Finite Group Databasebeta

← C2×#21458801 #30560915

Subgroups — C2×#21458801 #30560915

Order 15616.

2238 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840491C211yesmaximal, characteristic, complemented
2C2×#16840434C211yesmaximal, characteristic
3#21458801C2116yesmaximal, direct product factor
4C2×#16840135C213yesmaximal, complemented
5C2×#16839963C213yesmaximal, complemented
6C2×#16839968C213yesmaximal, complemented
7C2×C4×#11758190C213yesmaximal, complemented
8C2×C8×Q8×C61C211yesmaximal, characteristic, complemented
9C22×#11758226—21no—
10C22×#11758190C2213yes—
11C22×#11758190C2216yes—
12#16840491—24no—
13#16840491C2218yescomplemented
14#16840434—24no—
15#16840434C2218yes—
16C2×#14519777C2213yes—
17C2×#14519774C2213yes—
18C2×#14519768—23no—
19C2×#14519752—23no—
20C2×Q8×Dic61—21no—
21C2×C4×Dic122C2213yes—
22C2×C4×D244C2213yes—
23#16840135C22124yescomplemented
24#16839968C22124yescomplemented
25#16839963C22124yescomplemented
26C4×#11758190C22124yescomplemented
27C2×#14519709C2211yescharacteristic
28C2×#14519702C2213yes—
29C2×#14519699C2213yes—
30C2×C4×Q8×C61C2211yescharacteristic
31C8×Q8×C61C2218yescomplemented
32C2×C4⋊C8×C61C2213yes—
33C2×C4×C8×C61C2213yes—
34C2×#11758226—28no—
35C2×#11758226—48no—
36C22×Dic122C2313yes—
37C22×D244—23no—
38C22×D244—23no—
39C22×D244C2313yes—
40C22×C4×D61—23no—
41C2×#11758190—212no—
42C2×#11758190—412no—
43C2×#11758190C23112yes—
44C2×#11758190C23124yes—
45#14519777—26no—
46#14519777C23112yes—
47#14519774—26no—
48#14519774C23112yes—
49#14519768—224no—
50#14519752—224no—
51Q8×Dic61—28no—
52C4×Dic122—26no—
53C4×Dic122C23112yes—
54C4×D244—26no—
55C4×D244C23112yes—
56C2×C4⋊Dic61—23no—
57C2×C4⋊Dic61—23no—
58C2×C4⋊Dic61C2311yescharacteristic
59C2×C4⋊Dic61C2311yescharacteristic
60C2×#11758196—23no—
61C2×#11758198—23no—
62C2×C4×Dic61—23no—
63#14519709C2314yes—
64#14519702C23112yes—
65#14519699C23112yes—
66C22×Q8×C61D411yescharacteristic
67C22×C8×C61C2313yes—
68C22×C8×C61C2311yescharacteristic
69C4×Q8×C61D414yes—
70C4×Q8×C61C2314yes—
71C2×C4⋊C4×C61D413yes—
72C2×C42×C61C2313yes—
73C4⋊C8×C61C23112yes—
74C4×C8×C61C23112yes—
75C23×D61—23no—
76C2×Q8×C61SD1618yescomplemented
77C2×Q8×C61C2×D414yes—
78C22×C4×C61C2×D413yes—
79C22×C4×C61C2×D413yes—
80C22×C4×C61C2411yescharacteristic
81C22×Dic61—21no—
82C22×Dic61—23no—
83C22×Dic61—21no—
84#11758226—432no—
85C2×D244—26no—
86C2×D244—26no—
87C2×D244—212no—
88C2×D244—23no—
89C2×D244—212no—
90C2×D244—412no—
91C2×D244—86no—
92C2×D244C2416yes—
93C2×C4×D61—212no—
94C2×C4×D61—412no—
95C2×Dic122—26no—
96C2×Dic122—26no—
97C2×Dic122—23no—
98C2×Dic122C2416yes—
99C2×C8×C61—26no—
100C2×C8×C61#4114yescomplemented
101C2×C8×C61C2416yes—
102C2×C8×C61C2412yes—
103C4⋊C4×C61C2×D4112yes—
104C42×C61C2×D416yes—
105C42×C61C2416yes—
106#11758198—212no—
107C4⋊Dic61—212no—
108C4⋊Dic61—212no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4⋊Dic61C2412yes—
112C4⋊Dic61C2412yes—
113#11758196—212no—
