Finite Group Databasebeta

← #28477217

Subgroups — #28477217

Order 15104.

378 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 95 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#21432482C211yesmaximal, characteristic
2#21424211C211yesmaximal, characteristic
3#21423948C211yesmaximal, characteristic
4#21421920C211yesmaximal, characteristic
5#21421919C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#1271C211yesmaximal, characteristic
8C2×Dic59⋊C8—21no—
9C2×Dic59⋊C8—21no—
10C2×#14273637—21no—
11#16837301C411yescharacteristic
12#16837300C2211yescharacteristic
13#16837298C411yescharacteristic
14#16837288—21no—
15#16837287—21no—
16#16837284—21no—
17#16837283—21no—
18#16837267C411yescharacteristic
19#16837267C411yescharacteristic
20C42×Dic59C2211yescharacteristic
21#16837157C2211yescharacteristic
22#16837157C2211yescharacteristic
23#16837156—21no—
24C59×#389C2211yescharacteristic
25C59×#336C2211yescharacteristic
26C59×#336C2211yescharacteristic
27C22×C59⋊C8—21no—
28C22×C59⋊C8—21no—
29C2×C4⋊Dic59—21no—
30C2×C4⋊Dic59C2×C411yescharacteristic
31C2×C4⋊Dic59C2×C411yescharacteristic
32C2×Dic59⋊C4—21no—
33C2×Dic59⋊C4—21no—
34C2×C4×Dic59C2×C411yescharacteristic
35C2×C4×Dic59C2×C411yescharacteristic
36C2×C4×Dic59D411yescharacteristic
37C2×C4×Dic59D411yescharacteristic
38C2×C4×Dic59D411yescharacteristic
39C2×C4×Dic59D411yescharacteristic
40Dic59⋊C8—24no—
41Dic59⋊C8—42no—
42#14273637—42no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C59⋊#95—21no—
50C22×C8×C59—21no—
51C22×C8×C59—21no—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59C2×C411yescharacteristic
54C2×C4⋊C4×C59C2×C411yescharacteristic
55C2×C42×C59C2311yescharacteristic
56#95×C59—21no—
57C22×C4×C59—21no—
58C22×C4×C59—21no—
59C22×C4×C59C22×C411yescharacteristic
60C22×C4×C59C2×D411yescharacteristic
61C22×C4×C59C2×D411yescharacteristic
62C22×Dic59—21no—
63C22×Dic59—21no—
64C22×Dic59C22⋊C411yescharacteristic
65C22×Dic59C22⋊C411yescharacteristic
66C22×Dic59C22⋊C411yescharacteristic
67C22×Dic59C22⋊C411yescharacteristic
68C2×C8×C59—22no—
69C2×C8×C59—41no—
70C2×C8×C59—41no—
71C2×C8×C59—41no—
72C2×C8×C59—41no—
73C2×C8×C59—41no—
74C4⋊C4×C59—21no—
75C4⋊C4×C59—21no—
76C4⋊C4×C59—41no—
77C4⋊C4×C59—41no—
78C4⋊C4×C59—41no—
79C42×C59—41no—
80C4⋊Dic59—21no—
81C4⋊Dic59—21no—
82C4⋊Dic59—42no—
83C4⋊Dic59—41no—
84Dic59⋊C4—42no—
85Dic59⋊C4—41no—
86Dic59⋊C4—41no—
87C4×Dic59—21no—
88C4×Dic59—21no—
89C4×Dic59—21no—
90C4×Dic59—21no—
91C4×Dic59—21no—
92C4×Dic59—21no—
93C4×Dic59—22no—
94C4×Dic59—22no—
95C4×Dic59—41no—
96C2×C59⋊C8—22no—
97C2×C59⋊C8—41no—
98C2×C59⋊C8—41no—
99C2×C59⋊C8—41no—
100C2×C59⋊C8—41no—
101C2×C59⋊C8—41no—
102C23×C59C2×C22⋊C411yescharacteristic
103C2×C4×C59—21no—
104C2×C4×C59—21no—
105C2×C4×C59—21no—
106C2×C4×C59—21no—
107C2×C4×C59—21no—
108C2×C4×C59—21no—
109C2×C4×C59—41no—
110C2×C4×C59—41no—
111C2×C4×C59—41no—
112C2×C4×C59—41no—
113C2×C4×C59—41no—
114C2×C4×C59—41no—
115C2×C4×C59#13111yescharacteristic
116C2×C4×C59#13111yescharacteristic
117C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C59#13711yescharacteristic
120C2×C4×C59#13711yescharacteristic
121C2×Dic59—21no—
122C2×Dic59—21no—
123C2×Dic59—21no—
124C2×Dic59—21no—
125C2×Dic59—21no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—41no—
132C2×Dic59—41no—
133C2×Dic59—41no—
134C2×Dic59—41no—
135C2×Dic59—41no—
136C2×Dic59—41no—
137C2×Dic59#10112yes—
138C2×Dic59#10412yes—
139C8×C59—42no—
140C8×C59—81no—
141C59⋊C8—42no—
142C59⋊C8—81no—
143#7697—591nomaximal, Sylow
144C22×C59#40811yescharacteristic
145C22×C59#41011yescharacteristic
146C22×C59C2×#10111yescharacteristic
147C22×C59#41711yescharacteristic
148C22×C59#41711yescharacteristic
149C22×C59C2×#10411yescharacteristic
150C22×C59#42111yescharacteristic
151C4×C59—21no—
152C4×C59—21no—
153C4×C59—21no—
154C4×C59—21no—
155C4×C59—21no—
156C4×C59—21no—
157C4×C59—81no—
158C4×C59—81no—
159Dic59—22no—
160Dic59—22no—
