Finite Group Databasebeta

← #21455102

Subgroups — #21455102

Order 7808.

732 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519824C211yesmaximal, characteristic, complemented
2C2×#14519801C211yesmaximal, characteristic, complemented
3C2×SD16×D61C211yesmaximal, characteristic, complemented
4#16840328C211yesmaximal, characteristic, complemented
5#16839908C211yesmaximal, characteristic, complemented
6#16839907C211yesmaximal, characteristic, complemented
7#16839904C211yesmaximal, characteristic, complemented
8#16839903C211yesmaximal, characteristic, complemented
9#16839902C211yesmaximal, characteristic, complemented
10#16839900C211yesmaximal, characteristic, complemented
11#16839899C211yesmaximal, characteristic, complemented
12#16839769C211yesmaximal, characteristic, complemented
13#16839755C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic, complemented
15C61×#449C211yesmaximal, characteristic, complemented
16#14519824—24no—
17#14519824—24no—
18C2×#11758222—21no—
19C2×#11758222C2211yescharacteristic
20C2×#11758224—21no—
21C2×#11758224—21no—
22C2×#11758224C2211yescharacteristic
23C2×#11758224C2211yescharacteristic, complemented
24C22×Dic122—21no—
25C22×Dic122C2211yescharacteristic, complemented
26C2×Q8×D61C2211yescharacteristic
27C2×Q8×D61C2211yescharacteristic, complemented
28C2×D4×D61C2211yescharacteristic
29#14519801—24no—
30C2×#11758190C2211yescharacteristic
31C2×#11758190C2211yescharacteristic
32C2×#11758200C2211yescharacteristic
33C2×#11758200C2211yescharacteristic
34C2×#11758201C2211yescharacteristic
35SD16×D61—24no—
36C2×#11758199C2211yescharacteristic
37C2×#11758189C2211yescharacteristic
38C2×C8×D61C2211yescharacteristic
39#14519773—21no—
40#14519763—21no—
41#14519752C2211yescharacteristic
42#14519751C2211yescharacteristic
43#14519748C2211yescharacteristic
44#14519747—21no—
45#14519745—21no—
46#14519735C2211yescharacteristic
47#14519702C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519701C2211yescharacteristic, complemented
50#14519700C2211yescharacteristic, complemented
51#14519700C2211yescharacteristic, complemented
52#14519698C2211yescharacteristic, complemented
53C22⋊#92418C2211yescharacteristic, complemented
54#14519689C2211yescharacteristic, complemented
55#14519689C2211yescharacteristic, complemented
56C2×#41×C61C2211yescharacteristic, complemented
57C2×SD16×C61C2211yescharacteristic
58C2×D8×C61C2211yescharacteristic
59#121×C61C2211yescharacteristic
60#103×C61C2211yescharacteristic, complemented
61#102×C61C2211yescharacteristic, complemented
62C22⋊C8×C61C2211yescharacteristic, complemented
63C23×D61—21no—
64#41×C61—22no—
65#41×C61—22no—
66C2×Q8×C61C2311yescharacteristic
67C2×D4×C61—21no—
68C2×D4×C61—21no—
69C2×D4×C61C2311yescharacteristic
70C2×D4×C61C2311yescharacteristic
71C22×C4×C61—21no—
72C22×C4×C61C2311yescharacteristic
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76C2×C22⋊D61—21no—
