Finite Group Databasebeta

← #38745530

Subgroups — #38745530

Order 25216.

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×D197C211yesmaximal, characteristic
2C2×C4×C22⋊D197C211yesmaximal, characteristic, complemented
3C2×#20263286C211yesmaximal, characteristic, complemented
4C22×#15691335C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D197C211yesmaximal, characteristic, complemented
6#27160979C211yesmaximal, characteristic, complemented
7#27160979C211yesmaximal, characteristic, complemented
8#27160959C211yesmaximal, characteristic, complemented
9#27160957C211yesmaximal, characteristic, complemented
10#27160957C211yesmaximal, characteristic, complemented
11#27160938C211yesmaximal, characteristic, complemented
12#27160934C211yesmaximal, characteristic, complemented
13#27160934C211yesmaximal, characteristic, complemented
14#27160926C211yesmaximal, characteristic, complemented
15#386×C197C211yesmaximal, characteristic, complemented
16C24×D197C2211yescharacteristic
17C24×D197C2211yescharacteristic
18C22×D788C2211yescharacteristic
19C22×C22⋊D197C2211yescharacteristic
20C22×C22⋊D197C2211yescharacteristic
21C2×D4×D197—24no—
22C2×D4×D197—24no—
23C2×D4×D197C418yescomplemented
24C23×Dic197C2211yescharacteristic, complemented
25C22×C4×D197C2211yescharacteristic
26C22×C4×D197C2211yescharacteristic, complemented
27C22×C4×D197C2211yescharacteristic, complemented
28C4×C22⋊D197—24no—
29#20263286—24no—
30C2×#15691337C2211yescharacteristic, complemented
31C2×#15691337C2211yescharacteristic, complemented
32C2×C22⋊Dic197C2211yescharacteristic, complemented
33C2×C22⋊Dic197C2211yescharacteristic, complemented
34C2×C22⋊Dic197C2211yescharacteristic, complemented
35C2×#15691335—24no—
36C2×#15691335C2211yescharacteristic
37C2×#15691335C2211yescharacteristic
38C2×#15691335C2211yescharacteristic
39C2×#15691335C2211yescharacteristic
40C2×#15691335C2211yescharacteristic, complemented
41C2×#15691335C2211yescharacteristic, complemented
42C2×#15691335C2211yescharacteristic, complemented
43C2×#15691335C2211yescharacteristic, complemented
44C2×#15691335C2211yescharacteristic, complemented
45C2×#15691335C2211yescharacteristic, complemented
46C22⋊C4×D197—24no—
47C2×C4×Dic197C2211yescharacteristic, complemented
48C2×C4×Dic197C2211yescharacteristic, complemented
49#20263233C2211yescharacteristic, complemented
50#20263233C2211yescharacteristic, complemented
51C22×D4×C197C2211yescharacteristic
52C23×C4×C197C2211yescharacteristic, complemented
53C2×C22⋊C4×C197C2211yescharacteristic, complemented
54C2×C22⋊C4×C197C2211yescharacteristic, complemented
55C2×C22⋊C4×C197C2211yescharacteristic, complemented
56#95×C197C2211yescharacteristic, complemented
57#95×C197C2211yescharacteristic, complemented
58C23×D197—22no—
59C23×D197—22no—
60C23×D197—22no—
61C23×D197—22no—
62C23×D197—22no—
63C23×D197—22no—
64C23×D197—22no—
65C23×D197—22no—
66C23×D197—41no—
67C23×D197—41no—
68C23×D197—41no—
69C23×D197—41no—
70C23×D197C2×C414yescomplemented
71C23×D197C2×C414yescomplemented
72C23×D197C2311yescharacteristic
73C23×D197C2311yescharacteristic
