Finite Group Databasebeta

← C22×#16839787 #30543627

Subgroups — C22×#16839787 #30543627

Order 15616.

3006 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758189C211yesmaximal, characteristic
2C23×C8×D61C211yesmaximal, characteristic
3C22×#14519734C211yesmaximal, characteristic
4C2×#16839787C2124yesmaximal, direct product factor
5C22×C4⋊#92418C211yesmaximal, characteristic, complemented
6C22×#14519706C211yesmaximal, characteristic, complemented
7C22×#14519706C211yesmaximal, characteristic, complemented
8C22×C4⋊C8×C61C211yesmaximal, characteristic, complemented
9C23×C4×D61C2211yescharacteristic
10C22×#11758189—28no—
11C22×#11758189C22112yes—
12C23×#92418C2211yescharacteristic
13C23×#92418C2211yescharacteristic
14C22×C8×D61—28no—
15C22×C8×D61C22112yes—
16C2×#14519734C4112yes—
17C2×#14519734C22112yes—
18C22×#11758196C411yescharacteristic
19C22×#11758196C411yescharacteristic
20C22×#11758198C411yescharacteristic
21C22×#11758198C411yescharacteristic
22C22×C4×Dic61C2211yescharacteristic
23#16839787C22164yesdirect product factor
24C2×C4⋊#92418C22112yescomplemented
25C2×#14519706C22112yescomplemented
26C2×#14519706C22112yescomplemented
27C23×C8×C61C2211yescharacteristic
28C23×C8×C61C2211yescharacteristic
29C22×C42×C61C2211yescharacteristic
30C2×C4⋊C8×C61C22112yescomplemented
31C24×D61C2×C411yescharacteristic
32C23×Dic61C2×C411yescharacteristic
33C23×Dic61C2×C411yescharacteristic
34C23×Dic61C2×C411yescharacteristic
35C22×C4×D61C2×C416yes—
36C22×C4×D61D418yes—
37C22×C4×D61Q818yes—
38C22×C4×D61C2316yes—
39C2×#11758189—248no—
40C2×#11758189C23116yes—
41C22×#92418—24no—
42C22×#92418—24no—
43C22×#92418C2316yes—
44C22×#92418C2316yes—
45C2×C8×D61—248no—
46C2×C8×D61C23116yes—
47#14519734C2×C4148yes—
48#14519734C23116yes—
49C2×#11758196C2×C4112yes—
50C2×#11758196C2×C4112yes—
51C2×#11758198C2×C4112yes—
52C2×#11758198C2×C4112yes—
53C2×C4×Dic61C2×C416yes—
54C2×C4×Dic61C2316yes—
55C4⋊#92418C23116yescomplemented
56#14519706C23116yescomplemented
57#14519706C23116yescomplemented
58C23×C4×C61C2×C411yescharacteristic
59C23×C4×C61C2×C411yescharacteristic
60C23×C4×C61C2311yescharacteristic
61C22×C8×C61—24no—
62C22×C8×C61—24no—
63C22×C8×C61C2316yes—
64C22×C8×C61C2316yes—
65C2×C42×C61C2×C416yes—
66C2×C42×C61C2316yes—
67C4⋊C8×C61C23116yescomplemented
68C24×C61C22×C411yescharacteristic
69C23×D61—24no—
70C23×D61—24no—
71C23×D61C4⋊C418yes—
72C23×D61C22×C416yes—
73C22×C4×C61—24no—
74C22×C4×C61—24no—
75C22×C4×C61C22×C416yes—
76C22×C4×C61C22×C416yes—
77C22×C4×C61C22×C413yes—
78C22×C4×C61C2×D414yes—
79C22×C4×C61C2×Q814yes—
80C22×C4×C61C2413yes—
81C22×Dic61—24no—
82C22×Dic61—24no—
83C22×Dic61C4⋊C418yes—
84C22×Dic61C22×C416yes—
85C22×Dic61C22×C416yes—
86C22×Dic61C22×C416yes—
87C2×C4×D61C4⋊C4148yes—
88C2×C4×D61C22×C4112yes—
89C2×C4×D61C2×D4124yes—
90C2×C4×D61C2×Q8124yes—
91C2×C4×D61C2414yes—
92C2×C8×C61—212no—
93C2×C8×C61—212no—
94C2×C8×C61C2414yes—
95C2×C8×C61C2414yes—
96C42×C61C22×C4112yes—
97C42×C61C2414yes—
98#11758198C22×C4116yes—
99#11758198C22×C4116yes—
