Finite Group Databasebeta

← C2×#21458491 #30559610

Subgroups — C2×#21458491 #30559610

Order 15616.

2174 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×Q8×Dic122C211yesmaximal, characteristic, complemented
2C2×#16840434C211yesmaximal, characteristic
3#21458491C2116yesmaximal, direct product factor
4C2×#16840109C213yesmaximal, complemented
5C2×#16840053C213yesmaximal, complemented
6C2×#16839963C213yesmaximal, complemented
7C2×C4×#11758190C213yesmaximal, complemented
8C2×C8×Q8×C61C211yesmaximal, characteristic, complemented
9C22×#11758226—21no—
10C22×#11758190C2213yes—
11Q8×Dic122—24no—
12Q8×Dic122C2218yescomplemented
13#16840434—24no—
14#16840434C2218yes—
15C2×#14519777C2213yes—
16C2×#14519776—23no—
17C2×#14519774C2213yes—
18C2×#14519752—23no—
19C2×Q8×Dic61—21no—
20C2×C4×Dic122C2213yes—
21C2×C4×D244C2213yes—
22#16840109C22124yescomplemented
23#16840053C22124yescomplemented
24#16839963C22124yescomplemented
25C4×#11758190C22124yescomplemented
26C2×#14519709C2213yes—
27C2×#14519702C2211yescharacteristic
28C2×#14519699C2216yes—
29C2×#14519699C2213yes—
30C2×C4×Q8×C61C2211yescharacteristic
31C8×Q8×C61C2218yescomplemented
32C2×C4⋊C8×C61C2213yes—
33C2×C4×C8×C61C2213yes—
34C2×#11758226—28no—
35C2×#11758226—48no—
36C22×Dic122—23no—
37C22×Dic122C2311yescharacteristic
38C22×D244—23no—
39C22×D244—23no—
40C22×D244C2313yes—
41C22×C4×D61—23no—
42C2×#11758190—212no—
43C2×#11758190C23112yes—
44#14519777—26no—
45#14519777C23112yes—
46#14519776—224no—
47#14519774—26no—
48#14519774C23112yes—
49#14519752—224no—
50Q8×Dic61—28no—
51C4×Dic122—26no—
52C4×Dic122C23112yes—
53C4×D244—26no—
54C4×D244C23112yes—
55C2×C4⋊Dic61—23no—
56C2×C4⋊Dic61C2311yescharacteristic
57C2×C4⋊Dic61C2313yes—
58C2×#11758196—23no—
59C2×#11758198—23no—
60C2×C4×Dic61—23no—
61#14519709C23112yes—
62#14519702C2314yes—
63#14519699C23124yes—
64#14519699C23112yes—
65C22×Q8×C61D411yescharacteristic
66C22×C8×C61C2311yescharacteristic
67C22×C8×C61C2313yes—
68C4×Q8×C61D414yes—
69C4×Q8×C61C2314yes—
70C2×C4⋊C4×C61D413yes—
71C2×C42×C61C2313yes—
72C4⋊C8×C61C23112yes—
73C4×C8×C61C23112yes—
74C23×D61—23no—
75C2×Q8×C61SD1618yescomplemented
76C2×Q8×C61C2×D414yes—
77C22×C4×C61C2×D413yes—
78C22×C4×C61C2×D413yes—
79C22×C4×C61C2411yescharacteristic
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—23no—
83#11758226—432no—
84C2×D244—26no—
85C2×D244—26no—
86C2×D244—212no—
87C2×D244—23no—
88C2×D244—212no—
89C2×D244—412no—
90C2×D244—86no—
91C2×D244C2416yes—
92C2×C4×D61—212no—
93C2×C4×D61—412no—
94C2×Dic122—21no—
95C2×Dic122—22no—
96C2×Dic122—212no—
97C2×Dic122—86no—
98C2×Dic122#4114yescomplemented
99C2×Dic122C2412yes—
100C2×C8×C61—26no—
101C2×C8×C61—22no—
102C2×C8×C61C2412yes—
103C2×C8×C61C2416yes—
104C4⋊C4×C61C2×D4112yes—
105C42×C61C2×D416yes—
106C42×C61C2416yes—
107#11758198—212no—
108C4⋊Dic61—212no—
109C4⋊Dic61—21no—
110C4⋊Dic61—23no—
