Finite Group Databasebeta

← #28477982

Subgroups — #28477982

Order 15104.

404 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 81 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#21431055C211yesmaximal, characteristic
2#21425658C211yesmaximal, characteristic, complemented
3#21425658C211yesmaximal, characteristic, complemented
4#21421920C211yesmaximal, characteristic, complemented
5#21421918C211yesmaximal, characteristic, complemented
6#21421917C211yesmaximal, characteristic
7C59×#2094C211yesmaximal, characteristic
8C2×#14273720—21no—
9#16837338—21no—
10#16837325—21no—
11#16837316—21no—
12#16837300C2211yescharacteristic
13#16837300C2211yescharacteristic
14#16837297—21no—
15#16837295—21no—
16#16837164—21no—
17#16837164—21no—
18#16837164—21no—
19#16837164—21no—
20#16837157C2211yescharacteristic
21#16837157C2211yescharacteristic
22C2×#106×C59—21no—
23C2×#102×C59—21no—
24C59×#390C2211yescharacteristic
25C59×#384C2211yescharacteristic
26C59×#336C2211yescharacteristic
27C22×C59⋊C8—21no—
28C22×C59⋊C8—21no—
29#14273720—42no—
30#14273720—42no—
31C2×C4⋊Dic59D411yescharacteristic
32C2×C4⋊Dic59D411yescharacteristic
33C2×C4⋊Dic59D411yescharacteristic
34C2×C4⋊Dic59D411yescharacteristic
35C2×Dic59⋊C4—21no—
36C2×Dic59⋊C4—21no—
37C2×Dic59⋊C4—21no—
38C2×Dic59⋊C4—21no—
39C2×C22⋊Dic59—21no—
40C2×C22⋊Dic59—21no—
41C2×C22⋊Dic59—21no—
42C2×C22⋊Dic59—21no—
43C2×C4×Dic59—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C22×D4×C59D411yescharacteristic
48C22×C8×C59—21no—
49C2×C4⋊C4×C59—21no—
50C2×C4⋊C4×C59—21no—
51C2×C4⋊C4×C59—21no—
52C2×C4⋊C4×C59D411yescharacteristic
53C2×C22⋊C4×C59—21no—
54C2×C22⋊C4×C59—21no—
55C2×C42×C59C2311yescharacteristic
56#106×C59—42no—
57#102×C59—42no—
58C24×C59—21no—
59C2×D4×C59—21no—
60C2×D4×C59—21no—
61C2×D4×C59—41no—
62C2×D4×C59—41no—
63C22×C4×C59—21no—
64C22×C4×C59—41no—
65C22×C4×C59C2×D411yescharacteristic
66C22×C4×C59C2×D411yescharacteristic
67C22×C4×C59C2×D411yescharacteristic
68C22×Dic59—21no—
69C22×Dic59—21no—
70C22×Dic59—21no—
71C22×Dic59—21no—
72C2×C8×C59—22no—
73C2×C8×C59—41no—
74C2×C8×C59—41no—
75C4⋊C4×C59—41no—
76C4⋊C4×C59—41no—
77C4⋊C4×C59—41no—
78C4⋊C4×C59—42no—
79C4⋊C4×C59—42no—
80C22⋊C4×C59—41no—
81C22⋊C4×C59—41no—
82C22⋊C4×C59—41no—
83C22⋊C4×C59—41no—
84C42×C59—41no—
85C22⋊Dic59—42no—
86C22⋊Dic59—42no—
87C22⋊Dic59—81no—
88C22⋊Dic59—81no—
89C4⋊Dic59—21no—
90C4⋊Dic59—21no—
91C4⋊Dic59—21no—
92C4⋊Dic59—41no—
93C4⋊Dic59—41no—
94C4⋊Dic59SD1612yes—
95Dic59⋊C4—42no—
96Dic59⋊C4—41no—
97Dic59⋊C4—41no—
98Dic59⋊C4—41no—
99Dic59⋊C4—41no—
100Dic59⋊C4—81no—
101C4×Dic59—42no—
102C2×C59⋊C8—41no—
103C2×C59⋊C8—41no—
104C2×C59⋊C8—41no—
105C2×C59⋊C8—41no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8—41no—
108C23×C59—41no—
109C23×C59—41no—
110C23×C59—41no—
111C23×C59—41no—
112C23×C59—41no—
113C23×C59—41no—
114C23×C59—41no—
115C23×C59#12011yescharacteristic
116D4×C59—42no—
117D4×C59—81no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—41no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—81no—
128C2×C4×C59—81no—
129C2×C4×C59—81no—
130C2×C4×C59C2×SD1611yescharacteristic
131C2×C4×C59#13511yescharacteristic
132C2×C4×C59#13511yescharacteristic
133C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C59#13711yescharacteristic
135C2×C4×C59#13711yescharacteristic
136C2×Dic59—22no—
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—
146C2×Dic59—41no—
147C2×Dic59—41no—
148C8×C59—42no—
149C59⋊C8—81no—
150C59⋊C8—81no—
151#7828—591nomaximal, Sylow
152C22×C59—81no—
153C22×C59—81no—
154C22×C59—81no—
155C22×C59—81no—
156C22×C59—81no—
157C22×C59—81no—
158C22×C59—81no—
159C22×C59#45011yescharacteristic
160C22×C59#45211yescharacteristic
161C22×C59#45211yescharacteristic
162C22×C59#45311yescharacteristic
163C22×C59#45411yescharacteristic
164C22×C59#45411yescharacteristic
165C22×C59#45811yescharacteristic
166C4×C59—21no—
167C4×C59—21no—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—21no—
171C4×C59—21no—
