Finite Group Databasebeta

← C2×#21425660 #28618598

Subgroups — C2×#21425660 #28618598

Order 15104.

998 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837300C211yesmaximal, characteristic
2C2×#16837272C211yesmaximal, characteristic
3#21425660C218yesmaximal, direct product factor
4C2×#16837165C212yesmaximal
5C2×#16837165C212yesmaximal
6C2×C59×#336C211yesmaximal, characteristic
7C22×C4⋊Dic59—21no—
8C22×C4⋊Dic59—21no—
9C22×C4⋊Dic59C2212yes—
10C22×C4⋊Dic59C2211yescharacteristic
11C22×C4⋊Dic59C2211yescharacteristic
12C22×Dic59⋊C4—21no—
13#16837300—22no—
14#16837300C2214yes—
15#16837272—22no—
16#16837272C2214yes—
17C2×C59⋊#95—21no—
18#16837165C2218yes—
19#16837165C2218yes—
20C23×C8×C59C2212yes—
21C22×C42×C59C2211yescharacteristic
22C59×#336C2214yes—
23C23×Dic59—21no—
24C23×Dic59—21no—
25C23×Dic59—22no—
26C2×C4⋊Dic59—21no—
27C2×C4⋊Dic59—22no—
28C2×C4⋊Dic59—28no—
29C2×C4⋊Dic59—24no—
30C2×C4⋊Dic59—22no—
31C2×C4⋊Dic59—24no—
32C2×C4⋊Dic59—24no—
33C2×C4⋊Dic59—21no—
34C2×C4⋊Dic59—44no—
35C2×C4⋊Dic59—44no—
36C2×C4⋊Dic59Q814yes—
37C2×C4⋊Dic59C2314yes—
38C2×C4⋊Dic59C2312yes—
39C2×C4⋊Dic59C2312yes—
40C2×Dic59⋊C4—24no—
41C2×Dic59⋊C4—44no—
42C59⋊#95—24no—
43C23×C4×C59D411yescharacteristic
44C23×C4×C59D411yescharacteristic
45C23×C4×C59C2311yescharacteristic
46C22×C8×C59—24no—
47C22×C8×C59—24no—
48C22×C8×C59—24no—
49C22×C8×C59C2314yes—
50C2×C42×C59—24no—
51C2×C42×C59D412yes—
52C2×C42×C59C2312yes—
53C24×C59C2×D411yescharacteristic
54C22×C4×C59—22no—
55C22×C4×C59—22no—
56C22×C4×C59—22no—
57C22×C4×C59—22no—
58C22×C4×C59SD1614yes—
59C22×C4×C59Q1614yes—
60C22×C4×C59C2×D412yes—
61C22×C4×C59C2×D412yes—
62C22×C4×C59C2×D411yescharacteristic
63C22×C4×C59C2×Q812yes—
64C22×C4×C59#4112yes—
65C22×C4×C59#4114yes—
66C22×C4×C59#4114yes—
67C22×C4×C59C2411yescharacteristic
68C22×Dic59—24no—
69C22×Dic59—22no—
70C22×Dic59—22no—
71C22×Dic59—24no—
72C22×Dic59—42no—
73C22×Dic59—42no—
74C22×Dic59—42no—
75C22×Dic59—44no—
76C22×Dic59—42no—
77C22×Dic59—44no—
78C22×Dic59—44no—
79C22×Dic59—42no—
80C2×C8×C59—24no—
81C2×C8×C59—24no—
82C2×C8×C59—24no—
83C2×C8×C59—48no—
84C42×C59—24no—
85C42×C59—24no—
86C4⋊Dic59—24no—
87C4⋊Dic59—22no—
88C4⋊Dic59—24no—
89C4⋊Dic59—28no—
90C4⋊Dic59—48no—
91C4⋊Dic59—48no—
92C4⋊Dic59—42no—
93C4⋊Dic59—44no—
94C4⋊Dic59C2×Q814yes—
95Dic59⋊C4—48no—
96C23×C59C22⋊Q812yes—
97C23×C59#12312yes—
98C23×C59#12412yes—
99C23×C59C2×SD1612yes—
100C23×C59C2×Q1612yes—
101C23×C59AGL(1,ℤ/8)12yes—
102C23×C59AGL(1,ℤ/8)12yes—
103C23×C59C22×D411yescharacteristic
104C2×C4×C59—22no—
105C2×C4×C59—22no—
106C2×C4×C59—22no—
107C2×C4×C59—22no—
108C2×C4×C59—28no—
109C2×C4×C59—28no—
110C2×C4×C59C22⋊Q812yes—
111C2×C4×C59#12312yes—
112C2×C4×C59#12412yes—
113C2×C4×C59#12518yes—