111C4⋊Dic61C2416yes—
112C4⋊Dic61C2412yes—
113#11758196—212no—
114C4×Dic61—212no—
115#11758190—224no—
116C23×C61C22×D411yescharacteristic
117C22×D61—26no—
118C22×D61—46no—
119C22×D61—46no—
120C22×D61—46no—
121Q8×C61C2×SD16116yescomplemented
122C2×C4×C61—26no—
123C2×C4×C61C2×SD16112yes—
124C2×C4×C61C22×D416yes—
125C2×C4×C61C22×D411yescharacteristic
126C2×C4×C61C22×D416yes—
127C2×C4×C61C2×#4112yes—
128C2×C4×C612−1+412yes—
129C2×C4×C61C2511yescharacteristic
130C2×Dic61—24no—
131C2×Dic61—22no—
132C2×Dic61—26no—
133C2×Dic61—22no—
134C2×Dic61—42no—
135C2×Dic61—46no—
136D244—26no—
137D244—26no—
138D244—46no—
139D244—424no—
140D244—812no—
141C4×D61—424no—
142Dic122—24no—
143Dic122—22no—
144Dic122—812no—
145Dic122C2×#4114yescomplemented
146C8×C61—26no—
147C8×C61—22no—
148C2×#3362—611nomaximal, Sylow
149C22×C61#54812yes—
150C22×C61C22×SD1612yes—
151C22×C61#57612yes—
152C22×C61C23×D411yescharacteristic
153C2×D61—46no—
154C2×D61—46no—
155C2×D61—46no—
156C2×D61—812no—
157C4×C61—26no—
158C4×C61#54812yes—
159C4×C61C22×SD16112yes—
160C4×C61C22×#4111yescharacteristic
161C4×C61C2×2−1+411yescharacteristic
162Dic61—24no—
163Dic61—42no—
164Dic61—46no—
165C2×Q82—611no—
166C2×#550—611no—
167#3362—6116no—
168C2×#486—613no—
169C2×#476—613no—
170C2×#460—613no—
171C2×C8×Q8D6111yescharacteristic, complemented
172C2×C4×SD16—613no—
173C2×C61#336214yescomplemented
174C2×C61C2×#54811yescharacteristic
175C2×C61C23×SD1611yescharacteristic
176C2×C61C2×#57611yescharacteristic
177D61—86no—
178C22×#41—1221no—
179C22×SD16—613no—
180Q82—618no—
181Q82—1224no—
182#550—618no—
183#550—1224no—
184C2×C4⋊Q8—613no—
185C2×C4⋊Q8—1223no—
186C2×#127—613no—
187C2×#121—1223no—
188C2×C4×Q8—613no—
189C2×C4×Q8—1221no—
190C2×C4×Q8C2×D6111yescharacteristic
191C2×C4×D4—613no—
192#486—6124no—
193#476—6124no—
194#460—6124no—
195C8×Q8C2×D6118yescomplemented
196C4×SD16—6124no—
197C2×#106—613no—
198C2×C4⋊C8C2×D6113yes—
199C2×#103—611no—
200C2×#102—613no—
201C2×#102—616no—
202C2×C4×C8C2×D6113yes—
203C61C2×#336211yescharacteristic, complemented, Sylow
204C2×#41—1228no—
205C2×#41—2448no—
206C22×Q8—611no—
207C22×Q8—1223no—
208C22×Q8D24411yescharacteristic
209C22×D4—613no—
210C22×D4—1223no—
211C22×D4—1223no—
212C23×C4—1223no—
213C2×SD16—6112no—
214C2×SD16—12212no—
215C22×C8C22×D6113yes—
216C22×C8C22×D6111yescharacteristic
217C4⋊Q8—6112no—
218C4⋊Q8—12224no—
219C4⋊Q8—1226no—
220#127—6112no—
221#127—1226no—
222#121—12224no—
223C4×Q8—6112no—
224C4×Q8—1228no—
225C4×Q8—1226no—
226C4×Q8D24414yes—
227C4×Q8C22×D6114yes—
228C4×D4—6112no—
229C4×D4—1226no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—613no—
232C2×C4⋊C4—1223no—
233C2×C4⋊C4—1223no—
234C2×C4⋊C4D24413yes—
235C2×C22⋊C4—1223no—
236C2×C42—1223no—
237C2×C42C22×D6113yes—
238#106—6112no—
239C4⋊C8C22×D61112yes—
240#103—614no—
241#102—6112no—
242#102—6124no—
243C4×C8C22×D61112yes—
244C24—1223no—
