
232C23×C4—612no—
233C23×C4—618no—
234C23×C4—1228no—
235C23×C4—2448no—
236C23×C4C22×D6114yes—
237C23×C4C22×D6111yescharacteristic
238C23×C4C22×D6111yescharacteristic
239C23×C4C22×D6111yescharacteristic
240#125—12232no—
241C4×D4—12232no—
242C2×C4⋊C4—614no—
243C2×C4⋊C4—618no—
244C2×C4⋊C4—618no—
245C2×C4⋊C4—614no—
246C2×C4⋊C4—614no—
247C2×C4⋊C4—6116no—
248C2×C4⋊C4—1224no—
249C2×C4⋊C4—1228no—
250C2×C4⋊C4—1228no—
251C2×C4⋊C4—1224no—
252C2×C4⋊C4—1224no—
253C2×C4⋊C4—2448no—
254C2×C22⋊C4—618no—
255C2×C22⋊C4—6116no—
256C2×C22⋊C4—6116no—
257C2×C22⋊C4—12216no—
258C2×C22⋊C4—1228no—
259C2×C22⋊C4—2448no—
260C2×C42D24418yes—
261C2×C42C22×D6114yes—
262#95—6116no—
263#95C22×D6118yes—
264#95C22×D6118yes—
265#95C22×D6118yes—
266C24—618no—
267C24—614no—
268C24—1224no—
269C24—1224no—
270C24—1228no—
271C24—1228no—
272C24C23×D6111yescharacteristic
273C2×D4—12216no—
274C2×D4—12232no—
275C2×D4—1228no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—28no—
280C22×C4—28no—
281C22×C4—28no—
282C22×C4—614no—
283C22×C4—614no—
284C22×C4—614no—
285C22×C4—1224no—
286C22×C4—1224no—
287C22×C4—1224no—
288C22×C4—1228no—
289C22×C4—1224no—
290C22×C4—1224no—
291C22×C4—1228no—
292C22×C4—12216no—
293C22×C4—24416no—
294C22×C4—24432no—
295C22×C4C2×D24414yes—
296C22×C4C2×D24414yes—
297C22×C4C2×D24414yes—
298C22×C4C23×D6118yes—
299C22×C4C23×D6112yes—
300C22×C4C23×D6112yes—
301C22×C4C23×D6112yes—
302C4⋊C4—12216no—
303C4⋊C4—12216no—
304C4⋊C4—1228no—
305C4⋊C4—1228no—
306C4⋊C4—1228no—
307C4⋊C4—24416no—
308C22⋊C4—12232no—
309C22⋊C4—12216no—
310C22⋊C4—24416no—
311C42C2×D244116yes—
312C23—618no—
313C23—12216no—
314C23—1224no—
315C23—1224no—
316C23—1228no—
317C23—1228no—
318C23—12232no—
319C23—2448no—
320C23—2448no—
321C23—24416no—
322C23C22×D24412yes—
323C23#41×D6114yes—
324C23#1451982314yes—
325C23#1451982414yes—
326C23C24×D6111yescharacteristic
327D4—12232no—
328C2×C4—28no—
329C2×C4—28no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—28no—
333C2×C4—24no—
334C2×C4—28no—
335C2×C4—28no—
336C2×C4—28no—
337C2×C4—416no—
338C2×C4—1224no—
339C2×C4—1224no—
340C2×C4—1224no—
341C2×C4—1228no—
342C2×C4—1224no—
343C2×C4—1224no—
344C2×C4—1228no—
345C2×C4—24432no—
346C2×C4—2448no—
347C2×C4—2448no—
348C2×C4—2448no—
349C2×C4C22×D24414yes—
350C2×C4C22×D24414yes—
351C2×C4C22×D24414yes—
352C22—1228no—
353C22—12216no—
354C22—24432no—
355C22—2444no—
356C22—2444no—
357C22—2448no—
358C22#1684027414yes—
359C22#1684033114yes—
360C22#1684033814yes—
361C22#16840353116yes—
362C22C23×D24411yescharacteristic
363C22C2×#41×D6112yes—
364C22C2×#1451982312yes—
365C22C2×#1451982412yes—
366C4—24no—
367C4—24no—
368C4—24no—
369C4—48no—
370C4—2444no—
371C4—2444no—
372C4—2444no—
373C2—2448no—
374C2#2145169018yesdirect product factor
375C2C2×#1684027411yescharacteristic
376C2C2×#1684033111yescharacteristic
377C2C2×#1684033811yescharacteristic
378C2C2×#1684035314yes—
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#383C2
socleC24×C61C24
prime radicalC23×D244C22
hypercenterC2×#383D61
hypocenterC61C2×#2633
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
1. C22×#14519769C2semidirect
3. #21451690C2direct (N × H)
4. C2×#16839699C2semidirect
5. C2×#16839694C2semidirect
6. C2×#16839689C2semidirect
8. C2×#16839636C2semidirect
9. C2×C61×#383C2semidirect
13. C2×#14519769C22semidirect
25. #16839699C22semidirect
26. #16839694C22semidirect
27. #16839689C22semidirect
29. #16839636C22semidirect
32. C61×#383C22semidirect
192. C2×#383D61semidirect
193. C2×C61#2633semidirect
220. #383C2×D61semidirect
225. C61C2×#2633semidirect
374. C2#21451690direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197692
C22×C4×D2442
#214516902
C2×#168396992
C2×#168396942
C2×#168396892
C2×#168396802
C2×#168396362
C2×C61×#3832
C2×#263361