Finite Group Databasebeta

← #21447004

Subgroups — #21447004

Order 7808.

368 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14519752C211yesmaximal, characteristic
2C2×#14519710C211yesmaximal, characteristic, complemented
3C2×#14519699C211yesmaximal, characteristic, complemented
4C2×#14519697C211yesmaximal, characteristic, complemented
5C2×#14519689C211yesmaximal, characteristic, complemented
6#16839619C211yesmaximal, characteristic, complemented
7C61×#340C211yesmaximal, characteristic, complemented
8C22×D244—21no—
9C22×D244C2211yescharacteristic
10C22×C4×D61C2211yescharacteristic
11C22×#92418C2211yescharacteristic
12#14519752—22no—
13#14519752—22no—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×#11758198—21no—
16C2×#11758198—21no—
17#14519710—22no—
18#14519699—22no—
19#14519697—22no—
20#14519689—22no—
21#14519684—21no—
22C22×C8×C61C2211yescharacteristic
23C2×C4⋊C4×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2211yescharacteristic
25C23×D61—21no—
26C23×D61D411yescharacteristic
27C22×C4×C61—21no—
28C22×C4×C61—21no—
29C22×C4×C61C2311yescharacteristic
30C22×Dic61—21no—
31C22×Dic61D411yescharacteristic
32C2×D244—21no—
33C2×D244—21no—
34C2×D244—21no—
35C2×D244—21no—
36C2×D244—24no—
37C2×D244—21no—
38C2×D244—42no—
39C2×D244—42no—
40C2×D244D412yes—
41C2×C4×D61—21no—
42C2×C4×D61—21no—
43C2×C4×D61—21no—
44C2×C4×D61—21no—
45C2×C4×D61—21no—
46C2×C4×D61—21no—
47C2×C8×C61—21no—
48C2×C8×C61—21no—
49C2×C8×C61—21no—
50C4⋊C4×C61—21no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53C4⋊C4×C61D412yes—
54#11758198—24no—
55#11758198—42no—
56C4⋊Dic61—21no—
57C4⋊Dic61—21no—
58C2×#92418—21no—
59C2×#92418—21no—
60C2×#92418D412yescomplemented
61C23×C61C2×D411yescharacteristic
62C22×D61—21no—
63C22×D61—21no—
64C22×D61—21no—
65C22×D61—21no—
66C22×D61—21no—
67C22×D61—21no—
68C22×D61—22no—
69C22×D61—41no—
70C22×D61—41no—
71C22×D61—41no—
72C22×D61—41no—
73C22×D61—41no—
74C22×D61—41no—
75C22×D61D812yes—
76C2×C4×C61—22no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61#4111yescharacteristic
86C2×C4×C61#4111yescharacteristic
87C2×C4×C61#4111yescharacteristic
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93C2×Dic61—41no—
94D244—22no—
95D244—22no—
96D244—48no—
97D244—41no—
98D244—41no—
99C4×D61—41no—
100C4×D61—41no—
101C4×D61—41no—
102C4×D61—41no—
103C8×C61—41no—
104#92418—22no—
105C22×C61#12011yescharacteristic
106C22×C61#12111yescharacteristic
107C22×C61#12311yescharacteristic
108C22×C61C2×D811yescharacteristic
109C22×C61#13511yescharacteristic
110C22×C61AGL(1,ℤ/8)11yescharacteristic
111C22×C61#13711yescharacteristic
112C2×D61—22no—
113C2×D61—22no—
114C2×D61—22no—
115C2×D61—41no—
116C2×D61—41no—
117C2×D61—41no—
118C2×D61—41no—
119C2×D61—42no—
120C2×D61—42no—
121C2×D61—42no—
122C2×D61—81no—
123C2×D61—81no—
124C2×D61—81no—
125C2×D61—81no—
126C4×C61—42no—
127C4×C61—81no—
128C4×C61#12111yescharacteristic
129C4×C61#12111yescharacteristic
130C4×C61#12311yescharacteristic
131C4×C61#12411yescharacteristic
132Dic61—41no—
133Dic61—81no—
134#2033—611nomaximal, Sylow
135C2×C61#39411yescharacteristic
136C2×C61#44711yescharacteristic
137C2×C61#45211yescharacteristic
138C2×C61#46611yescharacteristic
139C2×C61#46811yescharacteristic
140C2×C61#48011yescharacteristic
