Finite Group Databasebeta

← C2×#21434673 #29458423

Subgroups — C2×#21434673 #29458423

Order 15104.

2566 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837950C212yesmaximal, complemented
2#21434673C2116yesmaximal, direct product factor
3C2×#16837807C211yesmaximal, characteristic, complemented
4C2×#16837748C212yesmaximal, complemented
5C2×#16837635C214yesmaximal, complemented
6C2×D8×Dic59C214yesmaximal, complemented
7C2×C4×C8×D59C211yesmaximal, characteristic, complemented
8C2×C59×#493C211yesmaximal, characteristic, complemented
9C22×#11745687—22no—
10C22×C8×D59C2212yes—
11#16837950—28no—
12#16837950C22116yescomplemented
13C2×#14273727C2212yes—
14C2×#14273714—22no—
15C2×#14273698—22no—
16C2×#14273698C2214yes—
17C2×D4×Dic59—22no—
18C2×D4×Dic59C2214yes—
19C2×C42×D59C2211yescharacteristic
20#16837807C2218yescomplemented
21#16837748C22116yescomplemented
22#16837635C22132yescomplemented
23D8×Dic59C22132yescomplemented
24C2×#14273661C2214yes—
25C2×#14273648C2218yes—
26C2×C4×C59⋊C8C2211yescharacteristic
27C2×C8×Dic59C2212yes—
28C4×C8×D59C2218yescomplemented
29C22×D8×C59C2214yes—
30C2×#127×C59C2212yes—
31C59×#493C2218yescomplemented
32C2×C4×C8×C59C2211yescharacteristic
33C2×#11745687—216no—
34C2×#11745687—416no—
35C22×Dic118—22no—
36C22×C22⋊D59—24no—
37C23×Dic59—24no—
38C22×C4×D59D411yescharacteristic
39C22×C4×D59D411yescharacteristic
40C22×C4×D59C2311yescharacteristic
41C22×C59⋊C8C2312yes—
42C2×C8×D59—28no—
43C2×C8×D59C2318yes—
44#14273727—24no—
45#14273727C2318yes—
46#14273714—216no—
47#14273698—216no—
48#14273698—28no—
49#14273698C23116yes—
50D4×Dic59—28no—
51D4×Dic59—216no—
52D4×Dic59C23116yes—
53C2×C4⋊Dic59—22no—
54C2×C4⋊Dic59C2314yes—
55C2×C22⋊Dic59—24no—
56C2×C22⋊Dic59—24no—
57C2×C4×Dic59D411yescharacteristic
58C2×C4×Dic59D411yescharacteristic
59C2×C4×Dic59C2311yescharacteristic
60C42×D59D414yes—
61C42×D59C2314yes—
62#14273661C23116yes—
63#14273648C23132yes—
64C4×C59⋊C8C2314yes—
65C8×Dic59C2318yes—
66C22×D4×C59—22no—
67C22×D4×C59—22no—
68C22×D4×C59C2314yes—
69C2×D8×C59—216no—
70C2×D8×C59C23116yes—
71C22×C8×C59C2312yes—
72#127×C59—24no—
73#127×C59C2318yes—
74C2×C42×C59C2311yescharacteristic
75C4×C8×C59C2314yes—
76C24×C59—24no—
77C23×D59C2×D411yescharacteristic
78C2×D4×C59—24no—
79C2×D4×C59—28no—
80C2×D4×C59—28no—
81C2×D4×C59—216no—
82C2×D4×C59—48no—
83C2×D4×C59—48no—
84C2×D4×C59C2418yes—
85C22×C4×C59C2×D411yescharacteristic
86C22×C4×C59C2×D411yescharacteristic
87C22×C4×C59C2411yescharacteristic
88C2×C22⋊D59—216no—
89C2×C22⋊D59—416no—
90C22×Dic59—24no—
91C22×Dic59—216no—
92C22×Dic59—416no—
93C22×Dic59C2×D411yescharacteristic
94C22×Dic59C2×D411yescharacteristic
95C22×Dic59C2×D411yescharacteristic
96#11745687—464no—
97C2×C4×D59—24no—
98C2×C4×D59—24no—
99C2×C4×D59D818yescomplemented
100C2×C4×D59C2×D412yes—
101C2×C4×D59C2×D414yes—
102C2×C4×D59C2×D414yes—
103C2×C4×D59C2412yes—
104C2×Dic118—28no—
105C2×Dic118—48no—
106D8×C59—232no—
107C2×C8×C59#4118yescomplemented
108C2×C8×C59C2414yes—
109C42×C59C2×D412yes—
110C42×C59C2412yes—
111C22⋊Dic59—216no—
112C22⋊Dic59—216no—
113C4⋊Dic59—28no—
114C4⋊Dic59—24no—
115C4⋊Dic59C2418yes—
