Finite Group Databasebeta

← #28499290

Subgroups — #28499290

Order 15104.

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

normal subgroups only

This group has 514 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#21429052C211yesmaximal, characteristic
2C4×#14273644C211yesmaximal, characteristic, complemented
3#21422103C212yesmaximal, complemented
4#21422100C212yesmaximal, complemented
5C59×#1465C211yesmaximal, characteristic, complemented
6C2×#14273701C411yescharacteristic
7C2×#14273699—21no—
8C2×#14273644—21no—
9C4×#11745664—21no—
10#16837332C2211yescharacteristic
11#16837327C411yescharacteristic
12#16837319C2211yescharacteristic
13#16837311C411yescharacteristic
14#16837293—21no—
15#16837281—21no—
16#16837279—21no—
17C2×C59⋊#95C411yescharacteristic
18#16837171C2212yes—
19C2×C4×D4×C59C2211yescharacteristic
20C59×#407—21no—
21C59×#324C2212yes—
22C59×#323—21no—
23C22×D236C2×C411yescharacteristic
24C22×C22⋊D59—21no—
25C22×C22⋊D59—21no—
26C23×Dic59—21no—
27C2×#11745664—22no—
28#14273701—41no—
29#14273701—41no—
30#14273699—44no—
31C2×C4⋊Dic59C2×C411yescharacteristic
32C2×Dic59⋊C4—21no—
33C2×C22⋊Dic59—21no—
34C2×(C2×D59)⋊C4—21no—
35C2×(C2×D59)⋊C4—21no—
36C2×(C2×D59)⋊C4—21no—
37C2×(C2×D59)⋊C4—21no—
38#14273644—24no—
39#14273638—41no—
40C4×C59⋊C8—41no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95C2×C411yescharacteristic
45C59⋊#95C2×C411yescharacteristic
46C22×D4×C59D411yescharacteristic
47C23×C4×C59C2×C411yescharacteristic
48C23×C4×C59D411yescharacteristic
49C2×M16×C59—41no—
50C4×D4×C59—41no—
51C4×D4×C59—41no—
52C2×C4⋊C4×C59C2311yescharacteristic
53C2×C22⋊C4×C59C2×C411yescharacteristic
54C2×C22⋊C4×C59D411yescharacteristic
55C2×C42×C59D411yescharacteristic
56C22⋊C8×C59—22no—
57C22⋊C8×C59—41no—
58C24×C59C22⋊C411yescharacteristic
59C24×C59C22⋊C411yescharacteristic
60C23×D59—21no—
61C2×D4×C59—22no—
62C2×D4×C59—22no—
63C2×D4×C59—41no—
64C22×C4×C59—21no—
65C22×C4×C59—21no—
66C22×C4×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59—81no—
69C22×C4×C59—81no—
70C22×C4×C59C22⋊C411yescharacteristic
71C22×C4×C59C22⋊C411yescharacteristic
72C22×C4×C59C22×C411yescharacteristic
73C22×C4×C59C2×D411yescharacteristic
74C22×C4×C59C2×D411yescharacteristic
75C2×C22⋊D59—42no—
76C2×C22⋊D59—42no—
77C2×C22⋊D59—42no—
78C2×C22⋊D59—42no—
79C2×C22⋊D59—42no—
80C2×C22⋊D59—81no—
81C22×Dic59—21no—
82C22×Dic59—21no—
83C22×Dic59—21no—
84C22×Dic59—42no—
85C22×Dic59—42no—
86C22×Dic59—81no—
87C2×D236—41no—
88C2×D236—81no—
89M16×C59—82no—
90C2×C8×C59—42no—
91C4⋊C4×C59—41no—
92C22⋊C4×C59—41no—
93C22⋊C4×C59—41no—
94C42×C59—21no—
95C42×C59—21no—
96C22⋊Dic59—42no—
97(C2×D59)⋊C4—42no—
98(C2×D59)⋊C4—41no—
99(C2×D59)⋊C4—41no—
100(C2×D59)⋊C4—42no—
101(C2×D59)⋊C4—81no—
102C4⋊Dic59—41no—
103Dic59⋊C4—42no—
104#11745664—24no—
105#11745664—42no—