100#11758196C22×C4116yes—
101#11758196C22×C4116yes—
102C4×Dic61C22×C4112yes—
103C4×Dic61C2414yes—
104C2×#92418—212no—
105C2×#92418—212no—
106C2×#92418C2414yes—
107C2×#92418C2414yes—
108#11758189—232no—
109C8×D61—232no—
110C23×C61C2×C4⋊C414yes—
111C23×C61#13114yes—
112C23×C61#13114yes—
113C23×C61C23×C413yes—
114C22×D61—212no—
115C22×D61—212no—
116C22×D61—232no—
117C22×D61C2×C4⋊C4124yes—
118C22×D61C23×C414yes—
119C2×C4×C61—212no—
120C2×C4×C61—212no—
121C2×C4×C61C2×C4⋊C4112yes—
122C2×C4×C61C23×C414yes—
123C2×C4×C61C23×C414yes—
124C2×C4×C61C23×C413yes—
125C2×C4×C61C22×D416yes—
126C2×C4×C61C22×Q816yes—
127C2×C4×C61C2511yescharacteristic
128C2×Dic61—212no—
129C2×Dic61—212no—
130C2×Dic61C2×C4⋊C4124yes—
131C2×Dic61C23×C414yes—
132C2×Dic61C23×C414yes—
133C2×Dic61C23×C414yes—
134C4×D61C2×C4⋊C4148yes—
135C4×D61C22×D418yes—
136C4×D61C22×Q818yes—
137C8×C61—24no—
138C8×C61—24no—
139#92418—24no—
140#92418—24no—
141C22×#424—611nomaximal, Sylow
142C22×C61#424116yescomplemented
143C22×C61C22×C4⋊C416yes—
144C22×C61C2×#13116yes—
145C22×C61C2×#13116yes—
146C22×C61C24×C411yescharacteristic
147C2×D61—248no—
148C2×D61—24no—
149C2×D61—24no—
150C2×D61C22×C4⋊C418yes—
151C4×C61—24no—
152C4×C61—24no—
153C4×C61C22×C4⋊C416yes—
154C4×C61C23×D411yescharacteristic
155C4×C61C23×Q811yescharacteristic
156Dic61—24no—
157Dic61—24no—
158Dic61C22×C4⋊C418yes—
159C23×M16—611no—
160C24×C8—611no—
161C22×#117—611no—
162C2×#424—6124no—
163C22×C4⋊C8—611no—
164C22×C4⋊C8—611no—
165C22×C4⋊C8—611no—
166C22×C4⋊C8D6111yescharacteristic, complemented
167C2×C61C2×#424112yescomplemented
168C2×C61C23×C4⋊C411yescharacteristic
169C2×C61C22×#13111yescharacteristic
170C2×C61C22×#13111yescharacteristic
171D61—28no—
172C24×C4—611no—
173C22×M16—6112no—
174C22×M16—1228no—
175C23×C8—611no—
176C23×C8—611no—
177C23×C8—6112no—
178C23×C8—1228no—
179C23×C8C2×D6111yescharacteristic
180C23×C8C2×D6111yescharacteristic
181C2×#117—6112no—
182C2×#117—6112no—
183C22×C4⋊C4—611no—
184C22×C4⋊C4—611no—
185C22×C22⋊C4—611no—
186C22×C22⋊C4—611no—
187C22×C42—611no—
188C22×C42C2×D6111yescharacteristic
189#424—6164no—
190C2×C4⋊C8—6112no—
191C2×C4⋊C8—6112no—
192C2×C4⋊C8—6112no—
193C2×C4⋊C8C2×D61112yescomplemented
194C61C22×#42411yescharacteristic, complemented, Sylow
195C25—611no—
196C23×C4—611no—
197C23×C4—616no—
198C23×C4—618no—
199C23×C4—618no—
200C23×C4—616no—
201C23×C4—611no—
202C23×C4—611no—
203C23×C4C4×D6111yescharacteristic
204C23×C4C4×D6111yescharacteristic
205C23×C4C22×D6111yescharacteristic
206C2×M16—6116no—
207C2×M16—12248no—
208C22×C8—24no—
209C22×C8—24no—
210C22×C8—616no—
211C22×C8—616no—
212C22×C8—6116no—
213C22×C8—12248no—
214C22×C8—1224no—
215C22×C8—1224no—
216C22×C8C22×D6116yes—
217C22×C8C22×D6116yes—
218#117—6148no—
219#117—6116no—
220C2×C4⋊C4—6112no—
221C2×C4⋊C4—6112no—
222C2×C22⋊C4—6112no—
223C2×C22⋊C4—6112no—
224C2×C42—616no—
225C2×C42—616no—
226C2×C42C4×D6116yes—
227C2×C42C22×D6116yes—
228C4⋊C8—6116no—
229C4⋊C8—6116no—
230C4⋊C8—6116no—
231C4⋊C8C22×D61116yescomplemented
232C24—616no—
233C24—618no—
234C24—1224no—
