Finite Group Databasebeta

← #21458495

Subgroups — #21458495

Order 7808.

336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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
1Q8×Dic122C211yesmaximal, characteristic
2#16840490C211yesmaximal, characteristic
3#16840113C211yesmaximal, characteristic
4#16840111C212yesmaximal
5#16840057C211yesmaximal, characteristic
6#16840056C212yesmaximal
7#16839972C211yesmaximal, characteristic
8#16839970C212yesmaximal
9C8×Dic122C211yesmaximal, characteristic
10#16839854C212yesmaximal
11C4×Q16×C61C211yesmaximal, characteristic
12C2×#11758202C2212yes—
13#14519777—21no—
14#14519777C2211yescharacteristic
15#14519777C2211yescharacteristic
16#14519776—22no—
17#14519776C2212yes—
18#14519775C2212yes—
19#14519769—21no—
20#14519767—22no—
21Q8×Dic61C2212yes—
22C4×Dic122—21no—
23C4×Dic122—21no—
24C4×Dic122C2211yescharacteristic
25#14519742C2212yes—
26#14519710C2212yes—
27C4⋊#92418C2211yescharacteristic
28#14519706C2212yes—
29#14519702C2212yes—
30#14519702C2212yes—
31#14519701C2212yes—
32#14519700C2212yes—
33C8×Dic61C2212yes—
34C2×Q16×C61C2211yescharacteristic
35C4×Q8×C61C2211yescharacteristic
36C4×Q8×C61C2211yescharacteristic
37#107×C61C2211yescharacteristic
38#103×C61C2211yescharacteristic
39#103×C61C2211yescharacteristic
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61C2311yescharacteristic
42C2×Q8×C61C2311yescharacteristic
43C2×Dic122—21no—
44C2×Dic122—22no—
45C2×Dic122D411yescharacteristic
46C2×Dic122C2312yes—
47Q16×C61—22no—
48C2×C8×C61C2311yescharacteristic
49C2×C8×C61C2311yescharacteristic
50C4⋊C4×C61—21no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61C2311yescharacteristic
53C4⋊C4×C61C2311yescharacteristic
54C42×C61—21no—
55C42×C61—21no—
56C42×C61C2311yescharacteristic
57#11758202—24no—
58C4⋊Dic61—21no—
59C4⋊Dic61—21no—
60C4⋊Dic61—21no—
61C4⋊Dic61—22no—
62C4⋊Dic61D411yescharacteristic
63C4⋊Dic61C2312yes—
64#11758196—22no—
65#11758196—22no—
66#11758196—22no—
67#11758196—22no—
68#11758196D412yes—
69C4×Dic61—22no—
70C4×Dic61—22no—
71C4×Dic61C2312yes—
72C2×#92418C2312yes—
73Q8×C61—21no—
74Q8×C61—21no—
75Q8×C61—21no—
76Q8×C61#4112yes—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2411yescharacteristic
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61C2×D412yes—
87C2×Dic61C2×D412yes—
88Dic122—22no—
89Dic122—22no—
90Dic122—82no—
91Dic122—81no—
92Dic122Q1614yescomplemented
93C8×C61—21no—
94C8×C61—21no—
95#92418—22no—
96C22×C61C22×D411yescharacteristic
97C4×C61—22no—
98C4×C61—21no—
99C4×C61—41no—
100C4×C61—41no—
101C4×C61—41no—
102C4×C61C2×Q1612yes—
103C4×C61C2×#4111yescharacteristic
104C4×C612−1+411yescharacteristic
105Dic61—22no—
106Dic61—42no—
107Dic61—42no—
108Dic61C2×Q1614yes—
109#3363—611nomaximal, Sylow
110C2×C61#54811yescharacteristic
111C2×C61C22×Q1611yescharacteristic
112C2×C61#57711yescharacteristic
113Q82—611no—
114#557—611no—
115#487—612no—
116#487—611no—
117#477—611no—
118#477—612no—
119#462—612no—
120#462—611no—
121C8×Q8—611no—
122C4×Q16—612no—
123C4×Q16D6111yescharacteristic
124C61#336311yescharacteristic, complemented, Sylow
125C2×Q16—612no—
126C2×Q16C2×D6111yescharacteristic
127C4⋊Q8—612no—
128C4⋊Q8—612no—
129C4⋊Q8—611no—
130C4⋊Q8—611no—
131C4⋊Q8—1221no—
132C4⋊Q8—1222no—
133#125—1221no—
134#125—1222no—
135C4×Q8—611no—
136C4×Q8—612no—
137C4×Q8—612no—
138C4×Q8—1221no—
139C4×Q8—1221no—
140C4×Q8C2×D6111yescharacteristic
141C4×Q8C2×D6111yescharacteristic
142#107—612no—
143#107C2×D6111yescharacteristic
144C4⋊C8—612no—
145C4⋊C8—611no—
146#103—612no—
147#103—612no—
148#103—612no—
149#103—612no—
150#103C2×D6111yescharacteristic
151#103C2×D6111yescharacteristic
152C4×C8—612no—
153C4×C8C2×D6111yescharacteristic
154C2×Q8—611no—
155C2×Q8—612no—
156C2×Q8—1222no—
157C2×Q8—1221no—
158C2×Q8C22×D6111yescharacteristic
159C2×Q8C22×D6111yescharacteristic
160Q16—22no—
161Q16—1224no—
162C2×C8—612no—
163C2×C8C22×D6111yescharacteristic
164C2×C8C22×D6111yescharacteristic
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—612no—
168C4⋊C4—611no—
169C4⋊C4—612no—
170C4⋊C4—1222no—
171C4⋊C4—1222no—
172C4⋊C4—1222no—
173C4⋊C4—1222no—
174C4⋊C4—1222no—
175C4⋊C4—1221no—
176C4⋊C4—1221no—
177C4⋊C4—1221no—
178C4⋊C4C22×D6111yescharacteristic
179C4⋊C4C22×D6111yescharacteristic
180C42—21no—
181C42—21no—
182C42—612no—
183C42—1222no—
184C42—1222no—
185C42C22×D6111yescharacteristic
186Q8—21no—
187Q8—21no—
188Q8—21no—
189Q8—614no—
190Q8—1222no—
191Q8—1222no—
192Q8—4881no—
193Q8—4882no—
194Q8#1175822212yes—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—612no—
200C2×C4—612no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4D4×D6111yescharacteristic
204C2×C4D4×D6111yescharacteristic
205C2×C4C23×D6111yescharacteristic
206C8—21no—
207C8—21no—
208C8—1222no—
209C22C2×D4×D6111yescharacteristic
210C4—21no—
211C4—22no—
212C4—41no—
213C4—41no—
214C4—41no—
215C4—614no—
216C4—1222no—
217C4—2442no—
218C4—2442no—
219C4Q16×D6112yes—
220C4C2×#1175822211yescharacteristic
221C4#1451982411yescharacteristic
222C2#1684042111yescharacteristic
223C2C2×Q16×D6111yescharacteristic
224C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×Q16×C61C2
socleC22×C61C22×D4
hypercenterC4×Q16D61
hypocenterC61#3363
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
92. Dic122Q16semidirect
124. C61#3363semidirect