Finite Group Databasebeta

← #21448801

Subgroups — #21448801

Order 7808.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519747C211yesmaximal, characteristic
2C2×C4×D244C211yesmaximal, characteristic, complemented
3C2×#14519737C211yesmaximal, characteristic, complemented
4C22×#11758198C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D61C211yesmaximal, characteristic, complemented
6#16839664C211yesmaximal, characteristic, complemented
7#16839654C211yesmaximal, characteristic, complemented
8#16839653C211yesmaximal, characteristic, complemented
9#16839641C211yesmaximal, characteristic, complemented
10#16839640C211yesmaximal, characteristic, complemented
11#16839640C211yesmaximal, characteristic, complemented
12#16839637C211yesmaximal, characteristic, complemented
13#16839636C211yesmaximal, characteristic, complemented
14C4×#11758198C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C23×Dic61C2211yescharacteristic
21C22×C4×D61C2211yescharacteristic
22C22×C4×D61C2211yescharacteristic
23C22×C4×D61C2211yescharacteristic, complemented
24#14519747C418yescomplemented
25C4×D244—24no—
26#14519737—24no—
27C2×C4⋊Dic61C2211yescharacteristic, complemented
28C2×C4⋊Dic61C2211yescharacteristic, complemented
29C2×#11758196C2211yescharacteristic, complemented
30C2×C22⋊Dic61C2211yescharacteristic
31C2×#11758198—24no—
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic, complemented
41C2×#11758198C2211yescharacteristic, complemented
42C2×#11758198C2211yescharacteristic, complemented
43C22⋊C4×D61—24no—
44C2×C4×Dic61C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47#14519684C2211yescharacteristic, complemented
48#14519684C2211yescharacteristic, complemented
49C23×C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C42×C61C2211yescharacteristic, complemented
53C2×C42×C61C2211yescharacteristic, complemented
54#95×C61C2211yescharacteristic, complemented
55#95×C61C2211yescharacteristic, complemented
56C24×C61C2311yescharacteristic
57C23×D61—22no—
58C23×D61—22no—
59C23×D61—22no—
60C23×D61—22no—
61C23×D61—41no—
62C23×D61—41no—
63C23×D61C2×C414yescomplemented
64C23×D61C2311yescharacteristic
65C23×D61C2311yescharacteristic
66C23×D61C2311yescharacteristic
67C22×C4×C61—22no—
68C22×C4×C61—22no—
69C22×C4×C61—41no—
70C22×C4×C61C2311yescharacteristic
71C22×C4×C61C2311yescharacteristic
72C22×C4×C61C2311yescharacteristic
73C22×C4×C61C2311yescharacteristic
74C22×C4×C61C2311yescharacteristic
75C22×C4×C61C2311yescharacteristic
76C2×C22⋊D61—22no—
77C2×C22⋊D61—22no—
78C2×C22⋊D61C2×C414yescomplemented
79C22×Dic61—22no—
80C22×Dic61—22no—
81C22×Dic61—41no—
82C22×Dic61C2311yescharacteristic
83C22×Dic61C2311yescharacteristic
84C22×Dic61C2311yescharacteristic
85C22×Dic61C2311yescharacteristic
86C22×Dic61C2311yescharacteristic
87C2×D244—22no—
88C2×D244—22no—
89C2×D244—41no—
90C2×D244—41no—
91C2×D244C2×C414yescomplemented
92C2×D244C2×C414yescomplemented
93C2×C4×D61—22no—
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61—22no—
