Finite Group Databasebeta

← C2×#21462103 #30623969

Subgroups — C2×#21462103 #30623969

Order 15616.

1230 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 224 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840741C212yesmaximal
2#21462103C218yesmaximal, direct product factor
3C2×#16840669C214yesmaximal, complemented
4C2×#16840338C211yesmaximal, characteristic
5C2×#14519856—22no—
6#16840741—24no—
7#16840741C2218yes—
8C2×#14519836C2214yes—
9C2×#14519835—22no—
10#16840669C22116yescomplemented
11C22×#11758222C2211yescharacteristic
12C23×Dic122C411yescharacteristic, complemented
13#16840338—24no—
14#16840338C414yescomplemented
15#16840338C2214yes—
16C2×#14519777C412yescomplemented
17C2×#14519765C2212yes—
18C2×#14519761—22no—
19C2×#14519757—22no—
20C2×#117×C61C411yescharacteristic, complemented
21#14519856—28no—
22#14519856—44no—
23C2×C4⋊#6923—42no—
24C2×C22⋊#6923—24no—
25C2×C4×#6923—42no—
26#14519836—24no—
27#14519836C2318yes—
28#14519835—28no—
29C2×#11758222—42no—
30C2×#11758222—42no—
31C2×#11758222C2×C412yes—
32C2×#11758222D414yes—
33C2×#11758222C2312yes—
34C22×Dic122—21no—
35C22×Dic122—22no—
36C22×Dic122—42no—
37C22×Dic122—42no—
38C22×Dic122C2×C412yes—
39C22×Dic122C2×C411yescharacteristic
40C22×Dic122C2×C414yescomplemented
41C22×D244C2311yescharacteristic
42C22×C22⋊D61D412yes—
43C23×Dic61—21no—
44C22×C4×D61D412yes—
45#14519777—24no—
46#14519777C2×C418yescomplemented
47#14519765—24no—
48#14519765C2×C414yes—
49#14519765C2314yes—
50#14519761—28no—
51#14519761—28no—
52#14519757—28no—
53#14519757—28no—
54C2×C4⋊Dic61—24no—
55C2×#11758198—24no—
56C23×C4×C61C2×C411yescharacteristic
57#117×C61—22no—
58#117×C61C2×C414yescomplemented
59C2×C4⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C42×C61C2×C412yes—
62C24×C61C22⋊C411yescharacteristic
63C23×D61C2×D412yes—
64C22×#6923—44no—
65C22×C4×C61—22no—
66C22×C4×C61—22no—
67C22×C4×C61—22no—
68C22×C4×C61C22⋊C412yes—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C22×C412yes—
72C2×C22⋊D61—42no—
73C2×C22⋊D61—42no—
74C2×C22⋊D61C22⋊C414yes—
75C2×C22⋊D61C2×D414yes—
76C22×Dic61—22no—
77C22×Dic61—24no—
78C22×Dic61—42no—
79C22×Dic61—42no—
80C22×Dic61C22⋊C412yes—
81#11758222—44no—
82#11758222—44no—
83#11758222—44no—
84#11758222—44no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244C22×C411yescharacteristic
88C2×D244C2×D412yes—
89C2×D244C2411yescharacteristic
90C2×C4×D61—22no—
91C2×C4×D61—22no—
92C2×C4×D61—24no—
93C2×C4×D61C22⋊C414yes—
94C2×C4×D61C2×D414yes—
95C2×Dic122—22no—
96C2×Dic122—24no—
97C2×Dic122—41no—
98C2×Dic122—41no—
99C2×Dic122—48no—
100C2×Dic122—42no—
101C2×Dic122—42no—
102C2×Dic122—42no—
103C2×Dic122—42no—
104C2×Dic122—48no—
105C2×Dic122C22⋊C412yes—
106C2×Dic122C22×C414yes—
107C2×Dic122C22×C412yes—
108C22⋊#6923—28no—
109C22⋊#6923—44no—
110C4⋊#6923—48no—
111C4×#6923—48no—
112C4⋊C4×C61—24no—
113C22⋊C4×C61—24no—
114C42×C61—22no—
115C42×C61C22×C414yes—
