Finite Group Databasebeta

← #21446178

Subgroups — #21446178

Order 7808.

310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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#16840528C211yesmaximal, characteristic, complemented
3#16839756C211yesmaximal, characteristic, complemented
4#16839729C211yesmaximal, characteristic, complemented
5#16839532C211yesmaximal, characteristic, complemented
6#16839526C211yesmaximal, characteristic, complemented
7C61×#421C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808C412yescomplemented
10#14519807—21no—
11#14519803C412yescomplemented
12#14519802—21no—
13#14519797—22no—
14#14519785—22no—
15#14519783—22no—
16C2×#11758194C2211yescharacteristic
17C2×#11758194C2211yescharacteristic
18M16×D61—22no—
19C22×#92418C2211yescharacteristic
20#14519700—21no—
21#14519697—21no—
22C22⋊#92418—22no—
23C2×#41×C61C2211yescharacteristic
24C2×M16×C61C2211yescharacteristic
25#117×C61C2211yescharacteristic
26#104×C61—22no—
27#41×C61—21no—
28#41×C61—21no—
29#41×C61—21no—
30#41×C61—21no—
31C2×Q8×C61C2×C411yescharacteristic
32C2×D4×C61—21no—
33C2×D4×C61C2×C411yescharacteristic
34C22×C4×C61—21no—
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—21no—
37#11758222—21no—
38#11758222—21no—
39#11758222C2×C412yes—
40#11758222D412yes—
41C2×D244D411yescharacteristic
42C2×C4×D61—21no—
43C2×Dic122D411yescharacteristic
44M16×C61—21no—
45M16×C61D412yes—
46C2×C8×C61—21no—
47C4⋊C4×C61—21no—
48C22⋊C4×C61—21no—
49C42×C61—21no—
50#11758202—22no—
51#11758201—22no—
52#11758200—22no—
53#11758199—22no—
54#11758194—21no—
55#11758194—21no—
56#11758194—21no—
57#11758194C2×C412yes—
58C2×#92418—21no—
59C2×#92418—21no—
60C2×#92418—21no—
61C2×#92418—21no—
62C2×#92418D412yes—
63#11758189—24no—
64C8×D61—24no—
65C23×C61—21no—
66C23×C61#4111yescharacteristic
67C22×D61—21no—
68Q8×C61—21no—
69Q8×C61—21no—
70D4×C61—21no—
71D4×C61—21no—
72D4×C61—41no—
73D4×C61—41no—
74C2×C4×C61—21no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61C22×C411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61#4111yescharacteristic
84C22⋊D61—22no—
85C22⋊D61—22no—
86C2×Dic61—21no—
87D244—21no—
88D244C22⋊C412yes—
89C4×D61—22no—
90C4×D61—22no—
91Dic122—21no—
92Dic122C22⋊C412yes—
93C8×C61—22no—
94#92418—22no—
95#92418—22no—
96#92418—41no—
97C22×C61—41no—
98C22×C61—42no—
99C22×C61—41no—
100C22×C61C4×D411yescharacteristic
101C22×C61#12111yescharacteristic
102C22×C61#12311yescharacteristic
103C2×D61—22no—
104C2×D61—81no—
105C4×C61—41no—
106C4×C61—81no—
107C4×C61C2×C22⋊C411yescharacteristic
108C4×C61C4×D411yescharacteristic
109C4×C61#12011yescharacteristic
110C4×C61#12111yescharacteristic
111Dic61—22no—
112#1881—611nomaximal, Sylow
113C2×C61—21no—
114C2×C61—21no—
115C2×C61—21no—
116C2×C61—81no—
117C2×C61#38611yescharacteristic
118D61—42no—
119#575—611no—
120#568—611no—
121#421D6111yescharacteristic, complemented
122#416—611no—
123#408—611no—
124#344—611no—
125#341—611no—
126C61#188111yescharacteristic, complemented, Sylow
127C2×#41—611no—
128C2×#41C2×D6111yescharacteristic
129#137—612no—
130#137—1221no—
131AGL(1,ℤ/8)—612no—
132AGL(1,ℤ/8)—1221no—
133#135—1222no—
134#131—1222no—
135#131—1222no—
136C2×M16—611no—
137C2×M16—611no—
138C2×M16—1222no—
139C2×M16C2×D6111yescharacteristic
140C22×C8—611no—
141#117C2×D6111yescharacteristic
142#104—22no—
143#103—1221no—
144#102—1221no—
145C22⋊C8—1222no—
146#41—21no—
147#41—21no—
148#41—21no—
149#41—21no—
150#41—612no—
151#41—612no—
152#41—1221no—
153#41—1221no—
154C2×Q8—611no—
155C2×Q8C4×D6111yescharacteristic
156C2×D4—21no—
157C2×D4—611no—
158C2×D4—1221no—
159C2×D4C4×D6111yescharacteristic
160C22×C4—21no—
161C22×C4—1221no—
162C22×C4C22×D6111yescharacteristic
163Q16—1222no—
164SD16—1222no—
165SD16—1222no—
166D8—1222no—
167M16—21no—
168M16—612no—
169M16—1224no—
170M16—1221no—
171M16—1221no—
172M16—1221no—
173M16C22⋊D6112yes—
174C2×C8—21no—
175C2×C8—612no—
176C2×C8—1224no—
177C2×C8—1221no—
178C2×C8—1221no—
179C2×C8—1221no—
180C2×C8—1221no—
181C4⋊C4—21no—
182C22⋊C4—21no—
183C42—21no—
184C23—21no—
185C23—1221no—
186C23#1175822411yescharacteristic
187Q8—21no—
188Q8—21no—
189Q8—612no—
190Q8—1221no—
191D4—21no—
192D4—21no—
193D4—41no—
194D4—41no—
195D4—612no—
196D4—1222no—
197D4—1222no—
198D4—1221no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—1221no—
204C2×C4—1222no—
205C2×C4—1222no—
206C2×C4C2×C4×D6111yescharacteristic
207C2×C4#1175822211yescharacteristic
208C2×C4D4×D6111yescharacteristic
209C2×C4D4×D6111yescharacteristic
210C2×C4D4×D6111yescharacteristic
211C2×C4C2×C22⋊D6111yescharacteristic
212C8—22no—
213C8—1222no—
214C8—1222no—
215C8—2441no—
216C22—41no—
217C22—42no—
218C22—41no—
219C22—1222no—
220C22—4881no—
221C22#1451973711yescharacteristic
222C22#1451974811yescharacteristic
223C22#1451975911yescharacteristic
224C4—41no—
225C4—81no—
226C4—1222no—
227C4C22⋊C4×D6111yescharacteristic
228C4C4×C22⋊D6111yescharacteristic
229C4#1451974511yescharacteristic
230C4#1451975011yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—2442no—
236C2#1683963811yescharacteristic
subgroupG/H
centerC4#14519745
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#421C2
socleC2×C61#386
hypercenter#421D61
hypocenterC61#1881
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #16840528C2semidirect
3. #16839756C2semidirect
4. #16839729C2semidirect
5. #16839532C2semidirect
6. #16839526C2semidirect
7. C61×#421C2semidirect
9. #14519808C4semidirect
11. #14519803C4semidirect
121. #421D61semidirect
126. C61#1881semidirect