74C23×D197C2311yescharacteristic
75C2×D788—22no—
76C2×D788—22no—
77C2×D788C2×C414yescomplemented
78C2×C22⋊D197—22no—
79C2×C22⋊D197—22no—
80C2×C22⋊D197C2×C414yes—
81C2×C22⋊D197C2×C414yescomplemented
82C2×C22⋊D197D414yes—
83C2×C22⋊D197D414yes—
84D4×D197—232no—
85C22×Dic197—22no—
86C22×Dic197—22no—
87C22×Dic197—41no—
88C22×Dic197C2311yescharacteristic
89C22×Dic197C2311yescharacteristic
90C22×Dic197C2311yescharacteristic
91C22×Dic197C2311yescharacteristic
92C22×Dic197C2311yescharacteristic
93C2×C4×D197—22no—
94C2×C4×D197—22no—
95C2×C4×D197—22no—
96C2×C4×D197—22no—
97C2×C4×D197—22no—
98C2×C4×D197—22no—
99C2×C4×D197—41no—
100C2×C4×D197—41no—
101C2×C4×D197C2×C414yescomplemented
102#15691337—22no—
103#15691337—22no—
104C22⋊Dic197—22no—
105C22⋊Dic197—22no—
106C22⋊Dic197—41no—
107#15691335—22no—
108#15691335—22no—
109#15691335—22no—
110#15691335—22no—
111#15691335—22no—
112#15691335—22no—
113#15691335—22no—
114#15691335—41no—
115#15691335—41no—
116#15691335D414yescomplemented
117C4×Dic197—22no—
118C4×Dic197—22no—
119C24×C197C2311yescharacteristic
120C24×C197C2311yescharacteristic
121C2×D4×C197—22no—
122C2×D4×C197—22no—
123C2×D4×C197C2×C414yescomplemented
124C22×C4×C197—22no—
125C22×C4×C197—22no—
126C22×C4×C197—41no—
127C22×C4×C197C2311yescharacteristic
128C22×C4×C197C2311yescharacteristic
129C22×C4×C197C2311yescharacteristic
130C22×C4×C197C2311yescharacteristic
131C22×C4×C197C2311yescharacteristic
132C22⋊C4×C197—22no—
133C22⋊C4×C197—22no—
134C22⋊C4×C197—41no—
135C22×D197—21no—
136C22×D197—21no—
137C22×D197—21no—
138C22×D197—21no—
139C22×D197—21no—
140C22×D197—21no—
141C22×D197—21no—
142C22×D197—21no—
143C22×D197—28no—
144C22×D197—21no—
145C22×D197—21no—
146C22×D197—21no—
147C22×D197—21no—
148C22×D197—21no—
149C22×D197—21no—
150C22×D197—28no—
151C22×D197—28no—
152C22×D197—28no—
153C22×D197—44no—
154C22×D197—44no—
155C22×D197—44no—
156C22×D197—44no—
157C22×D197—44no—
158C22×D197—44no—
159C22×D197—44no—
160C22×D197—44no—
161C22×D197—44no—
162C22×D197—44no—
163C22×D197C22×C412yes—
164C22×D197C22×C412yes—
165C22×D197C22×C412yes—
166C22×D197C2×D412yes—
167C22×D197C2×D412yes—
168C22×D197C2×D412yes—
169C22×D197#4112yes—
170D788—28no—
171C22⋊D197—28no—
172C22⋊D197C22⋊C4116yescomplemented
173C2×Dic197—21no—
174C2×Dic197—21no—
175C2×Dic197—21no—
176C2×Dic197—21no—
177C2×Dic197—21no—
178C2×Dic197—21no—
179C2×Dic197—21no—
180C2×Dic197—21no—
181C2×Dic197—21no—
182C2×Dic197—21no—
183C2×Dic197—21no—
184C2×Dic197—44no—
185C2×Dic197C22×C412yes—
186C2×Dic197C2×D412yes—
187C2×Dic197C2×D412yes—
188C2×Dic197C2×D412yescomplemented
189C4×D197—28no—
190C4×D197—44no—
191C4×D197—44no—
192C23×C197—21no—
193C23×C197—21no—
194C23×C197—21no—
195C23×C197—21no—
196C23×C197—21no—
197C23×C197—21no—
198C23×C197—21no—
199C23×C197—21no—
200C23×C197—21no—
201C23×C197—21no—
202C23×C197C22×C412yes—
203C23×C197C22×C412yes—
204C23×C197C2×D412yes—
205C23×C197C2×D412yes—
206C23×C197C2411yescharacteristic
207D4×C197—28no—
208C2×C4×C197—21no—
209C2×C4×C197—21no—
210C2×C4×C197—21no—
211C2×C4×C197—21no—
212C2×C4×C197—21no—
213C2×C4×C197—21no—