77C2×C22⋊D61—21no—
78C2×C22⋊D61D411yescharacteristic
79C2×C22⋊D61D411yescharacteristic
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83Q8×D61—22no—
84Q8×D61—22no—
85Q8×D61—22no—
86Q8×D61D414yescomplemented
87#11758224—28no—
88#11758224—28no—
89#11758224—22no—
90#11758224—22no—
91#11758224—22no—
92#11758224D414yescomplemented
93D4×D61—22no—
94D4×D61—22no—
95#11758222—28no—
96#11758222—22no—
97#11758222—22no—
98C2×D244—21no—
99C2×D244D411yescharacteristic
100C2×D244C2311yescharacteristic
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61C2311yescharacteristic
104C2×C4×D61C2311yescharacteristic
105C2×Dic122—28no—
106C2×Dic122—21no—
107C2×Dic122—21no—
108C2×Dic122—21no—
109C2×Dic122—22no—
110C2×Dic122—22no—
111C2×Dic122D411yescharacteristic
112C2×Dic122C2311yescharacteristic
113C2×Dic122C2311yescharacteristic
114SD16×C61—22no—
115D8×C61—22no—
116C2×C8×C61C2311yescharacteristic
117C2×C8×C61C2311yescharacteristic
118C4⋊C4×C61C2311yescharacteristic
119C22⋊C4×C61—21no—
120C22⋊Dic61—21no—
121#11758201—22no—
122#11758200—22no—
123#11758200—22no—
124#11758199—22no—
125#11758198—21no—
126#11758198—21no—
127#11758198—21no—
128C4⋊Dic61C2311yescharacteristic
129C4×Dic61—21no—
130C2×#92418C2311yescharacteristic
131C2×#92418C2311yescharacteristic
132#11758190—22no—
133#11758190—22no—
134#11758189—22no—
135C8×D61—22no—
136C23×C61—21no—
137C23×C61—21no—
138C23×C61C2×D411yescharacteristic
139C22×D61—21no—
140C22×D61—42no—
141C22×D61—81no—
142C22×D61—81no—
143C22×D61C2×D411yescharacteristic
144C22×D61C2×D411yescharacteristic
145Q8×C61—21no—
146Q8×C61C2×D412yes—
147D4×C61—24no—
148D4×C61—21no—
149D4×C61—21no—
150D4×C61—21no—
151D4×C61—81no—
152D4×C61C2×D412yes—
153C2×C4×C61—24no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61C2×D411yescharacteristic
159C2×C4×C61C2411yescharacteristic
160C22⋊D61—24no—
161C22⋊D61—22no—
162C22⋊D61—24no—
163C22⋊D61—22no—
164C22⋊D61—42no—
165C22⋊D61—81no—
166C22⋊D61—81no—
167C2×Dic61—24no—
168C2×Dic61—24no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—24no—
172C2×Dic61—21no—
173C2×Dic61C2×D411yescharacteristic
174C2×Dic61C2×D411yescharacteristic
175D244—22no—
176D244—21no—
177D244—21no—
178D244—81no—
179C4×D61—24no—
180C4×D61—24no—
181C4×D61—21no—
182C4×D61—21no—
183C4×D61C2×D412yes—
184C4×D61C2×D412yes—
185Dic122—24no—
186Dic122—24no—
187Dic122—21no—
188Dic122—21no—
189Dic122—22no—
190Dic122—24no—
191Dic122C2×D412yes—
192Dic122C2×D412yes—
193C8×C61—21no—
194C8×C61—21no—
195#92418—21no—
196#92418—21no—
197C22×C61—21no—
198C22×C61—22no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61—41no—
204C22×C61—41no—
205C22×C61—41no—
206C22×C61C22×D411yescharacteristic
207C2×D61—21no—
208C2×D61—21no—
209C2×D61—21no—
210C2×D61—21no—
211C2×D61—21no—
212C2×D61—41no—
213C2×D61—41no—
214C2×D61—41no—
215C2×D61—84no—
216C2×D61#12012yes—
217C4×C61—21no—
218C4×C61—22no—
