Finite Group Databasebeta

← #21446182

Subgroups — #21446182

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#16840562C211yesmaximal, characteristic
2#16840528C211yesmaximal, characteristic, complemented
3#16839778C211yesmaximal, characteristic, complemented
4#16839759C211yesmaximal, characteristic, complemented
5#16839728C211yesmaximal, characteristic, complemented
6#16839534C211yesmaximal, characteristic, complemented
7C61×#341C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758222C2211yescharacteristic
10#14519810—21no—
11#14519810C412yescomplemented
12#14519805—21no—
13#14519805C412yescomplemented
14#14519799—22no—
15#14519785—22no—
16#14519783—22no—
17C2×#11758194C2211yescharacteristic
18M16×D61—22no—
19#14519736C2211yescharacteristic
20#14519703—22no—
21#14519702—21no—
22#14519699—21no—
23#14519689—22no—
24C2×M16×C61C2211yescharacteristic
25C2×M16×C61C2211yescharacteristic
26C22×C8×C61C2211yescharacteristic
27C22×C4×C61C2311yescharacteristic
28C2×C22⋊D61—21no—
29C2×C22⋊D61—21no—
30#11758222—21no—
31#11758222—21no—
32#11758222—21no—
33#11758222—21no—
34#11758222—21no—
35#11758222—21no—
36#11758222C2×C412yes—
37#11758222D412yes—
38C2×D244C2×C411yescharacteristic
39C2×D244D411yescharacteristic
40C2×C4×D61—21no—
41C2×C4×D61—21no—
42C2×Dic122C2×C411yescharacteristic
43C2×Dic122D411yescharacteristic
44M16×C61—21no—
45M16×C61—21no—
46M16×C61C2×C412yes—
47M16×C61D412yes—
48C2×C8×C61—21no—
49C2×C8×C61—21no—
50C2×C8×C61—21no—
51C2×C8×C61—21no—
52C2×C8×C61—21no—
53C22⋊Dic61—21no—
54C4⋊Dic61—21no—
55C4×Dic61—21no—
56#11758194—21no—
57#11758194—21no—
58C2×#92418D412yes—
59Dic244—22no—
60D488—22no—
61#11758190—22no—
62#11758190—22no—
63#11758189—24no—
64C8×D61—24no—
65C23×C61#4111yescharacteristic
66C22×D61—21no—
67C22×D61—21no—
68C2×C4×C61C22×C411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C22⋊D61—22no—
75C22⋊D61—22no—
76C22⋊D61—41no—
77C22⋊D61—41no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—41no—
81D244—21no—
82D244—21no—
83D244—21no—
84D244C22⋊C412yes—
85C4×D61—22no—
86C4×D61—22no—
87C4×D61—41no—
88C4×D61—41no—
89Dic122—21no—
90Dic122—21no—
91Dic122—21no—
92Dic122C22⋊C412yes—
93C8×C61—22no—
94C8×C61—22no—
95C8×C61—41no—
96#92418—22no—
97C22×C61—41no—
98C22×C61C4×D411yescharacteristic
99C22×C61#12111yescharacteristic
100C22×C61#12311yescharacteristic
101C2×D61—22no—
102C2×D61—42no—
103C2×D61—41no—
104C2×D61—81no—
105C4×C61C2×C22⋊C411yescharacteristic
106C4×C61C4×D411yescharacteristic
107C4×C61#12011yescharacteristic
108C4×C61#12111yescharacteristic
109Dic61—22no—
110Dic61—41no—
111Dic61—81no—
112#1881—611nomaximal, Sylow
113C2×C61—21no—
114C2×C61—21no—
115C2×C61—21no—
116C2×C61#38611yescharacteristic
117D61—42no—
118D61—81no—
119#575—611no—
120#568—611no—
121#421—611no—
122#416—611no—
123#408—611no—
124#344—611no—
125#341D6111yescharacteristic, complemented
126C61#188111yescharacteristic, complemented, Sylow
127C2×#41—611no—
128C2×#41—611no—
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—1222no—
138C2×M16C2×D6111yescharacteristic
139C2×M16C2×D6111yescharacteristic
140C22×C8C2×D6111yescharacteristic
141#117—611no—
142#104—1222no—
143#103—1221no—
144#102—1221no—
145C22⋊C8—1222no—
146#41—612no—
147#41—612no—
148#41—1221no—
149#41—1221no—
150#41—1221no—
151#41—1221no—
152#41—1221no—
153#41—1221no—
154C2×Q8—611no—
155C2×Q8—611no—
156C2×D4—611no—
157C2×D4—611no—
158C2×D4—1221no—
159C2×D4—1221no—
160C22×C4—1221no—
161C22×C4—1221no—
162C22×C4C22×D6111yescharacteristic
163Q16—1222no—
164SD16—1222no—
165SD16—1222no—
166D8—1222no—
167M16—21no—
168M16—21no—
169M16—1224no—
170M16—1221no—
171M16—1221no—
172M16C4×D6112yes—
173M16D24412yes—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—612no—
180C2×C8—1224no—
181C4⋊C4—1221no—
182C22⋊C4—1221no—
183C42—1221no—
184C23—1221no—
185C23—1221no—
186C23#1175822611yescharacteristic
187Q8—612no—
188Q8—1221no—
189Q8—1221no—
190Q8—1221no—
191D4—612no—
192D4—1222no—
193D4—1222no—
194D4—1221no—
195D4—1221no—
196D4—1221no—
197D4—2441no—
198D4—2441no—
199C2×C4—1221no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—1221no—
203C2×C4—2441no—
204C2×C4—2441no—
205C2×C4—2441no—
206C2×C4C2×C4×D6111yescharacteristic
207C2×C4C2×D24411yescharacteristic
208C2×C4#1175822211yescharacteristic
209C2×C4D4×D6111yescharacteristic
210C2×C4D4×D6111yescharacteristic
211C2×C4D4×D6111yescharacteristic
212C8—22no—
213C8—22no—
214C8—41no—
215C8—1222no—
216C22—41no—
217C22—1222no—
218C22—4881no—
219C22—2442no—
220C22—2441no—
221C22#1451973911yescharacteristic
222C22#1451975211yescharacteristic
223C22#1451976211yescharacteristic
224C4—1222no—
225C4—4881no—
226C4—2441no—
227C4C22⋊C4×D6111yescharacteristic
228C4C4×D24411yescharacteristic
229C4#1451974711yescharacteristic
230C4#1451975011yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—4881no—
235C2—2442no—
236C2#1683964011yescharacteristic
subgroupG/H
centerC4#14519747
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#341C2
socleC2×C61#386
hypercenter#341D61
hypocenterC61#1881
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #341

Complements

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

NH ≅ G/Ntype
2. #16840528C2semidirect
3. #16839778C2semidirect
4. #16839759C2semidirect
5. #16839728C2semidirect
6. #16839534C2semidirect
7. C61×#341C2semidirect
11. #14519810C4semidirect
13. #14519805C4semidirect
125. #341D61semidirect
126. C61#1881semidirect