Finite Group Databasebeta

← C2×#21460914 #30606296

Subgroups — C2×#21460914 #30606296

Order 15616.

1154 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 168 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
1C22×#14519836C212yesmaximal
2#21460914C214yesmaximal, direct product factor
3C2×#16839663C211yesmaximal, characteristic
4C22×C22⋊#6923—22no—
5C2×#14519836—22no—
6C2×#14519836—24no—
7C2×#14519836C418yescomplemented
8C2×#14519836C2214yes—
9C23×D244C2211yescharacteristic
10C22×#11758198—22no—
11C22×C4×Dic61C411yescharacteristic, complemented
12#16839663—22no—
13#16839663C412yescomplemented
14#16839663C2212yes—
15C22×C4⋊C4×C61C411yescharacteristic, complemented
16C23×#6923—42no—
17C2×C22⋊#6923—28no—
18C2×C22⋊#6923—24no—
19C2×C22⋊#6923—42no—
20C2×C22⋊#6923—44no—
21#14519836—28no—
22#14519836—24no—
23#14519836C2×C418yescomplemented
24C24×D61D412yes—
25C22×D244—41no—
26C22×D244—41no—
27C22×D244—42no—
28C22×D244C2×C411yescharacteristic
29C22×D244C2×C414yes—
30C22×D244D412yes—
31C22×D244D412yes—
32C22×D244Q812yes—
33C22×D244C2311yescharacteristic
34C23×Dic61—21no—
35C2×#11758198—24no—
36C2×#11758198—24no—
37C2×#11758198—48no—
38C2×C4×Dic61—21no—
39C2×C4×Dic61—42no—
40C2×C4×Dic61C2×C412yescomplemented
41C23×C4×C61—21no—
42C23×C4×C61C2×C411yescharacteristic
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—41no—
45C2×C4⋊C4×C61—41no—
46C2×C4⋊C4×C61C2×C412yescomplemented
47C24×C61C22⋊C411yescharacteristic
48C23×D61—22no—
49C23×D61—24no—
50C23×D61—22no—
51C23×D61—44no—
52C23×D61—44no—
53C23×D61C22⋊C412yes—
54C23×D61C22⋊C414yes—
55C23×D61C4⋊C414yes—
56C23×D61C2×D412yes—
57C22×#6923—48no—
58C22×#6923—44no—
59C22×#6923—84no—
60C22×#6923—84no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—22no—
64C22×C4×C61—22no—
65C22×C4×C61—44no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61C4212yes—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C4⋊C412yes—
71C22×C4×C61C22×C411yescharacteristic
72C22×Dic61—24no—
73C22×Dic61—22no—
74C22×Dic61—42no—
75C22×Dic61—42no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—44no—
79C2×D244—44no—
80C2×D244—42no—
81C2×D244—42no—
82C2×D244—42no—
83C2×D244—42no—
84C2×D244—42no—
85C2×D244—42no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244C4212yes—
89C2×D244C22⋊C414yes—
90C2×D244C4⋊C414yes—
91C2×D244C4⋊C412yes—
92C2×D244C22×C412yes—
93C2×D244C2×D411yescharacteristic
94C2×D244C2×Q811yescharacteristic
95C22⋊#6923—28no—
96C22⋊#6923—48no—
97C22⋊#6923—44no—
98C4⋊C4×C61—42no—
99C4⋊C4×C61—42no—
100#11758198—48no—
101#11758198—48no—
102C4×Dic61—42no—
103C4×Dic61—42no—
104C23×C61—22no—
105C23×C61—22no—
106C23×C61#9512yes—
107C23×C61#9911yescharacteristic
108C23×C61#9912yes—
109C23×C61#9911yescharacteristic
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—24no—
112C22×D61—24no—
113C22×D61—22no—
114C22×D61—22no—
115C22×D61—24no—
116C22×D61—24no—
117C22×D61—22no—
118C22×D61—22no—
119C22×D61—44no—
120C22×D61—44no—
121C22×D61—42no—
122C22×D61—42no—
123C22×D61—42no—
124C22×D61—48no—
