Finite Group Databasebeta

← #28488355

Subgroups — #28488355

Order 15104.

466 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C2×#16837781C211yesmaximal, characteristic
2#21425085C211yesmaximal, characteristic
3#21422851C211yesmaximal, characteristic
4#21422778C211yesmaximal, characteristic
5#21422777C211yesmaximal, characteristic
6#21422383C211yesmaximal, characteristic
7C59×#1997C211yesmaximal, characteristic
8C22×#11745672C414yes—
9C2×#14273727C2211yescharacteristic
10#16837781—21no—
11#16837781—21no—
12#16837781—22no—
13#16837455C2211yescharacteristic
14#16837426C2211yescharacteristic
15C2×C4×C59⋊C8C2211yescharacteristic
16#16837170—22no—
17#16837152—22no—
18#16837151—22no—
19#16837150—22no—
20#16837124—21no—
21#16837124—21no—
22C2×C4⋊Q8×C59C2211yescharacteristic
23C59×#423C2211yescharacteristic
24C4×M16×C59C2211yescharacteristic
25C59×#343—22no—
26C22×Dic118C2×C412yes—
27C2×#11745672—24no—
28C2×#11745672—24no—
29C2×#11745672—48no—
30C2×#11745664—21no—
31C22×C59⋊C8C2×C412yes—
32#14273727—21no—
33#14273727—21no—
34#14273727—21no—
35#14273727—21no—
36C2×C4⋊Dic59—21no—
37C2×C4⋊Dic59—21no—
38C4⋊(C59⋊C8)—21no—
39C4⋊(C59⋊C8)—21no—
40C4⋊(C59⋊C8)D412yes—
41C22⋊(C59⋊C8)—21no—
42C4×C59⋊C8—21no—
43C4×C59⋊C8D411yescharacteristic
44C4×C59⋊C8D411yescharacteristic
45C4×C59⋊C8D412yes—
46C22×Q8×C59C2×C412yes—
47C2×M16×C59—21no—
48C2×M16×C59D412yes—
49C4⋊Q8×C59—21no—
50C4⋊Q8×C59—21no—
51C4⋊Q8×C59—21no—
52C4⋊Q8×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59—21no—
55C2×C42×C59C2311yescharacteristic
56C4⋊C8×C59—21no—
57C4⋊C8×C59—21no—
58#97×C59—21no—
59C4×C8×C59—21no—
60C2×Q8×C59—22no—
61C2×Q8×C59—22no—
62C2×Q8×C59—44no—
63C22×C4×C59—22no—
64C22×C4×C59C22×C411yescharacteristic
65C22×C4×C59C2×D411yescharacteristic
66C22×C4×C59#4111yescharacteristic
67C22×Dic59—22no—
68C2×Dic118—22no—
69C2×Dic118—22no—
70C2×Dic118—44no—
71M16×C59—22no—
72M16×C59—22no—
73M16×C59—42no—
74C2×C8×C59—22no—
75C2×C8×C59—41no—
76C4⋊C4×C59—41no—
77C4⋊C4×C59—41no—
78C4⋊C4×C59—41no—
79C4⋊C4×C59—41no—
80C42×C59C2×D411yescharacteristic
81C42×C59C2×D411yescharacteristic
82C42×C59C2×D411yescharacteristic
83C42×C59#4111yescharacteristic
84#11745672—48no—
85#11745672—48no—
86C4⋊Dic59—41no—
87C4⋊Dic59—41no—
88C4⋊Dic59—41no—
89C4⋊Dic59—41no—
90#11745664—42no—
91C2×C59⋊C8—24no—
92C2×C59⋊C8—22no—
93C2×C59⋊C8—41no—
94C2×C59⋊C8C22⋊C412yes—
95C2×C59⋊C8C22⋊C412yes—
96C23×C59C4×D411yescharacteristic
97Q8×C59—44no—
98Q8×C59—82no—
99C2×C4×C59—22no—
100C2×C4×C59—22no—
101C2×C4×C59—42no—
102C2×C4×C59—82no—
103C2×C4×C59C2×C22⋊C411yescharacteristic
104C2×C4×C59C4×D411yescharacteristic
105C2×C4×C59#12111yescharacteristic
106C2×C4×C59#12111yescharacteristic
107C2×C4×C59#12411yescharacteristic
108C2×C4×C59#12711yescharacteristic
109C2×C4×C59#13712yes—
110C2×C4×C59#13712yes—
111C2×Dic59—42no—
112C2×Dic59—82no—
113Dic118—44no—
114Dic118—82no—
115C8×C59—42no—
116C8×C59—81no—
117C59⋊C8—22no—
118C59⋊C8—42no—
119C59⋊C8—81no—
120C59⋊C8#10014yes—
121#9807—591nomaximal, Sylow
122C22×C59—21no—
123C22×C59—21no—
124C22×C59#39011yescharacteristic
125C22×C59#44112yes—
126C4×C59—21no—
127C4×C59—21no—
128C4×C59—82no—
129C4×C59C2×#10012yes—
130C4×C59#47012yes—
131C4×C59#47312yes—
132C4×C59#49711yescharacteristic
133C4×C59#49711yescharacteristic
134Dic59—82no—
135C2×#494—591no—
136#1997—591no—
