Finite Group Databasebeta

← #28484755

Subgroups — #28484755

Order 15104.

622 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 127 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
1#21429838C211yesmaximal, characteristic
2#21426714C211yesmaximal, characteristic, complemented
3#21422665C212yesmaximal
4#21421964C212yesmaximal, complemented
5C2×C59×#324C211yesmaximal, characteristic, complemented
6C2×#14273710—21no—
7C2×#14273701C2211yescharacteristic
8C2×#14273686—21no—
9#16837332C412yescomplemented
10#16837324—22no—
11#16837319C412yescomplemented
12#16837301—24no—
13#16837281—21no—
14#16837262—21no—
15#16837262C2211yescharacteristic
16#16837262C2212yes—
17#16837137—24no—
18C22×C4⋊C4×C59C2211yescharacteristic
19C2×C22⋊C8×C59C2212yes—
20C59×#324—22no—
21C22×D236C2×C411yescharacteristic
22C22×C22⋊D59—21no—
23#14273710—42no—
24#14273710—42no—
25#14273701—22no—
26#14273701—22no—
27#14273686—42no—
28#14273686—42no—
29C2×C4⋊Dic59—22no—
30C2×C4⋊Dic59—22no—
31C2×C4⋊Dic59—22no—
32C2×C4⋊Dic59—21no—
33C2×C4⋊Dic59C2×C411yescharacteristic
34C2×Dic59⋊C4—22no—
35C2×C22⋊Dic59—21no—
36C2×C22⋊Dic59—22no—
37C2×(C2×D59)⋊C4—22no—
38C2×(C2×D59)⋊C4—21no—
39C2×(C2×D59)⋊C4—22no—
40C2×C4×Dic59—22no—
41C59⋊#95—22no—
42C59⋊#95—22no—
43C59⋊#95C2×C412yes—
44C59⋊#95D414yes—
45C23×C4×C59D411yescharacteristic
46C23×C4×C59D411yescharacteristic
47C23×C4×C59C2311yescharacteristic
48C22×C8×C59—22no—
49C2×C4⋊C4×C59—22no—
50C2×C4⋊C4×C59—22no—
51C2×C4⋊C4×C59C2×C412yes—
52C2×C4⋊C4×C59D412yes—
53C22⋊C8×C59—22no—
54C22⋊C8×C59—22no—
55C24×C59C2×D411yescharacteristic
56C23×D59—21no—
57C22×C4×C59—21no—
58C22×C4×C59—21no—
59C22×C4×C59—21no—
60C22×C4×C59—21no—
61C22×C4×C59—21no—
62C22×C4×C59—21no—
63C22×C4×C59—81no—
64C22×C4×C59—81no—
65C22×C4×C59C22⋊C412yes—
66C22×C4×C59C22⋊C412yes—
67C22×C4×C59D812yes—
68C22×C4×C59SD1612yes—
69C22×C4×C59C22×C411yescharacteristic
70C22×C4×C59C2×D412yes—
71C22×C4×C59C2×D411yescharacteristic
72C22×C4×C59#4112yes—
73C2×C22⋊D59—41no—
74C2×C22⋊D59—41no—
75C2×C22⋊D59—41no—
76C2×C22⋊D59—41no—
77C2×C22⋊D59—41no—
78C2×C22⋊D59—41no—
79C22×Dic59—21no—
80C22×Dic59—22no—
81C22×Dic59—24no—
82C2×D236—22no—
83C2×D236—81no—
84C2×C8×C59—42no—
85C2×C8×C59—82no—
86C4⋊C4×C59—24no—
87C4⋊C4×C59—24no—
88C22⋊Dic59—42no—
89C22⋊Dic59—41no—
90C22⋊Dic59—41no—
91C22⋊Dic59—42no—
92(C2×D59)⋊C4—44no—
93(C2×D59)⋊C4—42no—
94(C2×D59)⋊C4—82no—
95C4⋊Dic59—22no—
96C4⋊Dic59—44no—
97C4⋊Dic59—82no—
98C4⋊Dic59—82no—
99C4⋊Dic59—81no—
100Dic59⋊C4—44no—
101C4×Dic59—44no—
102C23×C59—41no—
103C23×C59—41no—
104C23×C59C2×C22⋊C411yescharacteristic
105C23×C59#12011yescharacteristic
106C23×C59#12311yescharacteristic
107C23×C59C2×D811yescharacteristic
108C23×C59C2×SD1611yescharacteristic
