Finite Group Databasebeta

← #21452038

Subgroups — #21452038

Order 7808.

932 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519773C211yesmaximal, characteristic, complemented
2C2×#14519750C211yesmaximal, characteristic, complemented
3C2×#14519748C211yesmaximal, characteristic, complemented
4C2×#14519747C211yesmaximal, characteristic, complemented
5C2×#14519745C211yesmaximal, characteristic, complemented
6C2×#14519745C211yesmaximal, characteristic, complemented
7#16839678C211yesmaximal, characteristic, complemented
8#16839677C211yesmaximal, characteristic, complemented
9#16839671C211yesmaximal, characteristic, complemented
10#16839670C211yesmaximal, characteristic, complemented
11#16839670C211yesmaximal, characteristic, complemented
12#16839654C211yesmaximal, characteristic, complemented
13#16839650C211yesmaximal, characteristic, complemented
14#16839640C211yesmaximal, characteristic, complemented
15C61×#392C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C22×C22⋊D61C2211yescharacteristic
22C22×C22⋊D61C2211yescharacteristic
23C22×C22⋊D61C2211yescharacteristic
24C22×C22⋊D61C2211yescharacteristic, complemented
25C22×C22⋊D61C2211yescharacteristic, complemented
26C22×C4×D61C2211yescharacteristic, complemented
27#14519773—24no—
28#14519750—24no—
29#14519748—24no—
30#14519747—24no—
31#14519745—24no—
32#14519745—24no—
33C2×C4⋊Dic61C2211yescharacteristic, complemented
34C2×#11758196C2211yescharacteristic, complemented
35C2×C22⋊Dic61C2211yescharacteristic
36C2×C22⋊Dic61C2211yescharacteristic
37C2×C22⋊Dic61C2211yescharacteristic, complemented
38C2×C22⋊Dic61C2211yescharacteristic, complemented
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43C2×#11758198C2211yescharacteristic
44C2×#11758198C2211yescharacteristic
45C2×#11758198C2211yescharacteristic, complemented
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—41no—
64C23×D61—41no—
65C23×D61—41no—
66C23×D61—41no—
67C23×D61C2311yescharacteristic
68C23×D61C2311yescharacteristic
69C23×D61C2311yescharacteristic
70C2×D4×C61—22no—
71C2×D4×C61—22no—
72C2×D4×C61—22no—
73C2×D4×C61—22no—
74C2×D4×C61—41no—
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C22×C4×C61C2311yescharacteristic
80C22×C4×C61C2311yescharacteristic
81C22×C4×C61C2311yescharacteristic
82C22×C4×C61C2311yescharacteristic
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—22no—
93C2×C22⋊D61—22no—
94C2×C22⋊D61—22no—
95C2×C22⋊D61—22no—
96C2×C22⋊D61—41no—
97C2×C22⋊D61—41no—
98C2×C22⋊D61—41no—
99C2×C22⋊D61—41no—
100C2×C22⋊D61—41no—
101C2×C22⋊D61—41no—
102C2×C22⋊D61—41no—
103C2×C22⋊D61—41no—
104C22×Dic61C2311yescharacteristic
105C22×Dic61C2311yescharacteristic
106C22×Dic61C2311yescharacteristic
107C22×Dic61C2311yescharacteristic
108C22×Dic61C2311yescharacteristic
109C2×D244—22no—
110C2×D244—22no—
111C2×D244—41no—
112C2×D244—41no—
113C2×D244—41no—
114C2×D244D414yescomplemented
