Finite Group Databasebeta

← #21447124

Subgroups — #21447124

Order 7808.

264 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 65 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#16840560C211yesmaximal, characteristic
2#16839789C211yesmaximal, characteristic, complemented
3#16839758C211yesmaximal, characteristic, complemented
4#16839756C211yesmaximal, characteristic, complemented
5#16839735C211yesmaximal, characteristic, complemented
6#16839518C211yesmaximal, characteristic, complemented
7C61×#410C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808—21no—
10#14519807—21no—
11#14519803—21no—
12#14519802—21no—
13#14519797—22no—
14C2×#11758194C2211yescharacteristic
15C22×#92418C2211yescharacteristic
16#14519736C2211yescharacteristic
17C4⋊#92418—22no—
18#14519701—21no—
19#14519700—21no—
20#14519698—21no—
21#14519697—21no—
22#14519691—22no—
23C2×#41×C61C2211yescharacteristic
24#117×C61C2211yescharacteristic
25#117×C61C2211yescharacteristic
26#99×C61—22no—
27#41×C61—21no—
28#41×C61—21no—
29#41×C61—21no—
30#41×C61—21no—
31C2×Q8×C61D411yescharacteristic
32C2×D4×C61—21no—
33C2×D4×C61D411yescharacteristic
34C22×C4×C61—21no—
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—21no—
37#11758222—21no—
38#11758222—21no—
39#11758222—21no—
40#11758222—21no—
41C2×D244D411yescharacteristic
42C2×C4×D61—21no—
43C2×Dic122D411yescharacteristic
44C4⋊C4×C61—21no—
45C4⋊C4×C61—21no—
46C22⋊C4×C61—21no—
47C22⋊C4×C61D412yes—
48C42×C61—21no—
49C42×C61—21no—
50C22⋊Dic61—21no—
51#11758202—22no—
52#11758201—22no—
53#11758200—22no—
54#11758199—22no—
55C4⋊Dic61—21no—
56C4×Dic61—21no—
57#11758194—21no—
58#11758194—21no—
59C2×#92418—21no—
60C2×#92418—21no—
61C2×#92418—21no—
62C2×#92418D412yes—
63C23×C61—21no—
64C23×C61C2×D411yescharacteristic
65C22×D61—21no—
66Q8×C61—21no—
67Q8×C61—21no—
68D4×C61—21no—
69D4×C61—21no—
70D4×C61—41no—
71D4×C61—41no—
72C2×C4×C61—22no—
73C2×C4×C61—21no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61#4111yescharacteristic
81C2×C4×C61#4111yescharacteristic
82C2×C4×C61#4111yescharacteristic
83C22⋊D61—41no—
84C22⋊D61—41no—
85C2×Dic61—21no—
86C2×Dic61—41no—
87D244—21no—
88D244—21no—
89C4×D61—41no—
90C4×D61—41no—
91Dic122—21no—
92Dic122—21no—
93#92418—22no—
94#92418—41no—
95C22×C61—41no—
96C22×C61—41no—
97C22×C61—81no—
98C22×C61#12111yescharacteristic
99C22×C61#12111yescharacteristic
100C22×C61#12111yescharacteristic
101C2×D61—41no—
102C2×D61—81no—
103C4×C61—42no—
104C4×C61—41no—
105C4×C61—81no—
106C4×C61#12011yescharacteristic
107C4×C61#12311yescharacteristic
108C4×C61#12311yescharacteristic
109C4×C61#12411yescharacteristic
110Dic61—41no—
111Dic61—81no—
112#2053—611nomaximal, Sylow
113C2×C61—21no—
114C2×C61—21no—
115C2×C61—21no—
116C2×C61—81no—
117C2×C61#39411yescharacteristic
118D61—81no—
119#575—611no—
120#424—611no—
121#416—611no—
122#416—611no—
123#410—611no—
124#410D6111yescharacteristic, complemented
125H(3,ℤ/4)—611no—
126C61#205311yescharacteristic, complemented, Sylow
127C2×#41—611no—
128C2×#41C2×D6111yescharacteristic
129#137—1221no—
130#137—1221no—
131AGL(1,ℤ/8)—1221no—
132AGL(1,ℤ/8)—1221no—
133#135—1222no—
134C2×M16—611no—
135C22×C8—611no—
136#117—611no—
137#117C2×D6111yescharacteristic
138#117C2×D6111yescharacteristic
139C4⋊C8—1222no—
140#103—1221no—
141#103—1221no—
142#102—1221no—
143#102—1221no—
144#99—22no—
145#99—1222no—
146#41—21no—
147#41—21no—
148#41—21no—
149#41—21no—
150#41—1221no—
151#41—1221no—
152#41—1221no—
153#41—1221no—
154C2×Q8—611no—
155C2×Q8D24411yescharacteristic
156C2×D4—21no—
157C2×D4—611no—
158C2×D4—1221no—
159C2×D4D24411yescharacteristic
160C22×C4—21no—
161C22×C4—1221no—
162C22×C4C22×D6111yescharacteristic
163Q16—1222no—
164SD16—1222no—
165SD16—1222no—
166D8—1222no—
167M16—1221no—
168M16—1221no—
169C2×C8—612no—
170C2×C8—1221no—
171C2×C8—1221no—
172C2×C8—1221no—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—1221no—
176C22⋊C4—21no—
177C22⋊C4—1221no—
178C22⋊C4C22⋊D6112yes—
179C42—21no—
180C42—21no—
181C42—1221no—
182C23—21no—
183C23—1221no—
184C23C2×C22⋊D6111yescharacteristic
185Q8—21no—
186Q8—21no—
187Q8—1221no—
188Q8—1221no—
189D4—21no—
190D4—21no—
191D4—41no—
192D4—41no—
193D4—1221no—
194D4—1221no—
195D4—2441no—
196D4—2441no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—1221no—
203C2×C4—2441no—
204C2×C4—2441no—
205C2×C4—2441no—
206C2×C4C2×D24411yescharacteristic
207C2×C4#1175822211yescharacteristic
208C2×C4D4×D6111yescharacteristic
209C2×C4D4×D6111yescharacteristic
210C2×C4#1175822411yescharacteristic
211C2×C4#1175822411yescharacteristic
212C8—1222no—
213C8—2441no—
214C22—41no—
215C22—41no—
216C22—81no—
217C22—4881no—
218C22—2441no—
219C22#1451974811yescharacteristic
220C22#1451974911yescharacteristic
221C22#1451975111yescharacteristic
222C4—42no—
223C4—41no—
224C4—81no—
225C4—4881no—
226C4—2441no—
227C4#1451974711yescharacteristic
228C4#1451975911yescharacteristic
229C4#1451976111yescharacteristic
230C4#1451976311yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—4881no—
236C2#1683967811yescharacteristic
subgroupG/H
centerC4#14519763
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#410C2
socleC2×C61#394
hypercenter#410D61
hypocenterC61#2053
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #16839789C2semidirect
3. #16839758C2semidirect
4. #16839756C2semidirect
5. #16839735C2semidirect
6. #16839518C2semidirect
7. C61×#410C2semidirect
124. #410D61semidirect
126. C61#2053semidirect