Finite Group Databasebeta

← C2×#21461070 #30609943

Subgroups — C2×#21461070 #30609943

Order 15616.

1326 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840782C212yesmaximal, complemented
2#21461070C218yesmaximal, direct product factor
3C2×#16840607C212yesmaximal, complemented
4C2×#16840605C212yesmaximal
5C22×#14519736C211yesmaximal, characteristic
6#16840782—24no—
7#16840782C2218yescomplemented
8C2×#14519844—22no—
9C2×C22⋊#92420C2214yes—
10C2×#14519832—22no—
11#16840607C2218yescomplemented
12#16840605C2218yes—
13C2×#14519736—22no—
14C2×#14519736—22no—
15C2×#14519736—24no—
16C2×#14519736C414yes—
17C2×#14519736C2214yes—
18C22×C4⋊Dic61C411yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C411yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C4×Dic61C411yescharacteristic
23C22×C4×Dic61C2211yescharacteristic
24C24×C4×C61C411yescharacteristic
25C22×#92420—24no—
26#14519844—28no—
27C22⋊#92420—24no—
28C22⋊#92420C2318yes—
29#14519832—28no—
30C23×Dic61C2×C411yescharacteristic
31C23×Dic61C2×C411yescharacteristic
32C23×Dic61C2×C411yescharacteristic
33C23×Dic61C2311yescharacteristic
34#14519736—28no—
35#14519736—28no—
36#14519736—28no—
37#14519736—28no—
38C2×C4⋊Dic61—22no—
39C2×C4⋊Dic61—22no—
40C2×C4⋊Dic61—22no—
41C2×C4⋊Dic61—22no—
42C2×C4⋊Dic61C2×C414yes—
43C2×C4⋊Dic61C2×C412yes—
44C2×C4⋊Dic61C2312yes—
45C2×C22⋊Dic61—22no—
46C2×C22⋊Dic61—22no—
47C2×C22⋊Dic61—22no—
48C2×C22⋊Dic61—22no—
49C2×C22⋊Dic61C2×C414yes—
50C2×C22⋊Dic61C2×C412yes—
51C2×C22⋊Dic61C2312yes—
52C2×C4×Dic61—22no—
53C2×C4×Dic61—21no—
54C2×C4×Dic61—21no—
55C2×C4×Dic61C2×C414yes—
56C2×C4×Dic61C2×C412yes—
57C2×C4×Dic61D412yes—
58C2×C4×Dic61D412yes—
59C2×C4×Dic61D414yes—
60C2×C4×Dic61C2312yes—
61C25×C61C2×C411yescharacteristic
62C23×C4×C61—24no—
63C23×C4×C61—22no—
64C23×C4×C61—21no—
65C23×C4×C61—21no—
66C23×C4×C61—24no—
67C23×C4×C61C2×C414yes—
68C23×C4×C61C2×C411yescharacteristic
69C23×C4×C61C2×C411yescharacteristic
70C24×C61—21no—
71C24×C61—21no—
72C24×C61—22no—
73C24×C61—42no—
74C24×C61—42no—
75C24×C61M1614yes—
76C24×C61C22×C411yescharacteristic
77C24×C61C22×C412yes—
78C22×C4×C61—216no—
79C22×C4×C61—28no—
80C22×C4×C61—28no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—28no—
84C22×C4×C61—22no—
85C22×C4×C61—22no—
86C22×C4×C61—22no—
87C22×C4×C61—24no—
88C22×C4×C61—24no—
89C22×C4×C61—28no—
90C22×C4×C61C22⋊C412yes—
91C22×C4×C61C22⋊C411yescharacteristic
92C22×C4×C61C22⋊C411yescharacteristic
93C22×C4×C61M1614yes—
94C22×C4×C61C22×C412yes—
95C22×C4×C61C22×C412yes—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61—21no—
100C22×Dic61—42no—
101C22×Dic61—42no—
102C22×Dic61—42no—
103C22×Dic61—42no—
104C22×Dic61C22⋊C412yes—
105C22×Dic61C22⋊C412yes—
106C22×Dic61C22×C412yes—
107C22×Dic61C22×C412yes—
108C22×Dic61C22×C412yes—
109C22×Dic61C22×C411yescharacteristic
110C22×Dic61C2×D412yes—
111C22×Dic61C2×D412yes—
112C22×Dic61C2411yescharacteristic
113C2×#92420—28no—
114C2×#92420—48no—
115C22⋊Dic61—24no—
116C22⋊Dic61—28no—
117C22⋊Dic61—24no—
118C4⋊Dic61—24no—
119C4⋊Dic61—28no—
120C4⋊Dic61—24no—
121C4×Dic61—24no—
122C4×Dic61—24no—
123C4×Dic61C22⋊C414yes—
124C4×Dic61C22⋊C414yes—
125C4×Dic61C2×D414yes—
126C4×Dic61C2×D414yes—
