Finite Group Databasebeta

← #28488737

Subgroups — #28488737

Order 15104.

572 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837286C211yesmaximal, characteristic
2#21424076C211yesmaximal, characteristic
3#21421938C212yesmaximal
4#21421938C212yesmaximal
5C4×C22⋊C8×C59C211yesmaximal, characteristic
6C22×Dic59⋊C4C411yescharacteristic
7C22×Dic59⋊C4C411yescharacteristic
8C2×C4⋊(C59⋊C8)—21no—
9C2×C22⋊(C59⋊C8)C2212yes—
10#16837286—21no—
11#16837286—21no—
12#16837286—21no—
13#16837286—21no—
14C2×C59⋊#95C411yescharacteristic
15C2×C59⋊#95C411yescharacteristic
16C2×C59⋊#95C2211yescharacteristic
17C2×C59⋊#95C2211yescharacteristic
18#16837157—21no—
19C22×C42×C59C2211yescharacteristic
20C2×C22⋊C8×C59C2212yes—
21C2×C4×C8×C59—21no—
22C59×#336—21no—
23C23×Dic59C2×C411yescharacteristic
24C23×Dic59C2×C411yescharacteristic
25C23×Dic59C2×C411yescharacteristic
26C23×Dic59C2×C411yescharacteristic
27C22×C59⋊C8—22no—
28C2×Dic59⋊C4—21no—
29C2×Dic59⋊C4—21no—
30C2×Dic59⋊C4—22no—
31C2×Dic59⋊C4—21no—
32C2×Dic59⋊C4—21no—
33C2×Dic59⋊C4—42no—
34C2×Dic59⋊C4C814yescomplemented
35C4⋊(C59⋊C8)—42no—
36C22⋊(C59⋊C8)—24no—
37C59⋊#95—21no—
38C59⋊#95—21no—
39C59⋊#95—21no—
40C59⋊#95—21no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C23×C4×C59C2×C411yescharacteristic
46C23×C4×C59C2×C411yescharacteristic
47C23×C4×C59C2311yescharacteristic
48C22×C8×C59—22no—
49C2×C42×C59—42no—
50C2×C42×C59D411yescharacteristic
51C2×C42×C59D411yescharacteristic
52C2×C42×C59D411yescharacteristic
53C2×C42×C59D411yescharacteristic
54C22⋊C8×C59—22no—
55C22⋊C8×C59Q814yes—
56C4×C8×C59—42no—
57C24×C59C22×C411yescharacteristic
58C22×C4×C59—22no—
59C22×C4×C59—22no—
60C22×C4×C59—41no—
61C22×C4×C59—41no—
62C22×C4×C59—41no—
63C22×C4×C59—41no—
64C22×C4×C59—41no—
65C22×C4×C59C22⋊C411yescharacteristic
66C22×C4×C59C22⋊C411yescharacteristic
67C22×C4×C59C22⋊C411yescharacteristic
68C22×C4×C59C22⋊C411yescharacteristic
69C22×C4×C59C2×C812yes—
70C22×C4×C59M1612yes—
71C22×C4×C59C2×D411yescharacteristic
72C22×C4×C59C2×D411yescharacteristic
73C22×C4×C59C2×Q812yes—
74C22×C4×C59#4112yes—
75C22×Dic59—21no—
76C22×Dic59—21no—
77C22×Dic59—21no—
78C22×Dic59—21no—
79C22×Dic59—21no—
80C22×Dic59—21no—
81C22×Dic59—22no—
82C22×Dic59—22no—
83C22×Dic59—41no—
84C22×Dic59—41no—
85C22×Dic59—41no—
86C22×Dic59—41no—
87C22×Dic59—41no—
88C22×Dic59—41no—
89C22×Dic59—41no—
90C22×Dic59—41no—
91C22×Dic59C2×C812yes—
92C22×Dic59C2×C812yes—
93C2×C8×C59—24no—
94C2×C8×C59—42no—
95C2×C8×C59—42no—
96C42×C59—22no—
97C42×C59—22no—
98C42×C59—41no—
99C42×C59—41no—
100Dic59⋊C4—24no—
101Dic59⋊C4—24no—
102Dic59⋊C4—42no—
103Dic59⋊C4—42no—
104C2×C59⋊C8—42no—
105C2×C59⋊C8—42no—
106C2×C59⋊C8—42no—
107C23×C59—21no—
108C23×C59—21no—
109C23×C59—21no—
110C23×C59—21no—
111C23×C59C2×C22⋊C411yescharacteristic
112C23×C59C4×Q812yes—
113C23×C59C22×C811yescharacteristic
114C23×C59C2×M1611yescharacteristic
115C23×C59#13112yes—
