Finite Group Databasebeta

← #21452377

Subgroups — #21452377

Order 7808.

680 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519762C211yesmaximal, characteristic, complemented
2C2×#14519747C211yesmaximal, characteristic
3#16839689C211yesmaximal, characteristic, complemented
4#16839688C211yesmaximal, characteristic, complemented
5#16839684C211yesmaximal, characteristic, complemented
6#16839679C211yesmaximal, characteristic, complemented
7#16839678C211yesmaximal, characteristic, complemented
8#16839663C211yesmaximal, characteristic, complemented
9#16839656C211yesmaximal, characteristic, complemented
10#16839652C211yesmaximal, characteristic, complemented
11#16839640C211yesmaximal, characteristic, complemented
12#16839638C211yesmaximal, characteristic, complemented
13#16839617C211yesmaximal, characteristic, complemented
14#16839617C211yesmaximal, characteristic, complemented
15C61×#396C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic, complemented
21#14519762—24no—
22#14519747—24no—
23C2×C4⋊Dic61C2211yescharacteristic, complemented
24C2×#11758196C2211yescharacteristic, complemented
25C2×C22⋊Dic61C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic, complemented
38C2×#11758198C2211yescharacteristic, complemented
39C2×#11758198C2211yescharacteristic, complemented
40C2×C4×Dic61C2211yescharacteristic, complemented
41#14519684C2211yescharacteristic, complemented
42#14519684C2211yescharacteristic, complemented
43#14519684C2211yescharacteristic, complemented
44#14519684C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46C2×C4⋊C4×C61C2211yescharacteristic, complemented
47C2×C4⋊C4×C61C2211yescharacteristic, complemented
48C2×C4⋊C4×C61C2211yescharacteristic, complemented
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic, complemented
53C24×C61C2311yescharacteristic
54C23×D61—22no—
55C23×D61—22no—
56C23×D61—22no—
57C23×D61—41no—
58C23×D61—41no—
59C23×D61—41no—
60C23×D61—41no—
61C23×D61C2311yescharacteristic
62C23×D61C2311yescharacteristic
63C23×D61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C2×C22⋊D61—22no—
71C2×C22⋊D61—22no—
72C2×C22⋊D61—41no—
73C22×Dic61C2311yescharacteristic
74C22×Dic61C2311yescharacteristic
75C22×Dic61C2311yescharacteristic
76C22×Dic61C2311yescharacteristic
77C22×Dic61C2311yescharacteristic
78C2×D244—22no—
79C2×D244—22no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244D414yes—
84C2×C4×D61—22no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C4⋊C4×C61—22no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C22⋊C4×C61—22no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊Dic61—22no—
94C22⋊Dic61—41no—
95#11758198—22no—
96#11758198—22no—
97#11758198—22no—
98#11758198—22no—
99#11758198—22no—
100#11758198—22no—
101#11758198—41no—
102#11758198—41no—
103#11758198—41no—
104#11758198—41no—
105#11758198—41no—
106#11758198—41no—
107#11758198—41no—
108C4⋊Dic61—41no—
109#11758196—22no—
110C4×Dic61—41no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61#4112yes—
118C23×C61C2411yescharacteristic
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—44no—
138C22×D61—44no—
139C22×D61—44no—
140C22×D61—44no—
141C22×D61—44no—
142C22×D61—44no—
143C22×D61—44no—
144C22×D61C2×D412yes—
145C22×D61C2×D412yes—
146C22×D61#4112yes—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61C2×D412yes—
