Finite Group Databasebeta

← C2×#21461073 #30609947

Subgroups — C2×#21461073 #30609947

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×#16840783C212yesmaximal, complemented
2#21461073C218yesmaximal, direct product factor
3C2×#16840607C212yesmaximal, complemented
4C2×#16840606C212yesmaximal
5C22×#14519735C211yesmaximal, characteristic
6#16840783—24no—
7#16840783C2218yescomplemented
8C2×C4⋊#92420—22no—
9C2×C22⋊#92420C2214yes—
10C2×#14519832—22no—
11#16840607C2218yescomplemented
12#16840606C2218yes—
13C23×C4×D61C411yescharacteristic
14C2×#14519735—22no—
15C2×#14519735—22no—
16C2×#14519735—24no—
17C2×#14519735C414yes—
18C2×#14519735C2214yes—
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758198C411yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×C4×Dic61C411yescharacteristic
23C22×C4×Dic61C2211yescharacteristic
24C22×C4⋊C4×C61C411yescharacteristic
25C22×#92420—24no—
26C4⋊#92420—28no—
27C22⋊#92420—24no—
28C22⋊#92420C2318yes—
29#14519832—28no—
30C24×D61C2×C411yescharacteristic
31C23×Dic61C2×C411yescharacteristic
32C23×Dic61C2×C411yescharacteristic
33C23×Dic61C2311yescharacteristic
34C22×C4×D61—24no—
35C22×C4×D61—24no—
36C22×C4×D61—22no—
37C22×C4×D61—21no—
38C22×C4×D61—21no—
39C22×C4×D61C2×C414yes—
40#14519735—28no—
41#14519735—28no—
42#14519735—28no—
43#14519735—28no—
44C2×C4⋊Dic61—22no—
45C2×C4⋊Dic61—22no—
46C2×C4⋊Dic61C2×C412yes—
47C2×C4⋊Dic61C2312yes—
48C2×#11758198—22no—
49C2×#11758198—22no—
50C2×#11758198—22no—
51C2×#11758198—22no—
52C2×#11758198C2×C414yes—
53C2×#11758198C2×C412yes—
54C2×#11758198C2312yes—
55C2×C4×Dic61—22no—
56C2×C4×Dic61—21no—
57C2×C4×Dic61—21no—
58C2×C4×Dic61C2×C414yes—
59C2×C4×Dic61C2×C412yes—
60C2×C4×Dic61D412yes—
61C2×C4×Dic61D412yes—
62C2×C4×Dic61D414yes—
63C2×C4×Dic61C2312yes—
64C23×C4×C61C2×C411yescharacteristic
65C23×C4×C61C2×C411yescharacteristic
66C23×C4×C61C2×C411yescharacteristic
67C2×C4⋊C4×C61—22no—
68C2×C4⋊C4×C61—22no—
69C2×C4⋊C4×C61C2×C414yes—
70C24×C61C22×C411yescharacteristic
71C23×D61—21no—
72C23×D61—21no—
73C23×D61—22no—
74C23×D61—42no—
75C23×D61—42no—
76C23×D61M1614yes—
77C23×D61C22×C412yes—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—22no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—42no—
84C22×C4×C61—42no—
85C22×C4×C61C22⋊C412yes—
86C22×C4×C61C22⋊C412yes—
87C22×C4×C61M1614yes—
88C22×C4×C61C22×C412yes—
89C22×C4×C61C22×C412yes—
90C22×C4×C61C22×C412yes—
91C22×Dic61—22no—
92C22×Dic61—22no—
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—42no—
96C22×Dic61—42no—
97C22×Dic61C22⋊C412yes—
98C22×Dic61C22⋊C411yescharacteristic
99C22×Dic61C22⋊C411yescharacteristic
100C22×Dic61C22×C412yes—
101C22×Dic61C22×C412yes—
102C22×Dic61C22×C411yescharacteristic
103C22×Dic61C2×D412yes—
104C22×Dic61C2×D412yes—
105C22×Dic61C2411yescharacteristic
106C2×C4×D61—216no—
107C2×C4×D61—28no—
108C2×C4×D61—28no—
109C2×C4×D61—28no—