214C2×C4×C197—21no—
215C2×C4×C197—21no—
216C2×C4×C197—21no—
217C2×C4×C197—21no—
218C2×C4×C197—21no—
219C2×C4×C197—21no—
220C2×C4×C197—21no—
221C2×C4×C197—44no—
222C2×C4×C197C22×C412yes—
223C2×C4×C197C2×D412yescomplemented
224C22×C197—22no—
225C22×C197—22no—
226C22×C197—22no—
227C22×C197—22no—
228C22×C197—22no—
229C22×C197—22no—
230C22×C197—22no—
231C22×C197—22no—
232C22×C197—22no—
233C22×C197—41no—
234C22×C197—41no—
235C22×C197—41no—
236C22×C197—41no—
237C22×C197C2×C22⋊C414yescomplemented
238C22×C197C23×C411yescharacteristic
239C22×C197C22×D411yescharacteristic
240C22×C197C22×D411yescharacteristic
241C22×C197C22×D411yescharacteristic
242C22×C197C2×#4111yescharacteristic
243C22×C197H(5,𝔽2)11yescharacteristic
244C22×C197H(5,𝔽2)11yescharacteristic
245C2×D197—22no—
246C2×D197—22no—
247C2×D197—22no—
248C2×D197—22no—
249C2×D197—22no—
250C2×D197—22no—
251C2×D197—22no—
252C2×D197—22no—
253C2×D197—22no—
254C2×D197—22no—
255C2×D197—22no—
256C2×D197—22no—
257C2×D197—22no—
258C2×D197—22no—
259C2×D197—22no—
260C2×D197—416no—
261C2×D197—416no—
262C2×D197—41no—
263C2×D197—41no—
264C2×D197—41no—
265C2×D197—41no—
266C2×D197C2×C22⋊C414yescomplemented
267C2×D197C4×D414yescomplemented
268C4×C197—22no—
269C4×C197—22no—
270C4×C197—41no—
271C4×C197—41no—
272C4×C197—41no—
273Dic197—22no—
274Dic197—41no—
275Dic197—41no—
276Dic197—41no—
277Dic197C2×C22⋊C414yescomplemented
278C2×C197—24no—
279C2×C197—42no—
280C2×C197C22×C22⋊C411yescharacteristic
281C2×C197C2×C4×D411yescharacteristic
282C2×C197#51811yescharacteristic
283C2×C197D4211yescharacteristic
284C2×C197D4211yescharacteristic
285C2×C197#54611yescharacteristic
286C2×C197#54611yescharacteristic
287D197—24no—
288D197—24no—
289D197—42no—
290C197D4×C22⋊C411yescharacteristic, complemented, Sylow
291D4×C22⋊C4—1971nomaximal, Sylow
292C23×D4—1971no—
293C2×C4×D4—1971no—
294C2×C4×D4—1971no—
295C22×C22⋊C4—1971no—
296C22×C22⋊C4—1971no—
297#390—1971no—
298#390—1971no—
299#386—1971no—
300#386—1971no—
301#386—1971no—
302#386D19711yescharacteristic, complemented
303#380—1971no—
304#379—1971no—
305#379—1971no—
306C4×C22⋊C4—1971no—
307C25—1971no—
308C25—1971no—
309C22×D4—3944no—
310C22×D4—3944no—
311C22×D4—1971no—
312C22×D4—1978no—
313C22×D4—1971no—
314C22×D4—1971no—
315C22×D4C2×D19711yescharacteristic
316C23×C4—1971no—
317C23×C4—1971no—
318C23×C4—1971no—
319C23×C4—1971no—
320C23×C4C2×D19711yescharacteristic, complemented
321C4×D4—3944no—
322C4×D4—3944no—
323C2×C4⋊C4—1971no—
324C2×C4⋊C4—1971no—
325C2×C22⋊C4—3944no—
326C2×C22⋊C4—3944no—
327C2×C22⋊C4—1971no—
328C2×C22⋊C4—1971no—
329C2×C22⋊C4—1971no—
330C2×C22⋊C4—1971no—
331C2×C22⋊C4—1971no—
332C2×C22⋊C4—1971no—
333C2×C22⋊C4—1971no—
334C2×C22⋊C4—1971no—
335C2×C22⋊C4—1971no—
336C2×C22⋊C4—1971no—
337C2×C22⋊C4—1971no—
338C2×C22⋊C4—1971no—
339C2×C22⋊C4—1971no—
340C2×C22⋊C4C2×D19711yescharacteristic, complemented
341C2×C22⋊C4C2×D19711yescharacteristic, complemented
342C2×C22⋊C4C2×D19711yescharacteristic, complemented
343C2×C42—1971no—
344C2×C42—1971no—
345#95—1971no—
346#95—1971no—
347#95C2×D19711yescharacteristic, complemented
