Finite Group Databasebeta

← #27173950

Subgroups — #27173950

Order 12928.

1252 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D101C211yesmaximal, characteristic
2C2×C4×C22⋊D101C211yesmaximal, characteristic, complemented
3C2×#15692215C211yesmaximal, characteristic, complemented
4C22×#13108051C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D101C211yesmaximal, characteristic, complemented
6#20265077C211yesmaximal, characteristic, complemented
7#20265077C211yesmaximal, characteristic, complemented
8#20265057C211yesmaximal, characteristic, complemented
9#20265055C211yesmaximal, characteristic, complemented
10#20265055C211yesmaximal, characteristic, complemented
11#20265036C211yesmaximal, characteristic, complemented
12#20265032C211yesmaximal, characteristic, complemented
13#20265032C211yesmaximal, characteristic, complemented
14#20265024C211yesmaximal, characteristic, complemented
15#386×C101C211yesmaximal, characteristic, complemented
16C24×D101C2211yescharacteristic
17C24×D101C2211yescharacteristic
18C22×D404C2211yescharacteristic
19C22×C22⋊D101C2211yescharacteristic
20C22×C22⋊D101C2211yescharacteristic
21C2×D4×D101—24no—
22C2×D4×D101—24no—
23C2×D4×D101C418yescomplemented
24C23×Dic101C2211yescharacteristic, complemented
25C22×C4×D101C2211yescharacteristic
26C22×C4×D101C2211yescharacteristic, complemented
27C22×C4×D101C2211yescharacteristic, complemented
28C4×C22⋊D101—24no—
29#15692215—24no—
30C2×#13108053C2211yescharacteristic, complemented
31C2×#13108053C2211yescharacteristic, complemented
32C2×C22⋊Dic101C2211yescharacteristic, complemented
33C2×C22⋊Dic101C2211yescharacteristic, complemented
34C2×C22⋊Dic101C2211yescharacteristic, complemented
35C2×#13108051—24no—
36C2×#13108051C2211yescharacteristic
37C2×#13108051C2211yescharacteristic
38C2×#13108051C2211yescharacteristic
39C2×#13108051C2211yescharacteristic
40C2×#13108051C2211yescharacteristic, complemented
41C2×#13108051C2211yescharacteristic, complemented
42C2×#13108051C2211yescharacteristic, complemented
43C2×#13108051C2211yescharacteristic, complemented
44C2×#13108051C2211yescharacteristic, complemented
45C2×#13108051C2211yescharacteristic, complemented
46C22⋊C4×D101—24no—
47C2×C4×Dic101C2211yescharacteristic, complemented
48C2×C4×Dic101C2211yescharacteristic, complemented
49#15692162C2211yescharacteristic, complemented
50#15692162C2211yescharacteristic, complemented
51C22×D4×C101C2211yescharacteristic
52C23×C4×C101C2211yescharacteristic, complemented
53C2×C22⋊C4×C101C2211yescharacteristic, complemented
54C2×C22⋊C4×C101C2211yescharacteristic, complemented
55C2×C22⋊C4×C101C2211yescharacteristic, complemented
56#95×C101C2211yescharacteristic, complemented
57#95×C101C2211yescharacteristic, complemented
58C23×D101—22no—
59C23×D101—22no—
60C23×D101—22no—
61C23×D101—22no—
62C23×D101—22no—
63C23×D101—22no—
64C23×D101—22no—
65C23×D101—22no—
66C23×D101—41no—
67C23×D101—41no—
68C23×D101—41no—
69C23×D101—41no—
70C23×D101C2×C414yescomplemented
71C23×D101C2×C414yescomplemented
72C23×D101C2311yescharacteristic
73C23×D101C2311yescharacteristic
