Finite Group Databasebeta

← C2×#21446658 #29683776

Subgroups — C2×#21446658 #29683776

Order 15616.

2206 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519774C211yesmaximal, characteristic
2C22×#14519693C214yesmaximal, complemented
3C2×C4×#11758194C211yesmaximal, characteristic, complemented
4#21446658C218yesmaximal, direct product factor
5C2×C61×#423C211yesmaximal, characteristic, complemented
6C23×D244C414yes—
7C23×D244C2212yes—
8C22×#11758194C2212yes—
9C2×#14519774—21no—
10C2×#14519774—21no—
11C2×#14519774—22no—
12C2×#14519774—22no—
13C2×#14519774—22no—
14C2×#14519774C414yes—
15C2×#14519774C2214yes—
16C2×#14519693—216no—
17C2×#14519693C22116yescomplemented
18C4×#11758194—22no—
19C4×#11758194C2214yescomplemented
20C2×#14519688—21no—
21C2×C4×#92418—21no—
22C22×M16×C61C2212yes—
23C22×C42×C61C2211yescharacteristic
24C61×#423—22no—
25C61×#423C2214yescomplemented
26C2×C4⋊C8×C61—22no—
27C24×D61C2×C414yes—
28C22×D244—28no—
29C22×D244—24no—
30C22×D244—24no—
31C22×D244—28no—
32C22×D244—22no—
33C22×D244—22no—
34C22×D244—22no—
35C22×D244—22no—
36C22×D244—28no—
37C22×D244—416no—
38C22×D244C2×C414yes—
39C22×D244C2×C4116yes—
40C22×D244C2314yes—
41C2×#11758194—22no—
42C2×#11758194—24no—
43C2×#11758194D418yescomplemented
44C2×#11758194C2314yes—
45C22×#92418—22no—
46#14519774—24no—
47#14519774—28no—
48#14519774—24no—
49#14519774—24no—
50#14519774—24no—
51#14519774—28no—
52#14519693—232no—
53#14519688—24no—
54C4×#92418—24no—
55C23×C4×C61C2×C412yes—
56C23×C4×C61C2311yescharacteristic
57C2×M16×C61—22no—
58C2×M16×C61—28no—
59C2×M16×C61C2314yes—
60C22×C8×C61—22no—
61C2×C42×C61C2×C412yes—
62C2×C42×C61D411yescharacteristic
63C2×C42×C61D411yescharacteristic
64C2×C42×C61D412yes—
65C2×C42×C61D412yes—
66C2×C42×C61D412yes—
67C2×C42×C61C2312yes—
68C4⋊C8×C61—28no—
69C24×C61C22×C411yescharacteristic
70C23×D61—24no—
71C23×D61—24no—
72C23×D61—216no—
73C23×D61—416no—
74C23×D61C22×C418yes—
75C22×C4×C61—28no—
76C22×C4×C61C22⋊C412yes—
77C22×C4×C61C22⋊C414yes—
78C22×C4×C61C22⋊C412yes—
79C22×C4×C61C22×C414yes—
80C22×C4×C61C22×C411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D414yes—
86C22×C4×C61#4114yes—
87C22×C4×C61C2411yescharacteristic
88C2×D244—216no—
89C2×D244—24no—
90C2×D244—24no—
91C2×D244—216no—
92C2×D244—216no—
93C2×D244—28no—
94C2×D244—24no—
95C2×D244—24no—
96C2×D244—28no—
97C2×D244—416no—
98C2×D244—432no—
99C2×D244—416no—
100C2×D244—48no—
101C2×D244—48no—
102C2×D244—44no—
103C2×D244—44no—
104C2×D244—44no—
105C2×D244—44no—
106C2×D244—432no—
107M16×C61—28no—
108M16×C61—44no—
109C2×C8×C61—24no—
110C2×C8×C61—44no—
111C42×C61C22⋊C412yes—
112C42×C61C22⋊C414yes—
113C42×C61C22⋊C412yes—
114C42×C61C2×D412yes—
115C42×C61C2×D412yes—
116C42×C61C2×D414yes—
117#11758194—28no—
118#11758194—24no—
119#11758194C2×D418yescomplemented
120C2×#92418—28no—
121C2×#92418—24no—
122C23×C61—24no—
123C23×C61C2×C22⋊C411yescharacteristic
124C23×C61C2×C22⋊C411yescharacteristic
125C23×C61C4×D414yes—
126C23×C61C23×C411yescharacteristic
127C22×D61—28no—
128C22×D61—216no—
129C22×D61—416no—
130C22×D61—48no—
131C22×D61—48no—
132C22×D61—416no—
133C22×D61—416no—
