Finite Group Databasebeta

← #21445793

Subgroups — #21445793

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×#14519824C211yesmaximal, characteristic
2#16839779C211yesmaximal, characteristic, complemented
3#16839772C211yesmaximal, characteristic, complemented
4#16839770C211yesmaximal, characteristic, complemented
5#16839744C211yesmaximal, characteristic, complemented
6#16839735C211yesmaximal, characteristic, complemented
7C61×#421C211yesmaximal, characteristic, complemented
8#14519824—22no—
9#14519824—22no—
10#14519824—22no—
11#14519824—22no—
12C2×#11758222—21no—
13C2×#11758222C2211yescharacteristic
14C2×#11758224—22no—
15C2×#11758224C412yescomplemented
16C22×Dic122—21no—
17C22×Dic122C2211yescharacteristic
18C2×Q8×D61C412yescomplemented
19C2×#11758194C2211yescharacteristic
20#14519736C2211yescharacteristic
21#14519704—22no—
22#14519702—22no—
23#14519700—22no—
24#14519695—21no—
25#14519693—21no—
26#14519691—22no—
27C2×#41×C61C2211yescharacteristic
28C2×M16×C61C2211yescharacteristic
29#117×C61C2211yescharacteristic
30#104×C61—22no—
31#41×C61—21no—
32#41×C61—21no—
33#41×C61D412yes—
34#41×C61D412yes—
35C2×Q8×C61C2×C411yescharacteristic
36C2×D4×C61—21no—
37C2×D4×C61C2×C411yescharacteristic
38C22×C4×C61—21no—
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—22no—
41C2×C22⋊D61D412yes—
42C22×Dic61—21no—
43C22×Dic61—22no—
44Q8×D61—24no—
45Q8×D61—24no—
46#11758224—28no—
47#11758224—28no—
48#11758224—24no—
49#11758224—24no—
50#11758222—24no—
51#11758222—24no—
52#11758222—21no—
53#11758222—21no—
54#11758222—21no—
55#11758222—21no—
56C2×D244D411yescharacteristic
57C2×C4×D61—22no—
58C2×C4×D61C2×C412yes—
59C2×Dic122—24no—
60C2×Dic122—24no—
61C2×Dic122—21no—
62C2×Dic122—21no—
63C2×Dic122—21no—
64C2×Dic122—22no—
65C2×Dic122C2×C412yes—
66C2×Dic122D411yescharacteristic
67C2×Dic122D412yes—
68C2×Dic122D412yes—
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×C61—21no—
82C23×C61C2×D411yescharacteristic
83C22×D61C22⋊C412yes—
84Q8×C61—21no—
85Q8×C61C22⋊C412yes—
86D4×C61—22no—
87D4×C61—22no—
88D4×C61—21no—
89D4×C61C22⋊C412yes—
90C2×C4×C61—21no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—41no—
94C2×C4×C61C22×C411yescharacteristic
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2×D411yescharacteristic
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2×D411yescharacteristic
100C22⋊D61—28no—
101C22⋊D61—22no—
102C22⋊D61—22no—
103C2×Dic61—28no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—41no—
108C2×Dic61C22⋊C412yes—
109D244—21no—
110D244—21no—
111C4×D61—28no—
112C4×D61—22no—
113C4×D61—22no—
114Dic122—28no—
115Dic122—22no—
116Dic122—21no—
117Dic122—21no—
118Dic122—22no—
119Dic122—22no—
120Dic122C22⋊C414yes—
121C8×C61—41no—
122#92418—41no—
123C22×C61—22no—
124C22×C61—41no—
125C22×C61—42no—
126C22×C61C2×C22⋊C411yescharacteristic
127C22×C61#12011yescharacteristic
128C22×C61#12011yescharacteristic
129C2×D61—22no—
130C2×D61—42no—
131C4×C61—22no—
132C4×C61—81no—
133C4×C61C2×C22⋊C411yescharacteristic
134C4×C61C2×C22⋊C411yescharacteristic
135C4×C61#12011yescharacteristic
136C4×C61#12011yescharacteristic
137Dic61—22no—
138Dic61—24no—
139Dic61—81no—
140#1796—611nomaximal, Sylow
141C2×C61—21no—
142C2×C61—21no—
143C2×C61—21no—
144C2×C61—42no—
145C2×C61#37911yescharacteristic
146D61—42no—
147C2×2−1+4—611no—
148#421—611no—
149#421D6111yescharacteristic, complemented
150#419—611no—
151#419—611no—
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—1221no—
162C2×#41—1222no—
163C2×#41C2×D6111yescharacteristic
164C22×Q8—612no—
165C22×Q8—611no—
166C22×Q8—1221no—
167C2×M16—611no—
168C2×M16C2×D6111yescharacteristic
169#117—611no—
170#117C2×D6111yescharacteristic
171#104—22no—
172#104—1222no—
173#103—1222no—
174#103—1222no—
175#101—1221no—
176#100—1221no—
177#99—1222no—
178#41—21no—
179#41—21no—
180#41—1224no—
181#41—1224no—
182#41—1224no—
183#41—1228no—
184#41—1228no—
185#41—1224no—
186#41—1221no—
187#41—1221no—
188#41—1221no—
189#41—1221no—
190#41D24412yes—
191#41C22⋊D6112yes—
192C2×Q8—611no—
193C2×Q8—612no—
194C2×Q8—612no—
195C2×Q8—612no—
196C2×Q8—1222no—
197C2×Q8—1224no—
198C2×Q8—1224no—
199C2×Q8—1224no—
200C2×Q8—1224no—
201C2×Q8—1221no—
202C2×Q8—1221no—
203C2×Q8—1221no—
204C2×Q8C4×D6111yescharacteristic
205C2×D4—21no—
206C2×D4—612no—
207C2×D4—611no—
208C2×D4—1222no—
209C2×D4C4×D6111yescharacteristic
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—21no—
229C23—612no—
230C23D4×D6111yescharacteristic
231Q8—21no—
232Q8—614no—
233Q8—1228no—
234Q8—1222no—
235Q8—1221no—
236Q8—1222no—
237Q8—1221no—
238Q8—1222no—
239Q8#1175819812yes—
240D4—22no—
241D4—22no—
242D4—21no—
243D4—1228no—
244D4—1222no—
245D4—1222no—
246D4—1221no—
247D4—1221no—
248D4#1175819812yes—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—612no—
254C2×C4—1228no—
255C2×C4—1228no—
256C2×C4—1222no—
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—22no—
271C22—41no—
272C22—42no—
273C22—1222no—
274C22—2442no—
275C22C22⋊C4×D6111yescharacteristic
276C22#1451974511yescharacteristic
277C22#1451974711yescharacteristic
278C4—22no—
279C4—81no—
280C4—1222no—
281C4—1224no—
282C4—4881no—
283C4C22⋊C4×D6111yescharacteristic
284C4C2×#1175819811yescharacteristic
285C4#1451974511yescharacteristic
286C4#1451974711yescharacteristic
287C2—21no—
288C2—21no—
289C2—21no—
290C2—42no—
291C2—2442no—
292C2#1683961711yescharacteristic
subgroupG/H
centerC2#16839617
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#421C2
socleC2×C61#379
hypercenter#421D61
hypocenterC61#1796
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #16839779C2semidirect
3. #16839772C2semidirect
4. #16839770C2semidirect
5. #16839744C2semidirect
6. #16839735C2semidirect
7. C61×#421C2semidirect
15. C2×#11758224C4semidirect
18. C2×Q8×D61C4semidirect
149. #421D61semidirect
154. C61#1796semidirect