Finite Group Databasebeta

← #28477980

Subgroups — #28477980

Order 15104.

404 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 83 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#21431057C211yesmaximal, characteristic
2#21425658C211yesmaximal, characteristic, complemented
3#21425630C211yesmaximal, characteristic
4#21421920C211yesmaximal, characteristic, complemented
5#21421919C211yesmaximal, characteristic, complemented
6#21421916C211yesmaximal, characteristic
7C59×#2100C211yesmaximal, characteristic, complemented
8C2×#14273722—21no—
9C2×#14273658—21no—
10C2×#14273647—21no—
11#16837339—21no—
12#16837324—21no—
13#16837319—21no—
14#16837304C2211yescharacteristic
15#16837301—21no—
16#16837300C2211yescharacteristic
17#16837294—21no—
18#16837164—21no—
19#16837164—21no—
20#16837157C2211yescharacteristic
21#16837157C2211yescharacteristic
22C59×#389C2211yescharacteristic
23C59×#384C2211yescharacteristic
24C59×#340—21no—
25C59×#340—21no—
26C59×#336C2211yescharacteristic
27C22×D236D411yescharacteristic
28C22×C59⋊C8—21no—
29C22×C59⋊C8—21no—
30#14273722—42no—
31#14273722—42no—
32C2×C4⋊Dic59—21no—
33C2×C4⋊Dic59—21no—
34C2×C4⋊Dic59D411yescharacteristic
35C2×C4⋊Dic59D411yescharacteristic
36C2×C4⋊Dic59D411yescharacteristic
37C2×Dic59⋊C4—21no—
38C2×(C2×D59)⋊C4—21no—
39C2×(C2×D59)⋊C4—21no—
40C2×(C2×D59)⋊C4—21no—
41C2×(C2×D59)⋊C4—21no—
42C2×(C2×D59)⋊C4—21no—
43C2×(C2×D59)⋊C4—21no—
44C2×C4×Dic59—21no—
45#14273658—42no—
46#14273647—42no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C22×C8×C59—21no—
50C2×C4⋊C4×C59—21no—
51C2×C4⋊C4×C59—21no—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59D411yescharacteristic
55C2×C4⋊C4×C59D411yescharacteristic
56C2×C42×C59C2311yescharacteristic
57#95×C59—21no—
58C23×D59—21no—
59C22×C4×C59—21no—
60C22×C4×C59—21no—
61C22×C4×C59—41no—
62C22×C4×C59C2×D411yescharacteristic
63C22×C4×C59C2×D411yescharacteristic
64C22×C4×C59C2×D411yescharacteristic
65C22×Dic59—21no—
66C22×Dic59—21no—
67C22×Dic59—21no—
68C2×D236—21no—
69C2×D236—21no—
70C2×D236—41no—
71C2×D236—41no—
72C2×C8×C59—41no—
73C2×C8×C59—41no—
74C2×C8×C59—41no—
75C4⋊C4×C59—21no—
76C4⋊C4×C59—41no—
77C4⋊C4×C59—42no—
78C4⋊C4×C59—42no—
79C4⋊C4×C59—41no—
80C4⋊C4×C59—41no—
81C4⋊C4×C59—41no—
82C4⋊C4×C59—41no—
83C4⋊C4×C59SD1612yes—
84C42×C59—41no—
85(C2×D59)⋊C4—42no—
86(C2×D59)⋊C4—42no—
87(C2×D59)⋊C4—41no—
88(C2×D59)⋊C4—41no—
89(C2×D59)⋊C4—41no—
90(C2×D59)⋊C4—41no—
91(C2×D59)⋊C4—81no—
92(C2×D59)⋊C4—81no—
93C4⋊Dic59—21no—
94C4⋊Dic59—21no—
95C4⋊Dic59—42no—
96C4⋊Dic59—41no—
97C4⋊Dic59—41no—
98C4⋊Dic59—81no—
99Dic59⋊C4—41no—
100Dic59⋊C4—41no—
101C4×Dic59—42no—
102C2×C59⋊C8—22no—
103C2×C59⋊C8—41no—
104C2×C59⋊C8—41no—
105C2×C59⋊C8—41no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8—41no—
108C23×C59#12011yescharacteristic
109C22×D59—41no—
110C22×D59—41no—
111C22×D59—41no—
112C22×D59—41no—
113C22×D59—41no—
114C22×D59—41no—
115C22×D59—41no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—22no—
123C2×C4×C59—41no—
124C2×C4×C59—41no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—41no—
128C2×C4×C59—81no—
129C2×C4×C59—81no—
130C2×C4×C59—81no—
131C2×C4×C59C2×SD1611yescharacteristic
132C2×C4×C59#13511yescharacteristic
133C2×C4×C59#13511yescharacteristic
134C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C59#13711yescharacteristic
136C2×C4×C59#13711yescharacteristic
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59—41no—
142C2×Dic59—41no—
143C2×Dic59—41no—
144C2×Dic59—41no—
145C2×Dic59—41no—
146D236—42no—
147D236—81no—
148C8×C59—81no—
149C59⋊C8—42no—
150C59⋊C8—81no—
151#7828—591nomaximal, Sylow
152C22×C59#45011yescharacteristic
153C22×C59#45211yescharacteristic
154C22×C59#45211yescharacteristic
155C22×C59#45311yescharacteristic
156C22×C59#45411yescharacteristic
157C22×C59#45411yescharacteristic
158C22×C59#45811yescharacteristic
159C2×D59—81no—
160C2×D59—81no—
161C2×D59—81no—
162C2×D59—81no—
163C2×D59—81no—
164C2×D59—81no—
165C2×D59—81no—
166C4×C59—21no—
167C4×C59—21no—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—21no—
171C4×C59—21no—
172C4×C59—42no—
173C4×C59—81no—
174C4×C59—161no—
175Dic59—81no—
176Dic59—81no—