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—21no—
128C2×C4×C59—21no—
129C2×C4×C59—42no—
130C2×C4×C59—42no—
131C2×C4×C59—42no—
132C2×C4×C59—42no—
133C2×C4×C59—44no—
134C2×C4×C59C22⋊C812yes—
135C2×C4×C59C22⋊C812yes—
136C2×C4×C59#9912yes—
137C2×C4×C59C22⋊Q812yes—
138C2×C4×C59#12411yescharacteristic
139C2×C4×C59C4⋊Q811yescharacteristic
140C2×Dic59—22no—
141C2×Dic59—22no—
142C2×Dic59—42no—
143C2×Dic59—42no—
144C2×Dic59—41no—
145C2×Dic59—41no—
146C2×Dic59—41no—
147C2×Dic59—41no—
148C2×Dic59—42no—
149C2×Dic59—42no—
150C2×Dic59—41no—
151C2×Dic59—41no—
152C2×Dic59—41no—
153C2×Dic59—41no—
154C2×Dic59—41no—
155C2×Dic59—41no—
156C2×Dic59—82no—
157C2×Dic59—82no—
158C8×C59—44no—
159C59⋊C8—82no—
160#9880—591nomaximal, Sylow
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—21no—
164C22×C59—21no—
165C22×C59—22no—
166C22×C59—22no—
167C22×C59—22no—
168C22×C59—22no—
169C22×C59#39111yescharacteristic
170C22×C59C2×C22⋊C811yescharacteristic
171C22×C59#40811yescharacteristic
172C22×C59C2×#9911yescharacteristic
173C22×C59#41011yescharacteristic
174C22×C59#41311yescharacteristic
175C22×C59#41311yescharacteristic
176C22×C59C8×Q812yes—
177C22×C59#44612yes—
178C4×C59—22no—
179C4×C59—22no—
180C4×C59—22no—
181C4×C59—21no—
182C4×C59—22no—
183C4×C59—21no—
184C4×C59—41no—
185Dic59—42no—
186Dic59—42no—
187Dic59—81no—
188Dic59—81no—
189C2×#387—591no—
190#1797—591no—
191C4×C22⋊C8D5911yescharacteristic
192#1280—592no—
193#1280—592no—
194C2×C59—22no—
195C2×C59—22no—
196C2×C59#145811yescharacteristic
197C2×C59#145911yescharacteristic
198C2×C59#146811yescharacteristic
199C2×C59#147311yescharacteristic
200C2×C59#198411yescharacteristic
201C2×C59#199611yescharacteristic
202C2×C59#199811yescharacteristic
203C22×C4⋊C4—591no—
204C22×C4⋊C4—591no—
205C22×C42C2×D5911yescharacteristic
206C2×C4⋊C8—1181no—
207C2×C22⋊C8—592no—
208C2×C22⋊C8C2×D5912yes—
209C2×C4×C8—21no—
210#387—1181no—
211#387—1181no—
212#387—1181no—
213#387—1181no—
214C2×#95—591no—
215C2×#95—591no—
216C2×#95—591no—
217C2×#95—591no—
218#336—21no—
219#336—1181no—
220C59#988011yescharacteristic, complemented, Sylow
221C23×C4—591no—
222C23×C4—591no—
223C23×C4—591no—
224C23×C4—591no—
225C23×C4C4×D5911yescharacteristic
226C23×C4C4×D5911yescharacteristic
227C23×C4C22×D5911yescharacteristic
228C22×C8—22no—
229C22×C8—1182no—
230C2×C4⋊C4—594no—
231C2×C4⋊C4—1182no—
232C2×C4⋊C4—1181no—
233C2×C4⋊C4—1181no—
234C2×C4⋊C4—1181no—
235C2×C4⋊C4—1181no—
236C2×C4⋊C4—2362no—
237C2×C42—42no—
238C2×C42D23611yescharacteristic
239C2×C42D23611yescharacteristic
240C2×C42C22⋊D5911yescharacteristic
241C2×C42C22⋊D5911yescharacteristic
242C4⋊C8—2362no—
243C22⋊C8—22no—
244C22⋊C8—1184no—
245C22⋊C8Dic11814yes—
246C4×C8—42no—
247#95—1181no—
248#95—1181no—
249#95—1181no—
250#95—1181no—
251#95—1181no—
252#95—1181no—
253#95—1181no—
254#95—1181no—
255C24C2×C4×D5911yescharacteristic
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—592no—
