Finite Group Databasebeta

← #21449351

Subgroups — #21449351

Order 7808.

922 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519749C211yesmaximal, characteristic, complemented
2C2×#14519748C211yesmaximal, characteristic, complemented
3C2×#14519746C211yesmaximal, characteristic, complemented
4C2×#14519737C211yesmaximal, characteristic, complemented
5C22×C22⋊Dic61C211yesmaximal, characteristic, complemented
6#16839685C211yesmaximal, characteristic, complemented
7#16839678C211yesmaximal, characteristic, complemented
8#16839676C211yesmaximal, characteristic, complemented
9#16839670C211yesmaximal, characteristic, complemented
10#16839665C211yesmaximal, characteristic, complemented
11#16839650C211yesmaximal, characteristic, complemented
12#16839642C211yesmaximal, characteristic, complemented
13#16839638C211yesmaximal, characteristic, complemented
14#16839637C211yesmaximal, characteristic, complemented
15C2×#120×C61C211yesmaximal, characteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic, complemented
20C23×Dic61C2211yescharacteristic
21C23×Dic61C2211yescharacteristic
22C22×C4×D61C2211yescharacteristic, complemented
23#14519749—24no—
24#14519748—24no—
25#14519746—24no—
26#14519737—24no—
27C2×C4⋊Dic61C2211yescharacteristic, complemented
28C2×C4⋊Dic61C2211yescharacteristic, complemented
29C2×#11758196C2211yescharacteristic, complemented
30C2×#11758196C2211yescharacteristic, complemented
31C2×C22⋊Dic61—24no—
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×C22⋊Dic61C2211yescharacteristic
37C2×C22⋊Dic61C2211yescharacteristic
38C2×C22⋊Dic61C2211yescharacteristic
39C2×C22⋊Dic61C2211yescharacteristic, complemented
40C2×C22⋊Dic61C2211yescharacteristic, complemented
41C2×C22⋊Dic61C2211yescharacteristic, complemented
42C2×#11758198C2211yescharacteristic, complemented
43C2×#11758198C2211yescharacteristic, complemented
44C2×C4×Dic61C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47#14519684C2211yescharacteristic, complemented
48#14519684C2211yescharacteristic, complemented
49C25×C61C2211yescharacteristic
50C22×D4×C61C2211yescharacteristic
51C22×D4×C61C2211yescharacteristic
52C22×D4×C61C2211yescharacteristic
53#120×C61—24no—
54C2×C22⋊C4×C61C2211yescharacteristic
55C2×C22⋊C4×C61C2211yescharacteristic
56C2×C22⋊C4×C61C2211yescharacteristic
57C24×C61—22no—
58C24×C61—22no—
59C24×C61—22no—
60C24×C61—22no—
61C24×C61—22no—
62C24×C61—41no—
63C24×C61—41no—
64C24×C61C2311yescharacteristic
65C24×C61C2311yescharacteristic
66C24×C61C2311yescharacteristic
67C24×C61C2311yescharacteristic
68C23×D61C2311yescharacteristic
69C2×D4×C61—22no—
70C2×D4×C61—22no—
71C2×D4×C61—22no—
72C2×D4×C61—22no—
73C2×D4×C61—22no—
74C2×D4×C61—22no—
75C2×D4×C61—22no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C22×C4×C61C2311yescharacteristic
79C22×C4×C61C2311yescharacteristic
80C22×C4×C61C2311yescharacteristic
81C2×C22⋊D61—22no—
82C2×C22⋊D61—22no—
83C2×C22⋊D61—22no—
84C2×C22⋊D61—22no—
85C2×C22⋊D61—22no—
86C2×C22⋊D61—22no—
87C2×C22⋊D61—22no—
88C2×C22⋊D61—22no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C2×C22⋊D61—41no—