172C4×C59—81no—
173C4×C59—161no—
174Dic59—42no—
175Dic59—81no—
176Dic59—81no—
177Dic59—81no—
178#2727—591no—
179#2100—591no—
180#2100—591no—
181#2094D5911yescharacteristic
182#1271—591no—
183#1271—591no—
184#1270—591no—
185C2×C59—161no—
186C2×C59#161511yescharacteristic
187C2×C59#161611yescharacteristic
188C2×C59#161811yescharacteristic
189C2×C59#163111yescharacteristic
190C2×C59#163511yescharacteristic
191C2×C59#163811yescharacteristic
192C2×C59#165711yescharacteristic
193C2×#126—1181no—
194C2×#106—21no—
195C2×#102—21no—
196#399—1181no—
197#396—1181no—
198#394—1181no—
199#390C2×D5911yescharacteristic
200#389—591no—
201#389—591no—
202#389—1181no—
203#388—1181no—
204#384C2×D5911yescharacteristic
205#340—1181no—
206#340—1181no—
207#340—1181no—
208#340—1181no—
209#336—591no—
210#336—591no—
211#336C2×D5911yescharacteristic
212C59#782811yescharacteristic, complemented, Sylow
213C22×D4C22⋊D5911yescharacteristic
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—591no—
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⋊C4—1181no—
230C2×C4⋊C4C22⋊D5911yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—1181no—
234C2×C22⋊C4—1181no—
235C2×C22⋊C4—1181no—
236C2×C22⋊C4—1181no—
237C2×C42—1181no—
238C2×C42C22×D5911yescharacteristic
239#106—42no—
240#102—42no—
241#95—1181no—
242#95—1181no—
243#95—1181no—
244C24—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—41no—
248C2×D4—41no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—1181no—
252C22×C4—1181no—
253C22×C4—1181no—
254C22×C4—1181no—
255C22×C4D4×D5911yescharacteristic
256C22×C4D4×D5911yescharacteristic
257C22×C4C2×C22⋊D5911yescharacteristic
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—2361no—
262C2×C8—2361no—
263C2×C8—2361no—
264C2×C8—2361no—
265C2×C8—2361no—
266C2×C8—2361no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—592no—
273C4⋊C4—1181no—
274C4⋊C4—1181no—
275C4⋊C4—1181no—
276C4⋊C4—4721no—
277C4⋊C4—2361no—
278C4⋊C4—2361no—
279C4⋊C4—2362no—
280C4⋊C4—2361no—
281C4⋊C4—2361no—
282C4⋊C4—2361no—
283C4⋊C4—2361no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—4721no—
289C22⋊C4—4721no—
290C22⋊C4—2362no—
291C22⋊C4—2362no—
292C42—41no—
293C42—2362no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23#1427369511yescharacteristic
302D4—42no—
303D4—81no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—1182no—
317C2×C4—2361no—
318C2×C4—2361no—
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×C4SD16×D5911yescharacteristic
329C2×C4#1427374711yescharacteristic
330C2×C4#1427374811yescharacteristic
331C2×C4#1427375411yescharacteristic
332C2×C4#1427375611yescharacteristic
333C2×C4#1427375811yescharacteristic
334C8—42no—
335C8—4721no—
336C8—4721no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22#1683755111yescharacteristic
345C22#1683756111yescharacteristic
346C22#1683756211yescharacteristic
347C22#1683756911yescharacteristic
348C22#1683757311yescharacteristic
349C22#1683757311yescharacteristic
350C22#1683759111yescharacteristic
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—81no—
358C4—161no—
359C4—4721no—
360C4—4721no—
361C4—4721no—
362C4—2362no—
363C2—161no—
364C2#2142312411yescharacteristic
365C2#2142313111yescharacteristic
366C2#2142314211yescharacteristic
367C2#2142322011yescharacteristic
368C2#2142324611yescharacteristic
369C2#2142326611yescharacteristic
370C2#2142339211yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2094C2
socleC23×C59#120
prime radicalC22×D4×C59D4
hypercenter#2094D59
hypocenterC59#7828
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2094

Complements

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

NH ≅ G/Ntype
2. #21425658C2semidirect
3. #21425658C2semidirect
4. #21421920C2semidirect
5. #21421918C2semidirect
212. C59#7828semidirect

Maximal subgroups

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

subgroupindex
#214310552
#214256582
#214219202
#214219182
#214219172
C59×#20942
#782859