165C22⋊D61—44no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181D244—44no—
182D244—44no—
183C4×D61—44no—
184C22×C61—22no—
185C22×C61—22no—
186C22×C61—22no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61C22×D411yescharacteristic
192C22×C61C2×#4111yescharacteristic
193C22×C61C2×#4111yescharacteristic
194C22×C61H(5,𝔽2)11yescharacteristic
195C22×C61H(5,𝔽2)11yescharacteristic
196C22×C61H(5,𝔽2)11yescharacteristic
197C22×C61H(5,𝔽2)11yescharacteristic
198C2×D61—22no—
199C2×D61—22no—
200C2×D61—22no—
201C2×D61—22no—
202C2×D61—22no—
203C2×D61—22no—
204C2×D61—22no—
205C2×D61—22no—
206C2×D61—22no—
207C2×D61—416no—
208C2×D61—41no—
209C2×D61—41no—
210C2×D61—41no—
211C2×D61—41no—
212C2×D61—41no—
213C2×D61—41no—
214C2×D61—41no—
215C2×D61—41no—
216C2×D61—41no—
217C2×D61—41no—
218C2×D61—41no—
219C2×D61—41no—
220C4×C61—22no—
221C4×C61—41no—
222C4×C61—41no—
223C4×C61—41no—
224C4×C61—41no—
225C4×C61—41no—
226Dic61—41no—
227Dic61—41no—
228Dic61—41no—
229Dic61—41no—
230Dic61—41no—
231#2697—611nomaximal, Sylow
232C2×C61—42no—
233C2×C61#53411yescharacteristic
234C2×C61#53811yescharacteristic
235C2×C61#53811yescharacteristic
236C2×C61#54611yescharacteristic
237C2×C61#54611yescharacteristic
238C2×C61#55111yescharacteristic
239C2×C61#56011yescharacteristic
240D61—42no—
241D61—42no—
242D61—42no—
243C2×#123—611no—
244C2×#120—611no—
245#397—611no—
246#397—611no—
247#396—611no—
248#396D6111yescharacteristic, complemented
249#394—611no—
250#394—611no—
251#390—611no—
252#388—611no—
253#388—611no—
254#386—611no—
255#386—611no—
256#379—611no—
257#379—611no—
258C61#269711yescharacteristic, complemented, Sylow
259C25—611no—
260C22×D4—611no—
261C22×D4—611no—
262C22×D4—611no—
263C23×C4—611no—
264#123—1224no—
265#120—1224no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—611no—
268C2×C4⋊C4C2×D6111yescharacteristic, complemented
269C2×C4⋊C4C2×D6111yescharacteristic, complemented
270C2×C4⋊C4C2×D6111yescharacteristic, complemented
271C2×C22⋊C4—611no—
272C2×C22⋊C4—611no—
273C2×C22⋊C4—611no—
274C2×C22⋊C4—611no—
275C2×C22⋊C4—611no—
276C2×C22⋊C4—611no—
277C2×C22⋊C4—611no—
278C2×C22⋊C4—611no—
279C2×C22⋊C4—611no—
280C2×C22⋊C4—611no—
281C2×C22⋊C4—611no—
282C2×C22⋊C4—611no—
283C2×C22⋊C4—611no—
284C2×C22⋊C4—611no—
285C2×C22⋊C4—611no—
286C2×C22⋊C4C2×D6111yescharacteristic
287C2×C22⋊C4C2×D6111yescharacteristic
288C2×C22⋊C4C2×D6111yescharacteristic
289C2×C42—611no—
290#95—611no—
291#95—611no—
292#95—611no—
293#95—611no—
294#95—611no—
295#95C2×D6111yescharacteristic, complemented
296C24—611no—
297C24—611no—
298C24—611no—
299C24—1222no—
300C24—1222no—
301C24—1222no—
302C24—2441no—
303C24—2441no—
304C24—2441no—
305C24—2441no—
306C24C22×D6111yescharacteristic
307C2×D4—614no—
308C2×D4—1222no—
309C2×D4—1222no—
310C2×D4—1222no—
311C2×D4—1222no—
312C2×D4—2441no—
313C2×D4—2441no—
314C2×D4—2441no—
315C2×D4—2441no—
316C22×C4—611no—
317C22×C4—611no—
318C22×C4—611no—
319C22×C4—611no—
320C22×C4—611no—
321C22×C4—1222no—
322C22×C4—2441no—
323C22×C4—2441no—
324C22×C4C22×D6111yescharacteristic
325C22×C4C22×D6111yescharacteristic
326C22×C4C22×D6111yescharacteristic
327C22×C4C22×D6111yescharacteristic
328C22×C4C22×D6111yescharacteristic
329C22×C4C22×D6111yescharacteristic
330C4⋊C4—22no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—1222no—
334C4⋊C4—2441no—