74C23×D101C2311yescharacteristic
75C2×D404—22no—
76C2×D404—22no—
77C2×D404C2×C414yescomplemented
78C2×C22⋊D101—22no—
79C2×C22⋊D101—22no—
80C2×C22⋊D101C2×C414yes—
81C2×C22⋊D101C2×C414yescomplemented
82C2×C22⋊D101D414yes—
83C2×C22⋊D101D414yes—
84D4×D101—232no—
85C22×Dic101—22no—
86C22×Dic101—22no—
87C22×Dic101—41no—
88C22×Dic101C2311yescharacteristic
89C22×Dic101C2311yescharacteristic
90C22×Dic101C2311yescharacteristic
91C22×Dic101C2311yescharacteristic
92C22×Dic101C2311yescharacteristic
93C2×C4×D101—22no—
94C2×C4×D101—22no—
95C2×C4×D101—22no—
96C2×C4×D101—22no—
97C2×C4×D101—22no—
98C2×C4×D101—22no—
99C2×C4×D101—41no—
100C2×C4×D101—41no—
101C2×C4×D101C2×C414yescomplemented
102#13108053—22no—
103#13108053—22no—
104C22⋊Dic101—22no—
105C22⋊Dic101—22no—
106C22⋊Dic101—41no—
107#13108051—22no—
108#13108051—22no—
109#13108051—22no—
110#13108051—22no—
111#13108051—22no—
112#13108051—22no—
113#13108051—22no—
114#13108051—41no—
115#13108051—41no—
116#13108051D414yescomplemented
117C4×Dic101—22no—
118C4×Dic101—22no—
119C24×C101C2311yescharacteristic
120C24×C101C2311yescharacteristic
121C2×D4×C101—22no—
122C2×D4×C101—22no—
123C2×D4×C101C2×C414yescomplemented
124C22×C4×C101—22no—
125C22×C4×C101—22no—
126C22×C4×C101—41no—
127C22×C4×C101C2311yescharacteristic
128C22×C4×C101C2311yescharacteristic
129C22×C4×C101C2311yescharacteristic
130C22×C4×C101C2311yescharacteristic
131C22×C4×C101C2311yescharacteristic
132C22⋊C4×C101—22no—
133C22⋊C4×C101—22no—
134C22⋊C4×C101—41no—
135C23×C101—21no—
136C23×C101—21no—
137C23×C101—21no—
138C23×C101—21no—
139C23×C101—21no—
140C23×C101—21no—
141C23×C101—21no—
142C23×C101—21no—
143C23×C101—21no—
144C23×C101—21no—
145C23×C101C22×C412yes—
146C23×C101C22×C412yes—
147C23×C101C2×D412yes—
148C23×C101C2×D412yes—
149C23×C101C2411yescharacteristic
150C22×D101—21no—
151C22×D101—21no—
152C22×D101—21no—
153C22×D101—21no—
154C22×D101—21no—
155C22×D101—21no—
156C22×D101—21no—
157C22×D101—21no—
158C22×D101—28no—
159C22×D101—21no—
160C22×D101—21no—
161C22×D101—21no—
162C22×D101—21no—
163C22×D101—21no—
164C22×D101—21no—
165C22×D101—28no—
166C22×D101—28no—
167C22×D101—28no—
168C22×D101—44no—
169C22×D101—44no—
170C22×D101—44no—
171C22×D101—44no—
172C22×D101—44no—
173C22×D101—44no—
174C22×D101—44no—
175C22×D101—44no—
176C22×D101—44no—
177C22×D101—44no—
178C22×D101C22×C412yes—
179C22×D101C22×C412yes—
180C22×D101C22×C412yes—
181C22×D101C2×D412yes—
182C22×D101C2×D412yes—
183C22×D101C2×D412yes—
184C22×D101#4112yes—
185D4×C101—28no—
186C2×C4×C101—21no—
187C2×C4×C101—21no—
188C2×C4×C101—21no—
189C2×C4×C101—21no—
190C2×C4×C101—21no—
191C2×C4×C101—21no—
192C2×C4×C101—21no—
193C2×C4×C101—21no—
194C2×C4×C101—21no—
195C2×C4×C101—21no—
196C2×C4×C101—21no—
197C2×C4×C101—21no—
198C2×C4×C101—21no—
199C2×C4×C101—44no—
200C2×C4×C101C22×C412yes—
201C2×C4×C101C2×D412yescomplemented
202C22⋊D101—28no—
203C22⋊D101C22⋊C4116yescomplemented
204C2×Dic101—21no—
205C2×Dic101—21no—
206C2×Dic101—21no—
207C2×Dic101—21no—
208C2×Dic101—21no—
209C2×Dic101—21no—
210C2×Dic101—21no—
211C2×Dic101—21no—
212C2×Dic101—21no—
213C2×Dic101—21no—
