Finite Group Databasebeta

← C2×#21423493 #28570950

Subgroups — C2×#21423493 #28570950

Order 15104.

726 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837805C211yesmaximal, characteristic, complemented
2C2×#16837692C211yesmaximal, characteristic
3C2×D4×C59⋊C8C211yesmaximal, characteristic
4#21423493C218yesmaximal, direct product factor
5C2×#16837154C211yesmaximal, characteristic, complemented
6C2×#16837151C211yesmaximal, characteristic, complemented
7C2×#16837150C211yesmaximal, characteristic, complemented
8C2×C59×#476C211yesmaximal, characteristic
9C23×C59⋊C8—21no—
10C2×#14273727C2211yescharacteristic
11#16837805—22no—
12#16837805C2214yescomplemented
13#16837692—22no—
14#16837692C2214yes—
15D4×C59⋊C8—22no—
16D4×C59⋊C8C2214yes—
17C2×#14273660—21no—
18C2×#14273660—21no—
19C2×#14273658—21no—
20C2×C4⋊(C59⋊C8)C2211yescharacteristic
21C2×C4⋊(C59⋊C8)C2211yescharacteristic
22C2×#14273648—21no—
23C2×C22⋊(C59⋊C8)—21no—
24C2×C4×C59⋊C8C2211yescharacteristic
25#16837154C2214yescomplemented
26#16837151C2214yescomplemented
27#16837150C2214yescomplemented
28C2×C4⋊Q8×C59C2211yescharacteristic
29C2×C4×D4×C59C2211yescharacteristic
30C59×#476—22no—
31C59×#476C2214yes—
32C2×#106×C59—21no—
33C2×C4⋊C8×C59C2211yescharacteristic
34C2×#102×C59—21no—
35C22×Dic118—21no—
36C22×C59⋊C8—21no—
37C22×C59⋊C8—21no—
38C22×C59⋊C8—24no—
39C22×C59⋊C8—44no—
40C22×C59⋊C8D411yescharacteristic
41C22×C59⋊C8D411yescharacteristic
42#14273727—21no—
43#14273727—21no—
44#14273727—21no—
45#14273727C2312yes—
46C2×C4⋊Dic59—21no—
47C2×C4⋊Dic59—21no—
48#14273660—24no—
49#14273660—24no—
50#14273658—24no—
51C4⋊(C59⋊C8)—21no—
52C4⋊(C59⋊C8)—21no—
53C4⋊(C59⋊C8)C2312yes—
54C4⋊(C59⋊C8)C2312yes—
55#14273648—24no—
56C22⋊(C59⋊C8)—24no—
57C4×C59⋊C8D412yes—
58C4×C59⋊C8C2312yes—
59C22×Q8×C59—21no—
60C22×D4×C59D411yescharacteristic
61C23×C4×C59—21no—
62C22×C8×C59—21no—
63C4⋊Q8×C59—21no—
64C4⋊Q8×C59—21no—
65C4⋊Q8×C59—21no—
66C4⋊Q8×C59C2312yes—
67C4×D4×C59—21no—
68C4×D4×C59—21no—
69C4×D4×C59D412yes—
70C4×D4×C59C2312yes—
71C2×C4⋊C4×C59—21no—
72C2×C4⋊C4×C59—21no—
73C2×C4⋊C4×C59D411yescharacteristic
74C2×C22⋊C4×C59—21no—
75C2×C42×C59C2311yescharacteristic
76#106×C59—24no—
77C4⋊C8×C59—21no—
78C4⋊C8×C59C2312yes—
79#102×C59—24no—
80C24×C59—21no—
81C2×Q8×C59—22no—
82C2×Q8×C59—41no—
83C2×Q8×C59—82no—
84C2×D4×C59—21no—
85C2×D4×C59—22no—
86C2×D4×C59Q1614yes—
87C2×D4×C59C2×D412yes—
88C22×C4×C59—21no—
89C22×C4×C59—22no—
90C22×C4×C59—22no—
91C22×C4×C59—42no—
92C22×C4×C59—42no—
93C22×C4×C59—41no—
94C22×C4×C59C2×D411yescharacteristic
95C22×C4×C59C2×D411yescharacteristic
96C22×C4×C59#4111yescharacteristic
97C22×Dic59—41no—
98C2×Dic118—22no—
99C2×Dic118—41no—
100C2×Dic118—82no—
101C2×C8×C59—22no—
102C2×C8×C59—42no—
103C4⋊C4×C59—21no—
104C4⋊C4×C59—22no—
105C4⋊C4×C59—22no—
106C4⋊C4×C59—41no—
107C4⋊C4×C59—41no—
108C4⋊C4×C59C2×D412yes—
109C22⋊C4×C59—22no—
110C22⋊C4×C59—22no—
111C42×C59C2×D411yescharacteristic
112C42×C59C2×D411yescharacteristic
113C42×C59#4111yescharacteristic
114C42×C59C2411yescharacteristic
115C4⋊Dic59—22no—
116C4⋊Dic59—22no—
117C4⋊Dic59—41no—
118C4⋊Dic59—41no—
