Finite Group Databasebeta

← #28494898

Subgroups — #28494898

Order 15104.

974 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21426708C211yesmaximal, characteristic
2C2×#16837169C211yesmaximal, characteristic
3C2×#16837168C212yesmaximal
4C2×#16837168C212yesmaximal
5C59×#2273C211yesmaximal, characteristic
6C22×C22⋊Dic59C2211yescharacteristic
7C22×C22⋊Dic59C2212yes—
8C22×C22⋊Dic59C2211yescharacteristic
9#16837275—22no—
10#16837274C414yescomplemented
11#16837260—22no—
12#16837169—22no—
13#16837168—24no—
14#16837168C418yescomplemented
15C22×C22⋊C4×C59C2211yescharacteristic
16C22×C22⋊C4×C59C2212yes—
17C4×C22⋊C4×C59—22no—
18C4×C22⋊C4×C59—24no—
19C23×Dic59—21no—
20C23×Dic59—22no—
21C23×Dic59C2×C412yes—
22C2×Dic59⋊C4—24no—
23C2×C22⋊Dic59—21no—
24C2×C22⋊Dic59—22no—
25C2×C22⋊Dic59—22no—
26C2×C22⋊Dic59—22no—
27C2×C22⋊Dic59—22no—
28C2×C22⋊Dic59—22no—
29C2×C22⋊Dic59—22no—
30C2×C22⋊Dic59—21no—
31C2×C22⋊Dic59—21no—
32C2×C22⋊Dic59—22no—
33C2×C22⋊Dic59—22no—
34C2×C22⋊Dic59C2×C414yes—
35C2×C22⋊Dic59C2×C414yes—
36C2×C22⋊Dic59C2×C412yes—
37C59⋊#95—24no—
38C25×C59C2311yescharacteristic
39C23×C4×C59—22no—
40C23×C4×C59D412yes—
41C2×C22⋊C4×C59—22no—
42C2×C22⋊C4×C59—22no—
43C2×C22⋊C4×C59—22no—
44C2×C22⋊C4×C59—22no—
45C2×C22⋊C4×C59—22no—
46C2×C22⋊C4×C59C2×C412yes—
47C2×C22⋊C4×C59C2×C414yes—
48C2×C22⋊C4×C59D412yes—
49C2×C22⋊C4×C59D414yes—
50C2×C22⋊C4×C59Q814yes—
51C2×C42×C59—24no—
52#95×C59—24no—
53C24×C59—82no—
54C24×C59C22×C411yescharacteristic
55C24×C59C22×C412yes—
56C24×C59C2×D411yescharacteristic
57C24×C59C2×D411yescharacteristic
58C24×C59C2×D412yes—
59C24×C59C2×Q812yes—
60C24×C59#4112yes—
61C24×C59#4112yes—
62C24×C59#4112yes—
63C22×C4×C59—22no—
64C22×C4×C59—24no—
65C22×C4×C59—24no—
66C22×C4×C59—24no—
67C22×C4×C59—22no—
68C22×C4×C59—82no—
69C22×C4×C59—84no—
70C22×C4×C59C22⋊C414yes—
71C22×Dic59—22no—
72C22×Dic59—24no—
73C22×Dic59—22no—
74C22×Dic59—24no—
75C22×Dic59—24no—
76C22×Dic59—42no—
77C22×Dic59—42no—
78C22×Dic59—82no—
79C22×Dic59—82no—
80C22×Dic59—84no—
81C22⋊C4×C59—24no—
82C22⋊C4×C59—24no—
83C22⋊C4×C59—24no—
84C22⋊C4×C59—24no—
85C22⋊C4×C59—24no—
86C22⋊C4×C59C4⋊C418yescomplemented
87C42×C59—84no—
88C22⋊Dic59—22no—
89C22⋊Dic59—24no—
90C22⋊Dic59—24no—
91C22⋊Dic59—24no—
92C22⋊Dic59—41no—
93C22⋊Dic59—42no—
94C22⋊Dic59—41no—
95C22⋊Dic59—42no—
96C22⋊Dic59—42no—
97C22⋊Dic59C4214yescomplemented
98Dic59⋊C4—84no—
99C23×C59—42no—
100C23×C59—42no—
101C23×C59—44no—
102C23×C59—42no—
103C23×C59—44no—
104C23×C59—82no—
105C23×C59—82no—
106C23×C59—82no—
107C23×C59—82no—
108C23×C59C2×C4211yescharacteristic
109C23×C59C2×C22⋊C411yescharacteristic
110C23×C59C2×C4⋊C412yes—
111C23×C59#11711yescharacteristic
112C23×C59#11712yes—
113C23×C59C4×D412yes—
114C23×C59C4×D412yes—
115C23×C59C4×D412yes—
116C23×C59C4×D412yes—
117C23×C59C4×Q812yes—
118C23×C59C4×Q812yes—
119C23×C59#12011yescharacteristic
120C23×C59#12112yes—
121C23×C59C22⋊Q812yes—
