Finite Group Databasebeta

← #28477102

Subgroups — #28477102

Order 15104.

438 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 101 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#21432464C211yesmaximal, characteristic
2#21424238C211yesmaximal, characteristic, complemented
3#21423944C211yesmaximal, characteristic, complemented
4#21421919C211yesmaximal, characteristic, complemented
5#21421916C211yesmaximal, characteristic
6#21421916C211yesmaximal, characteristic
7C59×#1271C211yesmaximal, characteristic, complemented
8C2×#14273722—21no—
9C2×Dic59⋊C8—21no—
10C2×C8×Dic59—21no—
11#16837304C2211yescharacteristic
12#16837303C411yescharacteristic
13#16837303C411yescharacteristic
14#16837301C411yescharacteristic
15#16837298C411yescharacteristic
16#16837294—21no—
17#16837292—21no—
18#16837291—21no—
19C42×Dic59C2211yescharacteristic
20#16837157C2211yescharacteristic
21#16837157C2211yescharacteristic
22#16837156—21no—
23#16837156—21no—
24C59×#389C2211yescharacteristic
25C59×#336C2211yescharacteristic
26C59×#336C2211yescharacteristic
27C22×D236C2×C411yescharacteristic
28C22×C59⋊C8—21no—
29C22×C59⋊C8—21no—
30#14273722—42no—
31#14273722—42no—
32C2×C4⋊Dic59—21no—
33C2×C4⋊Dic59C2×C411yescharacteristic
34C2×Dic59⋊C4—21no—
35C2×(C2×D59)⋊C4—21no—
36C2×(C2×D59)⋊C4—21no—
37C2×(C2×D59)⋊C4—21no—
38C2×(C2×D59)⋊C4—21no—
39C2×(C2×D59)⋊C4—21no—
40C2×(C2×D59)⋊C4—21no—
41C2×C4×Dic59C2×C411yescharacteristic
42C2×C4×Dic59C2×C411yescharacteristic
43C2×C4×Dic59D411yescharacteristic
44C2×C4×Dic59D411yescharacteristic
45C2×C4×Dic59D411yescharacteristic
46C2×C4×Dic59D411yescharacteristic
47Dic59⋊C8—24no—
48C8×Dic59—42no—
49C59⋊#95—21no—
50C59⋊#95—21no—
51C22×C8×C59—21no—
52C22×C8×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59C2×C411yescharacteristic
55C2×C4⋊C4×C59C2×C411yescharacteristic
56C2×C42×C59C2311yescharacteristic
57#95×C59—21no—
58C23×D59—21no—
59C22×C4×C59—21no—
60C22×C4×C59—21no—
61C22×C4×C59C22×C411yescharacteristic
62C22×C4×C59C2×D411yescharacteristic
63C22×C4×C59C2×D411yescharacteristic
64C22×Dic59—21no—
65C22×Dic59C22⋊C411yescharacteristic
66C22×Dic59C22⋊C411yescharacteristic
67C22×Dic59C22⋊C411yescharacteristic
68C22×Dic59C22⋊C411yescharacteristic
69C2×D236—21no—
70C2×D236—21no—
71C2×D236—41no—
72C2×D236—41no—
73C2×C8×C59—22no—
74C2×C8×C59—41no—
75C2×C8×C59—41no—
76C2×C8×C59—41no—
77C2×C8×C59—41no—
78C2×C8×C59—41no—
79C4⋊C4×C59—21no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59—41no—
82C4⋊C4×C59—41no—
83C4⋊C4×C59—41no—
84C42×C59—41no—
85(C2×D59)⋊C4—42no—
86(C2×D59)⋊C4—41no—
87(C2×D59)⋊C4—41no—
88(C2×D59)⋊C4—41no—
89(C2×D59)⋊C4—41no—
90(C2×D59)⋊C4—42no—
91(C2×D59)⋊C4—42no—
92(C2×D59)⋊C4—42no—
93C4⋊Dic59—42no—
94C4⋊Dic59—41no—
95Dic59⋊C4—42no—
96C4×Dic59—21no—
97C4×Dic59—21no—
98C4×Dic59—21no—
99C4×Dic59—21no—
100C4×Dic59—22no—
101C4×Dic59—41no—
102C4×Dic59—41no—
103C4×Dic59D812yes—
104C4×Dic59SD1612yes—
105C2×C59⋊C8—22no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8—41no—
