Finite Group Databasebeta

← #21452034

Subgroups — #21452034

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×#14519774C211yesmaximal, characteristic, complemented
2C2×#14519752C211yesmaximal, characteristic, complemented
3C2×#14519750C211yesmaximal, characteristic, complemented
4C2×#14519747C211yesmaximal, characteristic, complemented
5C2×#14519747C211yesmaximal, characteristic, complemented
6C2×#14519747C211yesmaximal, characteristic, complemented
7#16839680C211yesmaximal, characteristic, complemented
8#16839679C211yesmaximal, characteristic, complemented
9#16839672C211yesmaximal, characteristic, complemented
10#16839672C211yesmaximal, characteristic, complemented
11#16839671C211yesmaximal, characteristic, complemented
12#16839671C211yesmaximal, characteristic, complemented
13#16839653C211yesmaximal, characteristic, complemented
14#16839640C211yesmaximal, characteristic, complemented
15C61×#388C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×D244C2211yescharacteristic
20C22×D244C2211yescharacteristic
21C22×D244C2211yescharacteristic
22C22×D244C2211yescharacteristic
23C22×D244C2211yescharacteristic, complemented
24C22×D244C2211yescharacteristic, complemented
25C22×D244C2211yescharacteristic, complemented
26C22×C22⋊D61C2211yescharacteristic
27C22×C22⋊D61C2211yescharacteristic
28C22×C22⋊D61C2211yescharacteristic
29C22×C4×D61C2211yescharacteristic, complemented
30#14519774—24no—
31#14519752—24no—
32#14519750—24no—
33#14519747—24no—
34#14519747—24no—
35#14519747—24no—
36C2×#11758196C2211yescharacteristic, complemented
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43C2×#11758198C2211yescharacteristic, complemented
44C2×#11758198C2211yescharacteristic, complemented
45C2×#11758198C2211yescharacteristic, complemented
46C2×#11758198C2211yescharacteristic, complemented
47C2×#11758198C2211yescharacteristic, complemented
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—41no—
62C23×D61—41no—
63C23×D61—41no—
64C23×D61—41no—
65C23×D61C2311yescharacteristic
66C23×D61C2311yescharacteristic
67C23×D61C2311yescharacteristic
68C23×D61C2311yescharacteristic
69C23×D61C2311yescharacteristic
70C22×C4×C61C2311yescharacteristic
71C22×C4×C61C2311yescharacteristic
72C22×C4×C61C2311yescharacteristic
73C22×C4×C61C2311yescharacteristic
74C22×C4×C61C2311yescharacteristic
75C22×C4×C61C2311yescharacteristic
76C2×C22⋊D61—22no—
77C2×C22⋊D61—22no—
78C2×C22⋊D61—22no—
79C2×C22⋊D61—22no—
80C2×C22⋊D61—22no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—41no—
83C2×C22⋊D61—41no—
84C2×C22⋊D61—41no—
85C22×Dic61C2311yescharacteristic
86C22×Dic61C2311yescharacteristic
87C22×Dic61C2311yescharacteristic
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—22no—
97C2×D244—22no—
98C2×D244—22no—
99C2×D244—22no—
100C2×D244—22no—
101C2×D244—22no—
102C2×D244—41no—
103C2×D244—41no—
104C2×D244—41no—
105C2×D244—41no—
106C2×D244—41no—
107C2×D244—41no—
108C2×D244—41no—
109C2×D244—41no—
110C2×D244—41no—
111C2×D244—41no—
112C2×D244—41no—
113C2×D244—41no—
114C2×D244D414yescomplemented
115C2×C4×D61—22no—
116C2×C4×D61—22no—
117C2×C4×D61—41no—
118C4⋊C4×C61—22no—
119C22⋊C4×C61—22no—
120C22⋊C4×C61—22no—
121C22⋊C4×C61D414yescomplemented
122C42×C61—22no—
123#11758198—22no—
124#11758198—22no—
125#11758198—22no—
126#11758198—22no—
127#11758198—22no—
128#11758198—22no—
129#11758198—22no—
130#11758198—41no—
131#11758198—41no—
