Finite Group Databasebeta

← #21452142

Subgroups — #21452142

Order 7808.

802 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519759C211yesmaximal, characteristic, complemented
2C2×#14519752C211yesmaximal, characteristic, complemented
3C2×#14519747C211yesmaximal, characteristic, complemented
4C2×#14519747C211yesmaximal, characteristic, complemented
5#16839689C211yesmaximal, characteristic, complemented
6#16839684C211yesmaximal, characteristic, complemented
7#16839680C211yesmaximal, characteristic, complemented
8#16839678C211yesmaximal, characteristic, complemented
9#16839672C211yesmaximal, characteristic, complemented
10#16839671C211yesmaximal, characteristic, complemented
11#16839664C211yesmaximal, characteristic, complemented
12#16839664C211yesmaximal, characteristic, complemented
13#16839640C211yesmaximal, characteristic, complemented
14#16839617C211yesmaximal, characteristic, complemented
15C61×#388C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×D244C2211yescharacteristic
20C22×D244C2211yescharacteristic
21C22×D244C2211yescharacteristic, complemented
22C22×C22⋊D61C2211yescharacteristic
23C22×C22⋊D61C2211yescharacteristic
24C22×C4×D61C2211yescharacteristic, complemented
25#14519759—24no—
26#14519752—24no—
27#14519747—24no—
28#14519747—24no—
29C2×C4⋊Dic61C2211yescharacteristic, complemented
30C2×C4⋊Dic61C2211yescharacteristic, complemented
31C2×#11758196C2211yescharacteristic, complemented
32C2×C22⋊Dic61C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic, complemented
42C2×#11758198C2211yescharacteristic, complemented
43C2×#11758198C2211yescharacteristic, complemented
44C2×#11758198C2211yescharacteristic, complemented
45C2×#11758198C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47#14519684C2211yescharacteristic, complemented
48C2×C4⋊C4×C61C2211yescharacteristic, complemented
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C42×C61C2211yescharacteristic, complemented
53#95×C61C2211yescharacteristic, complemented
54#95×C61C2211yescharacteristic, complemented
55C24×C61C2311yescharacteristic
56C23×D61—22no—
57C23×D61—22no—
58C23×D61—22no—
59C23×D61—41no—
60C23×D61—41no—
61C23×D61—41no—
62C23×D61—41no—
63C23×D61C2311yescharacteristic
64C23×D61C2311yescharacteristic
65C23×D61C2311yescharacteristic
66C23×D61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C22×C4×C61C2311yescharacteristic
71C22×C4×C61C2311yescharacteristic
72C22×C4×C61C2311yescharacteristic
73C2×C22⋊D61—22no—
74C2×C22⋊D61—22no—
75C2×C22⋊D61—22no—
76C2×C22⋊D61—41no—
77C2×C22⋊D61—41no—
78C2×C22⋊D61—41no—
79C22×Dic61C2311yescharacteristic
80C22×Dic61C2311yescharacteristic
81C22×Dic61C2311yescharacteristic
82C22×Dic61C2311yescharacteristic
83C2×D244—22no—
84C2×D244—22no—
85C2×D244—22no—
86C2×D244—22no—
87C2×D244—22no—
88C2×D244—22no—
89C2×D244—22no—
90C2×D244—41no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244—41no—
95C2×D244—41no—
96C2×D244—41no—
97C2×D244D414yescomplemented
98C2×C4×D61—22no—
99C2×C4×D61—22no—
100C2×C4×D61—41no—
101C4⋊C4×C61—22no—
102C22⋊C4×C61—22no—
103C22⋊C4×C61—41no—
104C22⋊C4×C61D414yescomplemented
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#11758198—41no—
116#11758198—41no—
117#11758198—41no—
118#11758198—41no—
119#11758198—41no—
120C4⋊Dic61—22no—
121C4⋊Dic61—41no—
122#11758196—22no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61C2×D412yes—
130C23×C61C2411yescharacteristic
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
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—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—44no—
157C22×D61—44no—
158C22×D61—44no—
159C22×D61—44no—
160C22×D61—44no—
161C22×D61—44no—
162C22×D61—44no—
163C22×D61C2×D412yes—
164C22×D61C2×D412yes—
165C22×D61#4112yes—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
