Finite Group Databasebeta

← #21449358

Subgroups — #21449358

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×#14519749C211yesmaximal, characteristic, complemented
2C2×#14519748C211yesmaximal, characteristic, complemented
3C2×#14519745C211yesmaximal, characteristic, complemented
4C2×#14519745C211yesmaximal, characteristic, complemented
5C2×#14519737C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×D61C211yesmaximal, characteristic, complemented
7#16839685C211yesmaximal, characteristic, complemented
8#16839678C211yesmaximal, characteristic, complemented
9#16839677C211yesmaximal, characteristic, complemented
10#16839665C211yesmaximal, characteristic, complemented
11#16839654C211yesmaximal, characteristic, complemented
12#16839642C211yesmaximal, characteristic, complemented
13#16839638C211yesmaximal, characteristic, complemented
14#16839636C211yesmaximal, characteristic, complemented
15C61×#392C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C23×Dic61C2211yescharacteristic, complemented
22C22×C4×D61C2211yescharacteristic
23C22×C4×D61C2211yescharacteristic
24#14519749—24no—
25#14519748—24no—
26#14519745—24no—
27#14519745—24no—
28#14519737—24no—
29C2×C4⋊Dic61C2211yescharacteristic, complemented
30C2×C4⋊Dic61C2211yescharacteristic, complemented
31C2×#11758196C2211yescharacteristic, complemented
32C2×#11758196C2211yescharacteristic, complemented
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×C22⋊Dic61C2211yescharacteristic, complemented
37C2×C22⋊Dic61C2211yescharacteristic, complemented
38C2×C22⋊Dic61C2211yescharacteristic, complemented
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43C2×#11758198C2211yescharacteristic
44C2×#11758198C2211yescharacteristic
45C22⋊C4×D61—24no—
46C2×C4×Dic61C2211yescharacteristic, complemented
47#14519684C2211yescharacteristic, complemented
48#14519684C2211yescharacteristic, complemented
49#14519684C2211yescharacteristic, complemented
50C22×D4×C61C2211yescharacteristic
51C22×D4×C61C2211yescharacteristic
52C22×D4×C61C2211yescharacteristic, complemented
53C2×C22⋊C4×C61C2211yescharacteristic
54C2×C22⋊C4×C61C2211yescharacteristic, complemented
55C2×C22⋊C4×C61C2211yescharacteristic, complemented
56#95×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×C61C2311yescharacteristic
79C22×C4×C61C2311yescharacteristic
80C22×C4×C61C2311yescharacteristic
81C22×C4×C61C2311yescharacteristic
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—41no—
92C2×C22⋊D61—41no—
93C2×C22⋊D61D414yescomplemented
94C22×Dic61—22no—
95C22×Dic61—22no—
96C22×Dic61—41no—
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—
109C22⋊C4×C61—22no—
110C22⋊C4×C61—22no—
111C22⋊C4×C61—41no—
112C22⋊Dic61—22no—
113C22⋊Dic61—22no—
114C22⋊Dic61—22no—
115C22⋊Dic61—22no—
116C22⋊Dic61—22no—
117C22⋊Dic61—22no—
118#11758198—22no—
119#11758198—22no—
120#11758198—22no—
121#11758198—22no—
122#11758198D414yescomplemented
123#11758198D414yescomplemented
124C4⋊Dic61—22no—
125C4⋊Dic61—41no—
126#11758196—22no—
127#11758196—22no—
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×C61#4112yes—
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×D61C2×D412yes—
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—21no—
185C2×C4×C61C2×D412yes—
186C2×C4×C61C2×D412yes—
187C22⋊D61—28no—
188C22⋊D61—44no—
189C22⋊D61—44no—
190C22⋊D61—44no—
191C2×Dic61—21no—
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—44no—
207C2×Dic61C2×D412yes—
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—41no—
258C4×C61—41no—
259Dic61—22no—
260Dic61—22no—
261Dic61—22no—
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×#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#392D6111yescharacteristic, complemented
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×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⋊C4—611no—
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, complemented
329C2×C22⋊C4C2×D6111yescharacteristic, complemented
330C2×C42—611no—
331#95—611no—
332#95—611no—
333#95—611no—
334#95C2×D6111yescharacteristic, complemented
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—611no—
369C22×C4—611no—
370C22×C4—611no—
371C22×C4—611no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—1222no—
375C22×C4—1222no—
376C22×C4—1222no—
377C22×C4—1222no—
378C22×C4—1222no—
379C22×C4—1222no—
380C22×C4—2441no—
381C22×C4—2441no—
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—41no—
394C22⋊C4—614no—
395C22⋊C4—614no—
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—1222no—
405C22⋊C4—1222no—
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—
448C23#1175822412yes—
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—21no—
467C2×C4—612no—
468C2×C4—612no—
469C2×C4—612no—
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×C4—2444no—
488C2×C4D4×D6112yes—
489C2×C4D4×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
528C22C2×D4×D6111yescharacteristic
529C22#41×D6111yescharacteristic
530C22C2×#1175822411yescharacteristic
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—42no—
544C2—42no—
545C2—81no—
546C2—1224no—
547C2—2442no—
548C2#121×D6111yescharacteristic
549C2#1684027211yescharacteristic
550C2#1684034411yescharacteristic
551C2#1684039411yescharacteristic
552C2#1684039711yescharacteristic
553C2#1684039911yescharacteristic
554C2#1684039911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2424
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14519749C2semidirect
2. C2×#14519748C2semidirect
3. C2×#14519745C2semidirect
4. C2×#14519745C2semidirect
5. C2×#14519737C2semidirect
6. C2×C22⋊C4×D61C2semidirect
7. #16839685C2semidirect
8. #16839678C2semidirect
9. #16839677C2semidirect
10. #16839665C2semidirect
11. #16839654C2semidirect
12. #16839642C2semidirect
13. #16839638C2semidirect
14. #16839636C2semidirect
15. C61×#392C2semidirect
21. C23×Dic61C22semidirect
29. C2×C4⋊Dic61C22semidirect
30. C2×C4⋊Dic61C22semidirect
31. C2×#11758196C22semidirect
32. C2×#11758196C22semidirect
36. C2×C22⋊Dic61C22semidirect
37. C2×C22⋊Dic61C22semidirect
38. C2×C22⋊Dic61C22semidirect
46. C2×C4×Dic61C22semidirect
47. #14519684C22semidirect
48. #14519684C22semidirect
49. #14519684C22semidirect
52. C22×D4×C61C22semidirect
54. C2×C22⋊C4×C61C22semidirect
55. C2×C22⋊C4×C61C22semidirect
56. #95×C61C22semidirect
93. C2×C22⋊D61D4semidirect
122. #11758198D4semidirect
123. #11758198D4semidirect
254. C2×D61#121semidirect
287. #392D61semidirect
293. C61#2424semidirect
301. C22×D4C2×D61semidirect
328. C2×C22⋊C4C2×D61semidirect
329. C2×C22⋊C4C2×D61semidirect
334. #95C2×D61semidirect