Finite Group Databasebeta

← C2×#21460722 #30597290

Subgroups — C2×#21460722 #30597290

Order 15616.

942 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840732C212yesmaximal
2#21460722C214yesmaximal, direct product factor
3C2×#16839623C211yesmaximal, characteristic
4C22×#11758217—22no—
5#16840732—22no—
6#16840732—22no—
7#16840732C414yescomplemented
8#16840732C2214yes—
9C2×C22⋊#92420—22no—
10C2×C22⋊#92420C414yescomplemented
11C24×Dic61C2211yescharacteristic
12C22×C22⋊Dic61C411yescharacteristic
13#16839623—22no—
14#16839623C412yes—
15#16839623C2212yes—
16C2×#14519684—22no—
17C22×C22⋊C4×C61C411yescharacteristic
18C2×#11758217—24no—
19C2×#11758217—24no—
20C2×#11758217—44no—
21C2×#11758217—44no—
22C22×#92420—24no—
23C22⋊#92420—24no—
24C22⋊#92420—24no—
25C22⋊#92420—24no—
26C22⋊#92420C2×C418yescomplemented
27C23×Dic61—21no—
28C23×Dic61—42no—
29C23×Dic61—42no—
30C23×Dic61C2×C411yescharacteristic
31C23×Dic61C2×C412yes—
32C23×Dic61C2×C412yes—
33C23×Dic61D412yes—
34C23×Dic61D411yescharacteristic
35C23×Dic61D411yescharacteristic
36C23×Dic61D412yes—
37C23×Dic61Q811yescharacteristic
38C23×Dic61Q811yescharacteristic
39C23×Dic61C2311yescharacteristic
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—42no—
42C2×C22⋊Dic61C2×C412yes—
43#14519684—24no—
44#14519684—24no—
45C25×C61C2×C411yescharacteristic
46C23×C4×C61—21no—
47C2×C22⋊C4×C61—21no—
48C2×C22⋊C4×C61—42no—
49C2×C22⋊C4×C61C2×C412yes—
50C24×C61—22no—
51C24×C61—22no—
52C24×C61—44no—
53C24×C61C4211yescharacteristic
54C24×C61C4211yescharacteristic
55C24×C61C22⋊C411yescharacteristic
56C24×C61C22⋊C411yescharacteristic
57C24×C61C4⋊C411yescharacteristic
58C24×C61C4⋊C411yescharacteristic
59C24×C61C22×C411yescharacteristic
60C22×C4×C61—22no—
61C22×C4×C61—44no—
62C22×C4×C61—42no—
63C22×Dic61—24no—
64C22×Dic61—24no—
65C22×Dic61—22no—
66C22×Dic61—44no—
67C22×Dic61—44no—
68C22×Dic61—41no—
69C22×Dic61—41no—
70C22×Dic61—42no—
71C22×Dic61—42no—
72C22×Dic61—42no—
73C22×Dic61—42no—
74C22×Dic61—42no—
75C22×Dic61—42no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61—44no—
79C22×Dic61—42no—
80C22×Dic61C4212yes—
81C22×Dic61C22⋊C412yes—
82C22×Dic61C22⋊C412yes—
83C22×Dic61C22⋊C412yes—
84C22×Dic61C22⋊C412yes—
85C22×Dic61C22⋊C412yes—
86C22×Dic61C4⋊C412yes—
87C22×Dic61C4⋊C412yes—
88C22×Dic61C4⋊C411yescharacteristic
89C22×Dic61C4⋊C411yescharacteristic
90C22×Dic61C4⋊C412yes—
91C22×Dic61C4⋊C412yes—
92C22×Dic61C22×C412yes—
93C22×Dic61C2×D412yes—
94C22×Dic61C2×D411yescharacteristic
95C22×Dic61C2×Q811yescharacteristic
96#11758217—48no—
97#11758217—44no—
98#11758217—44no—
99C2×#92420—28no—
100C2×#92420—48no—
101C22⋊C4×C61—42no—
102C22⋊C4×C61—42no—
103C22⋊Dic61—42no—
104C22⋊Dic61—42no—
105C23×C61—24no—
106C23×C61—22no—
107C23×C61—22no—
108C23×C61—22no—
109C23×C61—22no—
110C23×C61—24no—
111C23×C61—24no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—42no—
117C23×C61—42no—
118C23×C61—42no—