119C2×C59⋊C8—22no—
120C2×C59⋊C8—22no—
121C2×C59⋊C8—22no—
122C2×C59⋊C8—42no—
123C2×C59⋊C8—42no—
124C2×C59⋊C8—48no—
125C2×C59⋊C8SD1614yes—
126C2×C59⋊C8C2×D412yes—
127C2×C59⋊C8C2×D412yes—
128C23×C59—22no—
129C23×C59—24no—
130C23×C59—42no—
131C23×C59—42no—
132C23×C59#12111yescharacteristic
133Q8×C59—82no—
134Q8×C59—82no—
135D4×C59—22no—
136D4×C59—24no—
137D4×C59C2×Q1614yes—
138C2×C4×C59—22no—
139C2×C4×C59—22no—
140C2×C4×C59—42no—
141C2×C4×C59—42no—
142C2×C4×C59—42no—
143C2×C4×C59—44no—
144C2×C4×C59—42no—
145C2×C4×C59—82no—
146C2×C4×C59#12111yescharacteristic
147C2×C4×C59#12111yescharacteristic
148C2×C4×C59#12111yescharacteristic
149C2×C4×C59C2×SD1612yes—
150C2×C4×C59C2×Q1612yes—
151C2×C4×C59#13512yes—
152C2×C4×C59#13712yes—
153C2×C4×C59C22×D411yescharacteristic
154C2×C4×C59C22×D411yescharacteristic
155C2×C4×C59C2×#4111yescharacteristic
156C2×Dic59—42no—
157C2×Dic59—82no—
158Dic118—82no—
159Dic118—82no—
160C8×C59—42no—
161C59⋊C8—22no—
162C59⋊C8—42no—
163C59⋊C8—42no—
164C59⋊C8C2×SD1614yes—
165C2×#1675—591nomaximal, Sylow
166C22×C59—24no—
167C22×C59—48no—
168C22×C59—42no—
169C22×C59—42no—
170C22×C59#46112yes—
171C22×C59#46712yes—
172C22×C59#47212yes—
173C22×C59C2×#12111yescharacteristic
174C4×C59—21no—
175C4×C59—21no—
176C4×C59—42no—
177C4×C59—82no—
178C4×C59#46112yes—
179C4×C59#46712yes—
180C4×C59C22×SD1611yescharacteristic
181C4×C59C22×Q1611yescharacteristic
182C4×C59C2×#13511yescharacteristic
183C4×C59C2×#13711yescharacteristic
184Dic59—82no—
185C2×#500—591no—
186C2×#476—591no—
187C2×#476D5911yescharacteristic
188C2×C8×D4—591no—
189#1675—598no—
190C2×#335—591no—
191C2×#333—591no—
192C2×#333—591no—
193C2×C59—44no—
194C2×C59#167514yescomplemented
195C2×C59C2×#46111yescharacteristic
196C2×C59C2×#46711yescharacteristic
197C2×C59C2×#47211yescharacteristic
198C23×C8—1181no—
199C2×C4⋊Q8—591no—
200C2×C4⋊Q8C2×D5911yescharacteristic
201C2×C4×D4C2×D5911yescharacteristic
202#500—594no—
203#500—1182no—
204#476—22no—
205#476—594no—
206#476—1182no—
207#476C2×D5914yes—
208C8×D4—594no—
209C8×D4—1182no—
210C2×#107—1181no—
211C2×#107—1181no—
212C2×#106—21no—
213C2×#106—1181no—
214C2×C4⋊C8—591no—
215C2×C4⋊C8—591no—
216C2×C4⋊C8C2×D5911yescharacteristic
217C2×#102—21no—
218C2×#102—1181no—
219C2×C22⋊C8—1181no—
220C2×C4×C8—591no—
221#335—594no—
222#333—594no—
223#333—594no—
224C59C2×#167511yescharacteristic, complemented, Sylow
225C22×Q8—21no—
226C22×Q8—1181no—
227C22×D4C22⋊D5911yescharacteristic
228C23×C4—21no—
229C22×C8—21no—
230C22×C8—591no—
231C22×C8—591no—
232C22×C8—1184no—
233C22×C8—1181no—
234C22×C8—1181no—
235C22×C8—2364no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—592no—
240C4⋊Q8—1181no—
241C4⋊Q8—1181no—
242C4⋊Q8—1181no—
243C4⋊Q8C22×D5912yes—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4C22⋊D5912yes—
247C4×D4C22×D5912yes—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—1181no—
251C2×C4⋊C4—1181no—
252C2×C4⋊C4C22⋊D5911yescharacteristic
253C2×C22⋊C4—21no—
254C2×C42C22×D5911yescharacteristic
255#107—1184no—
256#107—1184no—
257#106—24no—
258#106—1184no—
259C4⋊C8—21no—
260C4⋊C8—592no—
