Finite Group Databasebeta

← #28484095

Subgroups — #28484095

Order 15104.

604 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837286C211yesmaximal, characteristic
2#21424164C211yesmaximal, characteristic
3C2×#16837127C212yesmaximal
4#21421938C212yesmaximal
5C2×C59×#432C211yesmaximal, characteristic
6C22×Dic59⋊C4C411yescharacteristic
7C22×Dic59⋊C4C2211yescharacteristic
8C2×C22⋊(C59⋊C8)C2212yes—
9#16837286—21no—
10#16837286—21no—
11#16837286—21no—
12#16837286—21no—
13C2×C59⋊#95C411yescharacteristic
14C2×C59⋊#95C411yescharacteristic
15C2×C59⋊#95C411yescharacteristic
16C2×C59⋊#95C2211yescharacteristic
17#16837157—21no—
18#16837157—21no—
19#16837127—24no—
20C22×C42×C59C2211yescharacteristic
21C59×#432—24no—
22C2×C4⋊C8×C59—21no—
23C2×C22⋊C8×C59C2212yes—
24C2×#97×C59—21no—
25C23×Dic59C2×C411yescharacteristic
26C23×Dic59C2×C411yescharacteristic
27C23×Dic59C2×C411yescharacteristic
28C23×Dic59C2×C411yescharacteristic
29C22×C59⋊C8—22no—
30C2×Dic59⋊C4—21no—
31C2×Dic59⋊C4—21no—
32C2×Dic59⋊C4—22no—
33C2×Dic59⋊C4—22no—
34C2×Dic59⋊C4—22no—
35C2×Dic59⋊C4—21no—
36C2×Dic59⋊C4—21no—
37C2×Dic59⋊C4—22no—
38C22⋊(C59⋊C8)—22no—
39C22⋊(C59⋊C8)—22no—
40C59⋊#95—21no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C23×C4×C59C2×C411yescharacteristic
49C23×C4×C59C2×C411yescharacteristic
50C23×C4×C59C2311yescharacteristic
51C22×C8×C59—22no—
52C2×C42×C59—22no—
53C2×C42×C59—22no—
54C2×C42×C59D411yescharacteristic
55C2×C42×C59D411yescharacteristic
56C2×C42×C59D411yescharacteristic
57C2×C42×C59D411yescharacteristic
58C4⋊C8×C59—24no—
59C22⋊C8×C59—22no—
60C22⋊C8×C59D414yes—
61#97×C59—24no—
62C24×C59C22×C411yescharacteristic
63C22×C4×C59—22no—
64C22×C4×C59—22no—
65C22×C4×C59—21no—
66C22×C4×C59—21no—
67C22×C4×C59—22no—
68C22×C4×C59—22no—
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×C4×C59C2×D412yes—
79C22×C4×C59#4112yes—
80C22×Dic59—21no—
81C22×Dic59—21no—
82C22×Dic59—22no—
83C22×Dic59—21no—
84C22×Dic59—21no—
85C22×Dic59—22no—
86C22×Dic59—21no—
87C22×Dic59—21no—
88C22×Dic59—22no—
89C22×Dic59—22no—
90C22×Dic59—41no—
91C22×Dic59—41no—
92C22×Dic59—41no—
93C22×Dic59—41no—
94C22×Dic59—41no—
95C22×Dic59—41no—
96C22×Dic59M1612yes—
97C22×Dic59M1612yes—
98C2×C8×C59—24no—
99C2×C8×C59—42no—
100C2×C8×C59—42no—
101C42×C59—21no—
102C42×C59—21no—
103C42×C59—22no—
104C42×C59—22no—
105C42×C59—21no—
106C42×C59—21no—
107Dic59⋊C4—24no—
108Dic59⋊C4—24no—
109Dic59⋊C4—41no—
110Dic59⋊C4—42no—
111Dic59⋊C4—41no—
112C2×C59⋊C8—42no—
113C2×C59⋊C8—42no—
114C2×C59⋊C8—42no—
115C23×C59—21no—
116C23×C59—21no—
117C23×C59—21no—
118C23×C59—21no—
119C23×C59C2×C22⋊C411yescharacteristic
120C23×C59C4×D412yes—
121C23×C59C2×M1611yescharacteristic
122C23×C59C2×M1611yescharacteristic
123C23×C59#13112yes—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—42no—
140C2×C4×C59—42no—
141C2×C4×C59—44no—
