Finite Group Databasebeta

← #21457394

Subgroups — #21457394

Order 7808.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519810C211yesmaximal, characteristic, complemented
2C22×Dic244C211yesmaximal, characteristic, complemented
3D4×Dic122C211yesmaximal, characteristic, complemented
4#16840421C211yesmaximal, characteristic
5#16840156C211yesmaximal, characteristic, complemented
6#16840020C211yesmaximal, characteristic, complemented
7#16839991C211yesmaximal, characteristic, complemented
8#16839985C211yesmaximal, characteristic, complemented
9#16839973C211yesmaximal, characteristic, complemented
10#16839926C211yesmaximal, characteristic, complemented
11#16839920C211yesmaximal, characteristic, complemented
12#16839920C211yesmaximal, characteristic, complemented
13#16839903C211yesmaximal, characteristic, complemented
14#16839870C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18C22×Dic122C2211yescharacteristic
19C22×Dic122C2211yescharacteristic
20#14519810—24no—
21C2×Dic244—24no—
22C2×Dic244C2211yescharacteristic
23C2×Dic244C2211yescharacteristic
24C2×Dic244C2211yescharacteristic
25C2×Dic244C2211yescharacteristic
26C2×Dic244C2211yescharacteristic
27C2×Dic244C2211yescharacteristic
28C2×#11758190C2211yescharacteristic
29C2×#11758190C2211yescharacteristic
30C2×#11758190C2211yescharacteristic
31#14519777C2211yescharacteristic
32#14519776—21no—
33#14519765C2211yescharacteristic
34#14519763—21no—
35#14519756C2211yescharacteristic
36#14519756C2211yescharacteristic
37#14519756C2211yescharacteristic
38#14519755—21no—
39#14519754—21no—
40#14519754—21no—
41#14519751C2211yescharacteristic
42#14519749—21no—
43C4×Dic122C2211yescharacteristic
44C4×Dic122C2211yescharacteristic
45D4×Dic61—21no—
46#14519737—21no—
47#14519709C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519702C2211yescharacteristic
50#14519702C2211yescharacteristic
51#14519702C2211yescharacteristic
52#14519702C2211yescharacteristic
53#14519699C2211yescharacteristic
54C2×M16×C61C2211yescharacteristic
55C22×C8×C61C2211yescharacteristic
56C4×D4×C61C2211yescharacteristic
57C4⋊C8×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C22⋊C8×C61C2211yescharacteristic
60#97×C61C2211yescharacteristic
61C2×D4×C61D411yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69#11758222—22no—
70#11758222—41no—
71C2×D244C2311yescharacteristic
72C2×C4×D61—21no—
73C2×Dic122—22no—
74C2×Dic122—22no—
75C2×Dic122—22no—
76C2×Dic122—21no—
77C2×Dic122—21no—
78C2×Dic122—21no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82C2×Dic122C2311yescharacteristic
83C2×Dic122C2311yescharacteristic
84C2×Dic122C2311yescharacteristic
85C2×Dic122C2311yescharacteristic
86C2×Dic122C2311yescharacteristic
87M16×C61—22no—
88C2×C8×C61—22no—
89C2×C8×C61C2311yescharacteristic
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C2×C8×C61C2311yescharacteristic
93C4⋊C4×C61D411yescharacteristic
94C22⋊C4×C61D411yescharacteristic
95C22⋊C4×C61D411yescharacteristic
96C42×C61C2311yescharacteristic
97C22⋊Dic61—21no—
98C22⋊Dic61—21no—
99C22⋊Dic61—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61C2311yescharacteristic
106C4⋊Dic61C2311yescharacteristic
107#11758196—21no—
108#11758196—21no—
109#11758196—21no—
110#11758196—21no—
111#11758196—21no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114Dic244—22no—
115Dic244—22no—
116Dic244—22no—
117Dic244—22no—
118Dic244—41no—
119Dic244D414yescomplemented
120#11758190—22no—
121#11758190—22no—
122#11758190—41no—
123C23×C61C2×D411yescharacteristic
124C23×C61C2×D411yescharacteristic
125C22×D61—21no—
126D4×C61—22no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2411yescharacteristic
136C22⋊D61—42no—
137C22⋊D61—42no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—42no—
146C2×Dic61—42no—
147C2×Dic61—42no—
148D244—21no—
149D244—21no—
150C4×D61—42no—
151Dic122—21no—
152Dic122—21no—
153Dic122—21no—
154Dic122—21no—
155Dic122—21no—
156Dic122—21no—
157Dic122—21no—
158Dic122—21no—
159Dic122—42no—
160Dic122—42no—
161Dic122—42no—
162Dic122C2×D412yes—
163Dic122C2×D412yes—
164C8×C61—21no—
165C8×C61—21no—
166C8×C61—21no—
167C8×C61C2×D412yes—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61#13712yescomplemented
174C22×C61C22×D411yescharacteristic
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61C22×D411yescharacteristic
183C4×C61H(5,𝔽2)11yescharacteristic
184Dic61—22no—
