Finite Group Databasebeta

← #28485224

Subgroups — #28485224

Order 15104.

428 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21435240C211yesmaximal, characteristic
2#21433039C211yesmaximal, characteristic
3#21424941C211yesmaximal, characteristic
4#21422784C211yesmaximal, characteristic
5#21421993C211yesmaximal, characteristic
6#21421946C211yesmaximal, characteristic
7C2×C59×#332C211yesmaximal, characteristic
8#16837959C2211yescharacteristic
9#16837798—21no—
10#16837754—21no—
11#16837732C414yes—
12#16837684—22no—
13#16837531—22no—
14#16837529—21no—
15#16837526—21no—
16#16837455C2211yescharacteristic
17#16837428—21no—
18#16837426C2211yescharacteristic
19C2×#14273646—21no—
20C2×#14273646—21no—
21#16837357—21no—
22C4×#11745664C2211yescharacteristic
23#16837150—21no—
24#16837149—21no—
25C2×C4⋊Q8×C59C2211yescharacteristic
26C2×C4⋊C8×C59C2211yescharacteristic
27C2×C4⋊C8×C59C2211yescharacteristic
28C59×#332—21no—
29C59×#332—21no—
30C2×#11745664—21no—
31C2×#11745664D411yescharacteristic
32C2×#11745664D411yescharacteristic
33#14273727D411yescharacteristic
34#14273727D411yescharacteristic
35#14273719—21no—
36#14273706—21no—
37#14273706C2×C412yes—
38C4×Dic118—21no—
39C4×Dic118D412yes—
40#14273686—21no—
41#14273658—24no—
42C4⋊(C59⋊C8)—21no—
43C4⋊(C59⋊C8)—21no—
44C4⋊(C59⋊C8)—21no—
45Dic59⋊C8—22no—
46Dic59⋊C8—22no—
47#14273650—24no—
48#14273646—42no—
49#14273646—42no—
50C22⋊(C59⋊C8)C2×C412yes—
51#14273638—21no—
52#14273637—22no—
53C4×C59⋊C8—21no—
54C4×C59⋊C8—21no—
55C8×Dic59—22no—
56C22×Q8×C59—21no—
57C22×C8×C59—21no—
58C22×C8×C59—21no—
59C4⋊Q8×C59—21no—
60C4⋊Q8×C59—21no—
61C4⋊Q8×C59—21no—
62C4⋊Q8×C59—21no—
63C2×C4⋊C4×C59—21no—
64C2×C4⋊C4×C59C2×C412yes—
65C2×C42×C59C2311yescharacteristic
66C4⋊C8×C59—21no—
67C4⋊C8×C59—21no—
68C4⋊C8×C59—21no—
69C4⋊C8×C59D411yescharacteristic
70C4⋊C8×C59D411yescharacteristic
71C2×Q8×C59—41no—
72C2×Q8×C59—41no—
73C2×Q8×C59—41no—
74C2×Q8×C59—41no—
75C2×Q8×C59—41no—
76C2×Q8×C59—41no—
77C22×C4×C59—22no—
78C22×C4×C59C22×C411yescharacteristic
79C22×C4×C59C2×D411yescharacteristic
80C22×C4×C59#4111yescharacteristic
81C2×Dic118—21no—
82C2×Dic118C22⋊C412yes—
83C2×C8×C59—21no—
84C2×C8×C59—21no—
85C2×C8×C59—41no—
86C2×C8×C59—41no—
87C2×C8×C59—41no—
88C2×C8×C59—81no—
89C4⋊C4×C59—22no—
90C4⋊C4×C59—22no—
91C4⋊C4×C59—41no—
92C4⋊C4×C59—41no—
93C42×C59C2×D411yescharacteristic
94C42×C59C2×D411yescharacteristic
95C42×C59C2×D411yescharacteristic
96C42×C59#4111yescharacteristic
97C22⋊Dic59—22no—
98C4⋊Dic59—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59—21no—
101C4⋊Dic59C22⋊C412yes—
102Dic59⋊C4—22no—
103Dic59⋊C4—22no—
104C4×Dic59—22no—
105#11745664—21no—
106#11745664—21no—
107#11745664—21no—
108#11745664—41no—
109#11745664—41no—
110#11745664SD1612yes—
111C2×C59⋊C8—21no—
112C2×C59⋊C8—22no—
113C2×C59⋊C8—21no—
114C2×C59⋊C8—41no—
115C23×C59C4×D411yescharacteristic
116Q8×C59—81no—
117Q8×C59—81no—
118Q8×C59—81no—
119Q8×C59—81no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—41no—
123C2×C4×C59—42no—
124C2×C4×C59—42no—
125C2×C4×C59—42no—
126C2×C4×C59C2×C22⋊C411yescharacteristic
127C2×C4×C59C4×D411yescharacteristic
128C2×C4×C59#12011yescharacteristic
129C2×C4×C59#12111yescharacteristic
130C2×C4×C59#12111yescharacteristic
131C2×C4×C59#12311yescharacteristic
132C2×C4×C59C2×SD1611yescharacteristic
133C2×C4×C59#13511yescharacteristic
134C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C59#13711yescharacteristic
136C2×Dic59—22no—
137C2×Dic59—22no—
138Dic118—41no—
139Dic118—41no—
140Dic118—42no—
141C8×C59—41no—
142C8×C59—41no—
143C8×C59—81no—
144C59⋊C8—22no—
145C59⋊C8—42no—
146C59⋊C8—41no—
147C59⋊C8—81no—
148#9272—591nomaximal, Sylow
149C22×C59—21no—
150C22×C59—21no—
151C22×C59#38611yescharacteristic
152C22×C59C4×SD1611yescharacteristic
153C22×C59#44011yescharacteristic
154C4×C59—21no—
155C4×C59—21no—
156C4×C59—21no—
157C4×C59—82no—
158C4×C59#44811yescharacteristic
159C4×C59#44911yescharacteristic
160C4×C59#46011yescharacteristic
161C4×C59#46411yescharacteristic
