Finite Group Databasebeta

← #21449355

Subgroups — #21449355

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×#14519750C211yesmaximal, characteristic, complemented
3C2×#14519746C211yesmaximal, characteristic, complemented
4C2×#14519746C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊D61C211yesmaximal, characteristic, complemented
6#16839685C211yesmaximal, characteristic, complemented
7#16839677C211yesmaximal, characteristic, complemented
8#16839677C211yesmaximal, characteristic, complemented
9#16839671C211yesmaximal, characteristic, complemented
10#16839662C211yesmaximal, characteristic, complemented
11#16839655C211yesmaximal, characteristic, complemented
12#16839641C211yesmaximal, characteristic, complemented
13#16839638C211yesmaximal, characteristic, complemented
14#16839635C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic, complemented
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C22×C22⋊D61C2211yescharacteristic
22C22×C22⋊D61C2211yescharacteristic
23C22×C4×D61C2211yescharacteristic, complemented
24#14519751—24no—
25#14519750—24no—
26#14519746—24no—
27#14519746—24no—
28C4×C22⋊D61—24no—
29C2×C4⋊Dic61C2211yescharacteristic, complemented
30C2×#11758196C2211yescharacteristic, complemented
31C2×#11758196C2211yescharacteristic, complemented
32C2×#11758196C2211yescharacteristic, complemented
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×C22⋊Dic61C2211yescharacteristic
37C2×C22⋊Dic61C2211yescharacteristic
38C2×C22⋊Dic61C2211yescharacteristic
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
48#14519684C2211yescharacteristic, complemented
49C25×C61C2211yescharacteristic
50C23×C4×C61C2211yescharacteristic
51C23×C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61—24no—
53C2×C22⋊C4×C61C2211yescharacteristic
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
67C23×D61C2311yescharacteristic
68C23×D61C2311yescharacteristic
69C22×C4×C61—22no—
70C22×C4×C61—22no—
71C22×C4×C61—22no—
72C22×C4×C61—22no—
73C22×C4×C61—41no—
74C22×C4×C61—41no—
75C22×C4×C61C2311yescharacteristic
76C22×C4×C61C2311yescharacteristic
77C22×C4×C61C2311yescharacteristic
78C22×C4×C61C2311yescharacteristic
79C2×C22⋊D61—22no—
80C2×C22⋊D61—22no—
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—22no—
90C2×C22⋊D61—22no—
91C2×C22⋊D61—22no—
92C2×C22⋊D61—41no—
93C2×C22⋊D61—41no—
94C2×C22⋊D61—41no—
95C2×C22⋊D61—41no—
96C2×C22⋊D61D414yescomplemented
97C22×Dic61C2311yescharacteristic
98C22×Dic61C2311yescharacteristic
99C22×Dic61C2311yescharacteristic
100C22×Dic61C2311yescharacteristic
101C22×Dic61C2311yescharacteristic
102C22×Dic61C2311yescharacteristic
103C2×D244—22no—
104C2×D244—22no—
105C2×D244—41no—
106C2×C4×D61—22no—
107C2×C4×D61—22no—
108C2×C4×D61—41no—
109C22⋊C4×C61—22no—
110C22⋊C4×C61—22no—
111C22⋊C4×C61—22no—
112C22⋊C4×C61D414yescomplemented
113C22⋊Dic61—22no—
114C22⋊Dic61—22no—
115C22⋊Dic61—22no—
116C22⋊Dic61—22no—
117C22⋊Dic61—22no—
118C22⋊Dic61D414yescomplemented
119#11758198—22no—
120#11758198—22no—
121#11758198—22no—
122#11758198—22no—
123#11758198—41no—
124C4⋊Dic61—22no—
125#11758196—22no—
126#11758196—22no—
127#11758196—41no—
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—44no—
147C23×C61—44no—
148C23×C61—44no—
149C23×C61—44no—
150C23×C61—44no—
151C23×C61—44no—
152C23×C61C2×D412yes—
153C23×C61C2×D412yes—
154C23×C61C2×D412yes—
155C23×C61#4112yes—
156C23×C61#4112yes—
157C23×C61C2411yescharacteristic
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—21no—
162C22×D61—21no—
163C22×D61—21no—
164C22×D61—21no—
165C22×D61—21no—
166C22×D61—21no—
167C22×D61—21no—
168C22×D61—21no—
169C22×D61—21no—
170C22×D61—21no—
171C22×D61C2×D412yes—
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×C61—44no—
183C2×C4×C61—44no—
184C2×C4×C61C2×D412yes—
185C2×C4×C61C2×D412yes—
186C22⋊D61—28no—
187C22⋊D61—44no—
188C22⋊D61—44no—
189C22⋊D61—44no—
190C22⋊D61—44no—
191C22⋊D61—44no—
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—21no—
207C2×Dic61C2×D412yes—
208C2×Dic61C2×D412yes—
209C2×Dic61C2×D412yes—
210D244—44no—
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#12114yescomplemented
234C22×C61C22×D411yescharacteristic
235C22×C61C22×D411yescharacteristic
236C22×C61C22×D411yescharacteristic
237C22×C61C2×#4111yescharacteristic
238C22×C61C2×#4111yescharacteristic
239C22×C61H(5,𝔽2)11yescharacteristic
240C22×C61H(5,𝔽2)11yescharacteristic
