Finite Group Databasebeta

← #28494303

Subgroups — #28494303

Order 15104.

918 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C59⋊C8C211yesmaximal, characteristic
2C2×#16837157C212yesmaximal
3C2×#16837157C212yesmaximal
4C2×#16837157C211yesmaximal, characteristic
5C4×#95×C59C211yesmaximal, characteristic
6C23×C59⋊C8C2212yes—
7C23×C59⋊C8C2211yescharacteristic
8C23×C59⋊C8C2211yescharacteristic
9C2×C4×C59⋊C8—24no—
10C2×C4×C59⋊C8C414yescomplemented
11#16837157—24no—
12#16837157—24no—
13#16837157C414yescomplemented
14C22×C42×C59C2212yes—
15C22×C42×C59C2211yescharacteristic
16C2×#95×C59C412yes—
17C2×#95×C59C412yes—
18C22×C59⋊C8—22no—
19C22×C59⋊C8—22no—
20C22×C59⋊C8—22no—
21C22×C59⋊C8—21no—
22C22×C59⋊C8—21no—
23C22×C59⋊C8—22no—
24C22×C59⋊C8—22no—
25C22×C59⋊C8—22no—
26C22×C59⋊C8—22no—
27C22×C59⋊C8—22no—
28C22×C59⋊C8—22no—
29C22×C59⋊C8C2×C414yes—
30C22×C59⋊C8C2×C412yes—
31C22×C59⋊C8C2×C412yes—
32C22×C59⋊C8D414yes—
33C22×C59⋊C8D412yes—
34C22×C59⋊C8Q812yes—
35C4×C59⋊C8—28no—
36C23×C4×C59C2×C414yes—
37C23×C4×C59C2×C411yescharacteristic
38C23×C4×C59C2×C411yescharacteristic
39C23×C4×C59C2311yescharacteristic
40C2×C42×C59—22no—
41C2×C42×C59—22no—
42C2×C42×C59—22no—
43C2×C42×C59—22no—
44C2×C42×C59—22no—
45C2×C42×C59—22no—
46C2×C42×C59—22no—
47C2×C42×C59—22no—
48C2×C42×C59C2×C412yes—
49C2×C42×C59C2×C412yes—
50#95×C59—24no—
51#95×C59C818yescomplemented
52C24×C59C22×C411yescharacteristic
53C22×C4×C59—22no—
54C22×C4×C59—22no—
55C22×C4×C59—22no—
56C22×C4×C59—22no—
57C22×C4×C59—24no—
58C22×C4×C59—24no—
59C22×C4×C59—24no—
60C22×C4×C59—24no—
61C22×C4×C59—24no—
62C22×C4×C59—24no—
63C22×C4×C59C4212yes—
64C22×C4×C59C4212yes—
65C22×C4×C59C2×C818yes—
66C22×C4×C59C2×C814yes—
67C22×C4×C59M1614yes—
68C22×C4×C59C22×C411yescharacteristic
69C22×C4×C59C22×C411yescharacteristic
70C22×C4×C59C2×D412yes—
71C22×C4×C59C2×D411yescharacteristic
72C22×C4×C59C2×Q811yescharacteristic
73C22×C4×C59#4112yes—
74C22×C4×C59#4112yes—
75C22×C4×C59#4111yescharacteristic
76C22×C4×C59#4112yes—
77C22×C4×C59#4111yescharacteristic
78C42×C59—22no—
79C42×C59—22no—
80C42×C59—24no—
81C42×C59—42no—
82C42×C59—42no—
83C42×C59—42no—
84C42×C59—42no—
85C2×C59⋊C8—22no—
86C2×C59⋊C8—22no—
87C2×C59⋊C8—22no—
88C2×C59⋊C8—22no—
89C2×C59⋊C8—24no—
90C2×C59⋊C8—24no—
91C2×C59⋊C8—24no—
92C2×C59⋊C8—24no—
93C2×C59⋊C8—24no—
94C2×C59⋊C8—24no—
95C2×C59⋊C8—24no—
96C2×C59⋊C8—42no—
97C2×C59⋊C8—42no—
98C2×C59⋊C8—42no—
99C2×C59⋊C8—42no—
100C2×C59⋊C8C22⋊C414yes—
101C2×C59⋊C8C4⋊C414yes—
102C23×C59C2×C4211yescharacteristic
103C23×C59#11712yes—
104C23×C59C4×D412yes—
105C23×C59C4×D411yescharacteristic
106C23×C59C4×Q811yescharacteristic
107C23×C59C22×C812yes—
108C23×C59C2×M1612yes—
109C23×C59#13112yes—
110C23×C59#13112yes—
111C2×C4×C59—22no—
112C2×C4×C59—22no—
113C2×C4×C59—22no—
114C2×C4×C59—22no—
115C2×C4×C59—28no—
116C2×C4×C59—28no—
117C2×C4×C59—28no—
118C2×C4×C59—28no—
119C2×C4×C59—28no—
120C2×C4×C59—44no—
121C2×C4×C59—44no—
122C2×C4×C59—44no—
123C2×C4×C59—44no—
124C2×C4×C59C4×C814yes—
125C2×C4×C59#9714yes—
126C2×C4×C59C2×C22⋊C411yescharacteristic
