Finite Group Databasebeta

← #21449352

Subgroups — #21449352

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×#14519748C211yesmaximal, characteristic, complemented
2C2×#14519745C211yesmaximal, characteristic, complemented
3C2×#14519745C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊D61C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D61C211yesmaximal, characteristic, complemented
6#16839684C211yesmaximal, characteristic, complemented
7#16839676C211yesmaximal, characteristic, complemented
8#16839676C211yesmaximal, characteristic, complemented
9#16839670C211yesmaximal, characteristic, complemented
10#16839662C211yesmaximal, characteristic, complemented
11#16839655C211yesmaximal, characteristic, complemented
12#16839641C211yesmaximal, characteristic, complemented
13#16839638C211yesmaximal, characteristic, complemented
14#16839633C211yesmaximal, characteristic, complemented
15C2×#121×C61C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C22×C4×D61C2211yescharacteristic
22C22×C4×D61C2211yescharacteristic
23#14519748—24no—
24#14519745—24no—
25#14519745—24no—
26C4×C22⋊D61—24no—
27C2×C4⋊Dic61C2211yescharacteristic, complemented
28C2×#11758196C2211yescharacteristic, complemented
29C2×#11758196C2211yescharacteristic, complemented
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic, complemented
34C2×C22⋊Dic61C2211yescharacteristic, complemented
35C2×C22⋊Dic61C2211yescharacteristic, complemented
36C2×C22⋊Dic61C2211yescharacteristic, complemented
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43C22⋊C4×D61—24no—
44C2×C4×Dic61C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47#14519684C2211yescharacteristic, complemented
48#14519684C2211yescharacteristic, complemented
49C22×D4×C61C2211yescharacteristic
50C22×D4×C61C2211yescharacteristic
51C22×D4×C61C2211yescharacteristic, complemented
52C23×C4×C61C2211yescharacteristic, complemented
53#121×C61—24no—
54C2×C4⋊C4×C61C2211yescharacteristic, complemented
55C2×C22⋊C4×C61C2211yescharacteristic
56C2×C22⋊C4×C61C2211yescharacteristic, complemented
57C24×C61C2311yescharacteristic
58C24×C61C2311yescharacteristic
59C24×C61C2311yescharacteristic
60C23×D61—22no—
61C23×D61—22no—
62C23×D61—22no—
63C23×D61—22no—
64C23×D61—22no—
65C23×D61—41no—
66C23×D61—41no—
67C23×D61C2311yescharacteristic
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—41no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C22×C4×C61—22no—
79C22×C4×C61—22no—
80C22×C4×C61—41no—
81C22×C4×C61C2311yescharacteristic
82C22×C4×C61C2311yescharacteristic
83C22×C4×C61C2311yescharacteristic
84C22×C4×C61C2311yescharacteristic
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—22no—
93C2×C22⋊D61—22no—
94C2×C22⋊D61—41no—
95C2×C22⋊D61—41no—
96C2×C22⋊D61D414yescomplemented
97C22×Dic61C2311yescharacteristic
98C22×Dic61C2311yescharacteristic
99C22×Dic61C2311yescharacteristic
100C22×Dic61C2311yescharacteristic
101C22×Dic61C2311yescharacteristic
102C22×Dic61C2311yescharacteristic
103C2×C4×D61—22no—
104C2×C4×D61—22no—
105C2×C4×D61—22no—
106C2×C4×D61—22no—
107C2×C4×D61—41no—
108C2×C4×D61—41no—
109C4⋊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—41no—
119#11758198—22no—
120#11758198—22no—
121#11758198—22no—
122#11758198—22no—
123#11758198—22no—
124#11758198D414yescomplemented
125C4⋊Dic61—22no—
126#11758196—22no—
127#11758196—41no—
128C4×Dic61—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×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×C61C2×D412yes—
149C23×C61C2×D412yes—
150C23×C61C2411yescharacteristic
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61—28no—
156C22×D61—21no—
157C22×D61—21no—
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—21no—
162C22×D61—44no—
163C22×D61—44no—
164C22×D61—44no—
165C22×D61—44no—
166C22×D61—44no—
167C22×D61—44no—
168C22×D61C2×D412yes—
169C22×D61C2×D412yes—
170C22×D61#4112yes—
171C22×D61#4112yes—
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×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—44no—
185C2×C4×C61C2×D412yes—
186C2×C4×C61C2×D412yes—
187C2×C4×C61C2×D412yes—
188C22⋊D61—28no—
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×Dic61—21no—
208C2×Dic61C2×D412yes—
209C2×Dic61C2×D412yes—
210C4×D61—44no—
211C4×D61—44no—
212C22×C61—22no—
213C22×C61—22no—
214C22×C61—22no—
215C22×C61—22no—
216C22×C61—22no—
217C22×C61—22no—
218C22×C61—41no—
219C22×C61—41no—
220C22×C61—41no—
221C22×C61—41no—
222C22×C61—41no—
223C22×C61—41no—
224C22×C61—41no—
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×C61C22×D411yescharacteristic
234C22×C61C22×D411yescharacteristic
235C22×C61C22×D411yescharacteristic
236C22×C61C2×#4111yescharacteristic
237C22×C61C2×#4111yescharacteristic
238C22×C61H(5,𝔽2)11yescharacteristic
239C22×C61H(5,𝔽2)11yescharacteristic
240C2×D61—22no—
241C2×D61—22no—
242C2×D61—22no—
243C2×D61—22no—
244C2×D61—22no—
