Finite Group Databasebeta

← #28499031

Subgroups — #28499031

Order 15104.

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

normal subgroups only

This group has 486 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#21429980C211yesmaximal, characteristic
2#21422417C211yesmaximal, characteristic, complemented
3#21422119C212yesmaximal, complemented
4#21422092C212yesmaximal, complemented
5C4×#99×C59C211yesmaximal, characteristic, complemented
6C2×#14273701C411yescharacteristic, complemented
7#16837455—21no—
8#16837341C411yescharacteristic, complemented
9#16837338C2211yescharacteristic
10#16837319C411yescharacteristic, complemented
11#16837317—21no—
12#16837311C2211yescharacteristic
13#16837310—21no—
14#16837293—21no—
15#16837281—21no—
16#16837265C411yescharacteristic, complemented
17#16837126—21no—
18#16837126C2212yes—
19C2×C4×D4×C59C2211yescharacteristic
20C2×#99×C59—21no—
21C4×C22⋊C4×C59—21no—
22C59×#342C2212yes—
23C22×D236C2×C411yescharacteristic
24C22×C22⋊D59—21no—
25C22×C22⋊D59—21no—
26#14273701—41no—
27#14273701—41no—
28C2×C4⋊Dic59C2×C411yescharacteristic
29C2×Dic59⋊C4—21no—
30C2×C22⋊Dic59—21no—
31C2×C22⋊Dic59—21no—
32C2×(C2×D59)⋊C4—21no—
33C2×(C2×D59)⋊C4—21no—
34C2×(C2×D59)⋊C4—21no—
35C2×(C2×D59)⋊C4—21no—
36C4⋊(C59⋊C8)—41no—
37C22⋊(C59⋊C8)—22no—
38C4×C59⋊C8—41no—
39C59⋊#95—21no—
40C59⋊#95—21no—
41C59⋊#95—21no—
42C59⋊#95C2×C411yescharacteristic
43C59⋊#95C2×C411yescharacteristic
44C22×D4×C59D411yescharacteristic
45C23×C4×C59C2×C411yescharacteristic
46C23×C4×C59D411yescharacteristic
47C4×D4×C59—41no—
48C4×D4×C59—41no—
49C2×C4⋊C4×C59C2×C411yescharacteristic
50C2×C22⋊C4×C59—22no—
51C2×C22⋊C4×C59D411yescharacteristic
52C2×C22⋊C4×C59C2311yescharacteristic
53C2×C42×C59—41no—
54C2×C42×C59D411yescharacteristic
55#99×C59—24no—
56#95×C59—41no—
57C24×C59C22⋊C411yescharacteristic
58C24×C59C2×D411yescharacteristic
59C23×D59—21no—
60C2×D4×C59—22no—
61C2×D4×C59—22no—
62C2×D4×C59—41no—
63C22×C4×C59—21no—
64C22×C4×C59—21no—
65C22×C4×C59—21no—
66C22×C4×C59—21no—
67C22×C4×C59—42no—
68C22×C4×C59—81no—
69C22×C4×C59—81no—
70C22×C4×C59C22⋊C411yescharacteristic
71C22×C4×C59C22⋊C411yescharacteristic
72C22×C4×C59C22⋊C411yescharacteristic
73C22×C4×C59C22×C411yescharacteristic
74C22×C4×C59C2×D411yescharacteristic
75C2×C22⋊D59—42no—
76C2×C22⋊D59—42no—
77C2×C22⋊D59—81no—
78C2×C22⋊D59—81no—
79C2×C22⋊D59—81no—
80C2×C22⋊D59—81no—
81C22×Dic59—21no—
82C22×Dic59—21no—
83C22×Dic59—21no—
84C2×D236—41no—
85C2×D236—81no—
86C4⋊C4×C59—41no—
87C22⋊C4×C59—24no—
88C22⋊C4×C59—41no—
89C22⋊C4×C59—41no—
90C22⋊C4×C59—42no—
91C42×C59—21no—
92C42×C59—21no—
93C42×C59—82no—
94C22⋊Dic59—81no—
95C22⋊Dic59—81no—
96(C2×D59)⋊C4—41no—
97(C2×D59)⋊C4—41no—
98(C2×D59)⋊C4—42no—
99(C2×D59)⋊C4—81no—
100(C2×D59)⋊C4—81no—
101C4⋊Dic59—41no—
102Dic59⋊C4—81no—
103C2×C59⋊C8—42no—
104C23×C59—21no—
105C23×C59—21no—
106C23×C59—21no—
