Finite Group Databasebeta

← C2×#21428385 #28758510

Subgroups — C2×#21428385 #28758510

Order 15104.

2918 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273686C211yesmaximal, characteristic
2C23×Dic59⋊C4C211yesmaximal, characteristic
3#21428385C2116yesmaximal, direct product factor
4C2×#16837342C212yesmaximal, complemented
5C2×#16837334C212yesmaximal, complemented
6C2×#16837287C214yesmaximal, complemented
7C2×#16837277C212yesmaximal
8C2×#16837263C212yesmaximal
9C2×C59×#381C211yesmaximal, characteristic
10C24×Dic59C2211yescharacteristic
11C24×Dic59C2211yescharacteristic
12C2×#14273686—28no—
13C2×#14273686C2218yes—
14C22×C4⋊Dic59C2214yes—
15C22×C4⋊Dic59C2211yescharacteristic
16C22×C4⋊Dic59C2211yescharacteristic
17C22×Dic59⋊C4—28no—
18C22×Dic59⋊C4C2212yes—
19C22×Dic59⋊C4C2212yes—
20C22×Dic59⋊C4C2218yes—
21C22×C22⋊Dic59C2212yes—
22C22×C4×Dic59C2212yes—
23#16837342C22116yescomplemented
24#16837334C22116yescomplemented
25#16837287C22132yescomplemented
26#16837277C22116yes—
27#16837263C22116yes—
28C2×C59⋊#95C2214yes—
29C2×C59⋊#95C2214yes—
30C2×C59⋊#95C2214yes—
31C24×C4×C59C2211yescharacteristic
32C22×C22⋊C4×C59C2212yes—
33C59×#381C2218yes—
34C2×#95×C59C2212yes—
35C2×#95×C59C2212yes—
36C23×Dic59—24no—
37C23×Dic59—28no—
38C23×Dic59—24no—
39C23×Dic59—28no—
40C23×Dic59C2312yes—
41C23×Dic59C2314yes—
42C23×Dic59C2314yes—
43C23×Dic59C2312yes—
44C23×Dic59C2312yes—
45C23×Dic59C2312yes—
46#14273686—232no—
47C2×C4⋊Dic59—24no—
48C2×C4⋊Dic59—24no—
49C2×C4⋊Dic59—216no—
50C2×C4⋊Dic59C23116yes—
51C2×C4⋊Dic59C2314yes—
52C2×C4⋊Dic59C2314yes—
53C2×Dic59⋊C4—28no—
54C2×Dic59⋊C4—28no—
55C2×Dic59⋊C4—232no—
56C2×Dic59⋊C4C2318yes—
57C2×Dic59⋊C4C2318yes—
58C2×C22⋊Dic59—28no—
59C2×C22⋊Dic59C2318yes—
60C2×C4×Dic59—28no—
61C2×C4×Dic59C2318yes—
62C59⋊#95C23116yes—
63C59⋊#95C23116yes—
64C59⋊#95C23116yes—
65C25×C59C2311yescharacteristic
66C23×C4×C59—28no—
67C23×C4×C59D418yes—
68C23×C4×C59C2314yes—
69C23×C4×C59C2311yescharacteristic
70C23×C4×C59C2311yescharacteristic
71C23×C4×C59C2314yes—
72C2×C22⋊C4×C59—28no—
73C2×C22⋊C4×C59C2318yes—
74#95×C59C2318yes—
75#95×C59C2318yes—
76C24×C59—24no—
77C24×C59—24no—
78C24×C59C2×D414yes—
79C24×C59#4118yes—
80C24×C59C2412yes—
81C24×C59C2411yescharacteristic
82C22×C4×C59—232no—
83C22×C4×C59—216no—
84C22×C4×C59—24no—
85C22×C4×C59—24no—
86C22×C4×C59—28no—
87C22×C4×C59—28no—
88C22×C4×C59—28no—
89C22×C4×C59C2×D414yes—
90C22×C4×C59C2×D414yes—
91C22×C4×C59C2×D4116yes—
92C22×C4×C59C2418yes—
93C22×C4×C59C2412yes—
94C22×C4×C59C2412yes—
95C22×Dic59—232no—
96C22×Dic59—28no—
97C22×Dic59—24no—
98C22×Dic59—24no—
99C22×Dic59—216no—
100C22×Dic59—24no—
101C22×Dic59—24no—
102C22×Dic59—28no—
103C22×Dic59—24no—
104C22×Dic59—28no—
105C22×Dic59—216no—
106C22×Dic59—28no—
107C22×Dic59—28no—
108C22×Dic59—416no—
109C22×Dic59#4118yes—
110C22×Dic59C2414yes—
111C22×Dic59C2414yes—
112C22×Dic59C2414yes—
113C22×Dic59C2414yes—
114C22⋊C4×C59—216no—
115C22⋊Dic59—216no—
116C4⋊Dic59—28no—
