Finite Group Databasebeta

← C2×#21433190 #29453644

Subgroups — C2×#21433190 #29453644

Order 15104.

1750 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837959C211yesmaximal, characteristic
2#21433190C2116yesmaximal, direct product factor
3C2×#16837532C212yesmaximal, complemented
4C2×#16837531C214yesmaximal, complemented
5C2×C8×Dic118C212yesmaximal, complemented
6C2×#16837460C214yesmaximal
7C2×#16837459C211yesmaximal, characteristic
8C2×C59×#431C211yesmaximal, characteristic
9#16837959C418yes—
10#16837959C2218yes—
11C2×#14273727C411yescharacteristic
12C2×#14273727C411yescharacteristic
13C2×#14273719C412yes—
14C2×#14273706C412yes—
15C2×#14273706C412yes—
16C2×C4×Dic118C2212yes—
17C2×C4×Dic118C2212yes—
18C2×#14273686C2212yes—
19#16837532C22116yescomplemented
20#16837531C22132yescomplemented
21C8×Dic118C22116yescomplemented
22#16837460C22132yes—
23#16837459C2218yes—
24C2×C4⋊(C59⋊C8)C2212yes—
25C2×Dic59⋊C8C2214yes—
26C2×Dic59⋊C8C2214yes—
27C2×C22⋊(C59⋊C8)C2212yes—
28C2×#14273638C2212yes—
29C2×#14273637C2214yes—
30C2×C8×Dic59C2214yes—
31C22×C42×C59C2211yescharacteristic
32C59×#431C2218yes—
33C2×C4⋊C8×C59C2212yes—
34C2×C22⋊C8×C59C2212yes—
35C2×C4×C8×C59C2211yescharacteristic
36C2×C4×C8×C59C2211yescharacteristic
37C22×Dic118C2×C412yes—
38C22×Dic118C2×C412yes—
39C22×C59⋊C8C2314yes—
40#14273727C2×C418yes—
41#14273727C2×C418yes—
42#14273719C2×C4116yes—
43#14273706C2×C4116yes—
44#14273706C2×C4116yes—
45C4×Dic118C2×C418yes—
46C4×Dic118C2×C418yes—
47C4×Dic118C2318yes—
48C4×Dic118C2318yes—
49#14273686C2×C418yes—
50#14273686C2318yes—
51C2×C4⋊Dic59C2×C412yes—
52C2×C4⋊Dic59C2×C412yes—
53C2×C4⋊Dic59C2×C412yes—
54C2×C4⋊Dic59C2×C412yes—
55C2×Dic59⋊C4C2×C414yes—
56C2×Dic59⋊C4C2×C414yes—
57C2×C22⋊Dic59C2×C414yes—
58C2×C4×Dic59C2314yes—
59C4⋊(C59⋊C8)C2318yes—
60Dic59⋊C8C23116yes—
61Dic59⋊C8C23116yes—
62C22⋊(C59⋊C8)C2318yes—
63#14273638C2318yes—
64#14273637C23116yes—
65C8×Dic59C23116yes—
66C23×C4×C59C2×C411yescharacteristic
67C23×C4×C59C2×C411yescharacteristic
68C23×C4×C59C2311yescharacteristic
69C22×C8×C59C2312yes—
70C22×C8×C59C2312yes—
71C2×C42×C59C2×C411yescharacteristic
72C2×C42×C59C2×C411yescharacteristic
73C2×C42×C59C2×C414yes—
74C2×C42×C59C2311yescharacteristic
75C2×C42×C59C2314yes—
76C2×C42×C59C2311yescharacteristic
77C4⋊C8×C59C2318yes—
78C22⋊C8×C59C2318yes—
79C4×C8×C59C2314yes—
80C4×C8×C59C2314yes—
81C24×C59C22×C411yescharacteristic
82C22×C4×C59—24no—
83C22×C4×C59—24no—
84C22×C4×C59—42no—
85C22×C4×C59C22×C411yescharacteristic
86C22×C4×C59C22×C412yes—
87C22×C4×C59C22×C411yescharacteristic
88C22×C4×C59C22×C411yescharacteristic
89C22×C4×C59C22×C411yescharacteristic
90C22×C4×C59C22×C414yes—
91C22×C4×C59C22×C414yes—
92C22×C4×C59C22×C411yescharacteristic
93C22×C4×C59C2412yes—
94C22×C4×C59C2411yescharacteristic
95C22×Dic59C22×C414yes—
96C22×Dic59C22×C414yes—
97C2×Dic118—28no—
98C2×Dic118—44no—
99C2×Dic118C22×C418yes—
100C2×Dic118C22×C418yes—
101C2×C8×C59—24no—
102C2×C8×C59—24no—
103C2×C8×C59C2414yes—
104C2×C8×C59C2414yes—
