Finite Group Databasebeta

← C2×#21422365 #28510410

Subgroups — C2×#21422365 #28510410

Order 15104.

2942 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊Dic59C211yesmaximal, characteristic
2C22×C59⋊#95C214yesmaximal
3C22×C59⋊#95C211yesmaximal, characteristic
4#21422365C218yesmaximal, direct product factor
5C22×#95×C59C211yesmaximal, characteristic
6C24×Dic59C2212yes—
7C24×Dic59C2212yes—
8C22×C4⋊Dic59—24no—
9C22×C4⋊Dic59—24no—
10C22×C4⋊Dic59C418yescomplemented
11C22×C4⋊Dic59C2214yes—
12C2×C59⋊#95—216no—
13C2×C59⋊#95—24no—
14C2×C59⋊#95C22116yes—
15C2×C59⋊#95C2214yes—
16C24×C4×C59C2212yes—
17C24×C4×C59C2211yescharacteristic
18C2×#95×C59—24no—
19C2×#95×C59C2214yes—
20C23×Dic59—24no—
21C23×Dic59—28no—
22C23×Dic59—24no—
23C23×Dic59—24no—
24C23×Dic59—28no—
25C23×Dic59—28no—
26C23×Dic59—28no—
27C23×Dic59—24no—
28C23×Dic59C2×C418yes—
29C23×Dic59D418yes—
30C23×Dic59C2314yes—
31C23×Dic59C2314yes—
32C2×C4⋊Dic59—232no—
33C2×C4⋊Dic59—28no—
34C2×C4⋊Dic59—28no—
35C2×C4⋊Dic59C2×C4116yescomplemented
36C59⋊#95—28no—
37C59⋊#95—232no—
38C25×C59C2311yescharacteristic
39C23×C4×C59—28no—
40C23×C4×C59—24no—
41C23×C4×C59—28no—
42C23×C4×C59—24no—
43C23×C4×C59—28no—
44C23×C4×C59C2×C414yes—
45C23×C4×C59D414yes—
46C23×C4×C59D414yes—
47C23×C4×C59Q818yes—
48C23×C4×C59C2314yes—
49C23×C4×C59C2312yes—
50#95×C59—28no—
51C24×C59C22×C412yes—
52C24×C59C2×D412yes—
53C24×C59C2×D412yes—
54C24×C59C2×D414yes—
55C24×C59C2×Q814yes—
56C24×C59#4118yes—
57C24×C59#4114yes—
58C24×C59#4114yes—
59C24×C59C2411yescharacteristic
60C22×C4×C59—216no—
61C22×C4×C59—216no—
62C22×C4×C59—216no—
63C22×C4×C59—28no—
64C22×C4×C59—232no—
65C22×C4×C59—216no—
66C22×C4×C59—24no—
67C22×C4×C59—28no—
68C22×C4×C59—28no—
69C22×C4×C59—24no—
70C22×C4×C59—48no—
71C22×C4×C59—416no—
72C22×C4×C59—48no—
73C22×C4×C59C22⋊C4116yes—
74C22×C4×C59C22×C414yes—
75C22×C4×C59C2×D414yes—
76C22×C4×C59C2×D414yes—
77C22×C4×C59C2×Q818yes—
78C22×Dic59—216no—
79C22×Dic59—232no—
80C22×Dic59—216no—
81C22×Dic59—232no—
82C22×Dic59—28no—
83C22×Dic59—24no—
84C22×Dic59—24no—
85C22×Dic59—24no—
86C22×Dic59—28no—
87C22×Dic59—24no—
88C22×Dic59—28no—
89C22×Dic59—28no—
90C22×Dic59—416no—
91C22×Dic59—48no—
92C22×Dic59—48no—
93C22×Dic59—48no—
94C22×Dic59—416no—
95C22×Dic59—48no—
96C22×Dic59C22×C418yes—
97C22×Dic59C2×D418yes—
98C4⋊Dic59—232no—
99C23×C59C2×C22⋊C414yes—
100C23×C59#11718yes—
101C23×C59C4×D418yes—
102C23×C59C4×Q818yes—
103C23×C59#12118yes—
104C23×C59C22⋊Q8116yes—
105C23×C59C22⋊Q818yes—
106C23×C59#12318yes—
107C23×C59#123116yes—
108C23×C59#12318yes—
109C23×C59#12414yes—
110C23×C59#12414yes—
111C23×C59#125116yes—
112C23×C59#126116yes—
113C23×C59#12714yes—
114C23×C59C4⋊Q814yes—
115C23×C59C23×C411yescharacteristic
116C23×C59C22×D412yes—
117C23×C59C22×D411yescharacteristic
118C23×C59C22×D411yescharacteristic
119C23×C59C22×Q812yes—
120C23×C59C2×#4114yes—
121C23×C59C2×#4112yes—
122C23×C59C2×#4112yes—
123C2×C4×C59—28no—
124C2×C4×C59—28no—
125C2×C4×C59—28no—