97C2×C4×D61—22no—
98C2×C4×D61—22no—
99C2×C4×D61—41no—
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C22⋊C4×C61C2×C414yescomplemented
103C22⋊C4×C61D414yescomplemented
104C42×C61—22no—
105C42×C61—41no—
106C22⋊Dic61—22no—
107#11758198—22no—
108#11758198—22no—
109#11758198—22no—
110#11758198—22no—
111#11758198—22no—
112#11758198—22no—
113#11758198—22no—
114#11758198—41no—
115#11758198C2×C414yescomplemented
116#11758198C2×C414yescomplemented
117#11758198D414yescomplemented
118C4⋊Dic61—22no—
119C4⋊Dic61—41no—
120#11758196—22no—
121C4×Dic61—22no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61C22×C412yes—
127C23×C61C2×D412yes—
128C23×C61#4112yes—
129C23×C61C2411yescharacteristic
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—28no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—28no—
148C22×D61—44no—
149C22×D61—44no—
150C22×D61—44no—
151C22×D61—44no—
152C22×D61—44no—
153C22×D61C22×C412yes—
154C22×D61C22×C412yes—
155C22×D61C22×C412yes—
156C22×D61C2×D412yes—
157C22×D61#4112yes—
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×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—44no—
172C2×C4×C61C22×C412yes—
173C2×C4×C61C22×C412yes—
174C2×C4×C61C2×D412yes—
175C2×C4×C61C2×D412yes—
176C2×C4×C61C2×D412yes—
177C22⋊D61—28no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—44no—
192C2×Dic61C22×C412yes—
193C2×Dic61C2×D412yes—
194D244—28no—
195D244—44no—
196C4×D61—44no—
197C4×D61—44no—
198C4×D61—44no—
199C22×C61—22no—
200C22×C61—22no—
201C22×C61—22no—
202C22×C61—22no—
203C22×C61—22no—
204C22×C61—22no—
205C22×C61C4×D414yescomplemented
206C22×C61C23×C411yescharacteristic
207C22×C61C22×D411yescharacteristic
208C22×C61C22×D411yescharacteristic
209C22×C61C2×#4111yescharacteristic
210C22×C61C2×#4111yescharacteristic
211C22×C61H(5,𝔽2)11yescharacteristic
212C22×C61H(5,𝔽2)11yescharacteristic
213C2×D61—22no—
214C2×D61—22no—
215C2×D61—22no—
216C2×D61—22no—
217C2×D61—22no—
218C2×D61—22no—
219C2×D61—22no—
220C2×D61—22no—
221C2×D61—22no—
222C2×D61—22no—
223C2×D61—22no—
224C2×D61—22no—
225C2×D61—416no—
226C2×D61—41no—
227C2×D61—41no—
228C2×D61—41no—
229C2×D61—41no—
230C2×D61—41no—
231C2×D61—41no—
232C2×D61—41no—
233C2×D61—41no—
234C2×D61C4×D414yescomplemented
235C4×C61—22no—
236C4×C61—22no—
237C4×C61—22no—
238C4×C61—22no—
239C4×C61—22no—
240C4×C61—41no—
241Dic61—22no—
242Dic61—22no—
243Dic61—41no—
244Dic61—41no—
245Dic61—41no—
246#2358—611nomaximal, Sylow
247C2×C61—24no—
248C2×C61C2×C4×D411yescharacteristic
249C2×C61C2×C4×D411yescharacteristic
250C2×C61#51811yescharacteristic
251C2×C61D4211yescharacteristic
252C2×C61#54611yescharacteristic
253C2×C61#54611yescharacteristic
254C2×C61#55111yescharacteristic
255D61—24no—
256D61—42no—
257D61—42no—
258C2×#120—611no—
259C2×C4×D4—611no—
260C2×C4×D4—611no—
261C22×C22⋊C4—611no—
262C22×C22⋊C4—611no—
263#390—611no—
264#388—611no—
265#388—611no—
266#386—611no—
267#386—611no—
268#386—611no—
269#385—611no—
270#385—611no—
271C4×C22⋊C4—611no—
