Finite Group Databasebeta

← #21437030

Subgroups — #21437030

Order 7552.

326 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 133 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
1Q8×Dic118C211yesmaximal, characteristic
2#16838130C211yesmaximal, characteristic
3#16837811C212yesmaximal
4#16837800C211yesmaximal, characteristic
5#16837710C212yesmaximal
6#16837698C211yesmaximal, characteristic
7#16837688C211yesmaximal, characteristic
8#16837688C212yesmaximal
9#16837510C212yesmaximal
10C4×Dic236C211yesmaximal, characteristic
11C59×#446C211yesmaximal, characteristic
12C2×Dic236C2211yescharacteristic
13#14273727C2211yescharacteristic
14#14273727C2212yes—
15#14273727C2211yescharacteristic
16#14273726—21no—
17#14273726—22no—
18#14273725—21no—
19#14273719C2212yes—
20#14273717—22no—
21Q8×Dic59—21no—
22C4×Dic118C2211yescharacteristic
23C4×Dic118C2212yes—
24C4×Dic118C2211yescharacteristic
25C4×Dic118C2212yes—
26#14273692—21no—
27#14273661C2212yes—
28#14273661C2211yescharacteristic
29#14273659C2212yes—
30#14273659C2212yes—
31#14273659C2212yes—
32#14273652C2211yescharacteristic
33#14273652C2212yes—
34#14273652C2212yes—
35#14273652C2211yescharacteristic
36C4×Q8×C59C2211yescharacteristic
37C4⋊C8×C59C2211yescharacteristic
38C4⋊C8×C59C2212yes—
39#97×C59C2212yes—
40C4×C8×C59C2211yescharacteristic
41C2×Q8×C59D411yescharacteristic
42C2×Dic118—21no—
43C2×Dic118—22no—
44C2×Dic118—21no—
45C2×Dic118C2311yescharacteristic
46C2×Dic118C2311yescharacteristic
47C2×C8×C59C2311yescharacteristic
48C2×C8×C59C2312yes—
49C2×C8×C59C2311yescharacteristic
50C4⋊C4×C59D411yescharacteristic
51C4⋊C4×C59D412yes—
52C42×C59C2311yescharacteristic
53C42×C59C2312yes—
54C4⋊Dic59—22no—
55C4⋊Dic59—21no—
56C4⋊Dic59—21no—
57C4⋊Dic59C2312yes—
58C4⋊Dic59C2311yescharacteristic
59C4⋊Dic59C2312yes—
60C4⋊Dic59C2311yescharacteristic
61Dic59⋊C4—22no—
62Dic59⋊C4—21no—
63Dic59⋊C4—22no—
64Dic59⋊C4—22no—
65Dic59⋊C4—21no—
66Dic59⋊C4—22no—
67C4×Dic59—22no—
68C4×Dic59—21no—
69C4×Dic59—22no—
70C4×Dic59—21no—
71Dic236Q814yescomplemented
72Q8×C59—22no—
73C2×C4×C59C2×D412yes—
74C2×C4×C59C2×D412yes—
75C2×C4×C59C2×D411yescharacteristic
76C2×C4×C59C2×D411yescharacteristic
77C2×C4×C59C2411yescharacteristic
78C2×Dic59—21no—
79C2×Dic59—21no—
80C2×Dic59—21no—
81C2×Dic59—22no—
82C2×Dic59—22no—
83C2×Dic59—21no—
84Dic118—21no—
85Dic118—21no—
86Dic118—42no—
87Dic118—82no—
88Dic118—81no—
89Dic118C2×Q812yes—
90Dic118C2×Q812yes—
91C8×C59—21no—
92C8×C59—22no—
93C8×C59C2×Q812yes—
94C22×C59C22×D411yescharacteristic
95C4×C59—22no—
96C4×C59—22no—
97C4×C59—21no—
98C4×C59#13712yes—
99C4×C59C22×Q811yescharacteristic