115C2×C4×D61—22no—
116C2×C4×D61—22no—
117C2×C4×D61—41no—
118C22⋊C4×C61—22no—
119C22⋊C4×C61—22no—
120C22⋊C4×C61—41no—
121C22⋊Dic61—22no—
122C22⋊Dic61—22no—
123C22⋊Dic61—41no—
124C22⋊Dic61D414yescomplemented
125#11758198—22no—
126#11758198—22no—
127#11758198—22no—
128#11758198—22no—
129#11758198—22no—
130#11758198—41no—
131#11758198D414yescomplemented
132C4⋊Dic61—22no—
133#11758196—22no—
134C4×Dic61—22no—
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×C61—21no—
149C23×C61—21no—
150C23×C61—21no—
151C23×C61—21no—
152C23×C61—21no—
153C23×C61—21no—
154C23×C61—21no—
155C23×C61C2×D412yes—
156C23×C61C2411yescharacteristic
157C22×D61—21no—
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×D61—21no—
172C22×D61—21no—
173C22×D61—21no—
174C22×D61—21no—
175C22×D61—44no—
176C22×D61—44no—
177C22×D61—44no—
178C22×D61—44no—
179C22×D61—44no—
180C22×D61—44no—
181C22×D61—44no—
182C22×D61C2×D412yes—
183C22×D61C2×D412yes—
184C22×D61C2×D412yes—
185D4×C61—44no—
186D4×C61—44no—
187D4×C61—44no—
188C2×C4×C61—21no—
189C2×C4×C61—21no—
190C2×C4×C61—21no—
191C2×C4×C61—21no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61C2×D412yes—
199C2×C4×C61C2×D412yes—
200C22⋊D61—44no—
201C22⋊D61—44no—
202C22⋊D61—44no—
203C22⋊D61—44no—
204C22⋊D61—44no—
205C22⋊D61—44no—
206C22⋊D61—44no—
207C2×Dic61—21no—
208C2×Dic61—21no—
209C2×Dic61—21no—
210C2×Dic61—21no—
211C2×Dic61—21no—
212C2×Dic61—21no—
213C2×Dic61—21no—
214C2×Dic61—21no—
215C2×Dic61—21no—
216C2×Dic61—21no—
217C2×Dic61—21no—
218C2×Dic61—21no—
219C2×Dic61C2×D412yes—
220C2×Dic61C2×D412yes—
221C2×Dic61C2×D412yes—
222D244—44no—
223D244—44no—
224C4×D61—44no—
225C22×C61—22no—
226C22×C61—22no—
227C22×C61—22no—
228C22×C61—41no—
229C22×C61—41no—
230C22×C61—41no—
231C22×C61—41no—
232C22×C61—41no—
233C22×C61—41no—
234C22×C61—41no—
235C22×C61—41no—
236C22×C61—41no—
237C22×C61—41no—
238C22×C61—41no—
239C22×C61—41no—
240C22×C61—41no—
241C22×C61—41no—
242C22×C61—41no—
243C22×C61—41no—
244C22×C61—41no—
245C22×C61—41no—
246C22×C61C22×D411yescharacteristic
247C22×C61C22×D411yescharacteristic
248C22×C61C22×D411yescharacteristic
249C22×C61H(5,𝔽2)11yescharacteristic
250C22×C61H(5,𝔽2)11yescharacteristic
251C22×C61H(5,𝔽2)11yescharacteristic
252C22×C61H(5,𝔽2)11yescharacteristic
253C2×D61—22no—
254C2×D61—22no—
255C2×D61—22no—
256C2×D61—22no—
257C2×D61—22no—
258C2×D61—22no—
259C2×D61—22no—
260C2×D61—22no—
261C2×D61—22no—
262C2×D61—416no—
263C2×D61—41no—
264C2×D61—41no—
265C2×D61—41no—
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C2×D61—41no—
272C2×D61—41no—
273C2×D61—41no—
274C2×D61—41no—
275C4×C61—22no—
276C4×C61—22no—
277C4×C61—41no—
278C4×C61—41no—
279Dic61—22no—
280Dic61—22no—
281Dic61—22no—
282Dic61—41no—
283Dic61—41no—
284#2669—611nomaximal, Sylow
285C2×C61—42no—
286C2×C61—81no—
287C2×C61—81no—
288C2×C61#53411yescharacteristic
289C2×C61#53511yescharacteristic
290C2×C61#53511yescharacteristic