219C4×C61—41no—
220C4×C61C22×D411yescharacteristic
221C4×C61C22×D411yescharacteristic
222Dic61—21no—
223Dic61—22no—
224Dic61—22no—
225Dic61—41no—
226Dic61#12012yes—
227#3010—611nomaximal, Sylow
228C2×C61—41no—
229C2×C61—42no—
230C2×C61—81no—
231C2×C61C2×#12011yescharacteristic
232C2×C61#57711yescharacteristic
233C2×C61#57711yescharacteristic
234D61—22no—
235D61—41no—
236D61—81no—
237C2×2−1+4—611no—
238C2×AGL(1,ℤ/8)—611no—
239C22×SD16—611no—
240#535—611no—
241#449—611no—
242#449—611no—
243#449—611no—
244#449D6111yescharacteristic, complemented
245#448—611no—
246#448—611no—
247#448—611no—
248#448—611no—
249#419—611no—
250#416—611no—
251#408—611no—
252C61#301011yescharacteristic, complemented, Sylow
2532−1+4—1224no—
2542−1+4—1224no—
255C2×#41—611no—
256C2×#41—611no—
257C2×#41—611no—
258C2×#41—1221no—
259C2×#41—1221no—
260C2×#41—1221no—
261C2×#41C2×D6111yescharacteristic, complemented
262C22×Q8—611no—
263C22×Q8—611no—
264C22×Q8—611no—
265C22×Q8—1221no—
266C22×D4—611no—
267AGL(1,ℤ/8)—1224no—
268C2×SD16—611no—
269C2×SD16—611no—
270C2×SD16—611no—
271C2×SD16—611no—
272C2×SD16—611no—
273C2×SD16—1224no—
274C2×SD16C2×D6111yescharacteristic
275C2×D8—611no—
276C2×D8C2×D6111yescharacteristic
277C2×M16—611no—
278C22×C8—611no—
279#127—1221no—
280#124—1221no—
281#121—611no—
282#121—611no—
283#121—611no—
284#121C2×D6111yescharacteristic
285#120—1221no—
286#120—1221no—
287#117—611no—
288#103—611no—
289#103—611no—
290#103—611no—
291#103—611no—
292#103—611no—
293#103C2×D6111yescharacteristic, complemented
294#102—611no—
295#102C2×D6111yescharacteristic, complemented
296C22⋊C8—611no—
297C22⋊C8—611no—
298C22⋊C8—611no—
299C22⋊C8C2×D6111yescharacteristic, complemented
300C24—1221no—
301#41—22no—
302#41—22no—
303#41—614no—
304#41—1222no—
305#41—1222no—
306#41—1228no—
307#41—1222no—
308#41—1222no—
309#41—1228no—
310#41—1228no—
311#41—1222no—
312C2×Q8—611no—
313C2×Q8—614no—
314C2×Q8—611no—
315C2×Q8—611no—
316C2×Q8—1221no—
317C2×Q8—1221no—
318C2×Q8—1222no—
319C2×Q8—1222no—
320C2×Q8—1228no—
321C2×Q8—1222no—
322C2×Q8—1222no—
323C2×Q8—1222no—
324C2×Q8—1221no—
325C2×Q8C22×D6111yescharacteristic
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—611no—
329C2×D4—611no—
330C2×D4—611no—
331C2×D4—611no—
332C2×D4—1221no—
333C2×D4—1222no—
334C2×D4—1222no—
335C2×D4—1221no—
336C2×D4—1221no—
337C2×D4—1221no—
338C2×D4—1221no—
339C2×D4—1221no—
340C2×D4C22×D6111yescharacteristic
341C2×D4C22×D6111yescharacteristic
342C22×C4—21no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—1221no—
346C22×C4—1221no—
347C22×C4—1221no—
348C22×C4—1221no—
349C22×C4—1221no—
350C22×C4C22×D6111yescharacteristic
351SD16—22no—
352SD16—1222no—
353SD16—1222no—
354SD16—1222no—
355SD16—1222no—
356SD16—1222no—
357D8—22no—
358D8—1222no—
359M16—1222no—
360C2×C8—611no—
361C2×C8—611no—
362C2×C8—1222no—
363C2×C8C22×D6111yescharacteristic
364C2×C8C22×D6111yescharacteristic
365C4⋊C4—611no—