108C2×C59⋊C8—41no—
109C2×C59⋊C8—41no—
110C2×C59⋊C8—41no—
111C23×C59C2×C22⋊C411yescharacteristic
112C22×D59—41no—
113C22×D59—41no—
114C22×D59—41no—
115C22×D59—41no—
116C22×D59—41no—
117C22×D59—41no—
118C22×D59—41no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—41no—
128C2×C4×C59—41no—
129C2×C4×C59—41no—
130C2×C4×C59—41no—
131C2×C4×C59#13111yescharacteristic
132C2×C4×C59#13111yescharacteristic
133C2×C4×C59C2×D811yescharacteristic
134C2×C4×C59C2×SD1611yescharacteristic
135C2×C4×C59#13511yescharacteristic
136C2×C4×C59#13511yescharacteristic
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144C2×Dic59—21no—
145C2×Dic59—21no—
146C2×Dic59—41no—
147C2×Dic59—41no—
148C2×Dic59—41no—
149C2×Dic59#10212yes—
150C2×Dic59#10212yes—
151C2×Dic59#10412yes—
152D236—81no—
153D236—81no—
154C8×C59—42no—
155C8×C59—81no—
156C59⋊C8—42no—
157C59⋊C8—81no—
158#7672—591nomaximal, Sylow
159C22×C59#40811yescharacteristic
160C22×C59#41011yescharacteristic
161C22×C59#41311yescharacteristic
162C22×C59C2×#10211yescharacteristic
163C22×C59#41611yescharacteristic
164C22×C59C2×#10411yescharacteristic
165C22×C59#42111yescharacteristic
166C2×D59—81no—
167C2×D59—81no—
168C2×D59—81no—
169C2×D59—81no—
170C2×D59—81no—
171C2×D59—81no—
172C2×D59—81no—
173C4×C59—21no—
174C4×C59—21no—
175C4×C59—21no—
176C4×C59—21no—
177C4×C59—21no—
178C4×C59—21no—
179C4×C59—81no—
180C4×C59—81no—
181Dic59—22no—
182Dic59—22no—
183Dic59—22no—
184Dic59—41no—
185Dic59—81no—
186#2860—591no—
187#1839—591no—
188C4×C4⋊C8—591no—
189#1271—591no—
190#1271D5911yescharacteristic, complemented
191#1270—591no—
192#1270—591no—
193C2×C59#147311yescharacteristic
194C2×C59#148011yescharacteristic
195C2×C59#149411yescharacteristic
196C2×C59#150211yescharacteristic
197C2×C59#152111yescharacteristic
198C2×C59#152911yescharacteristic
199C2×C59#154011yescharacteristic
200D59—161no—
201C2×#126—1181no—
202C2×C4⋊C8—1181no—
203C2×C4×C8—1181no—
204#390—591no—
205#390—591no—
206#390—591no—
207#389—591no—
208#389—591no—
209#389C2×D5911yescharacteristic
210#388—1181no—
211#388—1181no—
212#388—1181no—
213C43—591no—
214#336—591no—
215#336—591no—
216#336—1181no—
217#336—1181no—
218#336C2×D5911yescharacteristic
219#336C2×D5911yescharacteristic
220C59#767211yescharacteristic, complemented, Sylow
221C22×D4—591no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—1181no—
225C22×C8—1181no—
226#126—2362no—
227#126—2362no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—591no—
230C2×C4⋊C4—1181no—
231C2×C4⋊C4—1181no—
232C2×C4⋊C4C4×D5911yescharacteristic
233C2×C4⋊C4C4×D5911yescharacteristic
234C2×C22⋊C4—1181no—
235C2×C22⋊C4—1181no—
236C2×C22⋊C4—1181no—
237C2×C22⋊C4—1181no—
238C2×C22⋊C4—1181no—
239C2×C22⋊C4—1181no—
240C2×C42—591no—
241C2×C42—591no—
242C2×C42—591no—
243C2×C42—591no—
244C2×C42—591no—
245C2×C42—591no—
246C2×C42C22×D5911yescharacteristic
247C4⋊C8—1184no—
248C4×C8—2362no—
249#95—21no—
250#95—1181no—