214C2×Dic101—21no—
215C2×Dic101—44no—
216C2×Dic101C22×C412yes—
217C2×Dic101C2×D412yes—
218C2×Dic101C2×D412yes—
219C2×Dic101C2×D412yescomplemented
220D404—28no—
221C4×D101—28no—
222C4×D101—44no—
223C4×D101—44no—
224C22×C101—22no—
225C22×C101—22no—
226C22×C101—22no—
227C22×C101—22no—
228C22×C101—22no—
229C22×C101—22no—
230C22×C101—22no—
231C22×C101—22no—
232C22×C101—22no—
233C22×C101—41no—
234C22×C101—41no—
235C22×C101—41no—
236C22×C101—41no—
237C22×C101C2×C22⋊C414yescomplemented
238C22×C101C23×C411yescharacteristic
239C22×C101C22×D411yescharacteristic
240C22×C101C22×D411yescharacteristic
241C22×C101C22×D411yescharacteristic
242C22×C101C2×#4111yescharacteristic
243C22×C101H(5,𝔽2)11yescharacteristic
244C22×C101H(5,𝔽2)11yescharacteristic
245C2×D101—22no—
246C2×D101—22no—
247C2×D101—22no—
248C2×D101—22no—
249C2×D101—22no—
250C2×D101—22no—
251C2×D101—22no—
252C2×D101—22no—
253C2×D101—22no—
254C2×D101—22no—
255C2×D101—22no—
256C2×D101—22no—
257C2×D101—22no—
258C2×D101—22no—
259C2×D101—22no—
260C2×D101—416no—
261C2×D101—416no—
262C2×D101—41no—
263C2×D101—41no—
264C2×D101—41no—
265C2×D101—41no—
266C2×D101C2×C22⋊C414yescomplemented
267C2×D101C4×D414yescomplemented
268C4×C101—22no—
269C4×C101—22no—
270C4×C101—41no—
271C4×C101—41no—
272C4×C101—41no—
273Dic101—22no—
274Dic101—41no—
275Dic101—41no—
276Dic101—41no—
277Dic101C2×C22⋊C414yescomplemented
278C2×C101—24no—
279C2×C101—42no—
280C2×C101C22×C22⋊C411yescharacteristic
281C2×C101C2×C4×D411yescharacteristic
282C2×C101#51811yescharacteristic
283C2×C101D4211yescharacteristic
284C2×C101D4211yescharacteristic
285C2×C101#54611yescharacteristic
286C2×C101#54611yescharacteristic
287D101—24no—
288D101—24no—
289D101—42no—
290D4×C22⋊C4—1011nomaximal, Sylow
291C101D4×C22⋊C411yescharacteristic, complemented, Sylow
292C23×D4—1011no—
293C2×C4×D4—1011no—
294C2×C4×D4—1011no—
295C22×C22⋊C4—1011no—
296C22×C22⋊C4—1011no—
297#390—1011no—
298#390—1011no—
299#386—1011no—
300#386—1011no—
301#386—1011no—
302#386D10111yescharacteristic, complemented
303#380—1011no—
304#379—1011no—
305#379—1011no—
306C4×C22⋊C4—1011no—
307C25—1011no—
308C25—1011no—
309C22×D4—1011no—
310C22×D4—1011no—
311C22×D4—1018no—
312C22×D4—1011no—
313C22×D4—2024no—
314C22×D4—2024no—
315C22×D4C2×D10111yescharacteristic
316C23×C4—1011no—
317C23×C4—1011no—
318C23×C4—1011no—
319C23×C4—1011no—
320C23×C4C2×D10111yescharacteristic, complemented
321C4×D4—2024no—
322C4×D4—2024no—
323C2×C4⋊C4—1011no—
324C2×C4⋊C4—1011no—
325C2×C22⋊C4—1011no—
326C2×C22⋊C4—1011no—
327C2×C22⋊C4—1011no—
328C2×C22⋊C4—1011no—
329C2×C22⋊C4—1011no—
330C2×C22⋊C4—1011no—
331C2×C22⋊C4—1011no—
332C2×C22⋊C4—1011no—
333C2×C22⋊C4—1011no—
334C2×C22⋊C4—1011no—
335C2×C22⋊C4—1011no—
336C2×C22⋊C4—1011no—
337C2×C22⋊C4—1011no—
338C2×C22⋊C4—2024no—
339C2×C22⋊C4—2024no—
340C2×C22⋊C4C2×D10111yescharacteristic, complemented
341C2×C22⋊C4C2×D10111yescharacteristic, complemented
342C2×C22⋊C4C2×D10111yescharacteristic, complemented
343C2×C42—1011no—
344C2×C42—1011no—
345#95—1011no—
346#95—1011no—
347#95C2×D10111yescharacteristic, complemented
