Finite Group Databasebeta

← #21448796

Subgroups — #21448796

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×#14519745C211yesmaximal, characteristic
2C2×C4×C22⋊D61C211yesmaximal, characteristic, complemented
3C22×#11758198C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D61C211yesmaximal, characteristic, complemented
5#16839662C211yesmaximal, characteristic, complemented
6#16839653C211yesmaximal, characteristic, complemented
7#16839652C211yesmaximal, characteristic, complemented
8#16839642C211yesmaximal, characteristic, complemented
9#16839641C211yesmaximal, characteristic, complemented
10#16839638C211yesmaximal, characteristic, complemented
11#16839635C211yesmaximal, characteristic, complemented
12#16839633C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
14C4×#11758198C211yesmaximal, characteristic, complemented
15C2×C4×D4×C61C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C23×Dic61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21C22×C4×D61C2211yescharacteristic
22#14519745C418yescomplemented
23C4×C22⋊D61—24no—
24C2×#11758196C2211yescharacteristic, complemented
25C2×#11758196C2211yescharacteristic, complemented
26C2×C22⋊Dic61C2211yescharacteristic
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic, complemented
29C2×C22⋊Dic61C2211yescharacteristic, complemented
30C2×#11758198—24no—
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C22⋊C4×D61—24no—
40C2×C4×Dic61C2211yescharacteristic, complemented
41C2×C4×Dic61C2211yescharacteristic, complemented
42#14519684C2211yescharacteristic, complemented
43#14519684C2211yescharacteristic, complemented
44#14519684C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47#14519684C2211yescharacteristic, complemented
48C22×D4×C61C2211yescharacteristic
49C23×C4×C61C2211yescharacteristic
50C23×C4×C61C2211yescharacteristic, complemented
51C4×D4×C61—24no—
52C2×C4⋊C4×C61C2211yescharacteristic, complemented
53C2×C22⋊C4×C61C2211yescharacteristic
54C2×C22⋊C4×C61C2211yescharacteristic, complemented
55C2×C42×C61C2211yescharacteristic, complemented
56C24×C61C2311yescharacteristic
57C24×C61C2311yescharacteristic
58C23×D61—22no—
59C23×D61—22no—
60C23×D61—22no—
61C23×D61—22no—
62C23×D61—41no—
63C23×D61—41no—
64C23×D61C2×C414yescomplemented
65C23×D61C2311yescharacteristic
66C23×D61C2311yescharacteristic
67C2×D4×C61—22no—
68C2×D4×C61—22no—
69C2×D4×C61C2×C414yescomplemented
70C22×C4×C61—22no—
71C22×C4×C61—22no—
72C22×C4×C61—22no—
73C22×C4×C61—22no—
74C22×C4×C61—41no—
75C22×C4×C61—41no—
76C22×C4×C61C2311yescharacteristic
77C22×C4×C61C2311yescharacteristic
78C22×C4×C61C2311yescharacteristic
79C22×C4×C61C2311yescharacteristic
80C22×C4×C61C2311yescharacteristic
81C2×C22⋊D61—22no—
82C2×C22⋊D61—22no—
83C2×C22⋊D61—41no—
84C2×C22⋊D61—41no—
85C2×C22⋊D61C2×C414yescomplemented
86C2×C22⋊D61C2×C414yescomplemented
87C22×Dic61—22no—
88C22×Dic61—22no—
89C22×Dic61—41no—
90C22×Dic61C2311yescharacteristic
91C22×Dic61C2311yescharacteristic
92C22×Dic61C2311yescharacteristic
93C22×Dic61C2311yescharacteristic
94C22×Dic61C2311yescharacteristic
95C22×Dic61C2311yescharacteristic
96C2×C4×D61—22no—
97C2×C4×D61—22no—
98C2×C4×D61—22no—
99C2×C4×D61—22no—
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C4⋊C4×C61—22no—
103C22⋊C4×C61—22no—
104C22⋊C4×C61D414yescomplemented
105C42×C61—22no—
106C22⋊Dic61—22no—
107C22⋊Dic61—22no—
108C22⋊Dic61—41no—
109C22⋊Dic61C2×C414yescomplemented
110#11758198—22no—
111#11758198—22no—
112#11758198—22no—
113#11758198—22no—
114#11758198—22no—
115#11758198C2×C414yescomplemented
116#11758198C2×C414yescomplemented
117#11758198D414yescomplemented
118#11758196—22no—
119#11758196—41no—
120C4×Dic61—22no—
