Finite Group Databasebeta

← #21455441

Subgroups — #21455441

Order 7808.

548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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×#14519802C211yesmaximal, characteristic, complemented
2C2×M16×D61C211yesmaximal, characteristic, complemented
3#16840269C211yesmaximal, characteristic, complemented
4C2×#14519752C211yesmaximal, characteristic, complemented
5#16840014C212yesmaximal, complemented
6#16840011C212yesmaximal, complemented
7#16839997C212yesmaximal, complemented
8#16839994C212yesmaximal, complemented
9#16839802C211yesmaximal, characteristic, complemented
10#16839768C211yesmaximal, characteristic, complemented
11C61×#417C211yesmaximal, characteristic, complemented
12C22×D244—21no—
13C22×D244C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15#14519802—24no—
16C2×#11758201C2212yescomplemented
17C2×#11758199C2212yescomplemented
18C2×#11758194C2211yescharacteristic
19C2×#11758189C2212yescomplemented
20M16×D61—24no—
21C2×C8×D61C2212yescomplemented
22#14519758—21no—
23#14519753C2211yescharacteristic, complemented
24#14519753C2211yescharacteristic, complemented
25#14519752—21no—
26#14519752—21no—
27#14519752C2212yes—
28#14519752C2212yes—
29#14519748C2211yescharacteristic, complemented
30#14519748C2211yescharacteristic, complemented
31#14519745—21no—
32C4×C22⋊D61—21no—
33C4×C22⋊D61—21no—
34#14519736C2211yescharacteristic
35C2×#11758198—21no—
36#14519710C2212yescomplemented
37#14519708C2212yescomplemented
38#14519699C2212yescomplemented
39#14519699C2212yescomplemented
40C2×#41×C61C2211yescharacteristic
41C2×M16×C61C2211yescharacteristic
42C2×C4⋊C4×C61C2211yescharacteristic
43#103×C61C2212yescomplemented
44#102×C61C2212yescomplemented
45C23×D61—21no—
46C23×D61D411yescharacteristic
47#41×C61—22no—
48#41×C61—22no—
49C2×Q8×C61C2311yescharacteristic
50C2×D4×C61—21no—
51C2×D4×C61C2311yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61C2311yescharacteristic
55C2×C22⋊D61—21no—
56C2×C22⋊D61—21no—
57C22×Dic61D411yescharacteristic
58C2×D244—22no—
59C2×D244—22no—
60C2×D244—22no—
61C2×D244—22no—
62C2×D244—21no—
63C2×D244—44no—
64C2×D244C2312yes—
65C2×C4×D61—22no—
66C2×C4×D61—22no—
67C2×C4×D61D411yescharacteristic
68C2×C4×D61D411yescharacteristic
69C2×C4×D61C2311yescharacteristic
70C2×C4×D61C2311yescharacteristic
71M16×C61—22no—
72C2×C8×C61C2312yes—
73C4⋊C4×C61—21no—
74C4⋊C4×C61C2312yes—
75C22⋊Dic61—21no—
76C22⋊Dic61—21no—
77C22⋊Dic61—21no—
78#11758201—24no—
79#11758199—24no—
80#11758198—21no—
81#11758198—21no—
82#11758198—22no—
83#11758198—22no—
84C4⋊Dic61C2311yescharacteristic
85C4⋊Dic61C2311yescharacteristic
86#11758196—21no—
87#11758196—21no—
88C4×Dic61—21no—
89#11758194D414yescomplemented
90C2×#92418C2312yes—
91#11758189—24no—
92C8×D61—24no—
93C23×C61—21no—
94C23×C61C2×D411yescharacteristic
95C22×D61—22no—
96C22×D61—22no—
97C22×D61—22no—
98C22×D61—41no—
99C22×D61—42no—
100C22×D61—42no—
101C22×D61—42no—
102C22×D61C2×D411yescharacteristic
103C22×D61C2×D411yescharacteristic
104Q8×C61—21no—
105Q8×C61—21no—
106D4×C61—21no—
107D4×C61—21no—
108D4×C61—42no—
109C2×C4×C61—21no—
110C2×C4×C61—22no—
111C2×C4×C61—42no—
112C2×C4×C61—42no—
113C2×C4×C61C2×D411yescharacteristic
114C2×C4×C61C2×D412yes—
115C2×C4×C61#4112yes—
116C2×C4×C61C2411yescharacteristic
117C22⋊D61—42no—
118C22⋊D61—42no—
119C2×Dic61—22no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61C2×D411yescharacteristic
123C2×Dic61C2×D411yescharacteristic
124D244—22no—
125D244—22no—
126D244—44no—
127D244—44no—
128D244—42no—
129C4×D61—22no—
130C4×D61—22no—
131C4×D61—21no—
132C4×D61—21no—
133C4×D61—21no—
134C4×D61—21no—
135C8×C61—22no—
136#92418C2×D414yescomplemented
137C22×C61—21no—
138C22×C61—21no—
139C22×C61—41no—
140C22×C61—41no—
141C22×C61—41no—
142C22×C61#12112yes—
143C22×C61C22×D411yescharacteristic
144C2×D61—21no—
145C2×D61—21no—
146C2×D61—21no—
147C2×D61—21no—
148C2×D61—21no—
149C2×D61—44no—
150C2×D61—42no—
151C2×D61—42no—
152C2×D61—42no—
153C2×D61—84no—
154C2×D61AGL(1,ℤ/8)12yescomplemented
155C4×C61—41no—
156C4×C61—42no—
157C4×C61#12112yes—
158C4×C61C22×D411yescharacteristic
159C4×C61C2×#4111yescharacteristic
160Dic61—21no—
161Dic61—21no—
162Dic61—41no—
163Dic61—41no—
