Finite Group Databasebeta

← #28483771

Subgroups — #28483771

Order 15104.

516 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 103 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#21433181C211yesmaximal, characteristic, complemented
2#21427379C211yesmaximal, characteristic
3#21422540C212yesmaximal
4#21421990C212yesmaximal, complemented
5C4×#101×C59C211yesmaximal, characteristic, complemented
6C2×C4×D236C2211yescharacteristic
7#16837533—24no—
8#16837459—21no—
9#16837459C2212yes—
10#16837455—21no—
11#16837341C411yescharacteristic
12#16837341C411yescharacteristic
13#16837328—21no—
14#16837319C411yescharacteristic
15#16837319C411yescharacteristic
16#16837313—21no—
17C4×(C2×D59)⋊C4—21no—
18C4×(C2×D59)⋊C4—21no—
19#16837248C2211yescharacteristic
20#16837131—24no—
21C2×C4×Q8×C59C2211yescharacteristic
22C2×#101×C59—21no—
23C4×M16×C59C2212yes—
24C59×#343—21no—
25C22×D236C2×C411yescharacteristic
26C22×C4×D59—21no—
27C4×D236—22no—
28C4×D236—22no—
29C2×C4⋊Dic59C2×C411yescharacteristic
30C2×(C2×D59)⋊C4—21no—
31C2×(C2×D59)⋊C4—21no—
32C2×(C2×D59)⋊C4—21no—
33C2×(C2×D59)⋊C4—21no—
34C2×(C2×D59)⋊C4—21no—
35C2×C4×Dic59—21no—
36C4⋊(C59⋊C8)—22no—
37C4⋊(C59⋊C8)—22no—
38C4⋊(C59⋊C8)D414yes—
39C22⋊(C59⋊C8)—22no—
40#14273638—22no—
41#14273638—22no—
42C4×C59⋊C8—22no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C59⋊#95C2×C411yescharacteristic
49C59⋊#95C2×C411yescharacteristic
50C22×Q8×C59D411yescharacteristic
51C2×M16×C59—22no—
52C4×Q8×C59—22no—
53C4×Q8×C59—22no—
54C2×C4⋊C4×C59C2×C411yescharacteristic
55C2×C4⋊C4×C59C2×C411yescharacteristic
56C2×C4⋊C4×C59D411yescharacteristic
57C2×C42×C59D411yescharacteristic
58C2×C42×C59D411yescharacteristic
59C2×C42×C59C2311yescharacteristic
60#101×C59—24no—
61#97×C59—22no—
62C4×C8×C59—22no—
63C23×D59—21no—
64C2×Q8×C59—22no—
65C2×Q8×C59—22no—
66C2×Q8×C59—41no—
67C22×C4×C59C22⋊C411yescharacteristic
68C22×C4×C59C22⋊C411yescharacteristic
69C22×C4×C59C22⋊C411yescharacteristic
70C22×C4×C59C22⋊C411yescharacteristic
71C22×C4×C59C22×C411yescharacteristic
72C22×C4×C59C2×D411yescharacteristic
73C22×C4×C59C2×D411yescharacteristic
74C22×Dic59—21no—
75C22×Dic59—21no—
76C22×Dic59—21no—
77C2×D236—22no—
78C2×D236—42no—
79C2×C4×D59—42no—
80C2×C4×D59—42no—
81C2×C4×D59—41no—
82C2×C4×D59—41no—
83M16×C59—24no—
84M16×C59—42no—
85C2×C8×C59—42no—
86C4⋊C4×C59—22no—
87C4⋊C4×C59—22no—
88C4⋊C4×C59—22no—
89C42×C59—21no—
90C42×C59—21no—
91C42×C59—21no—
92C42×C59—21no—
93C42×C59C2×D412yes—
94C42×C59#4112yes—
95(C2×D59)⋊C4—42no—
96(C2×D59)⋊C4—42no—
97(C2×D59)⋊C4—42no—
98(C2×D59)⋊C4—42no—
99(C2×D59)⋊C4—42no—
100C4⋊Dic59—22no—
101C4×Dic59—42no—
102C2×C59⋊C8—24no—
103C23×C59C2×C22⋊C411yescharacteristic
104C22×D59—22no—
105C22×D59—41no—
106C22×D59—41no—
107C22×D59—41no—
108C22×D59—41no—
109C22×D59—41no—
110C22×D59—41no—
111Q8×C59—44no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—22no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—41no—
123C2×C4×C59—41no—
124C2×C4×C59—41no—
125C2×C4×C59#10412yes—
126C2×C4×C59C4×D412yes—
127C2×C4×C59#12011yescharacteristic
128C2×C4×C59#12112yes—
129C2×C4×C59#12311yescharacteristic
130C2×Dic59—41no—
131C2×Dic59—41no—
132C2×Dic59—41no—
133C2×Dic59—41no—
134C2×Dic59—41no—
135C2×Dic59—41no—
136C2×Dic59—41no—
137C2×Dic59—41no—
138C2×Dic59—41no—
139D236—24no—
140D236—42no—
141C4×D59—82no—
142C4×D59—82no—
143C8×C59—44no—
144C59⋊C8—44no—
145#9032—591nomaximal, Sylow
146C22×C59—21no—
147C22×C59—21no—
148C22×C59#38611yescharacteristic
149C22×C59C2×#10411yescharacteristic
150C22×C59#42111yescharacteristic
151C2×D59—42no—
152C2×D59—42no—
153C2×D59—42no—
154C2×D59—81no—
155C2×D59—81no—
156C2×D59—81no—
157C2×D59—81no—
158C4×C59—22no—
159C4×C59—22no—
160C4×C59—21no—
161C4×C59—22no—
162C4×C59—41no—
163C4×C59—41no—
164C4×C59—41no—
165C4×C59#45412yes—
166Dic59—81no—
167Dic59—81no—
168Dic59—81no—
169#2983—591no—
170#2398—591no—
