Finite Group Databasebeta

← C2×#21458486 #30559605

Subgroups — C2×#21458486 #30559605

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
2#21458486C2116yesmaximal, direct product factor
3C2×#16840108C213yesmaximal, complemented
4C2×#16840052C213yesmaximal, complemented
5C2×#16839959C213yesmaximal, complemented
6C2×Q8×#92418C211yesmaximal, characteristic, complemented
7C2×C4×#11758200C213yesmaximal, complemented
8C2×C61×#550C211yesmaximal, characteristic
9C22×#11758200C2213yes—
10Q8×Dic122—24no—
11Q8×Dic122C2218yescomplemented
12C2×#14519777C2213yes—
13C2×#14519776—23no—
14C2×Q8×Dic61—21no—
15C2×C4×Dic122C2213yes—
16#16840108C22124yescomplemented
17#16840052C22124yescomplemented
18#16839959C22124yescomplemented
19Q8×#92418C2218yescomplemented
20C4×#11758200C22124yescomplemented
21C2×#14519708C2213yes—
22C2×C4⋊#92418C2213yes—
23C2×#14519700C2211yescharacteristic
24C2×#14519698C2216yes—
25C2×#14519698C2213yes—
26C2×C4×#92418C2213yes—
27C22×#41×C61—21no—
28C61×#550—24no—
29C61×#550C2218yes—
30C2×#127×C61C2213yes—
31C2×#121×C61—23no—
32C2×C4×Q8×C61C2211yescharacteristic
33C2×C4×D4×C61C2213yes—
34C22×Dic122—23no—
35C22×Dic122C2311yescharacteristic
36C2×#11758200—212no—
37C2×#11758200C23112yes—
38C22×#92418C2311yescharacteristic
39C22×#92418C2313yes—
40#14519777—26no—
41#14519777C23112yes—
42#14519776—224no—
43Q8×Dic61—28no—
44C4×Dic122—26no—
45C4×Dic122C23112yes—
46C2×C4⋊Dic61—23no—
47C2×C4⋊Dic61C2313yes—
48C2×#11758196—23no—
49C2×C4×Dic61—23no—
50#14519708C23112yes—
51C4⋊#92418C23112yes—
52#14519700C2314yes—
53#14519698C23124yes—
54#14519698C23112yes—
55C4×#92418C23112yes—
56C2×#41×C61—28no—
57C2×#41×C61—48no—
58C22×Q8×C61D411yescharacteristic
59C22×D4×C61—23no—
60C22×D4×C61—23no—
61C22×D4×C61C2313yes—
62C23×C4×C61—23no—
63#127×C61—26no—
64#127×C61C23112yes—
65#121×C61—224no—
66C4×Q8×C61D414yes—
67C4×Q8×C61C2314yes—
68C4×D4×C61—26no—
69C4×D4×C61C23112yes—
70C2×C4⋊C4×C61D413yes—
71C2×C4⋊C4×C61C2311yescharacteristic
72C2×C22⋊C4×C61—23no—
73C2×C42×C61C2313yes—
74C24×C61—23no—
75#41×C61—432no—
76C2×Q8×C61SD1618yescomplemented
77C2×Q8×C61C2×D414yes—
78C2×D4×C61—23no—
79C2×D4×C61—212no—
80C2×D4×C61—212no—
81C2×D4×C61—26no—
82C2×D4×C61—26no—
83C2×D4×C61—412no—
84C2×D4×C61—86no—
85C2×D4×C61C2416yes—
86C22×C4×C61—21no—
87C22×C4×C61—212no—
88C22×C4×C61—412no—
89C22×C4×C61C2×D413yes—
90C22×C4×C61C2×D413yes—
91C22×C4×C61C2411yescharacteristic
92C22×Dic61—21no—
93C22×Dic61—23no—
94C2×Dic122—21no—
95C2×Dic122—22no—
96C2×Dic122—212no—
97C2×Dic122—86no—
98C2×Dic122#4114yescomplemented
99C2×Dic122C2412yes—
100C4⋊C4×C61—21no—
101C4⋊C4×C61C2×D4112yes—
102C4⋊C4×C61C2412yes—
103C22⋊C4×C61—212no—
104C42×C61C2×D416yes—
105C42×C61C2416yes—
106#11758200—224no—
107C4⋊Dic61—212no—
108C4⋊Dic61—23no—
109C4⋊Dic61C2416yes—
110#11758196—212no—
111C4×Dic61—212no—