348#95C2×D19711yescharacteristic, complemented
349C24—7881no—
350C24—7881no—
351C24—7881no—
352C24—7881no—
353C24—3942no—
354C24—3942no—
355C24—3942no—
356C24—3942no—
357C24—3942no—
358C24—3942no—
359C24—3942no—
360C24—3942no—
361C24—1974no—
362C24—1974no—
363C24—1971no—
364C24—1971no—
365C24—1971no—
366C24C22×D19711yescharacteristic
367C24C22×D19711yescharacteristic
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—3942no—
371C2×D4—3942no—
372C2×D4—39432no—
373C2×D4—3942no—
374C2×D4—3942no—
375C2×D4—1974no—
376C2×D4—1974no—
377C2×D4—1974no—
378C2×D4—1974no—
379C2×D4—1974no—
380C2×D4C4×D19714yescomplemented
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—41no—
384C22×C4—7881no—
385C22×C4—7881no—
386C22×C4—7881no—
387C22×C4—3942no—
388C22×C4—3942no—
389C22×C4—3942no—
390C22×C4—3942no—
391C22×C4—3942no—
392C22×C4—3942no—
393C22×C4—3942no—
394C22×C4—3942no—
395C22×C4—1971no—
396C22×C4—1971no—
397C22×C4—1971no—
398C22×C4—1971no—
399C22×C4—1974no—
400C22×C4—1971no—
401C22×C4C22×D19711yescharacteristic
402C22×C4C22×D19711yescharacteristic
403C22×C4C22×D19711yescharacteristic
404C22×C4C22×D19711yescharacteristic
405C22×C4C22×D19711yescharacteristic
406C4⋊C4—3942no—
407C4⋊C4—3942no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—41no—
411C22⋊C4—7881no—
412C22⋊C4—7881no—
413C22⋊C4—7881no—
414C22⋊C4—3942no—
415C22⋊C4—3942no—
416C22⋊C4—3942no—
417C22⋊C4—3942no—
418C22⋊C4—3942no—
419C22⋊C4—3942no—
420C22⋊C4—3942no—
421C22⋊C4—3942no—
422C22⋊C4—3942no—
423C22⋊C4—1974no—
424C42—3942no—
425C42—3942no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—7884no—
437C23—7884no—
438C23—7884no—
439C23—7884no—
440C23—7884no—
441C23—7884no—
442C23—7884no—
443C23—7884no—
444C23—7884no—
445C23—7884no—
446C23—3948no—
447C23—3948no—
448C23—3948no—
449C23—3948no—
450C23—3941no—
451C23—3941no—
452C23—3941no—
453C23—3941no—
454C23—3941no—
455C23—3941no—
456C23—3941no—
457C23—3941no—
458C23—3941no—
459C23—3941no—
460C23—3941no—
461C23—3941no—
462C23—3941no—
463C23—3941no—
464C23—1972no—
465C23—1972no—
466C23—1972no—
467C23—1972no—
468C23—1972no—
469C23—1972no—
470C23—1972no—
471C23C2×C4×D19712yes—
472C23C2×C4×D19712yes—
473C23D4×D19712yes—
474C23D4×D19712yes—
475C23C23×D19711yescharacteristic
476D4—28no—
477D4—3948no—
478D4—3948no—
479D4—19716no—
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—7884no—
495C2×C4—7884no—
496C2×C4—7884no—
497C2×C4—3948no—
498C2×C4—3941no—
499C2×C4—3941no—
500C2×C4—3941no—
501C2×C4—3941no—
502C2×C4—3941no—
503C2×C4—3941no—
504C2×C4—3941no—
505C2×C4—3941no—
506C2×C4—3941no—
507C2×C4—3941no—
508C2×C4—3941no—
509C2×C4—1972no—
510C2×C4—1972no—
511C2×C4—1972no—
512C2×C4—1972no—
513C2×C4C2×C4×D19712yes—
514C2×C4D4×D19712yescomplemented
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—78816no—
529C22—78816no—
530C22—7881no—
531C22—7881no—
532C22—7881no—
533C22—7881no—
534C22—3942no—
535C22—3942no—
536C22—3942no—
537C22—3942no—
538C22—3942no—
539C22—3942no—
540C22—3942no—
541C22—3942no—
542C22—3942no—
543C22—3942no—
544C22—3942no—
545C22—3942no—
546C22—3942no—
547C22—3942no—
548C22—3942no—
