Finite Group Databasebeta

← #28498896

Subgroups — #28498896

Order 15104.

514 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837171C211yesmaximal, characteristic, complemented
2C2×#16837128C211yesmaximal, characteristic, complemented
3#21422102C212yesmaximal, complemented
4#21422099C212yesmaximal, complemented
5C59×#2618C211yesmaximal, characteristic
6C22×#11745664—21no—
7C2×C22⋊(C59⋊C8)—21no—
8#16837171—21no—
9#16837171C2212yes—
10#16837128—21no—
11#16837128C2212yes—
12C2×#123×C59—21no—
13C2×#121×C59C411yescharacteristic
14C22×C4⋊C4×C59C2211yescharacteristic
15C59×#398C411yescharacteristic
16C59×#398C2211yescharacteristic
17C59×#396—21no—
18C59×#396—21no—
19C59×#394C411yescharacteristic
20C59×#394C2211yescharacteristic
21C59×#386—21no—
22C59×#380C411yescharacteristic
23C2×#11745664—24no—
24C2×#11745664—22no—
25C2×#11745664—41no—
26C2×#11745664—42no—
27C22×C59⋊C8—41no—
28C22×C59⋊C8—41no—
29C22⋊(C59⋊C8)—22no—
30C22⋊(C59⋊C8)—41no—
31C22×D4×C59—21no—
32C22×D4×C59C2×C411yescharacteristic
33C23×C4×C59C2×C411yescharacteristic
34C23×C4×C59D411yescharacteristic
35C23×C4×C59D411yescharacteristic
36#123×C59—42no—
37#123×C59—42no—
38#121×C59—41no—
39#121×C59—41no—
40C2×C4⋊C4×C59—21no—
41C2×C4⋊C4×C59—21no—
42C2×C4⋊C4×C59—21no—
43C2×C4⋊C4×C59—41no—
44C2×C4⋊C4×C59—41no—
45C2×C4⋊C4×C59C2×C411yescharacteristic
46C2×C4⋊C4×C59C2×C411yescharacteristic
47C2×C4⋊C4×C59D411yescharacteristic
48C2×C4⋊C4×C59D411yescharacteristic
49C2×C4⋊C4×C59C2311yescharacteristic
50C2×C22⋊C4×C59—21no—
51C2×C22⋊C4×C59—21no—
52C2×C22⋊C4×C59—21no—
53C2×C22⋊C4×C59—21no—
54C2×C22⋊C4×C59—21no—
55C2×C22⋊C4×C59—21no—
56#95×C59—21no—
57#95×C59—21no—
58#95×C59C2×C411yescharacteristic
59#95×C59C2×C411yescharacteristic
60C24×C59—21no—
61C24×C59C22⋊C411yescharacteristic
62C2×D4×C59—41no—
63C2×D4×C59—41no—
64C2×D4×C59—41no—
65C2×D4×C59—42no—
66C2×D4×C59—42no—
67C2×D4×C59—81no—
68C22×C4×C59—21no—
69C22×C4×C59—21no—
70C22×C4×C59—22no—
71C22×C4×C59—21no—
72C22×C4×C59—21no—
73C22×C4×C59—21no—
74C22×C4×C59—21no—
75C22×C4×C59—21no—
76C22×C4×C59—21no—
77C22×C4×C59—21no—
78C22×C4×C59—81no—
79C22×C4×C59—81no—
80C22×C4×C59C22⋊C411yescharacteristic
81C22×C4×C59C22⋊C411yescharacteristic
82C22×C4×C59C22⋊C411yescharacteristic
83C22×C4×C59D812yes—
84C22×C4×C59SD1612yes—
85C22×C4×C59C22×C411yescharacteristic
86C22×C4×C59C2×D411yescharacteristic
87C22×C4×C59C2×D411yescharacteristic
88C4⋊C4×C59—41no—
89C4⋊C4×C59—41no—
90C4⋊C4×C59—41no—
91C4⋊C4×C59—41no—
92C4⋊C4×C59—41no—
93C4⋊C4×C59—42no—
94C4⋊C4×C59—41no—
95C4⋊C4×C59—41no—
96C4⋊C4×C59—81no—
97C22⋊C4×C59—42no—
98C22⋊C4×C59—42no—
99C22⋊C4×C59—42no—
100C22⋊C4×C59—41no—
101C22⋊C4×C59—41no—
102C22⋊C4×C59—81no—
103C22⋊C4×C59—81no—
104#11745664—24no—
105#11745664—44no—
106#11745664—42no—
107C2×C59⋊C8—44no—
108C2×C59⋊C8—42no—