126C2×C4×C59—232no—
127C2×C4×C59—216no—
128C2×C4×C59—28no—
129C2×C4×C59—44no—
130C2×C4×C59—48no—
131C2×C4×C59—44no—
132C2×C4×C59—432no—
133C2×C4×C59C2×C22⋊C418yes—
134C2×Dic59—28no—
135C2×Dic59—216no—
136C2×Dic59—28no—
137C2×Dic59—216no—
138C2×Dic59—48no—
139C2×Dic59—44no—
140C2×Dic59—44no—
141C2×Dic59—44no—
142C2×Dic59—48no—
143C2×Dic59—44no—
144C2×Dic59—432no—
145C2×Dic59—432no—
146C2×#1445—591nomaximal, Sylow
147C22×C59#38118yes—
148C22×C59#387132yes—
149C22×C59#39018yes—
150C22×C59#39118yes—
151C22×C59#397116yes—
152C22×C59#398116yes—
153C22×C59#399116yes—
154C22×C59#400116yes—
155C22×C59C22×C22⋊C411yescharacteristic
156C22×C59C2×#11712yes—
157C22×C59C2×C4×D412yes—
158C22×C59C2×C4×Q812yes—
159C22×C59C2×#12112yes—
160C22×C59C2×C22⋊Q814yes—
161C22×C59C2×C22⋊Q812yes—
162C22×C59C2×#12312yes—
163C22×C59C2×#12314yes—
164C22×C59C2×#12312yes—
165C22×C59C2×#12411yescharacteristic
166C22×C59C2×#12411yescharacteristic
167C22×C59C2×#12514yes—
168C22×C59C2×#12614yes—
169C22×C59C2×#12711yescharacteristic
170C22×C59C2×C4⋊Q811yescharacteristic
171C4×C59—28no—
172C4×C59—48no—
173Dic59—48no—
174Dic59—48no—
175C23×C4⋊C4—591no—
176C22×#95—594no—
177C22×#95—591no—
178C22×#95D5911yescharacteristic
179#1445—598no—
180C2×C59#1445116yescomplemented
181C2×C59C2×#38111yescharacteristic
182C2×C59C2×#38714yes—
183C2×C59C2×#39011yescharacteristic
184C2×C59C2×#39111yescharacteristic
185C2×C59C2×#39712yes—
186C2×C59C2×#39812yes—
187C2×C59C2×#39912yes—
188C2×C59C2×#40012yes—
189C24×C4—592no—
190C24×C4—592no—
191C24×C4C2×D5912yes—
192C24×C4C2×D5911yescharacteristic
193C22×C4⋊C4—598no—
194C22×C4⋊C4—594no—
195C22×C4⋊C4—1184no—
196C22×C4⋊C4—1184no—
197C2×#95—24no—
198C2×#95—5916no—
199C2×#95—594no—
200C2×#95—11816no—
201C2×#95—1184no—
202C2×#95C2×D5914yes—
203C59C2×#144511yescharacteristic, complemented, Sylow
204C25C22×D5911yescharacteristic
205C23×C4—28no—
206C23×C4—24no—
207C23×C4—28no—
208C23×C4—28no—
209C23×C4—24no—
210C23×C4—598no—
211C23×C4—598no—
212C23×C4—594no—
213C23×C4—594no—
214C23×C4—1184no—
215C23×C4—1184no—
216C23×C4—1188no—
217C23×C4—1188no—
218C23×C4—1188no—
219C23×C4—1188no—
220C23×C4—1184no—
221C23×C4—1184no—
222C23×C4Dic11818yes—
223C23×C4C4×D5914yes—
224C23×C4D23614yes—
225C23×C4C22⋊D5914yes—
226C23×C4C22×D5914yes—
227C23×C4C22×D5912yes—
228C2×C4⋊C4—5916no—
229C2×C4⋊C4—11832no—
230C2×C4⋊C4—1188no—
231C2×C4⋊C4—1188no—
232#95—28no—
233#95—11832no—
234#95—1188no—
235C24C2×Dic11814yes—
236C24C2×C4×D5912yes—
237C24C2×D23612yes—
238C24#1174568514yes—
239C24D4×D5914yes—
240C24#1174568718yes—
241C24#1174568914yes—
242C24C2×C22⋊D5912yes—
243C24C23×D5911yescharacteristic
244C22×C4—216no—
245C22×C4—216no—
246C22×C4—216no—
247C22×C4—28no—
248C22×C4—232no—
249C22×C4—216no—
250C22×C4—28no—
251C22×C4—24no—
252C22×C4—28no—
253C22×C4—24no—
254C22×C4—48no—
255C22×C4—416no—
256C22×C4—48no—
257C22×C4—598no—
258C22×C4—598no—
259C22×C4—11816no—
260C22×C4—11832no—
261C22×C4—11816no—
262C22×C4—11832no—
