Finite Group Databasebeta

← #21445791

Subgroups — #21445791

Order 7808.

536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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×#14519825C211yesmaximal, characteristic
2#16839780C211yesmaximal, characteristic, complemented
3#16839778C211yesmaximal, characteristic, complemented
4#16839771C211yesmaximal, characteristic, complemented
5#16839744C211yesmaximal, characteristic, complemented
6#16839735C211yesmaximal, characteristic, complemented
7C61×#419C211yesmaximal, characteristic, complemented
8#14519825—22no—
9#14519825—22no—
10#14519825—22no—
11#14519825—22no—
12C2×#11758226—21no—
13C2×#11758226C412yescomplemented
14C2×#11758222—22no—
15C2×#11758222C2211yescharacteristic
16C2×#11758222C2211yescharacteristic
17C2×Q8×D61—21no—
18C2×Q8×D61C412yescomplemented
19C2×#11758194C2211yescharacteristic
20#14519736C2211yescharacteristic
21#14519705—22no—
22#14519703—22no—
23#14519701—22no—
24#14519695—21no—
25#14519693—21no—
26#14519691—22no—
27C22×Q8×C61C2211yescharacteristic
28C2×M16×C61C2211yescharacteristic
29#117×C61C2211yescharacteristic
30#103×C61—22no—
31C2×Q8×C61—21no—
32C2×Q8×C61—21no—
33C2×Q8×C61—21no—
34C2×Q8×C61C2×C412yes—
35C2×Q8×C61D412yes—
36C2×Q8×C61D412yes—
37C22×C4×C61—21no—
38C22×C4×C61C2311yescharacteristic
39C2×C22⋊D61—21no—
40C2×C22⋊D61D412yes—
41#11758226—24no—
42#11758226—24no—
43#11758226—24no—
44#11758226—24no—
45Q8×D61—24no—
46Q8×D61—24no—
47Q8×D61—24no—
48Q8×D61—24no—
49#11758222—28no—
50#11758222—28no—
51#11758222—21no—
52#11758222—21no—
53#11758222—21no—
54#11758222—21no—
55#11758222—21no—
56#11758222—21no—
57#11758222D412yes—
58#11758222D412yes—
59C2×D244—22no—
60C2×D244C2×C411yescharacteristic
61C2×D244D411yescharacteristic
62C2×C4×D61—22no—
63C2×C4×D61—21no—
64C2×C4×D61—22no—
65C2×C4×D61C2×C412yes—
66C2×Dic122—22no—
67C2×Dic122C2×C411yescharacteristic
68C2×Dic122D411yescharacteristic
69M16×C61—21no—
70M16×C61—21no—
71C2×C8×C61—21no—
72C4⋊C4×C61—21no—
73C22⋊C4×C61—21no—
74C42×C61—21no—
75C22⋊Dic61—21no—
76C4⋊Dic61—21no—
77C4×Dic61—21no—
78#11758194—21no—
79#11758194—21no—
80C2×#92418—21no—
81C23×C61C2×D411yescharacteristic
82C22×D61—21no—
83C22×D61C22⋊C412yes—
84Q8×C61—22no—
85Q8×C61—22no—
86Q8×C61—22no—
87Q8×C61C22⋊C414yes—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—41no—
92C2×C4×C61C22×C411yescharacteristic
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2×D411yescharacteristic
97C2×C4×C61C2×D411yescharacteristic
98C22⋊D61—22no—
99C22⋊D61—22no—
100C22⋊D61—22no—
101C22⋊D61—22no—
102C2×Dic61—21no—
103C2×Dic61—41no—
104C2×Dic61C22⋊C412yes—
105D244—28no—
106D244—21no—
107D244—21no—
108D244—21no—
109D244C22⋊C412yes—
110C4×D61—28no—
111C4×D61—28no—
112C4×D61—22no—
113C4×D61—22no—
114C4×D61—22no—
115C4×D61—22no—
116Dic122—28no—
117Dic122—21no—
118Dic122—21no—
119Dic122—21no—
120Dic122C22⋊C412yes—
121C8×C61—41no—
122#92418—41no—
123C22×C61—41no—
124C22×C61C2×C22⋊C411yescharacteristic
125C22×C61#12011yescharacteristic
126C22×C61#12011yescharacteristic
127C2×D61—22no—
128C2×D61—22no—
129C2×D61—42no—
130C2×D61—42no—
131C4×C61—24no—
132C4×C61—81no—
133C4×C61C2×C22⋊C411yescharacteristic
134C4×C61C2×C22⋊C411yescharacteristic
135C4×C61#12011yescharacteristic
136C4×C61#12011yescharacteristic
137Dic61—22no—
138Dic61—22no—