125C22×D61—48no—
126C22×D61—42no—
127C22×D61—82no—
128C22×D61—82no—
129C22×D61—88no—
130C22×D61#9514yes—
131C22×D61C2×C22⋊C412yes—
132C22×D61C2×C4⋊C412yes—
133C2×#6923—48no—
134C2×#6923—84no—
135C2×#6923—84no—
136C2×#6923—816no—
137C2×C4×C61—22no—
138C2×C4×C61—22no—
139C2×C4×C61—22no—
140C2×C4×C61—22no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—44no—
146C2×C4×C61—42no—
147C2×C4×C61—82no—
148C2×C4×C61—82no—
149C2×C4×C61#9512yes—
150C2×C4×C61C2×C4211yescharacteristic
151C2×C4×C61C2×C4⋊C411yescharacteristic
152C2×Dic61—24no—
153C2×Dic61—42no—
154C2×Dic61—48no—
155C2×Dic61—42no—
156D244—42no—
157D244—44no—
158D244—44no—
159D244—42no—
160D244—42no—
161D244—41no—
162D244—41no—
163C2×#1393—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—24no—
169C22×C61—24no—
170C22×C61#34212yes—
171C22×C61#34212yes—
172C22×C61#35312yes—
173C22×C61#35412yes—
174C22×C61C2×#9511yescharacteristic
175C22×C61C2×#9911yescharacteristic
176C22×C61C2×#9911yescharacteristic
177C2×D61—22no—
178C2×D61—24no—
179C2×D61—22no—
180C2×D61—42no—
181C2×D61—42no—
182C2×D61—42no—
183C2×D61—42no—
184C2×D61—48no—
185C2×D61—48no—
186C2×D61—44no—
187C2×D61—42no—
188C2×D61—42no—
189C2×D61—82no—
190C2×D61—84no—
191C2×D61—82no—
192C2×D61—84no—
193#6923—88no—
194C4×C61—22no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—82no—
198Dic61—44no—
199C22×#99—612no—
200C2×#390—611no—
201#1393—614no—
202C2×C61—21no—
203C2×C61—21no—
204C2×C61—22no—
205C2×C61#139314yescomplemented
206C2×C61C2×#34211yescharacteristic
207C2×C61C2×#35311yescharacteristic
208C2×C61C2×#35411yescharacteristic
209D61—42no—
210D61—44no—
211D61—42no—
212C23×D4—611no—
213C22×C4⋊C4#692311yescharacteristic, complemented
214C22×C22⋊C4—1222no—
215C22×C22⋊C4—1222no—
216C22×C42—611no—
217C2×#99—618no—
218C2×#99—614no—
219C2×#99—1224no—
220C2×#99—1222no—
221#390—612no—
222#390—612no—
223#390—1222no—
224C61C2×#139311yescharacteristic, complemented, Sylow
225C25—612no—
226C22×D4—614no—
227C22×D4—612no—
228C22×D4—612no—
229C22×D4—612no—
230C22×D4—611no—
231C22×D4—611no—
232C22×D4—2441no—
233C22×D4—2441no—
234C22×D4—2442no—
235C23×C4—21no—
236C23×C4—1221no—
237C23×C4—2442no—
238C23×C4C2×#692311yescharacteristic
239C2×C4⋊C4—21no—
240C2×C4⋊C4—41no—
241C2×C4⋊C4—41no—
242C2×C4⋊C4C2×#692312yescomplemented
243C2×C22⋊C4—1228no—
244C2×C22⋊C4—1224no—
245C2×C22⋊C4—1224no—
246C2×C22⋊C4—1224no—
247C2×C22⋊C4—2448no—
248C2×C22⋊C4—2442no—
249C2×C22⋊C4—2444no—
250C2×C42—612no—
251C2×C42—1221no—
252C2×C42—2442no—
253#99—618no—
254#99—1228no—
255#99—1224no—
256C24—614no—
257C24—614no—
258C24—612no—
259C24—612no—
260C24—1222no—
261C24—1224no—
262C24—1222no—
263C24—2444no—
264C24—2444no—
265C24C22⋊#692311yescharacteristic
266C2×D4—614no—
267C2×D4—614no—
268C2×D4—612no—
269C2×D4—612no—
270C2×D4—611no—
271C2×D4—612no—
272C2×D4—611no—
273C2×D4—2442no—
274C2×D4—2441no—
275C2×D4—2441no—
276C2×D4—2442no—
277C2×D4—2441no—
278C2×D4—2441no—
279C2×D4—2444no—
280C2×D4—2444no—
281C2×D4—2442no—
282C2×D4—2442no—
283C2×D4—2442no—