114C2×C4×C59#12618yes—
115C2×C4×C59C2×SD1614yes—
116C2×C4×C59C2×Q1614yes—
117C2×C4×C59C22×Q811yescharacteristic
118C2×C4×C59C2×#4112yes—
119C2×C4×C59C2×#4111yescharacteristic
120C2×C4×C59C2×#4112yes—
121C2×Dic59—24no—
122C2×Dic59—42no—
123C2×Dic59—42no—
124C2×Dic59—48no—
125C2×Dic59—42no—
126C2×Dic59—44no—
127C2×Dic59—42no—
128C2×Dic59—44no—
129C2×Dic59—44no—
130C2×Dic59—42no—
131C2×Dic59—84no—
132C2×Dic59—88no—
133C8×C59—44no—
134C2×#2100—591nomaximal, Sylow
135C22×C59#40014yes—
136C22×C59#47614yes—
137C22×C59#47714yes—
138C22×C59#48114yes—
139C22×C59#48414yes—
140C22×C59#48714yes—
141C22×C59#49014yes—
142C22×C59C2×C22⋊Q811yescharacteristic
143C22×C59C2×#12311yescharacteristic
144C22×C59C2×#12411yescharacteristic
145C22×C59C22×SD1611yescharacteristic
146C22×C59C22×Q1611yescharacteristic
147C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
148C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
149C4×C59—24no—
150C4×C59—24no—
151C4×C59#40014yes—
152C4×C59C2×#12512yes—
153C4×C59C2×#12612yes—
154Dic59—44no—
155Dic59—82no—
156Dic59—84no—
157C2×#389—591no—
158C2×#384—591no—
159#2100—598no—
160C2×#340—592no—
161C2×#340—592no—
162C2×#336D5911yescharacteristic
163C2×C59#210018yescomplemented
164C2×C59C2×#40011yescharacteristic
165C2×C59C2×#47611yescharacteristic
166C2×C59C2×#47711yescharacteristic
167C2×C59C2×#48111yescharacteristic
168C2×C59C2×#48411yescharacteristic
169C2×C59C2×#48711yescharacteristic
170C2×C59C2×#49011yescharacteristic
171C23×C8C2×D5912yes—
172C22×C4⋊C4—591no—
173C22×C4⋊C4—592no—
174C22×C4⋊C4—591no—
175C22×C4⋊C4—1181no—
176C22×C4⋊C4—1181no—
177C22×C4⋊C4—1181no—
178C22×C42C2×D5911yescharacteristic
179#389—594no—
180#389—1182no—
181#384—594no—
182#384—1182no—
183C2×#95—1181no—
184#340—598no—
185#340—598no—
186#336C2×D5914yes—
187C59C2×#210011yescharacteristic, complemented, Sylow
188C23×C4—1181no—
189C23×C4—1182no—
190C23×C4—1181no—
191C23×C4D23611yescharacteristic
192C23×C4D23611yescharacteristic
193C23×C4C22×D5911yescharacteristic
194C22×C8—24no—
195C22×C8—24no—
196C22×C8—24no—
197C22×C8C22×D5914yes—
198C2×C4⋊C4—594no—
199C2×C4⋊C4—592no—
200C2×C4⋊C4—594no—
201C2×C4⋊C4—592no—
202C2×C4⋊C4—1181no—
203C2×C4⋊C4—1182no—
204C2×C4⋊C4—1188no—
205C2×C4⋊C4—1184no—
206C2×C4⋊C4—1182no—
207C2×C4⋊C4—1181no—
208C2×C4⋊C4—1184no—
209C2×C4⋊C4—1184no—
210C2×C4⋊C4—1184no—
211C2×C4⋊C4—2364no—
212C2×C4⋊C4—2364no—
213C2×C4⋊C4—2364no—
214C2×C42—24no—
215C2×C42D23612yes—
216C2×C42C22×D5912yes—
217#95—1184no—
218C24C2×D23611yescharacteristic
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—1184no—
224C22×C4—1182no—
225C22×C4—1182no—
226C22×C4—1184no—
227C22×C4—2362no—
228C22×C4—2364no—
229C22×C4—2362no—
230C22×C4—2364no—