92C2×C22⋊D61D414yescomplemented
93C22×Dic61—22no—
94C22×Dic61—22no—
95C22×Dic61—22no—
96C22×Dic61—22no—
97C22×Dic61—41no—
98C22×Dic61—41no—
99C22×Dic61C2311yescharacteristic
100C22×Dic61C2311yescharacteristic
101C22×Dic61C2311yescharacteristic
102C22×Dic61C2311yescharacteristic
103C22×Dic61C2311yescharacteristic
104C22×Dic61C2311yescharacteristic
105C22×Dic61C2311yescharacteristic
106C2×C4×D61—22no—
107C2×C4×D61—22no—
108C2×C4×D61—41no—
109C22⋊C4×C61—22no—
110C22⋊C4×C61—22no—
111C22⋊C4×C61D414yescomplemented
112C22⋊Dic61—22no—
113C22⋊Dic61—22no—
114C22⋊Dic61—22no—
115C22⋊Dic61—22no—
116C22⋊Dic61—22no—
117C22⋊Dic61—22no—
118C22⋊Dic61—22no—
119C22⋊Dic61—22no—
120C22⋊Dic61—41no—
121C22⋊Dic61D414yescomplemented
122#11758198—22no—
123#11758198—22no—
124C4⋊Dic61—22no—
125C4⋊Dic61—41no—
126#11758196—22no—
127#11758196—22no—
128C4×Dic61—22no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61—21no—
132C23×C61—21no—
133C23×C61—28no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—21no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—21no—
140C23×C61—21no—
141C23×C61—21no—
142C23×C61—21no—
143C23×C61—21no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61—21no—
148C23×C61—21no—
149C23×C61—21no—
150C23×C61—21no—
151C23×C61—21no—
152C23×C61—21no—
153C23×C61—44no—
154C23×C61—44no—
155C23×C61—44no—
156C23×C61—44no—
157C23×C61—44no—
158C23×C61—44no—
159C23×C61C2×D412yes—
160C23×C61C2×D412yes—
161C23×C61C2×D412yes—
162C23×C61#4112yes—
163C23×C61#4112yes—
164C23×C61C2411yescharacteristic
165C22×D61—21no—
166C22×D61—21no—
167C22×D61—21no—
168C22×D61—21no—
169C22×D61—21no—
170C22×D61—21no—
171C22×D61C2×D412yes—
172D4×C61—44no—
173D4×C61—44no—
174D4×C61—44no—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61—21no—
181C2×C4×C61—21no—
182C2×C4×C61C2×D412yes—
183C2×C4×C61C2×D412yes—
184C22⋊D61—28no—
185C22⋊D61—44no—
186C22⋊D61—44no—
187C22⋊D61—44no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—21no—
196C2×Dic61—21no—
197C2×Dic61—21no—
198C2×Dic61—21no—
199C2×Dic61—21no—
200C2×Dic61—21no—
201C2×Dic61—21no—
202C2×Dic61—21no—
203C2×Dic61—21no—
204C2×Dic61—21no—
205C2×Dic61—21no—
206C2×Dic61—44no—
207C2×Dic61—44no—
208C2×Dic61C2×D412yes—
209C2×Dic61C2×D412yes—
210C2×Dic61C2×D412yes—
211C4×D61—44no—
212C22×C61—22no—
213C22×C61—22no—
214C22×C61—22no—
215C22×C61—22no—
216C22×C61—22no—
217C22×C61—22no—
218C22×C61—22no—
219C22×C61—22no—
220C22×C61—22no—
221C22×C61—22no—
222C22×C61—22no—
223C22×C61—22no—
224C22×C61—416no—
225C22×C61—41no—
226C22×C61—41no—
227C22×C61—41no—
228C22×C61—41no—
229C22×C61—41no—
230C22×C61—41no—
231C22×C61—41no—
232C22×C61—41no—
233C22×C61—41no—
234C22×C61—41no—
235C22×C61—41no—
236C22×C61—41no—
237C22×C61—41no—
238C22×C61—41no—
239C22×C61—41no—
240C22×C61#12114yescomplemented
241C22×C61C22×D411yescharacteristic
242C22×C61C22×D411yescharacteristic
243C22×C61C22×D411yescharacteristic
244C22×C61C2×#4111yescharacteristic
245C22×C61C2×#4111yescharacteristic
246C22×C61H(5,𝔽2)11yescharacteristic
247C22×C61H(5,𝔽2)11yescharacteristic
248C2×D61—22no—
249C2×D61—22no—
250C2×D61—22no—
