Finite Group Databasebeta

← #21449360

Subgroups — #21449360

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×#14519752C211yesmaximal, characteristic, complemented
2C2×#14519750C211yesmaximal, characteristic, complemented
3C2×#14519747C211yesmaximal, characteristic, complemented
4C2×#14519747C211yesmaximal, characteristic, complemented
5C2×C4×D244C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×D61C211yesmaximal, characteristic, complemented
7#16839684C211yesmaximal, characteristic, complemented
8#16839678C211yesmaximal, characteristic, complemented
9#16839678C211yesmaximal, characteristic, complemented
10#16839672C211yesmaximal, characteristic, complemented
11#16839664C211yesmaximal, characteristic, complemented
12#16839640C211yesmaximal, characteristic, complemented
13#16839640C211yesmaximal, characteristic, complemented
14#16839636C211yesmaximal, 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
25C22×C4×D61C2211yescharacteristic
26C22×C4×D61C2211yescharacteristic, complemented
27#14519752—24no—
28#14519750—24no—
29#14519747—24no—
30#14519747—24no—
31C4×D244—24no—
32C2×C4⋊Dic61C2211yescharacteristic, complemented
33C2×C4⋊Dic61C2211yescharacteristic, complemented
34C2×#11758196C2211yescharacteristic, complemented
35C2×C22⋊Dic61C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic, complemented
43C2×#11758198C2211yescharacteristic, complemented
44C2×#11758198C2211yescharacteristic, complemented
45C2×#11758198C2211yescharacteristic, complemented
46C2×#11758198C2211yescharacteristic, complemented
47C22⋊C4×D61—24no—
48#14519684C2211yescharacteristic, complemented
49#14519684C2211yescharacteristic, complemented
50C2×C4⋊C4×C61C2211yescharacteristic, complemented
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic
53C2×C22⋊C4×C61C2211yescharacteristic
54C2×C42×C61C2211yescharacteristic, complemented
55#95×C61C2211yescharacteristic, complemented
56#95×C61C2211yescharacteristic, complemented
57C24×C61C2311yescharacteristic
58C23×D61—22no—
59C23×D61—22no—
60C23×D61—22no—
61C23×D61—22no—
62C23×D61—22no—
63C23×D61—41no—
64C23×D61—41no—
65C23×D61C2311yescharacteristic
66C23×D61C2311yescharacteristic
67C23×D61C2311yescharacteristic
68C23×D61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C22×C4×C61C2311yescharacteristic
71C22×C4×C61C2311yescharacteristic
72C22×C4×C61C2311yescharacteristic
73C22×C4×C61C2311yescharacteristic
74C22×C4×C61C2311yescharacteristic
75C2×C22⋊D61—22no—
76C2×C22⋊D61—22no—
77C2×C22⋊D61—22no—
78C2×C22⋊D61—22no—
79C2×C22⋊D61—41no—
80C2×C22⋊D61—41no—
81C22×Dic61C2311yescharacteristic
82C22×Dic61C2311yescharacteristic
83C22×Dic61C2311yescharacteristic
84C22×Dic61C2311yescharacteristic
85C2×D244—22no—
86C2×D244—22no—
87C2×D244—22no—
88C2×D244—22no—
89C2×D244—22no—
90C2×D244—22no—
91C2×D244—22no—
92C2×D244—22no—
93C2×D244—22no—
94C2×D244—22no—
95C2×D244—22no—
96C2×D244—41no—
97C2×D244—41no—
98C2×D244—41no—
99C2×D244D414yescomplemented
100C2×C4×D61—22no—
101C2×C4×D61—22no—
102C2×C4×D61—22no—
103C2×C4×D61—22no—
104C2×C4×D61—22no—
105C2×C4×D61—22no—
106C2×C4×D61—41no—
107C2×C4×D61—41no—
108C2×C4×D61—41no—
109C4⋊C4×C61—22no—
110C22⋊C4×C61—22no—
111C22⋊C4×C61—22no—
112C22⋊C4×C61D414yescomplemented
113C42×C61—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×C61C2×D412yes—
136C23×C61C2411yescharacteristic
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—28no—
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—21no—
157C22×D61—21no—
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—44no—
162C22×D61—44no—
163C22×D61—44no—
164C22×D61—44no—
165C22×D61—44no—
166C22×D61—44no—
167C22×D61C2×D412yes—
168C22×D61C2×D412yes—
169C22×D61C2×D412yes—
170C22×D61#4112yes—
171C22×D61#4112yes—
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—21no—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61C2×D412yes—
187C2×C4×C61C2×D412yes—
188C2×C4×C61C2×D412yes—
189C2×C4×C61C2×D412yes—
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×Dic61C2×D412yes—
204D244—28no—
205D244—44no—
206D244—44no—
207D244—44no—
208D244—44no—
209C4×D61—44no—
210C4×D61—44no—
211C4×D61—44no—
212C22×C61—22no—
213C22×C61—22no—
214C22×C61—22no—
215C22×C61—41no—
216C22×C61—41no—
217C22×C61—41no—
218C22×C61—41no—
219C22×C61C22×D411yescharacteristic
220C22×C61C22×D411yescharacteristic
221C22×C61C22×D411yescharacteristic
222C22×C61C2×#4111yescharacteristic
223C22×C61C2×#4111yescharacteristic
224C22×C61H(5,𝔽2)11yescharacteristic
225C22×C61H(5,𝔽2)11yescharacteristic
226C2×D61—22no—
227C2×D61—22no—
228C2×D61—22no—
229C2×D61—22no—
230C2×D61—22no—
231C2×D61—22no—
232C2×D61—22no—
233C2×D61—22no—
234C2×D61—22no—
235C2×D61—22no—
236C2×D61—22no—
237C2×D61—22no—
238C2×D61—416no—
239C2×D61—41no—
