Finite Group Databasebeta

← #21446309

Subgroups — #21446309

Order 7808.

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

normal subgroups only

This group has 346 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
1C2×#14519802C211yesmaximal, characteristic
2#16840236C211yesmaximal, characteristic, complemented
3#16839779C211yesmaximal, characteristic, complemented
4#16839766C211yesmaximal, characteristic, complemented
5#16839532C211yesmaximal, characteristic, complemented
6#16839518C211yesmaximal, characteristic, complemented
7C61×#410C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9#14519802—22no—
10#14519802—22no—
11C2×#11758201C412yescomplemented
12C2×#11758199C412yescomplemented
13C2×#11758194C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15C4×D244—22no—
16#14519739—22no—
17#14519736C2211yescharacteristic
18C22⋊C4×D61—22no—
19#14519704—22no—
20#14519697—22no—
21C2×#41×C61C2211yescharacteristic
22#117×C61C2211yescharacteristic
23#117×C61C2211yescharacteristic
24#99×C61—22no—
25C23×D61—21no—
26#41×C61—21no—
27#41×C61—21no—
28#41×C61—21no—
29#41×C61—21no—
30C2×Q8×C61C2×C411yescharacteristic, complemented
31C2×D4×C61—21no—
32C2×D4×C61C2×C411yescharacteristic, complemented
33C22×C4×C61—21no—
34C22×C4×C61C2311yescharacteristic
35C2×D244—21no—
36C2×D244—21no—
37C2×D244—21no—
38C2×D244C2×C412yes—
39C2×D244D412yes—
40C2×D244D412yes—
41C2×C4×D61—24no—
42C4⋊C4×C61—21no—
43C4⋊C4×C61—21no—
44C22⋊C4×C61—21no—
45C22⋊C4×C61D412yes—
46C42×C61—21no—
47C42×C61—21no—
48C22⋊Dic61—21no—
49#11758201—24no—
50#11758199—24no—
51#11758198—24no—
52C4⋊Dic61—21no—
53C4×Dic61D412yes—
54#11758194—21no—
55#11758194—21no—
56#11758194—21no—
57#11758194—21no—
58C2×#92418—21no—
59C2×#92418C2×C412yescomplemented
60C23×C61—21no—
61C23×C61C2×D411yescharacteristic
62C22×D61—22no—
63C22×D61—22no—
64C22×D61—22no—
65C22×D61—82no—
66Q8×C61—21no—
67Q8×C61—21no—
68D4×C61—21no—
69D4×C61—21no—
70D4×C61—41no—
71D4×C61—41no—
72C2×C4×C61—21no—
73C2×C4×C61—22no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61C22×C411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61#4111yescharacteristic
82C2×C4×C61#4111yescharacteristic
83C2×Dic61—22no—
84D244—22no—
85D244—22no—
86D244—22no—
87D244C22⋊C414yes—
88C4×D61—84no—
89#92418—22no—
90#92418—41no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61—81no—
94C22×C61C4×D411yescharacteristic
95C22×C61#12011yescharacteristic
96C22×C61#12111yescharacteristic
97C2×D61—24no—
98C2×D61—44no—
99C2×D61—82no—
100C2×D61—82no—
101C4×C61—42no—
102C4×C61—41no—
103C4×C61—81no—
104C4×C61C2×C22⋊C411yescharacteristic
105C4×C61C4×D411yescharacteristic
106C4×C61#12111yescharacteristic
107C4×C61#12311yescharacteristic
108Dic61—42no—
109#1904—611nomaximal, Sylow
110C2×C61—21no—
111C2×C61—21no—
112C2×C61—21no—
113C2×C61—81no—
114C2×C61#38611yescharacteristic
115D61—44no—
116C2×AGL(1,ℤ/8)—611no—
117#518—611no—
118#421—611no—
119#418—611no—
120#410D6111yescharacteristic, complemented
121#344—611no—
122H(3,ℤ/4)—611no—
123C61#190411yescharacteristic, complemented, Sylow
124C2×#41C2×D6111yescharacteristic
125C22×D4—611no—
126AGL(1,ℤ/8)—1222no—
127AGL(1,ℤ/8)—1222no—
128C2×SD16—612no—
129C2×D8—612no—
130C2×M16—611no—
131C2×M16—611no—
132C4×D4—1222no—
133C4×D4—1222no—
134#117—611no—
135#117C2×D6111yescharacteristic
136#117C2×D6111yescharacteristic
137C2×C22⋊C4—1222no—
138#104—1222no—
139#102—1222no—
140#99—22no—
141C24—1221no—
142#41—21no—
143#41—21no—
144#41—21no—
145#41—21no—
146C2×Q8C4×D6111yescharacteristic, complemented
147C2×D4—21no—
148C2×D4—612no—
149C2×D4—612no—
150C2×D4—612no—
151C2×D4—1221no—
152C2×D4—1221no—
153C2×D4—1221no—
154C2×D4C4×D6111yescharacteristic, complemented
155C22×C4—21no—
156C22×C4—1224no—
157C22×C4C22×D6111yescharacteristic
158SD16—1224no—
159D8—1224no—
160M16—1221no—
161M16—1221no—
162M16—1221no—
163M16—1221no—
164C2×C8—612no—
165C2×C8—1221no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—1221no—
169C22⋊C4—21no—
170C22⋊C4—1224no—
171C22⋊C4—1221no—
172C22⋊C4C22⋊D6112yes—
173C42—21no—
174C42—21no—
175C42—612no—
176C23—21no—
177C23—1222no—
178C23—1222no—
179C23—1222no—
180C23—4882no—
181C23C2×C22⋊D6111yescharacteristic
182Q8—21no—
183Q8—21no—
184D4—21no—
185D4—21no—
186D4—41no—
187D4—41no—
188D4—614no—
189D4—1222no—
190D4—1222no—
191D4—1222no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—1222no—
198C2×C4—4884no—
199C2×C4C2×C4×D6111yescharacteristic
200C2×C4#1175822211yescharacteristic
201C2×C4D4×D6111yescharacteristic
202C2×C4D4×D6111yescharacteristic
203C2×C4D4×D6111yescharacteristic
204C2×C4#1175822411yescharacteristic
205C8—1222no—
206C8—2441no—
207C22—41no—
208C22—41no—
209C22—81no—
210C22—1224no—
211C22—4882no—
212C22—4882no—
213C22—2444no—
214C22C4×C22⋊D6111yescharacteristic
215C22#1451974511yescharacteristic
216C22#1451974811yescharacteristic
217C4—42no—
218C4—41no—
219C4—81no—
220C4—2442no—
221C4C22⋊C4×D6111yescharacteristic
222C4#1451973711yescharacteristic
223C4#1451975011yescharacteristic
224C4#1451975911yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—81no—
229C2—2444no—
230C2#1683963811yescharacteristic
subgroupG/H
centerC2#16839638
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#410C2
socleC2×C61#386
hypercenter#410D61
hypocenterC61#1904
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #16840236C2semidirect
3. #16839779C2semidirect
4. #16839766C2semidirect
5. #16839532C2semidirect
6. #16839518C2semidirect
7. C61×#410C2semidirect
11. C2×#11758201C4semidirect
12. C2×#11758199C4semidirect
30. C2×Q8×C61C2×C4semidirect
32. C2×D4×C61C2×C4semidirect
59. C2×#92418C2×C4semidirect
120. #410D61semidirect
123. C61#1904semidirect
146. C2×Q8C4×D61semidirect
154. C2×D4C4×D61semidirect