134C22×D61—832no—
135C2×C4×C61—24no—
136C2×C4×C61—28no—
137C2×C4×C61—28no—
138C2×C4×C61#10018yescomplemented
139C2×C4×C61C2×C22⋊C414yes—
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C2×C4×C61C2×C22⋊C411yescharacteristic
142C2×C4×C61C2×C22⋊C414yes—
143C2×C4×C61C4×D414yes—
144C2×C4×C61#12114yes—
145C2×C4×C61#12114yes—
146C2×C4×C61#12412yes—
147C2×C4×C61#12412yes—
148C2×C4×C61#12712yes—
149C2×C4×C61#12712yes—
150C2×C4×C61C22×D411yescharacteristic
151C2×C4×C61C22×D412yes—
152C2×C4×C61C22×D411yescharacteristic
153C2×C4×C61C2×#4112yes—
154D244—432no—
155D244—48no—
156D244—44no—
157D244—44no—
158D244—48no—
159D244—48no—
160D244—432no—
161C8×C61—44no—
162#92418—28no—
163C2×#1965—611nomaximal, Sylow
164C22×C61—22no—
165C22×C61—22no—
166C22×C61—28no—
167C22×C61#39012yes—
168C22×C61#39012yes—
169C22×C61C2×#10014yes—
170C22×C61C22×C22⋊C411yescharacteristic
171C22×C61C2×C4×D412yes—
172C2×D61—416no—
173C2×D61—48no—
174C2×D61—816no—
175C2×D61—816no—
176C2×D61—816no—
177C4×C61—24no—
178C4×C61#39012yes—
179C4×C61#39012yes—
180C4×C61C2×#10018yescomplemented
181C4×C61C2×#12112yes—
182C4×C61C2×#12411yescharacteristic
183C4×C61C2×#12711yescharacteristic
184C22×#127—611no—
185C2×#423D6111yescharacteristic, complemented
186C22×#100—614no—
187C2×C4×M16—611no—
188#1965—618no—
189C2×C61—22no—
190C2×C61—22no—
191C2×C61#196514yescomplemented
192C2×C61C2×#39011yescharacteristic
193C2×C61C22×#10012yes—
194D61—88no—
195C23×D4—614no—
196C23×D4—612no—
197C22×M16—612no—
198C22×M16C2×D6112yes—
199C2×#127—614no—
200C2×#127—614no—
201C2×#127—1221no—
202C2×#127—1221no—
203C2×#127—1222no—
204C2×#127—1222no—
205C2×#127—1222no—
206C22×C42C2×D6111yescharacteristic
207#423—22no—
208#423C2×D6114yescomplemented
209C2×C4⋊C8—22no—
210C2×#100—6116no—
211C2×#100—12216no—
212C4×M16—614no—
213C4×M16—1222no—
214C2×#97—1221no—
215C2×C4×C8—1221no—
216C61C2×#196511yescharacteristic, complemented, Sylow
217C25—614no—
218C22×D4—614no—
219C22×D4—6116no—
220C22×D4—614no—
221C22×D4—1228no—
222C22×D4—1224no—
223C22×D4—1224no—
224C22×D4—1222no—
225C22×D4—1222no—
226C22×D4—1228no—
227C22×D4—1228no—
228C22×D4—1222no—
229C22×D4—1222no—
230C22×D4—24416no—
231C23×C4C4×D6112yes—
232C23×C4C22×D6111yescharacteristic
233C2×M16—22no—
234C2×M16—28no—
235C2×M16—618no—
236C2×M16—614no—
237C2×M16—1222no—
238C2×M16—1224no—
239C2×M16C22×D6114yes—
240C22×C8—22no—
241C22×C8—1222no—
242#127—1224no—
243#127—1228no—
244#127—1224no—
245#127—1224no—
246#127—1224no—
247#127—1228no—
248C2×C42C4×D6112yes—
249C2×C42D24411yescharacteristic
250C2×C42D24411yescharacteristic
251C2×C42D24412yes—
252C2×C42C22⋊D6112yes—
253C2×C42C22⋊D6112yes—
254C2×C42C22×D6112yes—
255C4⋊C8—28no—
256#100—12232no—
257#97—1224no—
258C4×C8—1224no—
259C24—618no—
260C24—12216no—
261C24—1224no—
262C24—1224no—
263C24—24416no—
264C24C2×C4×D6111yescharacteristic
265C2×D4—1228no—
266C2×D4—1224no—
267C2×D4—1224no—
268C2×D4—1228no—
269C2×D4—12216no—
270C2×D4—12216no—
271C2×D4—1224no—
272C2×D4—1224no—
273C2×D4—12216no—
274C2×D4—24416no—
275C2×D4—24432no—
276C2×D4—24432no—
277C2×D4—24416no—
278C2×D4—2448no—
279C2×D4—2448no—
280C2×D4—2444no—