116C4×Dic59C2×D412yes—
117C4×Dic59C2×D414yes—
118C4×Dic59C2×D414yes—
119C4×Dic59C2412yes—
120C2×C59⋊C8—24no—
121C2×C59⋊C8C2414yes—
122C8×D59—216no—
123C23×C59—28no—
124C23×C59—48no—
125C23×C59—48no—
126C23×C59—48no—
127C23×C59C22×D411yescharacteristic
128C22×D59—22no—
129C22×D59—22no—
130C22×D59C2×D814yes—
131C22×D59C22×D412yes—
132D4×C59—216no—
133D4×C59—48no—
134D4×C59—416no—
135D4×C59—416no—
136C2×C4×C59C2×D814yes—
137C2×C4×C59#13514yes—
138C2×C4×C59C22×D411yescharacteristic
139C2×C4×C59C22×D412yes—
140C2×C4×C59C22×D412yes—
141C2×C4×C59C2×#4114yes—
142C2×C4×C59C2511yescharacteristic
143C22⋊D59—432no—
144C2×Dic59—22no—
145C2×Dic59—22no—
146C2×Dic59—28no—
147C2×Dic59—48no—
148C2×Dic59—432no—
149C2×Dic59C2×D814yes—
150C2×Dic59C22×D412yes—
151C2×Dic59C22×D412yes—
152C2×Dic59C22×D412yes—
153C4×D59—24no—
154C4×D59—28no—
155C4×D59—24no—
156C4×D59C2×D8116yescomplemented
157Dic118—416no—
158C8×C59C2×#4118yescomplemented
159C59⋊C8—24no—
160C2×#3169—591nomaximal, Sylow
161C22×C59—48no—
162C22×C59—48no—
163C22×C59—48no—
164C22×C59—816no—
165C22×C59#53212yes—
166C22×C59C22×D812yes—
167C22×C59C2×#13512yes—
168C22×C59C23×D411yescharacteristic
169C2×D59—28no—
170C2×D59—22no—
171C2×D59—22no—
172C2×D59C22×D814yes—
173C4×C59#53212yes—
174C4×C59C22×D814yes—
175C4×C59C2×#13514yes—
176C4×C59C22×#4112yes—
177Dic59—22no—
178Dic59—22no—
179Dic59—48no—
180Dic59C22×D814yes—
181C2×#532—592no—
182#3169—5916no—
183C2×#500—591no—
184C2×#493D5911yescharacteristic, complemented
185C2×#486—592no—
186C2×#466—594no—
187C2×C4×D8—594no—
188C22×C4×C8—591no—
189C2×C59—88no—
190C2×C59#316914yescomplemented
191C2×C59C2×#53211yescharacteristic
192C2×C59C23×D811yescharacteristic
193C2×C59C22×#13511yescharacteristic
194D59—24no—
195C22×#41—1182no—
196C22×D8C2×D5914yes—
197C23×C8—592no—
198#532—5916no—
199#532—1188no—
200C2×C4⋊Q8—592no—
201C2×#127C2×D5912yes—
202C2×#124—1182no—
203C2×#121—594no—
204C2×#121—1182no—
205C2×C4×D4—594no—
206C2×C4×D4—1182no—
207C22×C42—591no—
208#500—598no—
209#493C2×D5918yescomplemented
210#486—5916no—
211#466—5932no—
212C4×D8—5932no—
213C2×#107—594no—
214C2×#102—598no—
215C2×C4×C8—592no—
216C2×C4×C8—591no—
217C2×C4×C8—598no—
218C2×C4×C8C2×D5911yescharacteristic
219C59C2×#316911yescharacteristic, complemented, Sylow
220C2×#41—11816no—
221C2×#41—23616no—
222C22×Q8—1182no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—1184no—
226C22×D4C22×D5914yes—
227C23×C4—591no—
228C23×C4—591no—
229C23×C4—591no—
230C23×C4—1184no—
231C2×D8—216no—
232C2×D8C22×D59116yes—
233C22×C8—592no—
234C22×C8—598no—
235C22×C8—1188no—
236C22×C8C22×D5912yes—
237C4⋊Q8—598no—
238C4⋊Q8—1184no—
239#127—24no—
240#127C22×D5918yes—
241#124—11816no—
242#121—5916no—
243#121—1188no—
244#121—11816no—
245C4×D4—5916no—
246C4×D4—1188no—
247C4×D4—11816no—
248C2×C4⋊C4—594no—
249C2×C4⋊C4—1182no—
250C2×C22⋊C4—1184no—
251C2×C22⋊C4—1184no—
252C2×C42—591no—
253C2×C42—591no—
254C2×C42—591no—
255C2×C42—594no—
256C2×C42—594no—
257C2×C42C22×D5911yescharacteristic
258#107—5916no—
259#102—5932no—
260C4×C8—598no—
261C4×C8—594no—
262C4×C8C22×D5914yes—
263C24—24no—
264C24—591no—