335C22⋊C4—22no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—1222no—
339C22⋊C4—1222no—
340C22⋊C4—1222no—
341C22⋊C4—1222no—
342C22⋊C4—1222no—
343C22⋊C4—1222no—
344C22⋊C4—1222no—
345C22⋊C4—2441no—
346C22⋊C4—2441no—
347C22⋊C4—2441no—
348C22⋊C4—2441no—
349C22⋊C4—2441no—
350C22⋊C4—2441no—
351C22⋊C4—2441no—
352C22⋊C4—2441no—
353C42—2441no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—612no—
361C23—612no—
362C23—612no—
363C23—1221no—
364C23—1221no—
365C23—1221no—
366C23—1221no—
367C23—1221no—
368C23—1221no—
369C23—1221no—
370C23—1221no—
371C23—1221no—
372C23—1221no—
373C23—1221no—
374C23—1221no—
375C23—1221no—
376C23—1221no—
377C23—1221no—
378C23—1221no—
379C23—1221no—
380C23—1221no—
381C23—2444no—
382C23—2444no—
383C23—2444no—
384C23—2444no—
385C23—2444no—
386C23—2444no—
387C23—2444no—
388C23#1175822612yes—
389C23C23×D6111yescharacteristic
390D4—2444no—
391D4—2444no—
392D4—2444no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—1221no—
414C2×C4—1221no—
415C2×C4—1221no—
416C2×C4—1221no—
417C2×C4—1221no—
418C2×C4—1221no—
419C2×C4—1221no—
420C2×C4—1221no—
421C2×C4—1221no—
422C2×C4—1221no—
423C2×C4—1221no—
424C2×C4—1221no—
425C2×C4—2444no—
426C2×C4D4×D6112yes—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—1222no—
435C22—1222no—
436C22—1222no—
437C22—1222no—
438C22—1222no—
439C22—1222no—
440C22—1222no—
441C22—1222no—
442C22—1222no—
443C22—24416no—
444C22—2441no—
445C22—2441no—
446C22—2441no—
447C22—2441no—
448C22—2441no—
449C22—2441no—
450C22—2441no—
451C22—2441no—
452C22—2441no—
453C22—2441no—
454C22—2441no—
455C22—2441no—
456C22C2×D4×D6111yescharacteristic
457C22#41×D6111yescharacteristic
458C22C2×#1175822611yescharacteristic
459C22#1451982211yescharacteristic
460C22#1451982211yescharacteristic
461C22#1451982311yescharacteristic
462C22#1451982311yescharacteristic
463C4—22no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—2441no—
470C4—2441no—
471C4—2441no—
472C4—2441no—
473C4—2441no—
474C2—42no—
475C2—2442no—
476C2—2442no—
477C2—2442no—
478C2#1684032011yescharacteristic
479C2#1684035111yescharacteristic
480C2#1684035211yescharacteristic
481C2#1684040311yescharacteristic
482C2#1684040911yescharacteristic
483C2#1684043911yescharacteristic
484C2#1684050011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#396C2
hypercenter#396D61
hypocenterC61#2697
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#14519762C2semidirect
3. #16839689C2semidirect
4. #16839688C2semidirect
5. #16839684C2semidirect
6. #16839679C2semidirect
7. #16839678C2semidirect
8. #16839663C2semidirect
9. #16839656C2semidirect
10. #16839652C2semidirect
11. #16839640C2semidirect
12. #16839638C2semidirect
13. #16839617C2semidirect
14. #16839617C2semidirect
15. C61×#396C2semidirect
20. C22×C4×D61C22semidirect
23. C2×C4⋊Dic61C22semidirect
24. C2×#11758196C22semidirect
37. C2×#11758198C22semidirect
38. C2×#11758198C22semidirect
39. C2×#11758198C22semidirect
40. C2×C4×Dic61C22semidirect
41. #14519684C22semidirect
42. #14519684C22semidirect
43. #14519684C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
46. C2×C4⋊C4×C61C22semidirect
47. C2×C4⋊C4×C61C22semidirect
48. C2×C4⋊C4×C61C22semidirect
52. #95×C61C22semidirect
248. #396D61semidirect
258. C61#2697semidirect
268. C2×C4⋊C4C2×D61semidirect
269. C2×C4⋊C4C2×D61semidirect
270. C2×C4⋊C4C2×D61semidirect
295. #95C2×D61semidirect