Finite Group Databasebeta

← #21457334

Subgroups — #21457334

Order 7808.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519810C211yesmaximal, characteristic, complemented
2C22×#11758190C211yesmaximal, characteristic, complemented
3D4×Dic122C211yesmaximal, characteristic, complemented
4#16840408C211yesmaximal, characteristic
5#16840156C211yesmaximal, characteristic, complemented
6#16840008C211yesmaximal, characteristic, complemented
7#16840003C211yesmaximal, characteristic, complemented
8#16839985C211yesmaximal, characteristic, complemented
9#16839968C211yesmaximal, characteristic, complemented
10#16839926C211yesmaximal, characteristic, complemented
11#16839920C211yesmaximal, characteristic, complemented
12#16839915C211yesmaximal, characteristic, complemented
13#16839903C211yesmaximal, characteristic, complemented
14#16839864C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18C22×Dic122C2211yescharacteristic, complemented
19C22×D244C2211yescharacteristic
20#14519810—24no—
21C2×Dic244C2211yescharacteristic, complemented
22C2×Dic244C2211yescharacteristic, complemented
23C2×Dic244C2211yescharacteristic, complemented
24C2×#11758190—24no—
25C2×#11758190C2211yescharacteristic
26C2×#11758190C2211yescharacteristic
27C2×#11758190C2211yescharacteristic
28C2×#11758190C2211yescharacteristic
29C2×#11758190C2211yescharacteristic
30C2×#11758190C2211yescharacteristic
31#14519777C2211yescharacteristic, complemented
32#14519776—21no—
33#14519765C2211yescharacteristic
34#14519762—21no—
35#14519756C2211yescharacteristic
36#14519756C2211yescharacteristic
37#14519756C2211yescharacteristic, complemented
38#14519754—21no—
39#14519754—21no—
40#14519751C2211yescharacteristic
41#14519750—21no—
42#14519745—21no—
43C4×Dic122C2211yescharacteristic, complemented
44C4×D244C2211yescharacteristic
45D4×Dic61—21no—
46C22⋊C4×D61—21no—
47#14519711C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519702C2211yescharacteristic, complemented
50#14519702C2211yescharacteristic, complemented
51#14519702C2211yescharacteristic, complemented
52#14519699C2211yescharacteristic
53#14519699C2211yescharacteristic
54C2×M16×C61C2211yescharacteristic, complemented
55C22×C8×C61C2211yescharacteristic
56C4×D4×C61C2211yescharacteristic
57C4⋊C8×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic
59C22⋊C8×C61C2211yescharacteristic, complemented
60#97×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C2×D4×C61D411yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69#11758222—22no—
70#11758222—41no—
71C2×D244—22no—
72C2×D244—21no—
73C2×D244—41no—
74C2×D244C2311yescharacteristic
75C2×D244C2311yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×Dic122—22no—
79C2×Dic122—22no—
80C2×Dic122—21no—
81C2×Dic122—21no—
82C2×Dic122—41no—
83C2×Dic122—41no—
84C2×Dic122C2311yescharacteristic
85C2×Dic122C2311yescharacteristic
86C2×Dic122C2311yescharacteristic
87C2×Dic122C2311yescharacteristic
88M16×C61—22no—
89C2×C8×C61—22no—
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C2×C8×C61C2311yescharacteristic
93C2×C8×C61C2311yescharacteristic
94C4⋊C4×C61D411yescharacteristic
95C22⋊C4×C61D411yescharacteristic
96C22⋊C4×C61D411yescharacteristic
97C42×C61C2311yescharacteristic
98C22⋊Dic61—21no—
99C22⋊Dic61—21no—
