Finite Group Databasebeta

← #21449349

Subgroups — #21449349

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×#14519751C211yesmaximal, characteristic, complemented
2C2×#14519749C211yesmaximal, characteristic, complemented
3C2×#14519747C211yesmaximal, characteristic, complemented
4C2×#14519745C211yesmaximal, characteristic, complemented
5C22×#11758198C211yesmaximal, characteristic, complemented
6#16839684C211yesmaximal, characteristic, complemented
7#16839679C211yesmaximal, characteristic, complemented
8#16839678C211yesmaximal, characteristic, complemented
9#16839671C211yesmaximal, characteristic, complemented
10#16839664C211yesmaximal, characteristic, complemented
11#16839653C211yesmaximal, characteristic, complemented
12#16839641C211yesmaximal, characteristic, complemented
13#16839641C211yesmaximal, characteristic, complemented
14#16839637C211yesmaximal, characteristic, complemented
15C2×C4×D4×C61C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C22×C22⋊D61C2211yescharacteristic
22C22×C22⋊D61C2211yescharacteristic, complemented
23C23×Dic61C2211yescharacteristic
24#14519751—24no—
25#14519749—24no—
26#14519747—24no—
27#14519745—24no—
28C2×C4⋊Dic61C2211yescharacteristic, complemented
29C2×C4⋊Dic61C2211yescharacteristic, complemented
30C2×#11758196C2211yescharacteristic, complemented
31C2×C22⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic, complemented
33C2×#11758198—24no—
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic, complemented
43C2×#11758198C2211yescharacteristic, complemented
44C2×#11758198C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47#14519684C2211yescharacteristic, complemented
48#14519684C2211yescharacteristic, complemented
49C22×D4×C61C2211yescharacteristic
50C23×C4×C61C2211yescharacteristic
51C23×C4×C61C2211yescharacteristic, complemented
52C4×D4×C61—24no—
53C2×C4⋊C4×C61C2211yescharacteristic, complemented
54C2×C22⋊C4×C61C2211yescharacteristic
55C2×C22⋊C4×C61C2211yescharacteristic, complemented
56C2×C42×C61C2211yescharacteristic, complemented
57C24×C61C2311yescharacteristic
58C24×C61C2311yescharacteristic
59C23×D61—22no—
60C23×D61—22no—
61C23×D61—22no—
62C23×D61—22no—
63C23×D61—22no—
64C23×D61—41no—
65C23×D61—41no—
66C23×D61C2311yescharacteristic
67C23×D61C2311yescharacteristic
68C23×D61C2311yescharacteristic
69C2×D4×C61—22no—
70C2×D4×C61—22no—
71C2×D4×C61D414yescomplemented
72C22×C4×C61—22no—
73C22×C4×C61—22no—
74C22×C4×C61—22no—
75C22×C4×C61—22no—
76C22×C4×C61—41no—
77C22×C4×C61—41no—
78C22×C4×C61C2311yescharacteristic
79C22×C4×C61C2311yescharacteristic
80C22×C4×C61C2311yescharacteristic
81C22×C4×C61C2311yescharacteristic
82C22×C4×C61C2311yescharacteristic
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—22no—
90C2×C22⋊D61—22no—
91C2×C22⋊D61—22no—
92C2×C22⋊D61—41no—
93C2×C22⋊D61—41no—
94C2×C22⋊D61—41no—
95C22×Dic61—22no—
96C22×Dic61—22no—
97C22×Dic61—41no—
98C22×Dic61C2311yescharacteristic
99C22×Dic61C2311yescharacteristic
100C22×Dic61C2311yescharacteristic
101C22×Dic61C2311yescharacteristic
102C22×Dic61C2311yescharacteristic
103C2×D244—22no—
104C2×D244—22no—
105C2×D244—22no—
106C2×D244—22no—
107C2×D244—41no—
108C2×D244—41no—
109C4⋊C4×C61—22no—
110C22⋊C4×C61—22no—
111C22⋊C4×C61D414yescomplemented
112C42×C61—22no—
113C22⋊Dic61—22no—
114C22⋊Dic61—22no—
115#11758198—22no—
116#11758198—22no—
117#11758198—22no—
118#11758198—22no—
119#11758198—22no—
120#11758198—22no—
121#11758198—22no—
122#11758198—22no—
123#11758198—22no—
124#11758198—41no—
125#11758198D414yescomplemented
126C4⋊Dic61—22no—
127C4⋊Dic61—41no—
128#11758196—22no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61—21no—
132C23×C61—21no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—21no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61C2×D412yes—