127C2×C4×C59C2×C4⋊C411yescharacteristic
128C2×C4×C59#11711yescharacteristic
129C2×C4×C59#11711yescharacteristic
130C2×C4×C59#11711yescharacteristic
131C2×C4×C59#11712yes—
132C2×C4×C59#11711yescharacteristic
133C2×C4×C59C4×D412yes—
134C2×C4×C59C4×D411yescharacteristic
135C2×C4×C59C4×Q811yescharacteristic
136C2×C4×C59#12112yes—
137C2×C4×C59C22⋊Q812yes—
138C2×C4×C59#12312yes—
139C2×C4×C59#12312yes—
140C2×C4×C59#12412yes—
141C2×C4×C59#12512yes—
142C2×C4×C59#12612yes—
143C2×C4×C59#12612yes—
144C59⋊C8—24no—
145C59⋊C8—24no—
146C59⋊C8—44no—
147#10797—591nomaximal, Sylow
148C22×C59#37611yescharacteristic
149C22×C59C4×C22⋊C411yescharacteristic
150C22×C59C4×C4⋊C411yescharacteristic
151C22×C59#38712yes—
152C22×C59#38812yes—
153C22×C59C2×C4×C811yescharacteristic
154C22×C59C2×#9711yescharacteristic
155C22×C59#40511yescharacteristic
156C22×C59#40511yescharacteristic
157C22×C59#43114yes—
158C22×C59#43314yes—
159C22×C59C8×D414yes—
160C22×C59C8×D412yes—
161C22×C59#43514yes—
162C22×C59#43612yes—
163C22×C59C8×Q812yes—
164C22×C59#44612yes—
165C4×C59—24no—
166C4×C59—24no—
167C4×C59—48no—
168C4×C59#38011yescharacteristic
169C4×C59#38111yescharacteristic
170C4×C59#38211yescharacteristic
171C4×C59#38311yescharacteristic
172C4×C59#38712yes—
173C4×C59#38812yes—
174C22×C4×C8—591no—
175C2×#336—591no—
176C2×#336—592no—
177C2×#336—592no—
178C4×#95D5911yescharacteristic
179C2×C59#143411yescharacteristic
180C2×C59#174411yescharacteristic
181C2×C59#174611yescharacteristic
182C2×C59C8×C22⋊C411yescharacteristic
183C2×C59#175211yescharacteristic
184C2×C59C8×C4⋊C411yescharacteristic
185C2×C59#177011yescharacteristic
186C2×C59#191614yes—
187C2×C59#192314yes—
188C23×C8—591no—
189C23×C8—591no—
190C23×C8—592no—
191C22×C42C2×D5912yes—
192C22×C42C2×D5911yescharacteristic
193C2×C4×C8—594no—
194C2×C4×C8—1184no—
195C2×#95Dic5912yes—
196C2×#95Dic5912yes—
197#336—594no—
198#336—1184no—
199#336—1184no—
200C59#1079711yescharacteristic, complemented, Sylow
201C23×C4C2×Dic5914yes—
202C23×C4C2×Dic5911yescharacteristic
203C23×C4C2×Dic5911yescharacteristic
204C23×C4C22×D5911yescharacteristic
205C22×C8—592no—
206C22×C8—592no—
207C22×C8—592no—
208C22×C8—594no—
209C22×C8—592no—
210C22×C8—594no—
211C22×C8—1182no—
212C22×C8—1182no—
213C22×C8—1182no—
214C22×C8—1181no—
215C22×C8—1181no—
216C22×C8—1182no—
217C22×C8—1182no—
218C22×C8—1182no—
219C22×C8—1182no—
220C22×C8—1182no—
221C22×C8—1182no—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42—22no—
226C2×C42—22no—
227C2×C42—22no—
228C2×C42—22no—
229C2×C42—22no—
230C2×C42C4×D5912yes—
231C2×C42C4×D5912yes—
232C4×C8—1188no—
233#95—24no—
234#95C59⋊C818yescomplemented
235C24C22×Dic5911yescharacteristic
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4C2×C59⋊C818yes—
247C22×C4C2×C59⋊C814yes—
248C22×C4#1174566414yes—
249C22×C4C4×Dic5912yes—
250C22×C4C4×Dic5912yes—
251C22×C4C2×C4×D5911yescharacteristic
252C22×C4C2×C4×D5911yescharacteristic
253C22×C4#1174568512yes—
254C22×C4#1174568512yes—
255C22×C4D4×D5912yes—
256C22×C4D4×D5911yescharacteristic
