Finite Group Databasebeta

← #21435971

Subgroups — #21435971

Order 7552.

388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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#16838113C211yesmaximal, characteristic
2#16838067C211yesmaximal, characteristic
3#16837736C212yesmaximal, complemented
4#16837694C211yesmaximal, characteristic, complemented
5#16837642C212yesmaximal, complemented
6#16837609C211yesmaximal, characteristic, complemented
7#16837559C212yesmaximal, complemented
8C4×Dic236C211yesmaximal, characteristic, complemented
9C8×D236C211yesmaximal, characteristic
10#103×D59C212yesmaximal, complemented
11C59×#487C211yesmaximal, characteristic, complemented
12C2×Q8×D59C2212yes—
13C2×Dic236C2211yescharacteristic
14C2×#11745672C2212yes—
15C2×C8×D59C2212yes—
16#14273726—21no—
17#14273718—21no—
18#14273707C2212yes—
19#14273705—22no—
20#14273703—22no—
21#14273703C2212yes—
22C4×Dic118C2211yescharacteristic
23C4×Dic118C2211yescharacteristic
24C4×D236C2211yescharacteristic
25#14273689—21no—
26#14273689—21no—
27C4⋊C4×D59C2212yes—
28#14273661C2211yescharacteristic
29#14273660C2212yes—
30C4⋊(C59⋊C8)C2211yescharacteristic
31#14273652C2211yescharacteristic
32#14273652C2211yescharacteristic
33#14273651C2212yes—
34#14273650C2212yes—
35(C2×D59)⋊C8C2212yes—
36C4⋊Q8×C59C2211yescharacteristic
37C4⋊Q8×C59C2211yescharacteristic
38#103×C59C2212yes—
39#103×C59C2212yes—
40C4×C8×C59C2211yescharacteristic
41C2×Q8×C59—21no—
42C2×Q8×C59C2312yes—
43Q8×D59—24no—
44Q8×D59—42no—
45C2×D236D411yescharacteristic
46C2×C4×D59—22no—
47C2×C4×D59—22no—
48C2×C4×D59C2312yes—
49C2×Dic118—22no—
50C2×Dic118C2311yescharacteristic
51C2×Dic118C2311yescharacteristic
52C2×C8×C59C2311yescharacteristic
53C2×C8×C59C2311yescharacteristic
54C4⋊C4×C59—21no—
55C4⋊C4×C59—21no—
56C4⋊C4×C59—21no—
57C4⋊C4×C59C2312yes—
58C42×C59C2311yescharacteristic
59#11745672—42no—
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4—22no—
62(C2×D59)⋊C4D412yes—
63C4⋊Dic59—22no—
64C4⋊Dic59D411yescharacteristic
65C4⋊Dic59C2311yescharacteristic
66C4⋊Dic59C2311yescharacteristic
67Dic59⋊C4—21no—
68Dic59⋊C4—21no—
69Dic59⋊C4—22no—
70Dic59⋊C4—22no—
71C4×Dic59—21no—
72C4×Dic59—21no—
73C2×C59⋊C8C2312yes—
74Dic236—22no—
75C8×D59—42no—
76C22×D59C2×D412yes—
77Q8×C59—22no—
78Q8×C59—22no—
79Q8×C59—81no—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2411yescharacteristic
85C2×Dic59—21no—
86C2×Dic59—21no—
87C2×Dic59—21no—
88C2×Dic59—21no—
89C2×Dic59C2×D412yes—
90D236Q1614yescomplemented
91C4×D59—22no—
92C4×D59—22no—
93C4×D59—44no—
94C4×D59—82no—
95Dic118—21no—
96Dic118—21no—
97Dic118—21no—
98Dic118—44no—
99Dic118#4112yes—
100C8×C59—21no—
101C8×C59—21no—
102C59⋊C8—22no—
103C22×C59C22×D411yescharacteristic
104C2×D59—22no—
105C2×D59—22no—
106C2×D59C2×Q1614yes—
107C4×C59—21no—
108C4×C59—42no—
109C4×C59—42no—
110C4×C59C2×Q1612yes—
111C4×C59C2×#4111yescharacteristic
112C4×C59H(5,𝔽2)11yescharacteristic
113Dic59—22no—