348#95C2×D10111yescharacteristic, complemented
349C24—1011no—
350C24—1011no—
351C24—1014no—
352C24—1014no—
353C24—1011no—
354C24—4041no—
355C24—4041no—
356C24—4041no—
357C24—4041no—
358C24—2022no—
359C24—2022no—
360C24—2022no—
361C24—2022no—
362C24—2022no—
363C24—2022no—
364C24—2022no—
365C24—2022no—
366C24C22×D10111yescharacteristic
367C24C22×D10111yescharacteristic
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—1014no—
371C2×D4—1014no—
372C2×D4—1014no—
373C2×D4—1014no—
374C2×D4—1014no—
375C2×D4—2022no—
376C2×D4—2022no—
377C2×D4—2022no—
378C2×D4—2022no—
379C2×D4—20232no—
380C2×D4C4×D10114yescomplemented
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—41no—
384C22×C4—1011no—
385C22×C4—1011no—
386C22×C4—1014no—
387C22×C4—1011no—
388C22×C4—1011no—
389C22×C4—1011no—
390C22×C4—4041no—
391C22×C4—4041no—
392C22×C4—4041no—
393C22×C4—2022no—
394C22×C4—2022no—
395C22×C4—2022no—
396C22×C4—2022no—
397C22×C4—2022no—
398C22×C4—2022no—
399C22×C4—2022no—
400C22×C4—2022no—
401C22×C4C22×D10111yescharacteristic
402C22×C4C22×D10111yescharacteristic
403C22×C4C22×D10111yescharacteristic
404C22×C4C22×D10111yescharacteristic
405C22×C4C22×D10111yescharacteristic
406C4⋊C4—2022no—
407C4⋊C4—2022no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—41no—
411C22⋊C4—1014no—
412C22⋊C4—4041no—
413C22⋊C4—4041no—
414C22⋊C4—4041no—
415C22⋊C4—2022no—
416C22⋊C4—2022no—
417C22⋊C4—2022no—
418C22⋊C4—2022no—
419C22⋊C4—2022no—
420C22⋊C4—2022no—
421C22⋊C4—2022no—
422C22⋊C4—2022no—
423C22⋊C4—2022no—
424C42—2022no—
425C42—2022no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—1012no—
437C23—1012no—
438C23—1012no—
439C23—1012no—
440C23—1012no—
441C23—1012no—
442C23—1012no—
443C23—4044no—
444C23—4044no—
445C23—4044no—
446C23—4044no—
447C23—4044no—
448C23—4044no—
449C23—4044no—
450C23—4044no—
451C23—4044no—
452C23—4044no—
453C23—2028no—
454C23—2028no—
455C23—2028no—
456C23—2021no—
457C23—2021no—
458C23—2021no—
459C23—2021no—
460C23—2021no—
461C23—2021no—
462C23—2028no—
463C23—2021no—
464C23—2021no—
465C23—2021no—
466C23—2021no—
467C23—2021no—
468C23—2021no—
469C23—2021no—
470C23—2021no—
471C23C2×C4×D10112yes—
472C23C2×C4×D10112yes—
473C23D4×D10112yes—
474C23D4×D10112yes—
475C23C23×D10111yescharacteristic
476D4—28no—
477D4—10116no—
478D4—2028no—
479D4—2028no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—44no—
494C2×C4—1012no—
495C2×C4—1012no—
496C2×C4—1012no—
497C2×C4—1012no—
498C2×C4—4044no—
499C2×C4—4044no—
500C2×C4—4044no—
501C2×C4—2028no—
502C2×C4—2021no—
503C2×C4—2021no—
504C2×C4—2021no—
505C2×C4—2021no—
506C2×C4—2021no—
507C2×C4—2021no—
508C2×C4—2021no—
509C2×C4—2021no—
510C2×C4—2021no—
511C2×C4—2021no—
512C2×C4—2021no—
513C2×C4C2×C4×D10112yes—
514C2×C4D4×D10112yescomplemented
515C22—22no—
516C22—22no—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—1014no—
529C22—1014no—
530C22—40416no—
531C22—40416no—
532C22—4041no—
533C22—4041no—
534C22—4041no—
535C22—4041no—
536C22—2022no—
537C22—2022no—
538C22—2022no—
539C22—2022no—
540C22—2022no—
541C22—2022no—
542C22—2022no—
543C22—2022no—
544C22—2022no—
545C22—2022no—
546C22—2022no—