177Dic59—81no—
178#2727—591no—
179#2100—591no—
180#2100D5911yescharacteristic, complemented
181#2094—591no—
182#1271—591no—
183#1271—591no—
184#1270—591no—
185C2×C59#161511yescharacteristic
186C2×C59#161611yescharacteristic
187C2×C59#161811yescharacteristic
188C2×C59#163111yescharacteristic
189C2×C59#163511yescharacteristic
190C2×C59#163811yescharacteristic
191C2×C59#165711yescharacteristic
192D59—161no—
193C2×#126—1181no—
194C2×#106—1181no—
195C2×#102—1181no—
196#399—1181no—
197#396—1181no—
198#394—1181no—
199#390—591no—
200#389—591no—
201#389—1181no—
202#389C2×D5911yescharacteristic
203#388—1181no—
204#384C2×D5911yescharacteristic
205#340—21no—
206#340—21no—
207#340—1181no—
208#340—1181no—
209#336—591no—
210#336—591no—
211#336C2×D5911yescharacteristic
212C59#782811yescharacteristic, complemented, Sylow
213C22×D4—591no—
214C22×C8—21no—
215C22×C8—1181no—
216C22×C8—1181no—
217#126—2362no—
218#126—2362no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—591no—
224C2×C4⋊C4—591no—
225C2×C4⋊C4—591no—
226C2×C4⋊C4—1181no—
227C2×C4⋊C4—1181no—
228C2×C4⋊C4—1181no—
229C2×C4⋊C4C22⋊D5911yescharacteristic
230C2×C4⋊C4C22⋊D5911yescharacteristic
231C2×C22⋊C4—1181no—
232C2×C22⋊C4—1181no—
233C2×C22⋊C4—1181no—
234C2×C22⋊C4—1181no—
235C2×C22⋊C4—1181no—
236C2×C22⋊C4—1181no—
237C2×C42—1181no—
238C2×C42C22×D5911yescharacteristic
239#106—2362no—
240#102—2362no—
241#95—21no—
242#95—1181no—
243#95—1181no—
244C24—1181no—
245C2×D4—1181no—
246C2×D4—1181no—
247C2×D4—2361no—
248C2×D4—2361no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—41no—
252C22×C4—1181no—
253C22×C4—1181no—
254C22×C4—1181no—
255C22×C4D4×D5911yescharacteristic
256C22×C4D4×D5911yescharacteristic
257C22×C4C2×C22⋊D5911yescharacteristic
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—1182no—
262C2×C8—2361no—
263C2×C8—2361no—
264C2×C8—2361no—
265C2×C8—2361no—
266C2×C8—2361no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—1181no—
276C4⋊C4—1181no—
277C4⋊C4—4721no—
278C4⋊C4—2361no—
279C4⋊C4—2361no—
280C4⋊C4—2362no—
281C4⋊C4—2361no—
282C4⋊C4—2361no—
283C4⋊C4#1174567112yes—
284C22⋊C4—4721no—
285C22⋊C4—4721no—
286C22⋊C4—2362no—
287C22⋊C4—2362no—
288C22⋊C4—2361no—
289C22⋊C4—2361no—
290C22⋊C4—2361no—
291C22⋊C4—2361no—
292C42—41no—
293C42—2362no—
294C23—2361no—
295C23—2361no—
296C23—2361no—
297C23—2361no—
298C23—2361no—
299C23—2361no—
300C23—2361no—
301C23#1427369511yescharacteristic
302D4—4721no—
303D4—2362no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—2361no—
320C2×C4—2361no—
321C2×C4—2361no—
322C2×C4—2361no—
323C2×C4—2361no—
324C2×C4—2361no—
325C2×C4—2361no—
326C2×C4—2361no—
327C2×C4—2361no—
328C2×C4C2×#1174567111yescharacteristic
329C2×C4#1427374811yescharacteristic
330C2×C4#1427375011yescharacteristic
331C2×C4#1427375211yescharacteristic
332C2×C4#1427375611yescharacteristic
333C2×C4#1427375911yescharacteristic
334C8—81no—
335C8—4721no—
336C8—2362no—
337C22—4721no—
338C22—4721no—
339C22—4721no—
340C22—4721no—
341C22—4721no—
342C22—4721no—
343C22—4721no—
344C22#1683755211yescharacteristic
345C22#1683756111yescharacteristic
346C22#1683756311yescharacteristic
347C22#1683756811yescharacteristic
348C22#1683757311yescharacteristic
349C22#1683757411yescharacteristic
350C22#1683759111yescharacteristic
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—42no—
358C4—81no—
359C4—161no—
360C4—4721no—
361C4—4721no—
362C4—4721no—
363C2—9441no—
364C2#2142312611yescharacteristic
365C2#2142313211yescharacteristic
366C2#2142314111yescharacteristic
367C2#2142322111yescharacteristic
368C2#2142324511yescharacteristic
369C2#2142326511yescharacteristic
370C2#2142339311yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2100C2
socleC23×C59#120
prime radicalC22×D236D4
hypercenter#2100D59
hypocenterC59#7828
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
2. #21425658C2semidirect
4. #21421920C2semidirect
5. #21421919C2semidirect
7. C59×#2100C2semidirect
180. #2100D59semidirect
212. C59#7828semidirect

Maximal subgroups

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

subgroupindex
#214310572
#214256582
#214256302
#214219202
#214219192
#214219162
C59×#21002
#782859