127C23×C61—22no—
128C23×C61—22no—
129C23×C61—22no—
130C23×C61—22no—
131C23×C61—24no—
132C23×C61—24no—
133C23×C61—42no—
134C23×C61—42no—
135C23×C61—48no—
136C23×C61—48no—
137C23×C61—42no—
138C23×C61—42no—
139C23×C61—42no—
140C23×C61—42no—
141C23×C61C2×C22⋊C411yescharacteristic
142C23×C61C2×C22⋊C411yescharacteristic
143C23×C61C2×M1612yes—
144C23×C61C2×M1612yes—
145C23×C61C2×M1614yes—
146C23×C61C23×C411yescharacteristic
147C2×C4×C61—216no—
148C2×C4×C61—216no—
149C2×C4×C61—22no—
150C2×C4×C61—22no—
151C2×C4×C61—22no—
152C2×C4×C61—22no—
153C2×C4×C61—24no—
154C2×C4×C61—22no—
155C2×C4×C61—22no—
156C2×C4×C61—24no—
157C2×C4×C61—24no—
158C2×C4×C61C2×C22⋊C412yes—
159C2×C4×C61C2×C22⋊C412yes—
160C2×C4×C61C2×M1614yes—
161C2×Dic61—24no—
162C2×Dic61—24no—
163C2×Dic61—22no—
164C2×Dic61—22no—
165C2×Dic61—42no—
166C2×Dic61—41no—
167C2×Dic61—42no—
168C2×Dic61—42no—
169C2×Dic61—41no—
170C2×Dic61—42no—
171C2×Dic61—42no—
172C2×Dic61—42no—
173C2×Dic61—42no—
174C2×Dic61—42no—
175C2×Dic61—42no—
176C2×Dic61C2×C22⋊C412yes—
177C2×Dic61C2×C22⋊C414yes—
178C2×Dic61C22×D412yes—
179#92420—48no—
180C2×#1464—611nomaximal, Sylow
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—24no—
186C22×C61—24no—
187C22×C61—24no—
188C22×C61—44no—
189C22×C61—44no—
190C22×C61—48no—
191C22×C61—42no—
192C22×C61—42no—
193C22×C61—48no—
194C22×C61#40712yes—
195C22×C61#40712yes—
196C22×C61#41012yes—
197C22×C61#41312yes—
198C22×C61C22×C22⋊C411yescharacteristic
199C22×C61C22×M1611yescharacteristic
200C22×C61C22×M1611yescharacteristic
201C4×C61—22no—
202C4×C61—22no—
203C4×C61—24no—
204Dic61—22no—
205Dic61—22no—
206Dic61—24no—
207Dic61—42no—
208Dic61—42no—
209C22×#117—611no—
210C2×#432—612no—
211#1464—618no—
212C2×#324—612no—
213C2×#323—612no—
214C2×C61—21no—
215C2×C61—21no—
216C2×C61—22no—
217C2×C61—44no—
218C2×C61#146414yescomplemented
219C2×C61C2×#40711yescharacteristic
220C2×C61C2×#41011yescharacteristic
221C2×C61C2×#41311yescharacteristic
222C24×C4#692311yescharacteristic
223C2×#117—614no—
224C2×#117—614no—
225C2×#117—1222no—
226C2×#117—1222no—
227C2×#117—1224no—
228C22×C4⋊C4—611no—
229C22×C4⋊C4—611no—
230C22×C22⋊C4—611no—
231C22×C22⋊C4—611no—
232C22×C42—611no—
233C22×C42—611no—
234#432—618no—
235#432—1224no—
236C2×C4⋊C8—1222no—
237C2×C22⋊C8—614no—
238C2×#97—1222no—
239#324—618no—
240#323—618no—
241C61C2×#146411yescharacteristic, complemented, Sylow
242C25C2×#692311yescharacteristic
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—22no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—611no—
249C23×C4—611no—
250C23×C4—611no—
251C23×C4—611no—
252C23×C4C2×#692314yes—
253C23×C4C2×#692311yescharacteristic
254C23×C4C2×#692311yescharacteristic
255C22×C8—1224no—
256#117—1228no—
257#117—1228no—
258#117—1228no—
259#117—1228no—
260C2×C4⋊C4—612no—
261C2×C4⋊C4—614no—
262C2×C4⋊C4—612no—
263C2×C4⋊C4—1222no—
264C2×C4⋊C4—1222no—
265C2×C4⋊C4—1222no—
266C2×C4⋊C4—1222no—
267C2×C22⋊C4—612no—
268C2×C22⋊C4—614no—
269C2×C22⋊C4—612no—
270C2×C22⋊C4—1222no—
271C2×C22⋊C4—1222no—
272C2×C22⋊C4—1222no—
273C2×C22⋊C4—1222no—
274C2×C42—612no—
275C2×C42—612no—
276C2×C42—614no—
277C2×C42—612no—
278C2×C42—612no—
279C2×C42—614no—
280C2×C42—1222no—
281C2×C42—1221no—