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#12114yescomplemented
255C4×C61—22no—
256C4×C61—22no—
257C4×C61—22no—
258C4×C61—22no—
259C4×C61—41no—
260C4×C61—41no—
261Dic61—22no—
262Dic61—41no—
263Dic61—41no—
264Dic61—41no—
265#2424—611nomaximal, Sylow
266C2×C61—42no—
267C2×C61C2×#12111yescharacteristic
268C2×C61#52511yescharacteristic
269C2×C61#53811yescharacteristic
270C2×C61D4211yescharacteristic
271C2×C61D4211yescharacteristic
272C2×C61#54611yescharacteristic
273C2×C61#54611yescharacteristic
274D61—24no—
275D61—42no—
276D61—42no—
277D61—81no—
278C2×#121—611no—
279C2×#121—611no—
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#388D6111yescharacteristic, complemented
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×D4—611no—
302C23×C4—611no—
303C23×C4—611no—
304C23×C4—611no—
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⋊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—1224no—
327C2×C22⋊C4C2×D6111yescharacteristic
328C2×C22⋊C4C2×D6111yescharacteristic
329C2×C22⋊C4C2×D6111yescharacteristic
330C2×C42C2×D6111yescharacteristic, complemented
331#95—611no—
332#95—611no—
333#95C2×D6111yescharacteristic, complemented
334#95C2×D6111yescharacteristic, complemented
335C24—611no—
336C24—611no—
337C24—611no—
338C24—611no—
339C24—1222no—
340C24—1222no—
341C24—1222no—
342C24—1222no—
343C24—1222no—
344C24—2441no—
345C24—2441no—
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—611no—
369C22×C4—611no—
370C22×C4—611no—
371C22×C4—611no—
372C22×C4—1222no—
373C22×C4—1222no—
374C22×C4—1222no—
375C22×C4—1222no—
376C22×C4—1222no—
377C22×C4—1222no—
378C22×C4—2441no—
379C22×C4—2441no—
380C22×C4—2441no—
381C22×C4C22×D6111yescharacteristic
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—22no—
393C22⋊C4—614no—
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⋊C4D24414yescomplemented
406C42—22no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—612no—
414C23—612no—
415C23—612no—
416C23—612no—
417C23—612no—
418C23—1228no—
419C23—1221no—
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—1221no—
440C23—1221no—
441C23—1221no—
442C23—2444no—
443C23—2444no—
444C23—2444no—
445C23—2444no—
446C23—2444no—
447C23—2444no—
448C23C2×D24412yes—
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—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
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—2444no—
484C2×C4—2444no—
485C2×C4—2444no—
486C2×C4C2×D24412yes—
487C2×C4C2×D24412yes—
488C2×C4D4×D6112yes—
489C2×C4D4×D6112yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—614no—
498C22—1222no—
499C22—1222no—
500C22—1222no—
501C22—1222no—
502C22—1222no—
503C22—1222no—
504C22—1222no—
505C22—1222no—
506C22—1222no—
507C22—1222no—
508C22—1222no—
509C22—1222no—
510C22—24416no—
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—2441no—
526C22C2×D4×D6111yescharacteristic
527C22C2×D4×D6111yescharacteristic
528C22C22×D24411yescharacteristic
529C22#41×D6111yescharacteristic
530C22#41×D6111yescharacteristic
531C22#1451982311yescharacteristic
532C22#1451982311yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—22no—
537C4—41no—
538C4—41no—
539C4—1222no—
540C4—2441no—
541C4—2441no—
542C4—2441no—
543C2—42no—
544C2—1224no—
545C2—4881no—
546C2—2442no—
547C2—2442no—
548C2#121×D6111yescharacteristic
549C2#1684027411yescharacteristic
550C2#1684035111yescharacteristic
551C2D4×D24411yescharacteristic
552C2D4×D24411yescharacteristic
553C2#1684040411yescharacteristic
554C2#1684040511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#388C2
hypercenter#388D61
hypocenterC61#2424
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#14519752C2semidirect
2. C2×#14519750C2semidirect
3. C2×#14519747C2semidirect
4. C2×#14519747C2semidirect
5. C2×C4×D244C2semidirect
6. C2×C22⋊C4×D61C2semidirect
7. #16839684C2semidirect
8. #16839678C2semidirect
9. #16839678C2semidirect
10. #16839672C2semidirect
11. #16839664C2semidirect
12. #16839640C2semidirect
13. #16839640C2semidirect
14. #16839636C2semidirect
15. C61×#388C2semidirect
21. C22×D244C22semidirect
26. C22×C4×D61C22semidirect
32. C2×C4⋊Dic61C22semidirect
33. C2×C4⋊Dic61C22semidirect
34. C2×#11758196C22semidirect
42. C2×#11758198C22semidirect
43. C2×#11758198C22semidirect
44. C2×#11758198C22semidirect
45. C2×#11758198C22semidirect
46. C2×#11758198C22semidirect
48. #14519684C22semidirect
49. #14519684C22semidirect
50. C2×C4⋊C4×C61C22semidirect
54. C2×C42×C61C22semidirect
55. #95×C61C22semidirect
56. #95×C61C22semidirect
99. C2×D244D4semidirect
112. C22⋊C4×C61D4semidirect
125. #11758198D4semidirect
254. C2×D61#121semidirect
289. #388D61semidirect
293. C61#2424semidirect
313. C2×C4⋊C4C2×D61semidirect
330. C2×C42C2×D61semidirect
333. #95C2×D61semidirect
334. #95C2×D61semidirect
405. C22⋊C4D244semidirect