110C2×C4×D61—28no—
111C2×C4×D61—24no—
112C2×C4×D61—24no—
113C2×#92420—28no—
114C2×#92420—48no—
115C4⋊C4×C61—28no—
116#11758198—28no—
117#11758198—24no—
118#11758198—24no—
119C4⋊Dic61—24no—
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×C61C2×C22⋊C411yescharacteristic
130C23×C61C2×C22⋊C411yescharacteristic
131C23×C61C2×M1612yes—
132C23×C61C2×M1612yes—
133C23×C61C23×C411yescharacteristic
134C22×D61—22no—
135C22×D61—22no—
136C22×D61—24no—
137C22×D61—24no—
138C22×D61—42no—
139C22×D61—42no—
140C22×D61—48no—
141C22×D61—42no—
142C22×D61—42no—
143C22×D61—48no—
144C22×D61—42no—
145C22×D61—42no—
146C22×D61C2×M1614yes—
147C2×C4×C61—22no—
148C2×C4×C61—22no—
149C2×C4×C61—24no—
150C2×C4×C61—24no—
151C2×C4×C61—24no—
152C2×C4×C61—22no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61—42no—
157C2×C4×C61—42no—
158C2×C4×C61C2×C22⋊C414yes—
159C2×C4×C61C2×M1614yes—
160C2×Dic61—22no—
161C2×Dic61—22no—
162C2×Dic61—24no—
163C2×Dic61—22no—
164C2×Dic61—22no—
165C2×Dic61—24no—
166C2×Dic61—22no—
167C2×Dic61—41no—
168C2×Dic61—42no—
169C2×Dic61—41no—
170C2×Dic61—42no—
171C2×Dic61—42no—
172C2×Dic61—42no—
173C2×Dic61C2×C22⋊C412yes—
174C2×Dic61C2×C22⋊C412yes—
175C2×Dic61C2×C22⋊C412yes—
176C2×Dic61C22×D412yes—
177C4×D61—216no—
178C4×D61—216no—
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#40712yes—
188C22×C61#40712yes—
189C22×C61#41012yes—
190C22×C61#41312yes—
191C22×C61C22×C22⋊C411yescharacteristic
192C22×C61C22×M1611yescharacteristic
193C22×C61C22×M1611yescharacteristic
194C2×D61—24no—
195C2×D61—44no—
196C2×D61—48no—
197C2×D61—42no—
198C2×D61—42no—
199C2×D61—48no—
200C2×D61—44no—
201C4×C61—24no—
202C4×C61—24no—
203C4×C61—42no—
204Dic61—22no—
205Dic61—22no—
206Dic61—22no—
207Dic61—22no—
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#146414yescomplemented
218C2×C61C2×#40711yescharacteristic
219C2×C61C2×#41011yescharacteristic
220C2×C61C2×#41311yescharacteristic
221D61—44no—
222C24×C4—611no—
223C2×#117—614no—
224C2×#117—614no—
225C2×#117—1222no—
226C2×#117—1222no—
227C2×#117—1224no—
228C22×C4⋊C4—611no—
229C22×C4⋊C4#692311yescharacteristic
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
242C25—611no—
243C23×C4—611no—
244C23×C4—611no—
245C23×C4—611no—
246C23×C4—614no—
247C23×C4—1222no—
248C23×C4—1221no—
249C23×C4—1221no—
250C23×C4—1224no—
251C23×C4—1224no—
252C23×C4C2×#692311yescharacteristic
253C23×C4C2×#692311yescharacteristic
254C23×C4C2×#692311yescharacteristic
255C22×C8—1224no—
256#117—1228no—
257#117—1228no—
258#117—1228no—
259#117—1228no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—612no—
263C2×C4⋊C4—612no—
264C2×C4⋊C4—1222no—
265C2×C4⋊C4—1222no—
266C2×C4⋊C4C2×#692314yes—
267C2×C22⋊C4—612no—
268C2×C22⋊C4—612no—
269C2×C22⋊C4—614no—
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—614no—
288C24—612no—
289C24—1221no—
290C24—1221no—
291C24—1222no—
292C24—2442no—
293C24—2442no—