132#11758198—41no—
133#11758198D414yescomplemented
134#11758196—22no—
135C23×C61—21no—
136C23×C61—21no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—21no—
140C23×C61—21no—
141C23×C61C2×D412yes—
142C23×C61C2411yescharacteristic
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—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—
185C2×C4×C61—21no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
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×C61—21no—
199C2×C4×C61C2×D412yes—
200C2×C4×C61C2×D412yes—
201C2×C4×C61C2×D412yes—
202C2×C4×C61C2×D412yes—
203C22⋊D61—44no—
204C22⋊D61—44no—
205C22⋊D61—44no—
206C2×Dic61—21no—
207C2×Dic61—21no—
208C2×Dic61—21no—
209C2×Dic61—21no—
210C2×Dic61—21no—
211C2×Dic61—21no—
212C2×Dic61—21no—
213C2×Dic61—21no—
214C2×Dic61C2×D412yes—
215D244—44no—
216D244—44no—
217D244—44no—
218D244—44no—
219D244—44no—
220D244—44no—
221D244—44no—
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×C61C22×D411yescharacteristic
233C22×C61C22×D411yescharacteristic
234C22×C61C22×D411yescharacteristic
235C22×C61H(5,𝔽2)11yescharacteristic
236C22×C61H(5,𝔽2)11yescharacteristic
237C22×C61H(5,𝔽2)11yescharacteristic
238C22×C61H(5,𝔽2)11yescharacteristic
239C2×D61—22no—
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—416no—
249C2×D61—41no—
250C2×D61—41no—
251C2×D61—41no—
252C2×D61—41no—
253C2×D61—41no—
254C2×D61—41no—
255C2×D61—41no—
256C2×D61—41no—
257C2×D61—41no—
258C2×D61—41no—
259C2×D61—41no—
260C2×D61—41no—
261C2×D61—41no—
262C2×D61—41no—
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—22no—
278C4×C61—22no—
279C4×C61—41no—
280C4×C61—41no—
281Dic61—22no—
282Dic61—41no—
283Dic61—41no—
284#2669—611nomaximal, Sylow
285C2×C61—42no—
286C2×C61#53411yescharacteristic
287C2×C61#53511yescharacteristic
288C2×C61#53511yescharacteristic
289C2×C61D4211yescharacteristic
290C2×C61D4211yescharacteristic
291C2×C61D4211yescharacteristic
292C2×C61#56011yescharacteristic
293D61—42no—
294D61—42no—
295D61—42no—
296D61—81no—
297D61—81no—
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#392—611no—
310#388—611no—
311#388D6111yescharacteristic, complemented
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×D4—611no—
325C22×D4—611no—
326C22×D4—611no—
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⋊C4C2×D6111yescharacteristic, complemented
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
349C2×C22⋊C4C2×D6111yescharacteristic
350C2×C42C2×D6111yescharacteristic, complemented
351#95—611no—
352#95—611no—
353#95C2×D6111yescharacteristic, complemented
354#95C2×D6111yescharacteristic, complemented
355C24—611no—
356C24—611no—
357C24—611no—
358C24—611no—
359C24—611no—
360C24—1222no—
361C24—1222no—
362C24—1222no—
363C24—2441no—
364C24—2441no—
365C24—2441no—
366C24—2441no—
367C24C22×D6111yescharacteristic
368C2×D4—614no—
369C2×D4—1222no—
370C2×D4—1222no—
371C2×D4—1222no—
372C2×D4—1222no—
373C2×D4—1222no—
374C2×D4—1222no—
375C2×D4—1222no—
376C2×D4—1222no—
377C2×D4—1222no—
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—2441no—
389C2×D4—2441no—
390C2×D4—2441no—
391C2×D4—2441no—
392C2×D4—2441no—
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—1222no—
408C22×C4—1222no—
409C22×C4—2441no—
410C22×C4C22×D6111yescharacteristic
411C22×C4C22×D6111yescharacteristic
412C22×C4C22×D6111yescharacteristic
413C22×C4C22×D6111yescharacteristic
414C22×C4C22×D6111yescharacteristic