281C2×D4—2444no—
282C2×D4—2444no—
283C2×D4—2444no—
284C22×C4—28no—
285C22×C4#1175819814yes—
286C22×C4#1175819812yes—
287C22×C4#1175819812yes—
288C22×C4C2×C4×D6114yes—
289C22×C4C2×C4×D6111yescharacteristic
290C22×C4C2×D24411yescharacteristic
291C22×C4C2×D24411yescharacteristic
292C22×C4D4×D6114yes—
293C22×C4#1175822614yes—
294C22×C4C2×C22⋊D6111yescharacteristic
295C22×C4C2×C22⋊D6111yescharacteristic
296C22×C4C23×D6111yescharacteristic
297M16—28no—
298M16—44no—
299M16—618no—
300M16—1224no—
301M16—1228no—
302C2×C8—24no—
303C2×C8—44no—
304C2×C8—1224no—
305C2×C8—1228no—
306C42#1175819812yes—
307C42#1175819814yes—
308C42#1175819812yes—
309C42C2×D24412yes—
310C42C2×D24412yes—
311C42C2×C22⋊D6114yes—
312C23—24no—
313C23—12216no—
314C23—1228no—
315C23—48832no—
316C23—24416no—
317C23—24416no—
318C23—24416no—
319C23—2448no—
320C23—2448no—
321C23C2×#1175819811yescharacteristic
322C23C2×#1175819811yescharacteristic
323C23#1451973914yes—
324C23C22×C4×D6111yescharacteristic
325D4—24432no—
326D4—24432no—
327D4—2448no—
328D4—2444no—
329D4—2444no—
330D4—2448no—
331D4—2448no—
332C2×C4—24no—
333C2×C4—28no—
334C2×C4—28no—
335C2×C4#1451969318yescomplemented
336C2×C4C2×#1175819814yes—
337C2×C4C2×#1175819814yes—
338C2×C4C2×#1175819811yescharacteristic
339C2×C4C2×#1175819811yescharacteristic
340C2×C4#1451973914yes—
341C2×C4#1451975214yes—
342C2×C4#1451975214yes—
343C2×C4#1451976612yes—
344C2×C4#1451976612yes—
345C2×C4#1451977312yes—
346C2×C4#1451977312yes—
347C2×C4C2×D4×D6112yes—
348C2×C4C22×C22⋊D6111yescharacteristic
349C2×C4C22×D24411yescharacteristic
350C2×C4C2×#1175822612yes—
351C8—44no—
352C8—1228no—
353C22—28no—
354C22—22no—
355C22—22no—
356C22—48816no—
357C22—48816no—
358C22—48816no—
359C22—2448no—
360C22—24416no—
361C22#1683966312yes—
362C22#1683966312yes—
363C22C2×#1451969314yes—
364C22C22×#1175819811yescharacteristic
365C22C2×#1451973912yes—
366C4—24no—
367C4#1683966312yes—
368C4#1683966312yes—
369C4C2×#1451969318yescomplemented
370C4C2×#1451975212yes—
371C4C2×#1451976611yescharacteristic
372C4C2×#1451977311yescharacteristic
373C2—22no—
374C2—22no—
375C2—4888no—
376C2#2144665814yesdirect product factor
377C2C2×#1683966311yescharacteristic
378C2C22×#1451969312yes—
subgroupG/H
centerC23C2×#11758198
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#423C2
socleC23×C61C2×C22⋊C4
prime radicalC22×#14519774C2
cosocleC22×C4×C61C24
hypercenterC2×#423D61
hypocenterC61C2×#1965
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
2. C22×#14519693C2semidirect
3. C2×C4×#11758194C2semidirect
4. #21446658C2direct (N × H)
5. C2×C61×#423C2semidirect
17. C2×#14519693C22semidirect
19. C4×#11758194C22semidirect
25. C61×#423C22semidirect
43. C2×#11758194D4semidirect
119. #11758194C2×D4semidirect
138. C2×C4×C61#100semidirect
180. C4×C61C2×#100semidirect
185. C2×#423D61semidirect
191. C2×C61#1965semidirect
208. #423C2×D61semidirect
216. C61C2×#1965semidirect
335. C2×C4#14519693semidirect
369. C4C2×#14519693semidirect
376. C2#21446658direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197742
C22×#145196932
C2×C4×#117581942
#214466582
C2×C61×#4232
C2×#196561