264C22×C4—592no—
265C22×C4—1181no—
266C22×C4—1181no—
267C22×C4—1181no—
268C22×C4—1181no—
269C22×C4—1182no—
270C22×C4—1182no—
271C22×C4—1181no—
272C22×C4—1181no—
273C22×C4—2361no—
274C22×C4—2361no—
275C22×C4—2361no—
276C22×C4—2361no—
277C22×C4—2361no—
278C22×C4—2361no—
279C22×C4—2361no—
280C22×C4—2361no—
281C22×C4C8×D5912yes—
282C22×C4#1174565912yes—
283C22×C4(C2×D59)⋊C411yescharacteristic
284C22×C4(C2×D59)⋊C411yescharacteristic
285C22×C4(C2×D59)⋊C411yescharacteristic
286C22×C4(C2×D59)⋊C411yescharacteristic
287C22×C4C2×Dic11812yes—
288C22×C4C2×D23611yescharacteristic
289C22×C4#1174568512yes—
290C22×C4C2×C22⋊D5911yescharacteristic
291C2×C8—24no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—2362no—
295C2×C8—2362no—
296C2×C8—2362no—
297C4⋊C4—1184no—
298C4⋊C4—1184no—
299C4⋊C4—2362no—
300C4⋊C4—2362no—
301C42—22no—
302C42—22no—
303C42—41no—
304C42—41no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23C2×(C2×D59)⋊C411yescharacteristic
310C23C4×Dic11812yes—
311C23C2×C8×D5911yescharacteristic
312C23C2×#1174565911yescharacteristic
313C23#1427373312yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—1182no—
333C2×C4—1182no—
334C2×C4—4722no—
335C2×C4—4722no—
336C2×C4—2361no—
337C2×C4—2361no—
338C2×C4—2361no—
339C2×C4—2361no—
340C2×C4—2361no—
341C2×C4—2361no—
342C2×C4—2362no—
343C2×C4—2362no—
344C2×C4—2361no—
345C2×C4—2361no—
346C2×C4—2361no—
347C2×C4—2361no—
348C2×C4—2362no—
349C2×C4—2362no—
350C2×C4(C2×D59)⋊C812yes—
351C2×C4(C2×D59)⋊C812yes—
352C2×C4#1427364112yes—
353C2×C4#1427370612yes—
354C2×C4#1427371511yescharacteristic
355C2×C4#1427372711yescharacteristic
356C8—44no—
357C8—4722no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22#1683730811yescharacteristic
367C22C2×(C2×D59)⋊C811yescharacteristic
368C22#1683736811yescharacteristic
369C22C2×#1427364111yescharacteristic
370C22#1683737511yescharacteristic
371C22#1683738411yescharacteristic
372C22#1683738411yescharacteristic
373C22C8×Dic11812yes—
374C22#1683753212yes—
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—21no—
380C4—21no—
381C4—41no—
382C4—4721no—
383C4—4721no—
384C4—2362no—
385C4—2362no—
386C2—22no—
387C2—22no—
388C2#2142240811yescharacteristic
389C2#2142241211yescharacteristic
390C2#2142244211yescharacteristic
391C2#2142246311yescharacteristic
392C2#2142503211yescharacteristic
393C2#2142508111yescharacteristic
394C2#2142508911yescharacteristic
subgroupG/H
centerC23C2×(C2×D59)⋊C4
commutatorC23×C59C22×C8
FrattiniC23×C4C22×D59
FittingC4×C22⋊C8×C59C2
socleC23×C59C2×C22⋊C4
prime radicalC24×C59C22×C4
cosocleC23×C4×C59C23
hypercenterC4×C22⋊C8D59
hypocenterC59#9880
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
34. C2×Dic59⋊C4C8semidirect
220. C59#9880semidirect

Maximal subgroups

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

subgroupindex
C2×#168372862
#214240762
#214219382
C4×C22⋊C8×C592
#988059