100C22⋊Dic61—21no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61C2311yescharacteristic
108C4⋊Dic61C2311yescharacteristic
109#11758196—21no—
110#11758196—21no—
111#11758196—21no—
112#11758196—21no—
113C4×Dic61—21no—
114Dic244—22no—
115Dic244—22no—
116Dic244—41no—
117#11758190—22no—
118#11758190—22no—
119#11758190—22no—
120#11758190—22no—
121#11758190—41no—
122#11758190D414yescomplemented
123C23×C61C2×D411yescharacteristic
124C23×C61C2×D411yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—81no—
130D4×C61—22no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2×D411yescharacteristic
137C2×C4×C61C2×D411yescharacteristic
138C2×C4×C61C2×D411yescharacteristic
139C2×C4×C61C2411yescharacteristic
140C22⋊D61—42no—
141C22⋊D61—81no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150D244—21no—
151D244—21no—
152D244—21no—
153D244—42no—
154D244C2×D412yes—
155C4×D61—42no—
156C4×D61—81no—
157Dic122—21no—
158Dic122—21no—
159Dic122—21no—
160Dic122—21no—
161Dic122—21no—
162Dic122—21no—
163Dic122—21no—
164Dic122—42no—
165Dic122—42no—
166Dic122C2×D412yes—
167C8×C61—21no—
168C8×C61—21no—
169C8×C61—21no—
170C8×C61C2×D412yes—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61#13712yescomplemented
177C22×C61C22×D411yescharacteristic
178C2×D61—22no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—84no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61C22×D411yescharacteristic
190C4×C61H(5,𝔽2)11yescharacteristic
191Dic61—22no—
192Dic61—41no—
193Dic61—41no—
194Dic61—41no—
195Dic61—41no—
196Dic61—41no—
197#3266—611nomaximal, Sylow
198C2×C61—22no—
199C2×C61—41no—
200C2×C61D4211yescharacteristic
201C2×C61C2×#13711yescharacteristic
202C2×C61#57711yescharacteristic
203D61—42no—
204D61—81no—
205C2×#137—611no—
206C22×SD16—611no—
207D4×Q8—611no—
208#546—611no—
209#497—611no—
210#468—611no—
211#467—611no—
212#464—611no—
213#461—611no—
214#452—611no—
215#451—611no—
216#450—611no—
217#448—611no—
218#440—611no—
219#435D6111yescharacteristic, complemented
220C61#326611yescharacteristic, complemented, Sylow
221C2×#41—611no—
222C22×Q8—611no—
223C22×Q8—611no—
224C22×D4—611no—
225#137—1224no—
226C2×Q16—611no—
227C2×Q16—611no—
228C2×Q16—611no—
229C2×SD16—611no—
230C2×SD16—611no—
231C2×SD16—611no—
232C2×SD16—611no—
233C2×SD16—611no—
234C2×SD16—611no—
235C2×SD16—1224no—
236C2×M16C2×D6111yescharacteristic, complemented
237C22×C8C2×D6111yescharacteristic
238C4⋊Q8—611no—
239C4⋊Q8—1221no—
240#124—611no—
241#123—1221no—
242C22⋊Q8—611no—
243C22⋊Q8—611no—
244C22⋊Q8—611no—
245C22⋊Q8—1221no—
246C22⋊Q8—1221no—
247#121—611no—
248#121—1221no—
249#120—1221no—
250C4×Q8—611no—
251C4×D4—611no—
252C4×D4—1221no—
253C4×D4C2×D6111yescharacteristic
254C2×C22⋊C4—1221no—
255#107—611no—
256C4⋊C8C2×D6111yescharacteristic, complemented
257#103—611no—
258#103—611no—
259#103—611no—
260#103—611no—
261#102—611no—
262#102—611no—
263C22⋊C8C2×D6111yescharacteristic
264C22⋊C8C2×D6111yescharacteristic, complemented
265#97C2×D6111yescharacteristic, complemented
266C24—1221no—
267#41—1222no—
268#41—2441no—
269C2×Q8—611no—
270C2×Q8—611no—
271C2×Q8—611no—
272C2×Q8—611no—
273C2×Q8—1222no—
274C2×Q8—1222no—
275C2×Q8—1221no—
276C2×Q8—1221no—
277C2×Q8—2441no—
278C2×Q8—2441no—
279C2×D4—611no—
280C2×D4—611no—
281C2×D4—1222no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—2441no—