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×C61C2×D412yes—
182C2×C4×C61C2×D412yes—
183C2×C4×C61C2×D412yes—
184C22⋊D61—44no—
185C22⋊D61—44no—
186C2×Dic61—21no—
187C2×Dic61—21no—
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—
198D244—44no—
199D244—44no—
200D244—44no—
201D244—44no—
202D244—44no—
203C4×D61—44no—
204C22×C61—22no—
205C22×C61—22no—
206C22×C61—22no—
207C22×C61—41no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61—41no—
211C22×C61C22×D411yescharacteristic
212C22×C61C22×D411yescharacteristic
213C22×C61C2×#4111yescharacteristic
214C22×C61H(5,𝔽2)11yescharacteristic
215C22×C61H(5,𝔽2)11yescharacteristic
216C22×C61H(5,𝔽2)11yescharacteristic
217C22×C61H(5,𝔽2)11yescharacteristic
218C2×D61—22no—
219C2×D61—22no—
220C2×D61—22no—
221C2×D61—22no—
222C2×D61—22no—
223C2×D61—22no—
224C2×D61—22no—
225C2×D61—22no—
226C2×D61—22no—
227C2×D61—416no—
228C2×D61—41no—
229C2×D61—41no—
230C2×D61—41no—
231C2×D61—41no—
232C2×D61—41no—
233C2×D61—41no—
234C2×D61—41no—
235C2×D61—41no—
236C2×D61—41no—
237C2×D61—41no—
238C2×D61—41no—
239C2×D61—41no—
240C2×D61—41no—
241C2×D61—41no—
242C2×D61—41no—
243C2×D61—41no—
244C2×D61—41no—
245C2×D61—41no—
246C2×D61—41no—
247C4×C61—22no—
248C4×C61—22no—
249C4×C61—22no—
250C4×C61—41no—
251C4×C61—41no—
252C4×C61—41no—
253Dic61—41no—
254Dic61—41no—
255Dic61—41no—
256Dic61—41no—
257#2678—611nomaximal, Sylow
258C2×C61—42no—
259C2×C61#53411yescharacteristic
260C2×C61#53511yescharacteristic
261C2×C61#53811yescharacteristic
262C2×C61D4211yescharacteristic
263C2×C61#54611yescharacteristic
264C2×C61#54611yescharacteristic
265C2×C61#56011yescharacteristic
266D61—42no—
267D61—42no—
268D61—42no—
269D61—81no—
270C2×#123—611no—
271C2×#121—611no—
272C2×#120—611no—
273C2×#120—611no—
274#397—611no—
275#396—611no—
276#394—611no—
277#394—611no—
278#392—611no—
279#392—611no—
280#390—611no—
281#390—611no—
282#388D6111yescharacteristic, complemented
283#386—611no—
284#379—611no—
285C61#267811yescharacteristic, complemented, Sylow
286C25—611no—
287C22×D4—611no—
288C22×D4—611no—
289C22×D4—611no—
290C22×D4—611no—
291C22×D4—611no—
292C22×D4—611no—
293C22×D4—611no—
294C23×C4—611no—
295#123—1224no—
296#121—1224no—
297#120—1224no—
298#120—1224no—
299C2×C4⋊C4—611no—
300C2×C4⋊C4—611no—
301C2×C4⋊C4—611no—
302C2×C4⋊C4C2×D6111yescharacteristic, complemented
303C2×C22⋊C4—611no—
304C2×C22⋊C4—611no—
305C2×C22⋊C4—611no—
306C2×C22⋊C4—611no—
307C2×C22⋊C4—611no—
308C2×C22⋊C4—611no—
309C2×C22⋊C4—611no—
310C2×C22⋊C4—611no—
311C2×C22⋊C4—611no—
312C2×C22⋊C4—611no—
313C2×C22⋊C4—611no—
314C2×C22⋊C4—611no—
315C2×C22⋊C4—611no—
316C2×C22⋊C4—611no—
317C2×C22⋊C4C2×D6111yescharacteristic
318C2×C22⋊C4C2×D6111yescharacteristic
319C2×C22⋊C4C2×D6111yescharacteristic
320C2×C42C2×D6111yescharacteristic, complemented
321#95—611no—
322#95—611no—
323#95C2×D6111yescharacteristic, complemented
324#95C2×D6111yescharacteristic, complemented
325C24—611no—
326C24—611no—
327C24—611no—
328C24—611no—
329C24—1222no—
330C24—1222no—
331C24—1222no—
332C24—2441no—
333C24—2441no—
334C24—2441no—
335C24—2441no—
336C24C22×D6111yescharacteristic
337C2×D4—614no—
338C2×D4—1222no—
339C2×D4—1222no—
340C2×D4—1222no—
341C2×D4—1222no—
342C2×D4—1222no—
343C2×D4—1222no—
344C2×D4—1222no—
345C2×D4—1222no—
346C2×D4—1222no—
347C2×D4—1222no—
348C2×D4—2441no—
349C2×D4—2441no—
350C2×D4—2441no—
351C2×D4—2441no—
352C2×D4—2441no—
353C2×D4—2441no—
354C2×D4—2441no—
355C2×D4—2441no—
356C2×D4—2441no—
357C2×D4—2441no—
358C22×C4—611no—
359C22×C4—611no—
360C22×C4—611no—
361C22×C4—611no—
362C22×C4—1222no—
363C22×C4—1222no—
364C22×C4—2441no—
365C22×C4C22×D6111yescharacteristic
366C22×C4C22×D6111yescharacteristic
367C22×C4C22×D6111yescharacteristic
368C22×C4C22×D6111yescharacteristic
369C22×C4C22×D6111yescharacteristic
370C22×C4C22×D6111yescharacteristic
371C4⋊C4—22no—
372C4⋊C4—1222no—
