Finite Group Databasebeta

← C2×#21436768 #29468286

Subgroups — C2×#21436768 #29468286

Order 15104.

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×Dic118C211yesmaximal, characteristic, complemented
2C2×#16838074C211yesmaximal, characteristic
3#21436768C2116yesmaximal, direct product factor
4C2×#16837749C213yesmaximal, complemented
5C2×#16837693C213yesmaximal, complemented
6C2×#16837603C213yesmaximal, complemented
7C2×C4×#11745660C213yesmaximal, complemented
8C2×C8×Q8×C59C211yesmaximal, characteristic, complemented
9C22×#11745689—21no—
10C22×#11745660C2213yes—
11Q8×Dic118—24no—
12Q8×Dic118C2218yescomplemented
13#16838074—24no—
14#16838074C2218yes—
15C2×#14273727C2213yes—
16C2×#14273726—23no—
17C2×#14273724C2213yes—
18C2×#14273702—23no—
19C2×Q8×Dic59—21no—
20C2×C4×Dic118C2213yes—
21C2×C4×D236C2213yes—
22#16837749C22124yescomplemented
23#16837693C22124yescomplemented
24#16837603C22124yescomplemented
25C4×#11745660C22124yescomplemented
26C2×#14273659C2213yes—
27C2×#14273652C2211yescharacteristic
28C2×#14273649C2213yes—
29C2×#14273649C2216yes—
30C2×C4×Q8×C59C2211yescharacteristic
31C8×Q8×C59C2218yescomplemented
32C2×C4⋊C8×C59C2213yes—
33C2×C4×C8×C59C2213yes—
34C2×#11745689—28no—
35C2×#11745689—48no—
36C22×Dic118—23no—
37C22×Dic118C2311yescharacteristic
38C22×D236—23no—
39C22×D236—23no—
40C22×D236C2313yes—
41C22×C4×D59—23no—
42C2×#11745660—212no—
43C2×#11745660C23112yes—
44#14273727—26no—
45#14273727C23112yes—
46#14273726—224no—
47#14273724—26no—
48#14273724C23112yes—
49#14273702—224no—
50Q8×Dic59—28no—
51C4×Dic118—26no—
52C4×Dic118C23112yes—
53C4×D236—26no—
54C4×D236C23112yes—
55C2×C4⋊Dic59—23no—
56C2×C4⋊Dic59C2313yes—
57C2×C4⋊Dic59C2311yescharacteristic
58C2×Dic59⋊C4—23no—
59C2×(C2×D59)⋊C4—23no—
60C2×C4×Dic59—23no—
61#14273659C23112yes—
62#14273652C2314yes—
63#14273649C23124yes—
64#14273649C23112yes—
65C22×Q8×C59D411yescharacteristic
66C22×C8×C59C2311yescharacteristic
67C22×C8×C59C2313yes—
68C4×Q8×C59D414yes—
69C4×Q8×C59C2314yes—
70C2×C4⋊C4×C59D413yes—
71C2×C42×C59C2313yes—
72C4⋊C8×C59C23112yes—
73C4×C8×C59C23112yes—
74C23×D59—23no—
75C2×Q8×C59SD1618yescomplemented
76C2×Q8×C59C2×D414yes—
77C22×C4×C59C2×D413yes—
78C22×C4×C59C2×D413yes—
79C22×C4×C59C2411yescharacteristic
80C22×Dic59—21no—
81C22×Dic59—23no—
82C22×Dic59—21no—
83#11745689—432no—
84C2×D236—26no—
85C2×D236—26no—
86C2×D236—23no—
87C2×D236—212no—
88C2×D236—212no—
89C2×D236—412no—
90C2×D236—86no—
91C2×D236C2416yes—
92C2×C4×D59—212no—
93C2×C4×D59—412no—
94C2×Dic118—21no—
95C2×Dic118—22no—
96C2×Dic118—212no—
97C2×Dic118—86no—
98C2×Dic118#4114yescomplemented
99C2×Dic118C2412yes—
100C2×C8×C59—26no—
101C2×C8×C59—22no—
102C2×C8×C59C2412yes—
103C2×C8×C59C2416yes—
104C4⋊C4×C59C2×D4112yes—
105C42×C59C2×D416yes—
106C42×C59C2416yes—
107(C2×D59)⋊C4—212no—
108C4⋊Dic59—212no—
109C4⋊Dic59—21no—
110C4⋊Dic59—23no—
111C4⋊Dic59C2416yes—
112C4⋊Dic59C2412yes—