109C2×C59⋊C8—42no—
110C2×C59⋊C8—82no—
111C23×C59—41no—
112C23×C59—41no—
113C23×C59—41no—
114C23×C59—41no—
115C23×C59—41no—
116C23×C59—41no—
117C23×C59—41no—
118C23×C59—41no—
119C23×C59—41no—
120C23×C59#9911yescharacteristic
121C23×C59#9911yescharacteristic
122C23×C59#10212yes—
123C23×C59#10412yes—
124C23×C59C2×C22⋊C411yescharacteristic
125D4×C59—82no—
126D4×C59—82no—
127D4×C59—82no—
128C2×C4×C59—22no—
129C2×C4×C59—22no—
130C2×C4×C59—22no—
131C2×C4×C59—22no—
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—21no—
140C2×C4×C59—42no—
141C2×C4×C59—41no—
142C2×C4×C59—41no—
143C2×C4×C59—41no—
144C2×C4×C59—41no—
145C2×C4×C59—41no—
146C2×C4×C59—41no—
147C2×C4×C59—41no—
148C2×C4×C59—41no—
149C2×C4×C59—41no—
150C2×C4×C59—41no—
151C2×C4×C59—41no—
152C2×C4×C59—41no—
153C2×C4×C59—41no—
154C2×C4×C59—81no—
155C2×C4×C59—81no—
156C2×C4×C59—81no—
157C2×C4×C59#10212yes—
158C2×C4×C59C2×D811yescharacteristic
159C2×C4×C59C2×SD1611yescharacteristic
160C59⋊C8—44no—
161C59⋊C8—82no—
162#11698—591nomaximal, Sylow
163C22×C59—21no—
164C22×C59—21no—
165C22×C59—21no—
166C22×C59—21no—
167C22×C59—21no—
168C22×C59—21no—
169C22×C59—42no—
170C22×C59—42no—
171C22×C59—81no—
172C22×C59—81no—
173C22×C59—81no—
174C22×C59—81no—
175C22×C59—81no—
176C22×C59—81no—
177C22×C59—81no—
178C22×C59#32712yes—
179C22×C59#32712yes—
180C22×C59C2×#9911yescharacteristic
181C22×C59C2×#10211yescharacteristic
182C22×C59C2×#10411yescharacteristic
183C4×C59—21no—
184C4×C59—22no—
185C4×C59—21no—
186C4×C59—41no—
187C4×C59—41no—
188C4×C59—41no—
189C4×C59—41no—
190C4×C59—81no—
191C4×C59—81no—
192C4×C59—81no—
193#2618D5911yescharacteristic
194C2×#343—591no—
195C2×#324—591no—
196#1346—592no—
197#1345—592no—
198C2×C59—21no—
199C2×C59—21no—
200C2×C59—22no—
201C2×C59—22no—
202C2×C59—161no—
203C2×C59C2×#32711yescharacteristic
204C2×C59#212111yescharacteristic
205C2×C59#213311yescharacteristic
206C22×M16—1181no—
207C2×#123—21no—
208C2×#121Dic5911yescharacteristic
209C22×C4⋊C4C2×D5911yescharacteristic
210C2×C22⋊C8—1181no—
211#398Dic5911yescharacteristic
212#398C2×D5911yescharacteristic
213#396—21no—
214#396—21no—
215#394Dic5911yescharacteristic
216#394C2×D5911yescharacteristic
217#386—21no—
218#380Dic5911yescharacteristic
219#343—592no—
220#343—1181no—
221#324—592no—
222#324—1181no—
223C59#1169811yescharacteristic, complemented, Sylow
224C22×D4—21no—
225C22×D4C2×Dic5911yescharacteristic
226C23×C4C2×Dic5911yescharacteristic
227C23×C4C22⋊D5911yescharacteristic
228C23×C4C22⋊D5911yescharacteristic
229C2×M16—1184no—
230C2×M16—1182no—
231C2×M16—2361no—
232C2×M16—2362no—
233C22×C8—2361no—
234C22×C8—2361no—
235#123—42no—
236#123—42no—
237#121—41no—
238#121—41no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—41no—
243C2×C4⋊C4—41no—
244C2×C4⋊C4C2×Dic5911yescharacteristic
245C2×C4⋊C4C2×Dic5911yescharacteristic
