Finite Group Databasebeta

← C2×#364×D59 #28741683

Subgroups — C2×#364×D59 #28741683

Order 15104.

782 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D59C212yesmaximal
2C2×C4×C8×D59C211yesmaximal, characteristic
3C2×#16837223C211yesmaximal, characteristic, complemented
4C2×#16837222C212yesmaximal, complemented
5#364×D59C218yesmaximal, direct product factor
6C2×C59×#364C211yesmaximal, characteristic, complemented
7C22×C8×D59C411yescharacteristic
8C22×C8×D59C2211yescharacteristic
9C2×C42×D59C411yescharacteristic
10C2×#14273667C2212yes—
11C2×#14273666—22no—
12M32×D59—24no—
13M32×D59C2218yes—
14C2×C16×D59—22no—
15C2×C4×C59⋊C8C411yescharacteristic
16C2×C8×Dic59C411yescharacteristic
17C2×C8×Dic59C2211yescharacteristic
18C4×C8×D59C414yes—
19C4×C8×D59C2214yes—
20#16837223C2214yescomplemented
21#16837222C2218yescomplemented
22C2×M32×C59C2212yes—
23C2×C4×C8×C59C2211yescharacteristic
24C59×#364C2214yescomplemented
25C22×C4×D59—21no—
26C22×C4×D59C2×C411yescharacteristic
27C22×C59⋊C8C2×C411yescharacteristic
28C22×C59⋊C8C2×C411yescharacteristic
29C2×C8×D59C812yes—
30C2×C8×D59C814yes—
31C2×C8×D59C812yes—
32C2×C8×D59C2×C412yes—
33C2×C8×D59C2×C414yes—
34C2×C8×D59D411yescharacteristic
35C2×C8×D59D412yes—
36C2×C8×D59D411yescharacteristic
37C2×C8×D59Q812yes—
38C2×C8×D59Q811yescharacteristic
39C2×C8×D59Q811yescharacteristic
40C2×C8×D59C2312yes—
41C2×C4×Dic59—21no—
42C2×C4×Dic59C2×C411yescharacteristic
43C42×D59—22no—
44C42×D59C2×C414yes—
45#14273667—22no—
46#14273667C2314yes—
47#14273666—28no—
48C2×C59⋊C16—22no—
49C16×D59—28no—
50C4×C59⋊C8C2×C414yes—
51C8×Dic59C2×C412yes—
52C8×Dic59C2×C414yes—
53C8×Dic59C2312yes—
54C22×C8×C59C2×C411yescharacteristic
55C22×C8×C59C2311yescharacteristic
56C2×C42×C59C2×C411yescharacteristic
57M32×C59—22no—
58M32×C59C2314yes—
59C2×C16×C59—22no—
60C4×C8×C59C2×C412yes—
61C4×C8×C59C2312yes—
62C23×D59M1611yescharacteristic
63C22×C4×C59—21no—
64C22×C4×C59C22×C411yescharacteristic
65C22×Dic59—21no—
66C22×Dic59M1611yescharacteristic
67C2×C4×D59—28no—
68C2×C4×D59—24no—
69C2×C4×D59C4⋊C412yes—
70C2×C4×D59C4⋊C411yescharacteristic
71C2×C4×D59C4⋊C411yescharacteristic
72C2×C4×D59C2×C811yescharacteristic
73C2×C4×D59C2×C812yes—
74C2×C4×D59C2×C811yescharacteristic
75C2×C4×D59M1612yes—
76C2×C4×D59C22×C412yes—
77C2×C8×C59C2×C812yes—
78C2×C8×C59C2×C812yes—
79C2×C8×C59C22×C411yescharacteristic
80C2×C8×C59C22×C412yes—
81C2×C8×C59C2×D411yescharacteristic
82C2×C8×C59C2×D411yescharacteristic
83C2×C8×C59C2×Q811yescharacteristic
84C2×C8×C59C2×Q811yescharacteristic
85C2×C8×C59C2411yescharacteristic
86C42×C59—21no—
87C42×C59C22×C412yes—
88C4×Dic59—21no—
89C4×Dic59—24no—
90C4×Dic59C22×C412yes—
91C2×C59⋊C8C4⋊C411yescharacteristic
92C2×C59⋊C8C4⋊C412yes—
93C2×C59⋊C8C4⋊C411yescharacteristic
94C2×C59⋊C8C2×C812yes—
95C2×C59⋊C8C2×C812yes—
96C2×C59⋊C8C22×C412yes—
97C2×C59⋊C8C22×C412yes—
98C8×D59C4⋊C412yes—
99C8×D59C4⋊C412yes—
100C8×D59C4⋊C412yes—
101C8×D59C4⋊C412yes—
102C8×D59C2×C818yes—
103C8×D59C2×C818yes—
104C8×D59C2×D412yes—
105C8×D59C2×D412yes—
106C8×D59C2×Q812yes—
107C8×D59C2×Q812yes—
108C16×C59—24no—
109C59⋊C16—24no—