241C2×D61—22no—
242C2×D61—22no—
243C2×D61—22no—
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—41no—
258C4×C61—41no—
259Dic61—22no—
260Dic61—22no—
261Dic61—22no—
262Dic61—41no—
263Dic61—41no—
264Dic61—41no—
265#2424—611nomaximal, Sylow
266C2×C61—24no—
267C2×C61—42no—
268C2×C61—42no—
269C2×C61C2×#12111yescharacteristic
270C2×C61#52511yescharacteristic
271C2×C61#53811yescharacteristic
272C2×C61D4211yescharacteristic
273C2×C61D4211yescharacteristic
274C2×C61#54611yescharacteristic
275C2×C61#54611yescharacteristic
276D61—42no—
277D61—81no—
278C2×#121—611no—
279C2×#121—611no—
280C2×#120—611no—
281C2×#120—611no—
282C2×C4×D4—611no—
283C22×C22⋊C4D6111yescharacteristic, complemented
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×D4—611no—
300C22×D4—611no—
301C22×D4—611no—
302C23×C4—611no—
303C23×C4C2×D6111yescharacteristic
304C23×C4C2×D6111yescharacteristic
305#121—1224no—
306#121—1224no—
307#120—1224no—
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—24no—
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⋊C4C2×D6111yescharacteristic
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—
343C24—611no—
344C24C22×D6111yescharacteristic
345C24C22×D6111yescharacteristic
346C24C22×D6111yescharacteristic
347C2×D4—614no—
348C2×D4—1222no—
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—1222no—
363C2×D4—2441no—
364C2×D4—2441no—
365C2×D4—2441no—
366C2×D4—2441no—
367C2×D4—2441no—
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—611no—
380C22×C4—1222no—
381C22×C4—1222no—
382C22×C4—2441no—
383C22×C4C22×D6111yescharacteristic
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—22no—
394C22⋊C4—614no—
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—44no—
425C23—44no—
426C23—44no—
427C23—44no—
428C23—44no—
429C23—44no—
430C23—612no—
431C23—1221no—
432C23—1221no—
433C23—1221no—
434C23—1221no—
435C23—1221no—
436C23—1221no—
437C23—1221no—
438C23—1221no—
439C23—1221no—
440C23—1221no—
441C23—1221no—
442C23—1221no—
443C23—1221no—
444C23#1175822212yes—
445C23#1175822212yes—
446C23D4×D6112yes—
447C23D4×D6112yes—
448C23C2×C22⋊D6112yes—
449C23C23×D6111yescharacteristic
450D4—1228no—
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—44no—
468C2×C4—44no—
469C2×C4—612no—
470C2×C4—612no—
471C2×C4—612no—
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—1221no—
486C2×C4—1221no—
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—1222no—
512C22—1222no—
513C22—1222no—
514C22—2441no—
515C22—2441no—
516C22—2441no—
517C22—2441no—
518C22—2441no—
519C22—2441no—
520C22—2441no—
521C22—2441no—
522C22—2441no—
523C22—2441no—
524C22—2441no—
525C22#1451975014yescomplemented
526C22C2×D4×D6111yescharacteristic
527C22C2×D4×D6111yescharacteristic
528C22C22×C22⋊D6111yescharacteristic
529C22C2×#1175822211yescharacteristic
530C22C2×#1175822211yescharacteristic
531C22#1451982211yescharacteristic
532C22#1451982211yescharacteristic
533C4—22no—
534C4—22no—
535C4—41no—
536C4—41no—
537C4—1222no—
538C4—1222no—
539C4—1222no—
540C4—2441no—
541C4—2441no—
542C4—2441no—
543C2—24no—
544C2—42no—
545C2—42no—
546C2—4881no—
547C2—2442no—
548C2C2×#1451975011yescharacteristic
549C2#1684027311yescharacteristic
550C2#1684035011yescharacteristic
551C2D4×C22⋊D6111yescharacteristic
552C2D4×C22⋊D6111yescharacteristic
553C2#1684040211yescharacteristic
554C2#1684040211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC22×C22⋊C4×C61C2
hypercenterC22×C22⋊C4D61
hypocenterC61#2424
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14519751C2semidirect
2. C2×#14519750C2semidirect
3. C2×#14519746C2semidirect
4. C2×#14519746C2semidirect
5. C2×C4×C22⋊D61C2semidirect
6. #16839685C2semidirect
7. #16839677C2semidirect
8. #16839677C2semidirect
9. #16839671C2semidirect
10. #16839662C2semidirect
11. #16839655C2semidirect
12. #16839641C2semidirect
13. #16839638C2semidirect
14. #16839635C2semidirect
15. C22×C22⋊C4×C61C2semidirect
16. C22×D244C22semidirect
23. C22×C4×D61C22semidirect
29. C2×C4⋊Dic61C22semidirect
30. C2×#11758196C22semidirect
31. C2×#11758196C22semidirect
32. 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. #14519684C22semidirect
96. C2×C22⋊D61D4semidirect
112. C22⋊C4×C61D4semidirect
118. C22⋊Dic61D4semidirect
233. C22×C61#121semidirect
283. C22×C22⋊C4D61semidirect
293. C61#2424semidirect
405. C22⋊C4C22⋊D61semidirect
525. C22#14519750semidirect