Finite Group Databasebeta

← #28484096

Subgroups — #28484096

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×#16837459C211yesmaximal, characteristic
2#21424164C211yesmaximal, characteristic
3C2×#16837128C212yesmaximal
4#21421939C212yesmaximal
5C2×C59×#387C211yesmaximal, characteristic
6#16837459—24no—
7C2×C4⋊(C59⋊C8)—21no—
8C2×C22⋊(C59⋊C8)C2212yes—
9C2×C22⋊(C59⋊C8)C2212yes—
10C2×#14273638—21no—
11#16837157—21no—
12#16837157—21no—
13#16837128—24no—
14C22×C4⋊C4×C59C411yescharacteristic
15C22×C4⋊C4×C59C2211yescharacteristic
16C22×C42×C59C2211yescharacteristic
17C59×#387—21no—
18C59×#387—21no—
19C59×#387—21no—
20C59×#387—21no—
21C2×#95×C59C411yescharacteristic
22C2×#95×C59C411yescharacteristic
23C2×#95×C59C411yescharacteristic
24C2×#95×C59C2211yescharacteristic
25C22×C59⋊C8—22no—
26C22×C59⋊C8—22no—
27C4⋊(C59⋊C8)—24no—
28C22⋊(C59⋊C8)—22no—
29C22⋊(C59⋊C8)—22no—
30C22⋊(C59⋊C8)—22no—
31C22⋊(C59⋊C8)D414yes—
32#14273638—24no—
33C23×C4×C59C2×C411yescharacteristic
34C23×C4×C59C2×C411yescharacteristic
35C23×C4×C59C2×C411yescharacteristic
36C23×C4×C59C2×C411yescharacteristic
37C23×C4×C59C2×C411yescharacteristic
38C23×C4×C59C2×C411yescharacteristic
39C23×C4×C59C2311yescharacteristic
40C2×C4⋊C4×C59—21no—
41C2×C4⋊C4×C59—21no—
42C2×C4⋊C4×C59—22no—
43C2×C4⋊C4×C59—22no—
44C2×C4⋊C4×C59—22no—
45C2×C4⋊C4×C59—21no—
46C2×C4⋊C4×C59—21no—
47C2×C4⋊C4×C59—22no—
48C2×C42×C59—22no—
49C2×C42×C59—22no—
50C2×C42×C59D411yescharacteristic
51C2×C42×C59D411yescharacteristic
52C2×C42×C59D411yescharacteristic
53C2×C42×C59D411yescharacteristic
54#95×C59—21no—
55#95×C59—21no—
56#95×C59—21no—
57#95×C59—21no—
58#95×C59—21no—
59#95×C59—21no—
60#95×C59—21no—
61#95×C59—21no—
62C24×C59C22×C411yescharacteristic
63C22×C4×C59—21no—
64C22×C4×C59—21no—
65C22×C4×C59—22no—
66C22×C4×C59—22no—
67C22×C4×C59—22no—
68C22×C4×C59—21no—
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59—22no—
73C22×C4×C59—22no—
74C22×C4×C59—22no—
75C22×C4×C59—21no—
76C22×C4×C59—21no—
77C22×C4×C59—22no—
78C22×C4×C59—22no—
79C22×C4×C59—41no—
80C22×C4×C59—41no—
81C22×C4×C59—41no—
82C22×C4×C59—41no—
83C22×C4×C59—41no—
84C22×C4×C59—41no—
85C22×C4×C59—41no—
86C22×C4×C59—41no—
87C22×C4×C59—41no—
88C22×C4×C59C22⋊C411yescharacteristic
89C22×C4×C59C22⋊C411yescharacteristic
90C22×C4×C59C22⋊C411yescharacteristic
91C22×C4×C59C22⋊C411yescharacteristic
92C22×C4×C59M1612yes—
93C22×C4×C59M1612yes—
94C22×C4×C59C2×D411yescharacteristic
95C22×C4×C59C2×D411yescharacteristic
96C22×C4×C59C2×D412yes—
97C22×C4×C59#4112yes—
98C4⋊C4×C59—24no—
99C4⋊C4×C59—24no—
100C4⋊C4×C59—41no—
101C4⋊C4×C59—42no—
102C4⋊C4×C59—41no—
103C42×C59—21no—
104C42×C59—21no—
105C42×C59—22no—
106C42×C59—22no—
107C42×C59—21no—
108C42×C59—21no—
109C2×C59⋊C8—24no—
110C2×C59⋊C8—42no—
111C2×C59⋊C8—42no—
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—22no—
136C2×C4×C59—22no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—24no—
142C2×C4×C59—42no—
143C2×C4×C59—42no—
144C2×C4×C59—44no—
145C2×C4×C59—42no—
146C2×C4×C59—41no—
147C2×C4×C59—41no—
148C2×C4×C59—41no—
149C2×C4×C59—41no—
150C2×C4×C59—42no—
151C2×C4×C59—42no—
152C2×C4×C59—42no—
153C2×C4×C59—42no—
154C2×C4×C59—41no—
155C2×C4×C59—41no—
156C2×C4×C59—41no—
157C2×C4×C59—41no—
158C2×C4×C59—41no—
159C2×C4×C59—41no—
160C2×C4×C59—82no—
161C2×C4×C59—82no—
162C2×C4×C59#10112yes—
163C2×C4×C59#12011yescharacteristic
164C2×C4×C59#12112yes—
165C2×C4×C59#12311yescharacteristic
166C59⋊C8—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—21no—
187C4×C59—22no—
188C4×C59—21no—
189C4×C59—22no—
190C4×C59—41no—
191C4×C59—41no—
192C4×C59—42no—
193C4×C59—41no—
194C4×C59—42no—
195C4×C59—81no—
196C4×C59—81no—
