Finite Group Databasebeta

← C22×#16839530 #29677454

Subgroups — C22×#16839530 #29677454

Order 15616.

2494 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758194C211yesmaximal, characteristic
2C23×C4⋊Dic61C211yesmaximal, characteristic
3C2×#16839530C2112yesmaximal, direct product factor
4C23×M16×C61C211yesmaximal, characteristic
5C24×Dic61C412yes—
6C22×#11758194—23no—
7C22×#11758194—24no—
8C22×#11758194C418yescomplemented
9C22×#11758194C2216yes—
10C23×#92418—21no—
11C22×C4⋊Dic61—21no—
12C22×C4⋊Dic61—23no—
13C22×C4⋊Dic61—21no—
14C22×C4⋊Dic61—23no—
15C22×C4⋊Dic61C416yes—
16C22×C4⋊Dic61C2216yes—
17#16839530C22116yesdirect product factor
18C24×C4×C61C2211yescharacteristic
19C22×M16×C61—24no—
20C22×M16×C61—23no—
21C22×M16×C61C418yescomplemented
22C22×M16×C61C2216yes—
23C23×C8×C61—21no—
24C23×Dic61—26no—
25C23×Dic61—22no—
26C23×Dic61—48no—
27C23×Dic61C2×C4112yes—
28C2×#11758194—224no—
29C2×#11758194—212no—
30C2×#11758194—26no—
31C2×#11758194C2×C4124yescomplemented
32C2×#11758194C2314yes—
33C22×#92418—28no—
34C22×#92418—26no—
35C2×C4⋊Dic61—212no—
36C2×C4⋊Dic61—26no—
37C2×C4⋊Dic61—26no—
38C2×C4⋊Dic61—26no—
39C2×C4⋊Dic61—26no—
40C2×C4⋊Dic61—26no—
41C2×C4⋊Dic61—26no—
42C2×C4⋊Dic61C2×C4112yes—
43C2×C4⋊Dic61C2314yes—
44C25×C61C2×C411yescharacteristic
45C23×C4×C61C2×C413yes—
46C23×C4×C61C2×C414yes—
47C23×C4×C61C2×C414yes—
48C23×C4×C61D411yescharacteristic
49C23×C4×C61D413yes—
50C23×C4×C61D414yes—
51C23×C4×C61D411yescharacteristic
52C23×C4×C61D413yes—
53C23×C4×C61Q814yes—
54C23×C4×C61C2313yes—
55C2×M16×C61—224no—
56C2×M16×C61—212no—
57C2×M16×C61—26no—
58C2×M16×C61C2×C4124yescomplemented
59C2×M16×C61C2314yes—
60C22×C8×C61—28no—
61C22×C8×C61—26no—
62C24×C61—24no—
63C24×C61—24no—
64C24×C61C4214yes—
65C24×C61C22⋊C413yes—
66C24×C61C22⋊C411yescharacteristic
67C24×C61C4⋊C414yes—
68C24×C61C22×C413yes—
69C22×C4×C61C42112yes—
70C22×C4×C61C22⋊C416yes—
71C22×C4×C61C22⋊C413yes—
72C22×C4×C61C22⋊C413yes—
73C22×C4×C61C22⋊C414yes—
74C22×C4×C61C22⋊C4112yes—
75C22×C4×C61C22⋊C414yes—
76C22×C4×C61C22⋊C4112yes—
77C22×C4×C61C4⋊C4112yes—
78C22×C4×C61C4⋊C4112yes—
79C22×C4×C61C4⋊C414yes—
80C22×C4×C61C4⋊C4112yes—
81C22×C4×C61C4⋊C414yes—
82C22×C4×C61C22×C413yes—
83C22×C4×C61C22×C416yes—
84C22×C4×C61C22×C416yes—
85C22×C4×C61C2×D416yes—
86C22×C4×C61C2×D413yes—
87C22×C4×C61C2×D413yes—
88C22×C4×C61C2×D413yes—
89C22×C4×C61C2×D413yes—
90C22×C4×C61C2×Q816yes—
91C22×C4×C61C2411yescharacteristic
92C22×Dic61—212no—
93C22×Dic61—212no—
94C22×Dic61—424no—