142C2×C4×C59—42no—
143C2×C4×C59—42no—
144C2×C4×C59#10112yes—
145C2×C4×C59#12011yescharacteristic
146C2×C4×C59#12112yes—
147C2×C4×C59#12311yescharacteristic
148C2×Dic59—22no—
149C2×Dic59—22no—
150C2×Dic59—24no—
151C2×Dic59—42no—
152C2×Dic59—41no—
153C2×Dic59—41no—
154C2×Dic59—41no—
155C2×Dic59—41no—
156C2×Dic59—42no—
157C2×Dic59—42no—
158C2×Dic59—41no—
159C2×Dic59—41no—
160C2×Dic59—41no—
161C2×Dic59—41no—
162C2×Dic59—41no—
163C2×Dic59—41no—
164C2×Dic59—82no—
165C2×Dic59—82no—
166C8×C59—44no—
167C59⋊C8—82no—
168#9086—591nomaximal, Sylow
169C22×C59—22no—
170C22×C59—22no—
171C22×C59—21no—
172C22×C59—21no—
173C22×C59—21no—
174C22×C59—21no—
175C22×C59—22no—
176C22×C59—22no—
177C22×C59#38611yescharacteristic
178C22×C59#40711yescharacteristic
179C22×C59#40811yescharacteristic
180C22×C59#41011yescharacteristic
181C22×C59#41011yescharacteristic
182C22×C59C2×#10111yescharacteristic
183C22×C59#41311yescharacteristic
184C22×C59#43512yes—
185C22×C59#43612yes—
186C4×C59—22no—
187C4×C59—21no—
188C4×C59—21no—
189C4×C59—22no—
190C4×C59—41no—
191C4×C59—41no—
192C4×C59—41no—
193Dic59—42no—
194Dic59—42no—
195Dic59—81no—
196Dic59—81no—
197C2×#432D5911yescharacteristic
198C2×#387—591no—
199#1817—591no—
200C2×#324—592no—
201#1280—592no—
202C2×C59—22no—
203C2×C59—22no—
204C2×C59#146411yescharacteristic
205C2×C59#146711yescharacteristic
206C2×C59#147011yescharacteristic
207C2×C59#147311yescharacteristic
208C2×C59#187011yescharacteristic
209C2×C59#189911yescharacteristic
210C2×C59#190111yescharacteristic
211C22×C4⋊C4—591no—
212C22×C4⋊C4—591no—
213C22×C42C2×D5911yescharacteristic
214#432—24no—
215C2×C4⋊C8—21no—
216C2×C22⋊C8—592no—
217C2×C22⋊C8C2×D5912yes—
218C2×#97—21no—
219#387—1181no—
220#387—1181no—
221#387—1181no—
222#387—1181no—
223C2×#95—591no—
224C2×#95—591no—
225C2×#95—591no—
226C2×#95—591no—
227#336—1181no—
228#336—1181no—
229#324—1184no—
230C59#908611yescharacteristic, complemented, Sylow
231C23×C4—591no—
232C23×C4—591no—
233C23×C4—591no—
234C23×C4—591no—
235C23×C4C4×D5911yescharacteristic
236C23×C4C4×D5911yescharacteristic
237C23×C4C22×D5911yescharacteristic
238C22×C8—22no—
239C22×C8—1182no—
240C2×C4⋊C4—1182no—
241C2×C4⋊C4—1182no—
242C2×C4⋊C4—1181no—
243C2×C4⋊C4—1181no—
244C2×C4⋊C4—1181no—
245C2×C4⋊C4—1182no—
246C2×C4⋊C4—1182no—
247C2×C4⋊C4—1181no—
248C2×C42—22no—
249C2×C42—22no—
250C2×C42D23611yescharacteristic
251C2×C42D23611yescharacteristic
252C2×C42C22⋊D5911yescharacteristic
253C2×C42C22⋊D5911yescharacteristic
254C4⋊C8—24no—
255C22⋊C8—22no—
256C22⋊C8—1182no—
257C22⋊C8—1182no—
258C22⋊C8C22⋊D5914yes—
259#97—24no—
260#95—1181no—
261#95—1181no—
262#95—1181no—
263#95—1181no—
264#95—1181no—
265#95—1181no—
266#95—1181no—
267#95—1181no—
268C24C2×C4×D5911yescharacteristic
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—592no—
279C22×C4—592no—