235C24—1224no—
236C24C2×C4×D6111yescharacteristic
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—616no—
240C22×C4—618no—
241C22×C4—6112no—
242C22×C4—6124no—
243C22×C4—6124no—
244C22×C4—614no—
245C22×C4—6148no—
246C22×C4—616no—
247C22×C4—616no—
248C22×C4—1224no—
249C22×C4—1224no—
250C22×C4C2×C4×D6116yes—
251C22×C4C2×C4×D6116yes—
252C22×C4C2×C4×D6113yes—
253C22×C4D4×D6114yes—
254C22×C4Q8×D6114yes—
255C22×C4C23×D6113yes—
256M16—12232no—
257C2×C8—212no—
258C2×C8—212no—
259C2×C8—614no—
260C2×C8—614no—
261C2×C8—12232no—
262C2×C8—12212no—
263C2×C8—12212no—
264C2×C8C23×D6114yes—
265C2×C8C23×D6114yes—
266C4⋊C4—6116no—
267C4⋊C4—6116no—
268C22⋊C4—6116no—
269C22⋊C4—6116no—
270C42—6112no—
271C42—614no—
272C42C2×C4×D61112yes—
273C42C23×D6114yes—
274C23—6124no—
275C23—614no—
276C23—12212no—
277C23—12212no—
278C23—12232no—
279C23C4⋊C4×D6114yes—
280C23#1451978314yes—
281C23#1451978514yes—
282C23C22×C4×D6113yes—
283C2×C4—212no—
284C2×C4—212no—
285C2×C4—6124no—
286C2×C4—614no—
287C2×C4—6148no—
288C2×C4—618no—
289C2×C4—618no—
290C2×C4—614no—
291C2×C4—614no—
292C2×C4—12212no—
293C2×C4—12212no—
294C2×C4C4⋊C4×D61112yes—
295C2×C4C22×C4×D6114yes—
296C2×C4C22×C4×D6114yes—
297C2×C4C22×C4×D6113yes—
298C2×C4C2×D4×D6116yes—
299C2×C4C2×Q8×D6116yes—
300C2×C4C24×D6111yescharacteristic
301C8—24no—
302C8—24no—
303C8—1224no—
304C8—1224no—
305C22—618no—
306C22—12248no—
307C22—1224no—
308C22—1224no—
309C22#16839787116yesdirect product factor
310C22C2×C4⋊C4×D6116yes—
311C22C2×#1451978316yes—
312C22C2×#1451978516yes—
313C22C23×C4×D6111yescharacteristic
314C4—24no—
315C4—24no—
316C4—618no—
317C4—1224no—
318C4—1224no—
319C4C2×C4⋊C4×D6116yes—
320C4C22×D4×D6111yescharacteristic
321C4C22×Q8×D6111yescharacteristic
322C2—1228no—
323C2C2×#16839787112yesdirect product factor
324C2C22×C4⋊C4×D6111yescharacteristic
325C2C22×#1451978311yescharacteristic
326C2C22×#1451978511yescharacteristic
subgroupG/H
centerC23×C4C22×D61
commutatorC22×C61C24×C4
FrattiniC2×C4C24×D61
FittingC22×C4⋊C8×C61C2
socleC24×C61C22×C4
prime radicalC24×D61C2×C4
cosocleC2×C4×C61C25
hypercenterC22×C4⋊C8D61
hypocenterC61C22×#424
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C22×C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×#16839787C2direct (N × H)
5. C22×C4⋊#92418C2semidirect
6. C22×#14519706C2semidirect
7. C22×#14519706C2semidirect
8. C22×C4⋊C8×C61C2semidirect
23. #16839787C22direct (N × H)
24. C2×C4⋊#92418C22semidirect
25. C2×#14519706C22semidirect
26. C2×#14519706C22semidirect
30. C2×C4⋊C8×C61C22semidirect
55. C4⋊#92418C23semidirect
56. #14519706C23semidirect
57. #14519706C23semidirect
67. C4⋊C8×C61C23semidirect
142. C22×C61#424semidirect
166. C22×C4⋊C8D61semidirect
167. C2×C61C2×#424semidirect
193. C2×C4⋊C8C2×D61semidirect
194. C61C22×#424semidirect
231. C4⋊C8C22×D61semidirect
309. C22#16839787direct (N × H)
323. C2C2×#16839787direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117581892
C23×C8×D612
C22×#145197342
C2×#168397872
C22×C4⋊#924182
C22×#145197062
C22×C4⋊C8×C612
C22×#42461