245#41—24432no—
246C2×Q8—614no—
247C2×Q8—612no—
248C2×Q8—1221no—
249C2×Q8—12212no—
250C2×Q8—1222no—
251C2×Q8—4886no—
252C2×Q8#1175819018yescomplemented
253C2×Q8C2×D24414yes—
254C2×D4—616no—
255C2×D4—12212no—
256C2×D4—1223no—
257C2×D4—12212no—
258C2×D4—1226no—
259C2×D4—1226no—
260C2×D4—4886no—
261C2×D4—24412no—
262C22×C4—1221no—
263C22×C4—1223no—
264C22×C4—1221no—
265C22×C4—12212no—
266C22×C4—24412no—
267C22×C4C2×D24413yes—
268C22×C4C2×D24413yes—
269C22×C4C23×D6111yescharacteristic
270SD16—12224no—
271C2×C8—26no—
272C2×C8—22no—
273C2×C8C23×D6112yes—
274C2×C8C23×D6116yes—
275C4⋊C4—616no—
276C4⋊C4—612no—
277C4⋊C4—1221no—
278C4⋊C4—1223no—
279C4⋊C4—12212no—
280C4⋊C4—12212no—
281C4⋊C4C2×D244112yes—
282C22⋊C4—12212no—
283C42—12212no—
284C42C2×D24416yes—
285C42C23×D6116yes—
286C23—1226no—
287C23—2446no—
288C23—2446no—
289C23—2446no—
290C23C22×D24411yescharacteristic
291Q8—614no—
292Q8—1222no—
293Q8—1224no—
294Q8—48812no—
295Q8C2×#11758190116yescomplemented
296D4—1226no—
297D4—1226no—
298D4—48812no—
299D4—24424no—
300D4—2446no—
301C2×C4—26no—
302C2×C4—1222no—
303C2×C4—1224no—
304C2×C4—1226no—
305C2×C4—1222no—
306C2×C4—2442no—
307C2×C4—2446no—
308C2×C4—24424no—
309C2×C4C2×#11758190112yes—
310C2×C4C22×D24416yes—
311C2×C4C22×D24416yes—
312C2×C4C22×D24411yescharacteristic
313C2×C4#41×D6112yes—
314C2×C4#1451982512yes—
315C2×C4C24×D6111yescharacteristic
316C8—26no—
317C8—22no—
318C22—48812no—
319C22—2446no—
320C22—2446no—
321C22—2446no—
322C22#1684042412yes—
323C22C22×#1175819012yes—
324C22#1684056712yes—
325C22C23×D24411yescharacteristic
326C4—26no—
327C4—1224no—
328C4—2442no—
329C4—2446no—
330C4#1684042412yes—
331C4C22×#11758190112yes—
332C4C2×#41×D6111yescharacteristic
333C4C2×#1451982511yescharacteristic
334C2—4886no—
335C2#2145849114yesdirect product factor
336C2C2×#1684042411yescharacteristic
337C2C23×#1175819011yescharacteristic
338C2C2×#1684056711yescharacteristic
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×#3362
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×Q8×Dic122C2semidirect
3. #21458491C2direct (N × H)
4. C2×#16840109C2semidirect
5. C2×#16840053C2semidirect
6. C2×#16839963C2semidirect
7. C2×C4×#11758190C2semidirect
8. C2×C8×Q8×C61C2semidirect
12. Q8×Dic122C22semidirect
22. #16840109C22semidirect
23. #16840053C22semidirect
24. #16839963C22semidirect
25. C4×#11758190C22semidirect
31. C8×Q8×C61C22semidirect
75. C2×Q8×C61SD16semidirect
98. C2×Dic122#41semidirect
121. Q8×C61C2×SD16semidirect
145. Dic122C2×#41semidirect
171. C2×C8×Q8D61semidirect
173. C2×C61#3362semidirect
195. C8×Q8C2×D61semidirect
203. C61C2×#3362semidirect
252. C2×Q8#11758190semidirect
295. Q8C2×#11758190semidirect
335. C2#21458491direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic1222
C2×#168404342
#214584912
C2×#168401092
C2×#168400532
C2×#168399632
C2×C4×#117581902
C2×C8×Q8×C612
C2×#336261