106C2×C59⋊C8—42no—
107C23×C59—21no—
108C23×C59—21no—
109C23×C59—21no—
110C23×C59—21no—
111C23×C59—21no—
112C23×C59—41no—
113C23×C59—41no—
114C23×C59—41no—
115C23×C59—41no—
116C23×C59#10412yes—
117C23×C59C2×C22⋊C411yescharacteristic
118C22×D59—41no—
119C22×D59—41no—
120C22×D59—41no—
121C22×D59—41no—
122C22×D59—41no—
123C22×D59—41no—
124C22×D59—41no—
125D4×C59—44no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—41no—
132C2×C4×C59—42no—
133C2×C4×C59—41no—
134C2×C4×C59—41no—
135C2×C4×C59—41no—
136C2×C4×C59—81no—
137C2×C4×C59—81no—
138C2×C4×C59—81no—
139C2×C4×C59#9911yescharacteristic
140C2×C4×C59#9911yescharacteristic
141C2×C4×C59AGL(1,ℤ/8)12yes—
142C22⋊D59—84no—
143C22⋊D59—84no—
144C2×Dic59—22no—
145C2×Dic59—41no—
146C2×Dic59—41no—
147C2×Dic59—41no—
148C2×Dic59—41no—
149C2×Dic59—41no—
150C2×Dic59—41no—
151C2×Dic59—41no—
152C2×Dic59—41no—
153C2×Dic59—84no—
154D236—82no—
155C8×C59—82no—
156C59⋊C8—44no—
157#11783—591nomaximal, Sylow
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—22no—
161C22×C59—42no—
162C22×C59—42no—
163C22×C59—42no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59—41no—
168C22×C59—41no—
169C22×C59—81no—
170C22×C59C2×#9911yescharacteristic
171C22×C59#41811yescharacteristic
172C22×C59C2×#10411yescharacteristic
173C2×D59—81no—
174C2×D59—81no—
175C2×D59—81no—
176C2×D59—81no—
177C2×D59—81no—
178C2×D59—81no—
179C2×D59—81no—
180C4×C59—21no—
181C4×C59—21no—
182C4×C59—22no—
183C4×C59—41no—
184C4×C59—41no—
185C4×C59—41no—
186Dic59—42no—
187Dic59—81no—
188Dic59—81no—
189#2543—591no—
190C4×#100—591no—
191#1465D5911yescharacteristic, complemented
192#1346—592no—
193#1345—592no—
194C2×C59—21no—
195C2×C59—21no—
196C2×C59—42no—
197C2×C59—81no—
198C2×C59#150711yescharacteristic
199C2×C59#212111yescharacteristic
200C2×C59#213211yescharacteristic
201D59—161no—
202C2×#121—591no—
203C2×#121—1181no—
204C2×C4×D4C2×D5911yescharacteristic
205C2×#100—1181no—
206#407—21no—
207C4×M16—1181no—
208#398—591no—
209#397—591no—
210#394—591no—
211#392—591no—
212#388—1181no—
213#386—1181no—
214#386—1181no—
215C2×#95—591no—
216#343—592no—
217#324C2×D5912yes—
218#323—21no—
219C59#1178311yescharacteristic, complemented, Sylow
220C22×D4—591no—
221C22×D4—1181no—
222C22×D4—1181no—
223C22×D4D23611yescharacteristic
224C23×C4—1181no—
225C23×C4C4×D5911yescharacteristic
226C23×C4C22⋊D5911yescharacteristic
227C2×M16—41no—
228C2×M16—1182no—
229#121—2364no—
230#121—2361no—
231#121—2361no—
232C4×D4—41no—
233C4×D4—41no—
234C2×C4⋊C4—591no—
235C2×C4⋊C4—1181no—
236C2×C4⋊C4C22×D5911yescharacteristic
237C2×C22⋊C4—1181no—
238C2×C22⋊C4—1181no—
239C2×C22⋊C4—1181no—
240C2×C22⋊C4—1181no—
241C2×C22⋊C4—1181no—
242C2×C22⋊C4C4×D5911yescharacteristic
243C2×C22⋊C4C22⋊D5911yescharacteristic
244C2×C42D23611yescharacteristic
245#100—1184no—
246C22⋊C8—22no—
247C22⋊C8—41no—