95C22×Dic61—48no—
96C22×Dic61—424no—
97C22×Dic61C22×C418yes—
98M16×C61—224no—
99M16×C61—24no—
100M16×C61C22×C418yescomplemented
101C2×C8×C61—224no—
102C2×C8×C61—24no—
103C4⋊Dic61—212no—
104C4⋊Dic61—212no—
105C4⋊Dic61—24no—
106C4⋊Dic61—24no—
107#11758194—224no—
108#11758194—24no—
109#11758194C22×C418yescomplemented
110C2×#92418—224no—
111C2×#92418—24no—
112C23×C61—216no—
113C23×C61—216no—
114C23×C61—26no—
115C23×C61—26no—
116C23×C61—26no—
117C23×C61—26no—
118C23×C61#95112yes—
119C23×C61#9514yes—
120C23×C61#10014yes—
121C23×C61#10114yes—
122C23×C61C2×C4216yes—
123C23×C61C2×C22⋊C413yes—
124C23×C61C2×C22⋊C413yes—
125C23×C61C2×C4⋊C416yes—
126C23×C61C23×C411yescharacteristic
127C2×C4×C61#95124yes—
128C2×C4×C61#95112yes—
129C2×C4×C61#95112yes—
130C2×C4×C61C2×C4216yes—
131C2×C4×C61C2×C22⋊C416yes—
132C2×C4×C61C2×C22⋊C416yes—
133C2×C4×C61C2×C22⋊C416yes—
134C2×C4×C61C2×C22⋊C416yes—
135C2×C4×C61C2×C22⋊C413yes—
136C2×C4×C61C2×C22⋊C413yes—
137C2×C4×C61C2×C4⋊C416yes—
138C2×C4×C61C2×C4⋊C416yes—
139C2×C4×C61C2×C4⋊C416yes—
140C2×C4×C61C2×C4⋊C416yes—
141C2×C4×C61C2×C4⋊C416yes—
142C2×C4×C61C23×C411yescharacteristic
143C2×C4×C61C23×C411yescharacteristic
144C2×C4×C61C22×D411yescharacteristic
145C2×C4×C61C22×D411yescharacteristic
146C2×C4×C61C22×D411yescharacteristic
147C2×C4×C61C22×Q811yescharacteristic
148C2×Dic61—28no—
149C2×Dic61—424no—
150C2×Dic61—424no—
151C2×Dic61—48no—
152C8×C61—28no—
153#92418—28no—
154C22×#343—611nomaximal, Sylow
155C22×C61—23no—
156C22×C61—21no—
157C22×C61—23no—
158C22×C61—21no—
159C22×C61—224no—
160C22×C61—212no—
161C22×C61—212no—
162C22×C61#343116yescomplemented
163C22×C61C2×#9516yes—
164C22×C61C2×#9516yes—
165C22×C61C2×#10016yes—
166C22×C61C2×#10116yes—
167C22×C61C22×C4211yescharacteristic
168C22×C61C22×C22⋊C411yescharacteristic
169C22×C61C22×C4⋊C411yescharacteristic
170C4×C61C2×#9516yes—
171C4×C61C2×#9516yes—
172C4×C61C22×C22⋊C411yescharacteristic
173C4×C61C22×C22⋊C411yescharacteristic
174C4×C61C22×C4⋊C411yescharacteristic
175C4×C61C22×C4⋊C411yescharacteristic
176Dic61—48no—
177C23×M16—611no—
178C23×M16D6111yescharacteristic
179C23×C4⋊C4—611no—
180C2×#343—6112no—
181C2×C61—21no—
182C2×C61—26no—
183C2×C61—21no—
184C2×C61C2×#343112yescomplemented
185C2×C61C22×#9511yescharacteristic
186C2×C61C22×#10011yescharacteristic
187C2×C61C22×#10111yescharacteristic
188C24×C4—612no—
189C24×C4C2×D6111yescharacteristic
190C22×M16—24no—
191C22×M16—23no—
192C22×M16—618no—
193C22×M16—616no—
194C22×M16—1223no—
195C22×M16—1224no—