109C23×C59AGL(1,ℤ/8)11yescharacteristic
110C23×C59#13711yescharacteristic
111C22×D59—42no—
112C22×D59—42no—
113C22×D59—41no—
114C22×D59—41no—
115C22×D59—41no—
116C2×C4×C59—22no—
117C2×C4×C59—22no—
118C2×C4×C59—22no—
119C2×C4×C59—22no—
120C2×C4×C59—22no—
121C2×C4×C59—22no—
122C2×C4×C59—22no—
123C2×C4×C59—42no—
124C2×C4×C59—41no—
125C2×C4×C59—42no—
126C2×C4×C59—41no—
127C2×C4×C59—42no—
128C2×C4×C59—42no—
129C2×C4×C59—81no—
130C2×C4×C59#10214yes—
131C2×C4×C59C4×D412yes—
132C2×C4×C59#12112yes—
133C22⋊D59—81no—
134C22⋊D59—81no—
135C22⋊D59—81no—
136C22⋊D59—81no—
137C2×Dic59—44no—
138C2×Dic59—42no—
139C2×Dic59—44no—
140C2×Dic59—42no—
141C2×Dic59—41no—
142C2×Dic59—41no—
143C2×Dic59—42no—
144C2×Dic59—41no—
145C2×Dic59—44no—
146D236—82no—
147C8×C59—82no—
148#9204—591nomaximal, Sylow
149C22×C59—21no—
150C22×C59—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59#38611yescharacteristic
160C22×C59C2×#10211yescharacteristic
161C22×C59#41711yescharacteristic
162C22×C59#44711yescharacteristic
163C22×C59#44811yescharacteristic
164C22×C59#48011yescharacteristic
165C22×C59#48111yescharacteristic
166C2×D59—82no—
167C2×D59—82no—
168C2×D59—81no—
169C2×D59—81no—
170C2×D59—81no—
171C4×C59—24no—
172C4×C59—22no—
173C4×C59—22no—
174C4×C59—42no—
175Dic59—84no—
176Dic59—82no—
177Dic59—81no—
178#2618—591no—
179#2316—591no—
180#1519—592no—
181C2×#324D5911yescharacteristic, complemented
182#1289—592no—
183C2×C59—21no—
184C2×C59—21no—
185C2×C59—21no—
186C2×C59—21no—
187C2×C59—21no—
188C2×C59—21no—
189C2×C59#187411yescharacteristic
190C2×C59#191211yescharacteristic
191C2×C59#191311yescharacteristic
192D59—161no—
193C2×#123—1181no—
194C2×#121—591no—
195C2×#117—1181no—
196C22×C4⋊C4C2×D5911yescharacteristic
197C2×C22⋊C8C2×D5912yes—
198#398—592no—
199#396—1182no—
200#394—592no—
201#389—1184no—
202#386—1181no—
203#380—591no—
204#380—592no—
205#380—1181no—
206#327—1184no—
207#324—22no—
208C59#920411yescharacteristic, complemented, Sylow
209C22×D4—591no—
210C22×D4—1181no—
211C23×C4D23611yescharacteristic
212C23×C4D23611yescharacteristic
213C23×C4C22×D5911yescharacteristic
214C22×C8—22no—
215#123—2362no—
216#123—2362no—
217#121—1182no—
218#121—1182no—
219#117—2362no—
220#117—2362no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—591no—
224C2×C4⋊C4—1182no—
225C2×C4⋊C4—1182no—
226C2×C4⋊C4—1181no—
227C2×C4⋊C4—1182no—
228C2×C4⋊C4—1182no—
229C2×C4⋊C4C4×D5912yes—
230C2×C4⋊C4C22⋊D5912yes—
231C2×C22⋊C4—1182no—
232C2×C22⋊C4—1182no—
233C2×C22⋊C4—1181no—
234C2×C22⋊C4—1182no—
235C2×C22⋊C4—1181no—
236C2×C42—1182no—
237C22⋊C8—22no—
238C22⋊C8—22no—
239#95—592no—
240#95—594no—
241#95—1182no—
242#95—1182no—
243C24—1181no—
244C24C2×D23611yescharacteristic
245C2×D4—1182no—
246C2×D4—4721no—
247C2×D4—2361no—
