Finite Group Databasebeta

← C2×#21423389 #28569815

Subgroups — C2×#21423389 #28569815

Order 15104.

1138 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1138 conjugacy classes of subgroups — too many to draw. Only its 187 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837792C212yesmaximal, complemented
2C2×#16837768C211yesmaximal, characteristic, complemented
3#21423389C218yesmaximal, direct product factor
4C2×#16837144C211yesmaximal, characteristic, complemented
5C2×#16837142C212yesmaximal, complemented
6C2×C59×#562C211yesmaximal, characteristic, complemented
7C22×#11745671—22no—
8C22×#11745669—22no—
9C2×#14273724C2211yescharacteristic
10#16837792—24no—
11#16837792C2218yescomplemented
12#16837768—22no—
13#16837768C2214yescomplemented
14C2×#14273647—22no—
15C2×#14273638C2211yescharacteristic
16C2×#14273638C2212yes—
17#16837144C2214yescomplemented
18#16837142C2218yescomplemented
19C59×#562—22no—
20C59×#562—24no—
21C59×#562C2214yescomplemented
22C2×#125×C59C2211yescharacteristic
23C2×#124×C59C2212yes—
24C2×#123×C59—22no—
25C2×C22⋊Q8×C59—22no—
26C2×#121×C59—22no—
27C22×D236—21no—
28C22×D236—22no—
29C2×#11745671—28no—
30C2×#11745671—48no—
31C2×#11745669—28no—
32C2×#11745669—48no—
33C22×C59⋊C8—22no—
34C22×C59⋊C8—21no—
35#14273724—21no—
36#14273724—22no—
37#14273724C2312yes—
38#14273647—28no—
39#14273638—21no—
40#14273638—22no—
41#14273638C2312yes—
42#14273638C2314yes—
43C22×Q8×C59D412yes—
44C22×D4×C59—22no—
45C22×D4×C59D412yes—
46C23×C4×C59—22no—
47#125×C59—22no—
48#125×C59D412yes—
49#125×C59C2312yes—
50#124×C59—22no—
51#124×C59—22no—
52#124×C59D414yes—
53#124×C59C2314yes—
54#123×C59—28no—
55#123×C59—28no—
56C22⋊Q8×C59—28no—
57C22⋊Q8×C59—28no—
58#121×C59—28no—
59#121×C59—28no—
60C2×C4⋊C4×C59—22no—
61C2×C4⋊C4×C59—22no—
62C2×C4⋊C4×C59D412yes—
63C2×C22⋊C4×C59—22no—
64C2×C22⋊C4×C59—22no—
65C2×C22⋊C4×C59—22no—
66C2×C42×C59C2311yescharacteristic
67C24×C59—22no—
68C23×D59—41no—
69C2×Q8×C59—22no—
70C2×Q8×C59—44no—
71C2×Q8×C59C2×D414yes—
72C2×D4×C59—28no—
73C2×D4×C59—22no—
74C2×D4×C59—44no—
75C2×D4×C59—84no—
76C2×D4×C59C2×D414yes—
77C22×C4×C59—22no—
78C22×C4×C59—22no—
79C22×C4×C59—28no—
80C22×C4×C59—84no—
81C22×C4×C59C2×D411yescharacteristic
82C22×C4×C59C2×D412yes—
83C2×D236—22no—
84C2×D236—24no—
85C2×D236—44no—
86C2×D236—44no—
87C2×D236—44no—
88C2×D236—41no—
89C2×D236—42no—
90C4⋊C4×C59—28no—
91C4⋊C4×C59—24no—
92C4⋊C4×C59—22no—
93C4⋊C4×C59—24no—
94C4⋊C4×C59C2×D414yes—
95C22⋊C4×C59—28no—
96C22⋊C4×C59—24no—
97C22⋊C4×C59—24no—
98C22⋊C4×C59—24no—
99C22⋊C4×C59—24no—
100C42×C59C2×D411yescharacteristic
101C42×C59C2×D412yes—
102C42×C59C2411yescharacteristic
103#11745671—416no—
104#11745669—416no—
105C2×C59⋊C8—28no—
106C2×C59⋊C8—24no—
107C2×C59⋊C8—22no—
108C2×C59⋊C8—42no—
109C23×C59—24no—
110C23×C59—44no—
111C23×C59—44no—
112C23×C59—44no—
113C23×C59#12011yescharacteristic
114C22×D59—42no—
115C22×D59—84no—
116C22×D59—82no—
117Q8×C59—44no—
118Q8×C59—82no—
119D4×C59—44no—
120D4×C59—82no—
121D4×C59—88no—
122C2×C4×C59—24no—
123C2×C4×C59—22no—
124C2×C4×C59—24no—
125C2×C4×C59—24no—
126C2×C4×C59—44no—
127C2×C4×C59—44no—
128C2×C4×C59—88no—
129C2×C4×C59#12011yescharacteristic
130C2×C4×C59#12012yes—
131C2×C4×C59C22×D411yescharacteristic
132C2×C4×C59C22×D412yes—
133D236—44no—
134D236—44no—
135D236—44no—
136D236—84no—
137D236—82no—
138C59⋊C8—28no—
139C59⋊C8—42no—
140C2×#1656—591nomaximal, Sylow
141C22×C59—44no—
142C22×C59—44no—
143C22×C59—44no—
144C22×C59—88no—
145C22×C59#45314yes—
146C22×C59#45412yes—
147C22×C59C2×#12011yescharacteristic
148C2×D59—84no—
149C2×D59—82no—
150C2×D59—164no—
151C4×C59—22no—
152C4×C59—22no—
153C4×C59—21no—
154C4×C59—21no—
155C4×C59—44no—
156C4×C59—44no—
157C2×#562D5911yescharacteristic, complemented
158C2×#496—592no—
159C2×#490—591no—
160#1656—598no—
161C2×#330—591no—
162C2×#329—592no—