114C4×Dic61—212no—
115#11758190—224no—
116#11758190—424no—
117C23×C61C22×D411yescharacteristic
118C22×D61—26no—
119C22×D61—46no—
120C22×D61—46no—
121C22×D61—46no—
122Q8×C61C2×SD16116yescomplemented
123C2×C4×C61—26no—
124C2×C4×C61C2×SD16112yes—
125C2×C4×C61C22×D416yes—
126C2×C4×C61C22×D411yescharacteristic
127C2×C4×C61C22×D416yes—
128C2×C4×C61C2×#4112yes—
129C2×C4×C61H(5,𝔽2)12yes—
130C2×C4×C61C2511yescharacteristic
131C2×Dic61—22no—
132C2×Dic61—26no—
133C2×Dic61—22no—
134C2×Dic61—46no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137D244—26no—
138D244—26no—
139D244—46no—
140D244—424no—
141D244—812no—
142C4×D61—424no—
143Dic122—26no—
144Dic122—26no—
145Dic122—46no—
146C8×C61—26no—
147C8×C61C2×#4114yescomplemented
148C2×#3392—611nomaximal, Sylow
149C22×C61#55012yes—
150C22×C61C22×SD1612yes—
151C22×C61#57712yes—
152C22×C61C23×D411yescharacteristic
153C2×D61—46no—
154C2×D61—46no—
155C2×D61—46no—
156C2×D61—812no—
157C4×C61—26no—
158C4×C61#55012yes—
159C4×C61C22×SD16112yes—
160C4×C61C22×#4111yescharacteristic
161C4×C61C2×H(5,𝔽2)11yescharacteristic
162Dic61—46no—
163Dic61—42no—
164Dic61—42no—
165C2×#557—611no—
166C2×#550—611no—
167#3392—6116no—
168C2×#492—613no—
169C2×#460—613no—
170C2×#461—613no—
171C2×C8×Q8D6111yescharacteristic, complemented
172C2×C4×SD16—613no—
173C2×C61#339214yescomplemented
174C2×C61C2×#55011yescharacteristic
175C2×C61C23×SD1611yescharacteristic
176C2×C61C2×#57711yescharacteristic
177D61—86no—
178C22×#41—1221no—
179C22×SD16—613no—
180C22×SD16—616no—
181#557—618no—
182#557—1224no—
183#550—618no—
184#550—1224no—
185C2×C4⋊Q8—613no—
186C2×#127—613no—
187C2×#125—1223no—
188C2×#121—1223no—
189C2×C4×Q8—613no—
190C2×C4×Q8—1221no—
191C2×C4×Q8C2×D6111yescharacteristic
192C2×C4×D4—613no—
193#492—6124no—
194#461—6124no—
195#460—6124no—
196C8×Q8C2×D6118yescomplemented
197C4×SD16—6124no—
198C2×#106—611no—
199C2×C4⋊C8C2×D6113yes—
200C2×#103—613no—
201C2×#102—613no—
202C2×C4×C8C2×D6113yes—
203C61C2×#339211yescharacteristic, complemented, Sylow
204C2×#41—1228no—
205C2×#41—2448no—
206C22×Q8—613no—
207C22×Q8D24411yescharacteristic
208C22×D4—613no—
209C22×D4—1223no—
210C22×D4—1223no—
211C23×C4—1223no—
212C2×SD16—6112no—
213C2×SD16—6124no—
214C2×SD16—12212no—
215C2×SD16—24412no—
216C22×C8C22×D6113yes—
217C22×C8C22×D6111yescharacteristic
218C4⋊Q8—6112no—
219C4⋊Q8—1226no—
220#127—6112no—
221#127—1226no—
222#125—12224no—
223#121—12224no—
224C4×Q8—6112no—
225C4×Q8—1228no—
226C4×Q8—1226no—
227C4×Q8D24414yes—
228C4×Q8C22×D6114yes—
229C4×D4—6112no—
230C4×D4—1226no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—1223no—
234C2×C4⋊C4—1223no—
235C2×C4⋊C4—1223no—
236C2×C4⋊C4D24413yes—
237C2×C22⋊C4—1223no—
238C2×C42—1223no—
239C2×C42C22×D6113yes—
240#106—614no—
241C4⋊C8C22×D61112yes—
242#103—6112no—
243#102—6112no—
244C4×C8C22×D61112yes—
245C24—1223no—
246#41—24432no—
247C2×Q8—616no—
248C2×Q8—1223no—
249C2×Q8—1226no—
250C2×Q8—1226no—
251C2×Q8#1175819018yescomplemented