257C22×C4#1174568712yes—
258C22×C4#1174568711yescharacteristic
259C22×C4Q8×D5911yescharacteristic
260C22×C4#1174568911yescharacteristic
261C2×C8—594no—
262C2×C8—594no—
263C2×C8—1182no—
264C2×C8—1182no—
265C2×C8—1182no—
266C2×C8—1182no—
267C2×C8—1184no—
268C2×C8—1184no—
269C2×C8—1184no—
270C2×C8—1184no—
271C2×C8—1184no—
272C2×C8—1184no—
273C2×C8—1184no—
274C2×C8—2362no—
275C2×C8—2362no—
276C2×C8—2362no—
277C2×C8—2362no—
278C42—22no—
279C42—22no—
280C42—24no—
281C42—42no—
282C42—42no—
283C42—42no—
284C42—42no—
285C23C2×C4×Dic5911yescharacteristic
286C23#1427368612yes—
287C23D4×Dic5912yes—
288C23D4×Dic5911yescharacteristic
289C23Q8×Dic5911yescharacteristic
290C23C22×C59⋊C812yes—
291C23C2×#1174566412yes—
292C23#1427373412yes—
293C23#1427373412yes—
294C2×C4—28no—
295C2×C4—28no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—28no—
301C2×C4—28no—
302C2×C4—28no—
303C2×C4—44no—
304C2×C4—44no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4C4×C59⋊C814yes—
308C2×C4#1427363814yes—
309C2×C4C22⋊C4×D5911yescharacteristic
310C2×C4C4⋊C4×D5911yescharacteristic
311C2×C4#1427368311yescharacteristic
312C2×C4#1427368411yescharacteristic
313C2×C4#1427368411yescharacteristic
314C2×C4#1427368412yes—
315C2×C4#1427368511yescharacteristic
316C2×C4(C22⋊D59)⋊C412yes—
317C2×C4#1427368911yescharacteristic
318C2×C4#1427369211yescharacteristic
319C2×C4#1427370012yes—
320C2×C4#1427370512yes—
321C2×C4#1427370912yes—
322C2×C4#1427371212yes—
323C2×C4#1427371312yes—
324C2×C4#1427371712yes—
325C2×C4#1427372012yes—
326C2×C4#1427372212yes—
327C8—1184no—
328C8—1184no—
329C8—2364no—
330C22#1683724811yescharacteristic
331C22C22⋊C4×Dic5911yescharacteristic
332C22C4⋊C4×Dic5911yescharacteristic
333C22#1683728812yes—
334C22#1683729512yes—
335C22C2×C4×C59⋊C811yescharacteristic
336C22C2×#1427363811yescharacteristic
337C22#1683735811yescharacteristic
338C22#1683735811yescharacteristic
339C22#1683745514yes—
340C22#1683746314yes—
341C22D4×C59⋊C814yes—
342C22D4×C59⋊C812yes—
343C22#1683747414yes—
344C22#1683748012yes—
345C22Q8×C59⋊C812yes—
346C22#1683753312yes—
347C4—24no—
348C4—24no—
349C4—48no—
350C4#1683726111yescharacteristic
351C4#1683726411yescharacteristic
352C4#1683726611yescharacteristic
353C4#1683726911yescharacteristic
354C4#1683728412yes—
355C4#1683729112yes—
356C2#2142232111yescharacteristic
357C2#2142384211yescharacteristic
358C2#2142384811yescharacteristic
359C2C22⋊C4×C59⋊C811yescharacteristic
360C2#2142387411yescharacteristic
361C2C4⋊C4×C59⋊C811yescharacteristic
362C2#2142396511yescharacteristic
363C2#2142465514yes—
364C2#2142470414yes—
subgroupG/H
center, FrattiniC23×C4C22×D59
commutatorC22×C59C2×C4×C8
FittingC4×#95×C59C2
socle, prime radicalC24×C59C22×C4
cosocleC23×C4×C59C23
hypercenterC4×#95D59
hypocenterC59#10797
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
10. C2×C4×C59⋊C8C4semidirect
13. #16837157C4semidirect
51. #95×C59C8semidirect
200. C59#10797semidirect
234. #95C59⋊C8semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C59⋊C82
C2×#168371572
C4×#95×C592
#1079759