141C2×C61#48211yescharacteristic
142D61—42no—
143D61—82no—
144C2×#121—611no—
145C2×#107—611no—
146C2×#102—611no—
147C2×#102—611no—
148C2×C22⋊C8—611no—
149#380—611no—
150#340D6111yescharacteristic, complemented
151C61#203311yescharacteristic, complemented, Sylow
152C22×D4—611no—
153C22×D4—1221no—
154C23×C4—611no—
155C22×C8—611no—
156C22×C8C2×D6111yescharacteristic
157#121—1222no—
158#121—1222no—
159C2×C4⋊C4—611no—
160C2×C4⋊C4C2×D6111yescharacteristic
161C2×C4⋊C4C2×D6111yescharacteristic
162C2×C22⋊C4—1221no—
163C2×C22⋊C4—1221no—
164#107—1222no—
165#102—1222no—
166#102—1222no—
167C22⋊C8—1222no—
168#95—1221no—
169C24—611no—
170C24—1221no—
171C2×D4—612no—
172C2×D4—1224no—
173C2×D4—1221no—
174C2×D4—1221no—
175C2×D4—1221no—
176C2×D4—1221no—
177C2×D4—1221no—
178C2×D4—2442no—
179C2×D4—2442no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—611no—
183C22×C4—1221no—
184C22×C4—1221no—
185C22×C4—1221no—
186C22×C4—1221no—
187C22×C4—1221no—
188C22×C4—1221no—
189C22×C4—1221no—
190C22×C4C22×D6111yescharacteristic
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—612no—
195C2×C8—1221no—
196C2×C8—1221no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—1221no—
201C4⋊C4—1221no—
202C4⋊C4D24412yes—
203C22⋊C4—1224no—
204C22⋊C4—2442no—
205C23—612no—
206C23—1221no—
207C23—1221no—
208C23—1221no—
209C23—1221no—
210C23—1221no—
211C23—1221no—
212C23—1222no—
213C23—2441no—
214C23—2441no—
215C23—2441no—
216C23—2441no—
217C23—2441no—
218C23—2441no—
219C23D4×D6111yescharacteristic
220D4—1222no—
221D4—1222no—
222D4—2448no—
223D4—2441no—
224D4—2441no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—1221no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—2441no—
235C2×C4—2441no—
236C2×C4—2441no—
237C2×C4—2441no—
238C2×C4—2441no—
239C2×C4—2441no—
240C2×C4—2441no—
241C2×C4C2×D24411yescharacteristic
242C2×C4#1175822211yescharacteristic
243C2×C4#1175822211yescharacteristic
244C2×C4D4×D6111yescharacteristic
245C2×C4D4×D6111yescharacteristic
246C2×C4#1175822611yescharacteristic
247C8—41no—
248C8—1222no—
249C22—1222no—
250C22—1222no—
251C22—1222no—
252C22—4881no—
253C22—4881no—
254C22—4881no—
255C22—4881no—
256C22—2442no—
257C22—2442no—
258C22—2442no—
259C22—2441no—
260C22—2441no—
261C22—2441no—
262C22—2441no—
263C22#1451974711yescharacteristic
264C22#1451975011yescharacteristic
265C22#1451976211yescharacteristic
266C22D8×D6111yescharacteristic
267C22#1451979811yescharacteristic
268C22#1451980411yescharacteristic
269C22#1451980911yescharacteristic
270C4—42no—
271C4—81no—
272C4—4881no—
273C4—2441no—
274C4#1451975011yescharacteristic
275C4#1451975211yescharacteristic
276C4#1451976211yescharacteristic
277C4#1451976511yescharacteristic
278C2—4882no—
279C2—2442no—
280C2#1683968011yescharacteristic
281C2#1683989711yescharacteristic
282C2#1683992711yescharacteristic
283C2#1683999711yescharacteristic
284C2#1684001111yescharacteristic
285C2#1684007711yescharacteristic
286C2#1684008811yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#2033
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#14519710C2semidirect
3. C2×#14519699C2semidirect
4. C2×#14519697C2semidirect
5. C2×#14519689C2semidirect
6. #16839619C2semidirect
7. C61×#340C2semidirect
60. C2×#92418D4semidirect
150. #340D61semidirect
151. C61#2033semidirect