231C22×C4—2364no—
232C22×C4—2362no—
233C22×C4—2362no—
234C22×C4—2362no—
235C22×C4#1174566014yes—
236C22×C4Dic23614yes—
237C22×C4C2×D23612yes—
238C22×C4C2×D23612yes—
239C22×C4C2×D23611yescharacteristic
240C22×C4#1174568514yes—
241C22×C4#1174568712yes—
242C22×C4#1174568714yes—
243C22×C4Q8×D5912yes—
244C22×C4C23×D5911yescharacteristic
245C2×C8—24no—
246C2×C8—24no—
247C2×C8—24no—
248C2×C8—48no—
249C4⋊C4—594no—
250C4⋊C4—1184no—
251C4⋊C4—1182no—
252C4⋊C4—1184no—
253C4⋊C4—1188no—
254C4⋊C4—2368no—
255C4⋊C4—2368no—
256C4⋊C4—2362no—
257C4⋊C4—2364no—
258C4⋊C4—2368no—
259C42—24no—
260C42—24no—
261C23#1427370712yes—
262C23#1427371112yes—
263C23#1427371512yes—
264C23C2×#1174566012yes—
265C23C2×Dic23612yes—
266C23#1427375512yes—
267C23#1427375512yes—
268C23C22×D23611yescharacteristic
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—28no—
274C2×C4—28no—
275C2×C4—1184no—
276C2×C4—4724no—
277C2×C4—4728no—
278C2×C4—2362no—
279C2×C4—2364no—
280C2×C4—2362no—
281C2×C4—2364no—
282C2×C4—2364no—
283C2×C4—2362no—
284C2×C4—2362no—
285C2×C4—2362no—
286C2×C4—2368no—
287C2×C4#1427370712yes—
288C2×C4#1427371112yes—
289C2×C4#1427371512yes—
290C2×C4#1427371718yes—
291C2×C4#1427372018yes—
292C2×C4C2×#1174566014yes—
293C2×C4C2×Dic23614yes—
294C2×C4C2×Q8×D5911yescharacteristic
295C2×C4C2×#1174568712yes—
296C2×C4C2×#1174568711yescharacteristic
297C2×C4C2×#1174568512yes—
298C8—44no—
299C22#1683734214yes—
300C22#1683769314yes—
301C22#1683769814yes—
302C22#1683772114yes—
303C22#1683773814yes—
304C22#1683775314yes—
305C22#1683776714yes—
306C22C2×#1427370711yescharacteristic
307C22C2×#1427371111yescharacteristic
308C22C2×#1427371511yescharacteristic
309C22C22×#1174566011yescharacteristic
310C22C22×Dic23611yescharacteristic
311C22C2×#1427375511yescharacteristic
312C22C2×#1427375511yescharacteristic
313C4—24no—
314C4—24no—
315C4—4724no—
316C4—4722no—
317C4—2364no—
318C4#1683734214yes—
319C4C2×#1427371712yes—
320C4C2×#1427372012yes—
321C2#2142566018yesdirect product factor
322C2C2×#1683734211yescharacteristic
323C2C2×#1683769311yescharacteristic
324C2C2×#1683769811yescharacteristic
325C2C2×#1683772111yescharacteristic
326C2C2×#1683773811yescharacteristic
327C2C2×#1683775311yescharacteristic
328C2C2×#1683776711yescharacteristic
subgroupG/H
centerC24C2×D236
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#336C2
socle, prime radicalC24×C59C2×D4
hypercenterC2×#336D59
hypocenterC59C2×#2100
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
3. #21425660C2direct (N × H)
163. C2×C59#2100semidirect
187. C59C2×#2100semidirect
321. C2#21425660direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168373002
C2×#168372722
#214256602
C2×#168371652
C2×C59×#3362
C2×#210059