121C4×Dic61—41no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61—21no—
132C23×C61C22×C412yes—
133C23×C61C22×C412yes—
134C23×C61C2×D412yes—
135C23×C61#4112yes—
136C23×C61C2411yescharacteristic
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—28no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—28no—
149C22×D61—44no—
150C22×D61—44no—
151C22×D61—44no—
152C22×D61—44no—
153C22×D61—44no—
154C22×D61C22×C412yes—
155C22×D61C22×C412yes—
156C22×D61C2×D412yes—
157C22×D61#4112yes—
158D4×C61—28no—
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—44no—
171C2×C4×C61—44no—
172C2×C4×C61C22×C412yes—
173C2×C4×C61C2×D412yes—
174C2×C4×C61C2×D412yes—
175C2×C4×C61C2×D412yes—
176C22⋊D61—28no—
177C22⋊D61—44no—
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—21no—
192C2×Dic61—21no—
193C2×Dic61—44no—
194C2×Dic61C22×C412yes—
195C2×Dic61C22×C412yes—
196C2×Dic61C2×D412yes—
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×C61—22no—
206C22×C61—22no—
207C22×C61—22no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61—41no—
211C22×C61—41no—
212C22×C61C4×D414yescomplemented
213C22×C61C23×C411yescharacteristic
214C22×C61C22×D411yescharacteristic
215C22×C61C22×D411yescharacteristic
216C22×C61C2×#4111yescharacteristic
217C22×C61C2×#4111yescharacteristic
218C22×C61H(5,𝔽2)11yescharacteristic
219C22×C61H(5,𝔽2)11yescharacteristic
220C2×D61—22no—
221C2×D61—22no—
222C2×D61—22no—
223C2×D61—22no—
224C2×D61—22no—
225C2×D61—22no—
226C2×D61—22no—
227C2×D61—22no—
228C2×D61—22no—
229C2×D61—416no—
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—41no—
240Dic61—22no—
241Dic61—22no—
242Dic61—22no—
243Dic61—41no—
244Dic61—41no—
245Dic61—41no—
246#2358—611nomaximal, Sylow
247C2×C61—24no—
248C2×C61—42no—
249C2×C61C2×C4×D411yescharacteristic
250C2×C61C2×C4×D411yescharacteristic
251C2×C61#51811yescharacteristic
252C2×C61D4211yescharacteristic
253C2×C61#54611yescharacteristic
254C2×C61#54611yescharacteristic
255C2×C61#55111yescharacteristic
256D61—24no—
257D61—42no—
258C2×#120—611no—
259C2×C4×D4—611no—
260C2×C4×D4D6111yescharacteristic, complemented
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⋊C4—611no—
273C61#235811yescharacteristic, complemented, Sylow
274C25—611no—
275C22×D4—611no—
276C22×D4—611no—
277C22×D4C2×D6111yescharacteristic
278C23×C4—611no—
279C23×C4—611no—
280C23×C4—611no—
281C23×C4C2×D6111yescharacteristic
282C23×C4C2×D6111yescharacteristic, complemented
283#120—618no—
284C4×D4—24no—
285C4×D4—1224no—
286C2×C4⋊C4—611no—
287C2×C4⋊C4—611no—
288C2×C4⋊C4C2×D6111yescharacteristic, complemented
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, complemented
305C2×C42—611no—
306C2×C42—611no—
307C2×C42C2×D6111yescharacteristic, complemented
308#95—611no—
309#95—611no—
310#95—611no—
311#95—611no—
312#95—611no—
313#95—611no—
314C24—611no—
315C24—611no—
316C24—614no—
317C24—1222no—
318C24—1222no—
319C24—1222no—
320C24—1222no—
321C24—2441no—
322C24—2441no—
323C24C22×D6111yescharacteristic
324C24C22×D6111yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—614no—
328C2×D4—614no—
329C2×D4—1222no—
330C2×D4—1222no—
331C2×D4—2441no—
332C2×D4—2441no—
333C2×D4C4×D6114yescomplemented
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—611no—
341C22×C4—611no—
342C22×C4—611no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—1222no—
347C22×C4—1222no—
348C22×C4—1222no—
349C22×C4—1222no—
350C22×C4—1222no—
351C22×C4—1222no—
352C22×C4—2441no—
353C22×C4—2441no—
354C22×C4—2441no—
355C22×C4C22×D6111yescharacteristic
356C22×C4C22×D6111yescharacteristic
357C22×C4C22×D6111yescharacteristic
358C22×C4C22×D6111yescharacteristic
359C22×C4C22×D6111yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—1222no—