162C4×C59#47111yescharacteristic
163C4×C59#47311yescharacteristic
164Dic59—42no—
165Dic59—42no—
166#3229—591no—
167#2962—591no—
168#1966—591no—
169#1550—591no—
170C2×#332D5911yescharacteristic
171#1301—591no—
172#1283—591no—
173C2×C59—21no—
174C2×C59—21no—
175C2×C59#188011yescharacteristic
176C2×C59#190811yescharacteristic
177C2×C59#191511yescharacteristic
178#533—591no—
179C2×C4⋊Q8C2×D5911yescharacteristic
180#498—1181no—
181#487—1181no—
182#483—594no—
183#475—1182no—
184#446—1182no—
185#446—1181no—
186C8×Q8—1181no—
187#431—591no—
188#424—1181no—
189#423—591no—
190C2×C4⋊C8C2×D5911yescharacteristic
191C2×C4⋊C8C2×D5911yescharacteristic
192C2×#101—1181no—
193C2×#101—1181no—
194#405—1181no—
195C4×M16—591no—
196#333—1181no—
197#332—21no—
198#332—21no—
199#332—1181no—
200C59#927211yescharacteristic, complemented, Sylow
201C22×Q8—21no—
202C2×M16—591no—
203C2×M16—591no—
204C2×M16—1181no—
205C22×C8—21no—
206C22×C8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—591no—
212C4⋊Q8—591no—
213#125—1181no—
214C22⋊Q8—592no—
215C22⋊Q8—1181no—
216C4×Q8—592no—
217C4×Q8—1181no—
218#117—1181no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4C4×D5912yes—
221C2×C42C22×D5911yescharacteristic
222#106—1184no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—1182no—
227C4⋊C8—1182no—
228C4⋊C8—1181no—
229C4⋊C8—1181no—
230C4⋊C8—1181no—
231C4⋊C8C22⋊D5911yescharacteristic
232C4⋊C8C22⋊D5911yescharacteristic
233#103—1184no—
234#101—2362no—
235#101—2362no—
236C22⋊C8—592no—
237#97—1182no—
238#97—1181no—
239C4×C8—1182no—
240C4×C8—1181no—
241C4×C8—1181no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—592no—
249C2×Q8—1181no—
250C22×C4—22no—
251C22×C4C2×C4×D5911yescharacteristic
252C22×C4D4×D5911yescharacteristic
253C22×C4#1174568711yescharacteristic
254M16—592no—
255M16—1181no—
256M16—1181no—
257M16—1181no—
258M16—2361no—
259M16—2361no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—81no—
266C2×C8—1181no—
267C2×C8—1182no—
268C2×C8—1181no—
269C2×C8—2361no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—592no—
275C4⋊C4—1182no—
276C4⋊C4—1181no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4—1182no—
280C22⋊C4—1182no—
281C42—1182no—
282C42#1174568511yescharacteristic
283C42D4×D5911yescharacteristic
284C42D4×D5911yescharacteristic
285C42C2×C22⋊D5911yescharacteristic
286C23(C22⋊D59)⋊C411yescharacteristic
287Q8—81no—
288Q8—81no—
289Q8—81no—
290Q8—81no—
291Q8—2362no—
292Q8—2361no—
293Q8—2361no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—1182no—
301C2×C4—1182no—
302C2×C4C22⋊C4×D5911yescharacteristic
303C2×C4C4×C22⋊D5911yescharacteristic
304C2×C4#1427369511yescharacteristic
305C2×C4#1427369811yescharacteristic
306C2×C4#1427370011yescharacteristic
307C2×C4#1427370911yescharacteristic
308C2×C4SD16×D5911yescharacteristic
309C2×C4#1427374611yescharacteristic
310C2×C4#1427375111yescharacteristic
311C2×C4#1427375611yescharacteristic
312C8—41no—
313C8—41no—
314C8—81no—
315C8—1182no—
316C8—4721no—
317C8—2362no—
318C8—2361no—
319C22—21no—
320C22—21no—
321C22#1683727811yescharacteristic
322C22#1683749311yescharacteristic
323C22#1683749911yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—82no—
328C4—2362no—
329C4—2362no—
330C4#1683753911yescharacteristic
331C4#1683754411yescharacteristic
332C4#1683760111yescharacteristic
333C4#1683762311yescharacteristic
334C4#1683766211yescharacteristic
335C4#1683767411yescharacteristic
336C2—21no—
337C2—21no—
338C2#2142444811yescharacteristic
339C2#2142461411yescharacteristic
340C2#2142464511yescharacteristic
subgroupG/H
centerC22#16837278
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC2×C59×#332C2
socleC22×C59#386
prime radicalC23×C59C4×D4
cosocleC2×C42×C59C23
hypercenterC2×#332D59
hypocenterC59#9272
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
200. C59#9272semidirect

Maximal subgroups

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

subgroupindex
#214352402
#214330392
#214249412
#214227842
#214219932
#214219462
C2×C59×#3322
#927259