113Dic59⋊C4—212no—
114C4×Dic59—212no—
115#11745660—224no—
116C23×C59C22×D411yescharacteristic
117C22×D59—26no—
118C22×D59—46no—
119C22×D59—46no—
120C22×D59—46no—
121Q8×C59C2×SD16116yescomplemented
122C2×C4×C59—26no—
123C2×C4×C59C2×SD16112yes—
124C2×C4×C59C22×D416yes—
125C2×C4×C59C22×D411yescharacteristic
126C2×C4×C59C22×D416yes—
127C2×C4×C59C2×#4112yes—
128C2×C4×C592−1+412yes—
129C2×C4×C59C2511yescharacteristic
130C2×Dic59—24no—
131C2×Dic59—22no—
132C2×Dic59—26no—
133C2×Dic59—22no—
134C2×Dic59—42no—
135C2×Dic59—46no—
136D236—26no—
137D236—26no—
138D236—46no—
139D236—424no—
140D236—812no—
141C4×D59—424no—
142Dic118—24no—
143Dic118—22no—
144Dic118—812no—
145Dic118C2×#4114yescomplemented
146C8×C59—26no—
147C8×C59—22no—
148C2×#3362—591nomaximal, Sylow
149C22×C59#54812yes—
150C22×C59C22×SD1612yes—
151C22×C59#57612yes—
152C22×C59C23×D411yescharacteristic
153C2×D59—46no—
154C2×D59—46no—
155C2×D59—46no—
156C2×D59—812no—
157C4×C59—26no—
158C4×C59#54812yes—
159C4×C59C22×SD16112yes—
160C4×C59C22×#4111yescharacteristic
161C4×C59C2×2−1+411yescharacteristic
162Dic59—24no—
163Dic59—42no—
164Dic59—46no—
165C2×Q82—591no—
166C2×#550—591no—
167#3362—5916no—
168C2×#486—593no—
169C2×#476—593no—
170C2×#460—593no—
171C2×C8×Q8D5911yescharacteristic, complemented
172C2×C4×SD16—593no—
173C2×C59#336214yescomplemented
174C2×C59C2×#54811yescharacteristic
175C2×C59C23×SD1611yescharacteristic
176C2×C59C2×#57611yescharacteristic
177D59—86no—
178C22×#41—1181no—
179C22×SD16—593no—
180Q82—598no—
181Q82—1184no—
182#550—598no—
183#550—1184no—
184C2×C4⋊Q8—593no—
185C2×C4⋊Q8—1183no—
186C2×#127—593no—
187C2×#121—1183no—
188C2×C4×Q8—593no—
189C2×C4×Q8—1181no—
190C2×C4×Q8C2×D5911yescharacteristic
191C2×C4×D4—593no—
192#486—5924no—
193#476—5924no—
194#460—5924no—
195C8×Q8C2×D5918yescomplemented
196C4×SD16—5924no—
197C2×#106—593no—
198C2×C4⋊C8C2×D5913yes—
199C2×#103—591no—
200C2×#102—593no—
201C2×#102—596no—
202C2×C4×C8C2×D5913yes—
203C59C2×#336211yescharacteristic, complemented, Sylow
204C2×#41—1188no—
205C2×#41—2368no—
206C22×Q8—591no—
207C22×Q8—1183no—
208C22×Q8D23611yescharacteristic
209C22×D4—593no—
210C22×D4—1183no—
211C22×D4—1183no—
212C23×C4—1183no—
213C2×SD16—5912no—
214C2×SD16—11812no—
215C22×C8C22×D5913yes—
216C22×C8C22×D5911yescharacteristic
217C4⋊Q8—5912no—
218C4⋊Q8—11824no—
219C4⋊Q8—1186no—
220#127—5912no—
221#127—1186no—
222#121—11824no—
223C4×Q8—5912no—
224C4×Q8—1188no—
225C4×Q8—1186no—
226C4×Q8D23614yes—
227C4×Q8C22×D5914yes—
228C4×D4—5912no—
229C4×D4—1186no—
230C2×C4⋊C4—591no—
231C2×C4⋊C4—593no—
232C2×C4⋊C4—1183no—
233C2×C4⋊C4—1183no—
234C2×C4⋊C4D23613yes—
235C2×C22⋊C4—1183no—
236C2×C42—1183no—
237C2×C42C22×D5913yes—
238#106—5912no—
239C4⋊C8C22×D59112yes—
240#103—594no—
241#102—5912no—
242#102—5924no—
243C4×C8C22×D59112yes—
244C24—1183no—
245#41—23632no—
246C2×Q8—594no—
247C2×Q8—592no—
248C2×Q8—1181no—
249C2×Q8—11812no—
250C2×Q8—1182no—
