Finite Group Databasebeta

← #21444738

Subgroups — #21444738

Order 7808.

368 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 51 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#16840320C211yesmaximal, characteristic, complemented
2#16839898C211yesmaximal, characteristic, complemented
3#16839895C211yesmaximal, characteristic, complemented
4#16839672C211yesmaximal, characteristic, complemented
5#16839495C211yesmaximal, characteristic, complemented
6#16839485C211yesmaximal, characteristic, complemented
7C61×#327C211yesmaximal, characteristic, complemented
8C22×D244—21no—
9C22×D244C2211yescharacteristic, complemented
10C2×D4×D61—21no—
11C2×D488—21no—
12C2×#11758199—21no—
13#14519762—21no—
14#14519759—21no—
15#14519751C2211yescharacteristic
16#14519749—21no—
17#14519747—21no—
18#14519745—21no—
19C2×#11758198—21no—
20C2×#11758198C2211yescharacteristic
21#14519699—21no—
22#14519697—21no—
23C22⋊#92418C2211yescharacteristic, complemented
24#121×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic, complemented
26#95×C61C2211yescharacteristic, complemented
27C23×D61—21no—
28C23×D61—21no—
29C23×D61D411yescharacteristic
30C2×D4×C61—21no—
31C2×D4×C61D411yescharacteristic, complemented
32C22×C4×C61—21no—
33C22×C4×C61C2311yescharacteristic
34C2×C22⋊D61—21no—
35C2×C22⋊D61—21no—
36C2×C22⋊D61—21no—
37C22×Dic61D411yescharacteristic
38D4×D61—42no—
39D4×D61—42no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244—21no—
43C2×D244—42no—
44C2×D244—42no—
45C2×D244—42no—
46C2×D244—42no—
47C2×D244D411yescharacteristic, complemented
48C2×C4×D61—21no—
49C2×C8×C61—21no—
50C4⋊C4×C61D411yescharacteristic, complemented
51C22⋊C4×C61—21no—
52C22⋊Dic61—21no—
53#11758199—42no—
54#11758198—21no—
55#11758198—21no—
56#11758198—21no—
57#11758198—21no—
58#11758198—42no—
59C4⋊Dic61D411yescharacteristic, complemented
60#11758196—21no—
61C2×#92418—21no—
62D488—42no—
63C23×C61—21no—
64C23×C61C2×D411yescharacteristic
65C22×D61—21no—
66C22×D61—21no—
67C22×D61—22no—
68C22×D61—21no—
69C22×D61—42no—
70C22×D61—41no—
71C22×D61—41no—
72C22×D61—41no—
73C22×D61—41no—
74C22×D61—41no—
75C22×D61—41no—
76C22×D61—41no—
77C22×D61—41no—
78C22×D61—81no—
79C22×D61—81no—
80C22×D61D812yescomplemented
81D4×C61—41no—
82D4×C61—41no—
83D4×C61—41no—
84C2×C4×C61—22no—
85C2×C4×C61—21no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C22⋊D61—42no—
92C22⋊D61—41no—
93C22⋊D61—41no—
94C22⋊D61—81no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—41no—
98D244—22no—
99D244—22no—
100D244—41no—
101D244—41no—
102D244—41no—
103D244—42no—
104D244—48no—
105C4×D61—42no—
106C8×C61—41no—
107#92418—41no—
108C22×C61—21no—
109C22×C61—21no—
110C22×C61—41no—
111C22×C61—41no—
112C22×C61—41no—
113C22×C61#12011yescharacteristic
114C22×C61C2×D811yescharacteristic
115C22×C61AGL(1,ℤ/8)11yescharacteristic
116C2×D61—22no—
117C2×D61—41no—
118C2×D61—41no—
119C2×D61—42no—
120C2×D61—42no—
121C2×D61—42no—
122C2×D61—41no—
123C2×D61—41no—
124C2×D61—42no—
125C2×D61—41no—
126C2×D61—81no—
127C2×D61—84no—
128C2×D61—81no—
129C2×D61—81no—
130C2×D61—81no—
131C2×D61—81no—
132C4×C61—21no—
133C4×C61—21no—
134C4×C61—42no—
135C4×C61—41no—
136Dic61—41no—
137Dic61—41no—
138#1595—611nomaximal, Sylow
139C2×C61—21no—
140C2×C61—21no—
141C2×C61—81no—
142C2×C61#44711yescharacteristic
143C2×C61#45311yescharacteristic
144C2×C61B(4,𝔽2)11yescharacteristic