112C2×#92418—26no—
113C2×#92418—22no—
114C2×#92418C2412yes—
115C2×#92418C2416yes—
116C23×C61—26no—
117C23×C61—46no—
118C23×C61—46no—
119C23×C61—46no—
120C23×C61C22×D411yescharacteristic
121Q8×C61C2×SD16116yescomplemented
122D4×C61—26no—
123D4×C61—26no—
124D4×C61—46no—
125D4×C61—424no—
126D4×C61—812no—
127C2×C4×C61—26no—
128C2×C4×C61—22no—
129C2×C4×C61—42no—
130C2×C4×C61—424no—
131C2×C4×C61C2×SD16112yes—
132C2×C4×C61C22×D416yes—
133C2×C4×C61C22×D411yescharacteristic
134C2×C4×C61C22×D416yes—
135C2×C4×C61C2×#4112yes—
136C2×C4×C612−1+412yes—
137C2×C4×C61C2511yescharacteristic
138C2×Dic61—24no—
139C2×Dic61—22no—
140C2×Dic61—26no—
141C2×Dic61—46no—
142Dic122—24no—
143Dic122—22no—
144Dic122—812no—
145Dic122C2×#4114yescomplemented
146#92418—26no—
147#92418—22no—
148C2×#3362—611nomaximal, Sylow
149C22×C61—46no—
150C22×C61—46no—
151C22×C61—46no—
152C22×C61—812no—
153C22×C61#54812yes—
154C22×C61C22×SD1612yes—
155C22×C61#57612yes—
156C22×C61C23×D411yescharacteristic
157C4×C61—26no—
158C4×C61—42no—
159C4×C61#54812yes—
160C4×C61C22×SD16112yes—
161C4×C61C22×#4111yescharacteristic
162C4×C61C2×2−1+411yescharacteristic
163Dic61—24no—
164Dic61—46no—
165C2×Q82—611no—
166C2×#550D6111yescharacteristic
167#3362—6116no—
168C2×#486—613no—
169C2×#476—613no—
170C2×#460—613no—
171C2×C8×Q8—611no—
172C2×C4×SD16—613no—
173C2×C61—86no—
174C2×C61#336214yescomplemented
175C2×C61C2×#54811yescharacteristic
176C2×C61C23×SD1611yescharacteristic
177C2×C61C2×#57611yescharacteristic
178C22×#41—21no—
179C22×SD16—613no—
180Q82—618no—
181Q82—1224no—
182#550—24no—
183#550C2×D6118yes—
184C2×C4⋊Q8—613no—
185C2×C4⋊Q8—1223no—
186C2×#127C2×D6113yes—
187C2×#121—23no—
188C2×C4×Q8—613no—
189C2×C4×Q8—1221no—
190C2×C4×Q8C2×D6111yescharacteristic
191C2×C4×D4C2×D6113yes—
192#486—6124no—
193#476—6124no—
194#460—6124no—
195C8×Q8—618no—
196C4×SD16—6124no—
197C2×#106—613no—
198C2×C4⋊C8—613no—
199C2×#103—611no—
200C2×#102—613no—
201C2×#102—616no—
202C2×C4×C8—613no—
203C61C2×#336211yescharacteristic, complemented, Sylow
204C2×#41—28no—
205C2×#41—48no—
206C22×Q8—611no—
207C22×Q8—1223no—
208C22×Q8C22⋊D6111yescharacteristic
209C22×D4—23no—
210C22×D4—23no—
211C22×D4C22×D6113yes—
212C23×C4—23no—
213C2×SD16—6112no—
214C2×SD16—12212no—
215C22×C8—613no—
216C22×C8—611no—
217C4⋊Q8—6112no—
218C4⋊Q8—12224no—
219C4⋊Q8—1226no—
220#127—26no—
221#127C22×D61112yes—
222#121—224no—
223C4×Q8—6112no—
224C4×Q8—1228no—
225C4×Q8—1226no—
226C4×Q8C22⋊D6114yes—
227C4×Q8C22×D6114yes—
228C4×D4—26no—
229C4×D4C22×D61112yes—
230C2×C4⋊C4—613no—
231C2×C4⋊C4—1223no—
232C2×C4⋊C4—1223no—
233C2×C4⋊C4C22⋊D6113yes—
234C2×C4⋊C4C22×D6111yescharacteristic
235C2×C22⋊C4—23no—
236C2×C42—1223no—
237C2×C42C22×D6113yes—
238#106—6112no—
239C4⋊C8—6112no—
240#103—614no—
241#102—6112no—
242#102—6124no—
243C4×C8—6112no—
244C24—23no—
245#41—432no—
246C2×Q8—614no—