280C22×C4—1181no—
281C22×C4—1181no—
282C22×C4—1182no—
283C22×C4—1181no—
284C22×C4—1181no—
285C22×C4—1182no—
286C22×C4—1182no—
287C22×C4—1182no—
288C22×C4—1181no—
289C22×C4—1181no—
290C22×C4—2361no—
291C22×C4—2361no—
292C22×C4—2361no—
293C22×C4—2361no—
294C22×C4—2361no—
295C22×C4—2361no—
296C22×C4(C2×D59)⋊C411yescharacteristic
297C22×C4(C2×D59)⋊C411yescharacteristic
298C22×C4(C2×D59)⋊C411yescharacteristic
299C22×C4(C2×D59)⋊C411yescharacteristic
300C22×C4C2×D23611yescharacteristic
301C22×C4#1174568512yes—
302C22×C4C2×C22⋊D5911yescharacteristic
303C22×C4C2×C22⋊D5912yes—
304C2×C8—24no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—2362no—
308C2×C8—2362no—
309C2×C8—2362no—
310C4⋊C4—1184no—
311C4⋊C4—1184no—
312C4⋊C4—2361no—
313C4⋊C4—2362no—
314C4⋊C4—2361no—
315C42—21no—
316C42—21no—
317C42—22no—
318C42—22no—
319C42—21no—
320C42—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23C2×(C2×D59)⋊C411yescharacteristic
326C23C4×C22⋊D5912yes—
327C23M16×D5911yescharacteristic
328C23M16×D5911yescharacteristic
329C23#1427373512yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—44no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—1184no—
351C2×C4—1182no—
352C2×C4—1182no—
353C2×C4—4722no—
354C2×C4—4722no—
355C2×C4—2361no—
356C2×C4—2361no—
357C2×C4—2361no—
358C2×C4—2361no—
359C2×C4—2361no—
360C2×C4—2361no—
361C2×C4—2362no—
362C2×C4—2361no—
363C2×C4—2362no—
364C2×C4—2361no—
365C2×C4—2361no—
366C2×C4—2361no—
367C2×C4—2362no—
368C2×C4#1427364512yes—
369C2×C4#1427369611yescharacteristic
370C2×C4#1427370112yes—
371C2×C4#1427371011yescharacteristic
372C8—44no—
373C8—4722no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22#1683728111yescharacteristic
383C22#1683736511yescharacteristic
384C22#1683737011yescharacteristic
385C22#1683737511yescharacteristic
386C22#1683737511yescharacteristic
387C22C2×#1427364511yescharacteristic
388C22#1683738411yescharacteristic
389C22#1683747112yes—
390C22#1683747812yes—
391C4—21no—
392C4—22no—
393C4—21no—
394C4—22no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—4721no—
399C4—4721no—
400C4—2362no—
401C4—2362no—
402C2—22no—
403C2—22no—
404C2#2142242811yescharacteristic
405C2#2142243911yescharacteristic
406C2#2142245311yescharacteristic
407C2#2142246611yescharacteristic
408C2#2142439311yescharacteristic
409C2#2142455411yescharacteristic
410C2#2142456411yescharacteristic
subgroupG/H
centerC23C2×(C2×D59)⋊C4
commutator, prime radicalC24×C59C22×C4
FrattiniC23×C4C22×D59
FittingC2×C59×#432C2
socleC23×C59C2×C22⋊C4
cosocleC23×C4×C59C23
hypercenterC2×#432D59
hypocenterC59#9086
LCSG ▷ C24×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
230. C59#9086semidirect

Maximal subgroups

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

subgroupindex
C2×#168372862
#214241642
C2×#168371272
#214219382
C2×C59×#4322
#908659