145D61—42no—
146D61—82no—
147D61—81no—
148#534—611no—
149#447—611no—
150#447—611no—
151#392—611no—
152#327—611no—
153#327D6111yescharacteristic, complemented
154#323—611no—
155C61#159511yescharacteristic, complemented, Sylow
156C22×D4—611no—
157C22×D4—1221no—
158C22×D4—1221no—
159C2×D8—1221no—
160C2×D8—1221no—
161#123—1221no—
162#123—1221no—
163#121—611no—
164#121—1221no—
165#121C2×D6111yescharacteristic
166#120—1221no—
167#120—1221no—
168C2×C22⋊C4—611no—
169C2×C22⋊C4—1221no—
170#102—1221no—
171#102—1221no—
172C22⋊C8—611no—
173C22⋊C8C2×D6111yescharacteristic, complemented
174#95C2×D6111yescharacteristic, complemented
175C24—611no—
176C24—1221no—
177C24—1221no—
178C2×D4—21no—
179C2×D4—611no—
180C2×D4—1221no—
181C2×D4—1221no—
182C2×D4—1221no—
183C2×D4—1221no—
184C2×D4—1221no—
185C2×D4—1221no—
186C2×D4—2442no—
187C2×D4—2442no—
188C2×D4—2442no—
189C2×D4—2442no—
190C2×D4—2442no—
191C2×D4—2442no—
192C2×D4D24411yescharacteristic, complemented
193C22×C4—21no—
194C22×C4—611no—
195C22×C4—1221no—
196C22×C4C22×D6111yescharacteristic
197D8—2442no—
198D8—2442no—
199C2×C8—21no—
200C2×C8—1221no—
201C4⋊C4—611no—
202C4⋊C4—1221no—
203C4⋊C4D24411yescharacteristic, complemented
204C22⋊C4—21no—
205C22⋊C4—1221no—
206C22⋊C4—1221no—
207C22⋊C4—1221no—
208C22⋊C4—1221no—
209C22⋊C4—1221no—
210C22⋊C4—2442no—
211C23—21no—
212C23—612no—
213C23—1222no—
214C23—1221no—
215C23—1221no—
216C23—1221no—
217C23—4881no—
218C23—4881no—
219C23—2441no—
220C23—2441no—
221C23—2441no—
222C23—2441no—
223C23—2441no—
224C23—2442no—
225C23—2441no—
226C23—2441no—
227C23—2441no—
228C23D4×D6111yescharacteristic
229D4—41no—
230D4—41no—
231D4—41no—
232D4—1222no—
233D4—1222no—
234D4—4881no—
235D4—2441no—
236D4—2441no—
237D4—2441no—
238D4—2442no—
239D4—2448no—
240D4—2442no—
241D4—2441no—
242D4—2441no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—2442no—
251C2×C4—2441no—
252C2×C4C2×D24411yescharacteristic
253C2×C4D4×D6111yescharacteristic
254C8—41no—
255C8—2441no—
256C22—21no—
257C22—21no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—1222no—
262C22—4881no—
263C22—4881no—
264C22—4881no—
265C22—4884no—
266C22—4881no—
267C22—4881no—
268C22—2442no—
269C22—2442no—
270C22—2442no—
271C22—2442no—
272C22—2441no—
273C22—2441no—
274C22—2441no—
275C22—2441no—
276C22—2441no—
277C22#1451974711yescharacteristic
278C22D8×D6111yescharacteristic
279C22#1451980411yescharacteristic
280C4—21no—
281C4—21no—
282C4—42no—
283C4—41no—
284C4—2441no—
285C4—2441no—
286C2—21no—
287C2—21no—
288C2—81no—
289C2—4882no—
290C2—4881no—
291C2—2442no—
292C2#1683989711yescharacteristic
293C2#1683993111yescharacteristic
294C2#1683995011yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#327C2
socleC22×C61#120
hypercenter#327D61
hypocenterC61#1595
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
1. #16840320C2semidirect
2. #16839898C2semidirect
3. #16839895C2semidirect
4. #16839672C2semidirect
5. #16839495C2semidirect
6. #16839485C2semidirect
7. C61×#327C2semidirect
9. C22×D244C22semidirect
23. C22⋊#92418C22semidirect
25. C22⋊C8×C61C22semidirect
26. #95×C61C22semidirect
31. C2×D4×C61D4semidirect
47. C2×D244D4semidirect
50. C4⋊C4×C61D4semidirect
59. C4⋊Dic61D4semidirect
80. C22×D61D8semidirect
153. #327D61semidirect
155. C61#1595semidirect
173. C22⋊C8C2×D61semidirect
174. #95C2×D61semidirect
192. C2×D4D244semidirect
203. C4⋊C4D244semidirect