246C2×C4⋊C4C22⋊D5911yescharacteristic
247C2×C4⋊C4C22⋊D5911yescharacteristic
248C2×C4⋊C4C22×D5911yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C22⋊C8—1182no—
256C22⋊C8—2361no—
257#95—21no—
258#95—21no—
259#95C2×Dic5911yescharacteristic
260#95C2×Dic5911yescharacteristic
261C24—21no—
262C24C22⋊Dic5911yescharacteristic
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—81no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—81no—
280C22×C4—81no—
281C22×C4#1174566912yes—
282C22×C4#1174567012yes—
283C22×C4C22⋊Dic5911yescharacteristic
284C22×C4C22⋊Dic5911yescharacteristic
285C22×C4C22⋊Dic5911yescharacteristic
286C22×C4C22×Dic5911yescharacteristic
287C22×C4C2×C22⋊D5911yescharacteristic
288C22×C4C2×C22⋊D5911yescharacteristic
289M16—1184no—
290M16—2364no—
291M16—2362no—
292C2×C8—4722no—
293C2×C8—2362no—
294C2×C8—2364no—
295C2×C8—2362no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—42no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—81no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—81no—
311C22⋊C4—81no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23#1427364211yescharacteristic
322C23#1427364211yescharacteristic
323C23#1427364812yes—
324C23#1427365412yes—
325C23C2×C22⋊Dic5911yescharacteristic
326D4—82no—
327D4—82no—
328D4—82no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
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—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4#1427364812yes—
359C2×C4C2×#1174566911yescharacteristic
360C2×C4C2×#1174567011yescharacteristic
361C8—4722no—
362C8—2364no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—42no—
370C22—42no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22#1683713612yes—
379C22#1683713612yes—
380C22C2×#1427364211yescharacteristic
381C22C2×#1427364811yescharacteristic
382C22C2×#1427365411yescharacteristic
383C4—21no—
384C4—22no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—81no—
391C4—81no—
392C4—81no—
393C2—21no—
394C2—21no—
395C2—22no—
396C2—22no—
397C2—161no—
398C2C2×#1683713611yescharacteristic
399C2#2142574211yescharacteristic
400C2#2142578511yescharacteristic
subgroupG/H
centerC22C2×#14273642
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC59×#2618C2
socleC22×C59C2×#99
prime radicalC2×#121×C59C4
cosocleC2×C4⋊C4×C59C23
hypercenter#2618D59
hypocenterC59#11698
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2618

Complements

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

NH ≅ G/Ntype
1. C2×#16837171C2semidirect
2. C2×#16837128C2semidirect
3. #21422102C2semidirect
4. #21422099C2semidirect
223. C59#11698semidirect

Maximal subgroups

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

subgroupindex
C2×#168371712
C2×#168371282
#214221022
#214220992
C59×#26182
#1169859