Finite Group Databasebeta

← C2×#21423103 #28560917

Subgroups — C2×#21423103 #28560917

Order 15104.

1028 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1028 conjugacy classes of subgroups — too many to draw. Only its 203 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×#16838033C211yesmaximal, characteristic
2C2×#16837732C212yesmaximal
3#21423103C218yesmaximal, direct product factor
4C2×#16837138C212yesmaximal
5C2×#16837128C211yesmaximal, characteristic
6C2×C59×#398C211yesmaximal, characteristic
7#16838033—24no—
8#16838033—22no—
9#16838033C2214yes—
10C2×#14273726—22no—
11C2×#14273718—22no—
12C2×#14273706—21no—
13C2×#14273706C2212yes—
14C2×#14273686—21no—
15#16837732—24no—
16#16837732C2218yes—
17C2×#14273658—22no—
18C2×#14273650—22no—
19C2×C22⋊(C59⋊C8)C2212yes—
20#16837138C2218yes—
21#16837128C2214yes—
22C22×C4⋊C4×C59—21no—
23C22×C4⋊C4×C59C2211yescharacteristic
24C22×C4⋊C4×C59C2211yescharacteristic
25C59×#398—22no—
26C59×#398C2214yes—
27C2×#95×C59—21no—
28C2×#95×C59C2211yescharacteristic
29C22×Dic118—21no—
30C22×Dic118D412yes—
31C22×C59⋊C8—22no—
32#14273726—28no—
33#14273726—28no—
34#14273718—28no—
35#14273718—28no—
36#14273706—24no—
37#14273706—24no—
38#14273706—22no—
39#14273706—22no—
40#14273706D414yes—
41#14273706C2314yes—
42#14273686—24no—
43#14273686—24no—
44C2×C4⋊Dic59—21no—
45C2×C4⋊Dic59—21no—
46C2×C4⋊Dic59—21no—
47C2×C4⋊Dic59D412yes—
48C2×Dic59⋊C4—22no—
49C2×Dic59⋊C4—22no—
50C2×C22⋊Dic59—22no—
51C2×C4×Dic59—22no—
52#14273658—28no—
53#14273650—28no—
54C22⋊(C59⋊C8)—22no—
55C22⋊(C59⋊C8)C2314yes—
56C23×C4×C59—21no—
57C23×C4×C59—21no—
58C23×C4×C59D411yescharacteristic
59C23×C4×C59D411yescharacteristic
60C23×C4×C59C2311yescharacteristic
61C2×C4⋊C4×C59—22no—
62C2×C4⋊C4×C59—22no—
63C2×C4⋊C4×C59—22no—
64C2×C4⋊C4×C59—22no—
65C2×C4⋊C4×C59—21no—
66C2×C4⋊C4×C59—24no—
67C2×C4⋊C4×C59—44no—
68C2×C4⋊C4×C59D412yes—
69C2×C4⋊C4×C59C2312yes—
70C2×C4⋊C4×C59C2312yes—
71#95×C59—24no—
72#95×C59—21no—
73#95×C59C2312yes—
74C24×C59C2×D411yescharacteristic
75C22×C4×C59—21no—
76C22×C4×C59—21no—
77C22×C4×C59—22no—
78C22×C4×C59—24no—
79C22×C4×C59—21no—
80C22×C4×C59—22no—
81C22×C4×C59—21no—
82C22×C4×C59—22no—
83C22×C4×C59—42no—
84C22×C4×C59—42no—
85C22×C4×C59—42no—
86C22×C4×C59—42no—
87C22×C4×C59—41no—
88C22×C4×C59—41no—
89C22×C4×C59—42no—
90C22×C4×C59—42no—
91C22×C4×C59SD1614yes—
92C22×C4×C59C2×D412yes—
93C22×C4×C59C2×D412yes—
94C22×C4×C59C2×D412yes—
95C22×C4×C59C2×D411yescharacteristic
96C22×C4×C59C2×D412yes—
97C22×C4×C59C2411yescharacteristic
98C22×Dic59—22no—
99C22×Dic59—22no—
100C2×Dic118—24no—
101C2×Dic118—22no—
102C2×Dic118—44no—
103C2×Dic118—82no—
104C2×Dic118C2×D414yes—
105C4⋊C4×C59—24no—
106C4⋊C4×C59—24no—
107C4⋊C4×C59—24no—
108C4⋊C4×C59—42no—
109C4⋊C4×C59—48no—