100C4×C592−1+411yescharacteristic
101Dic59—22no—
102Dic59—22no—
103Dic59—42no—
104Dic59—41no—
105Dic59—42no—
106Dic59—41no—
107#3387—591nomaximal, Sylow
108C2×C59D4×Q811yescharacteristic
109C2×C59C2×#13711yescharacteristic
110C2×C59#57711yescharacteristic
111Q82—591no—
112#557—591no—
113#501—592no—
114#498—591no—
115#479—592no—
116#477—591no—
117#475—592no—
118#475—591no—
119#446D5911yescharacteristic
120#441—592no—
121C4×Q16—591no—
122C59#338711yescharacteristic, complemented, Sylow
123C2×Q16—591no—
124C4⋊Q8—591no—
125C4⋊Q8—592no—
126C4⋊Q8—591no—
127C4⋊Q8—1181no—
128C4⋊Q8—1181no—
129C4⋊Q8—1182no—
130#125—592no—
131#125—1182no—
132C4×Q8—591no—
133C4×Q8—592no—
134C4×Q8—591no—
135C4×Q8—592no—
136C4×Q8—1181no—
137C4×Q8—1181no—
138C4×Q8C2×D5911yescharacteristic
139#107—591no—
140#107—592no—
141#106—592no—
142#106—592no—
143#106—592no—
144C4⋊C8C2×D5911yescharacteristic
145C4⋊C8C2×D5912yes—
146#103—591no—
147#103—591no—
148#103—592no—
149#103—592no—
150#97C2×D5912yes—
151C4×C8C2×D5911yescharacteristic
152C2×Q8—591no—
153C2×Q8—591no—
154C2×Q8—1182no—
155C2×Q8—1181no—
156C2×Q8—1181no—
157C2×Q8D23611yescharacteristic
158Q16—594no—
159C2×C8C22×D5911yescharacteristic
160C2×C8C22×D5912yes—
161C2×C8C22×D5911yescharacteristic
162C4⋊C4—592no—
163C4⋊C4—591no—
164C4⋊C4—592no—
165C4⋊C4—591no—
166C4⋊C4—1181no—
167C4⋊C4—1182no—
168C4⋊C4—1182no—
169C4⋊C4—1181no—
170C4⋊C4—1182no—
171C4⋊C4—1182no—
172C4⋊C4—1181no—
173C4⋊C4—1182no—
174C4⋊C4—1181no—
175C4⋊C4D23611yescharacteristic
176C4⋊C4D23612yes—
177C42—1182no—
178C42—1181no—
179C42—1182no—
180C42—1181no—
181C42C22×D5911yescharacteristic
182C42C22×D5912yes—
183Q8—22no—
184Q8—592no—
185Q8—592no—
186Q8—1181no—
187Q8—1181no—
188Q8—4722no—
189Q8—4721no—
190Q8—2362no—
191C2×C4—1181no—
192C2×C4—1181no—
193C2×C4—1181no—
194C2×C4—1182no—
195C2×C4—1182no—
196C2×C4—1181no—
197C2×C4C2×D23612yes—
198C2×C4C2×D23612yes—
199C2×C4C2×D23611yescharacteristic
200C2×C4C2×D23611yescharacteristic
201C2×C4C23×D5911yescharacteristic
202C8—21no—
203C8—22no—
204C8Q8×D5912yes—
205C22C22×D23611yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—1182no—
210C4—1182no—
211C4—2362no—
212C4—2362no—
213C4—2361no—
214C4—2361no—
215C4#1427376012yes—
216C4C2×Q8×D5911yescharacteristic
217C4#1427377411yescharacteristic
218C2Q8×D23611yescharacteristic
219C2C2×#1427376011yescharacteristic
220C2#1683821411yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#446C2
socleC22×C59C22×D4
hypercenter#446D59
hypocenterC59#3387
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
71. Dic236Q8semidirect
122. C59#3387semidirect