185Dic61—22no—
186Dic61—41no—
187Dic61—41no—
188Dic61—41no—
189Dic61—41no—
190Dic61—41no—
191#3270—611nomaximal, Sylow
192C2×C61—22no—
193C2×C61—41no—
194C2×C61D4211yescharacteristic
195C2×C61C2×#13711yescharacteristic
196C2×C61#57811yescharacteristic
197D61—81no—
198C2×#137—611no—
199C22×Q16—611no—
200D4×Q8—611no—
201#548—611no—
202#497—611no—
203#470—611no—
204#465—611no—
205#464—611no—
206#462—611no—
207#452—611no—
208#451—611no—
209#451—611no—
210#448—611no—
211#441—611no—
212#435D6111yescharacteristic, complemented
213C61#327011yescharacteristic, complemented, Sylow
214C2×#41—611no—
215C22×Q8—611no—
216C22×Q8—611no—
217C22×Q8—611no—
218#137—1224no—
219C2×Q16—611no—
220C2×Q16—611no—
221C2×Q16—611no—
222C2×Q16—611no—
223C2×Q16—611no—
224C2×Q16—611no—
225C2×Q16—1224no—
226C2×SD16—611no—
227C2×SD16—611no—
228C2×SD16—611no—
229C2×M16C2×D6111yescharacteristic
230C22×C8C2×D6111yescharacteristic
231C4⋊Q8—611no—
232C4⋊Q8—1221no—
233#124—611no—
234#124—1221no—
235C22⋊Q8—611no—
236C22⋊Q8—611no—
237C22⋊Q8—611no—
238C22⋊Q8—1221no—
239C22⋊Q8—1221no—
240C22⋊Q8—1221no—
241#121—611no—
242#121—1221no—
243C4×Q8—611no—
244C4×Q8—611no—
245C4×D4—1221no—
246C4×D4—1221no—
247C4×D4C2×D6111yescharacteristic
248#106—611no—
249C4⋊C8C2×D6111yescharacteristic
250#103—611no—
251#103—611no—
252#103—611no—
253#103—611no—
254#103—611no—
255#102—611no—
256C22⋊C8C2×D6111yescharacteristic
257C22⋊C8C2×D6111yescharacteristic
258#97C2×D6111yescharacteristic
259#41—1222no—
260#41—2441no—
261C2×Q8—611no—
262C2×Q8—611no—
263C2×Q8—611no—
264C2×Q8—611no—
265C2×Q8—611no—
266C2×Q8—1222no—
267C2×Q8—1222no—
268C2×Q8—1222no—
269C2×Q8—1221no—
270C2×Q8—1221no—
271C2×Q8—1221no—
272C2×Q8—2441no—
273C2×Q8—2441no—
274C2×Q8—2441no—
275C2×D4—611no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4D24411yescharacteristic
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4C22×D6111yescharacteristic
284C22×C4C22×D6111yescharacteristic
285Q16—614no—
286Q16—1222no—
287Q16—1222no—
288Q16—1222no—
289Q16—1222no—
290Q16—2441no—
291SD16—1222no—
292SD16—1222no—
293SD16—2441no—
294M16—22no—
295C2×C8—22no—
296C2×C8C22×D6111yescharacteristic
297C2×C8C22×D6111yescharacteristic
298C2×C8C22×D6111yescharacteristic
299C2×C8C22×D6111yescharacteristic
300C4⋊C4—611no—
301C4⋊C4—611no—
302C4⋊C4—1221no—
303C4⋊C4—1221no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4D24411yescharacteristic
310C22⋊C4—1221no—
311C22⋊C4—1221no—
312C22⋊C4—1221no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4D24411yescharacteristic
317C22⋊C4D24411yescharacteristic
318C42—1221no—
319C42—1221no—
320C42C22×D6111yescharacteristic
321C23—1221no—
322C23C2×D24411yescharacteristic
323C23C2×D24411yescharacteristic
324Q8—612no—
325Q8—612no—
326Q8—1221no—
327Q8—1221no—
328Q8—1221no—
329Q8—1221no—
330Q8—1221no—
331Q8—1221no—
332Q8—1221no—
333Q8—1221no—
334Q8—2442no—
335Q8—2442no—
336Q8—2442no—
337D4—22no—
338D4—1221no—
339D4—1221no—
340D4—2442no—
341D4—2442no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4C2×D24411yescharacteristic
358C2×C4C2×D24411yescharacteristic
359C2×C4C2×D24411yescharacteristic
360C2×C4C2×D24411yescharacteristic
361C2×C4C23×D6111yescharacteristic
362C8—21no—
363C8—21no—
364C8—21no—
365C8D4×D6112yes—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—2441no—
372C22—2441no—
373C22—2441no—
374C22#1451981012yescomplemented
375C22C22×D24411yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—1222no—
381C4—1222no—
382C4—2441no—
383C4—2441no—
384C4—2441no—
385C4—2441no—
386C4—2441no—
387C4C2×D4×D6111yescharacteristic
388C4#1451982311yescharacteristic
389C2—22no—
390C2—41no—
391C2—4881no—
392C2D4×D24411yescharacteristic
393C2C2×#1451981011yescharacteristic
394C2#1684057911yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#435C2
socleC22×C61C22×D4
hypercenter#435D61
hypocenterC61#3270
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#14519810C2semidirect
2. C22×Dic244C2semidirect
3. D4×Dic122C2semidirect
5. #16840156C2semidirect
6. #16840020C2semidirect
7. #16839991C2semidirect
8. #16839985C2semidirect
9. #16839973C2semidirect
10. #16839926C2semidirect
11. #16839920C2semidirect
12. #16839920C2semidirect
13. #16839903C2semidirect
14. #16839870C2semidirect
15. C61×#435C2semidirect
119. Dic244D4semidirect
173. C22×C61#137semidirect
212. #435D61semidirect
213. C61#3270semidirect
374. C22#14519810semidirect