282C2×C42—1221no—
283C4⋊C8—1228no—
284C22⋊C8—618no—
285C22⋊C8—1224no—
286#97—1228no—
287C24—21no—
288C24—21no—
289C24—22no—
290C24—42no—
291C24—42no—
292C24#1175821714yes—
293C24C22×#692311yescharacteristic
294C24C22×#692312yes—
295C22×C4—216no—
296C22×C4—28no—
297C22×C4—28no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—28no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—28no—
307C22×C4—612no—
308C22×C4—612no—
309C22×C4—612no—
310C22×C4—612no—
311C22×C4—611no—
312C22×C4—611no—
313C22×C4—612no—
314C22×C4—612no—
315C22×C4—612no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—2442no—
321C22×C4—2442no—
322C22×C4—2442no—
323C22×C4—2442no—
324C22×C4#1175821714yes—
325C22×C4C22⋊#692312yes—
326C22×C4C22⋊#692311yescharacteristic
327C22×C4C22⋊#692311yescharacteristic
328C22×C4C22×#692312yes—
329C22×C4C22×#692312yes—
330C2×C8—1228no—
331C2×C8—2448no—
332C4⋊C4—1224no—
333C4⋊C4—1228no—
334C4⋊C4—1224no—
335C22⋊C4—1224no—
336C22⋊C4—1228no—
337C22⋊C4—1224no—
338C42—614no—
339C42—614no—
340C42—614no—
341C42—614no—
342C42—1224no—
343C42—1224no—
344C23—22no—
345C23—22no—
346C23—24no—
347C23—24no—
348C23—22no—
349C23—22no—
350C23—48no—
351C23—42no—
352C23—42no—
353C23—48no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23C2×C22⋊#692311yescharacteristic
359C23C2×C22⋊#692311yescharacteristic
360C23C2×#1175821712yes—
361C23C2×#1175821712yes—
362C23C2×#1175821714yes—
363C23C23×#692311yescharacteristic
364C2×C4—216no—
365C2×C4—216no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—612no—
376C2×C4—614no—
377C2×C4—612no—
378C2×C4—1224no—
379C2×C4—1224no—
380C2×C4—1222no—
381C2×C4—1222no—
382C2×C4—2441no—
383C2×C4—2442no—
384C2×C4—2441no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4—2442no—
388C2×C4—2442no—
389C2×C4—2442no—
390C2×C4—2442no—
391C2×C4—2442no—
392C2×C4—2442no—
393C2×C4C2×C22⋊#692312yes—
394C2×C4C2×C22⋊#692312yes—
395C2×C4C2×#1175821714yes—
396C8—2448no—
397C22—24no—
398C22—24no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—24no—
404C22—44no—
405C22—48no—
406C22—44no—
407C22—48no—
408C22—42no—
409C22—42no—
410C22#1684073212yes—
411C22#1684073212yes—
412C22#1684074112yes—
413C22#1684074812yes—
414C22C22×C22⋊#692311yescharacteristic
415C22C22×#1175821711yescharacteristic
416C22C22×#1175821711yescharacteristic
417C4—22no—
418C4—22no—
419C4—24no—
420C4—1222no—
421C4—1222no—
422C4—1224no—
423C4—2442no—
424C4—2442no—
425C2—22no—
426C2—21no—
427C2—21no—
428C2—44no—
429C2#2146107014yesdirect product factor
430C2C2×#1684073211yescharacteristic
431C2C2×#1684074111yescharacteristic
432C2C2×#1684074811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC24×C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC25×C61C2×C4
cosocleC22×Dic61C24
hypercenterC24×C4#6923
hypocenterC61C2×#1464
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. C2×#16840782C2semidirect
2. #21461070C2direct (N × H)
3. C2×#16840607C2semidirect
7. #16840782C22semidirect
11. #16840607C22semidirect
218. C2×C61#1464semidirect
241. C61C2×#1464semidirect
429. C2#21461070direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407822
#214610702
C2×#168406072
C2×#168406052
C22×#145197362
C2×#146461