196C22×M16Dic6118yescomplemented
197C22×M16C2×D6116yes—
198C23×C8—21no—
199C23×C8—1221no—
200C22×C4⋊C4—616no—
201C22×C4⋊C4—616no—
202C22×C4⋊C4—1223no—
203C22×C4⋊C4—1221no—
204C22×C4⋊C4—1223no—
205C22×C4⋊C4—1221no—
206#343—6116no—
207C61C22×#34311yescharacteristic, complemented, Sylow
208C25C4×D6111yescharacteristic
209C23×C4—6112no—
210C23×C4—1226no—
211C23×C4—1222no—
212C23×C4—2448no—
213C23×C4Dic12214yes—
214C23×C4C4×D6113yes—
215C23×C4C4×D6114yes—
216C23×C4D24413yes—
217C23×C4D24411yescharacteristic
218C23×C4C2×Dic6114yes—
219C23×C4C22⋊D6113yes—
220C23×C4C22⋊D6111yescharacteristic
221C23×C4C22⋊D6114yes—
222C23×C4C22×D6113yes—
223C2×M16—224no—
224C2×M16—26no—
225C2×M16—212no—
226C2×M16—6124no—
227C2×M16—614no—
228C2×M16—12224no—
229C2×M16—1226no—
230C2×M16—12212no—
231C2×M16C2×Dic61124yescomplemented
232C2×M16C22×D6114yes—
233C22×C8—28no—
234C22×C8—26no—
235C22×C8—1228no—
236C22×C8—1226no—
237C2×C4⋊C4—6112no—
238C2×C4⋊C4—614no—
239C2×C4⋊C4—12212no—
240C2×C4⋊C4—1226no—
241C2×C4⋊C4—1226no—
242C2×C4⋊C4—1226no—
243C2×C4⋊C4—1226no—
244C2×C4⋊C4—1226no—
245C2×C4⋊C4—1226no—
246C24—24no—
247C24—24no—
248C24C4×Dic6114yes—
249C24#1175819614yes—
250C24#1175819813yes—
251C24#1175819811yescharacteristic
252C24C2×C4×D6113yes—
253C22×C4—618no—
254C22×C4—12212no—
255C22×C4—12212no—
256C22×C4—24424no—
257C22×C4—2448no—
258C22×C4—24424no—
259C22×C4C4×Dic61112yes—
260C22×C4#11758196112yes—
261C22×C4#11758196112yes—
262C22×C4#1175819614yes—
263C22×C4C4⋊Dic61112yes—
264C22×C4C4⋊Dic6114yes—
265C22×C4#1175819816yes—
266C22×C4#1175819813yes—
267C22×C4#1175819813yes—
268C22×C4#1175819814yes—
269C22×C4#11758198112yes—
270C22×C4C22⋊Dic6114yes—
271C22×C4C22⋊Dic61112yes—
272C22×C4C2×Dic12216yes—
273C22×C4C2×C4×D6116yes—
274C22×C4C2×C4×D6113yes—
275C22×C4C2×D24413yes—
276C22×C4C2×D24413yes—
277C22×C4C22×Dic6116yes—
278C22×C4C2×C22⋊D6116yes—
279C22×C4C2×C22⋊D6113yes—
280C22×C4C2×C22⋊D6113yes—
281C22×C4C23×D6111yescharacteristic
282M16—24no—
283M16—224no—
284M16—618no—
285M16—1224no—
286M16—12224no—
287M16C22×Dic6118yescomplemented
288C2×C8—24no—
289C2×C8—224no—
290C2×C8—1224no—
291C2×C8—12224no—
292C4⋊C4—1224no—
293C4⋊C4—1224no—
294C4⋊C4—12212no—
295C4⋊C4—12212no—
296C23—26no—
297C23—26no—
298C23—26no—
299C23—26no—
300C23—216no—
301C23—216no—
302C23#14519684112yes—
303C23#1451968414yes—
304C23#1451969314yes—
305C23#1451969514yes—
306C23C2×C4×Dic6116yes—
307C23C2×#1175819813yes—
308C23C2×#1175819813yes—
309C23C2×#1175819616yes—