137#1997D5911yescharacteristic
138#1566—591no—
139#1548—591no—
140#1548—591no—
141#1451—591no—
142C2×C59—22no—
143C2×C59#196511yescharacteristic
144C2×C59#197111yescharacteristic
145C2×C59#197911yescharacteristic
146C22×Q16—594no—
147C2×C4⋊Q8—591no—
148C2×C4⋊Q8C2×D5911yescharacteristic
149#494—1181no—
150#494—1181no—
151#494—1182no—
152#431—591no—
153#423—591no—
154#423C2×D5911yescharacteristic
155C4×M16C2×D5911yescharacteristic
156C2×C4×C8—591no—
157#343—22no—
158#343—1182no—
159#334—1182no—
160#333—1182no—
161#333—1182no—
162#322—1181no—
163#322—1181no—
164C59#980711yescharacteristic, complemented, Sylow
165C22×Q8—592no—
166C22×Q8C4×D5912yes—
167C2×Q16—1184no—
168C2×Q16—1184no—
169C2×Q16—2368no—
170C2×M16—21no—
171C2×M16—1181no—
172C2×M16C22⋊D5912yes—
173C22×C8—592no—
174C4⋊Q8—21no—
175C4⋊Q8—21no—
176C4⋊Q8—21no—
177C4⋊Q8—21no—
178C4⋊Q8—1181no—
179C4⋊Q8—1181no—
180C4⋊Q8—1181no—
181C4⋊Q8—1181no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—1181no—
185C2×C4⋊C4—1181no—
186C2×C42C22×D5911yescharacteristic
187C4⋊C8—21no—
188C4⋊C8—21no—
189C4⋊C8—592no—
190C4⋊C8—1181no—
191C4⋊C8—1181no—
192C22⋊C8—1181no—
193#97—21no—
194C4×C8—21no—
195C4×C8—591no—
196C4×C8—591no—
197C4×C8—592no—
198C4×C8—1181no—
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—44no—
202C2×Q8—1182no—
203C2×Q8—1182no—
204C2×Q8—2364no—
205C22×C4—22no—
206C22×C4—1182no—
207C22×C4C2×C4×D5911yescharacteristic
208C22×C4#1174568511yescharacteristic
209C22×C4C2×C22⋊D5911yescharacteristic
210Q16—2368no—
211Q16—2368no—
212M16—22no—
213M16—22no—
214M16—42no—
215M16—2362no—
216C2×C8—22no—
217C2×C8—41no—
218C2×C8—592no—
219C2×C8—592no—
220C2×C8—1184no—
221C2×C8—1182no—
222C2×C8—2361no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—2361no—
228C4⋊C4—2361no—
229C4⋊C4—2361no—
230C4⋊C4—2361no—
231C42D4×D5911yescharacteristic
232C42D4×D5911yescharacteristic
233C42D4×D5911yescharacteristic
234C42#1174568711yescharacteristic
235C23C4×C22⋊D5911yescharacteristic
236Q8—44no—
237Q8—82no—
238Q8—4722no—
239Q8—2364no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—42no—
243C2×C4—82no—
244C2×C4—4722no—
245C2×C4—2362no—
246C2×C4C22⋊C4×D5911yescharacteristic
247C2×C4(C22⋊D59)⋊C411yescharacteristic
248C2×C4#1427369911yescharacteristic
249C2×C4#1427370011yescharacteristic
250C2×C4#1427371311yescharacteristic
251C2×C4#1427372311yescharacteristic
252C2×C4#1427375712yes—
253C2×C4#1427375812yes—
254C8—42no—
255C8—81no—
256C8—594no—
257C8—1182no—
258C8—4721no—
259C8—2362no—
260C22—21no—
261C22—21no—
262C22#1683730211yescharacteristic
263C22#1683750712yes—
264C4—21no—
265C4—21no—
266C4—82no—
267C4—4722no—
268C4#100×D5912yes—
269C4#1683765812yes—
270C4#1683767612yes—
271C4#1683779411yescharacteristic
272C4#1683779711yescharacteristic
273C2—22no—
274C2#2142493411yescharacteristic
275C2#2142496611yescharacteristic
276C2#2142500811yescharacteristic
subgroupG/H
centerC22#16837302
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1997C2
socleC22×C59#390
prime radicalC23×C59C4×D4
cosocleC2×C42×C59C23
hypercenter#1997D59
hypocenterC59#9807
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
164. C59#9807semidirect

Maximal subgroups

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

subgroupindex
C2×#168377812
#214250852
#214228512
#214227782
#214227772
#214223832
C59×#19972
#980759