110C23×C59C2×M1611yescharacteristic
111C22×D59—24no—
112C22×D59C4⋊C811yescharacteristic
113C22×D59C4⋊C812yes—
114C22×D59C4⋊C811yescharacteristic
115C22×D59C2×M1612yes—
116C2×C4×C59—24no—
117C2×C4×C59—22no—
118C2×C4×C59C2×C4⋊C411yescharacteristic
119C2×C4×C59C2×C4⋊C411yescharacteristic
120C2×C4×C59C22×C811yescharacteristic
121C2×C4×C59C22×C811yescharacteristic
122C2×C4×C59C2×M1611yescharacteristic
123C2×C4×C59C23×C411yescharacteristic
124C2×Dic59—24no—
125C2×Dic59—22no—
126C2×Dic59C4⋊C812yes—
127C2×Dic59C4⋊C811yescharacteristic
128C2×Dic59C4⋊C811yescharacteristic
129C2×Dic59C2×M1612yes—
130C4×D59—216no—
131C4×D59C4⋊C812yes—
132C4×D59C4⋊C812yes—
133C4×D59C4⋊C812yes—
134C4×D59C4⋊C812yes—
135C4×D59C2×C4⋊C412yes—
136C4×D59C2×C4⋊C412yes—
137C4×D59C22×C812yes—
138C4×D59C22×C812yes—
139C8×C59C2×C4⋊C411yescharacteristic
140C8×C59C2×C4⋊C411yescharacteristic
141C8×C59C22×C814yes—
142C8×C59C22×D411yescharacteristic
143C8×C59C22×Q811yescharacteristic
144C59⋊C8C2×C4⋊C412yes—
145C59⋊C8C2×C4⋊C412yes—
146C59⋊C8C22×C814yes—
147C22×#364—591nomaximal, Sylow
148C22×C59—22no—
149C22×C59C2×C4⋊C811yescharacteristic
150C22×C59C2×C4⋊C811yescharacteristic
151C22×C59C22×M1611yescharacteristic
152C2×D59—22no—
153C2×D59—24no—
154C2×D59—24no—
155C2×D59#36414yesdirect product factor
156C2×D59C2×C4⋊C812yes—
157C2×D59C2×C4⋊C812yes—
158C4×C59—24no—
159C4×C59C2×C4⋊C811yescharacteristic
160C4×C59C2×C4⋊C811yescharacteristic
161C4×C59C22×C4⋊C411yescharacteristic
162C4×C59C23×C811yescharacteristic
163Dic59—24no—
164Dic59C2×C4⋊C812yes—
165Dic59C2×C4⋊C812yes—
166C22×M32—592no—
167C22×C4×C8—591no—
168C2×#364—592no—
169C2×#364—591no—
170C2×#364—598no—
171C2×#364D5911yescharacteristic, direct product factor
172C2×C59—21no—
173C2×C59—21no—
174C2×C59C2×#36412yescomplemented
175C2×C59C22×C4⋊C811yescharacteristic
176D59—22no—
177D59C2×#36414yesdirect product factor
178C23×C8—591no—
179C23×C8—591no—
180C22×C42—591no—
181C2×M32—592no—
182C2×M32—598no—
183C2×M32—1182no—
184C2×M32—1184no—
185C2×M32C2×D5912yes—
186C22×C16—1182no—
187C2×C4×C8—591no—
188C2×C4×C8—591no—
189C2×C4×C8—591no—
190C2×C4×C8—594no—
191C2×C4×C8—594no—
192C2×C4×C8C2×D5911yescharacteristic
193#364—598no—
194#364—594no—
195#364C2×D5914yesdirect product factor
196C59C22×#36411yescharacteristic, complemented, Sylow
197C23×C4—591no—
198C23×C4—1181no—
199C22×C8—591no—
200C22×C8—591no—
201C22×C8—592no—
202C22×C8—594no—
203C22×C8—592no—
204C22×C8—592no—
205C22×C8—594no—
206C22×C8—592no—
207C22×C8—591no—
208C22×C8—591no—
209C22×C8—592no—
210C22×C8—591no—
211C22×C8—591no—
212C22×C8—592no—
213C22×C8C4×D5911yescharacteristic
214C22×C8C22×D5911yescharacteristic
215C2×C42—591no—
216C2×C42—594no—
217C2×C42—1182no—
218C2×C42—1181no—
219C2×C42C4×D5911yescharacteristic
220M32—22no—
221M32—594no—
222M32—1188no—
223M32—1182no—
224M32C22×D5914yes—
225C2×C16—22no—
226C2×C16—1188no—
227C2×C16—1182no—
228C4×C8—592no—
229C4×C8—594no—
230C4×C8—592no—
231C4×C8—594no—
232C4×C8C4×D5912yes—
233C4×C8C22×D5912yes—
234C24—591no—
235C22×C4—21no—
236C22×C4—591no—
237C22×C4—592no—
238C22×C4—591no—
239C22×C4—591no—
240C22×C4—591no—