310C23C22×C4×D6111yescharacteristic
311C2×C4—1228no—
312C2×C4—24424no—
313C2×C4—24424no—
314C2×C4—2448no—
315C2×C4#14519684124yes—
316C2×C4#14519684112yes—
317C2×C4#14519684112yes—
318C2×C4C2×C4×Dic6116yes—
319C2×C4C2×#1175819816yes—
320C2×C4C2×#1175819816yes—
321C2×C4C2×#1175819813yes—
322C2×C4C2×#1175819813yes—
323C2×C4C2×C22⋊Dic6116yes—
324C2×C4C2×C22⋊Dic6116yes—
325C2×C4C2×#1175819616yes—
326C2×C4C2×#1175819616yes—
327C2×C4C2×#1175819616yes—
328C2×C4C2×C4⋊Dic6116yes—
329C2×C4C2×C4⋊Dic6116yes—
330C2×C4C22×C4×D6111yescharacteristic
331C2×C4C23×Dic6111yescharacteristic
332C2×C4C22×C22⋊D6111yescharacteristic
333C2×C4C22×C22⋊D6111yescharacteristic
334C2×C4C22×D24411yescharacteristic
335C2×C4C22×Dic12211yescharacteristic
336C8—28no—
337C8—1228no—
338C22—224no—
339C22—212no—
340C22—212no—
341C22—21no—
342C22—23no—
343C22—21no—
344C22—23no—
345C22#16839530116yesdirect product factor
346C22C2×#1451968416yes—
347C22C2×#1451968416yes—
348C22C2×#1451969316yes—
349C22C2×#1451969516yes—
350C22C22×C4×Dic6111yescharacteristic
351C22C22×#1175819811yescharacteristic
352C22C22×#1175819611yescharacteristic
353C4—2448no—
354C4C2×#1451968416yes—
355C4C2×#1451968416yes—
356C4C22×#1175819811yescharacteristic
357C4C22×C22⋊Dic6111yescharacteristic
358C4C22×#1175819611yescharacteristic
359C4C22×C4⋊Dic6111yescharacteristic
360C2—21no—
361C2—21no—
362C2—26no—
363C2C2×#16839530112yesdirect product factor
364C2C22×#1451968411yescharacteristic
365C2C22×#1451969311yescharacteristic
366C2C22×#1451969511yescharacteristic
subgroupG/H
centerC24#11758198
commutatorC22×C61C22×C42
FrattiniC22×C4C23×D61
FittingC23×M16×C61C2
socleC24×C61C22⋊C4
prime radicalC25×C61C2×C4
cosocleC22×C4×C61C24
hypercenterC23×M16D61
hypocenterC61C22×#343
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C24×C4 ◁ C23×M16

Complements

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

NH ≅ G/Ntype
3. C2×#16839530C2direct (N × H)
8. C22×#11758194C4semidirect
17. #16839530C22direct (N × H)
21. C22×M16×C61C4semidirect
31. C2×#11758194C2×C4semidirect
58. C2×M16×C61C2×C4semidirect
100. M16×C61C22×C4semidirect
109. #11758194C22×C4semidirect
162. C22×C61#343semidirect
184. C2×C61C2×#343semidirect
196. C22×M16Dic61semidirect
207. C61C22×#343semidirect
231. C2×M16C2×Dic61semidirect
287. M16C22×Dic61semidirect
345. C22#16839530direct (N × H)
363. C2C2×#16839530direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117581942
C23×C4⋊Dic612
C2×#168395302
C23×M16×C612
C22×#34361