161Dic59—41no—
162Dic59—41no—
163Dic59—81no—
164Dic59—81no—
165#2864—591no—
166#1831—591no—
167#1767—591no—
168#1271—591no—
169#1271—591no—
170#1271—591no—
171#1271D5911yescharacteristic
172C2×C59#147011yescharacteristic
173C2×C59#148311yescharacteristic
174C2×C59#149511yescharacteristic
175C2×C59#150911yescharacteristic
176C2×C59#151211yescharacteristic
177C2×C59#153111yescharacteristic
178C2×C59#156111yescharacteristic
179C2×C4⋊C8—1181no—
180C2×C4⋊C8—1181no—
181C2×#97—1181no—
182#389—591no—
183#389—591no—
184#389—591no—
185#389C2×D5911yescharacteristic
186#387—1181no—
187#387—1181no—
188#387—1181no—
189#387—1181no—
190#382—591no—
191#382—591no—
192C43—591no—
193#336—591no—
194#336—591no—
195#336—1181no—
196#336C2×D5911yescharacteristic
197#336C2×D5911yescharacteristic
198C59#769711yescharacteristic, complemented, Sylow
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—1181no—
202C22×C8—1181no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—591no—
205C2×C4⋊C4—591no—
206C2×C4⋊C4—1181no—
207C2×C4⋊C4—1181no—
208C2×C4⋊C4—1181no—
209C2×C4⋊C4C4×D5911yescharacteristic
210C2×C4⋊C4C4×D5911yescharacteristic
211C2×C42—591no—
212C2×C42—591no—
213C2×C42—591no—
214C2×C42—591no—
215C2×C42—591no—
216C2×C42—591no—
217C2×C42C22×D5911yescharacteristic
218C4⋊C8—1184no—
219C4⋊C8—2362no—
220#97—2362no—
221#95—21no—
222#95—1181no—
223#95—1181no—
224#95—1181no—
225#95—1181no—
226#95—1181no—
227#95—1181no—
228#95—1181no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—591no—
232C22×C4—591no—
233C22×C4—591no—
234C22×C4—591no—
235C22×C4—1181no—
236C22×C4—1181no—
237C22×C4C2×C4×D5911yescharacteristic
238C22×C4D4×D5911yescharacteristic
239C22×C4D4×D5911yescharacteristic
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—1182no—
247C2×C8—2361no—
248C2×C8—2361no—
249C2×C8—2361no—
250C2×C8—2361no—
251C2×C8—2361no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—1181no—
258C4⋊C4—1181no—
259C4⋊C4—2361no—
260C4⋊C4—2362no—
261C4⋊C4—2362no—
262C4⋊C4—2361no—
263C4⋊C4—2361no—
264C42—41no—
265C42—1182no—
266C42—1182no—
267C42—1181no—
268C42—1181no—
269C42—1181no—
270C42—1181no—
271C42—1181no—
272C42—1181no—
273C42—2361no—
274C23C22⋊C4×D5911yescharacteristic
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—592no—
288C2×C4—592no—
289C2×C4—1181no—
290C2×C4—1181no—
291C2×C4—1181no—
292C2×C4—1181no—
293C2×C4—1181no—
294C2×C4—1181no—
295C2×C4—1181no—
296C2×C4—1181no—
297C2×C4—1181no—
298C2×C4—1181no—
299C2×C4—2361no—
300C2×C4—2361no—
301C2×C4—2361no—
302C2×C4—2361no—
303C2×C4—2361no—
304C2×C4—2361no—
305C2×C4#1427373311yescharacteristic
306C2×C4#1427373511yescharacteristic
307C2×C4#1427375111yescharacteristic
308C2×C4#1427375411yescharacteristic
309C2×C4#1427375611yescharacteristic
310C2×C4#1427375911yescharacteristic
311C8—42no—
312C8—81no—
313C8—4721no—
314C8—2362no—
315C22#1683736711yescharacteristic
316C22#1683737411yescharacteristic
317C22#101×D5911yescharacteristic
318C22#1683740011yescharacteristic
319C22#1683740211yescharacteristic
320C22#104×D5911yescharacteristic
321C22#1683741711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—81no—
329C4—81no—
330C4—1182no—
331C4—1182no—
332C4—4721no—
333C4—4721no—
334C4—2361no—
335C4—2361no—
336C2#2142245011yescharacteristic
337C2#2142250811yescharacteristic
338C2#2142255811yescharacteristic
339C2#2142261811yescharacteristic
340C2#2142263311yescharacteristic
341C2#2142270911yescharacteristic
342C2#2142283211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D59
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1271C2
socle, prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenter#1271D59
hypocenterC59#7697
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
198. C59#7697semidirect

Maximal subgroups

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

subgroupindex
#214324822
#214242112
#214239482
#214219202
#214219192
#214219182
C59×#12712
#769759