362C4⋊C4—2441no—
363C22⋊C4—22no—
364C22⋊C4—614no—
365C22⋊C4—614no—
366C22⋊C4—614no—
367C22⋊C4—614no—
368C22⋊C4—1222no—
369C22⋊C4—1222no—
370C22⋊C4—1222no—
371C22⋊C4—1222no—
372C22⋊C4—1222no—
373C22⋊C4—1222no—
374C22⋊C4—1222no—
375C22⋊C4—2441no—
376C22⋊C4C22⋊D6114yescomplemented
377C42—22no—
378C42—1222no—
379C42—2441no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—612no—
391C23—612no—
392C23—612no—
393C23—612no—
394C23—1228no—
395C23—1221no—
396C23—1221no—
397C23—1221no—
398C23—1221no—
399C23—1221no—
400C23—1221no—
401C23—1221no—
402C23—1221no—
403C23—1221no—
404C23—1221no—
405C23—1228no—
406C23—2444no—
407C23—2444no—
408C23—2444no—
409C23—2444no—
410C23—2444no—
411C23C2×C4×D6112yes—
412C23C2×C4×D6112yes—
413C23#1175822212yes—
414C23C2×C22⋊D6112yes—
415C23C23×D6111yescharacteristic
416D4—28no—
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—44no—
431C2×C4—44no—
432C2×C4—612no—
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—1221no—
449C2×C4—1221no—
450C2×C4—2444no—
451C2×C4—2444no—
452C2×C4—2444no—
453C2×C4C2×C4×D6112yes—
454C2×C4D4×D6112yes—
455C2×C4C2×C22⋊D6112yes—
456C2×C4C2×C22⋊D6112yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—614no—
471C22—1222no—
472C22—1222no—
473C22—1222no—
474C22—1222no—
475C22—1222no—
476C22—1222no—
477C22—1222no—
478C22—1222no—
479C22—1222no—
480C22—24416no—
481C22—2441no—
482C22—2441no—
483C22—2441no—
484C22—2441no—
485C22C4×C22⋊D6114yescomplemented
486C22C22×C4×D6111yescharacteristic
487C22C2×D4×D6111yescharacteristic
488C22C22×C22⋊D6111yescharacteristic
489C22#41×D6111yescharacteristic
490C22C2×#1175822211yescharacteristic
491C22#1451982211yescharacteristic
492C22#1451982311yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—1222no—
499C4—1222no—
500C4—1222no—
501C4—2441no—
502C4—2441no—
503C4—2441no—
504C2—24no—
505C2—42no—
506C2—1224no—
507C2—2442no—
508C2C4×D4×D6111yescharacteristic
509C2C2×C4×C22⋊D6111yescharacteristic
510C2#1684023411yescharacteristic
511C2D4×C22⋊D6111yescharacteristic
512C2#1684040011yescharacteristic
513C2#1684040811yescharacteristic
514C2#1684044111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC2×C4×D4×C61C2
socleC23×C61C24
hypercenterC2×C4×D4D61
hypocenterC61#2358
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D61C2semidirect
3. C22×#11758198C2semidirect
4. C2×C22⋊C4×D61C2semidirect
5. #16839662C2semidirect
6. #16839653C2semidirect
7. #16839652C2semidirect
8. #16839642C2semidirect
9. #16839641C2semidirect
10. #16839638C2semidirect
11. #16839635C2semidirect
12. #16839633C2semidirect
13. C22⋊C4×Dic61C2semidirect
14. C4×#11758198C2semidirect
15. C2×C4×D4×C61C2semidirect
22. #14519745C4semidirect
24. C2×#11758196C22semidirect
25. C2×#11758196C22semidirect
28. C2×C22⋊Dic61C22semidirect
29. C2×C22⋊Dic61C22semidirect
40. C2×C4×Dic61C22semidirect
41. C2×C4×Dic61C22semidirect
42. #14519684C22semidirect
43. #14519684C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
47. #14519684C22semidirect
50. C23×C4×C61C22semidirect
52. C2×C4⋊C4×C61C22semidirect
54. C2×C22⋊C4×C61C22semidirect
55. C2×C42×C61C22semidirect
64. C23×D61C2×C4semidirect
69. C2×D4×C61C2×C4semidirect
85. C2×C22⋊D61C2×C4semidirect
86. C2×C22⋊D61C2×C4semidirect
104. C22⋊C4×C61D4semidirect
109. C22⋊Dic61C2×C4semidirect
115. #11758198C2×C4semidirect
116. #11758198C2×C4semidirect
117. #11758198D4semidirect
212. C22×C61C4×D4semidirect
234. C2×D61C4×D4semidirect
260. C2×C4×D4D61semidirect
273. C61#2358semidirect
282. C23×C4C2×D61semidirect
288. C2×C4⋊C4C2×D61semidirect
304. C2×C22⋊C4C2×D61semidirect
307. C2×C42C2×D61semidirect
333. C2×D4C4×D61semidirect
376. C22⋊C4C22⋊D61semidirect
485. C22C4×C22⋊D61semidirect