366C4⋊C4C22×D6111yescharacteristic
367C22⋊C4—21no—
368C22⋊C4—1221no—
369C22⋊C4—1221no—
370C22⋊C4—1221no—
371C22⋊C4—1221no—
372C42—1221no—
373C23—21no—
374C23—21no—
375C23—611no—
376C23—611no—
377C23—1221no—
378C23—4881no—
379C23—4881no—
380C23—2442no—
381C23D4×D6111yescharacteristic
382Q8—21no—
383Q8—612no—
384Q8—612no—
385Q8—1222no—
386Q8—1224no—
387Q8—1224no—
388Q8—1224no—
389Q8—1221no—
390Q8—1221no—
391Q8D4×D6112yes—
392D4—24no—
393D4—21no—
394D4—21no—
395D4—21no—
396D4—81no—
397D4—1222no—
398D4—1222no—
399D4—1222no—
400D4—1224no—
401D4—1224no—
402D4—1221no—
403D4—1221no—
404D4—4881no—
405D4—4881no—
406D4—4881no—
407D4—2442no—
408D4D4×D6112yes—
409C2×C4—24no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—611no—
415C2×C4—612no—
416C2×C4—612no—
417C2×C4—611no—
418C2×C4—1224no—
419C2×C4—1224no—
420C2×C4—1224no—
421C2×C4—1224no—
422C2×C4—1224no—
423C2×C4—1221no—
424C2×C4—1221no—
425C2×C4—1221no—
426C2×C4—1221no—
427C2×C4—1221no—
428C2×C4D4×D6111yescharacteristic
429C2×C4C23×D6111yescharacteristic
430C8—21no—
431C8—21no—
432C8—1221no—
433C8—1221no—
434C22—21no—
435C22—22no—
436C22—21no—
437C22—21no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—612no—
444C22—1221no—
445C22—1221no—
446C22—1221no—
447C22—1221no—
448C22—1221no—
449C22—4884no—
450C22—2441no—
451C22—2441no—
452C22—2441no—
453C22C2×D4×D6111yescharacteristic
454C4—21no—
455C4—22no—
456C4—41no—
457C4—612no—
458C4—1221no—
459C4—1222no—
460C4—1222no—
461C4—2441no—
462C4C2×D4×D6111yescharacteristic
463C4C2×D4×D6111yescharacteristic
464C2—41no—
465C2—42no—
466C2—81no—
467C2—1222no—
468C2—4881no—
469C2—2441no—
470C2#120×D6111yescharacteristic
471C2#1684056911yescharacteristic
472C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#449C2
socleC22×C61C22×D4
hypercenter#449D61
hypocenterC61#3010
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#14519824C2semidirect
2. C2×#14519801C2semidirect
3. C2×SD16×D61C2semidirect
4. #16840328C2semidirect
5. #16839908C2semidirect
6. #16839907C2semidirect
7. #16839904C2semidirect
8. #16839903C2semidirect
9. #16839902C2semidirect
10. #16839900C2semidirect
11. #16839899C2semidirect
12. #16839769C2semidirect
13. #16839755C2semidirect
14. #16839727C2semidirect
15. C61×#449C2semidirect
23. C2×#11758224C22semidirect
25. C22×Dic122C22semidirect
27. C2×Q8×D61C22semidirect
47. #14519702C22semidirect
48. #14519702C22semidirect
49. #14519701C22semidirect
50. #14519700C22semidirect
51. #14519700C22semidirect
52. #14519698C22semidirect
53. C22⋊#92418C22semidirect
54. #14519689C22semidirect
55. #14519689C22semidirect
56. C2×#41×C61C22semidirect
60. #103×C61C22semidirect
61. #102×C61C22semidirect
62. C22⋊C8×C61C22semidirect
86. Q8×D61D4semidirect
92. #11758224D4semidirect
244. #449D61semidirect
252. C61#3010semidirect
261. C2×#41C2×D61semidirect
293. #103C2×D61semidirect
295. #102C2×D61semidirect
299. C22⋊C8C2×D61semidirect