294C24C22×#692311yescharacteristic
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—612no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—612no—
306C22×C4—612no—
307C22×C4—612no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—612no—
311C22×C4—1224no—
312C22×C4—1224no—
313C22×C4—1228no—
314C22×C4—12216no—
315C22×C4—1228no—
316C22×C4—1228no—
317C22×C4—1222no—
318C22×C4—1222no—
319C22×C4—1228no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—2442no—
323C22×C4—2442no—
324C22×C4#1175821314yes—
325C22×C4C22⋊#692312yes—
326C22×C4C22⋊#692312yes—
327C22×C4C22×#692312yes—
328C22×C4C22×#692312yes—
329C22×C4C22×#692312yes—
330C2×C8—1228no—
331C2×C8—2448no—
332C4⋊C4—28no—
333C4⋊C4—1224no—
334C4⋊C4—1224no—
335C22⋊C4—1224no—
336C22⋊C4—1224no—
337C22⋊C4—1228no—
338C42—614no—
339C42—614no—
340C42—614no—
341C42—614no—
342C42—1224no—
343C42—1224no—
344C23—22no—
345C23—22no—
346C23—614no—
347C23—1224no—
348C23—1224no—
349C23—1222no—
350C23—1222no—
351C23—2448no—
352C23—2442no—
353C23—2442no—
354C23—2448no—
355C23—2442no—
356C23—2442no—
357C23—2442no—
358C23—2442no—
359C23C2×C22⋊#692311yescharacteristic
360C23C2×C22⋊#692311yescharacteristic
361C23D61⋊M1612yes—
362C23C2×#1175821312yes—
363C23C23×#692311yescharacteristic
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—612no—
376C2×C4—612no—
377C2×C4—612no—
378C2×C4—612no—
379C2×C4—12216no—
380C2×C4—12216no—
381C2×C4—1224no—
382C2×C4—1222no—
383C2×C4—1222no—
384C2×C4—1224no—
385C2×C4—1222no—
386C2×C4—1222no—
387C2×C4—1222no—
388C2×C4—2441no—
389C2×C4—2442no—
390C2×C4—2441no—
391C2×C4—2442no—
392C2×C4—2442no—
393C2×C4—2442no—
394C2×C4C2×C22⋊#692314yes—
395C2×C4C2×#1175821314yes—
396C8—2448no—
397C22—24no—
398C22—24no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—1224no—
404C22—2444no—
405C22—2448no—
406C22—2444no—
407C22—2448no—
408C22—2442no—
409C22—2442no—
410C22#1684073312yes—
411C22#1684073312yes—
412C22#1684074312yes—
413C22#1684074912yes—
414C22C22×C22⋊#692311yescharacteristic
415C22C2×D61⋊M1611yescharacteristic
416C22C22×#1175821311yescharacteristic
417C4—24no—
418C4—24no—
419C4—42no—
420C4—1222no—
421C4—1222no—
422C4—1222no—
423C4—1222no—
424C4—2442no—
425C2—22no—
426C2—21no—
427C2—21no—
428C2—2444no—
429C2#2146107314yesdirect product factor
430C2C2×#1684073311yescharacteristic
431C2C2×#1684074311yescharacteristic
432C2C2×#1684074911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC22×Dic61C24
hypercenterC22×C4⋊C4#6923
hypocenterC61C2×#1464
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16840783C2semidirect
2. #21461073C2direct (N × H)
3. C2×#16840607C2semidirect
7. #16840783C22semidirect
11. #16840607C22semidirect
217. C2×C61#1464semidirect
241. C61C2×#1464semidirect
429. C2#21461073direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407832
#214610732
C2×#168406072
C2×#168406062
C22×#145197352
C2×#146461