117C4⋊Dic59—28no—
118C4⋊Dic59—232no—
119Dic59⋊C4—216no—
120Dic59⋊C4—216no—
121C4×Dic59—216no—
122C23×C59—28no—
123C23×C59—28no—
124C23×C59—232no—
125C23×C59—24no—
126C23×C59—24no—
127C23×C59#123116yes—
128C23×C59C22×D414yes—
129C23×C59C22×D412yes—
130C23×C59C2×#4114yes—
131C23×C59C2×#4118yes—
132C23×C59C2×#4114yes—
133C23×C592−1+414yes—
134C23×C59C2511yescharacteristic
135C2×C4×C59—232no—
136C2×C4×C59—28no—
137C2×C4×C59—28no—
138C2×C4×C59—24no—
139C2×C4×C59—24no—
140C2×C4×C59—28no—
141C2×C4×C59—28no—
142C2×C4×C59—28no—
143C2×C4×C59—416no—
144C2×C4×C59C22×D414yes—
145C2×C4×C59C22×D414yes—
146C2×Dic59—232no—
147C2×Dic59—216no—
148C2×Dic59—24no—
149C2×Dic59—24no—
150C2×Dic59—24no—
151C2×Dic59—24no—
152C2×Dic59—24no—
153C2×Dic59—28no—
154C2×Dic59—28no—
155C2×Dic59—28no—
156C2×Dic59—416no—
157C2×Dic59—48no—
158C2×Dic59—48no—
159C2×Dic59—48no—
160C2×Dic59C2×#4118yes—
161C2×#2484—591nomaximal, Sylow
162C22×C59—24no—
163C22×C59—24no—
164C22×C59—216no—
165C22×C59—232no—
166C22×C59C2×#12318yes—
167C22×C59C2×#12314yes—
168C22×C59#52514yes—
169C22×C59#53614yes—
170C22×C59#552116yes—
171C22×C59C23×D411yescharacteristic
172C22×C59C22×#4112yes—
173C22×C59C22×#4112yes—
174C22×C59C2×2−1+412yes—
175C4×C59—24no—
176C4×C59—24no—
177C4×C59—48no—
178Dic59—28no—
179Dic59—44no—
180Dic59—44no—
181Dic59—44no—
182C22×#117—591no—
183C23×C4⋊C4—591no—
184#2484—5916no—
185C2×#400—592no—
186C2×#398—592no—
187C2×#387—594no—
188C2×#385—592no—
189C2×#381—592no—
190C2×#381D5911yescharacteristic
191C2×C59—28no—
192C2×C59#248418yescomplemented
193C2×C59C22×#12311yescharacteristic
194C2×C59C2×#52511yescharacteristic
195C2×C59C2×#53611yescharacteristic
196C2×C59C2×#55214yes—
197C24×C4—591no—
198C24×C4—591no—
199C24×C4C2×D5911yescharacteristic
200C2×#117—598no—
201C2×#117—1188no—
202C22×C4⋊C4—591no—
203C22×C4⋊C4—592no—
204C22×C4⋊C4—594no—
205C22×C4⋊C4—591no—
206C22×C4⋊C4—598no—
207C22×C4⋊C4—592no—
208C22×C4⋊C4—1188no—
209C22×C22⋊C4—592no—
210C22×C22⋊C4C2×D5912yes—
211C22×C42—592no—
212#400—5916no—
213#398—5916no—
214#387—5932no—
215#385—5916no—
216#381—5916no—
217#381C2×D5918yes—
218C2×#95—594no—
219C2×#95—594no—
220C2×#95—594no—
221C2×#95C2×D5912yes—
222C2×#95C2×D5912yes—
223C59C2×#248411yescharacteristic, complemented, Sylow
224C25C22×D5911yescharacteristic
225C23×C4—28no—
226C23×C4—592no—
227C23×C4—594no—
228C23×C4—594no—
229C23×C4—592no—
230C23×C4—592no—
231C23×C4—592no—
232C23×C4—1188no—
233C23×C4—1184no—
234C23×C4—1184no—
235C23×C4—1188no—
236C23×C4D23618yes—
237C23×C4C22×D5914yes—
238C23×C4C22×D5914yes—
239C23×C4C22×D5911yescharacteristic
240C23×C4C22×D5911yescharacteristic
241#117—11832no—
242C2×C4⋊C4—598no—
243C2×C4⋊C4—598no—
244C2×C4⋊C4—594no—
245C2×C4⋊C4—594no—
246C2×C4⋊C4—5916no—
247C2×C4⋊C4—11816no—
248C2×C4⋊C4—1188no—
249C2×C4⋊C4—1188no—
250C2×C4⋊C4—11832no—
251C2×C4⋊C4—1184no—
252C2×C4⋊C4—1184no—
253C2×C22⋊C4—28no—
254C2×C22⋊C4—598no—
255C2×C22⋊C4—1188no—
256C2×C22⋊C4C22×D5918yes—