291C2×C61D4211yescharacteristic
292C2×C61D4211yescharacteristic
293C2×C61D4211yescharacteristic
294C2×C61#56011yescharacteristic
295D61—42no—
296D61—42no—
297D61—42no—
298C2×#127—611no—
299C2×#121—611no—
300C2×#121—611no—
301C2×#120—611no—
302C2×#120—611no—
303C2×#120—611no—
304#394—611no—
305#394—611no—
306#392—611no—
307#392—611no—
308#392—611no—
309#392D6111yescharacteristic, complemented
310#388—611no—
311#388—611no—
312#386—611no—
313C61#266911yescharacteristic, complemented, Sylow
314C25—611no—
315C22×D4—611no—
316C22×D4—611no—
317C22×D4—611no—
318C22×D4—611no—
319C22×D4—611no—
320C22×D4—611no—
321C22×D4—611no—
322C22×D4—611no—
323C22×D4—611no—
324C22×D4C2×D6111yescharacteristic
325C22×D4C2×D6111yescharacteristic
326C22×D4C2×D6111yescharacteristic, complemented
327C23×C4—611no—
328#127—1224no—
329#121—1224no—
330#121—1224no—
331#120—1224no—
332#120—1224no—
333#120—1224no—
334C2×C4⋊C4—611no—
335C2×C4⋊C4—611no—
336C2×C22⋊C4—611no—
337C2×C22⋊C4—611no—
338C2×C22⋊C4—611no—
339C2×C22⋊C4—611no—
340C2×C22⋊C4—611no—
341C2×C22⋊C4—611no—
342C2×C22⋊C4—611no—
343C2×C22⋊C4—611no—
344C2×C22⋊C4—611no—
345C2×C22⋊C4—611no—
346C2×C22⋊C4—611no—
347C2×C22⋊C4C2×D6111yescharacteristic
348C2×C22⋊C4C2×D6111yescharacteristic, complemented
349C2×C22⋊C4C2×D6111yescharacteristic, complemented
350C2×C42—611no—
351#95—611no—
352#95—611no—
353#95—611no—
354#95C2×D6111yescharacteristic, complemented
355C24—611no—
356C24—611no—
357C24—611no—
358C24—1222no—
359C24—1222no—
360C24—1222no—
361C24—2441no—
362C24—2441no—
363C24—2441no—
364C24—2441no—
365C24C22×D6111yescharacteristic
366C24C22×D6111yescharacteristic
367C24C22×D6111yescharacteristic
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—614no—
378C2×D4—1222no—
379C2×D4—1222no—
380C2×D4—1222no—
381C2×D4—1222no—
382C2×D4—1222no—
383C2×D4—1222no—
384C2×D4—1222no—
385C2×D4—1222no—
386C2×D4—1222no—
387C2×D4—1222no—
388C2×D4—1222no—
389C2×D4—1222no—
390C2×D4—1222no—
391C2×D4—1222no—
392C2×D4—1222no—
393C2×D4—2441no—
394C2×D4—2441no—
395C2×D4—2441no—
396C2×D4—2441no—
397C2×D4—2441no—
398C2×D4—2441no—
399C2×D4—2441no—
400C2×D4—2441no—
401C2×D4—2441no—
402C2×D4—2441no—
403C2×D4—2441no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—611no—
409C22×C4—1222no—
410C22×C4—1222no—
411C22×C4—2441no—
412C22×C4C22×D6111yescharacteristic
413C22×C4C22×D6111yescharacteristic
414C22×C4C22×D6111yescharacteristic
415C22×C4C22×D6111yescharacteristic
416C4⋊C4—1222no—
417C4⋊C4—1222no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—41no—
421C22⋊C4—614no—
422C22⋊C4—614no—
423C22⋊C4—1222no—
424C22⋊C4—1222no—
425C22⋊C4—1222no—
426C22⋊C4—1222no—
427C22⋊C4—1222no—
428C22⋊C4—1222no—
429C22⋊C4—1222no—
430C22⋊C4—2441no—
431C22⋊C4—2441no—
432C42—1222no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—612no—
454C23—612no—
455C23—612no—
456C23—1221no—
457C23—1221no—
458C23—1221no—
459C23—1221no—
460C23—1221no—