122C23×C59C22⋊Q812yes—
123C23×C59#12311yescharacteristic
124C23×C59#12312yes—
125C23×C59#12411yescharacteristic
126C23×C59#12512yes—
127C23×C59#12612yes—
128C23×C59C4⋊Q811yescharacteristic
129C2×C4×C59—28no—
130C2×C4×C59—24no—
131C2×C4×C59—48no—
132C2×C4×C59—44no—
133C2×C4×C59—44no—
134C2×C4×C59—82no—
135C2×C4×C59—84no—
136C2×C4×C59—84no—
137C2×Dic59—24no—
138C2×Dic59—44no—
139C2×Dic59—44no—
140C2×Dic59—42no—
141C2×Dic59—44no—
142C2×Dic59—84no—
143C2×Dic59—84no—
144C2×Dic59—84no—
145C2×Dic59—84no—
146C2×Dic59—84no—
147#10915—591nomaximal, Sylow
148C22×C59—22no—
149C22×C59—24no—
150C22×C59—24no—
151C22×C59—22no—
152C22×C59—22no—
153C22×C59—42no—
154C22×C59—42no—
155C22×C59—42no—
156C22×C59—42no—
157C22×C59—42no—
158C22×C59—41no—
159C22×C59—42no—
160C22×C59—41no—
161C22×C59—42no—
162C22×C59—42no—
163C22×C59—42no—
164C22×C59—42no—
165C22×C59—42no—
166C22×C59—41no—
167C22×C59—42no—
168C22×C59—41no—
169C22×C59C4×C22⋊C411yescharacteristic
170C22×C59C4×C4⋊C412yes—
171C22×C59#38512yes—
172C22×C59#38611yescharacteristic
173C22×C59#38712yes—
174C22×C59#38712yes—
175C22×C59#38812yes—
176C22×C59#38912yes—
177C22×C59#39111yescharacteristic
178C4×C59—48no—
179C4×C59—44no—
180Dic59—44no—
181Dic59—84no—
182Dic59—82no—
183#2315—591no—
184#2273D5911yescharacteristic
185C2×#342—592no—
186C2×#342—592no—
187C2×#342—591no—
188C2×C59—21no—
189C2×C59—22no—
190C2×C59—22no—
191C2×C59—22no—
192C2×C59—22no—
193C2×C59—22no—
194C2×C59—22no—
195C2×C59—21no—
196C2×C59#143611yescharacteristic
197C2×C59#191312yes—
198C22×C22⋊C4—591no—
199C22×C22⋊C4—592no—
200C22×C22⋊C4—591no—
201C22×C22⋊C4C2×D5911yescharacteristic
202C22×C22⋊C4C2×D5912yes—
203#385—594no—
204#385—1182no—
205#380—1182no—
206C4×C22⋊C4—22no—
207C4×C22⋊C4—24no—
208#342—598no—
209#342—1182no—
210#342—1184no—
211C59#1091511yescharacteristic, complemented, Sylow
212C25C22×D5911yescharacteristic
213C23×C4—22no—
214C23×C4—592no—
215C23×C4—1181no—
216C23×C4—1182no—
217C23×C4C22⋊D5912yes—
218C2×C4⋊C4—1184no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—594no—
225C2×C22⋊C4—592no—
226C2×C22⋊C4—594no—
227C2×C22⋊C4—1182no—
228C2×C22⋊C4—1181no—
229C2×C22⋊C4—1182no—
230C2×C22⋊C4—1182no—
231C2×C22⋊C4—1182no—
232C2×C22⋊C4—1182no—
233C2×C22⋊C4—1181no—
234C2×C22⋊C4—1182no—
235C2×C22⋊C4—1182no—
236C2×C22⋊C4—1182no—
237C2×C22⋊C4—1181no—
238C2×C22⋊C4Dic11814yes—
239C2×C22⋊C4C4×D5912yes—
240C2×C22⋊C4C4×D5914yes—
241C2×C22⋊C4D23612yes—
242C2×C22⋊C4C22⋊D5914yes—
243C2×C42—24no—
244#95—24no—
245#95—1184no—
246C24—82no—
247C24C2×Dic11812yes—
248C24C2×C4×D5911yescharacteristic
249C24C2×C4×D5912yes—
250C24C2×D23611yescharacteristic
251C24#1174568512yes—
252C24#1174568512yes—
253C24#1174568512yes—
254C24C2×C22⋊D5911yescharacteristic
255C24C2×C22⋊D5912yes—
256C22×C4—22no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—22no—
261C22×C4—82no—
262C22×C4—84no—
263C22×C4—1184no—
264C22×C4—1182no—