107C23×C59—21no—
108C23×C59—21no—
109C23×C59—41no—
110C23×C59—41no—
111C23×C59—41no—
112C23×C59—41no—
113C23×C59C2×C22⋊C411yescharacteristic
114C23×C59#13512yes—
115C22×D59—41no—
116C22×D59—41no—
117C22×D59—41no—
118C22×D59—41no—
119C22×D59—41no—
120C22×D59—41no—
121C22×D59—41no—
122D4×C59—44no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—41no—
129C2×C4×C59—42no—
130C2×C4×C59—41no—
131C2×C4×C59—41no—
132C2×C4×C59—41no—
133C2×C4×C59—44no—
134C2×C4×C59—81no—
135C2×C4×C59—81no—
136C2×C4×C59—81no—
137C2×C4×C59—82no—
138C2×C4×C59—82no—
139C2×C4×C59#9911yescharacteristic
140C2×C4×C59#9911yescharacteristic
141C2×C4×C59#10412yes—
142C22⋊D59—84no—
143C22⋊D59—84no—
144C2×Dic59—41no—
145C2×Dic59—41no—
146C2×Dic59—41no—
147C2×Dic59—41no—
148C2×Dic59—41no—
149C2×Dic59—41no—
150C2×Dic59—41no—
151C2×Dic59—41no—
152C2×Dic59—41no—
153D236—82no—
154C59⋊C8—82no—
155#11729—591nomaximal, Sylow
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—22no—
159C22×C59—42no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59—81no—
166C22×C59—81no—
167C22×C59—81no—
168C22×C59C2×#9911yescharacteristic
169C22×C59#41611yescharacteristic
170C22×C59C2×#10411yescharacteristic
171C2×D59—81no—
172C2×D59—81no—
173C2×D59—81no—
174C2×D59—81no—
175C2×D59—81no—
176C2×D59—81no—
177C2×D59—81no—
178C4×C59—21no—
179C4×C59—21no—
180C4×C59—22no—
181C4×C59—41no—
182C4×C59—41no—
183C4×C59—41no—
184C4×C59—84no—
185Dic59—81no—
186Dic59—81no—
187Dic59—81no—
188#2635—591no—
189C4×#99D5911yescharacteristic, complemented
190#1460—591no—
191#1352—592no—
192#1343—592no—
193C2×C59—21no—
194C2×C59—21no—
195C2×C59—42no—
196C2×C59—81no—
197C2×C59#150111yescharacteristic
198C2×C59#212111yescharacteristic
199C2×C59#212811yescharacteristic
200D59—161no—
201C2×#121—591no—
202C2×C4×D4C2×D5911yescharacteristic
203#431—1181no—
204C2×#99—21no—
205#400—591no—
206#399—591no—
207#394—591no—
208#394—1181no—
209#392—591no—
210#392—1181no—
211#388—1181no—
212#386—1181no—
213#381—591no—
214C4×C22⋊C4—21no—
215#342C2×D5912yes—
216#323—592no—
217#323—1181no—
218C59#1172911yescharacteristic, complemented, Sylow
219C22×D4—591no—
220C22×D4—1181no—
221C22×D4—1181no—
222C22×D4C22⋊D5911yescharacteristic
223C23×C4C4×D5911yescharacteristic
224C23×C4C22⋊D5911yescharacteristic
225#121—2361no—
226#121—2361no—
227C4×D4—41no—
228C4×D4—41no—
229C2×C4⋊C4—591no—
230C2×C4⋊C4—1181no—
231C2×C4⋊C4C4×D5911yescharacteristic
232C2×C22⋊C4—22no—
233C2×C22⋊C4—1181no—
234C2×C22⋊C4—1181no—
235C2×C22⋊C4—1181no—
236C2×C22⋊C4—1181no—
237C2×C22⋊C4—1181no—
238C2×C22⋊C4—1181no—
239C2×C22⋊C4D23611yescharacteristic
240C2×C22⋊C4C22×D5911yescharacteristic
241C2×C42—41no—
242C2×C42D23611yescharacteristic
243C4⋊C8—2361no—
244#99—24no—
245C22⋊C8—1182no—
246C4×C8—2361no—
247#95—41no—
248#95—591no—
249#95—591no—
250#95—1181no—
251#95—1181no—
252#95—1181no—
253C24—1181no—