263C22×C4—1188no—
264C22×C4—1184no—
265C22×C4—1184no—
266C22×C4—1184no—
267C22×C4—1188no—
268C22×C4—1188no—
269C22×C4—1184no—
270C22×C4—1188no—
271C22×C4—23616no—
272C22×C4—2368no—
273C22×C4—2368no—
274C22×C4—2368no—
275C22×C4—23616no—
276C22×C4—2368no—
277C22×C4(C2×D59)⋊C4116yes—
278C22×C4C2×Dic11818yes—
279C22×C4C2×C4×D5914yes—
280C22×C4C2×D23614yes—
281C22×C4C2×C22⋊D5914yes—
282C4⋊C4—11832no—
283C23C2×(C2×D59)⋊C414yes—
284C23#1427368318yes—
285C23#1427368918yes—
286C23C4×Dic11818yes—
287C23#1427370218yes—
288C23#14273704116yes—
289C23#1427370618yes—
290C23#1427370818yes—
291C23#14273709116yes—
292C23#1427371118yes—
293C23#1427371514yes—
294C23#1427371614yes—
295C23#14273718116yes—
296C23#14273722116yes—
297C23#1427372314yes—
298C23#1427372714yes—
299C23C22×C4×D5911yescharacteristic
300C23C2×D4×D5912yes—
301C23C22×C22⋊D5911yescharacteristic
302C23C22×D23611yescharacteristic
303C23C22×Dic11812yes—
304C23C2×#1174568714yes—
305C23C2×#1174568512yes—
306C23C2×#1174568912yes—
307C2×C4—28no—
308C2×C4—28no—
309C2×C4—232no—
310C2×C4—28no—
311C2×C4—216no—
312C2×C4—28no—
313C2×C4—44no—
314C2×C4—48no—
315C2×C4—44no—
316C2×C4—432no—
317C2×C4—1188no—
318C2×C4—11816no—
319C2×C4—1188no—
320C2×C4—11816no—
321C2×C4—2368no—
322C2×C4—2364no—
323C2×C4—2364no—
324C2×C4—2364no—
325C2×C4—2368no—
326C2×C4—2364no—
327C2×C4—23632no—
328C2×C4—23632no—
329C2×C4C2×(C2×D59)⋊C418yes—
330C22#1683726318yes—
331C22#16837285132yes—
332C22#1683730318yes—
333C22#1683730818yes—
334C22#16837329116yes—
335C22#16837334116yes—
336C22#16837338116yes—
337C22#16837341116yes—
338C22C22×(C2×D59)⋊C411yescharacteristic
339C22C2×#1427368312yes—
340C22C2×#1427368912yes—
341C22C2×C4×Dic11812yes—
342C22C2×#1427370212yes—
343C22C2×#1427370414yes—
344C22C2×#1427370612yes—
345C22C2×#1427370812yes—
346C22C2×#1427370914yes—
347C22C2×#1427371112yes—
348C22C2×#1427371511yescharacteristic
349C22C2×#1427371611yescharacteristic
350C22C2×#1427371814yes—
351C22C2×#1427372214yes—
352C22C2×#1427372311yescharacteristic
353C22C2×#1427372711yescharacteristic
354C4—28no—
355C4—48no—
356C4—2368no—
357C4—2368no—
358C2#21422365116yesdirect product factor
359C2C2×#1683726311yescharacteristic
360C2C2×#1683728514yes—
361C2C2×#1683730311yescharacteristic
362C2C2×#1683730811yescharacteristic
363C2C2×#1683732912yes—
364C2C2×#1683733412yes—
365C2C2×#1683733812yes—
366C2C2×#1683734112yes—
subgroupG/H
centerC25C22×D59
commutatorC23×C59C23×C4
FrattiniC24C23×D59
FittingC22×#95×C59C2
socle, prime radicalC25×C59C23
cosocleC24×C59C24
hypercenterC22×#95D59
hypocenterC59C2×#1445
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C25 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
4. #21422365C2direct (N × H)
10. C22×C4⋊Dic59C4semidirect
35. C2×C4⋊Dic59C2×C4semidirect
180. C2×C59#1445semidirect
203. C59C2×#1445semidirect
358. C2#21422365direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊Dic592
C22×C59⋊#952
#214223652
C22×#95×C592
C2×#144559