114Dic59—22no—
115Dic59—41no—
116Dic59—41no—
117Dic59—41no—
118#3299—591nomaximal, Sylow
119C2×C59#54611yescharacteristic
120C2×C59C22×Q1611yescharacteristic
121C2×C59#57711yescharacteristic
122D59—24no—
123#554—591no—
124D4×Q8—591no—
125#487D5911yescharacteristic, complemented
126#484—592no—
127#477—591no—
128#467—592no—
129#462—591no—
130#451—592no—
131C4×Q16—591no—
132C8×D4—591no—
133C2×#103—592no—
134C59#329911yescharacteristic, complemented, Sylow
135C22×Q8—592no—
136C2×Q16—592no—
137C2×Q16—591no—
138C22×C8—592no—
139C4⋊Q8—1181no—
140C4⋊Q8C2×D5911yescharacteristic
141C4⋊Q8C2×D5911yescharacteristic
142#125—1181no—
143C22⋊Q8—592no—
144C22⋊Q8—592no—
145C22⋊Q8—1182no—
146C22⋊Q8—1182no—
147C4×Q8—591no—
148C4×Q8—591no—
149C4×D4—591no—
150C4×D4—1181no—
151C4×D4—1181no—
152C2×C4⋊C4—592no—
153#107—591no—
154#107—592no—
155C4⋊C8—591no—
156#103—592no—
157#103—591no—
158#103—591no—
159#103—592no—
160#103C2×D5912yes—
161#103C2×D5912yes—
162C22⋊C8—592no—
163C4×C8C2×D5911yescharacteristic
164C2×Q8—21no—
165C2×Q8—591no—
166C2×Q8—591no—
167C2×Q8—1182no—
168C2×Q8—1184no—
169C2×Q8—2362no—
170C2×Q8C22×D5912yes—
171C2×D4—591no—
172C22×C4—592no—
173C22×C4—1182no—
174C22×C4—1182no—
175Q16—1182no—
176Q16—2362no—
177C2×C8—592no—
178C2×C8—2362no—
179C2×C8C22×D5911yescharacteristic
180C2×C8C22×D5911yescharacteristic
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—591no—
185C4⋊C4—591no—
186C4⋊C4—591no—
187C4⋊C4—1182no—
188C4⋊C4—1182no—
189C4⋊C4—1182no—
190C4⋊C4—1181no—
191C4⋊C4—1181no—
192C4⋊C4C22×D5912yes—
193C22⋊C4—592no—
194C22⋊C4—1182no—
195C22⋊C4—1182no—
196C42—1181no—
197C42—1181no—
198C42C22×D5911yescharacteristic
199C23—592no—
200Q8—22no—
201Q8—22no—
202Q8—81no—
203Q8—592no—
204Q8—1181no—
205Q8—1181no—
206Q8—1181no—
207Q8—2364no—
208D4—594no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—592no—
212C2×C4—1181no—
213C2×C4—1182no—
214C2×C4—1182no—
215C2×C4—1181no—
216C2×C4—1181no—
217C2×C4—1181no—
218C2×C4—4722no—
219C2×C4—2364no—
220C2×C4D4×D5911yescharacteristic
221C2×C4D4×D5911yescharacteristic
222C2×C4C23×D5911yescharacteristic
223C8—21no—
224C8—21no—
225C8—1182no—
226C22—594no—
227C22—1182no—
228C22—1182no—
229C22C2×D4×D5911yescharacteristic
230C4—21no—
231C4—42no—
232C4—42no—
233C4—1182no—
234C4—1182no—
235C4—2361no—
236C4—2361no—
237C4—2361no—
238C4Q16×D5912yes—
239C4#41×D5911yescharacteristic
240C4#1427377311yescharacteristic
241C2—1184no—
242C2#1683804511yescharacteristic
243C2C2×Q16×D5911yescharacteristic
244C2#1683820811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#487C2
socleC22×C59C22×D4
hypercenter#487D59
hypocenterC59#3299
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #16837736C2semidirect
4. #16837694C2semidirect
5. #16837642C2semidirect
6. #16837609C2semidirect
7. #16837559C2semidirect
8. C4×Dic236C2semidirect
10. #103×D59C2semidirect
11. C59×#487C2semidirect
90. D236Q16semidirect
125. #487D59semidirect
134. C59#3299semidirect