547C22—2022no—
548C22—2022no—
549C22—2022no—
550C22—2022no—
551C22C22⋊C4×D10114yescomplemented
552C22C22×C4×D10111yescharacteristic
553C22C2×D4×D10111yescharacteristic
554C22C2×D4×D10111yescharacteristic
555C22C2×D4×D10111yescharacteristic
556C22#41×D10111yescharacteristic
557C22#1569230011yescharacteristic
558C22#1569230111yescharacteristic
559C4—22no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—1014no—
565C4—4041no—
566C4—4041no—
567C4—4041no—
568C4—2022no—
569C2—24no—
570C2—42no—
571C2—4042no—
572C2—2024no—
573C2—2024no—
574C2C2×C22⋊C4×D10111yescharacteristic
575C2C4×D4×D10111yescharacteristic
576C2#2026564911yescharacteristic
577C2#2026580911yescharacteristic
578C2#2026581111yescharacteristic
579C2#2026581611yescharacteristic
580C2#2026581911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D101
commutatorC22×C101C23×C4
Fitting#386×C101C2
socle, cosocleC23×C101C24
prime radicalC22×D4×D101C2
hypercenter#386D101
hypocenterC101D4×C22⋊C4
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D101C2semidirect
3. C2×#15692215C2semidirect
4. C22×#13108051C2semidirect
5. C2×C22⋊C4×D101C2semidirect
6. #20265077C2semidirect
7. #20265077C2semidirect
8. #20265057C2semidirect
9. #20265055C2semidirect
10. #20265055C2semidirect
11. #20265036C2semidirect
12. #20265032C2semidirect
13. #20265032C2semidirect
14. #20265024C2semidirect
15. #386×C101C2semidirect
23. C2×D4×D101C4semidirect
24. C23×Dic101C22semidirect
26. C22×C4×D101C22semidirect
27. C22×C4×D101C22semidirect
30. C2×#13108053C22semidirect
31. C2×#13108053C22semidirect
32. C2×C22⋊Dic101C22semidirect
33. C2×C22⋊Dic101C22semidirect
34. C2×C22⋊Dic101C22semidirect
40. C2×#13108051C22semidirect
41. C2×#13108051C22semidirect
42. C2×#13108051C22semidirect
43. C2×#13108051C22semidirect
44. C2×#13108051C22semidirect
45. C2×#13108051C22semidirect
47. C2×C4×Dic101C22semidirect
48. C2×C4×Dic101C22semidirect
49. #15692162C22semidirect
50. #15692162C22semidirect
52. C23×C4×C101C22semidirect
53. C2×C22⋊C4×C101C22semidirect
54. C2×C22⋊C4×C101C22semidirect
55. C2×C22⋊C4×C101C22semidirect
56. #95×C101C22semidirect
57. #95×C101C22semidirect
70. C23×D101C2×C4semidirect
71. C23×D101C2×C4semidirect
77. C2×D404C2×C4semidirect
81. C2×C22⋊D101C2×C4semidirect
101. C2×C4×D101C2×C4semidirect
116. #13108051D4semidirect
123. C2×D4×C101C2×C4semidirect
201. C2×C4×C101C2×D4semidirect
203. C22⋊D101C22⋊C4semidirect
219. C2×Dic101C2×D4semidirect
237. C22×C101C2×C22⋊C4semidirect
266. C2×D101C2×C22⋊C4semidirect
267. C2×D101C4×D4semidirect
277. Dic101C2×C22⋊C4semidirect
291. C101D4×C22⋊C4semidirect
302. #386D101semidirect
320. C23×C4C2×D101semidirect
340. C2×C22⋊C4C2×D101semidirect
341. C2×C22⋊C4C2×D101semidirect
342. C2×C22⋊C4C2×D101semidirect
347. #95C2×D101semidirect
348. #95C2×D101semidirect
380. C2×D4C4×D101semidirect
514. C2×C4D4×D101semidirect
551. C22C22⋊C4×D101semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×D4×D1012
C2×C4×C22⋊D1012
C2×#156922152
C22×#131080512
C2×C22⋊C4×D1012
#202650772
#202650572
#202650552
#202650362
#202650322
#202650242
#386×C1012
D4×C22⋊C4101