Finite Group Databasebeta

← #21446931

Subgroups — #21446931

Order 7808.

362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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×#14519808C211yesmaximal, characteristic, complemented
2C2×#14519803C211yesmaximal, characteristic
3C2×#14519696C211yesmaximal, characteristic, complemented
4C2×#14519694C211yesmaximal, characteristic, complemented
5#16839728C211yesmaximal, characteristic, complemented
6#16839527C211yesmaximal, characteristic, complemented
7C22×SD16×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808—22no—
10#14519808—22no—
11#14519803—22no—
12#14519803—22no—
13C2×#11758202—21no—
14C2×#11758200—21no—
15C2×#11758201—21no—
16C2×#11758199—21no—
17C2×#11758194C2211yescharacteristic
18C2×#11758194C2211yescharacteristic
19C2×#11758194C2211yescharacteristic
20#14519696—22no—
21#14519694—22no—
22#14519689—22no—
23C22×Q8×C61C2211yescharacteristic
24C22×D4×C61C2211yescharacteristic
25C2×SD16×C61—22no—
26C2×SD16×C61—22no—
27C2×SD16×C61—22no—
28C22×C8×C61C2211yescharacteristic
29C24×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61—21no—
33C2×Q8×C61—21no—
34C2×Q8×C61—21no—
35C2×Q8×C61D412yes—
36C2×D4×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61—21no—
39C2×D4×C61—21no—
40C2×D4×C61—21no—
41C2×D4×C61D412yes—
42C22×C4×C61—21no—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—21no—
45#11758222—21no—
46#11758222—21no—
47#11758222—21no—
48#11758222—21no—
49C2×D244D411yescharacteristic
50C2×C4×D61—21no—
51C2×Dic122D411yescharacteristic
52SD16×C61—28no—
53C2×C8×C61—21no—
54C2×C8×C61—21no—
55C2×C8×C61D412yes—
56#11758202—24no—
57#11758201—24no—
58#11758200—24no—
59#11758199—24no—
60#11758194—21no—
61#11758194—21no—
62#11758194—21no—
63#11758194—21no—
64#11758194D412yes—
65#11758194D412yes—
66C2×#92418—21no—
67C2×#92418—21no—
68C2×#92418—21no—
69C23×C61—22no—
70C23×C61—41no—
71C23×C61—41no—
72C23×C61—82no—
73C23×C61#4111yescharacteristic
74C22×D61—21no—
75Q8×C61—22no—
76Q8×C61—22no—
77Q8×C61—41no—
78Q8×C61—41no—
79D4×C61—22no—
80D4×C61—22no—
81D4×C61—41no—
82D4×C61—41no—
83C2×C4×C61—22no—
84C2×C4×C61—41no—
85C2×C4×C61—41no—
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C22⋊D61—41no—
93C22⋊D61—41no—
94C2×Dic61—21no—
95D244—21no—
96D244—21no—
97C4×D61—41no—
98C4×D61—41no—
99Dic122—21no—
100Dic122—21no—
101C8×C61—22no—
102#92418—22no—
103#92418—22no—
104#92418—41no—
105C22×C61—22no—
106C22×C61—42no—
107C22×C61—82no—
108C22×C61—82no—
109C22×C61—82no—
110C22×C61#12111yescharacteristic
111C22×C61#12111yescharacteristic
112C22×C61#12111yescharacteristic
113C2×D61—41no—
114C2×D61—42no—
115C4×C61—42no—
116C4×C61#12011yescharacteristic
117C4×C61#12011yescharacteristic
118C4×C61#12011yescharacteristic
119C4×C61#12711yescharacteristic
120Dic61—41no—
121#2019—611nomaximal, Sylow
122C2×C61—21no—
123C2×C61—21no—
124C2×C61—82no—
125C2×C61#39211yescharacteristic
126C2×C61#47112yes—
127D61—81no—
128C2×#137—611no—
129C2×AGL(1,ℤ/8)—611no—
130C22×SD16D6111yescharacteristic, complemented
131C2×#101—611no—
132C2×#100—611no—
133#408—611no—
134#341—611no—
135C61#201911yescharacteristic, complemented, Sylow
136C2×#41—611no—
137C22×Q8C2×D6111yescharacteristic
138C22×D4C2×D6111yescharacteristic
139#137—1222no—
140#137—1222no—
141AGL(1,ℤ/8)—1222no—
142AGL(1,ℤ/8)—1222no—
143C2×Q16—1221no—
144C2×SD16—22no—
145C2×SD16—22no—
146C2×SD16—22no—
147C2×SD16—1221no—
148C2×SD16—1221no—
149C2×D8—1221no—
150C2×M16—611no—
151C2×M16—611no—
152C2×M16—611no—
153C22×C8C2×D6111yescharacteristic
154#101—1222no—
155#100—1222no—
156C22⋊C8—1222no—
157C24—21no—
158#41—1221no—
159#41—1221no—
160#41—1221no—
161#41—1221no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—611no—
168C2×Q8C22⋊D6112yes—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—611no—
175C2×D4—1221no—
176C2×D4C22⋊D6112yes—
177C22×C4—21no—
178C22×C4—1221no—
179C22×C4C22×D6111yescharacteristic
180Q16—1224no—
181SD16—28no—
182SD16—1224no—
183SD16—1224no—
184D8—1224no—
185M16—612no—
186M16—612no—
187M16—1221no—
188M16—1221no—
189M16—1221no—
190M16—1221no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—1221no—
194C2×C8—1221no—
195C2×C8—1221no—
196C2×C8C22⋊D6112yes—
197C23—22no—
198C23—41no—
199C23—41no—
200C23—82no—
201C23—1221no—
202C23#1175822411yescharacteristic
203Q8—22no—
204Q8—22no—
205Q8—41no—
206Q8—41no—
207Q8—1221no—
208Q8—1221no—
209D4—22no—
210D4—22no—
211D4—41no—
212D4—41no—
213D4—1221no—
214D4—1221no—
215D4—2441no—
216D4—2441no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—1221no—
221C2×C4—2441no—
222C2×C4—2441no—
223C2×C4D4×D6111yescharacteristic
224C2×C4D4×D6111yescharacteristic
225C2×C4D4×D6111yescharacteristic
226C2×C4C2×C22⋊D6111yescharacteristic
227C2×C4C2×C22⋊D6111yescharacteristic
228C2×C4C2×C22⋊D6111yescharacteristic
229C8—22no—
230C8—1222no—
231C8—1222no—
232C8—2441no—
233C22—22no—
234C22—42no—
235C22—82no—
236C22—82no—
237C22—82no—
238C22—2442no—
239C22—2441no—
240C22#1451974811yescharacteristic
241C22#1451974911yescharacteristic
242C22#1451974911yescharacteristic
243C4—42no—
244C4—2441no—
245C4#1451974511yescharacteristic
246C4#1451974511yescharacteristic
247C4#1451974611yescharacteristic
248C4#1451977311yescharacteristic
249C2—21no—
250C2—21no—
251C2—82no—
252C2—4881no—
253C2#1683967011yescharacteristic
254C2#1684002212yes—
subgroupG/H
centerC22#14519748
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC22×SD16×C61C2
socleC22×C61#121
hypercenterC22×SD16D61
hypocenterC61#2019
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14519808C2semidirect
3. C2×#14519696C2semidirect
4. C2×#14519694C2semidirect
5. #16839728C2semidirect
6. #16839527C2semidirect
7. C22×SD16×C61C2semidirect
130. C22×SD16D61semidirect
135. C61#2019semidirect