251#95—1181no—
252C24—1181no—
253C2×D4—1181no—
254C2×D4—1181no—
255C2×D4—2361no—
256C2×D4—2361no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—591no—
260C22×C4—591no—
261C22×C4—591no—
262C22×C4—591no—
263C22×C4—1181no—
264C22×C4C2×C4×D5911yescharacteristic
265C22×C4D4×D5911yescharacteristic
266C22×C4D4×D5911yescharacteristic
267C2×C8—22no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—1182no—
274C2×C8—2361no—
275C2×C8—2361no—
276C2×C8—2361no—
277C2×C8—2361no—
278C2×C8—2361no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—2361no—
285C4⋊C4—2362no—
286C4⋊C4—2362no—
287C22⋊C4—2362no—
288C22⋊C4—2362no—
289C22⋊C4—2362no—
290C22⋊C4—2362no—
291C22⋊C4—2361no—
292C22⋊C4—2361no—
293C22⋊C4—2361no—
294C22⋊C4—2361no—
295C42—41no—
296C42—592no—
297C42—592no—
298C42—1182no—
299C42—1181no—
300C42—1181no—
301C42—1181no—
302C42—1181no—
303C42—2361no—
304C42—2361no—
305C23—2361no—
306C23—2361no—
307C23—2361no—
308C23—2361no—
309C23—2361no—
310C23—2361no—
311C23—2361no—
312C23C22⋊C4×D5911yescharacteristic
313D4—4721no—
314D4—4721no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—592no—
328C2×C4—592no—
329C2×C4—592no—
330C2×C4—1181no—
331C2×C4—1181no—
332C2×C4—1181no—
333C2×C4—1181no—
334C2×C4—1181no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—1181no—
339C2×C4—2361no—
340C2×C4—2361no—
341C2×C4—2361no—
342C2×C4#1427373311yescharacteristic
343C2×C4#1427373511yescharacteristic
344C2×C4D8×D5911yescharacteristic
345C2×C4SD16×D5911yescharacteristic
346C2×C4#1427374811yescharacteristic
347C2×C4#1427375011yescharacteristic
348C8—42no—
349C8—81no—
350C8—4721no—
351C8—2362no—
352C22—4721no—
353C22—4721no—
354C22—4721no—
355C22—4721no—
356C22—4721no—
357C22—4721no—
358C22—4721no—
359C22#1683736711yescharacteristic
360C22#1683737411yescharacteristic
361C22#1683738511yescharacteristic
362C22#102×D5911yescharacteristic
363C22#1683739711yescharacteristic
364C22#104×D5911yescharacteristic
365C22#1683741711yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—81no—
373C4—81no—
374C4—1182no—
375C4—1182no—
376C4—1182no—
377C4—4721no—
378C4—2361no—
379C2—9441no—
380C2#2142246411yescharacteristic
381C2#2142249311yescharacteristic
382C2#2142255511yescharacteristic
383C2#2142258911yescharacteristic
384C2#2142267211yescharacteristic
385C2#2142270211yescharacteristic
386C2#2142274411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D59
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1271C2
socleC23×C59C2×C22⋊C4
prime radicalC22×D236C2×C4
cosocleC2×C42×C59C23
hypercenter#1271D59
hypocenterC59#7672
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
2. #21424238C2semidirect
3. #21423944C2semidirect
4. #21421919C2semidirect
7. C59×#1271C2semidirect
190. #1271D59semidirect
220. C59#7672semidirect

Maximal subgroups

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

subgroupindex
#214324642
#214242382
#214239442
#214219192
#214219162
C59×#12712
#767259