105C42×C59C22×C412yes—
106C42×C59C22×C412yes—
107C42×C59C22×C414yes—
108C42×C59C22×C414yes—
109C42×C59C2412yes—
110C42×C59C2412yes—
111C22⋊Dic59C22×C4116yes—
112C4⋊Dic59C22×C418yes—
113C4⋊Dic59C22×C418yes—
114C4⋊Dic59C22×C418yes—
115C4⋊Dic59C22×C418yes—
116Dic59⋊C4C22×C4116yes—
117Dic59⋊C4C22×C4116yes—
118C4×Dic59C22×C418yes—
119C4×Dic59C2418yes—
120C2×C59⋊C8—28no—
121C2×C59⋊C8C2418yes—
122C23×C59—22no—
123C23×C59—22no—
124C23×C59—22no—
125C23×C59C23×C412yes—
126C23×C59C23×C411yescharacteristic
127C2×C4×C59—22no—
128C2×C4×C59—22no—
129C2×C4×C59—22no—
130C2×C4×C59—22no—
131C2×C4×C59—24no—
132C2×C4×C59—28no—
133C2×C4×C59—24no—
134C2×C4×C59—44no—
135C2×C4×C59#13114yes—
136C2×C4×C59C23×C412yes—
137C2×C4×C59C23×C412yes—
138C2×C4×C59C23×C412yes—
139C2×C4×C59C23×C412yes—
140C2×C4×C59C23×C411yescharacteristic
141C2×C4×C59C23×C412yes—
142C2×C4×C592−1+414yes—
143C2×C4×C59C2511yescharacteristic
144C2×Dic59—28no—
145C2×Dic59—28no—
146C2×Dic59C23×C418yes—
147C2×Dic59C23×C418yes—
148Dic118—216no—
149Dic118—48no—
150C8×C59—24no—
151C8×C59—24no—
152C59⋊C8—28no—
153C2×#2985—591nomaximal, Sylow
154C22×C59—22no—
155C22×C59—22no—
156C22×C59—22no—
157C22×C59—44no—
158C22×C59#51912yes—
159C22×C59C2×#13112yes—
160C22×C59#56812yes—
161C22×C59C24×C411yescharacteristic
162C4×C59—22no—
163C4×C59—22no—
164C4×C59—22no—
165C4×C59—22no—
166C4×C59#51912yes—
167C4×C59C2×#13114yes—
168C4×C59C2×2−1+412yes—
169Dic59—28no—
170Dic59—28no—
171C2×#533—591no—
172#2985—5916no—
173C2×#446—594no—
174C2×#446—592no—
175C2×C8×Q8—592no—
176C2×#433—594no—
177C2×#432—591no—
178C2×#431D5911yescharacteristic
179C2×C59—42no—
180C2×C59#298514yescomplemented
181C2×C59C2×#51911yescharacteristic
182C2×C59C22×#13111yescharacteristic
183C2×C59C2×#56811yescharacteristic
184#533—598no—
185#533—598no—
186C2×C4⋊Q8—591no—
187C2×C4⋊Q8—591no—
188C2×#125—592no—
189C2×C22⋊Q8—592no—
190C2×C22⋊Q8—592no—
191C2×C4×Q8—592no—
192C2×C4×Q8—592no—
193C2×#117—592no—
194C22×C42C2×D5911yescharacteristic
195#446—5932no—
196#446—5916no—
197C8×Q8—5916no—
198#433—5932no—
199#432—598no—
200#431C2×D5918yes—
201C2×C4⋊C8—594no—
202C2×C4⋊C8—594no—
203C2×C4⋊C8—592no—
204C2×C4⋊C8C2×D5912yes—
205C2×C22⋊C8—592no—
206C2×C22⋊C8C2×D5912yes—
207C2×#97—594no—
208C2×#97—592no—
209C2×C4×C8—594no—
210C2×C4×C8C2×D5911yescharacteristic
211C2×C4×C8C2×D5911yescharacteristic
212C59C2×#298511yescharacteristic, complemented, Sylow
213C22×Q8—592no—
214C22×Q8—592no—
215C23×C4C4×D5911yescharacteristic
216C23×C4C4×D5911yescharacteristic
217C23×C4C22×D5911yescharacteristic
218C22×C8—594no—
219C22×C8C22×D5912yes—
220C22×C8C22×D5912yes—
221C4⋊Q8—598no—
222C4⋊Q8—598no—
223#125—5916no—
224C22⋊Q8—5916no—
225C22⋊Q8—5916no—
226C4×Q8—598no—
227C4×Q8—598no—
228C4×Q8—598no—
229C4×Q8—598no—
230#117—598no—
231#117—598no—
232C2×C4⋊C4—592no—
233C2×C4⋊C4—592no—
234C2×C4⋊C4—594no—
235C2×C4⋊C4—594no—
236C2×C4⋊C4—592no—
237C2×C4⋊C4—592no—
238C2×C22⋊C4—594no—
239C2×C42—594no—
240C2×C42C4×D5911yescharacteristic
