Finite Group Databasebeta

← #21452149

Subgroups — #21452149

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×#14519762C211yesmaximal, characteristic, complemented
2C2×#14519752C211yesmaximal, characteristic, complemented
3C2×#14519747C211yesmaximal, characteristic, complemented
4C2×#14519747C211yesmaximal, characteristic, complemented
5#16839691C211yesmaximal, characteristic, complemented
6#16839679C211yesmaximal, characteristic, complemented
7#16839679C211yesmaximal, characteristic, complemented
8#16839672C211yesmaximal, characteristic, complemented
9#16839671C211yesmaximal, characteristic, complemented
10#16839663C211yesmaximal, characteristic, complemented
11#16839662C211yesmaximal, characteristic, complemented
12#16839652C211yesmaximal, characteristic, complemented
13#16839638C211yesmaximal, characteristic, complemented
14#16839617C211yesmaximal, characteristic, complemented
15C61×#396C211yesmaximal, 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#14519762—24no—
26#14519752—24no—
27#14519747—24no—
28#14519747—24no—
29C2×#11758196C2211yescharacteristic, complemented
30C2×C22⋊Dic61C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic, complemented
40C2×#11758198C2211yescharacteristic, complemented
41C2×#11758198C2211yescharacteristic, complemented
42C2×#11758198C2211yescharacteristic, complemented
43C2×#11758198C2211yescharacteristic, complemented
44C2×C4×Dic61C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47#14519684C2211yescharacteristic, complemented
48C2×C4⋊C4×C61C2211yescharacteristic, complemented
49C2×C4⋊C4×C61C2211yescharacteristic, complemented
50C2×C4⋊C4×C61C2211yescharacteristic, complemented
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic
53C2×C22⋊C4×C61C2211yescharacteristic
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—22no—
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—41no—
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—
102C4⋊C4×C61—22no—
103C4⋊C4×C61—41no—
104C22⋊C4×C61—22no—
105C22⋊C4×C61—22no—
106C22⋊C4×C61—41no—
107C22⋊Dic61—41no—
108#11758198—22no—
109#11758198—22no—
110#11758198—22no—
111#11758198—22no—
112#11758198—22no—
113#11758198—22no—
114#11758198—22no—
115#11758198—41no—
116#11758198—41no—
117#11758198—41no—
118#11758198—41no—
119#11758198—41no—
120#11758198D414yescomplemented
121#11758196—22no—
122C4×Dic61—41no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61#4112yes—
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×D61C2×D412yes—
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×C61—21no—
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×Dic61C2×D412yes—
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—41no—
250C4×C61—41no—
251C4×C61—41no—
252C4×C61—41no—
253Dic61—22no—
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#396D6111yescharacteristic, complemented
276#394—611no—
277#394—611no—
278#392—611no—
279#392—611no—
280#390—611no—
281#390—611no—
282#388—611no—
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⋊C4C2×D6111yescharacteristic, complemented
301C2×C4⋊C4C2×D6111yescharacteristic, complemented
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×C42—611no—
321#95—611no—
322#95—611no—
323#95—611no—
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—22no—
373C4⋊C4—41no—
374C4⋊C4—1222no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—41no—
378C22⋊C4—614no—
379C22⋊C4—1222no—
380C22⋊C4—1222no—
381C22⋊C4—1222no—
382C22⋊C4—1222no—
383C22⋊C4—1222no—
384C22⋊C4—1222no—
385C22⋊C4—1222no—
386C22⋊C4—2441no—
387C22⋊C4—2441no—
388C22⋊C4—2441no—
389C22⋊C4—2441no—
390C22⋊C4—2441no—
391C22⋊C4—2441no—
392C42—2441no—
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—
434C23#1175822612yes—
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—21no—
459C2×C4—612no—
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—1221no—
471C2×C4—2444no—
472C2×C4D4×D6112yes—
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
511C22C2×D4×D6111yescharacteristic
512C22C2×#1175822611yescharacteristic
513C22#1451982211yescharacteristic
514C22#1451982311yescharacteristic
515C22#1451982311yescharacteristic
516C22#1451982311yescharacteristic
517C4—22no—
518C4—22no—
519C4—41no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—1222no—
524C4—2441no—
525C4—2441no—
526C4—2441no—
527C2—42no—
528C2—4881no—
529C2—2442no—
530C2—2442no—
531C2—2442no—
532C2#1684032011yescharacteristic
533C2#1684032811yescharacteristic
534C2#1684035211yescharacteristic
535C2#1684039611yescharacteristic
536C2#1684040311yescharacteristic
537C2#1684040311yescharacteristic
538C2#1684050311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#396C2
hypercenter#396D61
hypocenterC61#2678
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#14519762C2semidirect
2. C2×#14519752C2semidirect
3. C2×#14519747C2semidirect
4. C2×#14519747C2semidirect
5. #16839691C2semidirect
6. #16839679C2semidirect
7. #16839679C2semidirect
8. #16839672C2semidirect
9. #16839671C2semidirect
10. #16839663C2semidirect
11. #16839662C2semidirect
12. #16839652C2semidirect
13. #16839638C2semidirect
14. #16839617C2semidirect
15. C61×#396C2semidirect
21. C22×D244C22semidirect
24. C22×C4×D61C22semidirect
29. C2×#11758196C22semidirect
39. C2×#11758198C22semidirect
40. C2×#11758198C22semidirect
41. C2×#11758198C22semidirect
42. C2×#11758198C22semidirect
43. C2×#11758198C22semidirect
44. C2×C4×Dic61C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
47. #14519684C22semidirect
48. C2×C4⋊C4×C61C22semidirect
49. C2×C4⋊C4×C61C22semidirect
50. C2×C4⋊C4×C61C22semidirect
54. #95×C61C22semidirect
97. C2×D244D4semidirect
120. #11758198D4semidirect
275. #396D61semidirect
285. C61#2678semidirect
300. C2×C4⋊C4C2×D61semidirect
301. C2×C4⋊C4C2×D61semidirect
302. C2×C4⋊C4C2×D61semidirect
324. #95C2×D61semidirect