248#97—2361no—
249C4×C8—2361no—
250#95—591no—
251#95—591no—
252#95—1181no—
253#95—1181no—
254#95—1181no—
255C24—1181no—
256C24(C2×D59)⋊C411yescharacteristic
257C24(C2×D59)⋊C411yescharacteristic
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—41no—
261C2×D4—4721no—
262C2×D4—4721no—
263C2×D4—2361no—
264C2×D4—2362no—
265C2×D4—2362no—
266C2×D4—2362no—
267C2×D4—2362no—
268C2×D4—2362no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—81no—
274C22×C4—81no—
275C22×C4—1181no—
276C22×C4—1181no—
277C22×C4—1181no—
278C22×C4—4721no—
279C22×C4—2362no—
280C22×C4—2362no—
281C22×C4(C2×D59)⋊C411yescharacteristic
282C22×C4(C2×D59)⋊C411yescharacteristic
283C22×C4C2×C4×D5911yescharacteristic
284C22×C4C2×D23611yescharacteristic
285C22×C4C2×C22⋊D5911yescharacteristic
286M16—82no—
287M16—1184no—
288M16—2362no—
289C2×C8—42no—
290C2×C8—2362no—
291C4⋊C4—41no—
292C4⋊C4—2361no—
293C4⋊C4—2362no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—4721no—
297C22⋊C4—2362no—
298C22⋊C4—2362no—
299C22⋊C4—2361no—
300C22⋊C4—2361no—
301C22⋊C4—2362no—
302C42—21no—
303C42—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—2361no—
314C23—2361no—
315C23—2361no—
316C23—2361no—
317C23—2361no—
318C23—2361no—
319C23—2361no—
320C23#1427365312yes—
321C23C2×(C2×D59)⋊C411yescharacteristic
322D4—44no—
323D4—4722no—
324D4—4724no—
325D4—4724no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—1182no—
340C2×C4—4724no—
341C2×C4—2361no—
342C2×C4—2361no—
343C2×C4—2361no—
344C2×C4—2361no—
345C2×C4—2361no—
346C2×C4—2361no—
347C2×C4—2361no—
348C2×C4—2361no—
349C2×C4#1427364111yescharacteristic
350C2×C4#1427364111yescharacteristic
351C2×C4#1427375512yes—
352C8—82no—
353C8—2364no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—81no—
366C22—4721no—
367C22—4721no—
368C22—4721no—
369C22—4721no—
370C22—4721no—
371C22—4721no—
372C22—4721no—
373C22C2×#1427364111yescharacteristic
374C22#1683740811yescharacteristic
375C22C2×#1427365311yescharacteristic
376C4—22no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—4721no—
383C4—4721no—
384C4—2362no—
385C2—21no—
386C2—21no—
387C2—42no—
388C2—81no—
389C2—9441no—
390C2#2142261311yescharacteristic
391C2#2142574011yescharacteristic
392C2#2142577911yescharacteristic
subgroupG/H
centerC22C2×#14273641
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC59×#1465C2
socleC22×C59C2×#99
prime radical#21429052C2
cosocleC2×C4⋊C4×C59C23
hypercenter#1465D59
hypocenterC59#11783
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. C4×#14273644C2semidirect
3. #21422103C2semidirect
4. #21422100C2semidirect
5. C59×#1465C2semidirect
191. #1465D59semidirect
219. C59#11783semidirect

Maximal subgroups

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

subgroupindex
#214290522
C4×#142736442
#214221032
#214221002
C59×#14652
#1178359