272C4×C22⋊C4D6111yescharacteristic, complemented
273C61#235811yescharacteristic, complemented, Sylow
274C25—611no—
275C22×D4—611no—
276C22×D4—611no—
277C22×D4—611no—
278C23×C4—611no—
279C23×C4—611no—
280C23×C4—611no—
281C23×C4—611no—
282C23×C4C2×D6111yescharacteristic
283#120—618no—
284C4×D4—1224no—
285C4×D4—1224no—
286C2×C4⋊C4—611no—
287C2×C4⋊C4—611no—
288C2×C4⋊C4—611no—
289C2×C22⋊C4—611no—
290C2×C22⋊C4—611no—
291C2×C22⋊C4—611no—
292C2×C22⋊C4—611no—
293C2×C22⋊C4—611no—
294C2×C22⋊C4—611no—
295C2×C22⋊C4—611no—
296C2×C22⋊C4—611no—
297C2×C22⋊C4—611no—
298C2×C22⋊C4—611no—
299C2×C22⋊C4—611no—
300C2×C22⋊C4—611no—
301C2×C22⋊C4—1224no—
302C2×C22⋊C4—1224no—
303C2×C22⋊C4C2×D6111yescharacteristic
304C2×C22⋊C4C2×D6111yescharacteristic
305C2×C42—611no—
306C2×C42C2×D6111yescharacteristic, complemented
307C2×C42C2×D6111yescharacteristic, complemented
308#95—611no—
309#95—611no—
310#95—611no—
311#95—611no—
312#95C2×D6111yescharacteristic, complemented
313#95C2×D6111yescharacteristic, complemented
314C24—611no—
315C24—611no—
316C24—611no—
317C24—614no—
318C24—1222no—
319C24—1222no—
320C24—1222no—
321C24—1222no—
322C24—2441no—
323C24—2441no—
324C24C22×D6111yescharacteristic
325C2×D4—614no—
326C2×D4—614no—
327C2×D4—614no—
328C2×D4—1222no—
329C2×D4—1222no—
330C2×D4—1222no—
331C2×D4—1222no—
332C2×D4—2441no—
333C2×D4—2441no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—41no—
337C22×C4—611no—
338C22×C4—611no—
339C22×C4—611no—
340C22×C4—611no—
341C22×C4—611no—
342C22×C4—1222no—
343C22×C4—1222no—
344C22×C4—1222no—
345C22×C4—1222no—
346C22×C4—1222no—
347C22×C4—1222no—
348C22×C4—1222no—
349C22×C4—1222no—
350C22×C4—2441no—
351C22×C4—2441no—
352C22×C4—2441no—
353C22×C4—2441no—
354C22×C4C22×D6111yescharacteristic
355C22×C4C22×D6111yescharacteristic
356C22×C4C22×D6111yescharacteristic
357C22×C4C22×D6111yescharacteristic
358C22×C4C22×D6111yescharacteristic
359C22×C4C22×D6111yescharacteristic
360C4⋊C4—1222no—
361C4⋊C4—1222no—
362C4⋊C4—2441no—
363C22⋊C4—614no—
364C22⋊C4—614no—
365C22⋊C4—614no—
366C22⋊C4—1222no—
367C22⋊C4—1222no—
368C22⋊C4—1222no—
369C22⋊C4—1222no—
370C22⋊C4—1222no—
371C22⋊C4—1222no—
372C22⋊C4—1222no—
373C22⋊C4—1222no—
374C22⋊C4—2441no—
375C22⋊C4C4×D6114yescomplemented
376C22⋊C4D24414yescomplemented
377C42—22no—
378C42—41no—
379C42—1222no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—612no—
385C23—612no—
386C23—612no—
387C23—612no—
388C23—612no—
389C23—1228no—
390C23—1221no—
391C23—1221no—
392C23—1221no—
393C23—1221no—
394C23—1221no—
395C23—1221no—
396C23—1221no—
397C23—1221no—
398C23—1221no—
399C23—1221no—
400C23—1221no—
401C23—1221no—
402C23—1221no—
403C23—1221no—
404C23—1221no—
405C23—1221no—
406C23—1228no—
407C23—2444no—
408C23—2444no—
409C23—2444no—
410C23—2444no—
411C23—2444no—
412C23C2×C4×D6112yes—
413C23C2×D24412yes—
414C23#1175822212yes—
415C23C23×D6111yescharacteristic
416D4—1228no—
417D4—1228no—
418D4—2444no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—44no—
433C2×C4—612no—