245C2×D61—22no—
246C2×D61—22no—
247C2×D61—22no—
248C2×D61—22no—
249C2×D61—416no—
250C2×D61—41no—
251C2×D61—41no—
252C2×D61—41no—
253C2×D61—41no—
254C2×D61#12114yescomplemented
255C4×C61—22no—
256C4×C61—22no—
257C4×C61—22no—
258C4×C61—41no—
259Dic61—22no—
260Dic61—22no—
261Dic61—41no—
262Dic61—41no—
263Dic61—41no—
264Dic61—41no—
265#2424—611nomaximal, Sylow
266C2×C61—42no—
267C2×C61—42no—
268C2×C61—81no—
269C2×C61C2×#12111yescharacteristic
270C2×C61#52511yescharacteristic
271C2×C61#53811yescharacteristic
272C2×C61D4211yescharacteristic
273C2×C61D4211yescharacteristic
274C2×C61#54611yescharacteristic
275C2×C61#54611yescharacteristic
276D61—24no—
277D61—42no—
278C2×#121—611no—
279C2×#121D6111yescharacteristic, complemented
280C2×#120—611no—
281C2×#120—611no—
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
294C25—611no—
295C22×D4—611no—
296C22×D4—611no—
297C22×D4—611no—
298C22×D4—611no—
299C22×D4C2×D6111yescharacteristic
300C22×D4C2×D6111yescharacteristic
301C22×D4C2×D6111yescharacteristic, complemented
302C23×C4—611no—
303C23×C4—611no—
304C23×C4C2×D6111yescharacteristic, complemented
305#121—24no—
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⋊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×C42—611no—
331#95—611no—
332#95—611no—
333#95—611no—
334#95—611no—
335C24—611no—
336C24—611no—
337C24—1222no—
338C24—1222no—
339C24—1222no—
340C24—1222no—
341C24—1222no—
342C24—2441no—
343C24—2441no—
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—41no—
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—1222no—
366C2×D4—2441no—
367C2×D4—2441no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—41no—
371C22×C4—611no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—611no—
377C22×C4—1222no—
378C22×C4—1222no—
379C22×C4—1222no—
380C22×C4—1222no—
381C22×C4—2441no—
382C22×C4—2441no—
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—1222no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
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—612no—
427C23—612no—
428C23—612no—
429C23—612no—
430C23—1228no—
431C23—1221no—
432C23—1221no—
433C23—1221no—
434C23—1221no—
435C23—1221no—
436C23—1221no—
437C23—1221no—
438C23—1221no—
439C23—1221no—
440C23—1221no—
441C23—2444no—
442C23—2444no—
443C23—2444no—
444C23—2444no—
445C23—2444no—
446C23—2444no—
447C23D4×D6112yes—
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—21no—
465C2×C4—21no—
466C2×C4—44no—
467C2×C4—612no—
468C2×C4—612no—
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×C4D4×D6112yes—
488C2×C4C2×C22⋊D6112yes—
489C2×C4C2×C22⋊D6112yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—614no—
512C22—1222no—
513C22—1222no—
514C22—1222no—
515C22—1222no—
516C22—1222no—
517C22—1222no—
518C22—1222no—
519C22—1222no—
520C22—1222no—
521C22—24416no—
522C22—2441no—
523C22—2441no—
524C22—2441no—
525C22—2441no—
526C22C2×D4×D6111yescharacteristic
527C22C2×D4×D6111yescharacteristic
528C22C22×C22⋊D6111yescharacteristic
529C22#41×D6111yescharacteristic
530C22#41×D6111yescharacteristic
531C22#1451982211yescharacteristic
532C22#1451982211yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—41no—
537C4—1222no—
538C4—1222no—
539C4—2441no—
540C4—2441no—
541C4—2441no—
542C4—2441no—
543C2—42no—
544C2—42no—
545C2—81no—
546C2—1224no—
547C2—2442no—
548C2#121×D6111yescharacteristic
549C2#1684026911yescharacteristic
550C2#1684034411yescharacteristic
551C2D4×C22⋊D6111yescharacteristic
552C2D4×C22⋊D6111yescharacteristic
553C2#1684040111yescharacteristic
554C2#1684040911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#121×C61C2
hypercenterC2×#121D61
hypocenterC61#2424
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14519748C2semidirect
2. C2×#14519745C2semidirect
3. C2×#14519745C2semidirect
4. C2×C4×C22⋊D61C2semidirect
5. C2×C22⋊C4×D61C2semidirect
6. #16839684C2semidirect
7. #16839676C2semidirect
8. #16839676C2semidirect
9. #16839670C2semidirect
10. #16839662C2semidirect
11. #16839655C2semidirect
12. #16839641C2semidirect
13. #16839638C2semidirect
14. #16839633C2semidirect
15. C2×#121×C61C2semidirect
27. C2×C4⋊Dic61C22semidirect
28. C2×#11758196C22semidirect
29. C2×#11758196C22semidirect
33. C2×C22⋊Dic61C22semidirect
34. C2×C22⋊Dic61C22semidirect
35. C2×C22⋊Dic61C22semidirect
36. C2×C22⋊Dic61C22semidirect
44. C2×C4×Dic61C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
47. #14519684C22semidirect
48. #14519684C22semidirect
51. C22×D4×C61C22semidirect
52. C23×C4×C61C22semidirect
54. C2×C4⋊C4×C61C22semidirect
56. C2×C22⋊C4×C61C22semidirect
96. C2×C22⋊D61D4semidirect
111. C22⋊C4×C61D4semidirect
124. #11758198D4semidirect
254. C2×D61#121semidirect
279. C2×#121D61semidirect
293. C61#2424semidirect
301. C22×D4C2×D61semidirect
304. C23×C4C2×D61semidirect
313. C2×C4⋊C4C2×D61semidirect
329. C2×C22⋊C4C2×D61semidirect
405. C22⋊C4C22⋊D61semidirect