284C2×D4—2442no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—44no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—1224no—
293C22×C4—1222no—
294C22×C4—4884no—
295C22×C4—4884no—
296C22×C4—2444no—
297C22×C4—2448no—
298C22×C4—2442no—
299C22×C4—2442no—
300C22×C4C4×#692312yes—
301C22×C4C4⋊#692312yes—
302C22×C4C22⋊#692311yescharacteristic
303C22×C4C22×#692311yescharacteristic
304C4⋊C4—42no—
305C4⋊C4—42no—
306C22⋊C4—1228no—
307C22⋊C4—2448no—
308C22⋊C4—2448no—
309C22⋊C4—2444no—
310C22⋊C4—2448no—
311C42—2442no—
312C42—2442no—
313C23—22no—
314C23—22no—
315C23—614no—
316C23—612no—
317C23—612no—
318C23—1222no—
319C23—1222no—
320C23—1224no—
321C23—1224no—
322C23—1222no—
323C23—1222no—
324C23—1224no—
325C23—1224no—
326C23—4882no—
327C23—4882no—
328C23—4888no—
329C23—2442no—
330C23—2442no—
331C23—2442no—
332C23—2442no—
333C23—2448no—
334C23—2448no—
335C23—2444no—
336C23—2444no—
337C23(C2×#6923)⋊C412yes—
338C23#1451983511yescharacteristic
339C23#1451983511yescharacteristic
340C23#1451983612yes—
341C23C2×C22⋊#692311yescharacteristic
342D4—2444no—
343D4—2444no—
344D4—2442no—
345D4—2442no—
346D4—2441no—
347D4—2442no—
348D4—2441no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—44no—
358C2×C4—42no—
359C2×C4—82no—
360C2×C4—82no—
361C2×C4—1224no—
362C2×C4—4884no—
363C2×C4—4884no—
364C2×C4—48816no—
365C2×C4—2448no—
366C2×C4—2442no—
367C2×C4—2448no—
368C2×C4—2442no—
369C2×C4(C2×#6923)⋊C412yes—
370C2×C4C2×C4×#692311yescharacteristic
371C2×C4C2×C4⋊#692311yescharacteristic
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—24no—
377C22—24no—
378C22—1222no—
379C22—1224no—
380C22—1222no—
381C22—4882no—
382C22—4882no—
383C22—4884no—
384C22—4884no—
385C22—2442no—
386C22—2444no—
387C22—2442no—
388C22—2442no—
389C22—2442no—
390C22—2442no—
391C22—2442no—
392C22—2448no—
393C22—2448no—
394C22#1684064012yes—
395C22#1684064012yes—
396C22#1684066612yes—
397C22#1684066812yes—
398C22C2×(C2×#6923)⋊C411yescharacteristic
399C22C2×#1451983511yescharacteristic
400C22C2×#1451983611yescharacteristic
401C4—22no—
402C4—21no—
403C4—21no—
404C4—82no—
405C4—4888no—
406C4—2444no—
407C2—21no—
408C2—22no—
409C2—21no—
410C2—2442no—
411C2—2442no—
412C2—2444no—
413C2#2146091414yesdirect product factor
414C2C2×#1684064011yescharacteristic
415C2C2×#1684066611yescharacteristic
416C2C2×#1684066811yescharacteristic
subgroupG/H
centerC23#14519835
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61#99
prime radicalC23×D244C22
cosocleC22×D244C23
hypercenterC22×C4⋊C4#6923
hypocenterC61C2×#1393
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #21460914C2direct (N × H)
7. C2×#14519836C4semidirect
11. C22×C4×Dic61C4semidirect
13. #16839663C4semidirect
15. C22×C4⋊C4×C61C4semidirect
23. #14519836C2×C4semidirect
40. C2×C4×Dic61C2×C4semidirect
46. C2×C4⋊C4×C61C2×C4semidirect
205. C2×C61#1393semidirect
213. C22×C4⋊C4#6923semidirect
224. C61C2×#1393semidirect
242. C2×C4⋊C4C2×#6923semidirect
413. C2#21460914direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198362
#214609142
C2×#168396632
C2×#139361