415C22×C4C22×D6111yescharacteristic
416C4⋊C4—22no—
417C4⋊C4—1222no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—614no—
421C22⋊C4—1222no—
422C22⋊C4—1222no—
423C22⋊C4—1222no—
424C22⋊C4—1222no—
425C22⋊C4—1222no—
426C22⋊C4—1222no—
427C22⋊C4—1222no—
428C22⋊C4—2441no—
429C22⋊C4—2441no—
430C22⋊C4—2441no—
431C22⋊C4D24414yescomplemented
432C42—22no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—612no—
440C23—612no—
441C23—612no—
442C23—1221no—
443C23—1221no—
444C23—1221no—
445C23—1221no—
446C23—1221no—
447C23—1221no—
448C23—1221no—
449C23—1221no—
450C23—1221no—
451C23—1221no—
452C23—1221no—
453C23—1221no—
454C23—1221no—
455C23—1221no—
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—
481C23C2×D24412yes—
482C23C23×D6111yescharacteristic
483D4—2444no—
484D4—2444no—
485D4—2444no—
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—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—612no—
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—2444no—
519C2×C4C2×D24412yes—
520C2×C4C2×D24412yes—
521C2×C4D4×D6112yes—
522C2×C4D4×D6112yes—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—1222no—
531C22—1222no—
532C22—1222no—
533C22—1222no—
534C22—1222no—
535C22—1222no—
536C22—1222no—
537C22—1222no—
538C22—1222no—
539C22—24416no—
540C22—2441no—
541C22—2441no—
542C22—2441no—
543C22—2441no—
544C22—2441no—
545C22—2441no—
546C22—2441no—
547C22—2441no—
548C22—2441no—
549C22—2441no—
550C22—2441no—
551C22—2441no—
552C22—2441no—
553C22—2441no—
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
568C22C22×D24411yescharacteristic
569C22#1451982311yescharacteristic
570C22#1451982311yescharacteristic
571C22#1451982311yescharacteristic
572C22#1451982311yescharacteristic
573C4—22no—
574C4—22no—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—41no—
579C4—1222no—
580C4—2441no—
581C4—2441no—
582C2—42no—
583C2—4881no—
584C2—4881no—
585C2—2442no—
586C2—2442no—
587C2—2442no—
588C2#1684032311yescharacteristic
589C2#1684033011yescharacteristic
590C2#1684033111yescharacteristic
591C2#1684039611yescharacteristic
592C2D4×D24411yescharacteristic
593C2D4×D24411yescharacteristic
594C2#1684050311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#388C2
hypercenter#388D61
hypocenterC61#2669
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#14519774C2semidirect
2. C2×#14519752C2semidirect
3. C2×#14519750C2semidirect
4. C2×#14519747C2semidirect
5. C2×#14519747C2semidirect
6. C2×#14519747C2semidirect
7. #16839680C2semidirect
8. #16839679C2semidirect
9. #16839672C2semidirect
10. #16839672C2semidirect
11. #16839671C2semidirect
12. #16839671C2semidirect
13. #16839653C2semidirect
14. #16839640C2semidirect
15. C61×#388C2semidirect
23. C22×D244C22semidirect
24. C22×D244C22semidirect
25. C22×D244C22semidirect
29. C22×C4×D61C22semidirect
36. C2×#11758196C22semidirect
43. C2×#11758198C22semidirect
44. C2×#11758198C22semidirect
45. C2×#11758198C22semidirect
46. C2×#11758198C22semidirect
47. C2×#11758198C22semidirect
48. #14519684C22semidirect
49. #14519684C22semidirect
50. C2×C4⋊C4×C61C22semidirect
54. C2×C42×C61C22semidirect
55. #95×C61C22semidirect
56. #95×C61C22semidirect
114. C2×D244D4semidirect
121. C22⋊C4×C61D4semidirect
133. #11758198D4semidirect
311. #388D61semidirect
313. C61#2669semidirect
335. C2×C4⋊C4C2×D61semidirect
350. C2×C42C2×D61semidirect
353. #95C2×D61semidirect
354. #95C2×D61semidirect
431. C22⋊C4D244semidirect