Finite Group Databasebeta

← #28477363

Subgroups — #28477363

Order 15104.

346 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 91 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#21432479C211yesmaximal, characteristic
2#21424238C211yesmaximal, characteristic
3#21424238C211yesmaximal, characteristic
4#21421921C211yesmaximal, characteristic
5#21421921C211yesmaximal, characteristic
6#21421919C211yesmaximal, characteristic
7C59×#1271C211yesmaximal, characteristic
8#16837308C2211yescharacteristic
9#16837307C411yescharacteristic
10#16837307C411yescharacteristic
11#16837301C411yescharacteristic
12#16837298C411yescharacteristic
13#16837288—21no—
14#16837285—21no—
15#16837283—21no—
16#16837269—21no—
17C42×Dic59C2211yescharacteristic
18#16837157C2211yescharacteristic
19#16837157C2211yescharacteristic
20#16837156—21no—
21#16837156—21no—
22#16837156—21no—
23#16837156—21no—
24C59×#389C2211yescharacteristic
25C59×#336C2211yescharacteristic
26C59×#336C2211yescharacteristic
27C22×Dic118C2×C411yescharacteristic
28C22×C59⋊C8—21no—
29C22×C59⋊C8—21no—
30C2×C4⋊Dic59—21no—
31C2×C4⋊Dic59C2×C411yescharacteristic
32C2×Dic59⋊C4—21no—
33C2×C4×Dic59C2×C411yescharacteristic
34C2×C4×Dic59C2×C411yescharacteristic
35C2×C4×Dic59D411yescharacteristic
36C2×C4×Dic59D411yescharacteristic
37C2×C4×Dic59D411yescharacteristic
38C2×C4×Dic59D411yescharacteristic
39C59⋊#95—21no—
40C59⋊#95—21no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C22×C8×C59—21no—
48C22×C8×C59—21no—
49C2×C4⋊C4×C59—21no—
50C2×C4⋊C4×C59C2×C411yescharacteristic
51C2×C4⋊C4×C59C2×C411yescharacteristic
52C2×C42×C59C2311yescharacteristic
53#95×C59—21no—
54C22×C4×C59—21no—
55C22×C4×C59—21no—
56C22×C4×C59C22×C411yescharacteristic
57C22×C4×C59C2×D411yescharacteristic
58C22×C4×C59C2×D411yescharacteristic
59C22×Dic59—21no—
60C22×Dic59—21no—
61C22×Dic59C22⋊C411yescharacteristic
62C22×Dic59C22⋊C411yescharacteristic
63C22×Dic59C22⋊C411yescharacteristic
64C22×Dic59C22⋊C411yescharacteristic
65C2×Dic118—21no—
66C2×Dic118—21no—
67C2×Dic118—41no—
68C2×Dic118—41no—
69C2×C8×C59—41no—
70C2×C8×C59—41no—
71C2×C8×C59—41no—
72C2×C8×C59—41no—
73C2×C8×C59—41no—
74C2×C8×C59—41no—
75C4⋊C4×C59—21no—
76C4⋊C4×C59—21no—
77C4⋊C4×C59—41no—
78C4⋊C4×C59—41no—
79C4⋊C4×C59—41no—
80C42×C59—41no—
81C4⋊Dic59—42no—
82C4⋊Dic59—41no—
83Dic59⋊C4—42no—
84C4×Dic59—21no—
85C4×Dic59—21no—
86C4×Dic59—21no—
87C4×Dic59—21no—
88C4×Dic59—21no—
89C4×Dic59—21no—
90C4×Dic59—41no—
91C4×Dic59—41no—
92C4×Dic59—41no—
93C2×C59⋊C8—41no—
94C2×C59⋊C8—41no—
95C2×C59⋊C8—41no—
96C2×C59⋊C8—41no—
97C2×C59⋊C8—41no—
98C2×C59⋊C8—41no—
99C23×C59C2×C22⋊C411yescharacteristic
100C2×C4×C59—21no—
101C2×C4×C59—21no—
102C2×C4×C59—21no—
103C2×C4×C59—21no—
104C2×C4×C59—21no—
105C2×C4×C59—21no—
106C2×C4×C59—41no—
107C2×C4×C59—41no—
108C2×C4×C59—41no—
109C2×C4×C59—41no—
110C2×C4×C59—41no—
111C2×C4×C59—41no—
112C2×C4×C59#13111yescharacteristic
113C2×C4×C59#13111yescharacteristic
114C2×C4×C59#13511yescharacteristic
115C2×C4×C59#13511yescharacteristic
116C2×C4×C59#13711yescharacteristic
117C2×C4×C59#13711yescharacteristic
118C2×Dic59—21no—
119C2×Dic59—21no—
120C2×Dic59—21no—
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—41no—
131C2×Dic59—41no—
132C2×Dic59—41no—
133C2×Dic59—41no—
134C2×Dic59—41no—
135C2×Dic59—41no—
136Dic118—81no—
137Dic118—81no—
138C8×C59—81no—
139C8×C59—81no—
140C59⋊C8—81no—
141C59⋊C8—81no—
142#7729—591nomaximal, Sylow
143C22×C59#40811yescharacteristic
144C22×C59#41011yescharacteristic
145C22×C59#41311yescharacteristic
146C22×C59#41611yescharacteristic
147C22×C59#41911yescharacteristic