251C2×D61—41no—
252C2×D61—41no—
253C2×D61—41no—
254C2×D61—41no—
255C4×C61—22no—
256C4×C61—22no—
257C4×C61—41no—
258Dic61—22no—
259Dic61—22no—
260Dic61—22no—
261Dic61—41no—
262Dic61—41no—
263Dic61—41no—
264Dic61—41no—
265#2424—611nomaximal, Sylow
266C2×C61—24no—
267C2×C61—42no—
268C2×C61—42no—
269C2×C61—81no—
270C2×C61C2×#12111yescharacteristic
271C2×C61#52511yescharacteristic
272C2×C61#53811yescharacteristic
273C2×C61D4211yescharacteristic
274C2×C61D4211yescharacteristic
275C2×C61#54611yescharacteristic
276C2×C61#54611yescharacteristic
277D61—42no—
278C2×#121—611no—
279C2×#121—611no—
280C2×#120—611no—
281C2×#120D6111yescharacteristic, complemented
282C2×C4×D4—611no—
283C22×C22⋊C4—611no—
284#396—611no—
285#394—611no—
286#394—611no—
287#392—611no—
288#390—611no—
289#388—611no—
290#386—611no—
291#386—611no—
292#385—611no—
293C61#242411yescharacteristic, complemented, Sylow
294C25C2×D6111yescharacteristic
295C22×D4—611no—
296C22×D4—611no—
297C22×D4—611no—
298C22×D4—611no—
299C22×D4C2×D6111yescharacteristic
300C22×D4C2×D6111yescharacteristic
301C22×D4C2×D6111yescharacteristic
302C23×C4—611no—
303C23×C4—611no—
304C23×C4—611no—
305#121—1224no—
306#121—1224no—
307#120—24no—
308#120—1224no—
309C4×D4—1224no—
310C2×C4⋊C4—611no—
311C2×C4⋊C4—611no—
312C2×C4⋊C4—611no—
313C2×C4⋊C4—611no—
314C2×C22⋊C4—611no—
315C2×C22⋊C4—611no—
316C2×C22⋊C4—611no—
317C2×C22⋊C4—611no—
318C2×C22⋊C4—611no—
319C2×C22⋊C4—611no—
320C2×C22⋊C4—611no—
321C2×C22⋊C4—611no—
322C2×C22⋊C4—611no—
323C2×C22⋊C4—611no—
324C2×C22⋊C4—611no—
325C2×C22⋊C4—611no—
326C2×C22⋊C4—1224no—
327C2×C22⋊C4C2×D6111yescharacteristic
328C2×C22⋊C4C2×D6111yescharacteristic
329C2×C22⋊C4C2×D6111yescharacteristic
330C2×C42—611no—
331#95—611no—
332#95—611no—
333#95—611no—
334#95—611no—
335C24—22no—
336C24—22no—
337C24—22no—
338C24—22no—
339C24—22no—
340C24—41no—
341C24—41no—
342C24—611no—
343C24C22×D6111yescharacteristic
344C24C22×D6111yescharacteristic
345C24C22×D6111yescharacteristic
346C24C22×D6111yescharacteristic
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—614no—
357C2×D4—1222no—
358C2×D4—1222no—
359C2×D4—1222no—
360C2×D4—1222no—
361C2×D4—1222no—
362C2×D4—1222no—
363C2×D4—1222no—
364C2×D4—1222no—
365C2×D4—2441no—
366C2×D4—2441no—
367C2×D4—2441no—
368C22×C4—611no—
369C22×C4—611no—
370C22×C4—611no—
371C22×C4—611no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—1222no—
376C22×C4—1222no—
377C22×C4—1222no—
378C22×C4—1222no—
379C22×C4—1222no—
380C22×C4—1222no—
381C22×C4—2441no—
382C22×C4—2441no—
383C22×C4—2441no—
384C22×C4C22×D6111yescharacteristic
385C22×C4C22×D6111yescharacteristic
386C22×C4C22×D6111yescharacteristic
387C4⋊C4—1222no—
388C4⋊C4—1222no—
389C4⋊C4—1222no—
390C4⋊C4—2441no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—614no—
394C22⋊C4—1222no—
395C22⋊C4—1222no—
396C22⋊C4—1222no—
397C22⋊C4—1222no—
398C22⋊C4—1222no—
399C22⋊C4—1222no—
400C22⋊C4—1222no—
401C22⋊C4—1222no—
402C22⋊C4—1222no—
403C22⋊C4—1222no—
404C22⋊C4—2441no—
405C22⋊C4C22⋊D6114yescomplemented
406C42—1222no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—28no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—44no—