140C23×C61C2×D412yes—
141C23×C61C2×D412yes—
142C23×C61#4112yes—
143C23×C61C2411yescharacteristic
144C22×D61—28no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—21no—
157C22×D61—21no—
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—21no—
162C22×D61—21no—
163C22×D61—21no—
164C22×D61—44no—
165C22×D61—44no—
166C22×D61—44no—
167C22×D61—44no—
168C22×D61—44no—
169C22×D61—44no—
170C22×D61C2×D412yes—
171C22×D61#4112yes—
172D4×C61—28no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
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×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—44no—
185C2×C4×C61—44no—
186C2×C4×C61C2×D412yes—
187C2×C4×C61C2×D412yes—
188C2×C4×C61C2×D412yes—
189C2×C4×C61C2×D412yes—
190C22⋊D61—44no—
191C22⋊D61—44no—
192C22⋊D61—44no—
193C22⋊D61—44no—
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—21no—
207C2×Dic61—21no—
208C2×Dic61—44no—
209C2×Dic61C2×D412yes—
210D244—44no—
211D244—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—41no—
222C22×C61—41no—
223C22×C61—41no—
224C22×C61—41no—
225C22×C61#12114yescomplemented
226C22×C61C22×D411yescharacteristic
227C22×C61C22×D411yescharacteristic
228C22×C61C22×D411yescharacteristic
229C22×C61C2×#4111yescharacteristic
230C22×C61C2×#4111yescharacteristic
231C22×C61H(5,𝔽2)11yescharacteristic
232C22×C61H(5,𝔽2)11yescharacteristic
233C2×D61—22no—
234C2×D61—22no—
235C2×D61—22no—
236C2×D61—22no—
237C2×D61—22no—
238C2×D61—22no—
239C2×D61—416no—
240C2×D61—41no—
241C2×D61—41no—
242C2×D61—41no—
243C2×D61—41no—
244C2×D61—41no—
245C2×D61—41no—
246C2×D61—41no—
247C2×D61—41no—
248C2×D61—41no—
249C2×D61—41no—
250C2×D61—41no—
251C2×D61—41no—
252C2×D61—41no—
253C2×D61—41no—
254C2×D61—41no—
255C4×C61—22no—
256C4×C61—22no—
257C4×C61—22no—
258C4×C61—22no—
259C4×C61—41no—
260Dic61—22no—
261Dic61—41no—
262Dic61—41no—
263Dic61—41no—
264Dic61—41no—
265#2424—611nomaximal, Sylow
266C2×C61—24no—
267C2×C61—42no—
268C2×C61C2×#12111yescharacteristic
269C2×C61#52511yescharacteristic
270C2×C61#53811yescharacteristic
271C2×C61D4211yescharacteristic
272C2×C61D4211yescharacteristic
273C2×C61#54611yescharacteristic
274C2×C61#54611yescharacteristic
275D61—42no—
276D61—42no—
277D61—81no—
278C2×#121—611no—
279C2×#121—611no—
280C2×#120—611no—
281C2×#120—611no—
282C2×C4×D4D6111yescharacteristic, complemented
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
294C25—611no—
295C22×D4—611no—
296C22×D4—611no—
297C22×D4—611no—
298C22×D4—611no—
299C22×D4—611no—
300C22×D4—611no—
301C22×D4C2×D6111yescharacteristic
302C23×C4—611no—
303C23×C4C2×D6111yescharacteristic
304C23×C4C2×D6111yescharacteristic, complemented
305#121—1224no—
306#121—1224no—
307#120—1224no—
308#120—1224no—
309C4×D4—24no—
310C2×C4⋊C4—611no—
311C2×C4⋊C4—611no—
312C2×C4⋊C4—611no—
313C2×C4⋊C4C2×D6111yescharacteristic, complemented
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—611no—
327C2×C22⋊C4—1224no—
328C2×C22⋊C4C2×D6111yescharacteristic
329C2×C22⋊C4C2×D6111yescharacteristic, complemented
330C2×C42C2×D6111yescharacteristic, complemented
331#95—611no—
332#95—611no—
333#95—611no—
334#95—611no—
335C24—611no—
336C24—611no—
337C24—611no—
338C24—1222no—
339C24—1222no—
340C24—1222no—
341C24—1222no—
342C24—1222no—
343C24—2441no—
344C24—2441no—
345C24C22×D6111yescharacteristic
346C24C22×D6111yescharacteristic
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—1222no—
350C2×D4—1222no—
351C2×D4—1222no—
352C2×D4—1222no—
353C2×D4—1222no—
354C2×D4—1222no—
355C2×D4—1222no—
356C2×D4—1222no—
357C2×D4—1222no—
358C2×D4—1222no—
359C2×D4—1222no—
360C2×D4—1222no—
361C2×D4—1222no—
362C2×D4—2441no—
363C2×D4—2441no—
364C2×D4—2441no—
365C2×D4—2441no—
366C2×D4—2441no—
367C2×D4D24414yescomplemented
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—611no—
379C22×C4—1222no—