139Dic61—81no—
140#1796—611nomaximal, Sylow
141C2×C61—21no—
142C2×C61—21no—
143C2×C61—21no—
144C2×C61#37911yescharacteristic
145D61—42no—
146D61—42no—
147C2×2−1+4—611no—
148#421—611no—
149#421—611no—
150#419—611no—
151#419D6111yescharacteristic, complemented
152#413—611no—
153#410—611no—
154C61#179611yescharacteristic, complemented, Sylow
1552−1+4—1222no—
1562−1+4—1222no—
1572−1+4—1222no—
1582−1+4—1222no—
159C2×#41—611no—
160C2×#41—612no—
161C2×#41—611no—
162C2×#41—1222no—
163C2×#41—1221no—
164C22×Q8—612no—
165C22×Q8—1221no—
166C22×Q8C2×D6111yescharacteristic
167C2×M16—611no—
168C2×M16C2×D6111yescharacteristic
169#117—611no—
170#117C2×D6111yescharacteristic
171#104—1222no—
172#104—1222no—
173#103—22no—
174#103—1222no—
175#101—1221no—
176#100—1221no—
177#99—1222no—
178#41—612no—
179#41—612no—
180#41—1228no—
181#41—1228no—
182#41—1224no—
183#41—1224no—
184#41—1224no—
185#41—1224no—
186#41—1221no—
187#41—1221no—
188#41—1221no—
189#41—1221no—
190#41—1221no—
191#41—1221no—
192C2×Q8—21no—
193C2×Q8—21no—
194C2×Q8—21no—
195C2×Q8—611no—
196C2×Q8—611no—
197C2×Q8—1222no—
198C2×Q8—1224no—
199C2×Q8—1224no—
200C2×Q8—1224no—
201C2×Q8—1224no—
202C2×Q8C4×D6112yes—
203C2×Q8D24412yes—
204C2×Q8C22⋊D6112yes—
205C2×D4—612no—
206C2×D4—611no—
207C2×D4—611no—
208C2×D4—1222no—
209C2×D4—1221no—
210C22×C4—21no—
211C22×C4—612no—
212C22×C4—1222no—
213C22×C4—1222no—
214C22×C4—1221no—
215C22×C4C22×D6111yescharacteristic
216M16—21no—
217M16—21no—
218M16—1221no—
219M16—1221no—
220C2×C8—21no—
221C2×C8—1221no—
222C4⋊C4—21no—
223C4⋊C4—1221no—
224C22⋊C4—21no—
225C22⋊C4—1221no—
226C42—21no—
227C42—1221no—
228C23—612no—
229C23—1221no—
230C23D4×D6111yescharacteristic
231Q8—22no—
232Q8—22no—
233Q8—22no—
234Q8—612no—
235Q8—1228no—
236Q8—1221no—
237Q8—1221no—
238Q8—1221no—
239Q8#1175819814yes—
240D4—612no—
241D4—1228no—
242D4—1222no—
243D4—1222no—
244D4—1222no—
245D4—1222no—
246D4—1221no—
247D4—1221no—
248D4—1221no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—612no—
254C2×C4—1228no—
255C2×C4—1228no—
256C2×C4—1221no—
257C2×C4—1222no—
258C2×C4—1222no—
259C2×C4—1222no—
260C2×C4—1222no—
261C2×C4—2441no—
262C2×C4C2×C4×D6111yescharacteristic
263C2×C4C2×D24411yescharacteristic
264C2×C4D4×D6111yescharacteristic
265C2×C4D4×D6111yescharacteristic
266C2×C4D4×D6111yescharacteristic
267C2×C4C2×C22⋊D6111yescharacteristic
268C8—41no—
269C8—2441no—
270C22—41no—
271C22—1222no—
272C22—1222no—
273C22—2442no—
274C22—2442no—
275C22C22⋊C4×D6111yescharacteristic
276C22#1451974511yescharacteristic
277C22#1451974711yescharacteristic
278C4—24no—
279C4—81no—
280C4—1222no—
281C4—1222no—
282C4—4881no—
283C4C22⋊C4×D6111yescharacteristic
284C4C2×#1175819811yescharacteristic
285C4#1451974511yescharacteristic
286C4#1451974711yescharacteristic
287C2—21no—
288C2—21no—
289C2—21no—
290C2—2442no—
291C2—2442no—
292C2#1683961711yescharacteristic
subgroupG/H
centerC2#16839617
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#419C2
socleC2×C61#379
hypercenter#419D61
hypocenterC61#1796
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. #16839780C2semidirect
3. #16839778C2semidirect
4. #16839771C2semidirect
5. #16839744C2semidirect
6. #16839735C2semidirect
7. C61×#419C2semidirect
13. C2×#11758226C4semidirect
18. C2×Q8×D61C4semidirect
151. #419D61semidirect
154. C61#1796semidirect