119C23×C61—42no—
120C23×C61—48no—
121C23×C61—48no—
122C23×C61#9511yescharacteristic
123C23×C61#9511yescharacteristic
124C23×C61#9511yescharacteristic
125C23×C61#9511yescharacteristic
126C23×C61#9912yes—
127C23×C61#9912yes—
128C23×C61C2×C4211yescharacteristic
129C23×C61C2×C22⋊C411yescharacteristic
130C23×C61C2×C4⋊C411yescharacteristic
131C2×C4×C61—44no—
132C2×C4×C61—42no—
133C2×C4×C61—84no—
134C2×Dic61—24no—
135C2×Dic61—24no—
136C2×Dic61—24no—
137C2×Dic61—24no—
138C2×Dic61—22no—
139C2×Dic61—22no—
140C2×Dic61—22no—
141C2×Dic61—22no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—42no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—44no—
153C2×Dic61—42no—
154C2×Dic61—84no—
155C2×Dic61#9512yes—
156C2×Dic61#9512yes—
157C2×Dic61C2×C22⋊C412yes—
158C2×Dic61C2×C4⋊C412yes—
159#92420—48no—
160C2×#1306—611nomaximal, Sylow
161C22×C61—24no—
162C22×C61—24no—
163C22×C61—22no—
164C22×C61—22no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—22no—
170C22×C61—22no—
171C22×C61—22no—
172C22×C61—22no—
173C22×C61—42no—
174C22×C61—42no—
175C22×C61—42no—
176C22×C61—42no—
177C22×C61—44no—
178C22×C61—44no—
179C22×C61—44no—
180C22×C61—44no—
181C22×C61#34212yes—
182C22×C61#34212yes—
183C22×C61#34414yes—
184C22×C61C2×#9511yescharacteristic
185C22×C61C2×#9911yescharacteristic
186C22×C61C2×#9911yescharacteristic
187C4×C61—82no—
188Dic61—22no—
189Dic61—22no—
190Dic61—22no—
191Dic61—22no—
192Dic61—82no—
193C2×#407—612no—
194C2×#381—611no—
195#1306—614no—
196C2×C61—21no—
197C2×C61—21no—
198C2×C61—22no—
199C2×C61—41no—
200C2×C61—41no—
201C2×C61—41no—
202C2×C61—41no—
203C2×C61#130614yescomplemented
204C2×C61C2×#34211yescharacteristic
205C2×C61C2×#34412yes—
206C24×C4—611no—
207C22×M16—1222no—
208C22×C22⋊C4—611no—
209C22×C22⋊C4#692311yescharacteristic
210#407—614no—
211#407—614no—
212#407—1222no—
213#407—1222no—
214C2×C22⋊C8—614no—
215C2×C22⋊C8—1222no—
216#381—612no—
217#381—612no—
218#381—1222no—
219C2×#95—1222no—
220C61C2×#130611yescharacteristic, complemented, Sylow
221C25C2×#692311yescharacteristic
222C23×C4—21no—
223C23×C4—612no—
224C23×C4—612no—
225C23×C4—612no—
226C23×C4—611no—
227C23×C4—611no—
228C23×C4—611no—
229C23×C4—611no—
230C23×C4—612no—
231C23×C4—611no—
232C23×C4—611no—
233C23×C4—1221no—
234C23×C4—2442no—
235C23×C4—2442no—
236C2×M16—1224no—
237C2×M16—1224no—
238C2×M16—2444no—
239C2×M16—2444no—
240C22×C8—1224no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—42no—
243C2×C22⋊C4—612no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—2442no—
246C2×C22⋊C4C2×#692312yes—
247C22⋊C8—618no—
248C22⋊C8—1224no—
249C22⋊C8—1224no—
250C22⋊C8—1224no—
251#95—1224no—
252#95—1224no—
253C24—22no—
254C24—22no—
255C24—44no—
256C24C4×#692311yescharacteristic
257C24C4×#692311yescharacteristic
258C24C4⋊#692311yescharacteristic
259C24C4⋊#692311yescharacteristic
260C24C22⋊#692311yescharacteristic
261C24C22⋊#692311yescharacteristic
