Finite Group Databasebeta

← #28484319

Subgroups — #28484319

Order 15104.

530 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432406C211yesmaximal, characteristic
2#21423858C211yesmaximal, characteristic
3C2×#16837143C212yesmaximal, complemented
4#21421978C212yesmaximal, complemented
5C2×C59×#432C211yesmaximal, characteristic
6C2×#14273719C2211yescharacteristic
7C2×C22⋊(C59⋊C8)—21no—
8C2×#14273638C2212yes—
9#16837300C411yescharacteristic
10#16837300C411yescharacteristic
11#16837286—21no—
12#16837286—21no—
13#16837275—21no—
14#16837275—21no—
15#16837268C2211yescharacteristic
16#16837262C411yescharacteristic
17#16837262C411yescharacteristic
18#16837157—21no—
19#16837143—24no—
20C22×C42×C59C2211yescharacteristic
21C59×#432—24no—
22C2×C4⋊C8×C59—21no—
23C2×C22⋊C8×C59—21no—
24C2×#97×C59C2212yes—
25C22×C59⋊C8—22no—
26#14273719—22no—
27#14273719—22no—
28C2×C4⋊Dic59C2×C411yescharacteristic
29C2×C4⋊Dic59C2×C411yescharacteristic
30C2×C4⋊Dic59C2×C411yescharacteristic
31C2×C4⋊Dic59C2×C411yescharacteristic
32C2×Dic59⋊C4—21no—
33C2×Dic59⋊C4—21no—
34C2×Dic59⋊C4—21no—
35C2×Dic59⋊C4—21no—
36C2×C22⋊Dic59—21no—
37C2×C22⋊Dic59—21no—
38C22⋊(C59⋊C8)—24no—
39#14273638—22no—
40#14273638—22no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C23×C4×C59C2×C411yescharacteristic
48C23×C4×C59D411yescharacteristic
49C23×C4×C59D411yescharacteristic
50C22×C8×C59—22no—
51C2×C42×C59—22no—
52C2×C42×C59—22no—
53C2×C42×C59C2×C411yescharacteristic
54C2×C42×C59D411yescharacteristic
55C2×C42×C59D411yescharacteristic
56C2×C42×C59C2311yescharacteristic
57C4⋊C8×C59—24no—
58C22⋊C8×C59—24no—
59#97×C59—22no—
60#97×C59D414yes—
61C24×C59C22⋊C411yescharacteristic
62C22×C4×C59—22no—
63C22×C4×C59—22no—
64C22×C4×C59—22no—
65C22×C4×C59—21no—
66C22×C4×C59—22no—
67C22×C4×C59—21no—
68C22×C4×C59—41no—
69C22×C4×C59—41no—
70C22×C4×C59—41no—
71C22×C4×C59—41no—
72C22×C4×C59C22⋊C411yescharacteristic
73C22×C4×C59C22⋊C411yescharacteristic
74C22×C4×C59C22⋊C411yescharacteristic
75C22×C4×C59C22×C411yescharacteristic
76C22×C4×C59C2×D411yescharacteristic
77C22×C4×C59C2×D411yescharacteristic
78C22×Dic59—21no—
79C22×Dic59—21no—
80C22×Dic59—21no—
81C22×Dic59—21no—
82C2×C8×C59—24no—
83C2×C8×C59—42no—
84C2×C8×C59—42no—
85C42×C59—22no—
86C42×C59—21no—
87C42×C59—22no—
88C42×C59—21no—
89C42×C59C2×D412yes—
90C42×C59#4112yes—
91C22⋊Dic59—42no—
92C22⋊Dic59—42no—
93C4⋊Dic59—22no—
94C4⋊Dic59—22no—
95C4⋊Dic59—41no—
96C4⋊Dic59—41no—
97Dic59⋊C4—42no—
98Dic59⋊C4—42no—
99Dic59⋊C4—41no—
100Dic59⋊C4—42no—
101Dic59⋊C4—41no—
102C2×C59⋊C8—24no—
103C2×C59⋊C8—42no—
104C2×C59⋊C8—42no—
105C23×C59—21no—
106C23×C59—21no—
107C23×C59—21no—
108C23×C59—21no—
109C23×C59—21no—
110C23×C59—21no—
111C23×C59#10112yes—
112C23×C59C2×C22⋊C411yescharacteristic
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—44no—
128C2×C4×C59—44no—
129C2×C4×C59—42no—
130C2×C4×C59—42no—
131C2×C4×C59#10412yes—
132C2×C4×C59C4×D412yes—
133C2×C4×C59#12011yescharacteristic
134C2×C4×C59#12112yes—
135C2×C4×C59#12311yescharacteristic
136C2×Dic59—41no—
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59—41no—
142C2×Dic59—41no—
143C2×Dic59—41no—
144C2×Dic59—41no—
145C2×Dic59—41no—
146C2×Dic59—41no—
147C2×Dic59—41no—
148C8×C59—44no—
149C59⋊C8—44no—
150#9126—591nomaximal, Sylow
151C22×C59—22no—
152C22×C59—22no—
153C22×C59—22no—
154C22×C59—41no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59#38611yescharacteristic
159C22×C59C2×#10111yescharacteristic
160C22×C59#41311yescharacteristic
161C22×C59C2×#10411yescharacteristic
162C22×C59#42111yescharacteristic
163C22×C59#42111yescharacteristic
164C22×C59#42111yescharacteristic
165C4×C59—22no—
166C4×C59—22no—
167C4×C59—21no—
168C4×C59—21no—
169C4×C59—22no—
170C4×C59—41no—
171C4×C59—41no—
172Dic59—81no—
173Dic59—81no—
174Dic59—81no—
175Dic59—81no—
176C2×#432D5911yescharacteristic
177#2851—591no—
178#1749—591no—
179C2×#330—592no—
180#1295—592no—
181C2×C59—42no—
182C2×C59#152911yescharacteristic