197C2×#432—591no—
198C2×#387D5911yescharacteristic
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⋊C4Dic5911yescharacteristic
212C22×C4⋊C4C2×D5911yescharacteristic
213C22×C42C2×D5911yescharacteristic
214#432—1184no—
215C2×C4⋊C8—1181no—
216C2×C22⋊C8—592no—
217C2×C22⋊C8—592no—
218C2×#97—1181no—
219#387—21no—
220#387—21no—
221#387—21no—
222#387—21no—
223C2×#95Dic5911yescharacteristic
224C2×#95Dic5911yescharacteristic
225C2×#95Dic5911yescharacteristic
226C2×#95C2×D5911yescharacteristic
227#336—1181no—
228#336—1181no—
229#324—1184no—
230C59#908611yescharacteristic, complemented, Sylow
231C23×C4C2×Dic5911yescharacteristic
232C23×C4C2×Dic5911yescharacteristic
233C23×C4C2×Dic5911yescharacteristic
234C23×C4C2×Dic5911yescharacteristic
235C23×C4C2×Dic5911yescharacteristic
236C23×C4C2×Dic5911yescharacteristic
237C23×C4C22×D5911yescharacteristic
238C22×C8—1182no—
239C22×C8—1182no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C42—22no—
249C2×C42—22no—
250C2×C42C22⋊D5911yescharacteristic
251C2×C42C22⋊D5911yescharacteristic
252C2×C42C22⋊D5911yescharacteristic
253C2×C42C22⋊D5911yescharacteristic
254C4⋊C8—1184no—
255C22⋊C8—594no—
256C22⋊C8—1182no—
257C22⋊C8—1182no—
258C22⋊C8—1182no—
259#97—1184no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268C24C22×Dic5911yescharacteristic
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4#1174566412yes—
295C22×C4#1174566412yes—
296C22×C4C22⋊Dic5911yescharacteristic
297C22×C4C22⋊Dic5911yescharacteristic
298C22×C4C22⋊Dic5911yescharacteristic
299C22×C4C22⋊Dic5911yescharacteristic
300C22×C4D4×D5912yes—
301C22×C4#1174568712yes—
302C22×C4C2×C22⋊D5911yescharacteristic
303C22×C4C2×C22⋊D5911yescharacteristic
304C2×C8—1184no—
305C2×C8—2362no—
306C2×C8—2362no—
307C2×C8—2362no—
308C2×C8—2362no—
309C2×C8—2362no—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C4⋊C4—41no—
313C4⋊C4—42no—
314C4⋊C4—41no—
315C42—21no—
316C42—21no—
317C42—22no—
318C42—22no—
319C42—21no—
320C42—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23C2×C22⋊Dic5911yescharacteristic
326C23D4×Dic5912yes—
327C23C2×#1174566411yescharacteristic
328C23C2×#1174566411yescharacteristic
329C23#1427373412yes—
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—24no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—44no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4#1427364612yes—
369C2×C4#1427369511yescharacteristic
370C2×C4#1427369912yes—
371C2×C4#1427370811yescharacteristic
372C8—4722no—
373C8—2364no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22#1683728211yescharacteristic
383C22#1683736611yescharacteristic
384C22#1683736911yescharacteristic
385C22#1683737611yescharacteristic
386C22#1683737611yescharacteristic
387C22C2×#1427364611yescharacteristic
388C22#1683738611yescharacteristic
389C22#1683747412yes—
390C22#1683748012yes—
391C4—22no—
392C4—21no—
393C4—21no—
394C4—22no—
395C4—42no—
396C4—41no—
397C4—41no—
398C4—42no—
399C4—41no—
400C4—81no—
401C4—81no—
402C2—22no—
403C2—22no—
404C2#2142243011yescharacteristic
405C2#2142244011yescharacteristic
406C2#2142245211yescharacteristic
407C2#2142246511yescharacteristic
408C2#2142439411yescharacteristic
409C2#2142455511yescharacteristic
410C2#2142456511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic59
commutator, prime radicalC24×C59C22×C4
FrattiniC23×C4C22×D59
FittingC2×C59×#387C2
socleC23×C59C2×C22⋊C4
cosocleC23×C4×C59C23
hypercenterC2×#387D59
hypocenterC59#9086
LCSG ▷ C24×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#387

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×#168374592
#214241642
C2×#168371282
#214219392
C2×C59×#3872
#908659