262C24C22×#692311yescharacteristic
263C22×C4—22no—
264C22×C4—44no—
265C22×C4—42no—
266C22×C4—612no—
267C22×C4—612no—
268C22×C4—612no—
269C22×C4—612no—
270C22×C4—612no—
271C22×C4—612no—
272C22×C4—612no—
273C22×C4—612no—
274C22×C4—612no—
275C22×C4—612no—
276C22×C4—612no—
277C22×C4—612no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—1224no—
283C22×C4—1224no—
284C22×C4—1222no—
285C22×C4—2441no—
286C22×C4—2442no—
287C22×C4—2441no—
288C22×C4—2441no—
289C22×C4—2442no—
290C22×C4—2441no—
291C22×C4—2442no—
292C22×C4—2444no—
293C22×C4—2442no—
294C22×C4—2444no—
295C22×C4—2442no—
296C22×C4—2442no—
297C22×C4—2444no—
298C22×C4—2442no—
299M16—2444no—
300M16—2444no—
301M16—2448no—
302C2×C8—1228no—
303C2×C8—2448no—
304C22⋊C4—42no—
305C22⋊C4—42no—
306C22⋊C4—2442no—
307C22⋊C4—2442no—
308C23—24no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—24no—
318C23—24no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—48no—
324C23—48no—
325C23(C2×#6923)⋊C411yescharacteristic
326C23(C2×#6923)⋊C411yescharacteristic
327C23(C2×#6923)⋊C411yescharacteristic
328C23(C2×#6923)⋊C411yescharacteristic
329C23#1451983512yes—
330C23#1451983612yes—
331C23C2×C4×#692311yescharacteristic
332C23C2×C22⋊#692311yescharacteristic
333C23C2×C4⋊#692311yescharacteristic
334C2×C4—44no—
335C2×C4—42no—
336C2×C4—84no—
337C2×C4—612no—
338C2×C4—612no—
339C2×C4—612no—
340C2×C4—612no—
341C2×C4—1222no—
342C2×C4—1222no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—1224no—
346C2×C4—1224no—
347C2×C4—1224no—
348C2×C4—1224no—
349C2×C4—4884no—
350C2×C4—2441no—
351C2×C4—2442no—
352C2×C4—2442no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2444no—
361C2×C4—2442no—
362C8—2448no—
363C22—22no—
364C22—22no—
365C22—24no—
366C22—24no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—42no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—44no—
380C22—44no—
381C22—44no—
382C22—44no—
383C22#1684064012yes—
384C22#1684064012yes—
385C22#1684064314yes—
386C22C2×(C2×#6923)⋊C411yescharacteristic
387C22C2×#1451983511yescharacteristic
388C22C2×#1451983611yescharacteristic
389C4—82no—
390C4—1222no—
391C4—1222no—
392C4—1222no—
393C4—1222no—
394C4—4882no—
395C2—21no—
396C2—21no—
397C2—22no—
398C2—41no—
399C2—41no—
400C2—41no—
401C2—41no—
402C2#2146072214yesdirect product factor
403C2C2×#1684064011yescharacteristic
404C2C2×#1684064312yes—
subgroupG/H
centerC23(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC22×C22⋊C4×C61C4
socleC23×C61#95
prime radicalC25×C61C2×C4
cosocleC23×Dic61C23
hypercenterC22×C22⋊C4#6923
hypocenterC61C2×#1306
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #21460722C2direct (N × H)
7. #16840732C4semidirect
10. C2×C22⋊#92420C4semidirect
26. C22⋊#92420C2×C4semidirect
203. C2×C61#1306semidirect
220. C61C2×#1306semidirect
402. C2#21460722direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407322
#214607222
C2×#168396232
C2×#130661