265C22×C4—1184no—
266C22×C4—1184no—
267C22×C4—1182no—
268C22×C4—4724no—
269C22×C4—4722no—
270C22×C4—4722no—
271C22×C4—2362no—
272C22×C4—2362no—
273C22×C4(C2×D59)⋊C414yes—
274C4⋊C4—4724no—
275C22⋊C4—24no—
276C22⋊C4—24no—
277C22⋊C4—24no—
278C22⋊C4—24no—
279C22⋊C4—24no—
280C22⋊C4—594no—
281C22⋊C4—1182no—
282C22⋊C4—1184no—
283C22⋊C4—1184no—
284C22⋊C4—1184no—
285C22⋊C4—2361no—
286C22⋊C4—2362no—
287C22⋊C4—2361no—
288C22⋊C4—2362no—
289C22⋊C4—2362no—
290C22⋊C4Dic59⋊C418yescomplemented
291C42—84no—
292C23—42no—
293C23—44no—
294C23—42no—
295C23—42no—
296C23—44no—
297C23—82no—
298C23—82no—
299C23—82no—
300C23—82no—
301C23C42×D5911yescharacteristic
302C23C2×(C2×D59)⋊C411yescharacteristic
303C23C2×Dic59⋊C412yes—
304C23#1427368411yescharacteristic
305C23#1427368412yes—
306C23C4×C22⋊D5912yes—
307C23C4×C22⋊D5912yes—
308C23C4×C22⋊D5912yes—
309C23C4×D23612yes—
310C23C4×Dic11812yes—
311C23C4×Dic11812yes—
312C23#1427369611yescharacteristic
313C23#1427370112yes—
314C23#1427370612yes—
315C23#1427370612yes—
316C23#1427371011yescharacteristic
317C23#1427371012yes—
318C23#1427371511yescharacteristic
319C23#1427371912yes—
320C23#1427372112yes—
321C23#1427372711yescharacteristic
322C2×C4—28no—
323C2×C4—24no—
324C2×C4—48no—
325C2×C4—44no—
326C2×C4—44no—
327C2×C4—82no—
328C2×C4—84no—
329C2×C4—84no—
330C2×C4—1184no—
331C2×C4—4724no—
332C2×C4—4724no—
333C2×C4—4724no—
334C2×C4—4724no—
335C2×C4—4724no—
336C2×C4—2364no—
337C2×C4—2362no—
338C2×C4—2364no—
339C2×C4—2364no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—24no—
344C22—24no—
345C22—42no—
346C22—42no—
347C22—42no—
348C22—42no—
349C22—42no—
350C22—41no—
351C22—42no—
352C22—41no—
353C22—42no—
354C22—42no—
355C22—42no—
356C22—42no—
357C22—42no—
358C22—41no—
359C22—42no—
360C22—41no—
361C22C4×(C2×D59)⋊C411yescharacteristic
362C22C4×Dic59⋊C412yes—
363C22#1683727512yes—
364C22#1683728111yescharacteristic
365C22#1683728612yes—
366C22#1683728612yes—
367C22#1683729312yes—
368C22#1683730012yes—
369C22#1683730811yescharacteristic
370C4—48no—
371C4—44no—
372C4—4724no—
373C4—4722no—
374C4—2364no—
375C2—22no—
376C2—22no—
377C2—21no—
378C2—22no—
379C2—22no—
380C2—22no—
381C2—22no—
382C2—21no—
383C2#2142232911yescharacteristic
384C2#2142463812yes—
subgroupG/H
centerC22#16837281
commutatorC23×C59C2×C42
FrattiniC25C22×D59
FittingC59×#2273C2
socleC22×C59#386
prime radical, cosocleC25×C59C23
hypercenter#2273D59
hypocenterC59#10915
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C25 ◁ #2273

Complements

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

NH ≅ G/Ntype
10. #16837274C4semidirect
14. #16837168C4semidirect
86. C22⋊C4×C59C4⋊C4semidirect
97. C22⋊Dic59C42semidirect
211. C59#10915semidirect
290. C22⋊C4Dic59⋊C4semidirect

Maximal subgroups

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

subgroupindex
#214267082
C2×#168371692
C2×#168371682
C59×#22732
#1091559