116#11758198—28no—
117#11758198—28no—
118C4⋊Dic61—216no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—42no—
122C23×C61C2×C22⋊C411yescharacteristic
123C23×C61C2×C22⋊C412yes—
124C22×D61—22no—
125C22×D61—22no—
126C22×D61—44no—
127C22×D61C2×C22⋊C412yes—
128C22×D61C22×D412yes—
129C2×#6923—48no—
130C2×#6923—88no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—24no—
134C2×C4×C61—24no—
135C2×C4×C61—24no—
136C2×C4×C61—44no—
137C2×C4×C61#9912yes—
138C2×C4×C61#9912yes—
139C2×C4×C61C2×C22⋊C411yescharacteristic
140C2×C4×C61C2×C22⋊C412yes—
141C2×C4×C61C23×C411yescharacteristic
142C22⋊D61—44no—
143C22⋊D61—44no—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—24no—
147C2×Dic61—48no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150C2×Dic61C2×C22⋊C414yes—
151D244—41no—
152D244—42no—
153D244—41no—
154C4×D61—24no—
155C4×D61—24no—
156C4×D61—24no—
157C4×D61—24no—
158Dic122—42no—
159Dic122—42no—
160Dic122—44no—
161Dic122—48no—
162Dic122—44no—
163C2×#2129—611nomaximal, Sylow
164C22×C61—22no—
165C22×C61—22no—
166C22×C61—42no—
167C22×C61—42no—
168C22×C61—42no—
169C22×C61C2×#9911yescharacteristic
170C22×C61C2×#9911yescharacteristic
171C22×C61C22×C22⋊C411yescharacteristic
172C2×D61—22no—
173C2×D61—22no—
174C2×D61—44no—
175C2×D61—42no—
176C2×D61—42no—
177C2×D61—82no—
178#6923—88no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—44no—
182C4×C61C2×#9914yes—
183Dic61—24no—
184Dic61—44no—
185C2×#536—611no—
186C2×#410—612no—
187#2129—618no—
188C2×#354—614no—
189C2×C61—21no—
190C2×C61—21no—
191C2×C61—42no—
192C2×C61#212912yescomplemented
193C2×C61C22×#9911yescharacteristic
194D61—42no—
195D61—42no—
196C22×#41—611no—
197C23×Q8—611no—
198#536—614no—
199#536—614no—
200#536—1224no—
201C2×C4⋊Q8—612no—
202C2×#124—612no—
203C2×#123—1222no—
204C2×C22⋊Q8—1222no—
205C2×#117—1222no—
206C2×#117#692311yescharacteristic, complemented
207#410—618no—
208#410—1224no—
209C2×#99—614no—
210C2×#99—1222no—
211#354—6116no—
212C61C2×#212911yescharacteristic, complemented, Sylow
213C2×#41—614no—
214C2×#41—612no—
215C2×#41—612no—
216C2×#41—2442no—
217C2×#41—2442no—
218C22×Q8—611no—
219C22×Q8—612no—
220C22×Q8—614no—
221C22×Q8—1222no—
222C22×Q8—1221no—
223C22×Q8—2442no—
224C22×Q8—2442no—
225C22×D4—612no—
226C22×D4—611no—
227C23×C4—612no—
228C23×C4—1221no—
229C23×C4C2×#692311yescharacteristic
230C4⋊Q8—618no—
231C4⋊Q8—1224no—
232#124—614no—
233#124—614no—
234#124—1224no—
235#123—1228no—
236#123—1228no—
237C22⋊Q8—1228no—
238C22⋊Q8—1228no—
239#117—22no—
240#117—1228no—
241#117—2444no—
242#117C2×#692314yescomplemented
243C2×C4⋊C4—21no—
244C2×C4⋊C4—1224no—
245C2×C4⋊C4—2442no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—1224no—
248C2×C22⋊C4—1224no—
249C2×C42—2442no—
250C2×C42C2×#692312yes—
251#99—618no—
252#99—1228no—
253#99—1224no—
254C24—612no—
255C24C22⋊#692311yescharacteristic
256#41—2444no—
257#41—2444no—
258#41—2444no—
259#41—2444no—
260C2×Q8—612no—