252C2×Q8C2×D24414yes—
253C2×D4—616no—
254C2×D4—12212no—
255C2×D4—1223no—
256C2×D4—12212no—
257C2×D4—1226no—
258C2×D4—1226no—
259C2×D4—4886no—
260C2×D4—24412no—
261C22×C4—1221no—
262C22×C4—1223no—
263C22×C4—1221no—
264C22×C4—12212no—
265C22×C4—24412no—
266C22×C4C2×D24413yes—
267C22×C4C2×D24413yes—
268C22×C4C23×D6111yescharacteristic
269SD16—12224no—
270SD16—24424no—
271C2×C8—26no—
272C2×C8#1175822614yescomplemented
273C2×C8C23×D6116yes—
274C2×C8C23×D6112yes—
275C4⋊C4—612no—
276C4⋊C4—612no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—12212no—
280C4⋊C4—12212no—
281C4⋊C4—12212no—
282C4⋊C4C2×D244112yes—
283C22⋊C4—12212no—
284C42—12212no—
285C42C2×D24416yes—
286C42C23×D6116yes—
287C23—1226no—
288C23—2446no—
289C23—2446no—
290C23—2446no—
291C23C22×D24411yescharacteristic
292Q8—1226no—
293Q8—1226no—
294Q8—2446no—
295Q8C2×#11758190116yescomplemented
296D4—1226no—
297D4—1226no—
298D4—48812no—
299D4—24424no—
300D4—2446no—
301C2×C4—26no—
302C2×C4—1222no—
303C2×C4—1226no—
304C2×C4—1222no—
305C2×C4—2442no—
306C2×C4—2442no—
307C2×C4—2446no—
308C2×C4—24424no—
309C2×C4C2×#11758190112yes—
310C2×C4C22×D24416yes—
311C2×C4C22×D24416yes—
312C2×C4C22×D24411yescharacteristic
313C2×C4C2×#1175822612yes—
314C2×C4#1451982312yes—
315C2×C4C24×D6111yescharacteristic
316C8—26no—
317C8C2×#1175822614yescomplemented
318C22—48812no—
319C22—2446no—
320C22—2446no—
321C22—2446no—
322C22#1684043412yes—
323C22C22×#1175819012yes—
324C22#1684057412yes—
325C22C23×D24411yescharacteristic
326C4—26no—
327C4—2442no—
328C4—2446no—
329C4—2442no—
330C4#1684043412yes—
331C4C22×#11758190112yes—
332C4C22×#1175822611yescharacteristic
333C4C2×#1451982311yescharacteristic
334C2—4886no—
335C2#2145880114yesdirect product factor
336C2C2×#1684043411yescharacteristic
337C2C23×#1175819011yescharacteristic
338C2C2×#1684057411yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C8×Q8×C61C2
socleC23×C61C22×D4
prime radicalC2×#16840434C2
hypercenterC2×C8×Q8D61
hypocenterC61C2×#3392
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16840491C2semidirect
3. #21458801C2direct (N × H)
4. C2×#16840135C2semidirect
5. C2×#16839963C2semidirect
6. C2×#16839968C2semidirect
7. C2×C4×#11758190C2semidirect
8. C2×C8×Q8×C61C2semidirect
13. #16840491C22semidirect
23. #16840135C22semidirect
24. #16839968C22semidirect
25. #16839963C22semidirect
26. C4×#11758190C22semidirect
31. C8×Q8×C61C22semidirect
76. C2×Q8×C61SD16semidirect
100. C2×C8×C61#41semidirect
122. Q8×C61C2×SD16semidirect
147. C8×C61C2×#41semidirect
171. C2×C8×Q8D61semidirect
173. C2×C61#3392semidirect
196. C8×Q8C2×D61semidirect
203. C61C2×#3392semidirect
251. C2×Q8#11758190semidirect
272. C2×C8#11758226semidirect
295. Q8C2×#11758190semidirect
317. C8C2×#11758226semidirect
335. C2#21458801direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404912
C2×#168404342
#214588012
C2×#168401352
C2×#168399632
C2×#168399682
C2×C4×#117581902
C2×C8×Q8×C612
C2×#339261