163C2×C59—84no—
164C2×C59#165614yescomplemented
165C2×C59C2×#45312yes—
166C2×C59C2×#45411yescharacteristic
167D59—162no—
168C22×SD16—1182no—
169C22×D8—1182no—
170#562—22no—
171#562—24no—
172#562C2×D5914yescomplemented
173C2×#127—591no—
174C2×#125C2×D5911yescharacteristic
175C2×#124C2×D5912yes—
176C2×#123—22no—
177C2×C22⋊Q8—22no—
178C2×#121—22no—
179#496—598no—
180#496—1184no—
181#490—594no—
182#490—1182no—
183C2×#102—1182no—
184C2×#97—591no—
185C2×#97—592no—
186#330—594no—
187#329—598no—
188C59C2×#165611yescharacteristic, complemented, Sylow
189C22×Q8C22⋊D5912yes—
190C22×D4—22no—
191C22×D4—1182no—
192C22×D4—1181no—
193C22×D4C22⋊D5912yes—
194C23×C4—22no—
195C2×SD16—1188no—
196C2×SD16—2368no—
197C2×D8—1188no—
198C2×D8—2368no—
199C22×C8—1182no—
200C22×C8—1181no—
201#127—592no—
202#127—1181no—
203#127—1182no—
204#125—22no—
205#125C22⋊D5912yes—
206#125C22×D5912yes—
207#124—22no—
208#124—22no—
209#124C22⋊D5914yes—
210#124C22×D5914yes—
211#123—28no—
212#123—28no—
213C22⋊Q8—28no—
214C22⋊Q8—28no—
215#121—28no—
216#121—28no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4C22⋊D5912yes—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C42C22×D5911yescharacteristic
224#102—1188no—
225#97—592no—
226#97—594no—
227#97—1181no—
228#97—1182no—
229C24—22no—
230C24—2361no—
231C2×Q8—22no—
232C2×Q8—44no—
233C2×Q8C2×C22⋊D5914yes—
234C2×D4—28no—
235C2×D4—22no—
236C2×D4—44no—
237C2×D4—84no—
238C2×D4—1182no—
239C2×D4—1184no—
240C2×D4—2364no—
241C2×D4—2364no—
242C2×D4—2364no—
243C2×D4—2361no—
244C2×D4—2362no—
245C2×D4C2×C22⋊D5914yes—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—28no—
249C22×C4—84no—
250C22×C4C2×C22⋊D5911yescharacteristic
251C22×C4C2×C22⋊D5912yes—
252SD16—23616no—
253D8—23616no—
254C2×C8—1188no—
255C2×C8—1184no—
256C2×C8—1182no—
257C2×C8—2362no—
258C4⋊C4—28no—
259C4⋊C4—24no—
260C4⋊C4—22no—
261C4⋊C4—24no—
262C4⋊C4C2×C22⋊D5914yes—
263C22⋊C4—28no—
264C22⋊C4—24no—
265C22⋊C4—24no—
266C22⋊C4—24no—
267C22⋊C4—24no—
268C42C2×C22⋊D5911yescharacteristic
269C42C2×C22⋊D5912yes—
270C42C23×D5911yescharacteristic
271C23—24no—
272C23—44no—
273C23—44no—
274C23—44no—
275C23—4724no—
276C23—4722no—
277C23—2362no—
278C23#1427369611yescharacteristic
279Q8—44no—
280Q8—82no—
281D4—44no—
282D4—82no—
283D4—88no—
284D4—4724no—
285D4—4722no—
286D4—2364no—
287D4—2364no—
288D4—2364no—
289C2×C4—24no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—88no—
296C2×C4#1427369611yescharacteristic
297C2×C4#1427369612yes—
298C2×C4C22×C22⋊D5911yescharacteristic
299C2×C4C22×C22⋊D5912yes—
300C8—1188no—
301C8—2362no—
302C22—44no—
303C22—44no—
304C22—44no—
305C22—88no—
306C22—9444no—
307C22—4724no—
308C22—4722no—
309C22#1683757014yes—
310C22#1683757512yes—
311C22C2×#1427369611yescharacteristic
312C4—22no—
313C4—22no—
314C4—21no—
315C4—21no—
316C4—44no—
317C4—44no—
318C2—84no—
319C2—9442no—
320C2#2142338914yesdirect product factor
321C2C2×#1683757012yes—
322C2C2×#1683757511yescharacteristic
subgroupG/H
centerC23#14273696
commutator, cosocleC42×C59C24
FrattiniC42C23×D59
FittingC2×C59×#562C2
socleC23×C59#120
hypercenterC2×#562D59
hypocenterC59C2×#1656
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#562

Complements

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

NH ≅ G/Ntype
1. C2×#16837792C2semidirect
2. C2×#16837768C2semidirect
3. #21423389C2direct (N × H)
4. C2×#16837144C2semidirect
5. C2×#16837142C2semidirect
6. C2×C59×#562C2semidirect
11. #16837792C22semidirect
13. #16837768C22semidirect
17. #16837144C22semidirect
18. #16837142C22semidirect
21. C59×#562C22semidirect
157. C2×#562D59semidirect
164. C2×C59#1656semidirect
172. #562C2×D59semidirect
188. C59C2×#1656semidirect
320. C2#21423389direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168377922
C2×#168377682
#214233892
C2×#168371442
C2×#168371422
C2×C59×#5622
C2×#165659