254C24(C2×D59)⋊C411yescharacteristic
255C24C2×C22⋊D5911yescharacteristic
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—41no—
259C2×D4—4721no—
260C2×D4—4721no—
261C2×D4—4721no—
262C2×D4—4721no—
263C2×D4—4721no—
264C2×D4—2361no—
265C2×D4—2362no—
266C2×D4—2362no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—42no—
272C22×C4—81no—
273C22×C4—81no—
274C22×C4—1181no—
275C22×C4—1181no—
276C22×C4—1181no—
277C22×C4(C2×D59)⋊C411yescharacteristic
278C22×C4(C2×D59)⋊C411yescharacteristic
279C22×C4(C2×D59)⋊C411yescharacteristic
280C22×C4C2×C4×D5911yescharacteristic
281C22×C4C2×D23611yescharacteristic
282C2×C8—2362no—
283C4⋊C4—41no—
284C4⋊C4—4721no—
285C4⋊C4—2361no—
286C22⋊C4—24no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—4721no—
291C22⋊C4—4721no—
292C22⋊C4—4721no—
293C22⋊C4—4721no—
294C22⋊C4—2361no—
295C22⋊C4—2361no—
296C22⋊C4—2362no—
297C42—21no—
298C42—21no—
299C42—82no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—2361no—
310C23—2361no—
311C23—2361no—
312C23—2361no—
313C23—2361no—
314C23—2361no—
315C23—2361no—
316C23C2×(C2×D59)⋊C411yescharacteristic
317C23#1427374712yes—
318D4—44no—
319D4—4722no—
320D4—4724no—
321D4—4724no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—44no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—2361no—
339C2×C4—2361no—
340C2×C4—2361no—
341C2×C4—2361no—
342C2×C4—2361no—
343C2×C4—2361no—
344C2×C4—2361no—
345C2×C4—2361no—
346C2×C4—2361no—
347C2×C4#1427364111yescharacteristic
348C2×C4#1427364111yescharacteristic
349C2×C4#1427365512yes—
350C8—4722no—
351C22—21no—
352C22—21no—
353C22—22no—
354C22—42no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—4721no—
364C22—4721no—
365C22—4721no—
366C22—4721no—
367C22—4721no—
368C22—4721no—
369C22—4721no—
370C22C2×#1427364111yescharacteristic
371C22#1683739611yescharacteristic
372C22C2×#1427365511yescharacteristic
373C4—21no—
374C4—21no—
375C4—22no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—84no—
380C4—4721no—
381C4—4721no—
382C4—4721no—
383C2—21no—
384C2—21no—
385C2—42no—
386C2—81no—
387C2—9441no—
388C2#2142258511yescharacteristic
389C2#2142574011yescharacteristic
390C2#2142576711yescharacteristic
subgroupG/H
centerC22C2×#14273641
commutatorC22×C4×C59C22×C4
FrattiniC2×C22⋊C4C22×D59
FittingC4×#99×C59C2
socleC22×C59C2×#99
prime radical#21429980C2
cosocleC2×C22⋊C4×C59C23
hypercenterC4×#99D59
hypocenterC59#11729
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #21422417C2semidirect
3. #21422119C2semidirect
4. #21422092C2semidirect
5. C4×#99×C59C2semidirect
6. C2×#14273701C4semidirect
8. #16837341C4semidirect
10. #16837319C4semidirect
16. #16837265C4semidirect
189. C4×#99D59semidirect
218. C59#11729semidirect

Maximal subgroups

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

subgroupindex
#214299802
#214224172
#214221192
#214220922
C4×#99×C592
#1172959