265#41—23664no—
266C2×Q8—1188no—
267C2×Q8—2368no—
268C2×D4—24no—
269C2×D4—28no—
270C2×D4—28no—
271C2×D4—216no—
272C2×D4—48no—
273C2×D4—48no—
274C2×D4—11816no—
275C2×D4—23616no—
276C2×D4C23×D5918yes—
277C22×C4—591no—
278C22×C4—598no—
279C22×C4—594no—
280C22×C4—591no—
281C22×C4—591no—
282C22×C4—594no—
283C22×C4—592no—
284C22×C4—592no—
285C22×C4—11816no—
286C22×C4—1184no—
287C22×C4—1184no—
288C22×C4—1184no—
289C22×C4—23616no—
290C22×C4D4×D5911yescharacteristic
291C22×C4D4×D5911yescharacteristic
292C22×C4C23×D5911yescharacteristic
293D8—232no—
294C2×C8—594no—
295C2×C8—1184no—
296C2×C8—11816no—
297C2×C8#1174568718yescomplemented
298C2×C8C23×D5914yes—
299C4⋊C4—598no—
300C4⋊C4—1184no—
301C4⋊C4—1188no—
302C22⋊C4—11816no—
303C22⋊C4—11816no—
304C42—594no—
305C42—592no—
306C42—594no—
307C42—592no—
308C42D4×D5912yes—
309C42C23×D5912yes—
310C23—28no—
311C23—48no—
312C23—48no—
313C23—48no—
314C23—594no—
315C23—592no—
316C23—1182no—
317C23—1182no—
318C23C2×D4×D5911yescharacteristic
319Q8—23616no—
320D4—216no—
321D4—416no—
322D4—416no—
323D4—48no—
324D4—23632no—
325C2×C4—594no—
326C2×C4—592no—
327C2×C4—5916no—
328C2×C4—592no—
329C2×C4—592no—
330C2×C4—1182no—
331C2×C4—1182no—
332C2×C4—1188no—
333C2×C4—1184no—
334C2×C4—1184no—
335C2×C4—1188no—
336C2×C4—23632no—
337C2×C4—2368no—
338C2×C4D8×D5914yes—
339C2×C4#1427374614yes—
340C2×C4C2×D4×D5912yes—
341C2×C4C2×D4×D5912yes—
342C2×C4C2×D4×D5911yescharacteristic
343C2×C4C2×#1174568714yes—
344C2×C4C24×D5911yescharacteristic
345C8—1184no—
346C8C2×#1174568718yescomplemented
347C22—48no—
348C22—48no—
349C22—48no—
350C22—816no—
351C22—594no—
352C22—1188no—
353C22—1182no—
354C22—1182no—
355C22#1683795012yes—
356C22C2×D8×D5912yes—
357C22C2×#1427374612yes—
358C22C22×D4×D5911yescharacteristic
359C4—594no—
360C4—1182no—
361C4—1182no—
362C4—2368no—
363C4#1683795012yes—
364C4C2×D8×D5914yes—
365C4C2×#1427374614yes—
366C4C22×#1174568712yes—
367C2—88no—
368C2—1184no—
369C2#2143467314yesdirect product factor
370C2C2×#1683795011yescharacteristic
371C2C22×D8×D5911yescharacteristic
372C2C22×#1427374611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#493C2
socleC23×C59C22×D4
hypercenterC2×#493D59
hypocenterC59C2×#3169
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#16837950C2semidirect
2. #21434673C2direct (N × H)
3. C2×#16837807C2semidirect
4. C2×#16837748C2semidirect
5. C2×#16837635C2semidirect
6. C2×D8×Dic59C2semidirect
7. C2×C4×C8×D59C2semidirect
8. C2×C59×#493C2semidirect
12. #16837950C22semidirect
20. #16837807C22semidirect
21. #16837748C22semidirect
22. #16837635C22semidirect
23. D8×Dic59C22semidirect
28. C4×C8×D59C22semidirect
31. C59×#493C22semidirect
99. C2×C4×D59D8semidirect
107. C2×C8×C59#41semidirect
156. C4×D59C2×D8semidirect
158. C8×C59C2×#41semidirect
184. C2×#493D59semidirect
190. C2×C59#3169semidirect
209. #493C2×D59semidirect
219. C59C2×#3169semidirect
297. C2×C8#11745687semidirect
346. C8C2×#11745687semidirect
369. C2#21434673direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379502
#214346732
C2×#168378072
C2×#168377482
C2×#168376352
C2×D8×Dic592
C2×C4×C8×D592
C2×C59×#4932
C2×#316959