110C22⋊Dic59—24no—
111C22⋊Dic59—24no—
112C4⋊Dic59—24no—
113C4⋊Dic59—24no—
114C4⋊Dic59—24no—
115C4⋊Dic59—22no—
116C4⋊Dic59C2×D414yes—
117Dic59⋊C4—28no—
118Dic59⋊C4—24no—
119Dic59⋊C4—24no—
120C4×Dic59—28no—
121C2×C59⋊C8—24no—
122C2×C59⋊C8—44no—
123C23×C59—22no—
124C23×C59—22no—
125C23×C59#12011yescharacteristic
126C23×C59#12011yescharacteristic
127C23×C59C2×SD1612yes—
128C23×C59#13712yes—
129C23×C59C22×D411yescharacteristic
130C2×C4×C59—22no—
131C2×C4×C59—22no—
132C2×C4×C59—24no—
133C2×C4×C59—24no—
134C2×C4×C59—24no—
135C2×C4×C59—24no—
136C2×C4×C59—22no—
137C2×C4×C59—42no—
138C2×C4×C59—41no—
139C2×C4×C59—41no—
140C2×C4×C59—48no—
141C2×C4×C59—42no—
142C2×C4×C59—42no—
143C2×C4×C59—42no—
144C2×C4×C59—42no—
145C2×C4×C59—42no—
146C2×C4×C59—42no—
147C2×C4×C59—42no—
148C2×C4×C59—81no—
149C2×C4×C59—82no—
150C2×C4×C59—82no—
151C2×C4×C59#12012yes—
152C2×C4×C59C2×SD1614yes—
153C2×C4×C59C22×D412yes—
154C2×Dic59—24no—
155C2×Dic59—24no—
156C2×Dic59—44no—
157C2×Dic59—44no—
158Dic118—44no—
159Dic118—82no—
160Dic118—84no—
161C59⋊C8—44no—
162C2×#1611—591nomaximal, Sylow
163C22×C59—24no—
164C22×C59—24no—
165C22×C59—21no—
166C22×C59—21no—
167C22×C59—21no—
168C22×C59—21no—
169C22×C59#44812yes—
170C22×C59#44812yes—
171C22×C59#45612yes—
172C22×C59#45812yes—
173C22×C59C2×#12011yescharacteristic
174C22×C59C22×SD1611yescharacteristic
175C22×C59C2×#13711yescharacteristic
176C4×C59—24no—
177C4×C59—22no—
178C4×C59—22no—
179C4×C59—44no—
180C4×C59—42no—
181C4×C59—82no—
182Dic59—44no—
183Dic59—44no—
184C2×#544—591no—
185C2×#483—592no—
186C2×#398D5911yescharacteristic
187#1611—598no—
188C2×#328—592no—
189C2×#324—591no—
190C2×C59—21no—
191C2×C59—21no—
192C2×C59—22no—
193C2×C59#161114yescomplemented
194C2×C59C2×#44811yescharacteristic
195C2×C59C2×#45611yescharacteristic
196C2×C59C2×#45811yescharacteristic
197#544—594no—
198#544—1184no—
199#544—1182no—
200C2×C4⋊Q8—1182no—
201C2×#125—1182no—
202C2×C22⋊Q8—592no—
203C2×C22⋊Q8—1181no—
204C2×#117—1181no—
205C22×C4⋊C4—21no—
206C22×C4⋊C4C2×D5911yescharacteristic
207C22×C4⋊C4C2×D5911yescharacteristic
208#483—598no—
209#483—1184no—
210C2×#106—1182no—
211C2×#103—1182no—
212C2×C22⋊C8—592no—
213#398—22no—
214#398C2×D5914yes—
215C2×#95—21no—
216C2×#95C2×D5911yescharacteristic
217#328—598no—
218#324—594no—
219C59C2×#161111yescharacteristic, complemented, Sylow
220C22×Q8—592no—
221C22×Q8—1181no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4C22⋊D5911yescharacteristic
225C23×C4C22⋊D5911yescharacteristic
226C23×C4C22×D5911yescharacteristic
227C22×C8—1182no—
228C4⋊Q8—1188no—
229C4⋊Q8—1188no—
230#125—1188no—
231#125—1188no—
232C22⋊Q8—594no—
233C22⋊Q8—594no—
234C22⋊Q8—1184no—
235C22⋊Q8—1182no—
236C22⋊Q8—1182no—
237C22⋊Q8—1184no—
238#117—1184no—