380C22×C4—1222no—
381C22×C4—2441no—
382C22×C4C22×D6111yescharacteristic
383C22×C4C22×D6111yescharacteristic
384C22×C4C22×D6111yescharacteristic
385C22×C4C22×D6111yescharacteristic
386C22×C4C22×D6111yescharacteristic
387C4⋊C4—22no—
388C4⋊C4—1222no—
389C4⋊C4—1222no—
390C4⋊C4—2441no—
391C22⋊C4—22no—
392C22⋊C4—614no—
393C22⋊C4—1222no—
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—22no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—612no—
418C23—612no—
419C23—1228no—
420C23—1221no—
421C23—1221no—
422C23—1221no—
423C23—1221no—
424C23—1221no—
425C23—1221no—
426C23—1221no—
427C23—1221no—
428C23—1221no—
429C23—1221no—
430C23—1221no—
431C23—1221no—
432C23—1221no—
433C23—1221no—
434C23—1221no—
435C23—1221no—
436C23—1221no—
437C23—1221no—
438C23—1221no—
439C23—2444no—
440C23—2444no—
441C23—2444no—
442C23—2444no—
443C23—2444no—
444C23—2444no—
445C23C2×D24412yes—
446C23C2×D24412yes—
447C23#1175822212yes—
448C23C2×C22⋊D6112yes—
449C23C23×D6111yescharacteristic
450D4—28no—
451D4—2444no—
452D4—2444no—
453D4—2444no—
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—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—44no—
469C2×C4—44no—
470C2×C4—612no—
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×C4C2×D24412yes—
487C2×C4D4×D6112yes—
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—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—1222no—
504C22—1222no—
505C22—1222no—
506C22—1222no—
507C22—1222no—
508C22—1222no—
509C22—24416no—
510C22—2441no—
511C22—2441no—
512C22—2441no—
513C22—2441no—
514C22—2441no—
515C22—2441no—
516C22—2441no—
517C22—2441no—
518C22—2441no—
519C22—2441no—
520C22—2441no—
521C22—2441no—
522C22—2441no—
523C22—2441no—
524C22—2441no—
525C22#1451975114yescomplemented
526C22C2×D4×D6111yescharacteristic
527C22C22×C22⋊D6111yescharacteristic
528C22C22×D24411yescharacteristic
529C22#41×D6111yescharacteristic
530C22C2×#1175822211yescharacteristic
531C22#1451982211yescharacteristic
532C22#1451982311yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—22no—
537C4—41no—
538C4—1222no—
539C4—2441no—
540C4—2441no—
541C4—2441no—
542C4—2441no—
543C2—24no—
544C2—42no—
545C2—4881no—
546C2—2442no—
547C2—2442no—
548C2C2×#1451975111yescharacteristic
549C2#1684027111yescharacteristic
550C2#1684034511yescharacteristic
551C2D4×C22⋊D6111yescharacteristic
552C2D4×D24411yescharacteristic
553C2#1684040011yescharacteristic
554C2#1684040711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C4×D4×C61C2
hypercenterC2×C4×D4D61
hypocenterC61#2424
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14519751C2semidirect
2. C2×#14519749C2semidirect
3. C2×#14519747C2semidirect
4. C2×#14519745C2semidirect
5. C22×#11758198C2semidirect
6. #16839684C2semidirect
7. #16839679C2semidirect
8. #16839678C2semidirect
9. #16839671C2semidirect
10. #16839664C2semidirect
11. #16839653C2semidirect
12. #16839641C2semidirect
13. #16839641C2semidirect
14. #16839637C2semidirect
15. C2×C4×D4×C61C2semidirect
22. C22×C22⋊D61C22semidirect
28. C2×C4⋊Dic61C22semidirect
29. C2×C4⋊Dic61C22semidirect
30. C2×#11758196C22semidirect
32. C2×C22⋊Dic61C22semidirect
42. C2×#11758198C22semidirect
43. C2×#11758198C22semidirect
44. C2×#11758198C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
47. #14519684C22semidirect
48. #14519684C22semidirect
51. C23×C4×C61C22semidirect
53. C2×C4⋊C4×C61C22semidirect
55. C2×C22⋊C4×C61C22semidirect
56. C2×C42×C61C22semidirect
71. C2×D4×C61D4semidirect
111. C22⋊C4×C61D4semidirect
125. #11758198D4semidirect
225. C22×C61#121semidirect
282. C2×C4×D4D61semidirect
293. C61#2424semidirect
304. C23×C4C2×D61semidirect
313. C2×C4⋊C4C2×D61semidirect
329. C2×C22⋊C4C2×D61semidirect
330. C2×C42C2×D61semidirect
367. C2×D4D244semidirect
405. C22⋊C4C22⋊D61semidirect
525. C22#14519751semidirect