286C2×D4D24411yescharacteristic
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4C22×D6111yescharacteristic
292C22×C4C22×D6111yescharacteristic
293Q16—1222no—
294Q16—1222no—
295Q16—2441no—
296SD16—614no—
297SD16—1222no—
298SD16—1222no—
299SD16—1222no—
300SD16—1222no—
301SD16—2441no—
302M16—22no—
303C2×C8—22no—
304C2×C8C22×D6111yescharacteristic
305C2×C8C22×D6111yescharacteristic
306C2×C8C22×D6111yescharacteristic
307C2×C8C22×D6111yescharacteristic
308C4⋊C4—611no—
309C4⋊C4—611no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4—1221no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C4⋊C4D24411yescharacteristic
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4D24411yescharacteristic
325C22⋊C4D24411yescharacteristic
326C42—1221no—
327C42C22×D6111yescharacteristic
328C23—1221no—
329C23—1221no—
330C23—4881no—
331C23—2442no—
332C23—2442no—
333C23C2×D24411yescharacteristic
334C23C2×D24411yescharacteristic
335Q8—612no—
336Q8—1221no—
337Q8—1221no—
338Q8—1221no—
339Q8—1221no—
340Q8—1221no—
341Q8—1221no—
342Q8—1221no—
343Q8—2442no—
344Q8—2442no—
345D4—22no—
346D4—612no—
347D4—1221no—
348D4—1221no—
349D4—1221no—
350D4—4881no—
351D4—2442no—
352D4—2442no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—4881no—
364C2×C4—2442no—
365C2×C4—2442no—
366C2×C4—2442no—
367C2×C4C2×D24411yescharacteristic
368C2×C4C2×D24411yescharacteristic
369C2×C4C2×D24411yescharacteristic
370C2×C4C2×D24411yescharacteristic
371C2×C4C23×D6111yescharacteristic
372C8—21no—
373C8—21no—
374C8—21no—
375C8D4×D6112yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—1222no—
382C22—4884no—
383C22—2441no—
384C22—2441no—
385C22—2441no—
386C22—2441no—
387C22—2441no—
388C22#1451981012yescomplemented
389C22C22×D24411yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—1222no—
395C4—2441no—
396C4—2441no—
397C4—2441no—
398C4—2441no—
399C4—2441no—
400C4C2×D4×D6111yescharacteristic
401C4#1451982311yescharacteristic
402C2—22no—
403C2—41no—
404C2—4881no—
405C2—2442no—
406C2D4×D24411yescharacteristic
407C2C2×#1451981011yescharacteristic
408C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#435C2
socleC22×C61C22×D4
hypercenter#435D61
hypocenterC61#3266
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×#11758190C2semidirect
3. D4×Dic122C2semidirect
5. #16840156C2semidirect
6. #16840008C2semidirect
7. #16840003C2semidirect
8. #16839985C2semidirect
9. #16839968C2semidirect
10. #16839926C2semidirect
11. #16839920C2semidirect
12. #16839915C2semidirect
13. #16839903C2semidirect
14. #16839864C2semidirect
15. C61×#435C2semidirect
18. C22×Dic122C22semidirect
21. C2×Dic244C22semidirect
22. C2×Dic244C22semidirect
23. C2×Dic244C22semidirect
31. #14519777C22semidirect
37. #14519756C22semidirect
43. C4×Dic122C22semidirect
47. #14519711C22semidirect
48. #14519702C22semidirect
49. #14519702C22semidirect
50. #14519702C22semidirect
51. #14519702C22semidirect
54. C2×M16×C61C22semidirect
57. C4⋊C8×C61C22semidirect
59. C22⋊C8×C61C22semidirect
60. #97×C61C22semidirect
122. #11758190D4semidirect
176. C22×C61#137semidirect
219. #435D61semidirect
220. C61#3266semidirect
236. C2×M16C2×D61semidirect
256. C4⋊C8C2×D61semidirect
264. C22⋊C8C2×D61semidirect
265. #97C2×D61semidirect
388. C22#14519810semidirect