241C22×C4—592no—
242C22×C4—591no—
243C22×C4—592no—
244C22×C4—592no—
245C22×C4—1184no—
246C22×C4—1188no—
247C22×C4—1181no—
248C22×C4C2×C4×D5911yescharacteristic
249C2×C8—592no—
250C2×C8—591no—
251C2×C8—591no—
252C2×C8—592no—
253C2×C8—592no—
254C2×C8—592no—
255C2×C8—592no—
256C2×C8—592no—
257C2×C8—592no—
258C2×C8—592no—
259C2×C8—592no—
260C2×C8—598no—
261C2×C8—598no—
262C2×C8—592no—
263C2×C8—592no—
264C2×C8—592no—
265C2×C8—592no—
266C2×C8C8×D5912yes—
267C2×C8C8×D5912yes—
268C2×C8C2×C4×D5911yescharacteristic
269C2×C8C2×C4×D5912yes—
270C2×C8D4×D5911yescharacteristic
271C2×C8D4×D5911yescharacteristic
272C2×C8Q8×D5911yescharacteristic
273C2×C8Q8×D5911yescharacteristic
274C2×C8C23×D5911yescharacteristic
275C42—21no—
276C42—592no—
277C42—1184no—
278C42—1181no—
279C42C2×C4×D5912yes—
280C16—24no—
281C16—1184no—
282C23—591no—
283C23—592no—
284C23—592no—
285C23—591no—
286C23—1184no—
287C23M16×D5911yescharacteristic
288C2×C4—24no—
289C2×C4—22no—
290C2×C4—592no—
291C2×C4—592no—
292C2×C4—591no—
293C2×C4—591no—
294C2×C4—592no—
295C2×C4—592no—
296C2×C4—592no—
297C2×C4—592no—
298C2×C4—592no—
299C2×C4—592no—
300C2×C4—592no—
301C2×C4—592no—
302C2×C4—11816no—
303C2×C4—1184no—
304C2×C4—1182no—
305C2×C4C4⋊C4×D5911yescharacteristic
306C2×C4C4⋊C4×D5911yescharacteristic
307C2×C4C2×C8×D5911yescharacteristic
308C2×C4C2×C8×D5911yescharacteristic
309C2×C4M16×D5911yescharacteristic
310C2×C4C22×C4×D5911yescharacteristic
311C8—594no—
312C8—592no—
313C8—592no—
314C8C4⋊C4×D5911yescharacteristic
315C8C4⋊C4×D5911yescharacteristic
316C8C2×C8×D5914yes—
317C8C2×D4×D5911yescharacteristic
318C8C2×Q8×D5911yescharacteristic
319C22—22no—
320C22—592no—
321C22—594no—
322C22—592no—
323C22—1184no—
324C22—1184no—
325C22—1182no—
326C22C4⋊C8×D5911yescharacteristic
327C22C4⋊C8×D5911yescharacteristic
328C22C2×M16×D5911yescharacteristic
329C4—24no—
330C4—592no—
331C4—592no—
332C4—1184no—
333C4C4⋊C8×D5911yescharacteristic
334C4C4⋊C8×D5911yescharacteristic
335C4C2×C4⋊C4×D5911yescharacteristic
336C4C22×C8×D5911yescharacteristic
337C2—21no—
338C2—21no—
339C2—594no—
340C2—1182no—
341C2#364×D5912yesdirect product factor
342C2C2×C4⋊C8×D5911yescharacteristic
subgroupG/H
centerC2×C8D4×D59
commutatorC4×C59C23×C8
FrattiniC2×C8C23×D59
FittingC2×C59×#364C2
socleC22×C59C2×C4⋊C8
prime radicalC23×D59M16
cosocleC2×C8×C59C24
hypercenterC2×#364D59
hypocenterC59C22×#364
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#364

Complements

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

NH ≅ G/Ntype
3. C2×#16837223C2semidirect
4. C2×#16837222C2semidirect
5. #364×D59C2direct (N × H)
6. C2×C59×#364C2semidirect
20. #16837223C22semidirect
21. #16837222C22semidirect
24. C59×#364C22semidirect
155. C2×D59#364direct (N × H)
171. C2×#364D59direct (N × H)
174. C2×C59C2×#364semidirect
177. D59C2×#364direct (N × H)
195. #364C2×D59direct (N × H)
196. C59C22×#364semidirect
341. C2#364×D59direct (N × H)

Maximal subgroups

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

subgroupindex
C2×M32×D592
C2×C4×C8×D592
C2×#168372232
C2×#168372222
#364×D592
C2×C59×#3642
C22×#36459