171C4×#101D5911yescharacteristic, complemented
172#1490—592no—
173#1300—592no—
174C2×C59—21no—
175C2×C59—21no—
176C2×C59#187111yescharacteristic
177C2×C59#188811yescharacteristic
178C2×C59#189111yescharacteristic
179D59—82no—
180C2×C4×Q8C2×D5911yescharacteristic
181C2×C4×D4—591no—
182#446—1184no—
183#432—592no—
184#432—1181no—
185#431—1181no—
186C2×#101—21no—
187C4×M16C2×D5912yes—
188#400—591no—
189#400—591no—
190#397—1181no—
191#394—591no—
192#394—591no—
193#393—1181no—
194C4×C22⋊C4—1181no—
195C4×C22⋊C4—1181no—
196#376—591no—
197#343—21no—
198D4⋊C8—1184no—
199C59#903211yescharacteristic, complemented, Sylow
200C22×Q8C22⋊D5911yescharacteristic
201C22×D4—591no—
202C23×C4—1181no—
203C2×M16—22no—
204C4×Q8—22no—
205C4×Q8—22no—
206C4×D4—1182no—
207C4×D4—1182no—
208C2×C4⋊C4—591no—
209C2×C4⋊C4C4×D5911yescharacteristic
210C2×C4⋊C4C4×D5911yescharacteristic
211C2×C4⋊C4C22⋊D5911yescharacteristic
212C2×C22⋊C4—1181no—
213C2×C22⋊C4—1181no—
214C2×C22⋊C4—1181no—
215C2×C22⋊C4—1181no—
216C2×C22⋊C4—1181no—
217C2×C42—1181no—
218C2×C42D23611yescharacteristic
219C2×C42D23611yescharacteristic
220C2×C42C22×D5911yescharacteristic
221C4⋊C8—594no—
222C4⋊C8—1182no—
223C4⋊C8—1182no—
224#101—24no—
225C22⋊C8—1182no—
226#97—22no—
227#97—1182no—
228#97—1182no—
229C4×C8—22no—
230C4×C8—1182no—
231#95—591no—
232#95—591no—
233#95—1181no—
234#95—1181no—
235#95—1181no—
236#95—1181no—
237#95—1181no—
238C24—1181no—
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×D4—1182no—
243C2×D4—2362no—
244C22×C4—1181no—
245C22×C4—1181no—
246C22×C4—1181no—
247C22×C4—2362no—
248C22×C4—2362no—
249C22×C4—2361no—
250C22×C4—2361no—
251C22×C4(C2×D59)⋊C411yescharacteristic
252C22×C4(C2×D59)⋊C411yescharacteristic
253C22×C4(C2×D59)⋊C411yescharacteristic
254C22×C4(C2×D59)⋊C411yescharacteristic
255C22×C4C2×C4×D5911yescharacteristic
256C22×C4C2×D23611yescharacteristic
257C22×C4C2×C22⋊D5911yescharacteristic
258M16—24no—
259M16—42no—
260C2×C8—42no—
261C2×C8—1184no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—1182no—
266C22⋊C4—2362no—
267C22⋊C4—2362no—
268C22⋊C4—2362no—
269C22⋊C4—2362no—
270C22⋊C4—2362no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—2362no—
276C42D4×D5912yes—
277C42#1174568712yes—
278C23—1182no—
279C23—2361no—
280C23—2361no—
281C23—2361no—
282C23—2361no—
283C23—2361no—
284C23—2361no—
285C23C2×(C2×D59)⋊C411yescharacteristic
286Q8—44no—
287D4—1184no—
288D4—2362no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—4722no—
303C2×C4—4722no—
304C2×C4—2361no—
305C2×C4—2361no—
306C2×C4—2361no—
307C2×C4—2361no—
308C2×C4—2361no—
309C2×C4—2361no—
310C2×C4—2361no—
311C2×C4—2361no—
312C2×C4—2361no—
313C2×C4#1427365512yes—
314C2×C4(C22⋊D59)⋊C412yes—
315C2×C4#1427369711yescharacteristic
316C2×C4#1427369912yes—
317C2×C4#1427371111yescharacteristic
318C8—44no—
319C8—2364no—
320C22—21no—
321C22—21no—
322C22—4721no—
323C22—4721no—
324C22—4721no—
325C22—4721no—
326C22—2362no—
327C22—2362no—
328C22—2362no—
329C22#1683727911yescharacteristic
330C22C2×#1427365511yescharacteristic
331C22#1683742011yescharacteristic
332C4—22no—
333C4—22no—
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—4721no—
340C4—4721no—
341C4—4721no—
342C4#1683757712yes—
343C2—21no—
344C2—21no—
345C2—4722no—
346C2#2142439611yescharacteristic
347C2#2142449711yescharacteristic
348C2#2142451211yescharacteristic
subgroupG/H
centerC2×C4#14273697
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC4×#101×C59C2
socleC22×C59#386
prime radicalC22×D236C2×C4
cosocleC2×C42×C59C23
hypercenterC4×#101D59
hypocenterC59#9032
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
1. #21433181C2semidirect
4. #21421990C2semidirect
5. C4×#101×C59C2semidirect
171. C4×#101D59semidirect
199. C59#9032semidirect

Maximal subgroups

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

subgroupindex
#214331812
#214273792
#214225402
#214219902
C4×#101×C592
#903259