549C22—1974no—
550C22—1974no—
551C22C22⋊C4×D19714yescomplemented
552C22C22×C4×D19711yescharacteristic
553C22C2×D4×D19711yescharacteristic
554C22C2×D4×D19711yescharacteristic
555C22C2×D4×D19711yescharacteristic
556C22#41×D19711yescharacteristic
557C22#2026337111yescharacteristic
558C22#2026337211yescharacteristic
559C4—22no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—7881no—
565C4—7881no—
566C4—7881no—
567C4—3942no—
568C4—1974no—
569C2—24no—
570C2—42no—
571C2—7882no—
572C2—3944no—
573C2—3944no—
574C2C2×C22⋊C4×D19711yescharacteristic
575C2C4×D4×D19711yescharacteristic
576C2#2716155111yescharacteristic
577C2#2716171111yescharacteristic
578C2#2716171311yescharacteristic
579C2#2716171811yescharacteristic
580C2#2716172111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D197
commutatorC22×C197C23×C4
Fitting#386×C197C2
socle, cosocleC23×C197C24
prime radicalC22×D4×D197C2
hypercenter#386D197
hypocenterC197D4×C22⋊C4
LCSG ▷ C22×C197 ▷ C197
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D197C2semidirect
3. C2×#20263286C2semidirect
4. C22×#15691335C2semidirect
5. C2×C22⋊C4×D197C2semidirect
6. #27160979C2semidirect
7. #27160979C2semidirect
8. #27160959C2semidirect
9. #27160957C2semidirect
10. #27160957C2semidirect
11. #27160938C2semidirect
12. #27160934C2semidirect
13. #27160934C2semidirect
14. #27160926C2semidirect
15. #386×C197C2semidirect
23. C2×D4×D197C4semidirect
24. C23×Dic197C22semidirect
26. C22×C4×D197C22semidirect
27. C22×C4×D197C22semidirect
30. C2×#15691337C22semidirect
31. C2×#15691337C22semidirect
32. C2×C22⋊Dic197C22semidirect
33. C2×C22⋊Dic197C22semidirect
34. C2×C22⋊Dic197C22semidirect
40. C2×#15691335C22semidirect
41. C2×#15691335C22semidirect
42. C2×#15691335C22semidirect
43. C2×#15691335C22semidirect
44. C2×#15691335C22semidirect
45. C2×#15691335C22semidirect
47. C2×C4×Dic197C22semidirect
48. C2×C4×Dic197C22semidirect
49. #20263233C22semidirect
50. #20263233C22semidirect
52. C23×C4×C197C22semidirect
53. C2×C22⋊C4×C197C22semidirect
54. C2×C22⋊C4×C197C22semidirect
55. C2×C22⋊C4×C197C22semidirect
56. #95×C197C22semidirect
57. #95×C197C22semidirect
70. C23×D197C2×C4semidirect
71. C23×D197C2×C4semidirect
77. C2×D788C2×C4semidirect
81. C2×C22⋊D197C2×C4semidirect
101. C2×C4×D197C2×C4semidirect
116. #15691335D4semidirect
123. C2×D4×C197C2×C4semidirect
172. C22⋊D197C22⋊C4semidirect
188. C2×Dic197C2×D4semidirect
223. C2×C4×C197C2×D4semidirect
237. C22×C197C2×C22⋊C4semidirect
266. C2×D197C2×C22⋊C4semidirect
267. C2×D197C4×D4semidirect
277. Dic197C2×C22⋊C4semidirect
290. C197D4×C22⋊C4semidirect
302. #386D197semidirect
320. C23×C4C2×D197semidirect
340. C2×C22⋊C4C2×D197semidirect
341. C2×C22⋊C4C2×D197semidirect
342. C2×C22⋊C4C2×D197semidirect
347. #95C2×D197semidirect
348. #95C2×D197semidirect
380. C2×D4C4×D197semidirect
514. C2×C4D4×D197semidirect
551. C22C22⋊C4×D197semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D1972
C2×C4×C22⋊D1972
C2×#202632862
C22×#156913352
C2×C22⋊C4×D1972
#271609792
#271609592
#271609572
#271609382
#271609342
#271609262
#386×C1972
D4×C22⋊C4197