435C23—44no—
436C23—44no—
437C23—612no—
438C23—1221no—
439C23—1221no—
440C23—1221no—
441C23—1221no—
442C23—1221no—
443C23—1221no—
444C23D4×D6112yes—
445C23D4×D6112yes—
446C23#1175822412yes—
447C23#1175822412yes—
448C23C2×C22⋊D6112yes—
449C23C23×D6111yescharacteristic
450D4—44no—
451D4—44no—
452D4—44no—
453D4—1228no—
454D4—2444no—
455D4—2444no—
456D4—2444no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—612no—
465C2×C4—612no—
466C2×C4—612no—
467C2×C4—1221no—
468C2×C4—1221no—
469C2×C4—1221no—
470C2×C4—1221no—
471C2×C4—1221no—
472C2×C4—1221no—
473C2×C4—1221no—
474C2×C4—1221no—
475C2×C4—1221no—
476C2×C4—1221no—
477C2×C4—1221no—
478C2×C4—1221no—
479C2×C4—1221no—
480C2×C4—1221no—
481C2×C4—1221no—
482C2×C4—1221no—
483C2×C4—1221no—
484C2×C4—1221no—
485C2×C4—2444no—
486C2×C4—2444no—
487C2×C4—2444no—
488C2×C4C2×C22⋊D6112yes—
489C2×C4C2×C22⋊D6112yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—22no—
502C22—416no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—1222no—
519C22—1222no—
520C22—1222no—
521C22—2441no—
522C22—2441no—
523C22—2441no—
524C22—2441no—
525C22#1451974814yescomplemented
526C22C2×D4×D6111yescharacteristic
527C22C2×D4×D6111yescharacteristic
528C22C22×C22⋊D6111yescharacteristic
529C22C2×#1175822411yescharacteristic
530C22C2×#1175822411yescharacteristic
531C22#1451982211yescharacteristic
532C22#1451982211yescharacteristic
533C4—22no—
534C4—22no—
535C4—41no—
536C4—1222no—
537C4—1222no—
538C4—1222no—
539C4—2441no—
540C4—2441no—
541C4—2441no—
542C4—2441no—
543C2—24no—
544C2—42no—
545C2—42no—
546C2—81no—
547C2—2442no—
548C2C2×#1451974811yescharacteristic
549C2#1684026811yescharacteristic
550C2#1684034711yescharacteristic
551C2#1684039411yescharacteristic
552C2D4×C22⋊D6111yescharacteristic
553C2#1684039911yescharacteristic
554C2#1684040611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#120×C61C2
hypercenterC2×#120D61
hypocenterC61#2424
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#14519749C2semidirect
2. C2×#14519748C2semidirect
3. C2×#14519746C2semidirect
4. C2×#14519737C2semidirect
5. C22×C22⋊Dic61C2semidirect
6. #16839685C2semidirect
7. #16839678C2semidirect
8. #16839676C2semidirect
9. #16839670C2semidirect
10. #16839665C2semidirect
11. #16839650C2semidirect
12. #16839642C2semidirect
13. #16839638C2semidirect
14. #16839637C2semidirect
15. C2×#120×C61C2semidirect
19. C22×C22⋊D61C22semidirect
22. C22×C4×D61C22semidirect
27. C2×C4⋊Dic61C22semidirect
28. C2×C4⋊Dic61C22semidirect
29. C2×#11758196C22semidirect
30. C2×#11758196C22semidirect
39. C2×C22⋊Dic61C22semidirect
40. C2×C22⋊Dic61C22semidirect
41. C2×C22⋊Dic61C22semidirect
42. C2×#11758198C22semidirect
43. C2×#11758198C22semidirect
44. C2×C4×Dic61C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
47. #14519684C22semidirect
48. #14519684C22semidirect
92. C2×C22⋊D61D4semidirect
111. C22⋊C4×C61D4semidirect
121. C22⋊Dic61D4semidirect
240. C22×C61#121semidirect
281. C2×#120D61semidirect
293. C61#2424semidirect
405. C22⋊C4C22⋊D61semidirect
525. C22#14519748semidirect