148C22×C59#42111yescharacteristic
149C22×C59#42111yescharacteristic
150C4×C59—21no—
151C4×C59—21no—
152C4×C59—21no—
153C4×C59—21no—
154C4×C59—21no—
155C4×C59—21no—
156C4×C59—81no—
157C4×C59—81no—
158Dic59—41no—
159Dic59—41no—
160Dic59—41no—
161Dic59—41no—
162Dic59—81no—
163Dic59—81no—
164#2863—591no—
165#1839—591no—
166#1839—591no—
167#1272—591no—
168#1272—591no—
169#1271—591no—
170#1271D5911yescharacteristic
171C2×C59#147311yescharacteristic
172C2×C59#148211yescharacteristic
173C2×C59#149711yescharacteristic
174C2×C59#151511yescharacteristic
175C2×C59#152111yescharacteristic
176C2×C59#153511yescharacteristic
177C2×C59#155411yescharacteristic
178#391—591no—
179#391—591no—
180#391—591no—
181#389—591no—
182#389—591no—
183#389C2×D5911yescharacteristic
184#387—1181no—
185#387—1181no—
186#387—1181no—
187#383—1181no—
188C43—591no—
189#336—591no—
190#336—591no—
191#336—1181no—
192#336—1181no—
193#336—1181no—
194#336—1181no—
195#336C2×D5911yescharacteristic
196#336C2×D5911yescharacteristic
197C59#772911yescharacteristic, complemented, Sylow
198C22×Q8—591no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—1181no—
202C22×C8—1181no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—591no—
205C2×C4⋊C4—1181no—
206C2×C4⋊C4—1181no—
207C2×C4⋊C4C4×D5911yescharacteristic
208C2×C4⋊C4C4×D5911yescharacteristic
209C2×C42—591no—
210C2×C42—591no—
211C2×C42—591no—
212C2×C42—591no—
213C2×C42—591no—
214C2×C42—591no—
215C2×C42C22×D5911yescharacteristic
216#95—21no—
217#95—1181no—
218#95—1181no—
219#95—1181no—
220#95—1181no—
221#95—1181no—
222#95—1181no—
223#95—1181no—
224#95—1181no—
225C2×Q8—1181no—
226C2×Q8—1181no—
227C2×Q8—2361no—
228C2×Q8—2361no—
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—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—2361no—
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—2361no—
258C4⋊C4—2362no—
259C4⋊C4—2362no—
260C42—41no—
261C42—1181no—
262C42—1181no—
263C42—1181no—
264C42—1181no—
265C42—1181no—
266C42—1181no—
267C42—2361no—
268C42—2361no—
269C42—2361no—
270C23C22⋊C4×D5911yescharacteristic
271Q8—4721no—
272Q8—4721no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—1181no—
286C2×C4—1181no—
287C2×C4—1181no—
288C2×C4—1181no—
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—2361no—
298C2×C4—2361no—
299C2×C4—2361no—
300C2×C4—2361no—
301C2×C4—2361no—
302C2×C4—2361no—
303C2×C4#1427373311yescharacteristic
304C2×C4#1427373511yescharacteristic
305C2×C4#1427374611yescharacteristic
306C2×C4#1427374811yescharacteristic
307C2×C4#1427375611yescharacteristic
308C2×C4#1427375911yescharacteristic
309C8—81no—
310C8—81no—
311C8—4721no—
312C8—4721no—
313C22#1683736711yescharacteristic
314C22#1683737411yescharacteristic
315C22#1683738511yescharacteristic
316C22#1683739511yescharacteristic
317C22#1683740911yescharacteristic
318C22#1683741711yescharacteristic
319C22#1683741711yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—81no—
327C4—81no—
328C4—4721no—
329C4—4721no—
330C4—2361no—
331C4—2361no—
332C4—2361no—
333C4—2361no—
334C2#2142246411yescharacteristic
335C2#2142250111yescharacteristic
336C2#2142256711yescharacteristic
337C2#2142264511yescharacteristic
338C2#2142267011yescharacteristic
339C2#2142272611yescharacteristic
340C2#2142280311yescharacteristic
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#7729
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
197. C59#7729semidirect

Maximal subgroups

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

subgroupindex
#214324792
#214242382
#214219212
#214219192
C59×#12712
#772959