241C2×C42C4×D5911yescharacteristic
242C2×C42C4×D5914yes—
243C2×C42C22×D5914yes—
244C2×C42C22×D5911yescharacteristic
245C2×C42C22×D5911yescharacteristic
246C4⋊C8—5916no—
247C4⋊C8—5916no—
248C4⋊C8—598no—
249C4⋊C8C22×D5918yes—
250C22⋊C8—598no—
251C22⋊C8C22×D5918yes—
252#97—5916no—
253#97—598no—
254C4×C8—5916no—
255C4×C8C22×D5914yes—
256C4×C8C22×D5914yes—
257C24C2×C4×D5911yescharacteristic
258C2×Q8—598no—
259C2×Q8—598no—
260C2×Q8—1188no—
261C2×Q8—2364no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—42no—
265C22×C4—594no—
266C22×C4—594no—
267C22×C4C2×C4×D5911yescharacteristic
268C22×C4C2×C4×D5912yes—
269C22×C4C2×C4×D5911yescharacteristic
270C22×C4C2×C4×D5911yescharacteristic
271C22×C4C2×C4×D5911yescharacteristic
272C22×C4C2×C4×D5914yes—
273C22×C4C2×C4×D5914yes—
274C22×C4C2×C4×D5911yescharacteristic
275C22×C4C23×D5912yes—
276C22×C4C23×D5911yescharacteristic
277C2×C8—24no—
278C2×C8—24no—
279C2×C8—598no—
280C2×C8—1188no—
281C2×C8C23×D5914yes—
282C2×C8C23×D5914yes—
283C4⋊C4—598no—
284C4⋊C4—598no—
285C4⋊C4—5916no—
286C4⋊C4—5916no—
287C4⋊C4—598no—
288C4⋊C4—598no—
289C22⋊C4—5916no—
290C42—598no—
291C42—598no—
292C42C2×C4×D5912yes—
293C42C2×C4×D5912yes—
294C42C2×C4×D5914yes—
295C42C2×C4×D5914yes—
296C42C23×D5912yes—
297C42C23×D5912yes—
298C23—22no—
299C23—22no—
300C23—22no—
301C23C22×C4×D5912yes—
302C23C22×C4×D5911yescharacteristic
303Q8—11816no—
304Q8—2368no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—28no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—44no—
313C2×C4—598no—
314C2×C4—598no—
315C2×C4—1188no—
316C2×C4—1188no—
317C2×C4#1427373314yes—
318C2×C4C22×C4×D5912yes—
319C2×C4C22×C4×D5912yes—
320C2×C4C22×C4×D5912yes—
321C2×C4C22×C4×D5912yes—
322C2×C4C22×C4×D5912yes—
323C2×C4C22×C4×D5911yescharacteristic
324C2×C4#1427377414yes—
325C2×C4C24×D5911yescharacteristic
326C8—24no—
327C8—24no—
328C8—1188no—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—44no—
333C22#1683787912yes—
334C22C2×#1427373312yes—
335C22#1683816812yes—
336C22C23×C4×D5911yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—1188no—
342C4—1188no—
343C4#1683787912yes—
344C4C2×#1427373314yes—
345C4C2×#1427377412yes—
346C2—42no—
347C2#2143319014yesdirect product factor
348C2C2×#1683787911yescharacteristic
349C2C22×#1427373311yescharacteristic
350C2C2×#1683816811yescharacteristic
subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C59×#431C2
socleC23×C59C23×C4
prime radicalC24×C59C22×C4
cosocleC2×C4×C59C25
hypercenterC2×#431D59
hypocenterC59C2×#2985
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
2. #21433190C2direct (N × H)
3. C2×#16837532C2semidirect
4. C2×#16837531C2semidirect
5. C2×C8×Dic118C2semidirect
19. #16837532C22semidirect
20. #16837531C22semidirect
21. C8×Dic118C22semidirect
180. C2×C59#2985semidirect
212. C59C2×#2985semidirect
347. C2#21433190direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379592
#214331902
C2×#168375322
C2×#168375312
C2×C8×Dic1182
C2×#168374602
C2×#168374592
C2×C59×#4312
C2×#298559