261C2×Q8—612no—
262C2×Q8—614no—
263C2×Q8—1224no—
264C2×Q8—1222no—
265C2×Q8—2441no—
266C2×Q8—2441no—
267C2×Q8—2448no—
268C2×Q8—2448no—
269C2×Q8—2442no—
270C2×Q8—2442no—
271C2×Q8—2442no—
272C2×Q8—2442no—
273C2×D4—614no—
274C2×D4—614no—
275C2×D4—612no—
276C2×D4—611no—
277C2×D4—611no—
278C2×D4—2441no—
279C2×D4—2441no—
280C2×D4—2442no—
281C2×D4—2442no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—612no—
286C22×C4—614no—
287C22×C4—614no—
288C22×C4—1222no—
289C22×C4—1222no—
290C22×C4—1224no—
291C22×C4—1222no—
292C22×C4—1224no—
293C22×C4—2444no—
294C22×C4—2442no—
295C22×C4—2442no—
296C22×C4C22⋊#692312yes—
297C22×C4C22⋊#692311yescharacteristic
298C22×C4C22×#692311yescharacteristic
299C22×C4C22×#692312yes—
300C4⋊C4—24no—
301C4⋊C4—12216no—
302C4⋊C4—2448no—
303C22⋊C4—24no—
304C22⋊C4—1228no—
305C22⋊C4—1228no—
306C22⋊C4—1228no—
307C22⋊C4—2444no—
308C42—22no—
309C42—2448no—
310C42C22×#692314yes—
311C23—21no—
312C23—21no—
313C23—42no—
314C23—612no—
315C23—612no—
316C23—1222no—
317C23—1222no—
318C23—2444no—
319C23C2×C22⋊#692311yescharacteristic
320C23C2×C22⋊#692312yes—
321Q8—2442no—
322Q8—2442no—
323Q8—2444no—
324Q8—2444no—
325Q8—2448no—
326D4—2442no—
327D4—2441no—
328D4—2441no—
329D4—2444no—
330D4—2444no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—44no—
337C2×C4—614no—
338C2×C4—1222no—
339C2×C4—1222no—
340C2×C4—1224no—
341C2×C4—1224no—
342C2×C4—1224no—
343C2×C4—1224no—
344C2×C4—1224no—
345C2×C4—4888no—
346C2×C4—2448no—
347C2×C4—2448no—
348C2×C4—2442no—
349C2×C4—2442no—
350C2×C4#1451983612yes—
351C2×C4#1451983612yes—
352C2×C4C2×C22⋊#692311yescharacteristic
353C2×C4C2×C22⋊#692312yes—
354C2×C4C23×#692311yescharacteristic
355C22—22no—
356C22—22no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22—1222no—
361C22—1222no—
362C22—4882no—
363C22—2442no—
364C22—2442no—
365C22—2444no—
366C22C2×#1451983611yescharacteristic
367C22C2×#1451983611yescharacteristic
368C22C22×C22⋊#692311yescharacteristic
369C4—21no—
370C4—21no—
371C4—44no—
372C4—1224no—
373C4—4888no—
374C4—2444no—
375C4C2×#1451983614yes—
376C2—21no—
377C2—21no—
378C2—42no—
379C2—2442no—
380C2—2442no—
381C2#2146210312yesdirect product factor
382C2C22×#1451983611yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#99
prime radicalC22×#11758222C22
cosocleC2×D244C24
hypercenterC2×#117#6923
hypocenterC61C2×#2129
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #21462103C2direct (N × H)
3. C2×#16840669C2semidirect
10. #16840669C22semidirect
12. C23×Dic122C4semidirect
14. #16840338C4semidirect
16. C2×#14519777C4semidirect
20. C2×#117×C61C4semidirect
40. C22×Dic122C2×C4semidirect
46. #14519777C2×C4semidirect
58. #117×C61C2×C4semidirect
192. C2×C61#2129semidirect
206. C2×#117#6923semidirect
212. C61C2×#2129semidirect
242. #117C2×#6923semidirect
381. C2#21462103direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407412
#214621032
C2×#168406692
C2×#168403382
C2×#212961