Finite Group Databasebeta

← #21461899

Subgroups — #21461899

Order 7808.

254 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 70 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×#14519846C211yesmaximal, characteristic
2C2×#14519840C211yesmaximal, characteristic
3(C2×#6923)⋊Q8C211yesmaximal, characteristic
4C4⋊C4×#6923C211yesmaximal, characteristic
5#16840635C211yesmaximal, characteristic
6(C2×#6923)⋊C8C211yesmaximal, characteristic
7#103×D61C211yesmaximal, characteristic
8C2×D61⋊C8C2211yescharacteristic
9C2×C4⋊#6923C2211yescharacteristic
10C2×C4⋊#6923C2211yescharacteristic
11C2×C4×#6923—21no—
12C2×C4×#6923C2211yescharacteristic
13#14519846—22no—
14#14519840—22no—
15(C2×#6923)⋊C4—21no—
16(C2×#6923)⋊C4—21no—
17(C2×#6923)⋊C4—21no—
18C2×Q8×D61C2211yescharacteristic
19C2×C8×D61C2211yescharacteristic
20C4⋊C4×D61C2211yescharacteristic
21#14519702C411yescharacteristic, complemented
22#14519701C411yescharacteristic, complemented
23#14519700C411yescharacteristic, complemented
24#103×C61C411yescharacteristic, complemented
25C22×#6923—21no—
26C22×#6923—21no—
27C22×#6923D411yescharacteristic
28C22×#6923D411yescharacteristic
29C2×Q8×C61C2×C411yescharacteristic
30Q8×D61—21no—
31Q8×D61—21no—
32Q8×D61—21no—
33Q8×D61—21no—
34C2×C4×D61—21no—
35C2×C4×D61—21no—
36C2×C4×D61C2311yescharacteristic
37C2×Dic122—21no—
38C2×Dic122C2×C411yescharacteristic
39C2×#92420—21no—
40C4⋊#6923—21no—
41C4⋊#6923—21no—
42C4⋊#6923—21no—
43C4⋊#6923D412yes—
44C4×#6923—21no—
45C4×#6923—21no—
46C4×#6923—42no—
47D61⋊C8—21no—
48D61⋊C8—21no—
49C2×C8×C61C2×C411yescharacteristic
50C4⋊C4×C61C2×C411yescharacteristic
51C4⋊Dic61C2×C411yescharacteristic
52#11758196—21no—
53C2×#92418C2×C411yescharacteristic
54C8×D61—21no—
55C8×D61—21no—
56C22×D61C2×D411yescharacteristic
57C2×#6923—21no—
58C2×#6923—21no—
59C2×#6923—22no—
60C2×#6923—21no—
61C2×#6923—21no—
62C2×#6923—21no—
63C2×#6923—41no—
64C2×#6923—41no—
65C2×#6923—41no—
66C2×#6923—41no—
67C2×#6923—41no—
68C2×#6923Q1612yes—
69Q8×C61—21no—
70Q8×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61C22×C411yescharacteristic
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61#4111yescharacteristic
77C4×D61—41no—
78C4×D61—41no—
79C4×D61—41no—
80C4×D61—41no—
81C4×D61C2×D411yescharacteristic
82C4×D61#4111yescharacteristic
83C4×D61#4111yescharacteristic
84C4×D61#4111yescharacteristic
85Dic122—21no—
86Dic122—21no—
87Dic122—41no—
88Dic122—41no—
89#92420—41no—
90C8×C61—21no—
91#92418—21no—
92C22×C61C4×D411yescharacteristic
93C2×D61#12111yescharacteristic
94C2×D61#12311yescharacteristic
95C2×D61C2×Q1611yescharacteristic
96C2×D61#13511yescharacteristic
97C2×D61AGL(1,ℤ/8)11yescharacteristic
98C2×D61#13711yescharacteristic
99#6923—22no—
100#6923—42no—
101#6923—41no—
102#6923—81no—
103C4×C61—41no—
104C4×C61—41no—
105C4×C61#11711yescharacteristic
106C4×C61C4×D411yescharacteristic