183C2×C59#153111yescharacteristic
184C2×C59#153411yescharacteristic
185C2×C59#153511yescharacteristic
186C2×C59#187111yescharacteristic
187C2×C59#189711yescharacteristic
188C2×C59#190111yescharacteristic
189C2×#125—591no—
190C22×C42C2×D5911yescharacteristic
191#432—24no—
192C2×C4⋊C8—21no—
193C2×C22⋊C8—21no—
194C2×C22⋊C8—1181no—
195C2×#97—592no—
196C2×#97C2×D5912yes—
197#389—591no—
198#389—591no—
199#387—1181no—
200#387—1181no—
201#385—1181no—
202#385—1181no—
203#382—591no—
204#380—591no—
205#380—591no—
206#336—1181no—
207#330—1184no—
208C59#912611yescharacteristic, complemented, Sylow
209C23×C4C4×D5911yescharacteristic
210C23×C4D23611yescharacteristic
211C23×C4C22⋊D5911yescharacteristic
212C22×C8—22no—
213C22×C8—1182no—
214#125—1182no—
215#125—1182no—
216C2×C4⋊C4—591no—
217C2×C4⋊C4—591no—
218C2×C4⋊C4—591no—
219C2×C4⋊C4—591no—
220C2×C4⋊C4—1181no—
221C2×C4⋊C4—1181no—
222C2×C4⋊C4—1181no—
223C2×C4⋊C4—1181no—
224C2×C22⋊C4—1181no—
225C2×C22⋊C4—1181no—
226C2×C42—22no—
227C2×C42—22no—
228C2×C42C4×D5911yescharacteristic
229C2×C42D23611yescharacteristic
230C2×C42C22⋊D5911yescharacteristic
231C2×C42C22×D5911yescharacteristic
232C4⋊C8—24no—
233C22⋊C8—24no—
234C22⋊C8—1184no—
235#97—22no—
236#97—1182no—
237#97—1182no—
238#97C22⋊D5914yes—
239#95—1181no—
240#95—1181no—
241#95—1181no—
242#95—1181no—
243#95—1181no—
244#95—1181no—
245C24(C2×D59)⋊C411yescharacteristic
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—1181no—
257C22×C4—1181no—
258C22×C4—1181no—
259C22×C4—1181no—
260C22×C4(C2×D59)⋊C411yescharacteristic
261C22×C4(C2×D59)⋊C411yescharacteristic
262C22×C4(C2×D59)⋊C411yescharacteristic
263C22×C4C2×C4×D5911yescharacteristic
264C22×C4C2×D23611yescharacteristic
265C22×C4C2×C22⋊D5911yescharacteristic
266C2×C8—24no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—1184no—
270C2×C8—2362no—
271C2×C8—2362no—
272C4⋊C4—1182no—
273C4⋊C4—1182no—
274C4⋊C4—2361no—
275C4⋊C4—2361no—
276C4⋊C4—2362no—
277C4⋊C4—2362no—
278C4⋊C4—2361no—
279C4⋊C4—2362no—
280C4⋊C4—2361no—
281C22⋊C4—2362no—
282C22⋊C4—2362no—
283C42—22no—
284C42—21no—
285C42—22no—
286C42—21no—
287C42#1174568512yes—
288C42C2×C22⋊D5912yes—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23#1427364512yes—
296C23C2×(C2×D59)⋊C411yescharacteristic
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—2361no—
316C2×C4—2361no—
317C2×C4—2361no—
318C2×C4—2361no—
319C2×C4—2361no—
320C2×C4—2361no—
321C2×C4—2361no—
322C2×C4—2361no—
323C2×C4—2361no—
324C2×C4—2361no—
325C2×C4—2361no—
326C2×C4—2361no—
327C2×C4#1427365312yes—
328C2×C4C4×C22⋊D5912yes—
329C2×C4#1427369611yescharacteristic
330C2×C4#1427370112yes—
331C2×C4#1427371011yescharacteristic
332C8—44no—
333C8—2364no—
334C22—22no—
335C22—22no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22#1683728111yescharacteristic
342C22C2×#1427364511yescharacteristic
343C22#1683738411yescharacteristic
344C22C2×#1427365311yescharacteristic
345C22#1683741811yescharacteristic
346C22#1683742011yescharacteristic
347C22#1683742011yescharacteristic
348C4—22no—
349C4—22no—
350C4—21no—
351C4—21no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—4721no—
356C4—4721no—
357C4—4721no—
358C4—4721no—
359C2—42no—
360C2#2142270411yescharacteristic
361C2#2142271211yescharacteristic
362C2#2142272211yescharacteristic
363C2#2142272511yescharacteristic
364C2#2142439811yescharacteristic
365C2#2142454411yescharacteristic
366C2#2142456411yescharacteristic
subgroupG/H
centerC23C2×(C2×D59)⋊C4
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC2×C59×#432C2
socleC23×C59C2×C22⋊C4
prime radicalC24×C59C22⋊C4
cosocleC2×C42×C59C23
hypercenterC2×#432D59
hypocenterC59#9126
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
3. C2×#16837143C2semidirect
4. #21421978C2semidirect
208. C59#9126semidirect

Maximal subgroups

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

subgroupindex
#214324062
#214238582
C2×#168371432
#214219782
C2×C59×#4322
#912659