257C2×C42—598no—
258C2×C42—1188no—
259#95—5916no—
260#95—5916no—
261#95—5916no—
262#95C22×D5918yes—
263#95C22×D5918yes—
264C24—24no—
265C24—24no—
266C24C2×D23614yes—
267C24#1174568718yes—
268C24C23×D5912yes—
269C24C23×D5911yescharacteristic
270C22×C4—232no—
271C22×C4—216no—
272C22×C4—24no—
273C22×C4—24no—
274C22×C4—28no—
275C22×C4—28no—
276C22×C4—28no—
277C22×C4—598no—
278C22×C4—594no—
279C22×C4—594no—
280C22×C4—594no—
281C22×C4—594no—
282C22×C4—11816no—
283C22×C4—11832no—
284C22×C4—1188no—
285C22×C4—1184no—
286C22×C4—1184no—
287C22×C4—1184no—
288C22×C4—1184no—
289C22×C4—1188no—
290C22×C4—1184no—
291C22×C4—1188no—
292C22×C4—11816no—
293C22×C4—1188no—
294C22×C4—1188no—
295C22×C4—23616no—
296C22×C4C2×D23614yes—
297C22×C4C2×D23614yes—
298C22×C4C2×D236116yes—
299C22×C4C23×D5918yes—
300C22×C4C23×D5912yes—
301C22×C4C23×D5912yes—
302C4⋊C4—11832no—
303C4⋊C4—11816no—
304C4⋊C4—11816no—
305C4⋊C4—1188no—
306C4⋊C4—1188no—
307C22⋊C4—216no—
308C22⋊C4—11816no—
309C42—11816no—
310C23—28no—
311C23—24no—
312C23—28no—
313C23—24no—
314C23—232no—
315C23#14273711116yes—
316C23C22×D23614yes—
317C23C22×D23612yes—
318C23#41×D5914yes—
319C23C2×#1174568718yes—
320C23C2×#1174568714yes—
321C23#1427377414yes—
322C23C24×D5911yescharacteristic
323C2×C4—232no—
324C2×C4—28no—
325C2×C4—28no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—28no—
329C2×C4—28no—
330C2×C4—28no—
331C2×C4—416no—
332C2×C4—598no—
333C2×C4—11832no—
334C2×C4—11816no—
335C2×C4—1184no—
336C2×C4—1184no—
337C2×C4—1184no—
338C2×C4—1184no—
339C2×C4—1184no—
340C2×C4—1188no—
341C2×C4—1188no—
342C2×C4—1188no—
343C2×C4—23616no—
344C2×C4—2368no—
345C2×C4—2368no—
346C2×C4—2368no—
347C2×C4C22×D23614yes—
348C2×C4C22×D23614yes—
349C22—24no—
350C22—232no—
351C22—216no—
352C22—24no—
353C22C2×#1427371118yes—
354C22C2×#1427371114yes—
355C22#1683791414yes—
356C22#1683797814yes—
357C22#16838089116yes—
358C22C23×D23611yescharacteristic
359C22C2×#41×D5912yes—
360C22C22×#1174568712yes—
361C22C2×#1427377412yes—
362C4—24no—
363C4—24no—
364C4—48no—
365C4—1188no—
366C4—2364no—
367C4—2364no—
368C4—2364no—
369C2—28no—
370C2#2142838518yesdirect product factor
371C2C22×#1427371111yescharacteristic
372C2C2×#1683791411yescharacteristic
373C2C2×#1683797811yescharacteristic
374C2C2×#1683808914yes—
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#381C2
socleC24×C59C24
prime radicalC25×C59C23
hypercenterC2×#381D59
hypocenterC59C2×#2484
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. #21428385C2direct (N × H)
4. C2×#16837342C2semidirect
5. C2×#16837334C2semidirect
6. C2×#16837287C2semidirect
23. #16837342C22semidirect
24. #16837334C22semidirect
25. #16837287C22semidirect
192. C2×C59#2484semidirect
223. C59C2×#2484semidirect
370. C2#21428385direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142736862
C23×Dic59⋊C42
#214283852
C2×#168373422
C2×#168373342
C2×#168372872
C2×#168372772
C2×#168372632
C2×C59×#3812
C2×#248459