461C23—1221no—
462C23—1221no—
463C23—1221no—
464C23—1221no—
465C23—1221no—
466C23—1221no—
467C23—1221no—
468C23—1221no—
469C23—1221no—
470C23—1221no—
471C23—1221no—
472C23—1221no—
473C23—1221no—
474C23—2444no—
475C23—2444no—
476C23—2444no—
477C23—2444no—
478C23—2444no—
479C23—2444no—
480C23—2444no—
481C23D4×D6112yes—
482C23C23×D6111yescharacteristic
483D4—44no—
484D4—44no—
485D4—44no—
486D4—2444no—
487D4—2444no—
488D4—2444no—
489D4—2444no—
490D4—2444no—
491D4—2444no—
492D4—2444no—
493D4—2444no—
494D4—2444no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—612no—
506C2×C4—612no—
507C2×C4—612no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—1221no—
517C2×C4—1221no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—2444no—
521C2×C4D4×D6112yes—
522C2×C4D4×D6112yes—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—1222no—
545C22—1222no—
546C22—1222no—
547C22—1222no—
548C22—1222no—
549C22—1222no—
550C22—1222no—
551C22—1222no—
552C22—1222no—
553C22—24416no—
554C22—2441no—
555C22—2441no—
556C22—2441no—
557C22—2441no—
558C22—2441no—
559C22—2441no—
560C22—2441no—
561C22—2441no—
562C22—2441no—
563C22—2441no—
564C22—2441no—
565C22—2441no—
566C22C2×D4×D6111yescharacteristic
567C22C2×D4×D6111yescharacteristic
568C22C2×D4×D6111yescharacteristic
569C22#1451982211yescharacteristic
570C22#1451982211yescharacteristic
571C22#1451982211yescharacteristic
572C22#1451982311yescharacteristic
573C4—22no—
574C4—22no—
575C4—41no—
576C4—41no—
577C4—1222no—
578C4—1222no—
579C4—1222no—
580C4—2441no—
581C4—2441no—
582C2—42no—
583C2—81no—
584C2—81no—
585C2—2442no—
586C2—2442no—
587C2—2442no—
588C2#1684032211yescharacteristic
589C2#1684032711yescharacteristic
590C2#1684032811yescharacteristic
591C2#1684039411yescharacteristic
592C2#1684039611yescharacteristic
593C2#1684039711yescharacteristic
594C2#1684050011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2669
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14519773C2semidirect
2. C2×#14519750C2semidirect
3. C2×#14519748C2semidirect
4. C2×#14519747C2semidirect
5. C2×#14519745C2semidirect
6. C2×#14519745C2semidirect
7. #16839678C2semidirect
8. #16839677C2semidirect
9. #16839671C2semidirect
10. #16839670C2semidirect
11. #16839670C2semidirect
12. #16839654C2semidirect
13. #16839650C2semidirect
14. #16839640C2semidirect
15. C61×#392C2semidirect
24. C22×C22⋊D61C22semidirect
25. C22×C22⋊D61C22semidirect
26. C22×C4×D61C22semidirect
33. C2×C4⋊Dic61C22semidirect
34. C2×#11758196C22semidirect
37. C2×C22⋊Dic61C22semidirect
38. C2×C22⋊Dic61C22semidirect
45. C2×#11758198C22semidirect
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
114. C2×D244D4semidirect
124. C22⋊Dic61D4semidirect
131. #11758198D4semidirect
309. #392D61semidirect
313. C61#2669semidirect
326. C22×D4C2×D61semidirect
348. C2×C22⋊C4C2×D61semidirect
349. C2×C22⋊C4C2×D61semidirect
354. #95C2×D61semidirect