373C4⋊C4—1222no—
374C4⋊C4—2441no—
375C22⋊C4—22no—
376C22⋊C4—41no—
377C22⋊C4—1222no—
378C22⋊C4—1222no—
379C22⋊C4—1222no—
380C22⋊C4—1222no—
381C22⋊C4—1222no—
382C22⋊C4—1222no—
383C22⋊C4—1222no—
384C22⋊C4—1222no—
385C22⋊C4—2441no—
386C22⋊C4—2441no—
387C22⋊C4—2441no—
388C22⋊C4—2441no—
389C22⋊C4—2441no—
390C22⋊C4—2441no—
391C22⋊C4D24414yescomplemented
392C42—41no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—612no—
400C23—612no—
401C23—612no—
402C23—1221no—
403C23—1221no—
404C23—1221no—
405C23—1221no—
406C23—1221no—
407C23—1221no—
408C23—1221no—
409C23—1221no—
410C23—1221no—
411C23—1221no—
412C23—1221no—
413C23—1221no—
414C23—1221no—
415C23—1221no—
416C23—1221no—
417C23—1221no—
418C23—1221no—
419C23—1221no—
420C23—1221no—
421C23—1221no—
422C23—1221no—
423C23—1221no—
424C23—1221no—
425C23—1221no—
426C23—1221no—
427C23—2444no—
428C23—2444no—
429C23—2444no—
430C23—2444no—
431C23—2444no—
432C23—2444no—
433C23—2444no—
434C23C2×D24412yes—
435C23C23×D6111yescharacteristic
436D4—2444no—
437D4—2444no—
438D4—2444no—
439D4—2444no—
440D4—2444no—
441D4—2444no—
442D4—2444no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—1221no—
459C2×C4—1221no—
460C2×C4—1221no—
461C2×C4—1221no—
462C2×C4—1221no—
463C2×C4—1221no—
464C2×C4—1221no—
465C2×C4—1221no—
466C2×C4—1221no—
467C2×C4—1221no—
468C2×C4—1221no—
469C2×C4—1221no—
470C2×C4—2444no—
471C2×C4C2×D24412yes—
472C2×C4C2×D24412yes—
473C2×C4D4×D6112yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—1222no—
482C22—1222no—
483C22—1222no—
484C22—1222no—
485C22—1222no—
486C22—1222no—
487C22—1222no—
488C22—1222no—
489C22—1222no—
490C22—24416no—
491C22—2441no—
492C22—2441no—
493C22—2441no—
494C22—2441no—
495C22—2441no—
496C22—2441no—
497C22—2441no—
498C22—2441no—
499C22—2441no—
500C22—2441no—
501C22—2441no—
502C22—2441no—
503C22—2441no—
504C22—2441no—
505C22—2441no—
506C22—2441no—
507C22—2441no—
508C22—2441no—
509C22—2441no—
510C22C2×D4×D6111yescharacteristic
511C22C22×D24411yescharacteristic
512C22#41×D6111yescharacteristic
513C22#1451982211yescharacteristic
514C22#1451982311yescharacteristic
515C22#1451982311yescharacteristic
516C22#1451982311yescharacteristic
517C4—22no—
518C4—22no—
519C4—22no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—2441no—
524C4—2441no—
525C4—2441no—
526C4—2441no—
527C2—42no—
528C2—4881no—
529C2—2442no—
530C2—2442no—
531C2—2442no—
532C2#1684032011yescharacteristic
533C2#1684033111yescharacteristic
534C2#1684035111yescharacteristic
535C2D4×D24411yescharacteristic
536C2#1684040511yescharacteristic
537C2#1684040711yescharacteristic
538C2#1684050211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#388C2
hypercenter#388D61
hypocenterC61#2678
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#14519759C2semidirect
2. C2×#14519752C2semidirect
3. C2×#14519747C2semidirect
4. C2×#14519747C2semidirect
5. #16839689C2semidirect
6. #16839684C2semidirect
7. #16839680C2semidirect
8. #16839678C2semidirect
9. #16839672C2semidirect
10. #16839671C2semidirect
11. #16839664C2semidirect
12. #16839664C2semidirect
13. #16839640C2semidirect
14. #16839617C2semidirect
15. C61×#388C2semidirect
21. C22×D244C22semidirect
24. C22×C4×D61C22semidirect
29. C2×C4⋊Dic61C22semidirect
30. C2×C4⋊Dic61C22semidirect
31. C2×#11758196C22semidirect
41. C2×#11758198C22semidirect
42. C2×#11758198C22semidirect
43. C2×#11758198C22semidirect
44. C2×#11758198C22semidirect
45. C2×#11758198C22semidirect
46. #14519684C22semidirect
47. #14519684C22semidirect
48. C2×C4⋊C4×C61C22semidirect
52. C2×C42×C61C22semidirect
53. #95×C61C22semidirect
54. #95×C61C22semidirect
97. C2×D244D4semidirect
104. C22⋊C4×C61D4semidirect
282. #388D61semidirect
285. C61#2678semidirect
302. C2×C4⋊C4C2×D61semidirect
320. C2×C42C2×D61semidirect
323. #95C2×D61semidirect
324. #95C2×D61semidirect
391. C22⋊C4D244semidirect