164#3055—611nomaximal, Sylow
165C2×C61—22no—
166C2×C61—81no—
167C2×C61C2×#12111yescharacteristic
168C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
169C2×C61#57511yescharacteristic
170D61—22no—
171D61—41no—
172D61—82no—
173C2×AGL(1,ℤ/8)—611no—
174C22×M16—611no—
175#525—611no—
176C2×#121—611no—
177#469—612no—
178#468—612no—
179#466—612no—
180#465—612no—
181#428—611no—
182#418—611no—
183#417D6111yescharacteristic, complemented
184C61#305511yescharacteristic, complemented, Sylow
185C2×#41C2×D6111yescharacteristic
186C22×D4—611no—
187C22×D4—1221no—
188C23×C4—611no—
189AGL(1,ℤ/8)—1224no—
190C2×SD16—612no—
191C2×D8—612no—
192C2×M16—611no—
193C2×M16—612no—
194C2×M16—1224no—
195C2×M16C2×D6111yescharacteristic
196C22×C8—612no—
197#123—1221no—
198C22⋊Q8—611no—
199C22⋊Q8—611no—
200#121—611no—
201#121—611no—
202#121—612no—
203#121—612no—
204#121—1221no—
205#121—1221no—
206#120—1221no—
207C4×D4—1221no—
208C4×D4—1221no—
209#117—611no—
210C2×C4⋊C4C2×D6111yescharacteristic
211C2×C22⋊C4—1221no—
212#107—612no—
213#106—612no—
214#103C2×D6112yescomplemented
215#102—612no—
216#102—612no—
217#102C2×D6112yescomplemented
218C24—611no—
219C24—1221no—
220#41—22no—
221#41—22no—
222C2×Q8C22×D6111yescharacteristic
223C2×D4—21no—
224C2×D4—612no—
225C2×D4—1222no—
226C2×D4—1222no—
227C2×D4—1221no—
228C2×D4—1221no—
229C2×D4—1222no—
230C2×D4—1222no—
231C2×D4—1221no—
232C2×D4—2444no—
233C2×D4C22×D6111yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—1222no—
242C22×C4—1222no—
243C22×C4C22×D6111yescharacteristic
244SD16—1224no—
245D8—1224no—
246M16—22no—
247M16—614no—
248M16—1224no—
249C2×C8—612no—
250C2×C8—1224no—
251C2×C8C22×D6112yes—
252C4⋊C4—21no—
253C4⋊C4—611no—
254C4⋊C4—611no—
255C4⋊C4—1221no—
256C4⋊C4—1221no—
257C4⋊C4C22×D6112yes—
258C22⋊C4—1222no—
259C22⋊C4—1222no—
260C22⋊C4—1221no—
261C22⋊C4—1221no—
262C22⋊C4—1221no—
263C22⋊C4—1221no—
264C22⋊C4—1221no—
265C42—1221no—
266C23—21no—
267C23—611no—
268C23—611no—
269C23—1222no—
270C23—1222no—
271C23—1222no—
272C23—2441no—
273C23—2442no—
274C23—2442no—
275C23—2442no—
276C23D4×D6111yescharacteristic
277Q8—21no—
278Q8—21no—
279D4—21no—
280D4—21no—
281D4—42no—
282D4—1222no—
283D4—1222no—
284D4—2444no—
285D4—2444no—
286D4—2442no—
287D4—2442no—
288D4—2442no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—611no—
294C2×C4—611no—
295C2×C4—1222no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1222no—
301C2×C4—1222no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4#1175822212yes—
305C2×C4D4×D6112yes—
306C2×C4D4×D6111yescharacteristic
307C2×C4C23×D6111yescharacteristic
308C8—22no—
309C8—614no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—612no—
316C22—1221no—
317C22—1221no—
318C22—1221no—
319C22—1221no—
320C22—1221no—
321C22—4884no—
322C22—2444no—
323C22—2442no—
324C22—2442no—
325C22—2442no—
326C22#1451975012yes—
327C22C2×D4×D6111yescharacteristic
328C4—41no—
329C4—42no—
330C4—1221no—
331C4—1221no—
332C4—2441no—
333C4—2441no—
334C4#1451975012yes—
335C4C2×D4×D6111yescharacteristic
336C4C2×#1175822211yescharacteristic
337C2—22no—
338C2—81no—
339C2—1222no—
340C2—4882no—
341C2—2441no—
342C2C2×#1451975011yescharacteristic
343C2AGL(1,ℤ/8)×D6111yescharacteristic
344C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#417C2
socleC22×C61C22×D4
hypercenter#417D61
hypocenterC61#3055
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#14519802C2semidirect
2. C2×M16×D61C2semidirect
3. #16840269C2semidirect
4. C2×#14519752C2semidirect
5. #16840014C2semidirect
6. #16840011C2semidirect
7. #16839997C2semidirect
8. #16839994C2semidirect
9. #16839802C2semidirect
10. #16839768C2semidirect
11. C61×#417C2semidirect
16. C2×#11758201C22semidirect
17. C2×#11758199C22semidirect
19. C2×#11758189C22semidirect
21. C2×C8×D61C22semidirect
23. #14519753C22semidirect
24. #14519753C22semidirect
29. #14519748C22semidirect
30. #14519748C22semidirect
36. #14519710C22semidirect
37. #14519708C22semidirect
38. #14519699C22semidirect
39. #14519699C22semidirect
43. #103×C61C22semidirect
44. #102×C61C22semidirect
89. #11758194D4semidirect
136. #92418C2×D4semidirect
154. C2×D61AGL(1,ℤ/8)semidirect
183. #417D61semidirect
184. C61#3055semidirect
214. #103C2×D61semidirect
217. #102C2×D61semidirect