107Dic61—41no—
108Dic61—41no—
109Dic61#12411yescharacteristic
110Dic61#12611yescharacteristic
111#1928—611nomaximal, Sylow
112C2×C61#38811yescharacteristic
113C2×C61C4×Q1611yescharacteristic
114C2×C61#44011yescharacteristic
115D61#46211yescharacteristic
116D61#46311yescharacteristic
117D61#48411yescharacteristic
118D61#48511yescharacteristic
119C2×#107—611no—
120C2×#103—611no—
121C2×#103—611no—
122#391—611no—
123C4×C4⋊C4—611no—
124#340—611no—
125#336—611no—
126C61#192811yescharacteristic, complemented, Sylow
127C22×Q8—611no—
128C22×C8—611no—
129C22×C8—611no—
130C2×C4⋊C4—611no—
131C2×C4⋊C4—611no—
132C2×C4⋊C4—611no—
133C2×C42—611no—
134C2×C42—1221no—
135#107—1222no—
136#103—611no—
137#103—611no—
138#103—611no—
139#103—1222no—
140#103#692311yescharacteristic, complemented
141#95—1221no—
142#95—1221no—
143#95—1221no—
144C2×Q8—611no—
145C2×Q8—1221no—
146C2×Q8—1221no—
147C2×Q8—1221no—
148C2×Q8—1221no—
149C2×Q8—1221no—
150C2×Q8C2×#692311yescharacteristic
151C22×C4—611no—
152C22×C4—611no—
153C22×C4—611no—
154C22×C4—1221no—
155C22×C4—1221no—
156C22×C4—1221no—
157C22×C4—1221no—
158C2×C8—611no—
159C2×C8—1221no—
160C2×C8—1221no—
161C2×C8—1221no—
162C2×C8—1221no—
163C2×C8—1221no—
164C2×C8C2×#692311yescharacteristic
165C4⋊C4—612no—
166C4⋊C4—611no—
167C4⋊C4—1221no—
168C4⋊C4—1221no—
169C4⋊C4—1221no—
170C4⋊C4—1221no—
171C4⋊C4C2×#692311yescharacteristic
172C42—1221no—
173C42—1221no—
174C42—2442no—
175C23—611no—
176Q8—21no—
177Q8—21no—
178Q8—1221no—
179Q8—1221no—
180Q8—2441no—
181Q8—2441no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—611no—
185C2×C4—611no—
186C2×C4—611no—
187C2×C4—611no—
188C2×C4—611no—
189C2×C4—612no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1222no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—2441no—
199C2×C4—2441no—
200C2×C4—2441no—
201C2×C4—2441no—
202C2×C4—2441no—
203C2×C4—2441no—
204C2×C4—2441no—
205C2×C4—2441no—
206C2×C4—2441no—
207C2×C4C22×#692311yescharacteristic
208C8—21no—
209C8—1221no—
210C8—2441no—
211C22—611no—
212C22—611no—
213C22—611no—
214C22—611no—
215C22—611no—
216C22—611no—
217C22D4×#692311yescharacteristic
218C4—41no—
219C4—41no—
220C4—611no—
221C4—611no—
222C4—1222no—
223C4—4881no—
224C4—2441no—
225C4—2442no—
226C4—2441no—
227C4—2441no—
228C4#1451985611yescharacteristic
229C4D4×#692311yescharacteristic
230C2—611no—
231C2—611no—
232C2—611no—
233C2—611no—
234C2#1684071211yescharacteristic
235C2Q16×#692311yescharacteristic
236C2#1684080111yescharacteristic
subgroupG/H
centerC22D4×#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#103×C61C4
socleC22×C61C4×D4
hypercenter#103#6923
hypocenterC61#1928
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
21. #14519702C4semidirect
22. #14519701C4semidirect
23. #14519700C4semidirect
24. #103×C61C4semidirect
126. C61#1928semidirect
140. #103#6923semidirect