239#117—1184no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—44no—
247C2×C4⋊C4—592no—
248C2×C4⋊C4—1181no—
249C2×C4⋊C4—1181no—
250C2×C4⋊C4—1181no—
251C2×C4⋊C4—1182no—
252C2×C4⋊C4—1182no—
253C2×C4⋊C4C22⋊D5912yes—
254C2×C4⋊C4C22×D5912yes—
255C2×C4⋊C4C22×D5912yes—
256C2×C22⋊C4—1182no—
257C2×C42—1182no—
258#106—1188no—
259#103—1188no—
260C22⋊C8—594no—
261C22⋊C8—1182no—
262#95—24no—
263#95—21no—
264#95C22×D5912yes—
265C24C2×C22⋊D5911yescharacteristic
266C2×Q8—594no—
267C2×Q8—1184no—
268C2×Q8—1182no—
269C2×Q8—4722no—
270C2×Q8—2364no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—24no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—1182no—
288C22×C4—1182no—
289C22×C4#1174567014yes—
290C22×C4D4×D5912yes—
291C22×C4D4×D5912yes—
292C22×C4C2×C22⋊D5912yes—
293C22×C4C2×C22⋊D5912yes—
294C22×C4C2×C22⋊D5911yescharacteristic
295C22×C4C23×D5911yescharacteristic
296C2×C8—1184no—
297C2×C8—2364no—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—24no—
301C4⋊C4—42no—
302C4⋊C4—48no—
303C4⋊C4—594no—
304C4⋊C4—1184no—
305C4⋊C4—1184no—
306C4⋊C4—1184no—
307C4⋊C4—1188no—
308C4⋊C4—1182no—
309C4⋊C4—1184no—
310C4⋊C4—1184no—
311C22⋊C4—1184no—
312C22⋊C4—1184no—
313C42—1188no—
314C23—22no—
315C23—22no—
316C23#1427369511yescharacteristic
317C23#1427369511yescharacteristic
318C23C2×#1174567012yes—
319C23#1427375712yes—
320C23C22×C22⋊D5911yescharacteristic
321Q8—4722no—
322Q8—4724no—
323Q8—2364no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—24no—
330C2×C4—22no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—48no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—1184no—
346C2×C4—1184no—
347C2×C4—2364no—
348C2×C4—2364no—
349C2×C4#1427369512yes—
350C2×C4C2×#1174567014yes—
351C2×C4C2×D4×D5912yes—
352C8—2364no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—24no—
358C22—24no—
359C22#1683754012yes—
360C22#1683754012yes—
361C22#1683758412yes—
362C22#1683759112yes—
363C22C2×#1427369511yescharacteristic
364C22C22×#1174567011yescharacteristic
365C22C2×#1427375711yescharacteristic
366C4—22no—
367C4—22no—
368C4—24no—
369C4—44no—
370C4—42no—
371C4—82no—
372C4—2364no—
373C4—2364no—
374C2—21no—
375C2—21no—
376C2—22no—
377C2#2142310314yesdirect product factor
378C2C2×#1683754011yescharacteristic
379C2C2×#1683758411yescharacteristic
380C2C2×#1683759111yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#398C2
socleC23×C59#120
prime radicalC24×C59C2×D4
hypercenterC2×#398D59
hypocenterC59C2×#1611
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #21423103C2direct (N × H)
193. C2×C59#1611semidirect
219. C59C2×#1611semidirect
377. C2#21423103direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380332
C2×#168377322
#214231032
C2×#168371382
C2×#168371282
C2×C59×#3982
C2×#161159