251C2×Q8—4726no—
252C2×Q8#1174566018yescomplemented
253C2×Q8C2×D23614yes—
254C2×D4—596no—
255C2×D4—11812no—
256C2×D4—1183no—
257C2×D4—11812no—
258C2×D4—1186no—
259C2×D4—1186no—
260C2×D4—4726no—
261C2×D4—23612no—
262C22×C4—1181no—
263C22×C4—1183no—
264C22×C4—1181no—
265C22×C4—11812no—
266C22×C4—23612no—
267C22×C4C2×D23613yes—
268C22×C4C2×D23613yes—
269C22×C4C23×D5911yescharacteristic
270SD16—11824no—
271C2×C8—26no—
272C2×C8—22no—
273C2×C8C23×D5912yes—
274C2×C8C23×D5916yes—
275C4⋊C4—596no—
276C4⋊C4—592no—
277C4⋊C4—1181no—
278C4⋊C4—1183no—
279C4⋊C4—11812no—
280C4⋊C4—11812no—
281C4⋊C4C2×D236112yes—
282C22⋊C4—11812no—
283C42—11812no—
284C42C2×D23616yes—
285C42C23×D5916yes—
286C23—1186no—
287C23—2366no—
288C23—2366no—
289C23—2366no—
290C23C22×D23611yescharacteristic
291Q8—594no—
292Q8—1182no—
293Q8—1184no—
294Q8—47212no—
295Q8C2×#11745660116yescomplemented
296D4—1186no—
297D4—1186no—
298D4—47212no—
299D4—23624no—
300D4—2366no—
301C2×C4—26no—
302C2×C4—1182no—
303C2×C4—1184no—
304C2×C4—1186no—
305C2×C4—1182no—
306C2×C4—2362no—
307C2×C4—2366no—
308C2×C4—23624no—
309C2×C4C2×#11745660112yes—
310C2×C4C22×D23616yes—
311C2×C4C22×D23616yes—
312C2×C4C22×D23611yescharacteristic
313C2×C4#41×D5912yes—
314C2×C4#1427377512yes—
315C2×C4C24×D5911yescharacteristic
316C8—26no—
317C8—22no—
318C22—47212no—
319C22—2366no—
320C22—2366no—
321C22—2366no—
322C22#1683806412yes—
323C22C22×#1174566012yes—
324C22#1683820712yes—
325C22C23×D23611yescharacteristic
326C4—26no—
327C4—1184no—
328C4—2362no—
329C4—2366no—
330C4#1683806412yes—
331C4C22×#11745660112yes—
332C4C2×#41×D5911yescharacteristic
333C4C2×#1427377511yescharacteristic
334C2—4726no—
335C2#2143676814yesdirect product factor
336C2C2×#1683806411yescharacteristic
337C2C23×#1174566011yescharacteristic
338C2C2×#1683820711yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C8×Q8×C59C2
socleC23×C59C22×D4
prime radicalC2×#16838074C2
hypercenterC2×C8×Q8D59
hypocenterC59C2×#3362
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
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×Dic118C2semidirect
3. #21436768C2direct (N × H)
4. C2×#16837749C2semidirect
5. C2×#16837693C2semidirect
6. C2×#16837603C2semidirect
7. C2×C4×#11745660C2semidirect
8. C2×C8×Q8×C59C2semidirect
12. Q8×Dic118C22semidirect
22. #16837749C22semidirect
23. #16837693C22semidirect
24. #16837603C22semidirect
25. C4×#11745660C22semidirect
31. C8×Q8×C59C22semidirect
75. C2×Q8×C59SD16semidirect
98. C2×Dic118#41semidirect
121. Q8×C59C2×SD16semidirect
145. Dic118C2×#41semidirect
171. C2×C8×Q8D59semidirect
173. C2×C59#3362semidirect
195. C8×Q8C2×D59semidirect
203. C59C2×#3362semidirect
252. C2×Q8#11745660semidirect
295. Q8C2×#11745660semidirect
335. C2#21436768direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic1182
C2×#168380742
#214367682
C2×#168377492
C2×#168376932
C2×#168376032
C2×C4×#117456602
C2×C8×Q8×C592
C2×#336259