248C2×D4—2361no—
249C2×D4—2361no—
250C2×D4—2361no—
251C2×D4—2361no—
252C2×D4—2361no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—81no—
260C22×C4—81no—
261C22×C4—1182no—
262C22×C4—1181no—
263C22×C4—1184no—
264C22×C4#1174566012yes—
265C22×C4D47212yes—
266C22×C4(C2×D59)⋊C412yes—
267C22×C4(C2×D59)⋊C412yes—
268C22×C4C2×C4×D5911yescharacteristic
269C22×C4D4×D5912yes—
270C22×C4#1174568712yes—
271C22×C4C2×C22⋊D5911yescharacteristic
272C2×C8—42no—
273C2×C8—82no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—1182no—
277C4⋊C4—4722no—
278C4⋊C4—4721no—
279C4⋊C4—4722no—
280C4⋊C4—2364no—
281C4⋊C4—2364no—
282C22⋊C4—4722no—
283C22⋊C4—2362no—
284C22⋊C4—2361no—
285C22⋊C4—2361no—
286C22⋊C4—2362no—
287C22⋊C4—2364no—
288C22⋊C4—2362no—
289C42—2364no—
290C23—41no—
291C23—41no—
292C23—2362no—
293C23—2362no—
294C23—2361no—
295C23—2361no—
296C23—2361no—
297C23C2×(C2×D59)⋊C411yescharacteristic
298C23#1427369711yescharacteristic
299C23#1427371111yescharacteristic
300C23C2×D47211yescharacteristic
301C23C2×#1174566011yescharacteristic
302C23#1427375511yescharacteristic
303C23#1427376011yescharacteristic
304D4—4722no—
305D4—4721no—
306D4—4721no—
307D4—4721no—
308D4—4721no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—81no—
323C2×C4—2362no—
324C2×C4—2364no—
325C2×C4—2364no—
326C2×C4—2362no—
327C2×C4—2362no—
328C2×C4—2361no—
329C2×C4—2361no—
330C2×C4—2361no—
331C2×C4—2364no—
332C2×C4#1427364914yes—
333C2×C4(C22⋊D59)⋊C412yes—
334C2×C4#1427369912yes—
335C8—82no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—4722no—
347C22—4722no—
348C22—4721no—
349C22—4721no—
350C22—4721no—
351C22#1683727911yescharacteristic
352C22C2×#1427364911yescharacteristic
353C22#1683740411yescharacteristic
354C22#1683753811yescharacteristic
355C22#1683754311yescharacteristic
356C22#1683771611yescharacteristic
357C22#1683772111yescharacteristic
358C4—24no—
359C4—22no—
360C4—22no—
361C4—42no—
362C4—4724no—
363C4—4722no—
364C4—4721no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2—21no—
371C2—9441no—
372C2#2142441111yescharacteristic
373C2#2142463111yescharacteristic
374C2#2142463611yescharacteristic
subgroupG/H
centerC22#16837279
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC2×C59×#324C2
socleC22×C59#386
prime radicalC2×#14273701C22
cosocleC23×C4×C59C23
hypercenterC2×#324D59
hypocenterC59#9204
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #21426714C2semidirect
4. #21421964C2semidirect
5. C2×C59×#324C2semidirect
9. #16837332C4semidirect
11. #16837319C4semidirect
181. C2×#324D59semidirect
208. C59#9204semidirect

Maximal subgroups

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

subgroupindex
#214298382
#214267142
#214226652
#214219642
C2×C59×#3242
#920459