261C4⋊C8—592no—
262C4⋊C8—1181no—
263C4⋊C8—1181no—
264C4⋊C8C22×D5912yes—
265#102—24no—
266#102—1184no—
267C22⋊C8—1184no—
268C4×C8—592no—
269C4×C8—592no—
270C24—21no—
271C2×Q8—22no—
272C2×Q8—41no—
273C2×Q8—82no—
274C2×Q8—1182no—
275C2×Q8—4722no—
276C2×Q8—2361no—
277C2×D4—21no—
278C2×D4—22no—
279C2×D4#1174567214yes—
280C2×D4C2×C22⋊D5912yes—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—41no—
287C22×C4—2361no—
288C22×C4D4×D5911yescharacteristic
289C22×C4#1174568711yescharacteristic
290C22×C4C2×C22⋊D5911yescharacteristic
291C2×C8—22no—
292C2×C8—42no—
293C2×C8—594no—
294C2×C8—592no—
295C2×C8—592no—
296C2×C8—1182no—
297C2×C8—1182no—
298C2×C8—1182no—
299C2×C8—2368no—
300C2×C8—2362no—
301C2×C8—2362no—
302C4⋊C4—21no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—1182no—
308C4⋊C4—1182no—
309C4⋊C4—2361no—
310C4⋊C4—2361no—
311C4⋊C4C2×C22⋊D5912yes—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C42D4×D5911yescharacteristic
315C42#1174568711yescharacteristic
316C42C2×C22⋊D5911yescharacteristic
317C42C23×D5911yescharacteristic
318C23—22no—
319C23—24no—
320C23—42no—
321C23—42no—
322C23#1427369911yescharacteristic
323Q8—82no—
324Q8—82no—
325Q8—4722no—
326Q8—4722no—
327D4—24no—
328D4—22no—
329D4C2×#1174567214yes—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—44no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4—4722no—
339C2×C4—2362no—
340C2×C4#1427369911yescharacteristic
341C2×C4#1427369911yescharacteristic
342C2×C4#1427369911yescharacteristic
343C2×C4SD16×D5912yes—
344C2×C4C2×#1174567212yes—
345C2×C4#1427374712yes—
346C2×C4#1427375612yes—
347C2×C4C2×D4×D5911yescharacteristic
348C2×C4C22×C22⋊D5911yescharacteristic
349C2×C4C2×#1174568711yescharacteristic
350C8—42no—
351C8—594no—
352C8—1182no—
353C8—2362no—
354C8—2362no—
355C22—24no—
356C22—48no—
357C22—42no—
358C22—42no—
359C22#1683760512yes—
360C22#1683764112yes—
361C22#1683767012yes—
362C22C2×#1427369911yescharacteristic
363C4—21no—
364C4—21no—
365C4—42no—
366C4—82no—
367C4—4722no—
368C4#1683760512yes—
369C4#1683764112yes—
370C4C2×SD16×D5911yescharacteristic
371C4C22×#1174567211yescharacteristic
372C4C2×#1427374711yescharacteristic
373C4C2×#1427375611yescharacteristic
374C2—44no—
375C2#2142349314yesdirect product factor
376C2C2×#1683760511yescharacteristic
377C2C2×#1683764111yescharacteristic
378C2C2×#1683767011yescharacteristic
subgroupG/H
centerC23#14273699
commutator, cosocleC42×C59C24
FrattiniC42C23×D59
FittingC2×C59×#476C2
socleC23×C59#121
prime radicalC22×D4×C59D4
hypercenterC2×#476D59
hypocenterC59C2×#1675
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#16837805C2semidirect
4. #21423493C2direct (N × H)
5. C2×#16837154C2semidirect
6. C2×#16837151C2semidirect
7. C2×#16837150C2semidirect
12. #16837805C22semidirect
25. #16837154C22semidirect
26. #16837151C22semidirect
27. #16837150C22semidirect
194. C2×C59#1675semidirect
224. C59C2×#1675semidirect
375. C2#21423493direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168378052
C2×#168376922
C2×D4×C59⋊C82
#214234932
C2×#168371542
C2×#168371512
C2×#168371502
C2×C59×#4762
C2×#167559