247C2×Q8—612no—
248C2×Q8—1221no—
249C2×Q8—12212no—
250C2×Q8—1222no—
251C2×Q8—4886no—
252C2×Q8#1175820018yescomplemented
253C2×Q8C2×C22⋊D6114yes—
254C2×D4—23no—
255C2×D4—212no—
256C2×D4—212no—
257C2×D4—26no—
258C2×D4—26no—
259C2×D4—412no—
260C2×D4—86no—
261C2×D4C23×D6116yes—
262C22×C4—21no—
263C22×C4—212no—
264C22×C4—412no—
265C22×C4—1221no—
266C22×C4—1223no—
267C22×C4C2×C22⋊D6113yes—
268C22×C4C2×C22⋊D6113yes—
269C22×C4C23×D6111yescharacteristic
270SD16—12224no—
271C2×C8—612no—
272C2×C8—616no—
273C2×C8—1226no—
274C2×C8—1222no—
275C4⋊C4—21no—
276C4⋊C4—616no—
277C4⋊C4—1223no—
278C4⋊C4—12212no—
279C4⋊C4—12212no—
280C4⋊C4C2×C22⋊D61112yes—
281C4⋊C4C23×D6112yes—
282C22⋊C4—212no—
283C42—12212no—
284C42C2×C22⋊D6116yes—
285C42C23×D6116yes—
286C23—26no—
287C23—46no—
288C23—46no—
289C23—46no—
290C23C22×C22⋊D6111yescharacteristic
291Q8—614no—
292Q8—1222no—
293Q8—1224no—
294Q8—48812no—
295Q8C2×#11758200116yescomplemented
296D4—26no—
297D4—26no—
298D4—424no—
299D4—46no—
300D4—812no—
301C2×C4—26no—
302C2×C4—22no—
303C2×C4—42no—
304C2×C4—424no—
305C2×C4—1222no—
306C2×C4—1224no—
307C2×C4—1226no—
308C2×C4—2446no—
309C2×C4C2×#11758200112yes—
310C2×C4C22×C22⋊D6116yes—
311C2×C4C22×C22⋊D6116yes—
312C2×C4C22×C22⋊D6111yescharacteristic
313C2×C4#41×D6112yes—
314C2×C4#1451982412yes—
315C2×C4C24×D6111yescharacteristic
316C8—1226no—
317C8—1222no—
318C22—46no—
319C22—46no—
320C22—46no—
321C22—812no—
322C22#1684041912yes—
323C22C22×#1175820012yes—
324C22#1684056512yes—
325C22C23×C22⋊D6111yescharacteristic
326C4—26no—
327C4—42no—
328C4—1224no—
329C4—2446no—
330C4#1684041912yes—
331C4C22×#11758200112yes—
332C4C2×#41×D6111yescharacteristic
333C4C2×#1451982411yescharacteristic
334C2—86no—
335C2#2145848614yesdirect product factor
336C2C2×#1684041911yescharacteristic
337C2C23×#1175820011yescharacteristic
338C2C2×#1684056511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
Fitting, prime radicalC2×C61×#550C2
socleC23×C61C22×D4
hypercenterC2×#550D61
hypocenterC61C2×#3362
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic122C2semidirect
2. #21458486C2direct (N × H)
3. C2×#16840108C2semidirect
4. C2×#16840052C2semidirect
5. C2×#16839959C2semidirect
6. C2×Q8×#92418C2semidirect
7. C2×C4×#11758200C2semidirect
11. Q8×Dic122C22semidirect
16. #16840108C22semidirect
17. #16840052C22semidirect
18. #16839959C22semidirect
19. Q8×#92418C22semidirect
20. C4×#11758200C22semidirect
76. C2×Q8×C61SD16semidirect
98. C2×Dic122#41semidirect
121. Q8×C61C2×SD16semidirect
145. Dic122C2×#41semidirect
174. C2×C61#3362semidirect
203. C61C2×#3362semidirect
252. C2×Q8#11758200semidirect
295. Q8C2×#11758200semidirect
335. C2#21458486direct (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
#214584862
C2×#168401082
C2×#168400522
C2×#168399592
C2×Q8×#924182
C2×C4×#117582002
C2×C61×#5502
C2×#336261