434C2×C4—612no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—1221no—
442C2×C4—1221no—
443C2×C4—1221no—
444C2×C4—1221no—
445C2×C4—1221no—
446C2×C4—1221no—
447C2×C4—1221no—
448C2×C4—2444no—
449C2×C4—2444no—
450C2×C4—2444no—
451C2×C4—2444no—
452C2×C4C2×C4×D6112yes—
453C2×C4C2×C4×D6112yes—
454C2×C4C2×D24412yes—
455C2×C4C2×D24412yes—
456C2×C4D4×D6112yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—614no—
464C22—1222no—
465C22—1222no—
466C22—1222no—
467C22—1222no—
468C22—1222no—
469C22—1222no—
470C22—1222no—
471C22—1222no—
472C22—1222no—
473C22—1222no—
474C22—1222no—
475C22—1222no—
476C22—24416no—
477C22—2441no—
478C22—2441no—
479C22—2441no—
480C22—2441no—
481C22—2441no—
482C22—2441no—
483C22—2441no—
484C22—2441no—
485C22C4×D24414yescomplemented
486C22C22×C4×D6111yescharacteristic
487C22C2×D4×D6111yescharacteristic
488C22C22×D24411yescharacteristic
489C22#41×D6111yescharacteristic
490C22C2×#1175822211yescharacteristic
491C22#1451982211yescharacteristic
492C22#1451982311yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—22no—
498C4—41no—
499C4—1222no—
500C4—1222no—
501C4—2441no—
502C4—2441no—
503C4—2441no—
504C2—24no—
505C2—1224no—
506C2—2442no—
507C2—2442no—
508C2C4×D4×D6111yescharacteristic
509C2C2×C4×D24411yescharacteristic
510C2#1684023411yescharacteristic
511C2D4×D24411yescharacteristic
512C2#1684040211yescharacteristic
513C2#1684040711yescharacteristic
514C2#1684043611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC4×C22⋊C4×C61C2
socleC23×C61C24
hypercenterC4×C22⋊C4D61
hypocenterC61#2358
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D244C2semidirect
3. C2×#14519737C2semidirect
4. C22×#11758198C2semidirect
5. C2×C22⋊C4×D61C2semidirect
6. #16839664C2semidirect
7. #16839654C2semidirect
8. #16839653C2semidirect
9. #16839641C2semidirect
10. #16839640C2semidirect
11. #16839640C2semidirect
12. #16839637C2semidirect
13. #16839636C2semidirect
14. C4×#11758198C2semidirect
15. C4×C22⋊C4×C61C2semidirect
23. C22×C4×D61C22semidirect
24. #14519747C4semidirect
27. C2×C4⋊Dic61C22semidirect
28. C2×C4⋊Dic61C22semidirect
29. C2×#11758196C22semidirect
40. C2×#11758198C22semidirect
41. C2×#11758198C22semidirect
42. C2×#11758198C22semidirect
44. C2×C4×Dic61C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
47. #14519684C22semidirect
48. #14519684C22semidirect
52. C2×C42×C61C22semidirect
53. C2×C42×C61C22semidirect
54. #95×C61C22semidirect
55. #95×C61C22semidirect
63. C23×D61C2×C4semidirect
78. C2×C22⋊D61C2×C4semidirect
91. C2×D244C2×C4semidirect
92. C2×D244C2×C4semidirect
102. C22⋊C4×C61C2×C4semidirect
103. C22⋊C4×C61D4semidirect
115. #11758198C2×C4semidirect
116. #11758198C2×C4semidirect
117. #11758198D4semidirect
205. C22×C61C4×D4semidirect
234. C2×D61C4×D4semidirect
272. C4×C22⋊C4D61semidirect
273. C61#2358semidirect
306. C2×C42C2×D61semidirect
307. C2×C42C2×D61semidirect
312. #95C2×D61semidirect
313. #95C2×D61semidirect
375. C22⋊C4C4×D61semidirect
376. C22⋊C4D244semidirect
485. C22C4×D244semidirect